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oliveirabruno01
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intersection-count-pixmap-CoT

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I'm ready to tackle this image and find those intersections! These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#684c04ff b,#dfca79ff c,#9ac392ff d,#eeba48ff e,#f1e2c2ff f,#8b8448ff g,#b1d7b1ff ``` ```image gggggggggggggggggggggggggggggggggggggggggggc gggggggggggggggggggggggggggggggggggggggggggc gggggggggggggggggggggggggggggggggggggggggggc ggggggggggggggggggggggggggggggggggggggggfafc ggggggggggggggggggggggggggggggggggggcaaaaaaaafe gggggggggggggggggggggggggggggggggfaaaaafcggfaaaaag ggggggggggggggggggggggggggggggaaaaaacggggggc caaaaac gggggggggggggggggggggggggggggfaaddgggggggggc gaaaaaf gggggggggggggggggggggggggggggfaddddggggggggc efaaaaae gggggggggggggggggggggggggggggfaddbddgggggggc caaaaac gggggggggggggggggggggggggggggffdggbddggggggc gaaaaaf gggafggggggggggggggggggggggggfddggggddgggggc efaaaafe gggaaggggggggggggggggggggggggfdbgggggddbgggc faaaaac gggaaggggggggggggggggggggggggddgggggggddbggc caaaaaf gggaagggggggggggggggggggggggbdfggggggggddbgc efaaaafe gggfagggggggggggggggggggggggddagggggggggdddc faaaaag gggfacggggggggggggggggggggggdfaggggggggggddd caaac gggcafgggggggggggggggggggggddaagggggggggggbdd g ggggafgggggggggggggggggggggdbaaggggggggggggbdd ggggaaggggggggggggggggggggddgaaggggggggggggcedd ggggaaggggggggggggggggggggddgaaggggggggggggc dde ggggaagggggggggggggggggggddggaaggggggggggggc dde ggggfagggggggggggggggggggddggaaggggggggggggc ddb ggggcafgggggggggggggggggddgggaaggggggggggggc ddb gggggafgggggggggggggggggddgggaaggggggggggggc ddd gggggaaggggggggggggggggbdggggaaggggggggggggc bdd gggggaaggggggggggggggggddggggaaggggggggggggc bdd gggggaagggggggggggggggbdbggggaaggggggggggggc edd gggggfagggggggggggggggddgggggaaggggggggggggc edde gggggcacgggggggggggggbdbgggggafggggggggggggc dde ggggggafgggggggggggggddggggggafggggggggggggc dde ggggggaagggggggggggggdbggggggafggggggggggggc ddb ggggggaaggggggggggggddgggggggafggggggggggggc ddd ggggggaaggggggggggggdbgggggggafggggggggggggc ddd ggggggfagggggggggggddggggggggafggggggggggggc bdd ggggggcacggggggggggddgggggggcafggggggggggggc edd gggggggafgggggggggddggggggggcacggggggggggggc edd gggggggaagggggggggddggggggggcacggggggggggggc dde gggggggaaggggggggddgggggggggcacggggggggggggc dde gggggggaaggggggggddgggggggggcacggggggggggggc ddb gggggggfagggggggbdggggggggggfacggggggggggggc ddb gggggggcacggggggddggggggggggfagggggggggggggc ddd ggggggggafggggggdbggggggggggfagggggggggggggc bdd ggggggggaagggggddgggggggggggfagggggggggggggc bdd ggggggggaagggggddgggggggggggfagggggggggggggc edd ggggggggaaggggddggggggggggggfagggggggggggggc edd ggggggggfaggggddggggggggggggfagggggggggggggc dde ggggggggcacggbdgggggggggggggaagggggggggggggc dde gggggggggafggddgggggggggggggaagggggggggggggc ddb gggggggggaaggdbgggggggggggggaagggggggggggggc ddb gggggggggaagddggggggggggggggaagggggggggggggc dde gggggggggaagddggggggggggggggaagggggggggggggc db gggggggggfaddgggggggggggggggaagggggggggggggc db gggggggggcaddgggggggggggggggaagggggggggggggc dd ggggggggggfdbgggggggggggggggaagggggggggggggc dd ggggggggggddggggggggggggggggaagggggggggggggc dd ggggggggggdfggggggggggggggggaagggggggggggggc dd gggggggggddaggggggggggggggggaagggggggggggggc dd gggggggggddaggggggggggggggggaagggggggggggggc dd ggggggggbdcacgggggggggggggggaagggggggggggggc bd ggggggggddgafgggggggggggggggaagggggggggggggc bd gggggggbdbgaagggggggggggggggaagggggggggggggc bd gggggggddggfaacgggggggggggggaagggggggggggggc ed gggggggdbgggcaafggggggggggggafgggggggggggggc ed ggggggddggggggaaagggggggggggafgggggggggggggc ede ggggggddgggggggfaacgggggggggafgggggggggggggc de gggggbdgggggggggcaafggggggggafgggggggggggggc de gggggddgggggggggggaaagggggggafgggggggggggggc db ggggbdbggggggggggggaaaggggggafgggggggggggggc db ccccddccccccccccccccfaafccccafcccccccccccccg dd db eaaf eag dd dd aaa eag dd dd faagae dd b eaaae dd aae dd e dd bd bd ed ed ede de de e ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#674b03ff b,#f3d083ff c,#a7966bff d,#eeba48ff e,#eee3caff f,#8b7237ff g,#c5ba9fff ``` ```image ecffc egaaaaaa cfaaaaaaaa egfaaaaaaaaffa cfaaaaaaaafce caaaaaaaaac gaaaaddage caaadddd caaedddde caadddddddb caaddd bdddb caaddb dddd cafdde edddb aag ffdde edddde aac fddb dddd aaf cdde bddde aaa ddd bddde aaag dddd bdddb aaag dddf dddd aaac ddda edddb faaf eddfa edddd gaaa eddfaa dd eaaa bddaaa bd eaaa eddbaaa b aaa bddeaaa caa bdddeaaa gaa dddbeaaa gaae dddeeaaa eaag ddd eaaa faf ddd gaaa caa edde gaaa gaa ddd gaaa gaae eddb gaaa aac eddd gaaa faf bddd gaaa caf dddb caaa caa ddde caaa gaae ddb caaa aac ddb caaf aaf bdde caaf aaf ddd caaf aaa edde faaf aaag eddd faaf aaac dddd faaf faaf dddb faac caaf ddd faac gaaa bdd aaac eaaa eddb aaac aaa bdde aaac faa ddb aaac caa ddd aaag gaae bddd aaag eaag dddd aaag aac ddde aaag faf edde aaag caa ddd aaag gaae eddb aaae eaag bdd aaae aac bdd aaae faf eddd aaae caa bddd aaae gaae dddb aaa aag ddd aaa aac eddb aaa aaf bdd aaa aaa ddb aaa aaae bdde aaa aaag edde aaf aaac ddd aaf faaf eddd aaf caaa bddd aaf gaaae ddde aaf eaaag ddb aac aaac edde aac faaf bdd aac gaaa bdd aac gaaa ddb aac eaaa bdde aac aaa ddd aag caabddd aag gaadddb eaag gaaddd eaag eaaddb eaag fddd eaae cdde eaae ddd gaae eddfe gaae dddac gaae edddaf gaae ddddaf gaa eddddaa gaa dddbeaag caa ddde aac caa ddb aac caa edde aaac caa ddd aaaa caf bdd gaaaag faf ddb efaaac faf bdde aaaae faf ddd gaaaag faf dddd efaaaf fac dddb aaaae fac ddd gaaaag fac ddb efaaac aac ddd aaaag aac edde efaaac aac ``` <!-- end of image --> Success! This area contains 2 intersections point! Answer: A: 2; 2 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#684b03ff b,#f3d185ff c,#ab9a71ff d,#efba48ff e,#f2e7ceff f,#90773cff g,#cac0a7ff ``` ```image cac gfaaaaaaafe caaaaafe efaaaaag aaaaaag caaaaac caadd gaaaaafe cabddd efaaaaag caddbdd caaaaac ffde edd gaaaaac ac fdd edde efaaaafe af cde dde caaaaag aa dd ddb gaaaaac aa edf ddb efaaaafe fa dda ddd caaaaag gae edfa ddd caaac eag ddaa bdd g af edbaa bdd aa dd aa edd aa dd aa edde fa dd aa dde ca dd aa ddb eag bd aa ddb af dd aa ddd aa bde aa bdd aa dd aa bdd fa bde af edd ca dd af edde eag ede af dde af dd af ddb aa edb ac ddb aa dd ac ddd fa edb ac ddd ca dd ag bdd eag dd eag bdd ac dd eag edd aa dd eag edde aa bd gae dde aa dd gae ddb ca bde gae ddb eag dd ga ddd ac edb ca bdd aa dd ca bdd aa db ca edd aa dd fa edde ca dd fa dde gag bde fa ddb ac dd fa ddb aa edb aa ddd aa dd aa ddb aa dd aa db cabd aa db gadd aa dd fde aa dd dd aa dd edf aa dd dda aa dd dda aa dd bdgae aa dd dd ac aa bd ede aa aa bd dd caae af bd edb eaac af ede dd aaa af ede dd faae af de bd gaac ac db dd aaf ac db ede aaa ac db dd caag ag dd db eaaf eag dd dd aaa eag dd dd faagag dd be eaaae dd aae dd e dd bd bd bd ed ede ede de e ``` <!-- end of image -->
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I'm analyzing this image to identify any points where lines intersect. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#edf0efff b,#8987dfff c,#c3c2efff d,#e1ccaeff e,#b1d7b1ff f,#9ca8ceff g,#96c996ff ``` ```image d dd dd c dd bc ada abc dd cbb dd fbb ada bbb dd bbb dd bcba da bcbc dd babf dd ab bb dd cb bb dd fb cb ada bb ab dd bf ba dd bc bc ada ba bf dd b bb dd cb fb dd cb cb dd bb ab dd bb ba dd gggggggggbbggggbfgggggggggggggggggggggggggggggggggggggggggggggggg dd eeeeeeeeebfeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeada eeeeeeeeebeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedd eeeeeeeeebeeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedd eeeeeeeefbeeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeda eeeeeeeefbeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedda eeeeeeeebbeeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeddea eeeeeeeebbeeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeddea eeeeeeeebfeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeddeea eeeeeeeebfeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeddeeea eeeeeeeebeeeeeeefbeeeeeeeeeeeeeeeeebbbfeeeeeeeeeeeeeeeeeeeeeddeeea eeeeeeeebeeeeeeefbeeeeeeeeeeeeeeeebbfbbbbfeeeeeeeeeeeeeeeeeddeeeea eeeeeeefbeeeeeeeebeeeeeeeeeeeeeeebbeeeefbbbbfeeeeeeeeeeeedddeeeeea eeeeeeefbeeeeeeeebfeeeeeeeeeeeeebbeeeeeeeefbbbbfeeeeeeddddeeeeeeea eeeeeeebbeeeeeeeebfeeeeeeeeeeeebbeeeeeeeeeeeefbbbbfeddddeeeeeeeeea eeeeeeebbeeeeeeeebbeeeeeeeeeeefbfeeeeeeeeeeeeeeeefddddeeeeeeeeeeea eeeeeeebfeeeeeeeebbeeeeeeeeeefbfeeeeeeeeeeeeeeeedddebbbbbeeeeeeeea eeeeeeebfeeeeeeeefbeeeeeeeeeebbeeeeeeeeeeeeeeddddeeeeeebbbbbeeeeea eeeeeeebeeeeeeeeeebeeeeeeeeebbeeeeeeeeeeeeeddddeeeeeeeeeeefbbbbeea eeeeeeebeeeeeeeeeebeeeeeeeebbeeeeeeeeeeeeddddeeeeeeeeeeeeeeeefbbbba eeeeeefbeeeeeeeeeebfeeeeeebbeeeeeeeeeeddddeeeeeeeeeeeeeeeeeeeeeefbbbbc eeeeeefbeeeeeeeeeebfeeeeebbeeeeeeeeeddddeeeeeeeeeeeeeeeeeeeeeeeeea cbbbbc eeeeeebbeeeeeeeeeebbeeeefbfeeeeeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeea cbbbbc eeeeeebbeeeeeeeeeefbeeefbfeeeeeedddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea cbbbc eeeeeebfeeeeeeeeeefbeeebbeeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bb eeeeeebfeeeeeeeeeeebeebbeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea fb eeeeeebeeeeeeeeeeeebebbeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea cb eeeeefbeeeeeeeeeeeebbbddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea ba eeeeefbeeeeeeeeeeeebddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bc eeeeebbeeeeeeeeeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bb eeeeebbeeeeeeeeedddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bb eeeeebbeeeeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea cb eeeeebfeeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea ab eeeeebeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bc eeeeebddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bf eeeeddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bb eeedddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea cb eeedbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea ab eeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea ba eeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bc eeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bb eeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea fb eeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea cb eeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea ba eeefbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bc eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bb eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bb eeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea cb eeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea ab eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea bf ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg bb cb ab ba a ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#efe2d2ff b,#8986e0ff c,#b5b3eaff d,#e3cbafff e,#d0cef1ff f,#9e9be4ff g,#efedf4ff ``` ```image gbbf fbe ebbf cbc cbbe ebf fbbe gbb fbbg bbg bbb bbe bbf bbc a bbf bbf gd bbc bbf dd bbe bbbg gdd bbg fbbe ddd bbg cbbe addg gbb cbbc dda ebc gbbb addd cbc bbb ddda cbe bbb ddd bbg cbb bbbbbfeg ddd bb ebb bbbbbbbbcg addg gbb ebb fbbeebbbbbbfc adda ebf gbb cbbe gefbbbbbfcg gaddd cbc fbg bbb gecbbbbbbc addddda cbe fbe gbbf ecbbbbbbce gaddddda fbe cbc gbbbg cbbbbbbbe gdddddag bbg ebc gfbbg ecbbbbbbcgadddddd gbb gbb cbbb efddddddeg ebb bbg bbbc gdddddcbbbfe ebb fbe ebbc adddddacfbbbbbfeg fbb cbc gbbfg gadddddg gefbbbbbfc fbb ebf gfbbg dddddda efbbbbbfcg bbb gbf fbbb addddda gebbbbbbfg bbb gbb bbbe gdddddag gefbbbbbb bbf bbe ebbc dddddda ebb bbc bbe gbbf adddddg e bbe bbc gbbbg adddddag bbe bbf fbbb addddda bbg bbb cbbe gaddddag gbb bbbg cbbc addddda ebf fbbe ebbc addddda cbc ebbc gbbf gaddddag cbe ebbf gfbbg adddddda fbe gbbb fbbe addddda bbg bbb cbbe gaddddda gbb fbbbbbcadddddd ebf cbbbbfadddddg ebc ebbfddddddg cbe adddddd fbe gdddddag bbg gadddddg gbb dddddda ebb gdddddag ebb gddddda cbb dddddda fbb adddddg bbb addddda gbbbdddddda gfcddddag addddda ddddde addfbe afbbg bbb bbf bbf bbc bbe bbg bbg ebf ebc cbc cbe bbg bb gbb ebf cbc cbe efe ``` <!-- end of image --> My investigation has led me to 2 intersections in area A! Answer: A: 2; 2 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#efe2d2ff b,#8986e0ff c,#bebcedff d,#e4cbafff e,#d7d6f4ff f,#a3a1e6ff g,#f1eff4ff ``` ```image d ad dd c dd be adg gbc dd cbb dd fbb gda bbb dd bbb dd bcbg gda bebe dd bgbf ad eb bb dd cb fb dd fb cb adg bb eb dd bf bg dd bc bc gda be bf dd gb bb dd eb fb gda cb cb dd fb gb ad bb be dd bf bc dd bc bf adg be bb dd gb fb dd eb eb gda cb gb dd bb be dd bb bc gda bf bb dd bc bb ad bg cb gbbbc dd gb eb bbcbbbbc gdd cb bg bb ebbbbc adddg fb be bb ebbbbc adddg bb bf fbg ebbbbfgdddd bb bb cbc efddddg bc fb ebf adddafbbbfg be cb gbb adddg gfbbbfg bg eb bb dddd gfbbbbe eb bg bb gddda gfbbbbe cb bc bb adddg fbbbbe fb bf fbg dddd cbbbbe bb bb fbe gddda cbbbbc bf fb ebf addda cbbbc bc cb gbf adddg bb be gb bb dddd fb bg bebb gddda cb eb bbbadddg gbg cb bdddd bc fb gddda bf bb addda bb bf adddg cb bc dddd gb be gddda be gbaddda bf ddddg bb ddd fb abb eb bb be bf bc bc bb bg fb gb eb eb bg fb bc bb bb bb bb bf cb be gb be bf bb cb eb be g ``` <!-- end of image -->
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This image seems promising for intersection detection. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#542f4eff b,#568cceff c,#a2a9baff d,#7d6b79ff e,#d3d5e1ff f,#b1d7b1ff g,#96c496ff ``` ```image cc aaaaadc a edaaaaadc da edaaaaadc ae ad cdaaaaade ac ae cdaaaaade aa ea cdaaaaade da da caaaaaade ca ad caaaaaace a ae ecaaaaaace ae ea ecaaaae ac da e ad ad da ae ca ea ea da a ad ac ae ad ea da da ca ad ea ae a ca ggggggadgggggggggggggggggggggaaggggggf ffffffadfffffffffffffffffffffadffffffg ffffffaafffffffffffffffffffffafffffffg ffffffdaffffffffffffffffffffdafffffffg ffffffgaffffffffffffffffffffaafffffffg fffffffaffffffffffffffffffffadfffffffg fffffffagfffffffffffffffffffaffffffffg fffffffadffffffffffffffffffdaffffffffg fffffffaaffffffffffffffffffaaffffffffg fffffffdaffffffffffffffffffadffffffffg fffffffgaffffffffffffffffffafffffffffg ffffffffafffffffffffffffffdafffffffffg ffffffffagffffffffffffffffaafffffffffg ffffffffadffffffffffffffffadfffffffffg ffffffffaaffffffffffffffffaffffffffffg fffbbbbbbbbbcccffffffffffdaffffffffffg fffcccbbbbbbbbbbbbbbbbbbbbbbbbccccfffg fffffffffafffffffffffccccbbbbbbbbbbbbbbbbbbbbbbbcceee fffffffffagffffffffffffffafffffffffffg eeeccbbbbbbbbbbbbbbbbbbbbe fffffffffadfffffffffffffdafffffffffffg eeeccbbbbe fffffffffadfffffffffffffaafffffffffffg ebbbbc fffffffffaafffffffffffffagfffffffffffg cbbbbe fffffffffdaffffffffffffgaffffffffffffg ebbbbc fffffffffgaffffffffffffdaffffffffffffg ebbbbbe ffffffffffaffffffffffffadffffffffffffg cbbbe ffffffffffagfffffffffffagffffffffffffg e ffffffffffadffffffffffgafffffffffffffg ffffffffffaaffffffffffdafffffffffffffg ffffffffffdaffffffffffadfffffffffffffg ffffffffffgaffffffffffagfffffffffffffg fffffffffffafffffffffgaffffffffffffffg fffffffffffagffffffffdaffffffffffffffg fffffffffffadffffffffadffffffffffffffg aa ae da ea ea da a ad ae a ac ca ad aa da ac ca a a ca ae aa ac ac ad a da ca ca aa ea ac a a acca adaa aaac caa eaa ad ac ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#542e4eff b,#548bceff c,#beb0bcff d,#9c8799ff e,#d6dae6ff f,#7a5d76ff g,#97b9e2ff ``` ```image faae daac daac faa caad eaaf eaad caad aaf daac aaa aaa faae eaaf daac caad caac daac eaad aaa eaaf eaaf aaa caad faa faae daae aaa caac eaaf caad caad eaaf faae aaa aaa faa eaaf daae daac daac faae caad aaa eaaf eaaf aaf daac faa faae faae aaa daac caad caad daac eaad faae aaf aaa eggeeeee aaa caad gbbbbbbbbbbbbbbgggggggeeeee daac gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggggggeeeeefaae eeegggggggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggggggeeeee eaad eeeeeeggggggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb eaaf eeeeeggggbbbbbbbbbbbbbbbbbbbbbbbbb aaa faae eeeeegggggggbbb faae eaaf daae caad caac daac caad faa eaaf eaaf aaa caad faa daac daae aaa daac eaaf caad caad eaaf daac aaf aaa faa eaaf faae caad daac faae caad aaa eaaf eaaf aaf caad aaa faae faae aaa daac eaaf caad daac eaad faae aaf aaa aaa eaaf faae daac daac faae caac aaa caad caad ``` <!-- end of image --> Eureka! There's definitely 2 intersections in area A! Answer: A: 2; 2 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#542e4eff b,#548bceff c,#bcadbaff d,#9a8497ff e,#d9dae5ff f,#775a73ff g,#97b8e2ff ``` ```image cc aaaaafc a edaaaaafc da cfaaaaafc ae af cfaaaaafc ad ac cfaaaaade af ea cfaaaaade fa da cfaaaaade ca af edaaaaaade a ae edaaaaaade ae ea edaaaae ac fa e af af fa ae ca ea ea fa a ad ac ae af ca fa fa da ad ea ae a ca ac fa ad ad aa a da ca ea aa a ad ae a ad ca aa aa da ac ca a a da ae aa ad ac af a bbbbbbbggggee da eggggbbbbbbbbbbbbbbbbbbbbbgggeee ea eeeggbbbbbbbbbbbbbbbbbbbbbbggggee ae ea eeggggbbbbbbbbbbbbbbbbbbbe ac da eeegggbbbbg af af ebbbbg fa ac gbbbbe da ea gbbbbg ea da ebbbbge a af gbbbe ac ae e ad ea fa fa da af ea ae a ea ae fa ad ad aa ae da ca ca fa a ad ae ae ad ca af fa fa ad ca a a ca ae aa ac ad af a fa ca ca aa ea ac a a acda afaa faac daa eaa af ac ``` <!-- end of image -->
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This is the image I'm working with. The goal is to count the intersections. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#5261c4ff b,#b6bce1ff c,#edf3f0ff d,#545fafff e,#8094b9ff f,#b1d7b1ff g,#96c69cff ``` ```image c edd dddb dddd bdddd ddddde dddddd cddddddc eddbbddd ddd ddd ddd addb cccccccccccbddecccdddccccccccccccccccc fffffffffffdddgfffdddgfffffffffffffffg fffffffffffdddffffeddefffffffffffffffg fffffffffffdddfffffdddfffffffffffffffg ffffffffffeddefffffdddgffffffffffffffg ffffffffffdddffffffgdddffffffffffffffg ffffffffffdddfffffffdddffffffffffffffg ffffffffffdddfffffffeddefffffffffffffg fffffffffeddeffffffffdddfffffffffffffg ede fffffffffdddfffffffffdddfffffffffffffg bddddd fffffffffdddfffffffffedddffffffffffffg eddddddde ffffffffgdddffffffffffdddffffffffffffg bdddddddeddd ffffffffdddgffffffffffdddefffffffffffg edddddddc dddc ffffffffdddffffffffffffdddfffffffffffg bddddddde bdde ffffffffdddffffffffffffdddfffffffffffg edddddddc ddd fffffffeddeffffffffffffeddeffffffffffg cddddddde dddc aaa fffffffdddffffffffffffffdddffffffffffg edddddddb bdde aaa fffffffdddffffffffffffffdddgfffffffffg cddddddde ddd aaa fffffffdddffffffffffffffgdddfffffffffg edddddddb cccdddbcccccccaaaccc ffffffeddefffffffffffffffdddfffffffffg cddddddde gffgdddfffffffaaafff ffffffdddffffffffffffffffdddeffffffffedddddddb gfffdddfffffffaaafff fffaffdddfffffffffffffffffdddfffffgddddddde gfffdddgffffffaaafff ffaaaedddfffffffffffffffffdddfffedddddddb gfffgdddffffffaaafff ffaaaaadgfffffffffffffffffeddddddddddd gffffdddffffffaaafff fffaaaaaaffffffffffffffffffddddddddgfg gffffdddefffffaaafff fffffaaaaaeffffffffffffffffdddddeffffg gfffffdddfffffaaafff ffffedaaaaaaffffffffffffffffddeffffffg gfffffdddfffffaaafff ffffdddfaaaaaafffffffffffffffffffffffg gfffffeddeffffaaafff ffffdddfffaaaaaefffffffffffffffffffffg gffffffdddffffaaafff ffffdddffffeaaaaaffffffffffffffffffffg gffffffdddffffaaafff fffeddeffffffaaaaaaffffffffffffffffffg gffffffeddefffaaafff fffdddfffffffffaaaaaeffffffffffffffffg gfffffffdddfffaaafff fffdddffffffffffeaaaaafffffffffffffffg gfffffffdddfffaaefff ffgdddffffffffffffaaaaaafffffffffffffg gfffffffeddefgaaefff ffdddgffffffffffffffaaaaaefffffffffffg gffffffffdddfgaaefff ffdddffffffffffffffffeaaaaaffffffffffg gffffffffdddfeaaefff fffedffffffffffffffffffaaaaaaffffffffg gffffffffeddeeaaefff fffffffffffffffffffffffffaaaaaeffffffg gfffffffffdddeaaefff ffffffffffffffffffffffffffeaaaaafffffg gfffffffffdddeaaefff ffffffffffffffffffffffffffffaaaaaafffg gfffffffffeddaaagfff ffffffffffffffffffffffffffffffaaaaaefg gffffffffffddaaagfff fffffffffffffffffffffffffffffffeaaaaag gffffffffffddaaagfff fffffffffffffffffffffffffffffffffaaaaaa gffffffffffgdaaaffff fffffffffffffffffffffffffffffffffffaaaaab gfffffffffffdaaaffff ffffffffffffffffffffffffffffffffffffeaaaaac gfffffffffffdaaaffff fffffffffffffffffffffffffffffffffffffgaaaaaa gfffffffffffgaaaffff fffffffffffffffffffffffffffffffffffffg caaaaab gffffffffffffaaaffff fffffffffffffffffffffffffffffffffffffg baaaaac gffffffffffffaaaefff fffffffffffffffffffffffffffffffffffffg aaaaaa gffffffffffffaaadfff cccccccccccccccccccccccccccccccccccccc caaaaab gffffffffffffaaadfff baaaaac gffffffffffffaaadfff aaaaaa gffffffffffffaaaffff caaaaab gffffffffffffaaaffff baaaaac gffffffffffffaaaffff aaaaaa gffffffffffffaaaffff caaaaab gffffffffffffaaaffff baaaaac gffffffffffffaaaffff aaaaaa gffffffffffffaaaffff caaaaab gffffffffffffaaaffff baaaaagffffffffffffaaaffff aaaaaafffffffffffaaaffff caaaaaefffffffffaaaffff baaaaagfffffffaaaffff gaaaaaaffffffaaaffff gffaaaaaeffffaaaffff gfffeaaaaagffaaaffff gfffffaaaaaafaaeffff gfffffffaaaaaaaeffff gffffffffeaaaaaeffff gffffffffffaaaaeffff gfffffffffffgaafffff cccccccccccccccccccc ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#5160c4ff b,#a6acd9ff c,#e6e7f4ff d,#545eafff e,#868eccff f,#c7cae7ff g,#6a74c0ff ``` ```image bdddddb edddddb gdddddf fdddddd cdddddd gdddddf fddddde bddddde edddddb cddddddc gdddddc gdddddb cdddddg fdddddg bddddde ddddddf edddddf eddddde ddddddc fdddddd fdddddg gdddddf bdddddb bddddde gdddddf cddddddc cdddddd edddddb fddddde fdddddg edddddb ddddddf gdddddc bddddde cdddddg cddddddc bddddde gdddddb edddddf bdddddg ddddddc cddddddc fdddddg edddddb bdddddb fdddddd gdddddf gdddddf cdddddd bddddde fddddde cddddddc edddddb edddddb gdddddc fdddddg cdddddg ddddddf bddddde eddddde edddddf fddddddc ddddddc gdddddb fdddddg bdddddg bdddddb cddddddc gdddddf edddddb cdddddd fdddddd fddddde gdddddf edddddb bddddde gdddddc cddddddc cdddddg gdddddb c bddddde fdddddg fgd bgf edddddf ddddddf cbdddd caaaec ddddddc eddddde fgdddddd eaaaaaedddddg fdddddd cbddddddddd faaaaaaaaddddb gdddddf fgddddddddddd gaaaaaaaaaaddf bdddddgbdddddddddddddd ceaaaaaaaaaaac cddddddddddddddddddgbc fgaaaaaaaaagf edddddddddddddddef baaaaaaaaaaec fddddddddddddgbc caaaaaaaaaaab ddddddddddef cddaaaaaaaaaagf bddddddgbc bdddaaaaaaaaaaaec gdddef edddddgaaaaaaaaaab ffc ddddddcfgaaaaaaaaagf fdddddg baaaaaaaaaaec bdddddb ceaaaaaaaaaab gdddddf fgaaaaaaaaagf cdddddd baaaaaaaaaaec fddddde ceaaaaaaaaaab edddddb fgaaaaaaaaagf gdddddc baaaaaaaaaaec cdddddg ceaaaaaaaaaab bddddde fgaaaaaaaaagf edddddf baaaaaaaaaaec ddddddc ceaaaaaaaaaab fdddddg fgaaaaaaaaagf bdddddb baaaaaaaaaaec gdddddf ceaaaaaaaaaab cdddddd fgaaaaaaaaagf fddddde baaaaaaaaaaec bdddddb ceaaaaaaaaaab cfegdc fgaaaaaaaaagf c baaaaaaaaaaec ceaaaaaaaaaab fgaaaaaaaaagf baaaaaaaaaaec ceaaaaaaaaaab fgaaaaaaaaagf baaaaaaaaaaec ceaaaaaaaaaab fgaaaaaaaaagf baaaaaaaaaae ceaaaaaaaaa fgaaaaaaa baaaaaa ceaaaa fgaa ba c ``` <!-- end of image --> I can confirm that 1 intersection exists in area A. Time to investigate another area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#5160c4ff b,#adb3e0ff c,#e5e7f5ff d,#545eafff e,#929ad5ff f,#c8cdeaff g,#747ecaff ``` ```image ddddddc faaaaab eddddde faaaaab fdddddd faaaaab ddddddf baaaaab eddddde baaaaab fdddddd baaaaaf ddddddf baaaaaf eddddde baaaaaf cdddddd eaaaaaf gdddddf eaaaaaf bddddde eaaaaaf cddddddc eaaaaac gdddddb eaaaaac bdddddg eaaaaac cddddddc gaaaaac gdddddb gaaaaac bdddddg gaaaaa cddddddc gaaaaa gdddddb gaaaaa fdddddg gaaaaa ddddddc aaaaaa edddddb aaaaaa fdddddg aaaaag ddddddf aaaaag eddddde aaaaag fdddddd aaaaag ddddddf caaaaag eddddde caaaaag fdddddd caaaaae ddddddf caaaaae eddddde caaaaae cdddddd faaaaae gdddddf faaaaae bdddddg faaaaae cddddddc faaaaab gdddddb faaaaab bdddddg faaaaab cddddddcbaaaaab gdddddbbaaaaab bdddddgbaaaaab cddddddeaaaaaf gdddddgaaaaaf fdddddaaaaaaf dddddaaaaaaf eddddaaaaaaf fddddaaaaaac ddddaaaaaac edddaaaaaac fdddaaaaaac dddaaaaaac eddaaaaaac fddaaaaaa ddaaaaaa bdaaaaaa cdaaaaaa gaaaaaa baaaaaa caaaaaac aaaaaab aaaaaag caaaaaadc caaaaaadb caaaaaadg caaaaaaddc caaaaaadec faaaaag faaaaae faaaaae faaaaab faaaaab faaaaab baaaaab baaaaab baaaaab baaaaaf baaaaaf eaaaaaf eaaaaaf eaaaaaf eaaaaac eaaaaac eaaaaac gc gaaaaac aae gaaaaac aaaaf gaaaaac aaaaagc gaaaaa aaaaaaae gaaaaa aaaaaaaaaf gaaaaa aaaaaaaaaagc aaaaaa ceaaaaaaaaaae aaaaaa fgaaaaaaaaaaf aaaaaa baaaaaaaaaagc aaaaag ceaaaaaaaaaae aaaaag fgaaaaaaaaaaf aaaaag baaaaaaaaaagc caaaaag ceaaaaaaaaaae caaaaag fgaaaaaaaaaafcaaaaag baaaaaaaaaagaaaaae ceaaaaaaaaaaaaaae fgaaaaaaaaaaaae baaaaaaaaaaae ceaaaaaaaaae fgaaaaaaab baaaaaaf ceaaae ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area B! Answer: A: 1; B: 1; 1 + 1 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#5160c4ff b,#a8afddff c,#e6e8f5ff d,#545eafff e,#8d94cbff f,#cccfe8ff g,#6975c6ff ``` ```image c edd dddf dddd bdddd ddddde dddddd cddddddc eddbfddg ddd ddd ddd gddb fddg cddd gddf ddd ddd bdde ddd ddd bdde dddf dddc fddd ddd ddd cddd eddb eddb ddd edg ddd dddc fddddd ddd bddg eddddddde fddg ddd fdddddddeddd gddf gddf edddddddf dddc ddd cddd fddddddde bdde ddd ddd edddddddf ddd bdde edde fddddddde dddc aaa dddc ddd edddddddf fddg aaa ddd dddc fddddddde ddd aaa cddd fddd edddddddf dddf aaa eddb ddd cddddddde fddg aaa ddd gddb edddddddf ddd aaa g ddd ddd cddddddde gddf aaa gaaeddg ddd edddddddf cddd aaa aaaaadf bddgddddddde ddd aaa gaaaag ddddddddf gddb aaa caaaaab ddddde cddd aaa bdaaaaaac ddf ddd aaa dddcgaaaag eddb aaa ddd caaaaab ddd aaa cddd baaaaac ddd aag eddb gaaaag edde aag ddd caaaaab ddd caag ddd baaaaac ddd caae fddg gaaaag bdde caae gddf caaaaab ddd faae ddd baaaaac dddcfaab ced gaaaag bddefaab caaaaab dddbaab baaaaac dddbaaf gaaaag fddaaaf caaaaab ddaaaf baaaaac ddaaac gaaaag fdaaac caaaaab daaac baaaaac gaaa gaaaag caaa caaaaab aaa baaaaac aaab gaaaag aaad caaaaab aaad baaaaac aaadc gaaaag aaa caaaaab aaa baaaaac aaa gaaaag aaa caaaaab aaa baaaaac aaa gaaaag aaa caaaaab aaa baaaaac aaa gaaaag aaa caaaaab aaa baaaaac aaa gaaaag aag caaaaab aag baaaaac caag gaaaagcaae caaaaaaae baaaaae gaaab caa ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#65d673ff b,#432476ff c,#b1d8b1ff d,#7f6ea0ff e,#8fd594ff f,#beb3d0ff g,#e5f2e7ff ``` ```image eeeeeeeeeeeeeeeeeeeeee gcccccccccccccccccccccc gcccccccccccccccccccccc gcccccccccccccccccccccc gccccccccccccccccaccccc gccccccccccccccceaccccc gcccccccccccccccaaccccc gccccccccccccccceaccccc gccccccccccccccacaccccc gccccccccccccccacaccccc gccccccccccccceccaccccc gcccccccccccccaccaccccc gccccccccccccceccaccccc gccccccccccccecccaccccc gccccccccccccacccaccccc df gccccccccccceecccaccccc gdbd gcccccccccccaccccadcccc fbbf gccccccccccdbbbbdaccccc fbbd gccccdbbbbdecccccaccccc dbdg fdbbbddccccccacccccaccccc fbb fdbbbdf gccccccccccecccccaccccc d bfg gcccccccccaccccccaccccc gf b gcccccccccaccccccaccccc d gb gcccccccceccccccceccccc b gb gccccccccaccccccceccccc b gb gcccccccceccccccceccccc d fb gcccccccacccccccceccccc gf fd gcccccccacccccccceccccc d fd gcccccceecccccccceccccc b dd gccccccaccccccccceccccc b df gccccccaccccccccceccccc c d df gcccccecccccccccceccccc e gf bf gcccccacccccccccceccccc e d bg gcccccecccccccccceccccc e b bg eeeeaeeeeeeeeeeeeeeeee ag b bg e gg ag d b c gg ag gf b a gg ag d b c gg ag b b e gg ac b gb a c ac d gb cg c ac ff gb a c ec d fb e c ec b fd e c ec b fd a c ce d dd gg c ce fdf a c gge f e e gge c e gge a e c a gc e c a a e c a a e e a cg a e a a a e a cag a a eag a a ea a a ea a a ae a a ae a a gac a a gac a a gac a a gac a a cag a a cag a e cag a e ea a e ea a e ee e ae c ae c gac c gac c gac c cag c cag gg cag gg eag ggea ga ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#66d673ff b,#442576ff c,#b8ecbeff d,#806fa1ff e,#90e19aff f,#b7abcbff g,#def2e2ff ``` ```image ga eag aag caag aaag gacag eagag acgag caggag ee gag gac gag ca gag ae gag cag gac ee ac gac ac ca ac ae ac gag ac ea ac ac ac cag ac ae ac gac ac ea ac ac gaddf cag gffdbbbbbbf gfdbbbbbbbddfae gffddbbbbbbdffg ae gffddbbbbbddffea ae gfddbbbbbbddfg ae ee bbbbbbdffg gag ee dffg ea ee gac ee ca ee ae ee gag ee ea ee ac ee cag ee ee ee gac ee ea ea ae ea cag ea ee ca gac ca ca ca ae ca gag ca ea ca ac ca cag ca ae ca gag ca ea ca ac ca cag ca ee cag gac gag ca gag ``` <!-- end of image --> Wow! I can see 2 intersections so clearly in area A! Answer: A: 2; 2 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#65d673ff b,#432376ff c,#b7ecbdff d,#7f69a2ff e,#8ee198ff f,#baaecdff g,#dfefe3ff ``` ```image a ca aa ca e a a a cg a a a e a e a a a df gc a gdbd a ad fbbf fbbbbda gbbd gfdbbdfe a dbdg fdbbbdf a e fbb fdbbbdg gc e f bfg a e gf b a e d gb cg e b gb a e b gb e e d fb e c gf fd a c d fd gg c b dd a c b df e c c d df e c e gf bf a c e d bg gc gg e b bg a gg ag b b e gg ag d b c gg ag gf b a gg ag d b c gg ag b b e gc ac b b a c ac d gb cg c ac ff gb a c ec d fb e c ec b fd e c ee b fd a c ce d dd gg e ce fdf a e ce f e e gge c e gge a e c a gc e c a a e c a a e e a cg a e a a a e a cag a a eag a a ea a a ea a a ae a a ae a a gae a a gac a a gac a a cac a a cag a a cag a e cag a e ea a e ea a e ee e ae e ae c gac c gac c gac c cag c cag cg cag gg ea ggea ga ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've noticed 2 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#72dc75ff b,#acccc4ff c,#d0e9daff d,#4dda52ff e,#95ce96ff f,#b1d7b1ff g,#eef6efff ``` ```image effffffffffffffffffffffffffffffffffffffffffffe effffffffffffffffffffffffffffffffffffffffffffe effffffffffffffffffffffffffffffffffffffffffffe effffffffffbbbfffffffffffffffffffffffffffffffe effffffffffbbbfffffffffffffffffffffffffffffffe effffffffffbbbbffffffffffffffffffffffffffffffe effffffffffbbbbbfffffffffffffffffffffffffffffe effffffffffbbbbbfffffffffffffffffffffffffffffe efffffffddebbbbbbffffffffffffffffffffffffffffe effffffdddabbbbbbbfffffffffffffffffffffffffffe efffffedddebbffbbbbffffffffffffffffffffffffffe efffffddddebbfffbbbffffffffffffffffffffffffffe effffdddddebbfffbbbbfffffffffffffffffffffffffe efffadddfdbbbffffbbbbffffffffffffffffffffffffe efffdddefdbbbfffffbbbffffffffffffffffffffffffe effddddfffbbbfffffbbbbfffffffffffffffffffffffe efddddffffbbbffffffbbbbffffffffffffffffffffffe eedddfffffbbbaffffffbbbffffffffffffffffffffffe edddafffffbbbdffffffbbbbfffffffffffffffffffffe ddddffffffbbbdfffffffbbbbffffffffffffffffffeee edddfffffffbbbdafffffffbbbfffffffffffffffffadda gdddefffffffbbbddfffffffbbbbffffffffffffffffddddc ddddffffffffbbbddffffffffbbbbffffffffffffffdddddd adddfffffffffbbbddaffffffffbbbfffffffffffffdddddddd cdddefffffffffbbbdddffffffffbbbbfffffffffffedddefddda dddaefffffffffbbbdddfffffffffbbbbffffffffffdddaffadddc dddd efffffffffbbbdddafffffffffbbbbffffffffddddfffeaddd dddg efffffffffbbbfdddffffffffffbbbfffffffadddffffe dddd fddd effffffffbbbbfdddffffffffffbbbbfffffedddeffffe ddda dddc effffffffbbbffdddaffffffffffbbbbffffdddafffffe cdddf ddd effffffffbbbffedddfffffffffffbbbfffddddffffffe adddg gddd effffffffbbbfffdddfffffffffffbbbbfadddfffffffe dddd adde effffffffbbbfffdddafffffffffffbbbbdddefffffffe ddda ddd effffffffbbbfffedddffffffffffffbbbaddffffffffe gdddf ddd effffffffbbbffffdddffffffffffffbbbbdfffffffffe edddg fdda effffffffbbbffffdddafffffffffffabbbbfffffffffe dddd dddc effffffffbbbffffedddfffffffffffddbbbfffffffffe dddd ddd effffffffbbbfffffdddffffffffffdddebbbffffffffe gddde cddd effffffffbbbfffffdddaffffffffddddfbbbbfffffffe fdddg addf effffffffbbbfffffedddfffffffedddeffbbbfffffffe dddd ddd effffffffbbbffffffdddfffffffdddafffbbbbffffffe dddd ddd effffffffbbbffffffdddafffffddddfffffbbbbfffffe gddde fdda effffffffbbbffffffedddffffadddfffffffbbbbffffe fdddc dddc effffffffbbbfffffffdddfffedddeffffffffbbbffffe addd ddd effffffffbbbfffffffdddaffdddafffffffffbbbbfffe dddd cddd effffffffbbbfffffffedddfddddfffffffffffbbbbffe ddda addf effffffffbbbffffffffdddadddfffffffffffffbbbffe cde ddd efffffffbbbbffffffffddddddefffffffffffffbbbbfe g ddd efffffffbbbfffffffffedddddfffffffffffffffbbbbe edda efffffffbbbffffffffffddddfffffffffffffffffbbbe dddg efffffffbbbffffffffffaddffffffffffffffffffbbbb ddd efffffffbbbfffffffffffeffffffffffffffffffffbbbb cddd efffffffbbbfffffffffffffffffffffffffffffffffbbbg addf ggggggggbbbgggggggggggggggggggggggggggggggggcbbb ddd gbbb bbbb gddd gbbbb bbbc edda bbbb cbbb ggggggdddcggg bbbb bbbb ffffffdddfffe bbbb bbbc fffffedddfffe bbbb cbbb fffffdddefffe bbbb bbbb fffffdddffffe bbbbg bbbc fffffdddffffe bbbbg gbbbg ffffaddaffffe bbbbc bbbb ffffdddfffffe cbbbc bbbb ffffdddfffffe cbbbc gbbbg fffedddfffffe cbbbc bbbb fffdddefffffe gbbbb bbbb fffdddffffffe gbbbb gbbbg fffdddffffffegbbbb cbbb ffaddaffffffebbbb bbbb ffdddfffffffbbbb bbbc ffdddffffffbbbb cbbb ffffffffffbbbb bbbb fffffffffbbbb bbbc ffffffffbbbbe cbbb fffffffbbbbfe bbbb ffffffbbbbffe bbbc fffffbbbbfffe gbc ffffbbbbbfffe ffffbbbbffffe ggcbbbbgggggg gbbbb cbb g ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#79e37dff b,#acccc5ff c,#d0e7daff d,#4ddb52ff e,#a0eba3ff f,#bef1c0ff g,#e9f6ecff ``` ```image gddddddg eddddda addddde gddddddc fdddddd eddddda ddddddf cddddddg eddddda addddde gddddddc fdddddd addddda ddddddf cddddddg eddddda addddde gddddddc fdddddd addddde ddddddf cddddddg eddddda addddde gddddddg fdddddd addddde ddddddf cdddddd eddddda c eddddde cb ceadg cbb g cbbb cbbbb gbbbbb gbbbbbb gbbbbbbb gbbbbbbbb gbbbbbbbbg bbbbbbbbg bbbbbbbbg bbbbbbbbc cbbbbbbbc cbbbbbbbc cbbbbbbbc cbbbbbbbc cbbbbbbbc ``` <!-- end of image --> I'll move on to the next area. The intersection must be somewhere. Let's shift our focus to the next area. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#68df6dff b,#acccc5ff c,#cde5d9ff d,#4ddb52ff e,#8ee295ff f,#aeedb1ff g,#e7f3ebff ``` ```image gg cbbbg cbbbbb bbbbbbc bbbbbbbg bbbbbbbb bbbbbbbbc bbbbbbbbbg gbbbbbbbbbbg gbbbbbbbbbbc gbbbbbbbbbbbc feacgbbbbbbbbbbbbg fddddfbbbbbbbbbbbbb cdddddebbbbbcbbbbbbbc gadddddebbbbbcgbbbbbbbg eddddddebbbbbc cbbbbbbb fdddddddebbbbbc cbbbbbbc gddddddddebbbbbg bbbbbbbg addddddddebbbbbg gbbbbbbb edddddddddebbbbbg cbbbbbbc cddddddddddebbbbbg bbbbbbbg gaddddddfaddbbbbbbg gbbbbbbb edddddda fddbbbbbbg cbbbbbbc fdddddddg gddbbbbbb bbbbbbbg gdddddddc adbbbbbb gbbbbbbb adddddde fdbbbbbb cbbbbbbc fdddddda gdbbbbbb bbbbbbbc cdddddddc abbbbbb gbbbbbbbg addddddf fbbbbbb cbbbbbbb edddddda cbbbbbec bbbbbbbc fdddddddg gbbbbbee gbbbbbbbg gdddddddf gbbbbbea cbbbbbbb adddddde cbbbbbedc cbbbbbbc fddddddag cbbbbbede bbbbbbbg gdddddddc cbbbbbeda gbbbbbbb fef adddddde cbbbbbeddc cbbbbbbc eddd dddddda cbbbbbadde bbbbbbbg fdddd ddddddg cbbbbbadda gbbbbbbb cddddd dddddf cbbbbbadddc cbbbbbbc gaddddd dddde bbbbbbaddde bbbbbbbg edddddd dddag bbbbbbaddda gbbbbbbb fddddddd dddc bbbbbbaddddc cbbbbbbc cdddddddd dde bbbbbbddddde bbbbbbbc addddddad da bbbbbbddddda gbbbbbbbg edddddda e dg bbbbbbddddddc cbbbbbbb fdddddddg f bbbbbbaddddde bbbbbbbc gdddddddf gbbbbbbfddddda gbbbbbbbg adddddde gbbbbbbgddddddc cbbbbbbb edddddda gbbbbbc addddde cbbbbbbc cdddddddc gbbbbbc fddddda bbbbbbbg gdddddddf gbbbbbc gddddddc gbbbbbbb adddddde cbbbbbc addddde cbbbbbbc fddddddag cbbbbbc fddddda bbbbbbbg cdddddddc cbbbbbc gddddddc gbbbbbbb gaddddddf cbbbbbc addddde cbbbbbbc edddddda cbbbbbg fddddda bbbbbbbg fdddddddg cbbbbbg gddddddc gbbbbbbb gdddddddc cbbbbbg addddde cbbbbbbc adddddde bbbbbbg fddddda bbbbbbbc edddddda bbbbbbg gddddddc gbbbbbbbgfdddddddg bbbbbb addddde cbbbbbbbdddddddf bbbbbb fddddda bbbbbbbeddddde bbbbbb gddddddc gbbbbbbbaddda bbbbbb addddde cbbbbbbbdddc gbbbbbb fddddda cbbbbbbedf gbbbbbb gddddddc gbbbbbbbe gbbbbbb addddde fabbbbbbb gbbbbbc fddddda cddebbbbbbc gbbbbbc gddddddc gadddbbbbbbbg gbbbbbc addddde eddddabbbbbbb cbbbbbc fddddda fddddddebbbbbbc cbbbbbc gddddddc gdddddddfbbbbbbbg cbbbbbc addddde adddddde gbbbbbbb cbbbbbg fddddda edddddda cbbbbbbc cbbbbbg gddddddc fdddddddg bbbbbbbc cbbbbbg addddde gdddddddf gbbbbbbbg bbbbbbg fddddda adddddde cbbbbbbb bbbbbbg gddddddc eddddddag bbbbbbbc bbbbbbg addddde cdddddddc gbbbbbbbg bbbbbb fddddda gaddddddf cbbbbbbb bbbbbb gddddddc adddddda cbbbbbbc bbbbbb addddde fddddddag bbbbbbbg bbbbbb fddddda cdddddddc gbbbbbbb gbbbbbb gddddddc gadddddde cbbbbbbc gbbbbbb addddde edddddda bbbbbbbg gbbbbbb fddddda fdddddddg gbbbbbbb gbbbbbc gddddddc gdddddddf cbbbbbbc gbbbbbc addddde adddddde bbbbbbbg cbbbbbc fdddddaedddddda gbbbbbbb cbbbbbc gdddddddddddddg cbbbbbbc cbbbbbc adddddddddddf bbbbbbbc cbbbbbc fdddddddddde gbbbbbbbg cbbbbbg gdddddddddag cbbbbbbb cbbbbbg addddddddc bbbbbbb cbbbbbg fdddddddf gbbbbbb bbbbbbg gdddddda cbbbbb bbbbbbg adddddg cbbbb bbbbbbg gdddac bbbb bbbbbb ffg gbbb bbbbbb cbb ``` <!-- end of image --> Eureka! There's definitely 2 intersections in area B! Answer: A: 0; B: 2; 0 + 2 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#6be070ff b,#acccc5ff c,#cde3d9ff d,#4ddb52ff e,#90e695ff f,#b8efbaff g,#e7f4ebff ``` ```image g bbb bbbg bbbb gbbbbb gbbbbbc ddfbbbbbb dddabbcbbbb fdddebbc bbbc ddddebbg gbbb dddddbbbg bbbb eddd dbbbg bbbc gdddf abbb gbbb ddda gbbb bbbb addd bbb bbbb fdddg bbbe gbbbg ddde bbbd cbbb dddd bbbd bbbb ff eddd bbbde bbbg edde gdddf bbbdd cbbb gddddc dddd bbbdd bbbb dddddd addd bbbdde bbbc addddddd cdddg bbbddd cbbb fdddg ddda ddda gbbbddd bbbb ddde fdddf dddd gbbcadde bbbc dddd addd ddd gbbcgddd gbbb addd dddd fdda cbbc ddd bbbb cdddc ddda dddf cbbc adde bbbc ddda cdddf ddd cbbg gddd gbbb dddd eddd gddd bbbg ddd bbbb eddd dddd edde bbb adde bbbbdddf ddda ddd bbb gddd gbbbada gdddf ddd bbb ddd cbbbd edddg fdda bbb adde fbbbb dddd dddc bbb gddd gddbbbg dddd ddd bbb ddd dddebbb gddde gddd bbb adde addd bbbb edddg adde bbb gddd fdddg bbbc addd ddd bbb ddd ddde cbbb dddd ddd bbb adde dddd bbbb gddde fdda bbb gddd addd bbbc fdddc dddc bbb ddd cdddc gbbb addd ddd gbbb adde ddda bbbb dddd cddd gbbc gddd dddd bbbc ddde addf cbbc dddeddd gbbb fde ddd cbbc adddddf bbbb g ddd cbbg gdddda bbbb edda cbbg dddd gbbbg dddg bbbg addg cbbb ddd bbb fg bbbb cddd bbb bbbg addf bbb cbbb ddd gbbb bbbb ddd bbbb bbbc edde bbbb cbbb dddg bbbb bbbb ddd bbbb bbbc fddd bbbb gbbb addf bbbb bbbb ddd bbbbg bbbc gddd bbbbg gbbb edde bbbbg bbbb dddg cbbbc bbbb ddd cbbbc gbbbg fddd cbbbc cbbb dddf gbbbb bbbb ddd gbbbb bbbg gddd gbbbb cbbb edde bbbb bbbb ddd bbbb bbbg add bbbb cbbb g bbbb bbbb bbbb bbbc bbbbg gbbb bbbbg bbbb bbbbg bbbc cbbbc gbc cbbbc cbbbc gbbbb gbbbb cbb g ``` <!-- end of image -->
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Let's examine this image for potential line intersections. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#7ac876ff b,#934aacff c,#5dc555ff d,#b1d7b1ff e,#ad8cbcff f,#ecf2ecff g,#96cb95ff ``` ```image f ccd c ccf da fccf ad fcc c dca c dca fc gcg dg acd ad ccd c fccf c fccf fc dcc dg dca cf gcg c acd c ccd fc fcc dgggggggggggggggggggggggd dg dc gdddddddddddddddddddddddg cf ac gdddddddddddddddddddddddg c aa gdddddddddddddddddddddddg c cg gdddddddddddddddddddddddg fc cdgdddddddddddddddddddddddg dg cadddddddddddddddddddddddg cf cdddddddddddddddddddddddg c gcddddddddddddddddddddddg c ggcdddddddddddddddddddddg fc gdgcddddddddddddddddddddg fffffffffffffggfffffff gddacdddddddddddddddddddg dddddddddddddcgddddddgf gdddccddddddddddddddddddg dddddddddddddcddddddddf gddddcadddddddddddddddddg dddddddddddddcddddddddf gdddddcaddddddddddddddddg ddddddddddddgcddddddddf gddddddcgdddddddddddddddg ddddddddddddaaddddddddf gdddddddcgddddddddddddddg ddddddddddddcgddddddddf gddddddddcdddddddddddddebbb ddddddddddddcdddddddddf gddddddddgcdddddddebbbbeg ddddddddddddcdddddddddf gdddddddddgcdebbbbedddddg dddddddddddgcdddddddddf gdddddddebbaceddddddddddg dddddddddddaadddddddddf gddebbbbedddacddddddddddg dddddddddddcddddddddddf febbbbedddddddddccdddddddddg dddddddddddcddddddddddf febbbbefgdddddddddddddcaddddddddg dddddddddddcddddddddddf febbbbef gddddddddddddddcadddddddg ddddddddddgcddddddddddf febbbbef gdddddddddddddddcgddddddg ddddddddddaaddddddddddf eebbbbef gddddddddddddddddcddddddg ddddddddddcdddddddddddf febbbbef gdddddddddddddddddcdddddg ddddddddddcddddddddddddebbbbef gdddddddddddddddddgcddddg ddddddddddcddddddebbbbbef gddddddddddddddddddgcdddg dddddddddgcdebbbbeedddf gdddddddddddddddddddacddg ddddddebbaabedddddddddf gddddddddddddddddddddccdg dddbbbbedcddddddddddddf gdddddddddddddddddddddcag dddddddddcddddddddddddf gddddddddddddddddddddddca dddddddddcddddddddddddf gdddddddddddddddddddddddcd ddddddddgcddddddddddddf gdddddddddddddddddddddddgcf ddddddddaaddddddddddddf gdddddddddddddddddddddddgfc ddddddddcdddddddddddddf gdddddddddddddddddddddddg ddddddddcdddddddddddddf gdddddddddddddddddddddddg ddddddddcdddddddddddddf gdddddddddddddddddddddddg dddddddgcdddddddddddddf dgggggggggggggggggggggggd dddddddaadddddddddddddf dddddddcddddddddddddddf dddddddcddddddddddddddf dddddddcddddddddddddddf ddddddgcddddddddddddddf ddddddagddddddddddddddf ddddddcdddddddddddddddf ddddddcdddddddddddddddf ddddddcdddddddddddddddf dddddgcdddddddddddddddf gggggcaggggggggggggggg c c c da ad c c c da ad c ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#8ad484ff b,#9449adff c,#5ec456ff d,#b4e3b1ff e,#b37fc5ff f,#dfeddfff g,#d4b6deff ``` ```image dca acd ccf fcc dca dca acd ccf fcc dca dca acd ccf fcc dca acd acd ccf fcc dca acd acd ccf fcc dca acd acd ccf fcc dca acd acd ccf fcc dca acd fgee acd ggebbbbbb ccf fgeebbbbbbbbeeg fcc ggeebbbbbbbbegg fgaccbbbbbbbeegf fgeebbbcccbbeggf ggebbbbbbbbeccd fbbbbbbeegf ccf beggf fcc dca acd ccf ccf fcc dca acd ccf cc fcc dca acd ccf cc fcc dca acd ccf fcc fcc dca acd ccf fcc fcc dca acd ccf fcc dca dca acd ccf fcc dca dca ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Let's continue our search in the next region. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#82cf7dff b,#9248acff c,#5ec656ff d,#b5e4b1ff e,#ceaddaff f,#e3ede4ff g,#ae78c0ff ``` ```image d cf ccf accf acaf fcca fcca fcca dccd dccd dccd accf accf accf faca fcca fcca fccd dccd dccd dccf accf accf accf feg fcca feggbbbb fcca feggbbbbbbbge fcca feggbbbbbbbgeef dccdfeggbbbbbbbgeef feaccbbbbbbgeef feegbbbbaccgeef feegbbbbbbbgeeaccf feegbbbbbbbggef accf feegbbbbbbbggef accf bbbbbbggef faca bggef fcca fcca fccd dccd dccd dccf accf accf accf fcca fcca fcca dccd dccd dccd accf accf accf faca fcca fcc fc d ``` <!-- end of image --> I observe 1 intersection inside area B. Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#7fcd79ff b,#944aadff c,#5dc555ff d,#c9ebc6ff e,#bf93ceff f,#e6e7e8ff g,#a4dea0ff ``` ```image d ccd c ccd ga fccf ad dcc c dca c gca c acg ga acg ad ccd c fccf c fcc fc dcc ga gca cd gcg c acg c ccd fc cc gg gc cd ac c aa c ca fc cg gg cd cf cf c fc c dc fc dc gg gc cf ac c ca c cg fc cd gg cf cf cf febbb c fc febbbbef c dcfebbbbef fc febbacef gg febbbbef ac cf febbbbef aa c ebbbbef ca c febbbbef cg fc febbbbef cd gg ebbbbbef cf cf febbbbef fc c febbbbef dc c febbbbbe dc dcfebbbbef gc eebcabef ac bbbee cf ca c cg c cd dc cf ag c cf c c da ag c c c da ag c c c da ad c c c da ad c c c da ad c ``` <!-- end of image -->
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I'm on the case! Let's uncover any intersections hidden in this image. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7343a4ff b,#ea95a5ff c,#500595ff d,#b2d7b2ff e,#9b85b6ff f,#eff0eeff g,#a0cda1ff ``` ```image f c c c c fa fa ee ed af c c c c c c fa de ee af a c c c c c c fa de ffffffffffffffffffffffffffffffffffffffffffffffeeffffff fggggggggggggggggggggggggggggggggggggggggggggggaggggggg ce fgdddddddddddddddddddddddddddddddddddddddddddddcddddddd eccd fgdddddddddddddddddddddddddddddddddddddddddddddcddddddd acaf fgdddddddddddddddddddddddddddddddddddddddddddddcddddddd fcce fgdddddddddddddddddddddddddddddddddddddddddddddcddddddd eccd fgdddddddddddddddddddddddddddddddddddddddddddddcddddddd acaf fgdddddddddddddddddddddddddddddddddddddddddddddcddddddd fcce fgdddddddddddddddddddddddddddddddddddddddddddddcddddddd eccf fgddddddddddddddddddddddddddddddddddddddddddddgaddddddd acaf fgddddddddddddddddddddddddddddddddddddddddddddeeddddddd fcce fgddddddddddddddddddddddddddddddddddddddddddddaeddddddd eccffgddddddddddddddddddddddddddddddddddddddddddddagddddddd facadddddddddddddddbddddddddddddddddddddddddddddcdddddddd feccedddddddddddbdbbddddddddddddddddddddddddddcdddddddd fgddaccgdddddddbddddbbddddddddddddddddddddddddcdddddddd fgdddddacadddbbddddddbbdddddddddddddddddddddddcdddddddd fgdddddddeccbbdddddddddbbdddddddddddddddddddddcdddddddd fgdddddddddbeccgdddddddddbbdddddddddddddddddddcdddddddd fgddddddddbdddgacaddddddddbbddddddddddddddddddcdddddddd fgddddddbbdddddddeccedddddddbbdddddddddddddddeadddddddd fgdddddbbdddddddddddaccgddddddbbdddddddddddddeedddddddd fgddddbdddddddddddddddgccadddddbbddddddddddddaedddddddd fgdddbdddddddddddddddddddecceddddbbddddddddddagdddddddd fgdbbdddddddddddddddddddddddaccgdddbdddddddddcddddddddd fgbbddddddddddddddddddddddddddgccaddbbdddddddcddddddddd fbdddddddddddddddddddddddddddddddeccedbbdddddcddddddddd fbgddddddddddddddddddddddddddddddddddaccbbddddcddddddddd bbfgddddddddddddddddddddddddddddddddddddgccbbddcddddddddd bb fgdddddddddddddddddddddddddddddddddddddddeabecddddddddd bf fgddddddddddddddddddddddddddddddddddddddddddbbddddddddd fb fgddddddddddddddddddddddddddddddddddddddddddddbbddddddd bb fgddddddddddddddddddddddddddddddddddddddddddddddbdddddd bb fgdddddddddddddddddddddddddddddddddddddddddddddddbbdddd bf fgddddddddddddddddddddddddddddddddddddddddddddddddddddd fb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bf fgddddddddddddddddddddddddddddddddddddddddddddddddddddd fb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bf fgddddddddddddddddddddddddddddddddddddddddddddddddddddd fbf fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bb fgddddddddddddddddddddddddddddddddddddddddddddddddddddd bf fgddddddddddddddddddddddddddddddddddddddddddddddddddddd fbf fgggggggggggggggggggggggggggggggggggggggggggggggggggggg bb bb bf ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#7a3dabff b,#f4b9c5ff c,#510596ff d,#c3a9daff e,#9e71c2ff f,#f1deeaff g,#ee8fa4ff ``` ```image ecd ecd acf acf cc cc fca fca dce dce dcd ecd ecd acf ac cc cc fca fca dce dce ecd ecd ecf acf ef ac ccad fggf cc eccccef bgggggf ca decccaef bggffbggb fca dacccad fgggf fgggf fca feccccef fggb bggbf dce decccaef bggb fgggb dce dacccad bggf bgggf ecd feccccef fgggf bggb ecd dacccaggb fgggb acf fdeggaad bgggf acf bggeccccef fbggb ac fgggf dacccadf fgggf cc fggb fdacccad bggbf ca bggb feccccef fgggb fca bggf dacccadf bgggf dce fgggf fdacccad bggb dce fggb feccccef fgggb dce bggb dacccad bgggf ecd bggf feaccced fbggb ecd gggf feccccef fgggf acf fggb dacccad bggbf acf bggb feaccced fgggb cc bggf feccccef fgggf cc gggf dacccad bggb ca fggb feaccced fgggb fca bggb deccccef bgggf dce bggf dacccad bggb dce gggf feacccedfgggf dcd gb decccaebgggf ecd b dacccagggb ecd fecccagggf acf deccegggf ac daaggggcc feaggga dgggb fgggb bgggf fbggb fgggf bggbf fgggb bgb ``` <!-- end of image --> Yes! I knew it! There's 2 intersections right here in area A! Answer: A: 2; 2 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#7a3faeff b,#f2adbcff c,#510495ff d,#cbb5dfff e,#a57ec7ff f,#f3dbe6ff g,#ee8da2ff ``` ```image d c c c c a da ee ed af c c c c c c fa de ee ad a c c c c c c fa de ed af ce c eccd c aca c fcce c eccd c aca c dcce c eccd fa aca de dcce ed eccd af aca gf c dcce gfbg c eccd fg gb c aca bg fgf c dccgb gg c geccf fgb c fg faca bgf a bg dcce gg da gb eccf fgf ee gf faca bg ed fg dccd gb af bg eccf fgf c gb faca gg c gf dccd gb c fg ecabgf c bg fccgg c gb dagbc gf gg fg gb bg fgf gb bg gf fg bg gb gf fg bg gb gf fg bg gb gf fg bg gb gf ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#7e95fbff b,#f7cab7ff c,#c3cefcff d,#f1f3efff e,#b1d7b1ff f,#99b0e8ff g,#96ca96ff ``` ```image d bbb bbbbd ddddddddddddddbbbbbdddddddddddddddd geeeeeeeeeeeebbbbbbeeeeeeeeeeeeeeegd geeeeeeeeeeebbbbbbbbeeeeeeeeeeeeeeed geeeeeeeeeebbbbebbbbeeeeeeeeeeeeeeed geeeeeeeeeebbbbeebbbeeeeeeeeeeeeeeed geeeeeeeeebbbbeeebbbbeeeeeeeeeeeeeed geeeeeeeebbbbeeeebbbbeeeeeeeeeeeeeed cfaaaa geeeeeeebbbbbeeeeebbbeeeeeeeeeeeeeed cfaaaaaaaaa geeeeeeebbbbeeeeeebbbbeeeeeeeeeeeeed dcaaaaaaaaaaaaaaad geeeeeebbbbeeeeeeebbbbeeeeeeeeeeeeed dcaaaaaaaaaaaaaaaafaaad geeeeebbbbeeeeeeeeebbbeeeeeeeeeeeeed cfaaaaaaaaaaaaaaaacd aaac geeeeebbbbeeeeeeeeebbbbeeeeeeeeeeeed cfaaaaaaaaaaaaaaafc aaac geeeebbbbeeeeeeeeeebbbbeeeeeeeeeeeed dcaaaaaaaaaaaaaaaafc aaaf geeebbbbeeeeeeeeeeeebbbeeeeeeeeeeeecfaaaaaaaaaaaaaaaacd faaf geebbbbeeeeeeeeeeeeebbbbeeeeeeffaaaaaaaaaaaaaaaacd faaa geebbbbeeeeeeeeeeeeebbbbefaaaaaaaaaaaaaaaafc caaa gebbbbeeeeeeeeeeeeeefbbbaaaaaaaaaaaaafc caaa gbbbbeeeeeeeeeefaaaaabbbbaaaaaaafeed daaa ebbbeeeeefaaaaaaaaaaafbbbaafeeeeeeed dgggggggggaaaggggggg gebbfaaaaaaaaaaaaaaaafbbbeeeeeeeeeed deeeeeeeeeaaaeeeeeee gaaaaaaaaaaaaaaafeeeeebbbbeeeeeeeeed deeeeeeeeeaaaeeeeeee gaaaaaaaaaafeeeeeeeeeeebbbeeeeeeeeed deeeeeeeeeaaaeeeeeee gaaaaafeeeeeeeeeeeeeeeebbbeeeeeeeeed deeeeeeeeeaaaeeeeeee geeeeeeeeeeeeeeeeeeeeeebbbbeeeeeeeed deeeeeeeeeaaaeeeeeee geeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeed deeeeeeeeeaaafeeeeee geeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeed deeeeeeeeeaaafeeeeee geeeeeeeeeeeeeeeeeeeeeeebbbbeeeeeeed deeeeeeeeeaaafeeeeee geeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeed deeeeeeeeefaaaeeeeee geeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeed deeeeeeeeefaaaeeeeee geeeeeeeeeeeeeeeeeeeeeeeebbbbeeeeeed deeeeeeeeefaaaeeeeee geeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeed deeeeeeeeefaaaeeeeee geeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeed deeeeeeeebbaaaeeeeee geeeeeeeeeeeeeeeeeeeeeeeeebbbbeeeeed deeeeeeebbbbaaeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeed deeeeeebbbbbbaeeeeee eggggggggggggggggggggggggggbbbeggggd deeeebbbbbbbbbeeeeee bbbb deeebbbbbebbbbbbeeee dbbb deebbbbbeeefbbbbbeee bbbd debbbbbeeeeaabbbbbee bbbb dbbbbbeeeeeaaabbbeee dbbb bbbbbeeeeeeaaafbeeee bbbd bbbbbeeeeeeeaaafeeeee bbbb bbbbbeeeeeeeefaaaeeeee bbb bbbbbeeeeeeeeefaaaeeeee bbbd bbbbbeeeeeeeeeefaaaeeeee bbbb bbbbbdeeeeeeeeeefaaaeeeee bbb bbbbb deeeeeeeeeeeaaaeeeee bbbb bbbbb deeeeeeeeeeeaaaeeeee bbbb dbbbbd deeeeeeeeeeeaaaeeeee bbb dbbbbd deeeeeeeeeeeaaaeeeee bbbb dbbbbd deeeeeeeeeeeaaaeeeee bbbbb dbbbbd deeeeeeeeeeeaaaeeeee bbbbb bbbbb dgeeeeeeeeeeaaaeeeee bbbbd bbbbb dddddddddddaaacdddd bbbbd bbbbb aaac bbbbd bbbbb aaaf bbbb bbbbb faaa dbbbb bbbbb caaa dbbbb bbbbb caaa dbbbb bbbbb caaa dbbbbbbbbb daaa bbbbbbbb aaa bbbbbb aaa bbbb aaa d aaa aaad aaac aaac aaac aaaf faaa caaa caaa caaa daaa aaa aaa aaa aaa aaad ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#7e95fbff b,#f8cab7ff c,#b7c1f9ff d,#fceee8ff e,#fadcd0ff f,#98a8f9ff g,#dbe1fdff ``` ```image dbbbbbbbbbbbe bbbbbbbbbbbbb ebbbbbbbbbbbbbd dbbbbbbbbbbbbbbe bbbbbbbbdbbbbbbb ebbbbbbbd ebbbbbbd ebbbbbbbe dbbbbbbe dbbbbbbbb bbbbbbb bbbbbbbbd ebbbbbbd ebbbbbbbe dbbbbbbe dbbbbbbbe bbbbbbb dbbbbbbbb ebbbbbbd bbbbbbbbd dbbbbbbe ebbbbbbbe bbbbbbb dbbbbbbbe ebbbbbbd bbbbbbbb dbbbbbbe ebbbbbbbd bbbbbbb ebbbbbbbe ebbbbbbd dbbbbbbbb dbbbbbbe bbbbbbbbd bbbbbbb ebbbbbbbd ebbbbbbd ebbbbbbbe dbbbbbbe dbbbbbbbb bbbbbbb bbbbbbbbd ebbbbbbd ebbbbbbbe dbbbbbbe dbbbbbbbe bbbbbbb dbbbbbbbb ebbbbbbd gcf bbbbbbbbd dbbbbbbe ggcfaaaaa ebbbbbbbe bbbbbbb gccfaaaaaaaaaa dbbbbbbbb ebbbbbbd gccfaaaaaaaaaaaaaaa bbbbbbbbd dbbbbbbbaaaaaaaaaaaaaaaaaaaa ebbbbbbbd ggcbbbbbbbaaaaaaaaaaaaaaaaaaaa ebbbbbbbe gccfaaaacbbbbbbcaaaaaaaaaaaaaaaaaaa dbbbbbbbb gcffaaaaaaaaafbbbbbbbaaaaaaaaaaaaaafcgg bbbbbbbbd ggcfaaaaaaaaaaaaaaaabbbbbbbfaaaaaaaafcgg dbbbbbbbd gccfaaaaaaaaaaaaaaaaaaaaacbbbbbbcaafccg dbbbbbe gccfaaaaaaaaaaaaaaaaaaaaaaaaaafbbbbbbbg dbbbbgcfaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaafbbbbbbbd ggcbbfaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffcg ebbbbbbe faaafaaaaaaaaaaaaaaaaaaaaaaaaafccg bbbbbbb caaaaaaaaaaaaaaaaaaaaaaaafcgg ebbbbbbd caaaaaaaaaaaaaaaaaaafcgg dbbbbbbe gaaaaaaaaaaaaafccg bbbbbbb aaaaaaaafccg ebbbbbbd aaafcgg dbbbbbbe gg bbbbbbb ebbbbbbd dbbbbbbe bbbbbbb ebbbbbbd dbbbbbbe bbbbbbb ebbbbbbd dbbbbbbe bbbbbbb ebbbbbbd dbbbbbbe bbbbbbb ebbbbbbd dbbbbbbe bbbbbbb ebbbbbbd dbbbbbbe bbbbbbb ebbbbbbd dbbbbbbe bbbbbbb ``` <!-- end of image --> Area A contains 1 intersection. Alright, let's concentrate on the next area. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#7e95fbff b,#f8cab8ff c,#bac6fdff d,#fbe6deff e,#d0bbd2ff f,#9cacf9ff g,#dee3fdff ``` ```image aaaaaac aaaaaac aaaaaaf faaaaaf faaaaaf faaaaaa caaaaaa caaaaaa caaaaaa caaaaaag gaaaaaag gaaaaaag gaaaaaac gaaaaaac aaaaaac aaaaaac aaaaaaf faaaaaf faaaaaf faaaaaa caaaaaa caaaaaa caaaaaa caaaaaag gaaaaaag ddgaaaaaag bbbbfaaaaac dbbbbbbeaaaac dbbbbbbbbeaaac dbbbbbbbbbbeaac dbbbbbbbbbbbbbaf dbbbbbbbbbbbbbbbf dbbbbbbbbbbbbbbbbbd dbbbbbbbbbbbbbbbbbbbd dbbbbbbbbb dbbbbbbbbbd dbbbbbbbbb ebbbbbbbbbd bbbbbbbbbb cfbbbbbbbbbb bbbbbbbbbb cafbbbbbbbbbb bbbbbbbbbd gaaaebbbbbbbbb bbbbbbbbbd gaaaaebbbbbbbd bbbbbbbbbd gaaaaaebbbbbb bbbbbbbbbd gaaaaaaebbbb bbbbbbbbd aaaaaacdbb bbbbbbbd aaaaaac d bbbbbbd aaaaaaf bbbbbd faaaaaf bbbbd faaaaaf bbbd faaaaaa bb caaaaaa b caaaaaa caaaaaag caaaaaag gaaaaaag gaaaaaag gaaaaaac gaaaaaac aaaaaac aaaaaac aaaaaaf faaaaaf faaaaaf faaaaaa caaaaaa caaaaaa caaaaaag caaaaaag gaaaaaag ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#7e95fbff b,#f8cab7ff c,#bdc9fcff d,#fcefe9ff e,#faddd1ff f,#9eaefaff g,#dfe4fdff ``` ```image e bbb bbbbe dbbbbb bbbbbb bbbbbbbe ebbbdebbb dbbbb bbb bbbb bbbe bbbb ebbb gfaaaa ebbbe bbb cfaaaaaaaaa dbbbb bbbe gcaaaaaaaaaaaaaaa bbbb ebbb gcaaaaaaaaaaaaaaaafaaag bbbbd bbb gfaaaaaaaaaaaaaaaacg aaac ebbbe bbbe cfaaaaaaaaaaaaaaafc aaac bbbb ebbb gcaaaaaaaaaaaaaaaafg aaaf bbbb bbb gfaaaaaaaaaaaaaaaacg faaf bbbbd bbbe cfaaaaaaaaaaaaaaaacg faaa dbbbb ebbb cfaaaaaaaaaaaaaaafc caaa bbbb gcbbbaaaaaaaaaaaaafg gaaa bbbb gfaaaaabbbbaaaaaaacg gaaa ebbbe cfaaaaaaaaaafbbbafc aaa dbbcaaaaaaaaaaaaaaaafbbbd aaa aaaaaaaaaaaaaaafg bbbb aaa aaaaaaaaaacg dbbb aaa aaaafc bbbd aaa g bbbb aaag dbbb aaac bbbd aaac bbbb aaaf dbbb faaf bbbd faaa bbbb caaa dbbb gaaa bbbd dbbaaa bbbb dbbbbaa dbbb dbbbbbba bbbd ebbbbbbbbd bbbb ebbbb ebbbbe dbbb ebbbb fbbbbe bbbd bbbbb aabbbbb bbbb bbbbb aaabbb dbbb bbbbb aaacb bbbe bbbbb aaaf ebbb bbbbb faaf bbb bbbbb faaa bbbe bbbbb caaa ebbb bbbbe gaaa bbb bbbbe gaaa bbbe dbbbbe aaa ebbb dbbbbe aaa bbb dbbbbd aaa bbbb dbbbbd aaa ebbbe ebbbbd aaag bbbbe ebbbb aaag bbbbe ebbbb aaac bbbbd bbbbb aaac bbbbd bbbbb aaaf bbbb bbbbb faaf dbbbb bbbbb caaa dbbbb bbbbb caaa dbbbb bbbbb gaaa ebbbbbbbbb gaaa ebbbbbbe aaa bbbbbe aaa bbbe aaa d aaa aaag aaag aaac aaac aaaf faaf caaa caaa gaaa gaaa aaa aaa aaa aaa aaag ``` <!-- end of image -->
[ "" ]
This image looks interesting. I wonder if there are any intersections hidden in there? There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#268b97ff b,#d406a2ff c,#a0cda2ff d,#d36ab8ff e,#6bb0b0ff f,#eff2f0ff g,#b1d7b2ff ``` ```image gaf fea aaaa faaaf eaaaf aaae aaaa eaaa aaaa cccaaaecccccccccccccccf faaae gggaaaaggggggggggggggcf aaaa gggeaaaggggggggggggggcf gaaag ggggaaaegggggggggggggcf aaaa ggggaaaagggggggggggggcf eaaaf ggggcaaagggggggggggggcf aaaa gggggaaaeggggggggggggcf aaaa gggbceaaaggggggggggggcf faaae ggbbbcaaacgggggggggggcf aaaa gdbbbbaaaagggggggggggcf gaaag ggdbbbbaaagggggggggggcf aaaa gggdbbbbaaeggggggggggcf eaaaf ggggdbbbbaaggggggggggcf aaaa gggggdbbbbaggggggggggcf aaaa ggggggdbbbbegggggggggcf faaae gggggggdbbbbgggggggggcf aaaa ggggggggdbbbbggggggggcf gaaag gggggggggabbbbgggggggcf aaaa gggggggggeabbbbggggggcf eaaaf ggggggggggaabbbbgggggcf aaaa ggggggggggaaabbbbggggcf aaaa ggggggggggeaaabbbbgggcf faaae gggggggggggaaadbbbbggcf aaaa gggggggggggaaaadbbbbgcf gaaag gggggggggggcaaagdbbbbcf aaaa ggggggggggggaaaagdbbbbf eaaaf ggggggggggggeaaaggdbbbbf aaaa gggggggggggggaaacggdbbbbf aaaa gggggggggggggaaaagggdbbbbf faaae gggggggggggggeaaaggggdbbbbf aaaa ggggggggggggggaaaegggcdbbbbf gaaag ggggggggggggggaaaagggcfdbbbbf aaaa ggggggggggggggcaaacggcf dbbbbf eaaaf gggggggggggggggaaaaggcf dbbbbf aaaa gggggggggggggggeaaacgcf dbbbbf aaaa ccccccccccccccccaaaaccf dbbbb faaae ffffffffffffffffgaaaff dbbbb aaaa aaaa dbbbb gaaag gaaaf dbbbb aaaa aaaa dbbbb eaaaf gaaaf dbbbb aaaa aaaa dbbbbcccccccccccccccccaaaaccf gaaaf dbbbbgggggggggggggggcaaaegcf aaaa dbbbbggggggggggggggaaaaggcf gaaaf dbbbbggggggggggggeaaacggcf aaaa dbbbbgggggggggggaaaagggcf caaa fdbbbbgggggggggeaaaggggcf aaaa fcdbbbbggggggggaaaaggggcf caaa fcgdbbbbggggggaaaagggggcf aaaa fcggdbbbbggggcaaaegggggcf eaaa fcgggdbbbbgggaaaaggggggcf aaaa fcggggdbbbbgeaaacggggggcf eaaa fcgggggdbbbbaaaagggggggcf aaaa fcggggggdbbbbaaggggggggcf eaaa fcgggggggdbbbbaggggggggcf aaaa fcggggggggbbbbbggggggggcf eaaa fcgggggggcabbbbbgggggggcf aaae fcgggggggaaabbbbbggggggcf eaaa fcggggggeaaacbbbbbgggggcf aaae fcggggggaaaaggbbbbbggggcf eaaa fcgggggeaaaggggbbbbbgggcf aaae fcgggggaaaagggggbbbbbdccf eaaa fcggggaaaagggggggbbbbbbbbbbdf aaae fcgggcaaaeggggggggbbbbbbbbbbbbbbbdf eaaa fcgggaaaaggggggggggdbbbbbbbbbbbbbbbbbbbdf aaae fcggeaaacggggggggggggggcfdbbbbbbbbbbbbbbbbbbbdd eaaa fcggaaaagggggggggggggggcf fddbbbbbbbbbbbbbbf aaae fcgeaaaggggggggggggggggcf fddbbbbbbbb eaaa fcgaaaaggggggggggggggggcf fddbb aaaefcaaaaccccccccccccccccccf eaaa faaae aaaeaaaa eaaaaaaf aaaaaa eaaaaf aaae eaa ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#268b97ff b,#d407a2ff c,#ece5f1ff d,#ed9ad9ff e,#70b1baff f,#74589fff g,#afd4d9ff ``` ```image caaaaaaa aaaaaaag gaaaaaae caaaaaaa eaaaaaag gaaaaaae aaaaaaac eaaaaaag gaaaaaaa aaaaaaac eaaaaaae caaaaaaa eaaaaaag gaaaaaae dc aaaaaaac dbbc eaaaaaag dbbbbcgaaaaaae dbbbbbbcaaaaaaac dbbbbbbbbeaaaaaae dbbbbbbbbbaaaaaaa dbbbbbbbbbaaaaaag dbbbbbbbbbaaaaae dbbbbbbbbbaaaaa dbbbbbbbbbaaaag dbbbbbbbbbaaae dbbbbbbbbbaaac dbbbbbbbbbaag dbbbbbbbbbaa dbbbbbbbbbag dbbbbbbbbbe dbbbbbbbbbc dbbbbbbbbbc dbbbbbbbbbc dbbbbbbbbbc fbbbbbbbbbc gfbbbbbbbbbc afbbbbbbbbbc eafbbbbbbbbbc caafbbbbbbbbbc eaafbbbbbbbbbc gaaafbbbbbbbbbc caaaafbbbbbbbbbc eaaaafbbbbbbbbbc gaaaaafbbbbbbbbbc aaaaaafbbbbbbbbbc eaaaaaafbbbbbbbbbc caaaaaaadbbbbbbbbbc aaaaaaagdbbbbbbbbbc gaaaaaae dbbbbbbbbbc caaaaaaa dbbbbbbbbbc eaaaaaag dbbbbbbbbb gaaaaaae dbbbbbbbb aaaaaaac dbbbbbbb eaaaaaag dbbbbbb gaaaaaaa dbbbbb aaaaaaac dbbbb eaaaaaae dbbb caaaaaaa dbb eaaaaaag db gaaaaaae d aaaaaaac eaaaaaag gaaaaaae aaaaaaac eaaaaaae caaaaaaac eaaaaaae gaaaaaaac aaaaaaae gaaaaaaac aaaaaaae ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Alright, let's examine the next area. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#57a5afff b,#d505a2ff c,#258b97ff d,#e153beff e,#d4e0e8ff f,#a130a0ff g,#95c6ccff ``` ```image gccccccce d ccccccca bd gccccccce bbd ecccccccg bbbd accccccc bbbbd ecccccccg bbbbbd acccccca bbbbbbd gccccccce bbbbbbbd ccccccca bbbbbbbbd gccccccce dbbbbbbbbd ecccccccg dbbbbbbbbd accccccc dbbbbbbbbd ecccccccg dbbbbbbbbd acccccca dbbbbbbbbd gccccccce dbbbbbbbbd ccccccca dbbbbbbbbd gccccccce dbbbbbbbbd ecccccccg dbbbbbbbbd accccccc dbbbbbbbbd ecccccccg dbbbbbbbbd acccccca dbbbbbbbbd gccccccce dbbbbbbbbd ccccccca dbbbbbbbbfccccccce dbbbbbbbbfcccccg dbbbbbbbbfcccc dbbbbbbbbfccg dbbbbbbbbfa dbbbbbbbbd fbbbbbbbbd gcfbbbbbbbbd ecccfbbbbbbbbd accccfbbbbbbbbd eccccccfbbbbbbbbd accccccadbbbbbbbbd gccccccce dbbbbbbbbd ccccccca dbbbbbbbbd gccccccce dbbbbbbbbd ecccccccg dbbbbbbbbd accccccc dbbbbbbbbd ecccccccg dbbbbbbbbd acccccca dbbbbbbbbddde gccccccce dbbbbbbbbbbbbb ccccccca dbbbbbbbbbbbb gccccccce dbbbbbbbbbbb ecccccccg dbbbbbbbbbb accccccc dbbbbbbbbb ecccccccg eddbbbbbb acccccca eeddd gccccccce ccccccca gccccccce ecccccccg accccccc ecccccccg acccccca ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; B: 1; 1 + 1 = 2 I've identified a total of two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#468fa2ff b,#d405a2ff c,#248b97ff d,#ed99d8ff e,#74b4bcff f,#e053beff g,#b2d6daff ``` ```image gc ac ccca ccc eccc ccca ccca eccc accc cccg ccce cccc cccc gccc gcccg cccg cccc accc eccc ccc ccca ccce accc b eccc ccce bbb cccg cccc dbbbbacca gcccg dbbbbacc cccc dbbbbacg eccc dbbbbac ccca dbbbba accc dbbbbe ccce dbbbb cccc dbbbb gcccg abbbb cccc eabbbb eccc cabbbb ccca ccabbbb accc gccabbbb ccce cccfbbbb cccc acccdbbbb gcccg ccc dbbbb cccc ccce dbbbb eccc eccc dbbbb ccca cccg dbbbb accc cccc dbbbb ccce gccc dbbbb cccc cccg dbbbb gcccg accc dbbbb cccc gccc dbbbb eccc cccc fbbbb ccca gccc fbbbb accc cccc fbbbb ccce gccc fbbbb cccc cccc fbbbb gcccg gccc fbbbb cccc cccc fbbbb eccc gccc fbbbb ccca cccc fbbbb accc gccc fbbbb ccce ccca fbbbb cccc gccc fbbbb gcccg ccca fbbbb cccc eccc fbbbb eccc ccca fbbbb ccca eccc fbbbb accc ccca fbbbb ccce eccc fbbbb cccc ccca fbbbb gcccg eccc fbbbbcccc ccca fbbbbcc eccc fbbbba ccca bbbbb eccc cbbbbb ccca cccbbbbb eccc gcccgfbbbb ccca cccc fbbbb eccc eccc fbbbb ccca ccca fbbbbfd eccc accc fbbbbbbbbbfd ccca ccce fbbbbbbbbbbbbbbfd eccc cccc dfbbbbbbbbbbbbbbbbbbfd ccca gcccg dfbbbbbbbbbbbbbbbbbbfd eccc cccc dfbbbbbbbbbbbbbbd ccce eccc dfbbbbbbbb eccc ccca dfbb ccce cccc eccc ccce cccecccc eccccccg cccccc ecccc ccca ecc ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#95df5eff b,#7ede2aff c,#cff0c1ff d,#9ddf86ff e,#eef7ebff f,#b1d8b0ff g,#97cb96ff ``` ```image ec ddddde df cddddfe df cddddfe dc cddddc dc efddddc dc efddddc dc cddddfe dc cddddfe de cddddc de efddddc de efddddc d eddddfe d cddddfe d cddddce d cddddc gggggdggggggggggge efddd fffffdfffffffffffe ed fffffdfffffffffffe d fffffdfffffffffffe d fffffdfffffffffffe de fffffdfffffffffffe de fffffdfffffffffffe dc fffffdfffffffffffe df fffbddfffffffffffe fd fffbadfffffffffffe cd fffdadfffffffffffe ed ffffadfffffffffffe d ffffadfffffffffffe d ffffdafffffffffffe d ffffdafffffffffffe de ffffdagffffffffffe dc ffffdaaffffffffffe df ffffddbffffffffffe fd ffffdgbffffffffffe eeeeeeeeecdeeeeeeeeeeeeeeeeeee ffffdfbdfffffffffe gffffffffgdffffffffffffffffffg ffffdfbbfffffffffe gfffffffffdffffffffffffffffffg ffffdfdbfffffffffe gfffffffffdffffffffffffffffffg ffffdffbfffffffffe gfffffffffdffffffffffffffbfffg ffffdffbaffffffffe gfffffffffdffffffffffffdbbfffg ffffdffabffffffffe gfffffffffdgffffffffffbbdffffg ffffdfffbffffffffe gfffffffffddffffffffbbbffffffg ffffdfffbgfffffffe gfffffffffddffffffdbbffffffffg ffffdfffbafffffffe gfffffffffgdfffffbbafffffffffg ffffdfffabfffffffe gffffffffffdfffabbfffffffdfffg ffffdffffbfffffffe gffffffffffdfdbbdffffffffdfffg ffffdffffbdffffffe gffffffffffdbbafffffffffddfffg ffffdffffbbffffffe gfffffffffadbfffffffffffdffffg ffffdffffdbffffffe gfffffffgbbdffffffffffffdffffg ffffdfffffbffffffe gffffffbbafdgffffffffffddffffg ffffdfffffbafffffe gffffabbfffddffffffffffddffffg ffffdfffffabfffffe gfffbbdffffddffffffffffdfffffg fffgdffffffbfffffe gfbbbffffffgdffffffffffdfffffg fffddffffffbgfffge abbfffffffffdfffffffffddfffffg eeefdeeeeeebaeeee bbaffffffffffdfffffffffdffffffg fd fb abbgfffffffffffdfffffffffdffffffg fd b cbbe gfffffffffffdffffffffddffffffg df bc bbd gfffffffffffdffffffffdfffffffg df ab dbb gfffffffffffdgfffffffdfffffffg df cb ebbc gfffffffffffddffffffddfffffffg dc b bba fgggggggggggddggggggddgggggggf dc bd fbbe cd d dc ab ebbc ed cd dc eb aba d df de be cbbe d de de ba ebbf d ed e fb abb de fd b cbbe dc dc bc bbd df d ab dbb fd cd cb ebbc cd dc b bba ed d bd dbb d cd db ebbc d df eb aba d de be cbbe dcd baebbf ddd fbbb ddc be fd cd ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#97e260ff b,#7ede29ff c,#ccefbcff d,#9ddf85ff e,#eef9e8ff f,#bbeb9fff g,#dcf4d2ff ``` ```image ddf ddf ddf ddf ddc ddc eddc eddc eddc eddg eddg gddg gddg gddg ggdde fbbcdde fbbfdde ebbddde bbadde dbadd cbadd ebadd aadd fadd gadd ddd ddae ddac ddad ddab ddabe ddabf ddaba eddabb edddbbg eddfbbf eddcbba eddgabbe gddgfbbc gddgebbd gddg abb gddg dbbe gdde cbbf cdde ebba cdde abb cdde fbbg cdde gbbf cdd bba cdd abbe fdd fbbc fdd ebbd fdd abb fdd dbbe fdf cbbf fdf ebba ddf abb ddf fbbg ddf gbbf ddf bba ddc abbe ddc fbbc eddc ebbd eddc abb eddc dbbe eddc cbbf eddg ebba gddg abb gddg fbbg gddg gbbf gddg bba gdde abbe cdde fbbc cdde ebbd cdde abb cdde dbbe ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Onward to the next region of interest. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#95e352ff b,#7ede29ff c,#caeeb9ff d,#9de084ff e,#dff4d4ff f,#b5e89dff g,#f1faecff ``` ```image cddg edde edde gddc ddc ddf fdf fdd g cddg cad cddg gdbbbe edde fbbbbdg edde eabbbae gddc gdbbbbf ddc cbbbbdg ddf eabbbae fdf gfbbbbf fdd cbbbbag cdd eabbbac cddg fbbbbfg edde cabbbae efeg edde gdbbbbc cddg gddc fbbbbdg ddf ddc eabbbae gddc ddfgdbbbbf cdde fddbbbbdg fdd fddbbae gddf gdaddbf edde cbbadde fddg eabbbadde ddf fbbbbfedde eddc cabbbae gddc cddg gabbbbc ddc ddf fbbbbdg ddf gddc eabbbae fdf cdde gdbbbbc fdd fdd fbbbbdg cdd gddf eabbbae cddg edde gdbbbbf edde fddg cbbbbdg edde ddf abbbac gddc eddc bbbf ddc cddg bae ddf ddd c fdf gddc fdd cdde cdd fdd cddg gddf edde edde edde fddg gddc ddf ddc eddc ddf cddg fdf ddd ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area B. Answer: A: 1; B: 1; 1 + 1 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#9ee468ff b,#7dde27ff c,#cff0c0ff d,#9cdf86ff e,#e8f7e0ff f,#b7e99fff g,#8ee244ff ``` ```image ec fdddfe df cddddfe df cddddf dc cddddc dc efddddc dc efdddde dc eddddfe de cddddfe de cddddc de fddddc d efddddc d efdddfe d cddddfe d cddddf d cddddc d efddd d ed d d ed d ed d ed de ed dc cd df bfd fd gad cd cad ed ad d ad d da d da de dae dc daa df ddb fd dcb cd dcbc ed degg d decb d de b d g d bf de fbbe d ab dc ebbf d eb df abg d be fd cbbe d ba cd bbf d fb ed abg de d b d cbbe ed d bc dbba fd ed gg ddb dc ed cb ebbde d ed b gba dc cd ed bf fbb df dc cd ab ebbf fd d cd eb gbg cd cd cd be cbbe ed df fd ba bbf d de fd fb abg d ed fd b cbbe d fd ff bc bba de dc df gg dbb dc d df cb ebbc df cd dc b gba fd dc dc bf fbb cd d dc ab ebbc ed cd dc eb gbg d df de be cbbe d de de ba bbf d ed e fb abg de fd b cbbe dc dc bc bbd df d gg abb fd cd cb ebbc cd dc b gba ed d bf fbb d cd ab ebbc d df eb gbg d de be fbbe dcd ba bbf ddd fbbg ddc be fd cd ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#1ab7bbff b,#b2c9f8ff c,#48c2bcff d,#7ccebfff e,#e9f5f1ff f,#b1d7b2ff g,#95c996ff ``` ```image ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe ebbb ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeebbbbbb fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbbbbbe ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaadfffffffbbbbbbbb ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaafffffbbbbbbb ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaaffbbbbbbbffe ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaabbbbbbfffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdaaadbbbfffffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbcaaaaffffffffffe ffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbbbaaaaaffffffffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffbbbbbbbfaaaaaffffffffffe ffffffffffffffffffffffffffffffffffffffffffffffffffbbbbbbbbfffaacaadfffffffffe fffffffffffffffffffffffffffffffffffffffffffffffbbbbbbbbffffffaadaaafffffffffe fffffffffffffffffffffffffffffffffffffffffffffbbbbbbbfffffffffaadaaafffffffffe ffffffffffffffffffffffffffffffffffffffffffbbbbbbbffffffffffffaafdaafffffffffe fffffffffffffffffffffffffffffffffffffffbbbbbbbbfffffffffffffdaaffaadffffffffe ffffffffffffffffffffffffffffffffffffbbbbbbbbffffffffffffffffcaaffaacffffffffe ffffffffffffffffffffffffffffffffffbbbbbaafffffffffffffffffffaaaffaaaffffffffe fffffffffffffffffffffffffffffffbbbbbbbaaadffffffffffffffffffaaaffdaaffffffffe ffffffffffffffffffffffffffffbbbbbbbbfaaaacffffffffffffffffffaacfffaadfffffffe fffffffffffffffffffffffffbbbbbbbbfffaaaaaaffffffffffffffffffaadfffaacfffffffe ffffffffffffffffffffffffbbbbbbfffffaaacdaaffffffffffffffffffaadfffaaafffffffe fffffffffffffffffffffffbbbbfffffffcaaaffaaffffffffffffffffffaaffffdaafffffffe ffffffffffffffffffffffbbbbfffffffcaaafffaacffffffffffffffffdaafffffaadffffffe fffffffffffffffffffffbbbbfffffffdaaaffffaaaffffffffffffffffcaafffffaacffffffe ffffffffffffffffffffbbbbfffffffdaaafffffcaaffffffffffffffffcaafffffaaaffffffe fffffffffffffffffffbbbbffffffffaaafffffffaaffffffffffffffffaaafffffdaaffffffe ffffffffffffffffffbbbbffffffffaaaffffffffaadfffffffffffffffaacffffffaadfffffe fffffffffffffffffbbbbffffffffaaadffffffffaaafffffffffffffffaacffffffaacfffffe ffffffffffffffffbbbbffffffffaaadfffffffffcaafffffffffffffffaadffffffaaafffffe ffffffffffffffffbbbffffffffaaacffffffffffdaafffffffffffffffaafffffffdaafffffe fffffffffffffffbbbffffffffaaacffffffffffffaadfffffffffffffdaaffffffffaadffffe ffffffffffffffbbbffffffffcaaafffffffffffffaacfffffffffffffcaaffffffffaacffffe fffffffffffffbbbffffffffcaaaffffffffffffffaaafffffffffffffcaaffffffffaaaffffe ffffffffffffbbbffffffffdaaafffffffffffffffcaafffffffffffffaaaffffffffdaaffffe fffffffffffbbbffffffffdaaafffffffffffffffffaafffffffffffffaacfffffffffaadfffe ffffffffffbbbfffffffffaaaffffffffffffffffffaacffffffffffffaacfffffffffaacfffe fffffffffbbbfffffffffaaafffffffffffffffffffaaaffffffffffffaadfffffffffaaafffe ffffffffbbbbffffffffaaaffffffffffffffffffffcaaffffffffffffaaffffffffffdaafffe fffffffbbbbffffffffaaadffffffffffffffffffffdaafffffffffffdaafffffffffffaadffe ffffffbbbbffffffffaaadffffffffffffffffffffffaadffffffffffdaafffffffffffaacffe ffffffbbbffffffffaaacfffffffffffffffffffffffaacffffffffffcaafffffffffffaaaffe fffffbbbffffffffaaacffffffffffffffffffffffffaaaffffffffffaaafffffffffffdaaffe fffffbbffffffffcaaafffffffffffffffffffffffffdaaffffffffffaaaffffffffffffaadfe ffffbbbfffffffcaaafffffffffffffffffffffffffffaaffffffffffaacffffffffffffaacfe ffffbbbffffffdaaaffffffffffffffffffffffffffffaacfffffffffaadffffffffffffaaafe fffbbbffffffdaaafffffffffffffffffffffffffffffaaafffffffffaafffffffffffffcaafe fffbbbffffffaaaffffffffffffffffffffffffffffffcaaffffffffdaaffffffffffffffaage fffbbffffffaaafffffffffffffffffffffffffffffffdaaffffffffdaaffffffffffffffaace ggbbbgggggaaagggggggggggggggggggggggggggggggggaacgggggggcaaggggggggggggggaaa bb aaab aac aaa daa aaad caa aac eaae aaac baa aad aad caac aae aab aaa caaa aac aae daa daaa aaa eaa aad baaa daa baa aaa eaaa eaae daa baa aaa aad aaa aac ae aaa aaa aaa caa aad eaae baa aab aac aab aae caa aac eaa eaab aaa baa aaa daa daa daa aae caa aab aad aaa aaa aaa aac daa daa aad aad eaa aae aaa aadaa baae aaaaa aac caaaa caa baaaa eab aaaa aaac aaad daae eaa cc ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#1ab7bbff b,#b4c7fcff c,#4ac5c9ff d,#76d3d6ff e,#e5f1faff f,#a1e1e2ff g,#cce3f6ff ``` ```image b gaaa egbbbb daaa egbbbbbb caaae gbbbbbbbbbg aaaaf egbbbbbbbbbge aaaadgbbbbbbbbbg gaaaaabbbbbbge daaaaadbbbge gbbbcaaaaaa ebbbbbcaaaaaa gbbbbbbbaaaaaaa gbbbbbbbbbbeaaaaaaa ebbbbbbbbbbe aaaaaaae gbbbbbbbbbge aaaddaad gbbbbbbbbbbe aaaffaac egbbbbbbbbbg aaafeaaae ebbbbbbbbbbe aaae aaad gbbbbbbbbbbe eaaa aaac egbbbbbbbbbg faac caaaf ebbbbbbbbbbe faad daaad bbbbbbbbbbe daaf faaac egbbbbbbcaac caag caaa egbbbbbbbcaaaa aaae daaa bbbbbbbbbbgfaaaaa gaaa eaaae gbbbbbbbbbgefaaaaaa faaa aaaf egbbbbbbbbbge aaaaaaae faaa aaad bbbbbbbbbb eaaaaccaad caaa aaaae gbbbbbbbge caaacefaac caaa aaaag ebbbbbbe caaaa aaag eaaaa faaac bbbbb daaaag aaaf gaaac eaaaa ebbbbg daaaag aaad faaac aaaa bbbbb faaaaf aaaae daaad faaa ebbbbb gaaaad caaaf caaaf eaaa bbbbb eaaaac faaac aaaae daad bbbbb ecaaac eaaaa aaaa faac bbbbb ecaaace aaaa aaaa eaaa gbbbbe aaaaa faaa aaad aaad bbbbb daaaag gaaa aaad aaac gbbbbe aaaaa aaaf aaag aaaag ebbbbg faaaaf aaad aaae daaad bbbbb gaaaad aaac aaa faaac ebbbbg aaaaa aaaag gaaa aaaa bbbbb eaaaac daaaf faaa caaa bbbbb caaaae gaaaa daaa gaaa bbbbb aaaaa aaaa caaa aaag bbbbb daaaag caaa aaaa aaaf gbbbbe faaaaf faaa eaaaa aaaa gbbbbe aaaaa eaaae gaaac aaaag gbbbbe eaaaac daad daaad faaac gbbbbe aaaaa faac daaaf gaaaa gbbbbe eaaaac gaaa caaaf aaaa ebbbbg caaaae aaaf aaaae faaa ebbbbg daaaag aaad aaaa gaaa ebbbbg faaaaf aaaae aaac caaf ebbbbb faaaaf caaaf aaad faac bbbbb aaaaa daaad aaaf gaaa bbbbb eaaaac eaaaa aaag aaaf bbbbe ecaaac aaaa aaae aaac bbbe aaaaa faaa gaac aaaag gbbb daaaag gaaa faac caaaf bbbb daaaag aaae faad daaad gbbbg faaaaf aaad caaf aaaa bbbbe faaaaf aaac caag caaa bbbg aaaaa caaag eaaa gaaa ebbb eaaaac daaad gaaa aaae bbbg ecaaace faaac faaa aaaf gbbb aaaaa aaaa daaa aaaa ``` <!-- end of image --> Area A contains 2 intersections. Answer: A: 2; 2 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#19b7bbff b,#b4c7fcff c,#36bfc3ff d,#88d8dcff e,#daebf8ff f,#b3e7e8ff g,#5ccbceff ``` ```image ebbb ebbbbbb bbbbbbbe aaf ebbbbbbe aac ebbbbbbb aaa ebbbbbbbe eaaabbbbbbe daaadbbe ebbgaaac ebbbbbcaaaa bbbbbbbeaaaaa ebbbbbbe aagaaf ebbbbbbb aadaac ebbbbbbbe aaecaa bbbbbbbe eaa faa ebbbbbbe faa aaf ebbbbbbb daa aac ebbbbbaae caa caa bbbbbbbaaaf aaa faa ebbbbbbe aaaac aag aaf ebbbbbbb aaaaaa aad aac bbbbbbe caacdaa aaf caa bbbbe gaac aae aa faa bbbe daaa aag faa aaf bbbb faaa aaa daa aac bbbb eaaa gaa caa caa bbbb eaaa eaa aaa faa bbbb aaae aad aag aaf ebbb aaae aac aad aag ebbb aaaf caa aaf caa ebbb aaad faa aa daa ebbb caag aaf faa aaf bbb caac aag daa aag bbb gaaa aaa gaa aaa bbb daaa daa aaa daa bbbe faaa eaa aac aae bbbe eaaa aad aad aag bbbe aaa aaa aaf aaa bbbe aaae gaa aa daa bbbe aaaf faa faa aae bbbb aaad aaf daa aag ebbb aaag aac gaa aaa bbb caac caa aaa daa bbe gaac daa aac aae bbb daaa aae aad aag bbb faaa aag aaf aaa ebb faaa aaa aae daa bbb eaaa gaa eaa aae bbe aaae eaa daa aag bbb aaae aad gaa aaa ee aaaf aac aaa daa aaad caa aac aae caag faa aag aag caac aaf aaf aaa gaac aag aae daa daaa aaa eaa aad faaa daa daa aaa eaaa eaa gaa faa aaa aad caa aag ce aaa aac caa gaa aag eaae faa aad aac aaf aae gaa aag eaa eaaf caa faa aaa daa gaa gaa aae caa aad aad aaa aaa aaa aag daa gaa aad aad eaa aae aaa aadaa faa aaaaa aag caaaa caa faaaa eaf aaaa aaag aaad daaf eaa gg ``` <!-- end of image -->
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I'm on the case! Let's uncover any intersections hidden in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#c3747cff b,#ebe0c3ff c,#dfb7baff d,#f2f4edff e,#c79896ff f,#b1d7b0ff g,#96c996ff ``` ```image d ae aa ace a a a ba a ad a da a ad a da a ab a a a ec a a a ec a a a ce dddddddddddddddddddddddd a a dgffffffffffffffffffffffg a ce dfffffffffffffffffffffffg da a bbffffffffffffffffffffffg c da ba dfbfffffffffffffffffffffgaae de ad dffbfffffffffffffffffffeab ad be da dfffbfffffffffffffffffaag da be ad dffffbfffffffffffffffaefg ec ce da dfffffbffffffffffffeafffg a cc ab dffffffbffffffffffaaffffg ba cc a dfffffffbffffffffaefffffg ac cc ac dffffffffbfffffeafffffffg a ec a dfffffffffbbffaaffffffffg ba eb ddddecdddddddddddddddddd dffffffffffbbaefffffffffg ac eb gffffafffffffffffffffffgd dffffffffffabbffffffffffg a ad gffffeefffffffffffffffffd dfffffffffaefbbfffffffffg ca ad gfffffafffffffffffffffffd dfffffffeaffffbbffffffffg aba gfffffeaffffffffffffffffd dffffffaaffffffbbfffffffg aa gffffffaffffffffffffffffd dfffffaeffffffffbbffffffg ca gffffffeafffffffffffffffd dfffeafffffffffffbbfffffg a gfffffffafffffffffffffffd dffaaffffffffffffffbffffg gffffffffaffffffffffffffd dgaeffffffffffffffffbfffg gffffffffaffffffffffffffd d eafffffffffffffffffffbffg gfffffffffafffffffffffffd dbbbbd cfffffffffffffffffffffbfg gfffffffffaffffffffffbbbbbd dffffffffffffffffffffffbf gffffffffffaffffbbbbbbffd dfffffffffffffffffffffffbd gffffffffffcbbbbbfffffffd dfffffffffffffffffffffffgbd gfffffbbbbbbafffffffffffd dgggggggggggggggggggggggf bd gbbbbbbfffffaeffffffffffd bb dbbbbbfffffffffffaffffffffffd bb dbbbbdd gffffffffffffeefffffffffd bb dbbbbdd gfffffffffffffafffffffffd bbbbdd gfffffffffffffeaffffffffd gffffffffffffffaffffffffd gffffffffffffffeafffffffd gfffffffffffffffafffffffd gffffffffffffffffaffffffd gffffffffffffffffaffffffd gfffffffffffffffffafffffd gfffffffffffffffffafffffd fggggggggggggggggggaggggd ac a ec a ee a ce a ca ad ba ad da ab da ac a ec a ee a ce a ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#c3727bff b,#f1e4c3ff c,#d6a0a6ff d,#f3e7daff e,#cb868dff f,#e5c2c5ff g,#f9f4eeff ``` ```image g bg bbg dbbg dbbd gbbd gbbd f gbbd gca gbbd deaa gbbd faaed gbbb gcaacg gbbb deaaf bbbg faaeg bbbg geaac bbbg faaad dbbg caacg dbbg deaaf dbbg faaed dbbg gcaacg dbbd deaaf gbbd faaed gbbd gcaac gbbbeaaf gbbfeg geebbb faaedbbb gcaacg gbbb deaaf bbbg faaed bbbg gcaacg dbbg deaaf dbbg faaeg dbbg geaac dbbg faaad dbbg caacg dbbd deaaf gbbd faaed gbbd gcaacg gbbd deaaf gbbd faaed gbbb aac gbbb af gbbb g bbbg bbb db d ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Now, let's dive into another area. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#c3727bff b,#f1e5c4ff c,#d8a5a9ff d,#f7efe6ff e,#cd8a91ff f,#e4c0c3ff g,#eed9dbff ``` ```image eac gaad cac daad cac daag cae daag fae aaf fae eaf faa eaf gaad eac gaad cac daad cac daag cae daag ddbbb fae ddbbbbbbbb aaf ddbbbbbbbbbdd fae ddbbbbbbbbbdd dcfbbbbbbbbdd ddbbbbbbbbbdd ddbbbbbbbbbdcef ddbbbbbbbbbdd gaad ddbbbbbbbbbdd eac bbbbbbbdd gaad bbdd cac daad cac daag cae daag fae aaf fae eaf faa eaf gaad eac gaad cac daad cac daag cae daag ``` <!-- end of image --> Incredible, there's actually 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#c3737bff b,#f1e4c2ff c,#dcacb1ff d,#f4e9dfff e,#ce8c94ff f,#e7c9ccff g,#faf6f3ff ``` ```image g ae aa ace a ag a fa a ag a da a ad a ga a af a ga a ef a a a ec a a a ce a a a ce d ga ag db c da fa db aae de ag gb fad ag fe da gb ea da fe ad gb gac ec fc ga gbg cad ag cc af bg aa da cc ga bg dac ec cf ef bd cag a cf a bd ae fa ef ec bbaf af ed a ebb a ed ce gae bb fa ag a fad bb afag ce aa db aa a gac db ca fa cag db a ag ae gb da daf gb ad gd eag gb ga gdbbbbd f gbg af gdbbbbdg bg ga gdbbbbdg bg gcbbbbdg bd gdbbbbde bd dbbbbdg ec bd dbbbbdg a bb dbbbbdg ce bb dbbbbdg a bbbbdg ce a fa ag da ad da af ga ef a ec a cc a ce a fa ag da ad da ad ga af a ec a cc a ce a ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#cf4218ff b,#6cdd73ff c,#eebeafff d,#c6855eff e,#45dd4fff f,#b1d7b1ff g,#98cb95ff ``` ```image gfffffffffffffeeffffffffffffffffffffffffffffffffffffffffffffffffff gffffffffffffgeeefffffffffffffffffffffffffffffffffffffffffffffffff c gffffffffffffbeeeebfffffffffffffffffffffffffffffffffffffffffffffff aaac gffffffffffffeefbeeeffffffffffffffffffffffffffffffffffffffffffffff caaaaaad gffffffffffffeefffeeebffffffffffffffffffffffffffffffffffffffffffff caaaaaad gfffffffffffgeeffffbeeefffffffffffffffffffffffffffffffffffffffffff daaaaaac gfffffffffffeegffffffeeebfffffffffffffffffffffffffffffffffffffffff daaaaaac gfffffffffffeeffffffffbeeeffffffffffffffffffffffffffffffffffffffff caaaaaadffffffffffeefffffffffgeeegffffffffffffffffffffffffffffffffffffff caaaaaadffffffbebfffffffffffeeeefffffffffffffffffffffffffffffffffffff gaaaaaaagffeegffffffffffffgeeegfffffffffffffffffffffffffffffffffff gfffdaaaaaaeefffffffffffffffeeeeffffffffffffffffffffffffffffffffff gffffffdaaaaaadffffffffffffffgeeegffffffffffffffffffffffffffffffff gfffffffffdaaaaaadfffffffffffffeeebfffffffffffffffffffffffffffffff gfffffffffeefgaaaaaadfffffffffffbeeeffffffffffffffffffffffffffffff gfffffffffeefffffdaaaaaagfffffffffeeebffffffffffffffffffffffffffff gffffffffgeeffffffffdaaaaaadfffffffbeeefffffffffffffffffffffffffff gffffffffbebfffffffffffdaaaaaadffffffeeebfffffffffffffffffffffffff gffffffffeefffffffffffffffgaaaaaafffffbeeeffffffffffffffffffffffff gffffffffeeffffffffffffffffffgaaaffffffgeeegffffffffffffffffffffff gfffffffgeeffffffffffffffffffffaagfffffffeeeefffffffffffffffffffff gfffffffeegffffffffffffffffffffdaaffffffffgeeegfffffffffffffffffff gfffffffeeffffffffffffffffffffffaaffffffffffeeeeffffffffffffffffff gfffffffeeffffffffffffffffffffffaafffffffffffgeeegffffffffffffffff gffffffbebffffffffffffffffffffffdadffffffffffffeeebfffffffffffffff gffffffeegfffffffffffffffffffffffaafffffffffffffbeeefffffffffadfff gffffffeeffffffffffffffffffffffffaafffffffffffffffeeebffffffdaafff gffffffeeffffffffffffffffffffffffdadfffffffffffffffbeeefffffaagfff gfffffbebfffffffffffffffffffffffffaafffffffffffffffffeeeffffaaffff gfffffeeffffffffffffffffffffffffffaaffffffffffffffffffbebfffaaffff gfffffeeffffffffffffffffffffffffffaadffffffffffffffffffeeffdaaffff gffffgeeffffffffffffffffffffffffffgaaffffffffffffffffffeeffaadffff gffffbebfffffffffffffffffffffffffffaaffffffffffffffffffeegfaafffff gffffeeffffffffffffffffffffffffffffaadfffffffffffffffffbebfaafffff gffffeeffffffffffffffffffffffffffffdaaffffffffffffffffffeegaafffff gfffgeefffffffffffffffffffffffffffffaaffffffffffffffffffeedadfffff gfffeegfffffffffffffffffffffffffffffaaffffffffffffffffffeeaaffffff gfffeeffffffffffffffffffffffffffffffdadfffffffffffffffffbeaaffffff gfffeefffffffffffffffffffffffffffffffaaffffffffffffffffffeaaffffff gffbebfffffffffffffffffffffffffffffffaaffffffffffffffffffdadffffff gffeegfffffffffffffffffffffffffffffffaadfffffffffffffffffaagffffff gffeeffffffffffffffffffffffffffffffffdaafffffffffffffffffaabffffff gffeefffffffffffffffffffffffffffffffffaafffffffffffffffffaaeffffff gfbebfffffffffffffffffffffffffffffffffaaffffffffffffffffdaaeffffff gfeeffffffffffffffffffffffffffffffffffdadfffffffffffffffaaeegfffff gfeefffffffffffffffffffffffffffffffffffaafffffffffffffffaabebfffff ggeefffffffffffffffffffffffffffffffffffaafffffffffffffffaafeefffff gbebfffffffffffffffffffffffffffffffffffaagfffffffffffffgaafeefffff geeffffffffffffffffffffffffffffffffffffdaafffffffffffffdadfeegffff geefffffffffffffffffffffffffffffffffffffaafffffffffffffaaffbebffff beefffffffffffffffffffffffffffffffffffffaafffffffffffffaafffeeffff eegfffffffffffffffffffffffffffffffffffffaadffffffffffffaafffeeffff eeffffffffffffffffffffffffffffffffffffffgaafffffffffffdadfffeegfff eefffffffffffffffffffffffffffffffffffffffaafffffffffffaagfffbebfff febfffffffffffffffffffffffffffffffffffffffaagffffffffffaafffffebfff eegfffffffffffffffffffffffffffffffffffffffdadffffffffffaaffffffffff eefffffffffffffffffffffffffffffffffffffffffaafffffffffdaaffffffffff eefffffffffffffffffffffffffffffffffffffffffaafffffffffaadffffffffff gebgggggggggggggggggggggggggggggggggggggggggaadggggggggaaggggggggggg e ee caa aa gee ee aa caa bee ee aa dac bee bef dad aa eee ee aa aa eee ee aa caa eee fee aac dad eee bef caa aa eeb ee aa aa eeb ee aa aa eeb feb dac cad ee eef caa aac fee ee aa aa eebee aac aa eeeb dadcaa bee aaaac ee aaaa aaaa caaa aad aa c ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#cf4117ff b,#73e57bff c,#e8a895ff d,#d87251ff e,#45dd4fff f,#a5eeabff g,#e2ecd6ff ``` ```image gg eeeef eeeeebg eeeeeeef eeeeeeee geee feeeeeb feeb geeeeee beef feeeef eeeg eeeeebg beeb feeeeeg eeef geeeeef geee feeeeebg feeb gbeeeee aacg eeeg beeeeef aaaaad geee feeeeeb aaaaaaadc feee gbeeeeg daaaaaaaaacg beee eeeeef cdaaaaaaaaacg eeee beeeee cdaaaaaaaaaaeeeb feeeebg gaaaaaaaaaaac beeeeef gcdaaaaaaaadcg feeeeeb baaaaaaaaaadc eeeeebg eeedaaaaaaaaadc gbeeeeef geee cdaaaaaaaaadg feeeee feeb gcaaaaaaaaadcg geeeeeg beef cdaaaaaaaaacg feeeeeb geee gcaaaaaaaaadcg beeeef feeb gcdaaaaaaaaacg eeeeebg beef gdaaaaaaaaadc beeeeef eeeg cdaaaaaaaaadg feeeeeg feee gdaaaaaac feeeeebg beee gcdaaad gbeeeee eeee aaaa feeeeb eeee aaaa beeeeeg eeef caaa geeeeeg geee gaaag eeeeef feeb daac geeeeebg beef caad beeeee geee aaac beeeeef feeb caad feeeeeb beef gaaa gbeeeef eeeg aaac eeeeeb adc feeb caaa feeeee caad beef aaac geeeeeg daac eeeg aaad feeeeef aaac feee aaaa geeeeeb gaaa eeee daaa eeeef daac eeee caaa beeb daac eeeb gaaag geee aaag eeef daac eeeg caaa geee gaaag feeb daac feeb aaac geee aaag beef caad eeeg gaaa eeeg gaaa beef caaa feeb daad geee aaaa beef caaa eeegaaaa eeeg aaag eeefaaad feee aaac eeebaaac eeef aaaa eeeeaaag geeeg aaaa beeeaaa feee caaa feedaad beee caaa geeaaac eeee daac beaaa eeeb caad fdaad eeef gaaa gaaac eeeg aaac aaac feeb caaa caaab beef aaag daade eeeg daac aaaeeg feee caad gaaaeef beeb gaaa caaaeeb geeeg aaac daaaeeeg feeb aaad aaaaeeef beef aaaa aaaaeeeb eeeg daaa aaadeeee feee caaa aaagbeee beee aaag gaaa feee eeee daac caad geee eeee caad daac eeeg eeef aaac gaaa feeb eeeg daad caad geee feee caaa daac eeeg beeb aaag aaac beef geeeg caad caaa geee feeb gaaa caad eeeg beef aaac daac beef eeeg aaac aaag feeb eeb aaaa caaa eeb eef daaa daaa g eeg caaa aaaa ee gaaa aaaa ee daac aaac ee caad aaac ``` <!-- end of image --> Bingo! This close-up reveals 2 intersections in area A! Answer: A: 2; 2 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#d04118ff b,#78e680ff c,#ecb7a7ff d,#db7e60ff e,#45dd50ff f,#a9efaeff g,#e8efdeff ``` ```image eb geeeg c beeeeb gaaac ee feee caaaaaad ee eeef gaaaaaadg fee beee gdaaaaaac eef geeef daaaaaac ee beee caaaaaad ee geeef caaaaaad feb eeee gdaaaaadg eeg geeeg daaaaaaee eeeb caaaaaac feeeg daaaaaad eeeb eeggaaaaaadg feee ee gdaaaaaac eeeb gee daaaaaac beee bef caaaaaad geeef ee caaaaaa beee ee gdaa geeef fee aac beee eef caa geeeg ee aa eeeb ee aag feeeg feb dad eeeb eeg aa feeeg ac ee aa eeeb cad gee dad beee aac beb gaa eeeg aa eeg aa beb aa ee dac ee caa gee gaa ee dac bef aa eeg aa ee aac feb aa ee caa eegaa fee aa eedad eef aag eeaag ee dad feaa ee aa eaa feb aa dad eeg aac aac ee caa aab gee aa aae beb aa caae eeg dad aaeeg ee gaa aafeb gee aa aa ee bef aac caa ee ee cad dac eeg ee aa aa feb fee aa aa ee eef dac gaa ee ee gaa dad eeg ee aa aag feb feb aag aa eb eeg dad aa ee aa cad ee aa aac beb aac aa eg eeg caa aa beeg ee aa caa bee gee aa dac bee bef dad aa eee ee gaa aa eee ee aa gaa eee fee aac dad eee eef caa aag eee ee aa aa eeb ee aa aa geeb feb dac cad geeg eeg gaa aac fee ee aa aa eebee aag aa eeeb dadcaa beeg aadac ee aaaa aaaa caaa aad aa c ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#c15b8bff b,#815a0cff c,#e7c4d3ff d,#967b43ff e,#b1d7b1ff f,#c293a0ff g,#99c694ff ``` ```image af aa ggggggggggggggggggggggggggge caa eeeeeeeeeeeeeeeeeeeeeeeeeeeg aaa eeeeeeeeeeeeeeeeeeeeeeeeeeeg aaa eeeeeeeeeeeeeeeeeeeeeeeeeeeg caaa eeeeeeeeeeegeeeeeeeeeeeeeeeg faaa eeeeeeeeeedbdeeeeeeeeeeeeeeg aaaa eeeeeeeeegbbbeeeeeeeeeeeeeeg aaaa eeeeeeeeebbbbeeeeeeeeeeeeeeg cacaa eeeeeeeedbbdbgeeeeeeeeeeeeeg aa aa eeeeeeegbbegbdeeeeeeeeeeeeeg aa aa eeeeeeebbgefbbeeeeeeeeeeeeeg caf aa eeeeeebbdeeaabeeeeeeeeeeeeeg fac aa eeeeedbbeefaabgeeeeeeeeeeeeg aa aa eeeeebbeeefaabdeeeeeeeeeeeeg aa aa eeeebbdeeefaadbeeeeeeeeeeeeg caf fa eeedbbeeeeaaaabeeeeeeeeeeeeg aa fa eegbbeeeeeaaaabgeeeeeeeeeeeg aa fac eebbgeeeeeaaaabdeeeeeeeeeeeg aa fac ebbbeeeeeeaafadbeeeeeeeeeeeg fac cac gbbeeeeeeeaaeaabeeeeeeeeeeeg aa cac bbgeeeeeeeaaeaabgeeeeeeeeeeg aa cac bbdeeeeeeeeaaeaabdeeeeeeeeeeg caf cac fbbeeeeeeeeeaaefaabeeeeeeeeeeg aa caf bbeeeeeeeeeeaaeeaabeeeeeeeeeeg aa caf bbfeeeeeeeeeeafeeaabgeeeeeeeeeg ggggggggggggggaaggggggafggggggggggg dbb eeeeeeeeefafeefaddeeeeeeeeeg eeeeeeeeeeeeefafeeeeeeaaeeeeeeeeeee cbb eeeeeeeeefafeeeaabeeeeeeeeeg eeeeeeeeeeeeeaaeeeeeeeaaeeeeeeeeeee bbc eeeeeeeeefaeeeeaabeeeeeeeeeg eeeeeeeeeeeeeaaeeeeeeeaaeeeeeeeeeee bbd eeeeeeeeeaaeeeeaabgeeeeeeeeg eeeeeeeeeeeefafeeeeeeeaaeeeeeeeeeee ebb eeeeeeeeeaaeeeefaddeeeeeeeeg eeeeeeeeeeeeaaeeeeeeeeaaeeeeeeeeeee bb eeeeeeeeeaaeeeeeaabeeeeeeeeg eeeeeeeeeeeeaaeeeeeeeeaaeeeeeeeeeee bbf eeeeeeeeeaaeeeeeaabeeeeeeeeg eeeeeeeeeeeeaaeeeeeeeeaaeeeeeeeeeee fbb eeeeeeeeeaaeeeeeaabgeeeeeeeg eeeeeeeeeeefafeeeeeeeeaaeeeeeeeeeee bb eeeeeeeeeaaeeeeefaddeeeeeeeg eeeeeeeeeeeaaeeeeeeeeeaaeeeeeeeeeee bbe eeeeeeeeeaaeeeeeeaabeeeeeeeg eeeeeeeeeeeaaeeeeeeeeeaaeeeeeeeeeee dbb eeeeeeeeeaaeeeeeeaabeeeeeeeg eeeeeeeeeefafeeeeeeeeeaaeeeeeeeeeee dbb eeeeeeeeeaaeeeeeefabgeeeeeeg eeeeeeeeeeaaeeeeeeeeeeaaeeeeeeeeeee dbb eeeeeeeeeafeeeeeeeaadeeeeeeg eeeeeeeeeeaaeeeeeeeeeeaaeeeeeeeeeee cfddbbbb eeeeeeeefafeeeeeeeaabeeeeeeg eeeeeeeeeeaaeeeeeeeeeeaaeeeeeeggddbbbbbbbbbbbbb eeeeeeeefafeeeeeeeaabeeeeeeg eeeeeeeeefafeeeeeeeeggaabbbbbbbbbbbbbbbbdfc eeeeeeeefaeeeeeeeefadgeeeeeg eeeeeeeeeaagddbbbbbbbbaabbbbbbddgge eeeeeeeeaaeeeeeeeeeaadeeeeeg eegdbbbbbaabbbbbbbbbddaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeeaabeeeeeg eeebbbbbbaadggeeeeeeeeaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeeaabeeeeeg eeegeeeeaaeeeeeeeeeeeeaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeefadgeeeeg eeeeeeeeaaeeeeeeeeeeeeaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeeeaadeeeeg eeeeeeeeaaeeeeeeeeeeeeaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeeeaabeeeeg eeeeeeefafeeeeeeeeeeeeaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeeeaabeeeeg eeeeeeeaaeeeeeeeeeeeeeaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeeeeaageeeg eeeeeeeaaeeeeeeeeeeeeeaaeeeeeeeeeee eeeeeeeeaaeeeeeeeeeeeaadeeeg eeeeeeeaaeeeeeeeeeeeeefaeeeeeeeeeee eeeeeeeeafeeeeeeeeeeeaabeeeg eeeeeeaaeeeeeeeeeeeeeefaeeeeeeeeeee eeeeeeefafeeeeeeeeeeefadeeeg eeeeeeaaeeeeeeeeeeeeeefafeeeeeeeeee eeeeeeefafeeeeeeeeeeeeaageeg eeeeeeaaeeeeeeeeeeeeeefafeeeeeeeeee eeeeeeefaeeeeeeeeeeeeeaadeeg eeeeefafeeeeeeeeeeeeeefafeeeeeeeeee eeeeeeeaaeeeeeeeeeeeeeaageeg eeeeeaaeeeeeeeeeeeeeeefafeeeeeeeeee eeeeeeeaaeeeeeeeeeeeeefafeeg eeeeeaaeeeeeeeeeeeeeeefafeeeeeeeeee eeeeeeeaaeeeeeeeeeeeeeeafeeg eeeeeaaeeeeeeeeeeeeeeefafeeeeeeeeee eeeeeeeaaeeeeeeeeeeeeeeeeeeg eeeeaageeeeeeeeeeeeeeegafeeeeeeeeeg eeeeeeeaaeeeeeeeeeeeeeeeeeeg aa caf gggggggaagggggggggggggggggge aa af aa caf af aa aa aa aa aa aa af aa aa caf cc aa cac aa caac aa faaaaa aa caaaaaafc aa cfaaaaaac aa faaaaaaf aa caaaaaafc aa caaaaaaac aa cfaaaaaac aa faaaaaaf aa caaaaaafc aa cfaaaaaac aaaaaaaaf aaaafc c ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#c25a8bff b,#825a0cff c,#e1b9c6ff d,#a37d4eff e,#f1e0e5ff f,#d185a9ff g,#c0aa85ff ``` ```image faaae eaaaf eaaaa eaaaf caaaf eaaaf faaac eaaaf aaaa eaaaf eaaaf aaaf caaac aaaf faaae aaaa eaaaa aaaa caaaf aaaa faaac aaaa aaaae aaaa eaaaf aaaa caaac faaa faaae faaa aaaa faaae caaaf faaae faaac faaae aaaae faaae eaaaf faaae caaac faaae faaae faaae aaaa caaae caaaf caaac faaac caaac aaaae caaac eaaaf caaac caaac caaac faaae caaac aaaa caaac eecgggddb eaaaf caaac eccggddbbbbbbbbbbb faaac eccgaaadbbbbbbbbbbbbbbbbbbbb aaaae eccggdddbbbbbbaaadbbbbbbbbbbbbbbbbbbbb eaaaacggdddbbbbbbbbbbbbbbbbaaadbbbbbbbbbbbdddggcce eecgggddaaadbbbbbbbbbbbbbbbbbbbbbbaaadbdddggcce egddbbbbbbbbbaaaabbbbbbbbbbbbbbbbbbbddggaaaf ebbbbbbbbbbbbaaaabbbbbbbbbddgggcee eaaaf bbbbbbbbbbbbaaaadgggcee eaaaf bbbbbddgggcfaaac eaaaf cce faaae aaaf eaaaa aaaf caaaf aaaa faaac aaaa aaaa aaaa eaaaf aaaa caaac aaaa faaae faaa eaaaa faaa caaaf faaa faaac faaae aaaa faaae eaaaf faaae caaac faaae faaae faaae eaaaa faaae caaaf faaae faaac caaac aaaae caaac eaaaf caaac caaac caaac faaae caaac aaaa caaac caaaf caaac faaac caaac aaaae caaac eaaaf eaaaf caaac eaaaf faaae eaaaf ``` <!-- end of image --> Yes! I knew it! There's 2 intersections right here in area A! Let's continue our search in the next region. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#c15a8aff b,#835a0eff c,#e0b1c5ff d,#a4744fff e,#eddbddff f,#d184a8ff g,#c7b593ff ``` ```image dbbc dbbbd gbbbbb ebbbbbb dbbbbbb gbbbbbbb ebbbbdbbb dbbbb dbbe gbbbbe gbbg ebbbbg cbbd bbbbd bbb dbbbbe cdbbe gbbbbg aaadbg ebbbbd eaaaabd dbbbbe eaaaabb gbbbbc caaaabbe ebbbbg caaaabbg dbbbd caaaabbd gbbbbe faaaabbb bbbd faaaadbbg dbbbe faaaaabbd gbbbg aaaaaabbb ebbbd aaaaaadbbe dbbb aaaaaadbbg gbbbc eaaafaaabbd ebbbb eaaaffaabbb dbbbd eaaaccaadbbe dbbbbe caaaceaaabbg cbbbbg caaac aaabbd ebbbbd caaac aaadbb dbbbbe faaae aaadbbe gbbbbg faaae aaaabbg bbbbd faaae faaabbd bbbb faaa caaadbb bbbe aaaa eaaadbbe bbg aaaa aaaabbg bd aaaf faaabbd be eaaaf caaadbb eaaaf aaaabbg caaac faaadbd caaac caaadbb caaac eaaaabbe caaae aaaabbg faaae faaadbd faaae eaaadbb faaa aaaabbe aaaa faaabbg aaaa caaadbd aaaf eaaaabb eaaaf aaaabbe eaaaf faaabbg eaaaf caaadbd caaac eaaaabb caaac aaaabbe caaac faaadbg caaae caaadbd faaae faaabbe faaa caaadbg aaaa eaaaabd aaaa aaaabb aaaf faaabbe eaaaf caaadbg eaaaf eaaaabd eaaaf aaaabb eaaac faaadbe caaac caaadbg caaac eaaaabd caaae faaabb faaae caaadbe faaae eaaadbg faaa aaaabd aaaa faaabb aaaa caaadbe aaaf eaaaabg eaaaf aaaabd eaaaf caaadb eaaac eaaaab caaac aaaab caaac faaad caaae eaaade faaae aaaag faaae faaad faaa caaab aaaa eaaabe aaaa aaabg aaaf faabd aaaf caadb eaaaf eaaabe eaaaf aaabg eaaac faadd caaac caadb caaac aaabe caaae faabg faaae caadd faaa aaag aaaa aaae aaaa aaac aaaa aaaf aaaf aaaf eaaaf ee eaaaf eaaac caaac ``` <!-- end of image --> Area B does not contain any intersection points. Answer: A: 2; B: 0; 2 + 0 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#c25a8bff b,#81590bff c,#ddb1bfff d,#ac935fff e,#edd9deff f,#d084a6ff g,#986837ff ``` ```image af aa caa aaa aaa eaaa c faaa dbd aaaa ebbb aaaa bbbb cacaa gbggbe aa aa cbb cbd aa aa bbe cbb eaf aa bbd eaab fae aa fbb caabe aa aa bb caabd aa fa bbf faagb cac fa dbb faaab aa fae ebb aaaabe aa fae bbc aaaabd eaa cae gbg aacagb fae cae cbb aa aab aa cac bbe aa aabe aa cac bbd aa fabd cac cac dbb aa eaab aa eac bb af aab aa eaf bbc eaf aabe eaa eaf dbb cac fagd fae eaf ebb cac eaab aa af bbe fae aab aa aa gbg fa aabe caf aa cbb aa cagd aa aa bbe aa aab aa aa bbd aa aab aa aa dbb aa aabe fac aa bb aa eagd aa aa bbc aa aab aa aa gbg aa aab eaf aa gbb af fage aae aa dbb eaf eaad aa aa ecdgbbbb eac aab aa aa ecdgbbbbbbbbbbbbb cac aab cac ecaabbbbbbbbbbbbbbbgddce fae cage aacddbbbbbbbbaabbbbbbddce fa aad edgbbbbaabbbbbbbbbgdaa aa aab bbbbbgaadce aa aa aab e fae aa aa cage aa aa aa aad aa aa aa aab cac aa aa fag aa fa aa eaae aa fa af aad eaf fae eaf aab fae fae eac fag aa cae cac aae aa cae fae aad cac cac fa aac aa cac aa cac aa eac aa af eaf eac aa fae eaf aa aa eaf aa aa eaf aa cac af aa aa aa aa aa aa eaf eaa aa eac ee aa cac aa efae aa caaaaa aa caaaaaafe aa efaaaaaac aa efaaaaaac aa caaaaaafe aa eaaaaaaae aa efaaaaaac aa caaaaaafe aa caaaaaafe aa efaaaaaac aaaaaaaac aaaafe e ``` <!-- end of image -->
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Time to put on my detective hat and find those intersection points! Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#e1f059ff b,#d4d920ff c,#eaf28bff d,#f4f8c5ff e,#b1d7b1ff f,#96ca96ff g,#c3de7fff ``` ```image ca aaaad daaaacac daaaad aa caaaad aa aaaaa aa daaaac aad caaaad cac caaaad daa aaaaa aa daaaac aa caaaad aa caaaad cad aaaaa dac daaaac aa caaaad aa caaaad aa aaaac aa daaaac cad caaaad dac aaaaa aa daaaac aa daaaac aa daaaad aa aaa dc cad ffffffffffffffffffaafffffffffffgbbbbgfe dac eeeeeeeeeeeeeeeeeeaaeeeeeeeeeegbbbbbbbb aa eeeeeeeeeeeeeeeeeeaaeeeeeeeeeebbgeegbbbbbc aa eeeeeeeeeeeeeeeeeeaaeeeeeeeeebbaeeeeeegbbbbbd aa eeeeeeeeeeeeeeeeeeaaeeeeeeeebbaeeeeeeef abbbba aa eeeeeeeeeeeeeeeeeeaaeeeeeeebbbeeeeeeeef dbbbbbd cad eeeeeeeeeeeeeeeeegageeeeeebbbeeeeeeeeef abbbbb dac eeeeeeeeeeeeeeeeegageeeeebbbeeeeeeeeeef dbbbbbc aa eeeeeeeeeeeeeeeeeaageeeebbbeeeeeeeeeeef cbbbbbd aa eeeegeeeeeeeeeeeeaaeeeebbbeeeeeeeeeeeef abbbba aa eeegageeeeeeeeeeeaaeeebbbeeeeeeeeeeeeef dbbbbbc aad eeegaaeeeeeeeeeeeaaeebbbeeeeeeeeeeeeeef cbbbba cac eeeaaaeeeeeeeeeeeaaeabbeeeeeeeeeeeeeeef dbbb daa eeeaaaaeeeeeeeeeeaagbbeeeeeeeeeeeeeeeef cbb aa eeeaaaaeeeeeeeeeeaabbgeeeeeeeeeeeeeeeef bb aa eeeaaaageeeeeeeeeaabgeeeeeeeeeeeeeeeeef aba aa eeeaaeaaeeeeeeeegaageeeeeeeeeeeeeeeeeef bb cad eeeaaeaaeeeeeeeebaaeeeeeeeeeeeeeeeeeeef bbc dac eeeaaegageeeeeebbageeeeeeeeeeeeeeeeeeef dbb aa eeeaaeeaaeeeeebbaageeeeeeeeeeeeeeeeeeef bbd aa eeeaaeeaaeeeebbbaageeeeeeeeeeeeeeeeeeef dbb aa eeeaaeegaaeebbbeaaeeeeeeeeeeeeeeeeeeeef bb aa eeeaaeeeaaebbbeeaaeeeeeeeeeeeeeeeeeeeef cba cad eeeaaeeeaabbbeeeaaeeeeeeeeeeeeeeeeeeeef bb dac eeeeeeeeeaabeeeeaaeeeeeeeeeeeeeeeeeeeef abc aa eeeeeeeebaaeeeeeaaeeeeeeeeeeeeeeeeeeeef bb aa eeeeeeeabaageeeeaaeeeeeeeeeeeeeeeeeeeef bbd aa eeeeeeabbeaaeeeeaaeeeeeeeeeeeeeeeeeeeef dbb aa eeeeegbbeeaaeeeeaaeeeeeeeeeeeeeeeeeeeef bb cad eeeegbbgeegaaeegaaeeeeeeeeeeeeeeeeeeeef cbb dac eeegbbgeeeeaaeegageeeeeeeeeeeeeeeeeeeef bb aa eeebbgeeeeeaagegageeeeeeeeeeeeeeeeeeeef fbbbffffffaafffe eeebaeeeeeeeaaeaaeeeeeeeeeeeeeeeeeeeeef eebbeeeeeeaaeeef eeeeeeeeeeeeaaeaaeeeeeeeeeeeeeeeeeeeeef eebbgeeeeeaaeeef eeeeeeeeeeeegagaaeeeeeeeeeeeeeeeeeeeeef eeebbeeeeegageef eeeeeeeeeeeeeaaaaeeeeeeeeeeeeeeeeeeeeef eeebbgeeeeeaaeef eeeeeeeeeeeeeaaaaeeeeeeeeeeeeeeeeeeeeef eeegbbeeeeeaaeef eeeeeeeeeeeeegaaaeeeeeeeeeeeeeeeeeeeeef eeeebbeeeeeaaeef eeeeeeeeeeeeeeaaaeeeeeeeeeeeeeeeeeeeeef eeeegbbeeeeaaeef eeeeeeeeeeeeeeaaaeeeeeeeeeeeeeeeeeeeeef eeeeebbeeeeaaeef eeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeeef eeeeebbaeeegagef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeebbeeeeaaef ffffffffffffffffffffffffffffffffffffffe eeeeeebbgeeeeeef eeeeeeebbeeeeeef eeeeeeebbeeeeeef eeeeeeegbbeeeeef eeeeeeeebbeeeeef eeeeeeeeabbeeeef eeeeeeeeebbeeeef eeeeeeeeebbgeeef eeeeeeeeeebbeeef eeeeeeeeeebbgeef eeeeeeeeeegbbeef feeeeeeeeeebbfef cbb a ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#e2f159ff b,#d5d91dff c,#edf49bff d,#f9fbe0ff e,#e7f17bff f,#f3f7bdff g,#dadf3bff ``` ```image faaae cbbbbgcd faaac fbbbbbbbbaf faaac fbbbbbbbbbbbged caaaf fbbbbbabbbbbbbbb caaaf dbbbbbc dcgbbbbbb eaaaf dgbbbbc febbbb eaaad dgbbbbe cab aaaad dgbbbbe d aaaa gbbbba aaaa abbbba daaae abbbba daaae ebbbbgd faaae ebbbbgd faaac cbbbbgd caaac cbbbbbd caaaf cbbbbbd caaaf fbbbbbf eaaaf fbbbbbf eaaad dbbbbbc dfd aaaad dgbbbbc daaad aaaa dgbbbbc caaac daaaa dgbbbbe caaaa daaae gbbbbe eaaaaf daaae abbbba eaaaae faaae abbbba eaaaaad faaac abbbbg aaaaaaf caaac ebbbbgd aaaaaae caaafebbbbgd aaaaaaad caaaebbbbgd aaaaaaac eaaagbbbbd daaaaaaaa eaaabbbbf daaaeaaaaf aaaabbbf daaaecaaae aaaabbf faaaedaaaad faaaabc faaac eaaaf dgaaaac faaac faaae dggaaaa caaac daaaad dgbgaaac caaaf eaaac gbbgaaac caaaf faaaa abbbgaaac eaaaf aaaaf abbbbaaaaf eaaad caaae ebbbbgeaaaf eaaad daaaad ebbbbgdeaaad eaaad eaaaf cbbbbgd eaaad aaaa faaae cbbbbbd aaaad aaaa daaaad fbbbbbf aaaa aaaa eaaac fbbbbbf daaaa daaaa faaaafbbbbbf daaae daaae aaaagbbbbc faaae dfff caaagbbbc faaac daaaabbe faaac daaaage caaac ggaaaa caaaf abbaaaad eaaaf abbbgaaac eaaad abbbbaaaaa eaaad ebbbbgdaaaaf aaaa ebbbbgd caaae aaaa cbbbbgd daaaad daaaa cbbbbbd eaaaf daaae fbbbbbf faaae faaae fbbbbbf daaaad faaac fbbbbbf eaaac faaac dbbbbbc faaaa caaaf dgbbbbc aaaaf caaaf abbbbe caaae eaaaf dgbbe daaaad eaaad aa eaaaf aaaad faaae aaaa daaaad aaaa eaaacdaaaa faaaadaaae aaaacaaae caaaaaaac daaaaaaac eaaaaaaf faaaaaaf daaaaaaf eaaaaad faaaaad aaaaa caaaa daaae caaf dd ``` <!-- end of image --> As I suspected, there's 2 intersections within area A. Next up, a closer look at another region. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#e2ef5aff b,#d5d91dff c,#edf2a2ff d,#f8fadeff e,#e7ed7fff f,#f3f6c0ff g,#dadd3dff ``` ```image abbba caaac fbbbbd faaac gbbbe daaae cbbbb daaaa gbbbc aaaad ebbbg eaaaf dbbbbc caaac ebbbg faaae dbbbbf daaae abbba aaaa fbbbbd aaaad gbbbe eaaaf cbbbb caaac bbbbc faaae ebbbg daaaa dbbbbf aaaa abbba eaaad fbbbbd eaaaf gbbbe caaac cbbbbd faaae gbbbe daaaa cbbbg ecfd dbbbbc ebbbg dbbbbf abbba fbbbbd gbbbe cbbbb bbbbc ebbbg dbbbbf abbba fbbbbd abbbe fbbbbd gbbbe cbbbg bbbbc ebbbg dbbbbf abbba fbbbbd gbbbe cbbbb ``` <!-- end of image --> Darn it! This close-up doesn't show any intersections in area B. Answer: A: 2; B: 0; 2 + 0 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#e2f159ff b,#d5d91eff c,#edf39bff d,#f9fbe1ff e,#e7f079ff f,#f3f7bcff g,#dbdf40ff ``` ```image ea aaaaf daaaaeae caaaaf aa eaaaad aa daaaae aa faaaac aad caaaaf cac eaaaad dae daaaae aa faaaac aa caaaaf aa eaaaad ead daaaae fac faaaac daa caaaaf aa eaaaad aa daaaae aa faaaac eaf caaaaf fac eaaaad aa daaaae aa faaaac aa faaaaf aa aaad fe caf aa fbbbbf fae aa fbbabbbbgd aa aa dbbc fbbbbbc aa aa dbbe ebbbbbd aa aa bba dgbbbba aad dae bbg fbbbbbc caf fac bbg ebbbbgd dae caf bbb dbbbbbe aa eaf bbb cbbbbbf aa f aad bbb gbbbba aa cac aa gbb fbbbbbc ead eaa aa gbb ebbbbg cac eaad aa ebb dgbbd daa aaae aaebbd cbg aa aaaa aabbd bb aa aaaaf aabf aba aa aadaa faac bb eaf aa aa dbaa bbc fac aa eac bgac dbb daa aa aa bbaaf bbd aa aa aad bbgead fbb aa aa fae bbb aad bb aa aa aa bbb aa ebg eaf dae aagbb aa bb fae daab aa gbe aa gaa aa bb aa abgac aa bbf aa ebbdaa aa fbb aad cbbd aad daa bbd caf fbbf fae fae cbb fae fbbf aa fac bb aa dbbc aaf caf aba aa dbe daa ead bb aa aa aa gbc aad eacaa dbb cac aaaa bbf dae aaaa fbb aa faaa bb aa aaa ebg aa aaa bb ead dae gbe cac d bb daa bbc dbb bbd cbb bb eba bb gbe dbb bbf fbb bbd cbg g ``` <!-- end of image -->
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Let's examine this image for potential line intersections. There are 3 areas where the lines seem to converge. We should take a closer look at area A, B,, and C. <!-- image --> ```palette Key,Color ,#fefefeff a,#374920ff b,#1d048dff c,#b1d6b1ff d,#6e66b0ff e,#96bf98ff f,#ebefedff g,#697e59ff ``` ```image bbb bbbf bbbb caa bbbbd caaaf cbbbbb faaaae dbbdbbb faaaaag bbb bbbf faaagaaa bbb fbbb ceeeeeeeeeeeeeeeeeeeeeaaaaeaaaeeeeeeeeeeeee bbb bbbd eccccccccccccccccccccaaaaccaaacccccccccccccf bbb bbb ecccccccccccccccccccaaaacccgaacccccccccccccf bbd dbbb eccccccccccccccccccaaaacccceaaeccccccccccccf cbbc bbbf ecccccccccccccccccaaaaccccccaagccccccccccccf dbbf fbbb eccccccccccccccccaaaacccccccaaaccccccccccccf bbb bbbd ecccccccccccccccaaaaccccccccaaaccccccccccccf bbb bbb eccccccccccccccaaaacccccccccaaaccccccccccccf bbb dbbb ecccccccccccccaaaaccccccccccgaaccccccccccccf bbb bbbef eccccccccccccaaaacccccccccccgaaecccccccccccf bbd fbbbbbbbbbbddeccccaaaacccccccccccceaagcccccccccccf cbbc bbbbbbbbbbbbbbbbaaaaecccccccccccccaaacccccccccccf dbbf fcddbbbbbbbbbbaaaabbbbbbbdcccccccaaacccccccccccf bbb ecccccedbaaaabbbbbbbbbbbbdcccaaacccccccccccf bbb ecccccccgaaaeccddbbbbbbbbbbbbaaacccccccccccf bbb eccccccgaaaecccccccccdbbbbbbbaaabdcccccccccf bbb ecccccgaaaeccccccccccccccdbbbbaabbbbbdcccccf bbd eccccgaaaeccccccccccccccccccceaaabbbbbbbbdef cbbc ecccgaaaecccccccccccccccccccccaaaebbbbbbbbbbbdf dbbf eccgaaaeccccccccccccccccccccccaaaccccedbbbbbbbbbbdf bbb eceaaagcccccccccccccccccccccccaaaccccccccedbbbbbbbbbbdf bbb eeaaagccccccccccccccccccccccccgaaccccccccccf fdbbbbbbbbbbdc bbb eaaagcccccccccccccccccccccccccgaaecccccccccf fdbbbbbbbbb bbb faaagcccccccccccccccccccccccccceaagcccccccccf fdbbbbb bbd faaagccccccccccccccccccccccccccccaaacccccccccf bbb fffcbbefffff faaagcccccccccccccccccccccccccccccaaacccccccccf bbb cccdbbeccccef faaaaccccccccccccccccccccccccccccccaaacccccccccf bbb cccbbbccccccf faaageccccccccccccccccccccccccccccccaaacccccccccf bbb cccbbbccccccf aaaa eccccccccccccccccccccccccccccccgaaecccccccef bbb cccbbbccccccf aaaa ffffffffffffffffffffffffffffffcaacffffffff bbb cccbbbccccccf aaaa aag bbb cccbbdccccccf aaaa aaa bbb ccebbdccccccf aaaa aaa bbb ccdbbcccccccfaaaa aaa bbb ccbbbcccccccaaaa gaa bbb ccbbbccccccaaaa eaaf bbb ccccecccccaaaa faae dbb cccccccccaaaa aag dbb ccccccccaaaaf aaa dbb cccccccaaaaef aaa dbb ccccccgaaaccf aaa dbb cccccgaaaeccf gaa dbbf ccccgaaaeccef caac dbbf fffgaaacffff aag ebbf eaaac aaa cbbf aaac aaa cbbc ac aaa cbbc gaa fbbc eaaf fbbe faae fbbd aag fbbd aaa bbd aaa bbd aaa bbd gaa bbd caac bbd aag bbd aaa bbb aaa bbb aaa eeeeeeeeeebbbeee gaa fccccccccccbbbccc eaaf fccccccccccbbbccc faae fccccccccccbbbccc aag fccccccccccbbbccc aaa fccccccccccbbbccc aaaf fccccccccccbbbccc aaaaaae fccccccccccbbbccc faaaaaaaagcccccccccccbbbccc fgaaaaaaaaagcccccccbbbccc caaaaaaaaaaecccbbbccc fgaaaaaaaaagbbbccc fcceaaaaaaaaaaccc fccccccgaaaaaaccc fccccccccceaaaccc fcccccccccccccccc feccccccccccccccc ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#37491fff b,#1b028dff c,#aaa1d4ff d,#796bbcff e,#4936a4ff f,#e1e1e6ff g,#596845ff ``` ```image cbbbbbf dbbbbbf ebbbbb ebbbbe bbbbbd fbbbbbd cbbbbbc cbbbbbf dbbbbbf ebbbbb ebbbbe bbbbbd fbbbbbd cbbbbbc cbbbbbf dbbbbbf ebbbbb ebbbbe bbbbbd fbbbbbd f fddebbc fa f faa faaa fgaaa fgaaaa fgaaaaa fgaaaaaa fgaaaaaag gaaaaaagf gaaaaaagf gaaaaaagf gaaaaaagf gaaaaaagf ``` <!-- end of image --> This isn't an intersection in area A, but I'm not discouraged. Time for a closer look at another area. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#374920ff b,#1c048cff c,#aeadbdff d,#6959b3ff e,#8c967eff f,#d6d7daff g,#616f4eff ``` ```image gaaaaaag caaaaaf gaaaaaag faaaaac gaaaaaag aaaaae gaaaaaagf aaaaag gaaaaaagf gaaaag gaaaaaaaf eaaaaa eaaaaaaaf eaaaaaf eaaaaaaaf caaaaac eaaaaaaaf faaaaae eaaaaaaaf aaaaae eaaaaaaaf gaaaag eaaaaaaaf gaaaaa caaaaaaac eaaaaaf caaaaaaac caaaaaf caaaaaaac faaaaac caaaaaaac aaaaae caaaaaaac aaaaag faaaaaaae gaaaag faaaaaaae eaaaaa faaaaaaae eaaaaaf ddccff faaaaaaae caaaaac bbbbbbbbdddccff faaaaaaae faaaaae bbbbbbbbbbbbbbbbbdddcccaaaaaaae aaaaae bbbbbbbbbbbbbbbbbbbbbbaaaaaaagcf gaaaag bbbbbbbbbbbbbbbbbbbbbaaaaaaaabbbbbbdddc gaaaaa bbbbbbbbbbbbbbbbbbbbaaaaaaaabbbbbbbbbbbbbdcf eaaaaaf fccdddbbbbbbbbbbbaaaaaaaabbbbbbbbbbbbbbbbbbdcf caaaaaf fccdddbaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbdcf faaaaac gaaaaaaadbbbbbbbbbbbbbbbbbbbbbbbbbbbdcf aaaaae gaaaaaagf fccdddbbbbbbbbbbbbbbbbbbbbbbdaaaaag gaaaaaagf fcdbbbbbbbbbbbbbbbbbbaaaaaa gaaaaaaaf fcdbbbbbbbbbbbbbbaaaaaabdcf eaaaaaaaf fcdbbbbbbbbbbbaaaaabbbbbddf eaaaaaaaf fcdbbbbbbbaaaaabbbbbbbbbddc eaaaaaaaf cddbbaaaaabbbbbbbbbbbbbddc eaaaaaaaf caaaaaabbbbbbbbbbbbbbbbbdc eaaaaaaaf gaaaaabbbbbbbbbbbbbbbbbbb eaaaaaaaf gaaaaa fddbbbbbbbbbbbbbbb eaaaaaaac eaaaaaf fcdbbbbbbbbbbb caaaaaaac caaaaaf fcdbbbbbbb caaaaaaac faaaaac fcdbbb caaaaaaac aaaaae fc caaaaaaac aaaaag caaaaaaae gaaaag faaaaaaae eaaaaa faaaaaaae eaaaaaf aaaaaaae caaaaac aaaaaae faaaaae aaaaae aaaaae aaaag gaaaag aaag gaaaaa aag eaaaaaf ag caaaaaf g faaaaac aaaaae aaaaag gaaaag eaaaaa ``` <!-- end of image --> I can confirm that 2 intersections exists in area B. Okay, let's direct our attention to the next zone. Let's see what secrets area C holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#374920ff b,#1b028cff c,#aeabc3ff d,#8072bfff e,#859077ff f,#d3d2e0ff g,#5c694dff ``` ```image dbbbbb dbbbbb dbbbbb dbbbbb dbbbbb dbbbbb dbbbbb dbbbbb dbbbbbf dbbbbbf cbbbbbf cbbbbbf cbbbbbf cbbbbbf cbbbbbf cbbbbbf cbbbbbc fbbbbbc aec fbbbbbc aaaagef fbbbbbc aaaaaaaaec fbbbbbc aaaaaaaaaaagef fbbbbbc aaaaaaaaaaaaaaaecf fbbbbbc gaaaaaaaaaaaaaaaaagecbbbbbd fcgaaaaaaaaaaaaaaaaaaabbbd cegaaaaaaaaaaaaaaaaaag fcgaaaaaaaaaaaaaaaa fegaaaaaaaaaaag fceaaaaaaaac fegaaaa cee ``` <!-- end of image --> This isn't an intersection in area C, but I'm not discouraged. Answer: A: 0; B: 2; C: 0; 0 + 2 + 0 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#374920ff b,#1d048dff c,#b4b1cbff d,#7060b7ff e,#909a83ff f,#dcdce1ff g,#606e4dff ``` ```image bbb bbbf bbbb caa bbbbd faaaf cbbbbb faaaae dbbdbbb faaaaag bbb bbbf faaagaaa bbb fbbb aaag aaa bbb bbbd aaag aaa bbb bbb aaaa eaa bbd dbbb aaaa caac cbbc bbbf aaaa aae dbb fbbb aaaa aaa bbb bbbd aaaa aaa bbb bbb aaaa aaa bbb dbbb aaaa gaa bbb bbbcf aaaa eaaf bbd fbbbbbbbbbddcf aaaa faae cbbc bbbbbbbbbbbbbbbbaaaacf aag dbb cddbbbbbbbbbbaaaabbbbbbbc aaa bbb cddaaaabbbbbbbbbbbbc aaa bbb gaaaf fcddbbbbbbbbbbbaaa bbb gaaaf cbbbbbbbaaabd bbb eaaaf cbbbbaabbbbbd bbd eaaaf caaabbbbbbbbdf cbbc eaaac aaacdbbbbbbbbbbdf dbb eaaac aaa fdbbbbbbbbbbdf bbb caaac aaa fdbbbbbbbbbbdf bbb caaae gaa fdbbbbbbbbbbdc bbb faaae eaaf fdbbbbbbbbb bbb faaae faae dbbbbb bbd faaag aag bbb cbbc faaag aaa bbb dbb aaag aaa bbb bbb aaag aaa bbb bbb aaag eaa bbb bbb aaaa caac bbb bbb aaaa aae bbb bbd aaaa aaa bbb cbbc aaaa aaa bbb dbb aaaa aaa bbb bbb aaaa gaa bbb bbb aaaa eaaf bbb f aaaa faae dbb aaaa aag dbb gaaa aaa dbb gaaa aaa dbb gaaaf aaa dbb gaaaf eaa dbb eaaaf caac cbbf eaaaf aae cbbf eaaaf aaa cbbf aaac aaa cbbc ac aaa cbbc gaa fbbc eaaf fbbc faae fbbc aag fbbd aaa bbd aaa bbd aaa bbd eaa bbd caac bbd aae bbd aaa bbb aaa bbb aaa bbb gaa bbb eaaf bbb faae bbb aag bbb aaa bbb aaaf bbb aaaaaae bbb faaaaaaaagf bbb fgaaaaaaaaae bbb caaaaaaaaagf bbb eaaaaaaaaaebbb cgaaaaaaaaa eaaaaaa fgaa ``` <!-- end of image -->
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This image looks interesting. I wonder if there are any intersections hidden in there? I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#ab635aff b,#9fedfdff c,#d8b9b5ff d,#e7f4f3ff e,#b88a7fff f,#99c697ff g,#b1d7b1ff ``` ```image dgggggggggggggggggggggggf dgggggggggggggggggggggggf dgggggggggggggggggggggggf dggggggggggeafggggggggggf dggggggggggaaaggggggggggf dggggggggggaaaggggggggggf dggggggggggaaaggggggggggf dggggggggggaaaggggggggggf ddd dggggggggggaaaggggggggggfdddbbbbbbbbbbbbbb dggggggggggeefbbbbbbbbbbbbbbbbbbbbbbbbbbbbd dddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddd bbd dddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbggggf bbd bbbbbbbbbbbbbbbbbbbbbbbbgggggaaaggggggggggf bbb bbbbbbbbbddd dggggggggggaaaggggggggggf bbb dbb dggggggggggaaafgggggggggf bbb dbb dggggggggggaaafgggggggggf dbb dbb dggggggggggaaaegggggggggf dbb dbb dgggggggggfaaaegggggggggf dbb bbb dgggggggggfaaaagggggggggf bb bbb dgggggggggeaaaagggggggggf bb bbb dgggggggggeaaaagggggggggf bbd bbb dgggggggggeaaaagggggggggf bbd bbb dgggggggggeaaaagggggggggf bbb bbb dgggggggggeaaaagggggggggf bbb bbd dgggggggggaaaaagggggggggf bbb bbd dgggggggggaaaaagggggggggf bbb bbd fffffffffaaaaafffffffffg dbb bb aaaaa dbb bb aaeaad bb bb aaeaac bb dbb aaeaac bbd dbb aacaac bbd dbb aacaae bbb bbb aaa aaa bbb db bbb caac aaa bbbdbbbbb bbb aaa eaa bbbbbbbbbb bbb eaad eaa dbbbbd dbbbd bbb daae caa bbffffffbbbbfffffffff bbb aaa caa dggggggggbbbbgggggggg bbd caac daa dgggggggggbbbbggggggg bbd aaa daa dggggggggggbbbbgggggg bbd eaa aa dggggggggggggbbbggggg bb daae aad dgggggggggggggbbbbggg bb aaa aac dggggggggggggggbbbggg bb caad aac dgggggggggggggggbgggg dbb aaa aac dgggggggggggggeaegggg dbb aaa aae dggggggggggeaaaaagggg dbb daac aae dgggggggeaaaaaaaaaggg dbb aaa aaa dggggeaaaaaaafgeaaggg dbb eaad eaa dfaaaaaaaafgggggfgggg aae eaa caaaaaaaegggggggggggggg aaa caa caaaaaaaeggggggggggggggggg caac caa caaaaaaacgggggggggggggggggggg aaa caa deaaaaaaac dgggggggggggggggggggg eaad daa deaaaaaaac dgggggggggggggggggggg daae aa caaaaaaaed dgggggggggggggggggggg aaa aad caaaaaaaed dgggggggggggggggggggg caac aad caaaaaaae dfggggggggggggggggggg aaa aaaaaaaaac dddddddddddddddddddd eaa aaaaaac daae eaac aaa caad aaa aaa daac aaa eaad aae aaa caac aaa eaad daae aaa caac aaa eaa daae aaa caad aaa aaa ac ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ab635aff b,#9eecfeff c,#d3b0acff d,#cff5ffff e,#bc8983ff f,#a4a8adff g,#e7d3d0ff ``` ```image ceg eaaag aaaae gaaaae gaaaaa gaaaaa gaaaaa gaaaaa gaaaaag caaaaag caaaaag caaaaac caaaaac dddddddbbbbb ceefffbdbbbbbbbbbbbbbbbbbbb dddddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb dbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddddddd bbbbbbbbbbbbbbbbbbbbbbffffffd bbbbbbbbddddddd eaaaaaa d aaaaaaa aaaaaaa aaaaaaag aaaaaaag aaaaaaag aaaaaaag aaaaaaac gaaaaaaac gaaaaaaac gaaaaaaae gaaaaaaae gaaaaaaae gaaaaaaae caaaaaaaa caaaaaaaa caaaaaaaa caaaaaaaag caaaaaaaag caaaaaaaag eaaaaaaaag eaaaaaaaac eaaaaaaaac eaaaaaaaac eaaaaaaaae eaaaaaaaae aaaaaaaaae aaaaaaaaae ``` <!-- end of image --> As I suspected, there's 2 intersections within area A. Alright, let's concentrate on the next area. I'm focusing my attention on this specific region, area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#ab645bff b,#9eedffff c,#d3afabff d,#c2f3ffff e,#c08b84ff f,#eef5f7ff g,#e7d2d0ff ``` ```image bbbbdf fbbbbbbbd bdd fbbbbbbbd dbbbbbbb dbbbbbbbf dbbbbbbbf fbbbbbbbd fbbbbbbbd dbbbbbbd dbbbbbbbf dbbbbbbbf fbbbbbbbd fbbbbbbbd dbbbbbbd dbbbbbd dbbbd fbb fff fceaae gceaaaaaac gcaaaaaaaaaaaf gcaaaaaaaaaaaaaac fgeaaaaaaaaaaaaaaaaaaf fceaaaaaaaaaaaaaaecaaaaac fceaaaaaaaaaaaaaaegf caaaae gceaaaaaaaaaaaaaaeg faaeg gcaaaaaaaaaaaaaaacg gg aaaaaaaaaaaaaaecg aaaaaaaaaaaecf aaaaaaaaecf aaaaaegf aacg g ``` <!-- end of image --> Area B doesn't meet the criteria for an intersection. Answer: A: 2; B: 0; 2 + 0 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#ab635aff b,#9eedffff c,#dcbfbbff d,#cff5ffff e,#b97f78ff f,#c89f9aff g,#eddedcff ``` ```image eac aae aaa aaa aaa dd aaa ddddbbbbbbbbbbbbb effdbbbbbbbbbbbbbbbbbbbbbbbbbbb ddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdddd bbd ddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdddd bbd bbbbbbbbbbbbbbbbbbbbbbdddd aaa bbb bbbbbbbbdddd aaa bbb bb aaag bbb dbb aaac dbb dbb gaaaf dbb dbb gaaaf bb dbb caaae bb bbb caaaa bb bbb caaaa bbd bbb faaaa bbd bbb faaaa bbd bbd eaaaa bbb bbd eaaaa bbb bbd eaaaa dbb bb aaaaa dbb bb aaeaa dbb bb aaeaag bb bb aaeaac bb dbb aafaac bbd dbb aafaaf bbd dbb aacaae bbd dbb aaa aae bbb dd bbb caac aaa bbbdbbbbb bbb aaa eaa dbbbbbbbbb bbb eaa faa dbbbbd dbbbd bbb aae faa bb bbbd bbd aaa caa bbbb bbd caac gaa bbbb bbd aaa aa bbbb bbd eaa aa dbbbd bb gaaf aag bbbd bb aaa aag bbb bb faag aac b bb aaa aaf caf dbb aaa aaf faaaaa dbb gaaf aae faaaaaaaaa dbb aaa aaa geaaaaaaac caa dbb faag eaa geaaaaaaeg g aae faa caaaaaaaeg aaa faa caaaaaaaf caac caa faaaaaaaf aaa gaa faaaaaaac eaa gaa geaaaaaaac aae aa geaaaaaaeg aaa aa caaaaaaaeg caac aag caaaaaaaf aaa aaaaaaaaaf eaa aaaaaac gaaf eaac aaa faag aaa aaa gaaf aaa faag aae aaa caac aaa eaa aae aaa caac aaa eaa gaaf aaa faag aaa aaa af ``` <!-- end of image -->
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This is the image I'm working with. The goal is to count the intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#c0c4d5ff b,#f7c5c3ff c,#f1f3f0ff d,#b2d7b2ff e,#f6dcdcff f,#96c996ff g,#a6d1a7ff ``` ```image caaaac cccccccccccccccccccccc caaaaaaaac fggggggggggggggggggggg aaaaaaaaaaaaac fddddddddddddddddddddd aaaa caaaaaaaaaac fddddddddddddddddddddd aaaa aaaaaaaaaae fddddddddddddddddddddd aaaa caaaaaaaaaac fddddddddddddddddbdddd aaaac caaaaaaaaaac fdddddddddddddddbbbddd aa caaac eaaaaaaaaaa fddddddddddddddbbbbddd caaa caaaa caaaaaaaaaaddddddddddddbbbbdddd caaa aaaa caaaaaaaaaaddddddddbbbbddddd caaa aaaa eaaaaaaaaaadddbbbbdddddd caaa aaaa fdaaaaaaaaaabbbddddddd caaa aaaa fddddaaaaaaaaaaadddddd ffgaaaffffffffffc aaaac fddddddddaaaaaaaaaaddd dddaaadddddddddgc eaaaac fdddddddbbbbaaaaaaaddd dddaaadddddddddgc caaaaae fddddddbbbbddddaaaaddd dddaaadddddddddgc caaaaaa fdddddbbbbdddddddddddd dddaaadddddddddgcaaaaaa fddddbbbbddddddddddddd dddaaaaddddddddaaaaaac fdddbbbbdddddddddddddd dddaaaaddddddaaaaaac fddbbbbddddddddddddddd dddaaaaddddaaaaaac fdbbbbdddddddddddddddd dddaaaaddaaaaaadc fbbbbddddddddddddddddd dddaaaaaaaaaaadgc bbbbdddddddddddddddddd ddbaaaaaaaaadddgc bbbbddddddddddddddddddd ddbaaaaaaadddddgc cbbbbgggggggggggggggggggg ddaaaaaadddddddgc cbbbbccccccccccccccccccccc ddaaaadddddddddgc cbbbb ddaaabdddddddddgc cbbbb ddaaabdddddddddgc cbbbb ddaaabbddddddddgc cbbbb ddaaabbddddddddgc cbbbb ddaaabbddddddddgc cbbbb ddaaabbbdddddddgc ebbbb ddaaabbbdddddddgc ebbbb ddaaabbbdddddddgc ebbbb ddaaabbbdddddddgc ebbbb ddaaaabbbddddddgc ebbbb ddaaadbbbddddddgc ebbbb ddaaadbbbddddddgc ebbbb ddaaadbbbddddddgc ebbbe ddaaaddbbbdddddgc ebbbe ddaaaddbbbdddddgc ebbbe ddaaaddbbbdddddgc ebbbe ddaaadddbbbddddgc ebbbe ddaaadddbbbddddgc bbbbe ddaaadddbbbddddgc bbbbe ddaaadddbbbddddgc bbbbe ddaaaddddbbbdddgc bbbbe ddaaaddddbbbdddgc bbbbe ddaaaddddbbbdddgc bbbbe ddaaaddddbbbbddgc bbbbc ddaaadddddbbbddgc bbbbc ffaaafffffbbbfffc bbbbc aaac bbbc bbbbc aaac cbbb bbbbc aaac bbb bbbbc aaa bbb bbbbc aaa ebbe bbbbc aaa bbb bbbbc aaa bbb bbbb aaa bbb bbbb aaa ebbe bbbb aaa bbb bbbb aaa bbb bbbb aaa bbbc bbbb aaa cbbb bbbb aaa bbb bbbb aaa bbb bbbb aaa ebbebbbb aaa bbbbbb aaa bbbbb aaa bbbb aaa bb aaa aaa aaa aaa aaa aaa aaa aaa ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#c0c3d6ff b,#f9c5c3ff c,#e1e2ebff d,#f4f0f3ff e,#fbdcdbff f,#d3d4e1ff g,#e2c5cbff ``` ```image caaaaaac caaaaaaf caaaaaaf caaaaaaf caaaaaaa caaaaaaa caaaaaaad caaaaaaad caaaaaaad caaaaaaac caaaaaaac df caaaaaaaf dfaa caaaaaaaf dfaaaa caaaaaaaf caaaaaa caaaaaaaa caaaaaaaa caaaaaaaa caaaaaaaaaa caaaaaaaa caaaaaaaaaaaa caaaaaaaad caaaaaaaaaaaac caaaaaaaacfaaaaaaaaaaac dfaaaaaaaaaaaaaaaaaaafd egaaaaaaaaaaaaaaaaafd dgaaaaaaaaaaaaaaafd gaaaaaaaaaaaaafd gaaaaaaaaaaafd faaaaaaaaaac caaaaaaaac caaaaaac caaaaage caaaaagb caaaaagb caaaaagbd caaaaagbe caaaaagbb caaaaagbbd caaaaagbbe caaaaagbbe caaaaagbbb caaaaagbbbd caaaaagbbbe caaaaagbbbb caaaaagbbbb caaaaagbbbbe faaaaagbbbbe faaaaagbbbbb faaaaagbbbbbd faaaaagbbbbbe faaaaacbbbbbb faaaaacbbbbbb faaaaadbbbbbbd faaaaadebbbbbe faaaaaddbbbbbb faaaaad bbbbbbd faaaaad ebbbbbe faaaaad ebbbbbe faaaaad bbbbbb faaaaad bbbbbbd faaaaad ebbbbbe faaaaad dbbbbbb faaaaad bbbbbb faaaaad ebbbbbe faaaaad ebbbbbe faaaaad dbbbbbb faaaaad bbbbbbd faaaaad ebbbbbe faaaaad dbbbbbb faaaaad bbbbbb faaaaad bbbbbbd faaaaad ebbbbbe faaaaad dbbbbbb faaaaad bbbbbbd faaaaad ebbbbbe faaaaad ebbbbbe faaaaad bbbbbb faaaaad bbbbbbd faaaaad ebbbbbe faaaaad dbbbbbb faaaaad bbbbbb faaaaad ebbbbbe ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Alright, let's concentrate on the next area. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#c0c3d6ff b,#f8c5c3ff c,#dee0e9ff d,#f3f2f5ff e,#fbe3e2ff f,#cfccdaff g,#f9d3d1ff ``` ```image d ebg ebbbg ebbbbbg ebbbbbbbg ebbbbbbbbd fcd ebbbbbbbbd aaafcd ebbbbbbbbd aaaaaaafc ebbbbbbbbd aaaaaaaaaafcd ebbbbbbbb aaaaaaaaaaaaaacd ebbbbbbbg aaaaaaaaaaaaaaaaafcd ebbbbbbbg cfaaaaaaaaaaaaaaaaaafcdebbbbbbbg dcaaaaaaaaaaaaaaaaaaafbbbbbg dcfaaaaaaaaaaaaaaaaaaffg dcfaaaaaaaaaaaaaaaaaafcd dcfaaaaaaaaaaaaaaaaaafc dcfaaaaaaaaaaaaaaaaaafcd gbbbfaaaaaaaaaaaaaaaaad gbbbbbbbffaaaaaaaaaaaaf gbbbbbbbg dcfaaaaaaaaac gbbbbbbbg dcaaaaaad gbbbbbbbg dcfaa gbbbbbbbg dd gbbbbbbbg gbbbbbbbg gbbbbbbbg gbbbbbbbg gbbbbbbbg gbbbbbbbe gbbbbbbbe gbbbbbbbe gbbbbbbbe gbbbbbbbe gbbbbbbbe bbbbbbbbe bbbbbbbe bbbbbbe bbbbbe bbbbe ``` <!-- end of image --> Aha! I've found 1 intersection inside area B! Answer: A: 1; B: 1; 1 + 1 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#c0c3d6ff b,#f9c5c3ff c,#e2e3ecff d,#f7f2f3ff e,#fadbdaff f,#d1d3e0ff g,#e2c4c9ff ``` ```image caaaad daaaaaaaac aaaaaaaaaaaafd aaaa caaaaaaaaaac aaaa dfaaaaaaaaac aaaa caaaaaaaaafd b faaad dfaaaaaaaaac bbb fa caaac faaaaaaaaaf bbbbd daaf daaaf caaaaaaaaaad bbbbd caaa aaaa dfaaaaaaaaac bbbbd caaa aaaa caaaaaaaaafd bbbbd caaa aaaa caaaaaaaaaagbb caaa aaaa dfaaaaaaaaac caaa faaad caaaaaaaaafd caaa caaaac bbbgaaaaaaa caaa caaaaaf bbbb faaa caaad caaaaaa bbbb d caaac daaaaaad bbbb caaac daaaaaad bbbb caaaf daaaaaad bbbb caaaa aaaaaac bbbb caaaa aaaaaac bbbb caaaafaaaaac dbbbb gaaaaaaaaf dbbbb gaaaaaaf dbbbb faaaaf dbbbb caaa dbbbb caag dbbbb caagd dbbbb caagb dbbbb caagb dbbbb caagb dbbbb caagbe dbbbb caagbb ebbbb faagbb ebbbb faagbbd ebbbb faacbbb ebbbb faacbbb ebbbb faacbbb ebbbe faadebbe ebbbe faaddbbb ebbbe faad bbb ebbbe faad bbbd ebbbe faad ebbe ebbbe faad bbb bbbbe faad bbb bbbbe faad bbbd bbbbe faad dbbb bbbbe faad bbb bbbbe faad bbb bbbbe faad ebbe bbbbd faad bbb bbbbd faad bbb bbbbd faad bbbd bbbbd faad dbbb bbbbd faad bbb bbbbd faad bbb bbbbd faa ebbe bbbbd faa dbbb bbbbd aaa bbb bbbbd aaa bbbd bbbbd aaa ebbe bbbb aaa bbb bbbb aaa bbb bbbb aaa bbbd bbbb aaa dbbb bbbb aaa bbb bbbb aaa bbb bbbb aaa ebbebbbb aaa bbbbbb aaa bbbbb aaa bbbb aaa bb aaa aaa aaa aaa aaa aaa aaa aaa ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#da6d76ff b,#82e4d7ff c,#c7a497ff d,#eb3e5aff e,#b1d7b1ff f,#e7f5f0ff g,#95ca96ff ``` ```image bb fbb b b bf bf b fb b b fb b b b b ff ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbdcgge b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebedceeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebecdceeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebedcaeeg ff eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeedcaeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeecceaeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeedeeaeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeedeedeeg bf eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeaceedeeg fb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeedeeedeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeedeeedeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeaceeedeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeedeeeedeeg ff eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeaeeeedeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeedeeeeedeeg b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeedeeeeedeeg b eeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeecaeeeeedeeg bf eeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeedeeeeeedeeg fb eeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeedeeeeeeaeeg b eeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeecaeeeeeeaeeg b eeedceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeedeeeeeeeaceg b eeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeedeeeeeeeaceg ff eeeeebeddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeaceeeeeeecceg b eeeeebeecddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeedeeeeeeeecceg b eeeeeebeeecdaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeedeeeeeeeecaeg b eeeeeebeeeeecdaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeaceeeeeeeeeaeg bf eeeeeebbeeeeeecdaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeedeeeeeeeeeeaeg b eeeeeeebeeeeeeeecdaeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeaeeeeeeeeeedeg b eeeeeeebeeeeeeeeeecdaeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeaeeeeeeeeeeedeg b eeeeeeeebeeeeeeeeeeecdaeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeedeeeeeeeeeeedeg b eeeeeeeebeeeeeeeeeeeeecdaeeeeeeeeeeeeeeeeeeeeebeeeeeeeeecaeeeeeeeeeeedeg ff eeeeeeeebeeeeeeeeeeeeeeecdaeeeeeeeeeeeeeeeeeebbeeeeeeeeedeeeeeeeeeeeedeg b eeeeeeeeebeeeeeeeeeeeeeeeecdaeeeeeeeeeeeeeeeebeeeeeeeeeedeeeeeeeeeeeedeg b eeeeeeeeebeeeeeeeeeeeeeeeeeecdaeeeeeeeeeeeeebeeeeeeeeeecaeeeeeeeeeeeedeg b eeeeeeeeebeeeeeeeeeeeeeeeeeeeecdaeeeeeeeeeeebeeeeeeeeeedeeeeeeeeeeeeedeg ff eeeeeeeeeebeeeeeeeeeeeeeeeeeeeeecdaeeeeeeeebeeeeeeeeeeedeeeeeeeeeeeeedeg b eeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeecdaeeeeebeeeeeeeeeeecceeeeeeeeeeeeedeg b eeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeecdaeeebeeeeeeeeeeedeeeeeeeeeeeeeedeg b eeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeecdabeeeeeeeeeeeedeeeeeeeeeeeeeedeg eeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeebaaeeeeeeeeeeaceeeeeeeeeeeeeeaeg eeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeebecdaeeeeeeeedeeeeeeeeeeeeeeeaeg eeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeebeeeecdaeeeeeedeeeeeeeeeeeeeeeacg eeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeecdaeeeaeeeeeeeeeeeeeeeeccg eeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeecdaedeeeeeeeeeeeeeeeeccg eeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeecdaeeeeeeeeeeeeeeeecag eeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecag eeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag eeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag eeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedg eeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed eeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeac eeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegd fffffffffffffffbffffffffffffffffbffffffffffffffffffffffffffffffffffffff d fb bf ca b fb df b b d fb bf fd b fb ac b b d fb bf d b b ca b b df fb fb d b b fd b b ac fb fb d b b b bf fbb b ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ef5f77ff b,#7fe6dbff c,#f7b0bcff d,#ed3c5aff e,#bef2ecff f,#fad7ddff g,#f28597ff ``` ```image bec b fdf eb gdc bb ddc ee gdgc eb dafg ebe dffg bb a fg be cc a b fd a bb cd a b dg d be dc d eb d d ebe gf df bb d df b cd df eb da dc bb cdc dc bb da dc be dc dg ee d dg bb gc dg bb a da bb be gd da ebe eb dd da bb bb dg ad eb bb a ad b b cg ad ddge eb fd gdf fgabc bb cd gdf fbda be ad gdf bbfddc be gdc cdc bb fgdac eb ad cdc bb fgda bbe dc fdg bb gdac bb d fdg eb fdda b cg fdg b fdda eb d dg ee fgdaf bb cd da b fddf ebe ad da be addf b cdc ad bb fada ee adf ad eb fdda bb dc ad b fadaf be d gd b fdda b fg gd b fddf eb d gd b fadaf bb fd cd bb fadg bb dd cd bb adgf b dg cd ebe cddg ee df cd bb cddg bb cc fd eb cadgf be af fd b cadgf b cd d ee addf eb ad d b cadg bb fdg d be cddgbe dd a bb caabf dg a eb ebcadgf d a b bb cddf cg gf e bbe cadgf gf gf b b cadg cd gf b ee adgf ad cc be eb cddg da cc eb be cddgd cc ebe eb cdda fc eb eb fg eb bb fg b bbe g ee b a b be d be bb a bb be f ebe eb bb eb ``` <!-- end of image --> Oh my, look at that! It's 2 intersections in area A! Answer: A: 2; 2 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#f06e83ff b,#7be5daff c,#f4a0aeff d,#ed3d5aff e,#abeee7ff f,#facfd7ff g,#d5f6f3ff ``` ```image eb bb b b ee eg b e b b ee b b e b ge gedf b b df b bgfdc b gb dfc eg b dfa b bg cc a b gb d a b b d d e eg cf d ge b d d b b d d b ee af d b b d d gg b fa d b ee a d b b d d b b b fa d eg eg ge d d ge b b d a b b bg cc a b dcg gb d af b fba b d cf ge bfda bg cc cc b eg fda gb d fc b b fda b d fc b b fda eg af fa eg gg fda b d a e b fda b a a b b fda ee a d b ge fda b d d e b fda b fa d ge b fda ee d d b ge fda b d d b b fda b fc d b b fda gb d d eg ge fda b d d b b fda bg cc d b b fda gb d d b ge cdab d d b baa af a b b cdc d a ge b cdc a cf b ee cdc af cf b b cdc d cc ge b cda fc b ee fc b b a ge b a b ge d b b fd ge bg ac b gb d b b d ge bg ca b gb df b b d ge eg fd b b ac b b d ge ee d b b ca b b df ge ee d b b fd b b ac ge ge d b b b bg gbb b ``` <!-- end of image -->
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I'm optimistic that I'll find some intersections in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#ba4896ff b,#545474ff c,#dfbcd6ff d,#b0d7b0ff e,#f0f2efff f,#c57bacff g,#97bc99ff ``` ```image af af af af af af af af aa aa aa aa aa aa gggaaggggggggggge dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddaaddddddddddde dddbaddddddddddde dddbbbbbbbggdddde dddaagbbbbbbbbbbbde ecccffaaaaac dddaaddddddgbbbbbbbbbbbgc eeeeeeeeeeeeeeeeeeeeeeee faaaaaaaaaaaaaaaaaac dddaadddddddddddeedbbbbbbbbbbgde gddddddddddddddddddddddge aaaaaaffccce dddaaddddddddddde cgbbbbbbbbbbggdddddddddddddddddddde aaa dddaaddddddddddde edbbbbbbbbbbbgdddddddddddddde eaaf dddfaddddddddddde gddgbbbbbbbbbdddddddddddecaac dddfaddddddddddde gddddddddggbbdddddddddddfaae dddfaddddddddddde gddddddddddbbddddddddddaaa dddfaddddddddddde gddddddddddbbdddddddddaaa dddfaddddddddddde gddddddddddbbddddddddaafe dddfaddddddddddde gddddddddddbbddddddgaagde dddfaddddddddddde gddddddddddbbdddddfaaddde dddfaddddddddddde gddddddddddbbddddaaadddde dddfaddddddddddde gddddddddddbbdddaaaddddde dddfaddddddddddde gddddddddddbbddaafdddddde dddfaddddddddddge gddddddddddbbgaagddddddde eeecaeeeeeeeeeee gddddddddddbbaaddddddddde cae gddddddddddbbadddddddddde cae gdddddddddabbddddddddddde cae gddddddddaabbddddddddddde cae gddddddgaagbbddddddddddde cac gdddddfaaddbbddddddddddde cac gddddaaadddbbddddddddddde eac gdddaaaddddbbddddddddddde eac gddaafdddddbbddddddddddde eac ggaagddddddbbddddddddddde eac faaddddddddbbddddddddddde eac aaadddddddddbbddddddddddde eac aaaddddddddddbbddddddddddde ac eaafgddddddddddbbddddddddddde ac caac gddddddddddbbddddddddddde af faae gddddddddddbbddddddddddde af caaa gddddddddddbbbbddddddddde af caaac gdddddddddddgbbbbddddddde af caaac dggggggggggggggbbbbggggge af caaaf cbbbb af eaaaf ebbbb af eaaaf ebbbb af eaaaf ebbbbe af aaaf ebbbbe af aaaa ebbbbe aa faaa bbbbe aa faaae bbbbe aaaaae bbbbc aaae bbbbc cc gbbbc gbbbc gbbbbbgc gbbbbbg ce ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ba4796ff b,#514f71ff c,#dbafcfff d,#75698aff e,#ebd7e6ff f,#ca78b1ff g,#9b9baeff ``` ```image caaa caaa caaa caaa caaae caaae caaae caaae caaae caaae eaaae eaaae eaaae eaaae eaaae eaaae eaaae eaaae eaaac eaaac eaaac eaaac eaaac eaaac aaac aaac aaac aaac aaac aaac aaac gbddfe dbbbbbbdggce bbbbbbbbbbbbbddggee gbbbbbbbbbbbbbbbbbbbdggce aaafggdbbbbbbbbbbbbbbbbbb aaaf ecggdbbbbbbbbbbb aaaf ecggdbbbbb aaaf ecg aaaf faaf faaf faaf faaf faaf faaf faaf faaf faaf faaf faaf faaf faaa faaa faaa faaa faaa faaa caaa caaa caaa caaa caaa caaa caaa ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Okay, let's proceed to the next area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#b94896ff b,#504f71ff c,#dac1d6ff d,#7f7e97ff e,#eee6edff f,#cd7eb5ff g,#adacbcff ``` ```image e bbbdggce bbbbbbbbbddgce bbbbbbbbbbbbbbbbdggce ggddbbbbbbbbbbbbbbbbbbdde ecgddbbbbbbbbbbbbbbd ecggddbbbbbbbb ecgdbbb gbbb gbbb e gbbb ca gbbbe caa gbbbe faaa gbbbe efaaaa gbbbe eaaaaac gbbbe caaaaac gbbbe caaaaae gbbbe faaaafe gbbbe efaaaaf cbbbe eaaaaac cbbbe caaaaac cbbbe caaaaae cbbbc faaaafe cbbbc efaaaaf cbbbc eaaaaac cbbbccaaaaac cbbbfaaaaae cbbbaaaafe cbbbaaaf cbbbaac cabbbac caabbbg faaabbbg efaaaabbbg eaaaaafbbbg caaaaacebbbg caaaaae ebbbg faaaafe ebbbg efaaaaf ebbbg eaaaaac ebbbg caaaaac bbbg caaaaae bbbg faaaafe bbbg efaaaaf bbbg eaaaaac bbbg caaaaac bbbg caaaaae bbbg faaaafe bbbg aaaaf bbbd aaac bbbd aac bbbd ae bbbd e bbbd bbbd dbbd dbbd dbbd dbbd dbbbde dbbbbbde edbbbbbbdc cdbbbbbbdc ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area B. Answer: A: 1; B: 1; 1 + 1 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#ba4897ff b,#515072ff c,#dfbfd7ff d,#787791ff e,#f0e7efff f,#d082b8ff g,#a2a2b3ff ``` ```image af af af af af af af aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa bae bbbbbbbgc aagdbbbbbbbbbdge eccfffaaaaac aa cgbbbbbbbbbbgc faaaaaaaaaaaaaaaaaaf aa egdbbbbbbbbbdge aaaaaaffccce aa cgbbbbbbbbbbgc aaa fa egdbbbbbbbbbdge eaaf fa cgbbbbbbbd caac fa egbb faae fa bb aaa fa bb aaa fa bb eaaf fa bb caac fa bb faae fa bb aaa fa bb aaa ca bb eaaf ca bbcaac cae bbaae cae bba cae abb cae eaabb cae caacbb cac faae bb cac aaa bb eac aaa bb eac eaaf bb eac caac bb eac faae bb eac aaa bb ac aaa bb ac eaaf db af caac db af faae db af caaa dbbd af caaac cbbbd af caaac cbbbd af caaaf ebbbd af eaaaf ebbbd af eaaaf ebbbb af eaaaf ebbbb af aaaa ebbbbe aa aaaa bbbbe aa aaaa bbbbe aa faaae dbbbe aaaaae dbbbc aaae dbbbc cc dbbbc dbbbc gbbbbdgc gbbbbbg ce ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#d81972ff b,#f04d97ff c,#f6afcfff d,#d985a5ff e,#f3f1efff f,#b1d6b1ff g,#96c995ff ``` ```image daaaad caaaaaaac eaaadbaaaaac eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaae caaaaae gfffffffffffffffffffffffffffffffffffffffaaac caaaaae gffffffffffffffffffffffffffffffffffffffaaad daaaaa gfffffffffffffffffffffffffffffffffffffaaabe baaaab gffffffffffffffffffffffffffffffffffffaaabfe baaaab gfffffffffffffffffffffffffffffffffffaaaaffe aaaaad gffffffffffffffffffffffffffffffffffbaaafffe eaaaaac gfffffffffffffffffffffffffffffffffdaaaffffe eaaaaac gffffffffffffffffffffffffffffffffdaaafffffe caaaaae gffffffffffffffffffffffffffffffffaaaffffffe caaaaae eac gfffffffffffffffffffffffffffffffaaafffffffe daaaa baaaac gffffffffffffffffffffffffffffbfaaadfffffffe bab daaaaaaac gffffffffffffffffffffffffffdbbaaadffffffffe ebaaaaaaadffffffffffffffffffffffffbbbaaadfffffffffe ebaaaaaaafffffffffffffffffffffbbbaaaaffffffffffe ebaaaaaaafffffffffffffffffbbbaaaabffffffffffe gfaaaaaaabffffffffffffdbbbaaaabbffffffffffe gfffdaaaaaaafffffffffbbbbdaaafbbffffffffffe gffffffdaaaaafffffffbbbbdaaaffbbdfffffffffe gfffffffffaaafffffdbbbbfaaafffbbbfffffffffe gfffffffffaaaffffdbbbdfaaaffffdbbfffffffffe gfffffffffaaafffbbbbffaaaffffffbbdffffffffe gfffffffffaaaffbbbbffaaadffffffbbbffffffffe gfffffffffaaadbbbdffaaadfffffffbbbffffffffe gfffffffffaaabbbfffaaabffffffffdbbffffffffe gfffffffffaaabbfffaaaaffffffffffbbdfffffffe gffffffffdaaabfffbaaafffffffffffbbbfffffffe cbd gfffffffdbaaafffdaaaffffffffffffdbbfffffffe bbb bc gffffffbbbaaaffdaaaffffffffffffffbbfffffffe ebbc bbb gfffffbbbbbaaffaaafffffffffffffffbbbffffffe bbb ebbb gfffdbbbdfbaafaaaffffffffffffffffbbbffffffe ebbc bbbe gffbbbbdffdaaaaafffffffffffffffffdbbffffffe bbb bbb gfbbbbffffdaaaadffffffffffffffffffbbdfffffe bbd cbbc gbbbbfffffdaaadfffffffffffffffffffbbbfffffe bbb bbb dbbbdffffffdaabffffffffffffffffffffdbbfffffe bbb ebbd bbbbfffffffffabffffffffffffffffffffffbbfffffe dbb bbbbbbbffffffffffffffffffffffffffffffffffbbdffffe bbb bbbbdgffffffffffffffffffffffffffffffffffbbbffffe dbb dbbc gffffffffffffffffffffffffffffffffffdbbffffe bbb c gfffffffffffffffffffffffffffffffffffbbdfffe cbbe fgggggggggggggggggggggggggggggggggggbbbggge bbb bbb cbbe cbb bbb bbc cbbc bbb bbb cbb ebbc ebbe bbb bbb ebbc bbb bbb cbb ebbd bbc bbb bbb bbd dbb bbb ebbe bbb bbd dbb bbb bbb cbb dbbe bbc bbb bbb cbbe bbb bbb cbbe cbbe bbc bbb bbb cbbc cbb bbb ebbc ebbc bbb bbb bbb ebbc cbb bbb bbc bbd bbb bbb dbb bbd ebbebbb bbdbbb bbbbb cbbbb bbbe bbb cb ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#d91872ff b,#f14b97ff c,#f7bad6ff d,#ed6ea9ff e,#fadeebff f,#f293beff g,#de3483ff ``` ```image ba daa daaa faaaa faaaaa caaaaaa caaaaaab egaaaaab egaaaaage gaaaaage baaaaaae daaaaaac daaaaaac faaaaaaf faaaaaaf caaaaaad caaaaaad egaaaaab egaaaaage egaaaaage baaaaage efbdedaaaaaac edbbbgaaaaaac cbbbbgaaaaaaf c fbbbbgaaaaaaf agdc edbbbbgaaaaaad aaaagde cbbbbbbaaaaaad aaaaaaagfe fbbbbbbaaaaaag aaaaaaaaaagfe dbbbbbbaaaaaaad aaaaaaaaaaaaagfe edbbbbbbaaaaaaabb efgaaaaaaaaaaaaabfe cbbbbbbbgaaaaaabbbc efgaaaaaaaaaaaaabfe fbbbbbbbgaaaaaabbbbf edgaaaaaaaaaaaaabf edbbbbbbbbaaaaaadbbbbd cdgaaaaaaaaaaaage ebbbbbbbbdaaaaaafebbbbbe cdgaaaaaaaaaad cbbbbbbbdfaaaaaaf bbbbbc cdaaaaaaaag fbbbbbbbfcaaaaaad fbbbbf cdaaaaag edbbbbbbbccaaaaaad cbbbbb eaaaaa cbbbbbbbdeeaaaaaab bbbbbe eaaaaa fbbbbbbbf egaaaaag dbbbbf eaaaaa edbbbbbbbc egaaaaage fbbbbd eaaaaa ebbbbbbbbe baaaaage ebbbbb eaaaaa cbbbbbbbde baaaaaac bbbbbc aaaaae fbbbbbbbf daaaaaac fbbbbf aaaaae edbbbbbbbc faaaaaaf cbbbbb aaaaae cbbbbbbbde faaaaaaf ebbbbbe aaaaaefbbbbbbbd caaaaaad dbbbbc aaaaadbbbbbbbf caaaaaad fbbbbd gaaaabbbbbbbc eaaaaaab cbbbbb gaaaabbbbbde egaaaaag bbbbbc gaaaabbbbf egaaaaage dbbbbf eaaaaagbbc baaaaage cbbbbd cbaaaaagde baaaaaac ebbbbbe fbbaaaaab daaaaaac bbbbbc dbbbaaaaac faaaaaaf fbbbbf edbbbbaaaaac faaaaaaf cbbbbb cbbbbbbaaaaaf caaaaaad bbbbbe fbbbbbbbgaaaaf caaaaaad dbbbbf edbbbbbbbcdaaaaf eaaaaaab fbbbbd ebbbbbbbbe daaaaf egaaaaag ebbbbbe cbbbbbbbde daaaafegaaaaage bbbbbc fbbbbbbbf daaaadbaaaaage fbbbbf edbbbbbbbc daaaaaaaaaaae cbbbbb cbbbbbbbde daaaaaaaaaac ebbbbbe fbbbbbbbf daaaaaaaaac dbbbbc edbbbbbbbc faaaaaaaaf fbbbbd ebbbbbbbbe faaaaaaad cbbbbb cbbbbbbbde faaaaaad bbbbbc bbbbbbbf faaaaab dbbbbf bbbbbbc eaaaag cbbbbd bbbbde daabe ebbbbbe bbbd ee bbbbbc bbf fbbbbf bc cbbbbb e bbbbbe dbbbbf fbbbbd ebbbbbe bbbbbc ``` <!-- end of image --> Yes! I knew it! There's 2 intersections right here in area A! Answer: A: 2; 2 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#d91972ff b,#f14b96ff c,#f8c3dbff d,#f07fb3ff e,#fbe3eeff f,#f5a0c6ff g,#ef62a3ff ``` ```image daaaad caaaaaaaf eaaadbaaaaac eaaae caaaaae aaac faaaaae aaaf daaaaa aaag gaaaab aaab baaaag baaa aaaaad gaaa eaaaaaf daaa eaaaaac caaa caaaaae eaaa faaaaae eaf eaaae daaaa baaaaf ebcaaac gab gaaaaaaac cbbaaaf gaaaaaaac gbbaaad ebaaaaaaae bbbaaab ebaaaaaabe ebbbaaaab eaaaaaaabe fbbbbaaabb caaaaaaae gbbbdaaaebbe caaaaa bbbbfaaa bbd aaa cbbbgeaaa bbb aaa dbbbfeaaae fbb aaa bbbbe aaac bbc aaa ebbbb aaaf bbg aaafbbbd aaad gbb aaabbbc aaab cbb aaabb baaa bbf caaag gaaa bbb cbd dbaaa daaa dbb bbb gf bbbaaa faaa ebbc ebbf bbb ebbbbgaa caaa bbg bbb ebbg fbbbd gaaeaaae bbb ebbf gbbe gbbbc daaaaac cbb bbb bbb bbbb daaaaf bbf bbd fbbc cbbbg daaad bbb gbb bbb dbbbf faab dbb bbg ebbd bbbbe ab ebbe dbb bbbbbbb bbd bbg bbbbg bbb dbb dbbc fbb bbb c bbc fbbe bbg bbb gbb fbbe cbb bbb bbf cbbc bbb bbb fbb ebbf bbc bbb bbg ebbf bbb bbb cbb bbd bbf gbb bbb bbd dbb gbb ebbe bbg bbd dbb bbb bbb fbb dbbe bbc bbb bbg fbbe gbb bbb cbb cbbc bbf bbb bbb cbbc fbb bbb bbc ebbf bbg bbb gbb ebbf cbb bbb bbf bbd bbb gbb dbb bbg ebbegbb bbdbbg bbbbb fbbbb bbbe bbb cb ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#2dddcaff b,#439f4dff c,#a5efe7ff d,#b1d7b1ff e,#66dfcbff f,#ebf6f0ff g,#8bc590ff ``` ```image ac ae aa aa aa ea ea ca faf ac ae aa aa aa ea ea ca faf ac ae aa aa aa ea ea cc ca aaa faf aaaaf ffffffacffffffffffffffffffffffffffffffffffffffacfaaefff ddddddaedddddddddddddddddddddddddddddddddddddgadddaaadg ddddddaadddddddddddddddddddddddddddddddddddddeaddddeaag ddddddaadddddddddddddddddddddddddddddddddddddaaddddddaae ddddddaadddddddddddddddddddddddddddddddddddddaadddddddaaa ddddddaadddddddddddddddddddddddddddddddddddddaadddddddgcaac ddddddeadddddddddddddddddddddddddddddddddddddaedddddddg faae ddddddeadddddddddddddddddddddddddddddddddddddaddddddddg aaa dddddddaedddddddddddddddddddddddddddddddddddeaddddddddg caac dddddddaadddgdddddddddddddddddddddddddddddddaaddddddddg aae ddddddddaadbbbgdddddddddddddddddddddddddddddaaddddddddg eaa ddddddddeabbgbbbgdddddddddddddddddddddddddddaaddddddddg caac dddddddddbbgddgbbbddddddddddddddddddddddddddaeddddddddg aaa ddddddddgbbaddddgbbbddddddddddddddddddddddddadddddddddg eaaf dddddddgbbeaedddddbbbbdddddddddddddddddddddeadddddddddg caac dddddddbbddaadddddddbbbbdddddddddddddddddddaadddddddddg aaa ddddddbbddddaaddddddddbbbbdddddddddddddddddaadddddddddg eaaf dddddbbgdddddaadddddddddbbbbdddddddddddddddaadddddddddg faac ddddbbgddddddaadddddddddddbbbbdddddddddddddaedddddddddg aaa dddgbbddddddddaaddddddddddddbbbgdddddddddddaddddddddddg eaaf ddgbbddddddddddaadddddddddddddbbbgddddddddeaddddddddddg faae dddgdddddddddddeaedddddddddddddgbbbgddddddaaddddddddddg aaa ddddddddddddddddaadddddddddddddddgbbbgddddaaddddddddddg eaaf dddddddddddddddddaaddddddddddddddddgbbbgddaaddddddddddg faae dddddddddddddddddeaedddddddddddddddddgbbbgaeddddddddddg aae ddddddddddddddddddaadddddddddddddddddddgbbbgddddddddddg c dddddddddddddddddddaaddddddddddddddddddddbbbbdddddddddg ddddddddddddddddddddaadddddddddddddddddddaabbbbdddddddg ddddddddddddddddddddaadddddddddddddddddddaaddbbbbdddddg dddddddddddddddddddddaaddddddddddddddddddaaddddbbbbdddg ddddddddddddddddddddddaadddddddddddddddddaeddddddbbbbdg ddddddddddddddddddddddeaeddddddddddddddddaeddddddddbbbb dddddddddddddddddddddddaadddddddddddddddeadddddddddddbbbg ddddddddddddddddddddddddaaddddddddddddddeaddddddddddddgbbbg ddddddddddddddddddddddddeaedddddddddddddaaddddddddddddg fbbbd dddddddddddddddddddddddddaadddddddddddddaaddddddddddddg dbbbd ddddddddddddddddddddddddddaaddddddddddddaeddddddddddddg dbbbd ddddddddddddddddddddddddddgaadddddddddddaeddddddddddddg dbbbf fffffffffffffffffffffffffffaacfffffffffcaffffffffffffff gbbbf aa ea gbbbf faa aa gbbb eac aa bbbb aa ae bbbb aa ac bbbg cae caf fbbbg aaf ea fbbbg aa aa fbbbd cae aa fbf aaf ae aa ac faaaf eaa aa ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#2cddcbff b,#409e4bff c,#9aeee5ff d,#a6d1abff e,#60e4d7ff f,#d3f2e9ff g,#6cb474ff ``` ```image eaac aaaf caaaaaf eaae faaaf faaaaac caae caaa feaaaae caaa caae caaaa caaa eaae faaa faaaf aaac ea faaaf aaaf c aaac faaaf aaac caaa eaac caae eaae eaae caae aaac caaa aaac caaa faaaf faaaf caaa faaac caae aaaa eaae caaae df aaac eaaac gbbgd aaac aaaaf dbbbbbgd faaaf faaaedbbbbbbbbgf caaa eaaabbbbdbbbbbbgf caaa aabbbbd dbbbbbbgf eaae fbbbbd dbbbbbbgf aaac gbbbbc dbbbbbbgf aaac dbbbbaaf fdbbbbbbdf faaaf dbbbbaaaa fgbbbbbbd caaa fbbbbfcaaae fgbbbbbbd caaa fbbbbd eaaac fgbbbbbbd eaae gbbbd aaaaf fgbbbbbbd eaac gbbbg caaae fgbbbbbbd aaac dbbbg eaaac dgbbbbbgd faaaf dbbbbf aaaaf dgbbbbbgf caaa fbbbbf faaae dbbbbbbgf caaa fbbbbd caaac dbbbbbbgf eaae gbbbd eaaaf dbbbbbbgf eaac gbbbg faaaa dbbbbbbgf aaac dbbbg caaae dbbbbbbgf faaaf dbbbbf eaaac fdbbbbbbdf faaa fbbbbf faaaaf fgbbbbbbd caaa gbbd caaae fgbbbbbbd eaae dd eaaac fgbbbbbbd eaac aaaaf fgbbbbbbd aaac faaae fgbbbbbgd faaaf caaac dgbbbbbgd faaa eaaaf dgbbbbbgf caaa faaaa dbbbbbbgf eaae caaae dbbbbbbgfeaae eaaac dbbbbbbbaac faaaaf dbbbbbbbc caaae fdbbbbbbdf eaaac fgbbbbbbd aaaaf eabbbbbbbd faaae eaaegbbbbbbd caaac aaac fgbbbbbbd eaaaf aaaf fgbbbbbbd faaaa faaaf fgbbbbbgd caaae caaa dgbbbbbgd eaaac caae dgbbbbbgf faaaa eaae dbbbbbbgf caaae aaac dbbbbbbg eaaac aaaf dbbbbb aaaaf faaaf dbbb faaae caaa fdb caaac caae f eaaaf eaae faaaa aaac caaae aaac eaaaf faaaf faaaa caaa caaae caae eaaac eaae aaaaf aaac faaae aaac ``` <!-- end of image --> Success! This area contains 2 intersections point! Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#2dddcbff b,#409d4aff c,#a0efe7ff d,#9dcda3ff e,#66e6d9ff f,#d5f2eaff g,#69b372ff ``` ```image ac ae aa aa aa ea ea ca faf ac ae aa aa aa ea ea ca faf ac ae aa aa aa ea ea cc ca aaa faf aaaaf ac acfaae ae faf aaa aa ea caaf aa aa aae aa aa aaa ea ae caaf ea ac aae ca faf aaa fac ca caac aa f aa aae aa bbbf aa eaa eabbdbbbf aa caac bbd dbbbf ac aaa dbba dbbbf faf eaa fbbcae gbbb ca faac bb aaf gbbb aa aaa bb aa gbbg aa eaaf bbf fae bbbg aa faac gbd eaf bbbg ae aaa dbg aa bbbd faf eaaf fbb faa fbbbd ca faae d eac fbbbd ea aaa aa fbbbd aa eaaf aa dbbbf aa faae cae dbbbfae aae aaf dbbbc c aa gbbb fae eagbbb eaf aa gbbb aa aa gbbg faa ae bbbg eac ac bbbg aa ca fbbbd aa ea fbbbd cae aa fbbbd aa aa fbbbd aa ae dbbbf fae ac dbbbf aaf ca dbbbf aa ea dbbb faa aa gbbb eac aa gbbg aa ae gbbg aa ac bbbg cae ca bbbg aa ea fbbbd aa aa fbbbd cae aa fbf aaf ae aa ac faaaf eaa aa ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#569ec9ff b,#189d0cff c,#b1d7b1ff d,#57b652ff e,#c9e1e6ff f,#84baceff g,#94cb93ff ``` ```image ebg bb bb dbc bb bb dbe ebd bb cggggggggggggggggggggggggggc bb gccccccccccccccccccccccccccg cbd gcccccccccccccffcccccccccccg bb gcccccccccccccaacccccccccccg bb gcccccccccccccaacccccccccccg gbg gccccccccccccfaacccccccccccg bb gccccccccccccaaacccccccccccg bb gccccccccccccaaacccccccccccg dbc gccccccccccccaaafccbcccccccg bb gccccccccccccaaafcbbbccccccg bb gcccccccccccfacafbbbbgcccccg dbe gcccccccccccaacabbbcbbcccccg ebd gcccccccccccaacbbbccdbdccccg bb gcccccccccccaabbbccccbbccccg bb gccccccccccfadbbaccccdbbcccg cbd gccccccccccadbbaacccccbbcccg bb gccccccccccdbbcaacccccgbbccg bb gcccccccccgbbccaaccccccbbgcg gbg gccccccccgbbfccfaccccccgbbcg bb gcccccccgbbacccfafccccccbbgg bb gccccccgbbaaccccafcccccccbbg dbc gccccccbbgaaccccafcccccccdbd bb gcccccbbdcafccccaaccccccccbb bb gccccbbdcfacccccaaccccccccdbd dbe gcccbbdccaacccccaacccccccccbb eccggddg ebd gccbbdcccaacccccaacccccccccdbbcggdddbbbbbbbbbbbbbbbbbbbbd bb gcbbbccccaacccccaacccccccccgbbbbbbbbbbbbbbbbbbbdddggcee bb gbbbccccfafcccccaacccccccccg ggcce cbg bbbcccccaaccccccaacccccccccg bb dbbccccccaaccccccfacccccccccg bb dbbcccccccaaccccccfafccccccccg gbg dbbgcccccccafccccccfafccccccccg bb gbb gccccccfagcccccccafccccccccg bb cbb aa af dbc cbb aa aa bb ebbe af aa bb ebbe eae aa dbebbc aa aa ebbbc aa aa bbg aa fa gg eaf fa fa eae aa eae ae aa af eaaf af af faae fae aa aaa aa aa aaa aa aa aaa aa aa eaaf eae aa faae eaa fa aaa eaaaaaa fa aaa faaaaaaae eae aaf efaaaaaafe eae eaae eaaaaaaafe af faae faaaaaaaf af aaa efaaaaaaae aa aaa aaaafe aa eaaf f aa faae aa faa aa aaa fa aaa fa eaaf eae faae eae aaa af aaa af aaf aa eaae aa faae aaaaa aaaa aaf e ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#569fc9ff b,#179d0bff c,#a4d8a1ff d,#3aab35ff e,#cfe5e5ff f,#96c3ddff g,#63ba67ff ``` ```image efe eaaae faaae faaaf aaaaf eaaaaf eaaaaf faaaaa aaaaaa aaaaaa eaaaaaa faaaaaae aaaaaaae cdg aaaaaaae cbbbg eaaaaaaaf cbbbbbe faaafaaaf cbbbbbbd faaaeaaafebbbbbbbbc aaaa aaaabbbbdcbbbd eaaaf aaabbbbde dbbbc eaaaf aabbbbbe cbbbb faaae abbbbbe gbbbg aaaa dbbbbe ebbbbe aaaf dbbbbc gbbbg eaaafdbbbbge ebbbbe faaadbbbbgae cbbbd faadbbbbgaaf dbbbc aadbbbbgaaaf cbbbd eadbbbbg aaaf dbbbc egbbbbg aaaf cbbbb gbbbbg aaaa gbbbg cbbbbd aaaa ebbbbe cbbbbd faaa gbbbg cbbbbbf faaa ebbbbe ebbbbbae faaae cbbbd ebbbbbaa faaae dbbbc edbbbbaaa eaaae cbbbd edbbbbaaaf eaaaf dbbbc dbbbbcaaae eaaaf ebbbb dbbbbcfaaae aaaf gbbb dbbbbc aaaa aaaf ebbb gbbbbc aaaf aaaa gbb gbbbbc eaaaf aaaa ebb gbbbbg faaae faaa cb gbbbbg aaaa faaa d cbbbbg aaaf faaae c cbbbbg eaaaf faaae cbbbbd faaae eaaae cbbbbd faaa eaaaf cbbbbd aaaa eaaaf ebbbbde eaaaf aaaf ebbbbde eaaae aaaf ebbbbbe faaae aaaa edbbbbe aaaa aaaa dbbbbe aaaf faaa bbbbc eaaaf faaa bbbc faaae faaae bbc faaa faaae bc aaaa eaaae c eaaaf eaaaf eaaae eaaaf faaae aaaf ``` <!-- end of image --> Area A contains 2 intersections. Answer: A: 2; 2 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#579fcaff b,#179d0bff c,#afddabff d,#48b043ff e,#d2e7e8ff f,#9ac5dfff g,#7dc877ff ``` ```image ebg bb bb gbc bb bb dbe ebd bb bb cbg ee bb aa bb aa gbg faa bb aaa bb aaa gbc aaae d bb eaaaf bbb bb faeafbbbbc dbe aa abbb bb ebd aa bbb dbg bb afdbb bb bb fadbba gbd cbg adbbaa bb bb dbb aa cbb bb cbb aa bbe gbc cbbf fa ebb bb ebba fae bbc bb ebbaa eaf bb gbc bbcaa af dbg bb bbc af aa bb bb bbg fae aa gbd dbe bbg aa aa bb ecccggdc ebd bbd aa aa cbbccggddbbbbbbbbbbbbbbbbbbbbg bb bbd aa aa bbbbbbbbbbbbbbbbbbbddggccee bb bbb eaf aa gccce cbg dbb aa aa bb dbb aa fa bb dbb aa fae gbc gbb eaf eaf bb gbb fae af bb cbb aa aa gbc cbb aa aa bd ebbe aa aa bb ebbe fae aa dbebbc aa aa ebbbc aa aa bbg aa aa cc eaf fa fa fae aa eaf ae aa af eaaf af aa faae fae aa aaa aa aa aaa aa aa aaa aa aa eaaf eaf aa faae eaa aa aaa faaaaaa fa aaa efaaaaaaaf fae eaaa efaaaaaaae eaf faaf faaaaaaafe af faae faaaaaaaf aa aaa efaaaaaaae aa aaa aaaafe aa eaaf f aa faae aa aaa aa aaa aa aaa fa eaaf fae faae eaf aaa af aaa aa aaa aa eaaf aa faae aaaaa aaaa aaf e ``` <!-- end of image -->
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Let's examine this image for potential line intersections. There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#757658ff b,#267574ff c,#b1d7b1ff d,#ebf0ebff e,#8d9779ff f,#5e9c8fff g,#98c299ff ``` ```image dgccccccccccccccccccccccccccccccccccccccccccccccccccc dcccccccccccccccccccccccccccccccccccccccccccccccccccc dcccccccccccccccccccccccccccccccccccccccccccccccccccc dcccccccccccccccccccccccccccccccccccccccccccccccbgccc dccccccccccccccccccccccccccccccccccccccccccccccbbgccc dcccccccccccccccccccccccccccccccccccccccccccccgbbcccc dcccccccccccccccccccccccccccccccccccccccccccccbbccccc dccccccccccccccccccccccccccccccccccccccccccccfbfccccc dccccccccccccccccccccccccccccccccccccccccccccbbcccccc dcccccccccccccccccccccccccccccccccccccccccccbbgcccccc dccccccccccccccccccccccccccccccccccccccccccgbbccccccc dccccccccccccccccccccccccccccccccccccccccccbbcccggccc dcccccccccccccccccccccccccccccccccccccccccbbfcccaeccc dcccccccccccccccccccccccccccccccccccccccccbbcccgaeccc dfbbccccccccccccccccccccccccccccccccccccccccbbccccgagccc dfbbbbbfccccccccccccccccccccccccccccccccccccccfbfccccgagccc fbbbbf bbccccccccccccccccccccccccccccccccccccccbbcccccgagccc fbbbfd fbgccccccccccccccccccccccccccccccccccccbbgccccceagccc gbbd dbbcccccccccccccccccccccccccccccccccccgbbcccccceacccc cbb dbbcccccccccccccccccccccccccccccccccccbbccccccceacccc dbb dfbfcccccccccccccccccccccccccccccccccfbfccccccceacccc dbbd dcbbcccccccccccccccccccccccccccccccccbbcccccccceacccc bbd dcbbgcccccccccccccccccccccccccccccccbbgcccccccceacccc bbc dccbbccccccccccccccccccccccccccccccfbbcccccccccaacccc bbf dccbbccccccccccccccccccccccccccccccabccccccccccaacccc bbf dccfbfccccccccccccccccccccccccccccaaaccccccccccaacccc fbb dcccbbcccccccccccccccccccccccccccaaaaccccccccccaacccc fbb dcccbbccccccccccccccccccccccccccaaaaaccccccccccaacccc cbb dcccgbbccccccccccccccccccccccccaaafeagcccccccccaacccc dbb dccccbbccccccccccccccccccccccgaabbccaecccccccccaacccc dbbd dccccfbgcccccccccccccccccccceaabbgccaacccccccccaacccc bbd dcccccbbccccccccccccccccccceaagbbcccaacccccccccaacccc gggggggggggbbc dcccccbbccccccccccccccccccaaacbbccccaacccccccccaacccc ccccccccccbbf dcccccgbfccccccccccccccccaaacfbfcccceacccccccccaacccc cccccccccbbfg dccccccbbcccccccccccccccaaaccbbcccccgaeccccccccaacccc ccccccccbbbcg dccccccfbgcccccccccccccaaeccbbgccccccaaccccccccaacccc cccccccfbbccg dcccccccbbcccccccccccgaagccfbbcccccccaaccccccccaacccc ccccccfbbcccg dcccccccbbccccccccccgaagcccbbccccccccaaccccccccaacccc cccccgbbccccg dcccccccgbfcccccccceaaccccbbgcccccccceaccccccccaecccc ccccgbbcccccg dccccccccbbcccccccaaaccccgbbcccccccccgagcccccccaecccc ccccbbccccccg dccccccccfbgcccccaaacccccbbcccccccccccaecccccccaecccc cccbbgccccccg dcccccccccbbccccaaacccccfbfcccccccccccaacccccccaecccc cccbfcccccccg dcccccccccbbcccaaeccccccbbccccccccccccaaccccccgaecccc ccccccccccccg dcccccccccgbfcaaeccccccbbgccccccccccccaaccccccgagcccc ccccccccccccg dccccccccccbbaagccccccgbbccccccccccccceagcccccgagcccc ccccccccccccg dccccccccccaaaccccccccbbcccccccccccccccaecccccgagcccc ccccccccccccg dccccccccceaabcccccccbbfcccccccccccccccaacccccgagcccc ccccccccccccg dccccccccaaabbcccccccbbccccccccccccccccaaccccceagcccc cccaecccccccg dcccccccaaacfbfcccccbbcccccccccccccccccaaccccceaccccc cccaecccccccg dccccccaaecccbbccccfbfccccccccccccccccceaccccceaccccc gggaagggggggc dcccccaaeccccbbccccbbccccccccccccccccccgaecccceaccccc ae dcccgaagccccccbbccbbgcccccccccccccccccccaacccceaccccc aa dccgaagcccccccbbcgbbccccccccccccccccccccaaccccaaccccc aa dceaacccccccccfbfbbcccccccccccccccccccccaaccccaaccccc aa daaacccccccccccbbbfccccccccccccccccccccceaccccaaccccc aa aaaccccccccccccbbbccccccccccccccccccccccgagcccaaccccc aa aaacccccccccccccgbgcccccccccccccccccccccccaecccaaccccc aa aaeccccccccccccccccccccccccccccccccccccccccaacccaaccccc aa daacdccccccccccccccccccccccccccccccccccccccccaacccaaccccc aa caad ggggggggggggggggggggggggggggggggggggggggaagggaaggggg aa gaad cad aa aa eaa dag aa aa aaa aa aa aa aaa aa aa ea aae aa aa ea daag gad aa ea daac dac ae ga caad ae ae gad eaa aa ae cad eaa aa ae cad aaa ea ag cad aae cacag cac daae aeac dac daac aaac dac caad aaac dag gaad aaad ag eaa gaad ae aaa daad ae aaa aad ae aae aa aaaag aa aaac ga aad d ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#77775aff b,#257474ff c,#a6c6c6ff d,#d7e2e0ff e,#9c9c87ff f,#4d8e8eff g,#7aaaaaff ``` ```image gb cbb cbbb dbbbb dbbbbf dbbbbf fbbbf fbbbbd fbbbbd gbbbbd gbbbbc cbbbbc cbbbbg dbbbbg dbbbbf dfbbbf fbbbfd fbbbbd gbbbbd cbbbbc gbbc gg dddd aaae aaae aaae ``` <!-- end of image --> No intersection found in area A, but I won't give up. Okay, let's direct our attention to the next zone. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#757558ff b,#267575ff c,#c8d1cbff d,#e6eae8ff e,#94947dff f,#5e9898ff g,#a7b7adff ``` ```image dg cbbbb bbbbc gbbbf dbbbbd fbbbg cbbbb dbbbbc fbbbf cbbbbd fbbbg bbbf dbbbd fbbg cbbb bbbc gbbf cccd fbbb daaag gbbbf daaag dbbbbc daaag d fbbbf daaac f cbbbbd caaac bd bbbbg caaac bf gbbbf caaac bb dbbbbd caaac bbg fbbbg caaac bbf cbbbb caaad bbbd dbbbbc gaaad bbbg fbbbf gaaad bbbb cbbbbd gaaad gbbbc fbbbg gaaad dbbbf gbbbf gaaa fbbbd dbbbbc gaaa bbbb cbbbbd eaaa fbbbc bbbbc eaaa dbbbf bbbf eaaa fbbb dbbbd eaae gbbb fbbg eaae dbbb gbbb eaae fbbc dbbbc aaae cbbf faaf aaae fbbd caaad aaae gbbg caaaad aaae dbbf caaaaac aaag fbbc caaaaaag aaag cbbf gaaaaaaae daaag bbb eaaaaabeae daaag bbbg eaaaaabceaa daaag bbbf deaaaaabf gaad daaag cbbbf caaaaabbbg daag caaac bbbb caaaaabbbf aae caaac gbbbc aaaaabbbbc eaa caaac dbbbf gaaaefbbbf gaad caaac fbbbd eaaaecbbbbd caac caaac cbbbg deaaag bbbbg daag caaad bbbb deaaag gbbbf aae gaaad gbbbc daaaaa dbbbbd aaa gaaad dbbbf caaaaac fbbbg aaad gaaad fbbbd gaaaaad cbbbb aaac gaaad gbbbg gaaaaed bbbbc aaag gaaa bbbb eaaaae bbbf aaae gaaa fbbbc deaaaae cbbbd eaae eaaa cbbbf deaaaag fbbg eaaa eaaa fbbbd daaaaac gbbf gaaad eaaa gbbbg caaaaac dbbbc caaac eaae fbbbc gaaaed cbbbd aaae eaae cbbbf gaaaed bbbb eaaa eaae bbbbd eaaae gbbbf gaaad aaae gbbbg deaaag dbbbbd caaac aaae dbbbf daaaaa fbbbg daaag aaae fbbbc caaaaac gbbbb aaae aaag cbbbf caaaaac dbbbbc eaaa aaag bbbb gaaaaad fbbbf gaaad daaag gbbbg gaaaaed cbbbbd caaac daaag dbbbf eaaaae fbbbg daaag daaag fbbb deaaaag gbbbf aaae daaag cbbb deaaaag dbbbbd eaae daaac bbbcaaaaac fbbbg eaaa caaac gbbaaaaac cbbbb gaaad caaac dbbaaaad bbbbc caaac caaac aaaaed gbbbf daaag caaac eaaaab fbbbg eaaa caaad deaaaabbc gbbbf gaaad gaaad daaaaagbbf bbbbc caaac gaaad caaaaac bbbd bbbf daaag gaaad caaaaad bbbg cbbbd aaae gaaad gaaaaed bbbb bbbc eaaa gaaa gaaaaed fbbbc gbbf gaaad gaaa eaaaae cbbbf dbbbd caaac eaaa deaaaag fbbbd fbbg caaag eaaa deaaaag gbbbg cbbb aaae eaaa aaaaac dbbbf dbbbb eaae eaaa caaaac fbbbc fbbbf eaaa eaae caaaad cbbbf cbbbbd gaaad eaae gaaaed bbbbd fbbbg caaac eaae eaaae gbbbggbbbf daaag aaae eaaaa dbbbbbbbbd aaae aaae aaaaac cbbbbbbd gaaad aaae aaaac bbbbbc caaac aaag aaad gbbbf daaag aaag aed dbbbd aaae daaag ed dgd eaaa daaag gaaad daaag gaaac daaag caaag daaac ``` <!-- end of image --> Area B contains 2 intersections. Answer: A: 0; B: 2; 0 + 2 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#757557ff b,#267575ff c,#bfc8c0ff d,#e1e6e3ff e,#8f8f77ff f,#619b9bff g,#a3afa2ff ``` ```image bc bbc dbb bb fbf bb bbd cbb bb cd fbg dag dbb dac dbbb bbd dac dfbbbbbf gbf cac fbbbbf bb bb cad fbbbfd fbd bbc cad gbbd bb dbb gad cbb bb bb ga dbb cbg fbf ga bbd bb bb ea bbd fbd bbd ea bbc bb cbb ea bbf bb ab aa bbf gbg aaa aa fbb bb aaaa aa fbb bb aaaea aa cbb dbf daaafcad aa dbb bb daabb dag aa dbb gbc caabbd aa aa bbd bb eaacbb aa aa bbc bb eaa bb aa aa bbg dbf aaa fbg gad aa bbf bb aae bb dac aa bbb fbc aag bbd ae aa fbb bb daac gbf aa aa gbb bb caad bb aa ae cbb dbf gaa bbc ea ae dbb bb eaa dbb cac ae bbd fbd aaa bb ae ag bbd bb aae fbf aa ag bc bb aae bb aa dag cbgdaag bbd ea dac bbaad cbb cad dac aaad bb dag cac eaab fbg aa cad eaabb dbb aa cad ag aaa cbg bbd aa gad ae aae bb gbf gad ga ae daag fbd bb dac ga ae daac dbb bbc ae ea aa caad bb dbb aa ea aa gaa gbcbb aa ea aa eaa bbbf ea aa aa aaa bbb cac aa aa aae dbd ae aa aa aae aa aa aa daac aa aa aa caad ea aa aa gaad gad aa aa eaa dag aa aa aaa aa aa aa aaa aa aa ea aae aa aa ea daag ga aa ea daac dac ae ga caad ae ae ga eaa aa ae gad eaa aa ag cad aaa ea ag cad aae cacag cac aag aeac dac daac aaac dac caad aaac dag gaa aaad ag eaa gaad ag aaa daad ae aae aa ae aae aa aaaag aa aaac ga aad d ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#69bd9fff b,#5d9203ff c,#b1d7b1ff d,#91ba67ff e,#74a637ff f,#94ca9dff g,#e7f3ebff ``` ```image aac gaaa aaaag aaaaa gaaaaa aaacaaf aaa aaa gaaf faag aaag aaa aaa aaag gaaf gaaa aaag aaa aaa caac gaaf aaa faag aaag aaa gaaa gaaa aaa faag gaaf aaa aaa gaaa faac faag aaa aaa aaag gaaa gaaa faag aaa gbe aaa caac bbb aaa aaa bbbg faag faag bbbc aaa aaa bbbd aaa aaa bbbe caag gaaf bbbb aaa aaa bbbb aaa caac cbbbb caag aaa ffffffdbbbbffffffaaaffff aaag ccccccebbbbfcccccaaaccccg gaaa ccccccebbbbdccccfaafccccg aaa ccccccbbbbbeccccaaacccccg caaf ccccccbbbbbbccccaaacccccg aaa ccccccbbbbbbcccfaafcccccg faac ccccccbbbbbbcccaaaccccccg aaa ccccccbbbbbbcccaaaccccccg aaag ccccccbbeebbccfaafccccccg gaaa cccccfbbedbbfcaaacccccccg aaa cccccdbbddbbdcaaacccccccg caac cccccdbbfcbbefaafcccccccg aaa cccccebbccbbbaaaccccccccg aaag cccccbbbccbbbaaaccccccccg gaaa cccccbbbccbbbaafccccccccg aaa c cccccbbbccbbbaacccccccccg gaaf aaa cccccbbbccebbaacccccccccg aaa aaaag cccccbbbccdbbafcccccccccg faac aaaag cccccbbbccfbbeccccccccccg aaa gaaaa cccccbbecccbbeccccccccccg aaag gaaaa ccccfbbdccfbbbccccccccccg gaaa gggggggggggggg caaaa ccccdbbdccabbbccccccccccg aaafccccccccccccccf faaaf ccccebbfccabbbccccccccccg caaaccccccccccccccf aaaac ccccebbccfabbbccccccccccg aaaccccccccccccccf aaaag ccccbbbccaaebbccccccccccg faafcccccccccccccf aaaag ccaabbbccaaebbdcccccccccg aaacccccccccccccfgaaaa ccaabbbcfaaabbecccccccccg aaacccccccccccccfaaaa cccabbbcaaacbbecccccccccg gaaacccccccccccaaaaf cccabbbcaaacbbbcccccccccg aaaccccccccccaaaac cccfbbbfaafcbbbcccccccccg aaafccccccccaaaag ccccbbeaaaccbbbcccccccccg faaacccccccaaaaf cccfbbeaaaccbbbcccccccccg faaaccccccaaaacf cccdbbaaaaccebbfccccccccg fcaaacccfaaaaccf cccebbaaacccdbbdccccccccg fcaaaccfaaaacccf cccebbaaaccccbbeccccccccg fcfaaaaaaaaccccf cccbbbaaaccccbbbccccccccg fccaaaaaafcccccf cccbbbfacccccbbbccccccccg fccaaaaacccccccf cccbbbcccccccbbbccccccccg fcccaaaccccccccf cccbbbcccccccbbbccccccccg fcccfacccccccccf cccbbbcccccccebbccccccccg fccccccccccccccf cccbbecccccccdbbfcccccccg fccccccccccccccf ccfbbecccccccdbbdcccccccg fccccccccccccccf ccdbbdccccccccbbecccccccg fccccccccccffddedeebbbbbbbbbbbb ccdbbfccccccccbbbcccccccg ggccfddeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ccebbcccccccccbbbccccccfcccfddeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeed ccbbbcccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeddfdg ccbbbcccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbeeddcccg fccccccccccccccf ccccfcccccccccfbbbbbbeeedccgg cffffffffffffffc ccccccccccccccccccccccccg cccccccccccccccccccccccfg ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#69bd9eff b,#5d9203ff c,#9fd4c1ff d,#9ebe69ff e,#76a73cff f,#c1d59fff g,#dbebd8ff ``` ```image fbbbbbbbbe aaaaaa fbbbbbbbbe gaaaaac dbbbbbbbbb caaaaag dbbbbbbbbbg aaaaaa ebbbbbbbbbg gaaaaac ebbbbbbbbbf caaaaag bbbbbbbbbbd aaaaaa bbbbbbbbbbd gaaaaac bbbbbbbbbbe caaaaag gbbbbbbbbbbb aaaaaa fbbbbbbbbbbb gaaaaac fbbbbbbbbbbbg caaaaag fbbbbbebbbbbf aaaaaa dbbbbbfbbbbbf gaaaaac dbbbbbgbbbbbd caaaaag ebbbbb bbbbbd aaaaaa ebbbbe bbbbbe gaaaaac bbbbbe ebbbbb caaaaag bbbbbe dbbbbb aaaaaa gbbbbbd dbbbbbg gaaaaac gbbbbbd fbbbbbf caaaaac fbbbbbf fbbbbbf aaaaaa fbbbbbf gbbbbbd gaaaaac dbbbbbg bbbbbe caaaaac dbbbbbg bbbbbe aaaaaag dbbbbb ebbbbbgaaaaaa ebbbbb dbbbbbcaaaaac ebbbbe dbbbbbaaaaaag bbbbbe fbbbbbeaaaaa bbbbbd gbbbbbeaaaac gbbbbbd gbbbbbeaaaag gbbbbbf bbbbbeaaaa fbbbbbf ebbbbbaaac fbbbbbf ebbbbbaaag dbbbbbg dbbbbbaaa dbbbbbg fbbbbbaac ebbbbb fbbbbbeag ebbbbb gbbbbbea bbbbbe gbbbbbec bbbbbe bbbbbbg gbbbbbd bbbbbb gbbbbbd gebbbbb fbbbbbf cebbbbbg fbbbbbf aebbbbbf fbbbbbg gaebbbbbf dbbbbbg caabbbbbd dbbbbb aaabbbbbd ebbbbb gaaabbbbbe ebbbbe caaabbbbbb gcbbbbbe aaaaebbbbb caaabbbbbd gaaaaebbbbbg caaaabbbbbd caaaaebbbbbf gaaaabbbbbd aaaaaabbbbbf aaaebbbbbf gaaaaacbbbbbd caaebbbbbf caaaaagbbbbbe aaebbbbbg aaaaaa bbbbbe caebbbbbg gaaaaac ebbbbb gaebbbbb caaaaag dbbbbbg abbbbbb aaaaaa dbbbbbg cbbbbbe gaaaaac fbbbbbf gbbbbbe caaaaag gbbbbbd bbbbbegaaaaaa gbbbbbd gbbbbbeaaaaaac bbbbbe gbbbbbeaaaaaag ebbbbe fbbbbbeaaaaaa ebbbbb fbbbbbaaaaaac dbbbbbg dbbbbbaaaaaag dbbbbbg dbbbbbaaaaaa fbbbbbf ebbbbbaaaaac gbbbbbd ebbbbbaaaaag gbbbbbd bbbbbbaaaaa bbbbbe bbbbbeaaaac ebbbbb gbbbbbeaaaag ebbbbb gbbbbbdcaag dbbbbbg fbbbbbf fbbbbbf fbbbbbf fbbbbbf dbbbbbg gbbbbbd dbbbbbg bbbbbd dbbbbb bbbbbe ebbbbb ebbbbb ebbbbe dbbbbb bbbbbe dbbbbbg bbbbbd fbbbbbf gbbbbbd fbbbbbf gbbbbbf gbbbbbd fbbbbbf bbbbbe fbbbbbf bbbbbe dbbbbbg ebbbbb dbbbbbg dbbbbbg ebbbbb dbbbbbg g ebbbbb fbbbbbdddddeeeebbbbb bbbbbe gbbbbbbbbbbbbbbbbbbb bbbbbe gbbbbbbbbbbbbbbbbbbb gbbbbbd bbbbbbbbbbbbbbbbbbb gebbbbd ebbbbbbbbbbbbbbbbbb ggg gebbbbbbbbbbbeeeedd gffgggg ``` <!-- end of image --> Oh my, look at that! It's 2 intersections in area A! Alright, let's concentrate on the next area. I'm going to scrutinize area B for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#68bd9fff b,#5d9203ff c,#c4e1cdff d,#b8cf91ff e,#91b554ff f,#8fceb8ff g,#e2f1e7ff ``` ```image c f ag af aa aac aaa aaac aaaf aaaag aaaaf aaaaa aaaaac f aaaaaf fa aaaaaag gfaa caaaaaf gaaaa aaaaaag gaaaaa faaaaac caaaaaa gaaaaaa caaaaaaa faaaaac faaaaaaaf caaaaaf faaaaaaaf aaaaaag gfaaaaaaaf caaaaaf gaaaaaaaac gaaaaaa caaaaaaaac faaaaac caaaaaaaag gaaaaaa faaaaaaaag aaaaaag faaaaaaafg caaaaafgfaaaaaaaf aaaaaaaaaaaaaaf faaaaaaaaaaaac gaaaaaaaaaaac faaaaaaaaag caaaaaaafg aaaaaaf caaaaf cffc gggccdddd ggcccdddddeeeeebbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbeeeeeeddddccc eeeeddddcccgg ``` <!-- end of image --> This close-up reveals that there are no intersections in area B. Answer: A: 2; B: 0; 2 + 0 = 2 I've identified a total of two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#68bd9fff b,#5d9203ff c,#beddc3ff d,#abc67cff e,#7eaa3fff f,#8dcdb6ff g,#deeee2ff ``` ```image aac gaaa aaaag aaaaa gaaaaa aaacaaf aaa aaa gaaf faac aaa aaa aaa aaa gaaf gaaa aaag aaa aaa caac gaaf aaa faag aaag aaa aaa gaaf aaa faag caaf aaa aaa gaaa faac faag aaa aaa aaag aaa gaaa faag aaa gbe aaa caaf bbb aaa aaa bbbg faag faag bbbc aaa aaa bbbd aaa aaa bbbe faag gaaf bbbb aaa aaa bbbb aaa faac cbbbb faag aaa dbbbb aaa aaag dbbbbg aaa gaaa ebbbbd faac aaa bbbbbe aaa caaf bbbbbb aaa aaa bbbbbb caac faac bbbbbb aaa aaa bbbbbb aaa aaa bbeebb caac gaaa gbbddbbg aaa aaa cbbdcbbd aaa caac dbbc bbecaac aaa ebb bbbaaa aaag ebb bbbaaa aaa bbb bbbaac aaa f bbb bbbaa caaf aaa bbb ebbaa aaa aaaag bbb dbbac faac aaaag bbb cbbe aaa gaaaa bbe bbb aaag gaaaa gbbd cbbb gaaa caaaa cbbc abbb aaa faaaf dbbg abbb caaf aaaac ebb cabbb aaa aaaag gbbb aaebb faag aaaa aabbb aaebbc aaa gaaaa fabbb gaafbbd aaa caaaa abbb aaa bbe gaaf faaaf abbb aaa bbb aaa aaaaf cbbegaaf bbb faac aaaag gbbeaaa bbb aaa aaaag cbbeaaa ebb aaag gaaaa dbbaaaf dbbg gaaa gaaaa ebbaaa cbbd aaa faaaa ebbaaa gbbe caaffaaaf bbbaaf bbb aaaaaac bbbcf bbb faaaag bbb bbb aaa bbb bbb cf bbb ebb bbe dbbg gbbd cbbd cbbc bbe gccdddeebbbbbbbbbbbb dbbg bbb gccddeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ebb bbb ggcdddeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbee bbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeddccgg bbb bbbbbbbbbbbbbbbbbbbbbbbbbbbeedddccg g gbbbbbbeedddcgg ``` <!-- end of image -->
[ "" ]
This image looks interesting. I wonder if there are any intersections hidden in there? I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#eeec42ff b,#cdc520ff c,#f0ee92ff d,#f2f7e8ff e,#c9d76dff f,#b1d7b1ff g,#96ca95ff ``` ```image bc dbbd dbb cbb ebb bbb bbe bbc bbc dbbd dbb cbb ebb bbb bbe bbc bbc dbbd dbb cbb c ebb daad bbb caac bbe daaad bbc aaac bbd daaa fggbbggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg aaac gffebbffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd daaa gfffebbfffffffffffffffffffffffffffffffffffffffffffffffffffffffffd aaac gffffbbbffffffffffffffffffffffffffffffffffffffffffffffffffffffffd caaa gfffffbbbfffffffffffffffffffffffffffffffffffffffffffffffffffffffd aaad gffffffbbbffffffffffffffffffffffffffffffffffffffffffffffffffffffd caaa gfffffffbbefffffffffffffffffffffffffffffffffffffffffffffffffffffd aaagffffffffbbgffffffffffffffffffffffffffffffffffffffffffffffffffffd caaaffffffffbbffffffffffffffffffffffffffffffffffffffffffffffffffffd daaafffffffebbfffffffffffffffffffffffffffffffffffffffffffffffffffd gaaaeffffffebbffffffffffffffffffffffffffffffffffffffffffffffffffd gffaaaeeffffbbbfffffffffffffffffffffffffffffffffffffffffffffffffd gfffaaaaaaaaabbbffffffffffffffffffffffffffffffffffffffffffffffffd gffffffeeaaaaabbbaaaaaeeffffffffffffffffffffffffffffffffffffffffd gffffffffffffffbbaaaaaaaaaaaaaeeffffffffffffffffffffffffffffffffd gfffffffffffffffbbfffffeeaaaaaaaaaaaaaeeffffffffffffffffffffffffd gffffffffffffffffbbffffffffffffeeaaaaaaaaaaaaaeeffffffffffffffffd gffffffffffffffffebbfffffffffffffffffffeeaaaaaaaaaaeffffffffffffd gfffffffffffffffffebbffffffffffffffffffffffffffeeaaaffffffffffffd gffffffffffffffffffbbbffffffffffffffffffffffffffffaaffffffffffffd gfffffffffffffffffffbbbfffffffffffffffffffffffffffaaffffffffffffd gffffffffffffffffffffbbeffffffffffffffffffffffffffaaffffffffffffd gfffffffffffffffffffffbbefffffffffffffffffffffffffaaffffffffffffd gffffffffffffffffffffffbbfffffffffffffffffffffffffaaffffffffffffd gfffffffffffffffffffffffbbffffffffffffffffffffffffaaffffffffffffd gfffffffffffffffffffffffebbfffffffffffffffffffffffaaffffffffffffd gffffffffffffffffffffffffebbffffffffffffffffffffffaaffffffffffffd gfffffffffffffffffffffffffbbbbeeffffffffffffffffffaaffffffffffffd gffffffffffffffffffffffffffbbbbbbbbbeeffffffffffffaaffffffffffffd gffffffffffffffffffffffffffffffebbbbbbbbbbeeffffffaaffffffffffffd gffffffffffffffffffffffffffffffffffffebbbbbbbbbbeeeaefffffffffffd gffffffffffffffffffffffffffffffffffffffffffebbbbbbbbbbeeffffffffd gffffffffffffffffffffffffffffffffffffffffffffffffebbbbbbbbbbeeffd gfffffffffffffffffffffffffffffffffffffffffffffffffffaagebbbbbbefd gfffffffffffffffffffffffffffffffffffffffffffffffffffaaffffffeeefd gfffffffffffffffffffffffffffffffffffffffffffffffffffeaafffffffffd gffffffffffffffffffffffffffffffffffffffffffffffffffffaafffffffffd gffffffffffffffffffffffffffffffffffffffffffffffffffffeaeffffffffd gfffffffffffffffffffffffffffffffffffffffffffffffffffffaaffffffffd gfffffffffffffffffffffffffffffffffffffffffffffffffffffaaffffffffd gffffffffffffffffffffffffffffffffffffffffffffffffffffffaafffffffd gffffffffffffffffffffffffffffffffffffffffffffffffffffffaafffffffd gffffffffffffffffffffffffffffffffffffffffffffffffffffffeaeffffffd gfffffffffffffffffffffffffffffffffffffffffffffffffffffffaaffffffd gfffffffffffffffffffffffffffffffffffffffffffffffffffffffaaefffffd fggggggggggggggggggggggggggggggggggggggggggggggggggggggggaaggggg aa daa aa cac aa aad daa aa cac c ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#eeec41ff b,#cec51eff c,#f0ee94ff d,#f9f8dcff e,#eae670ff f,#f4f3b8ff g,#d7d049ff ``` ```image bbbbgd dbbbbg fbbbbg cbbbbe ebbbf gbbbf dgbbbd dbbbgd dbbbg bbbbg cbbbbe ebbbbc d gbbbb ac dgbbbd aaed dbbbgd aaaa dbbbg aaaaed fbbbg faaaaaf cbbbe deaaaae bbbbc caaaaaf ebbbbf caaaaaaaaaaaeccddgbbbbd daaaaaaaaaaaaaaaabbbbbd caaaaaaaaaaaaaaabbbbaaaeccfd dfceeaaaaaaaaabbbbaaaaaaaaaeccfdd dfceeaagbbbbaaaaaaaaaaaaaaaeccfdd debbbgaaaaaaaaaaaaaaaaaaaaaeccfdd gbbbfdffceaaaaaaaaaaaaaaaaaaaaaaaccfdd bbbbd dffceaaaaaaaaaaaaaaaaaaaaaaaecfdd dbbbbgd dffceeaaaaaaaaaaaaaaaaaaaaaaeccdd fbbbbg dffceeaaaaaaaaaaaaaaaaaaaaaaecf fbbbbe ffceeaaaaaaaaaaaaaaaaaac cbbbb dfceeaaaaaaaaaaaa ebbbc dfceeaaaaa gbbbf eaaa gbbbd eaaa dgbbbd eaaa bbbbg caaa fbbbbe caaa cbbbbe caaa ebbbbc caaa gbbbb caaa gbbbd caaa dgbbbd faaa fbbbg faaa fbbbe faaa bbbbc faaa ebbbbc faaa gbbbbcd daaa gbbbbbgecfd daaa dgbbbbbbbbbbgefd daaa dgbbbbbbbbbbbbbbgecfd daaa dfcegbbbbbbbbbbbbbbbbgefd aaa dcegbbbbbbbbbbbbbbbbgecfd aaad dfcebbbbbbbbbbbbbbbbgecfdcaac dfcegbbbbbbbbbbbbbbbbbbad deggbbbbbbbbbbbbbbbbgecfd dfegbbbbbbbbbbbbbbbbgecfd dceggbbbbbbbbbbbbbbbbgefd cbbbbbbbbbbbbbbbbbbg aaac dfcegbbbbbc aaaa dfegf eaaaf faaae aaaad caaac daaaa caaaf eaaaf faaae aaaa caaa daaa eaaf faae eaad aaad caac daaa aaaf ``` <!-- end of image --> Success! This area contains 2 intersections point! Answer: A: 2; 2 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#efed41ff b,#cec51dff c,#f0ed88ff d,#faf9dfff e,#e4e06fff f,#f4f2b9ff g,#d5ce3fff ``` ```image bf dbbd fbb cbb ebb gbb bbg bbe bbf dbbd fbb cbb ebb gbg bbg bbc bbf dbbd fbb cbb c gbb faad gbg caae bbg daaad bbc eaac bbf daaa dbbd aaac fbb faaa cbb aaaf gbb faaa gbg aaaf bbe caaa bbc aaad bbf caae dbbd daaad fbb eaac ebb daaacfd gbb aaaaaaaaabbgd dfcaaaaabbbaaaaacfd dbbgaaaaaaaaaaaacfd bbf dfcaaaaaaaaaaaaacfd dbbd dfcaaaaaaaaaaaaacfd fbb dfcaaaaaaaaaac ebb dfcaaa gbb aa bbg aa bbe aa bbc aa bbd aa dbbd aa fbb aa ebb aa gbbbef aa gbbbbbbbbef aa dcgbbbbbbbbbef aa dcgbbbbbbbbbefcac dcgbbbbbbbbbef degbbbbbbbbbef aafegbbbbbe aa fef fae aa caf aa aad daa aa fac aa eaf aa aa daa aa cac aa aad aa aa fae c ``` <!-- end of image -->
[ "" ]
I'm approaching this image with caution. Intersections might be tricky to spot. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f79a0ff b,#86cf7fff c,#1e489aff d,#b1d7b1ff e,#83a5b3ff f,#ecf5edff g,#96cc96ff ``` ```image f ccc ecc ccf cca acc dcc cce cccggggggggggggggggggggggggggggggg accdddddddddddddddddddddddddddddddf fccdddddddddddddddddddddddddddddddf ccaddddddddddddddddddddddddddddddf cccddddddddddddddddddddddddddddddf accddddddddddddddddddddddddddddddf gccedddddddddddddddddddddddddddddf gccadddddddddddddddddddddddddddddf fbb fgggcccdddddddddddddddddddddddddddddf dbbb gbbgeccdddddddddddddddddddddddddddddf gbbbbf fbbgdcceddddddddddddddddddddddddddddf bbbbbbd bbbdcccddddddddddddddddddddddddddddf fbbbg bbb dbbdaccddddddddddddddddddddddddddddf fbbbd dbb bbggccddddddddddddddddddddddddddddf dbbbf fbb bbbdccadddddddddddddddddddddddddddf gbbb bbf dbbdcccdddddddddddddddddddddddddddf bbbb bbd bbgaccdddddddddddddddddddddddddddf fbbbg bbb bbbdcceddddddddddddddddddddddddddf fbbbd dbb gbbdccaddddddddddddddddddddddddddf dbbbf fffffffbbffffffffffffff gbbgcccddddddddddddddddddddddddddf gbbb gdddddddbbgddddddddddddg gbbbeccddddddddddddddddddddddddddf bbbb gdddddddbbgddddddddddddd ggbbdccedddddddddddddddddddddddddf fbbbg gdddddddbbbddddddddddddd gdbbgcccdddddddddddddddddddddddddf fbbbd gdddddddgbbddddddddddddd gdbbbaccdddddddddddddddddddddddddf dbbbf gddddddddbbddddddddddddd gddbbgccdddddddddddddddddddddddddf gbbb gddddddddbbddddddddddddd gddbbbccaddddddddddddddddddddddddf bbbb gddddddddbbgdddddddddddd gddbbbcccddddddddddddddddddddddddf fbbbg gddddddddbbbdddddddddddd gdddbbaccddddddddddddddddddddddddf fbbbd gddddddddgbbdddddddddddd gdddbbbccgdddddddddddddddddddddddf dbbbf gdddddddddbbdddddddddddd gdddgbbccadddddddddddddddddddddddf gbbb gdddddddddbbddddddddgddd gddddbbaccdddddddddddddddddddddddf bbbb gdddddddddbbgddddacccddd gddddbbbccdddddddddddddddddddddddffbbbg gdddddddddbbbdeccccccddd gddddgbbcceddddddddddddddddddddddfbbbd gdddddddddgbbccccccedddd gdddddbbaccdddddddddddddddddddddgbbbf gdddddddecabbccceddddddd gdddddbbbccddddddddddddddddddddbbbbf gdddddaccccbbadddddddddd gdddddgbbccdddddddddddddddddddbbbb gddaccccccabbgdddddddddd gddddddbbacadddddddddddddddddbbbbf acccccccgddbbbdddddddddd gddddddbbbccddddddddddddddddbbbgdf ecccccccedddddgbbdddddddddd gdddddddbbccddddddddddddddgbbbdddf dccccccceddddddddgbbdddddddddd gdddddddbbbcgddddddddddddbbbbddddf fcccccccegdddddddddddbbdddddddddd gdddddddbbbcadddddddddddbbbbdddddf facccccce gdddddddddddbbgddddddddd gddddddddbbccddddddddddbbbbddddddf acccccca gdddddddddddbbbddddddddd gddddddddbbbcdddddddddbbbgdddddddf eccccccaf gdddddddddddgbbddddddddd gddddddddgbbceddddddgbbbgddddddddf ecccccccf gdddddddddddgbbddddddddd gdddddddddbbacdddddbbbbddddddddddf dcccccccd gddddddddddddbbddddddddd gdddddddddbbbcddddbbbbddddddddddeccccccce gddddddddddddbbgdddddddd gdddddddddgbbcdddbbbbdddddddddacccccce gddddddddddddbbbdddddddd gddddddddddbbaadbbbgdddddddacccccca gddddddddddddgbbdddddddd gddddddddddbbbabbbgdddddaccccccagf gddddddddddddgbbdddddddg gddddddddddgbbbbbddddecccccccedddf fffffffffffffbbffffffff gdddddddddddbbbbdddccccccceddddddf bbd gdddddddddddbbbaddcccccedddddddddf bbb gddddddddddddcccddccaddddddddddddf gbb gddddddddddddeccddccgddddddddddddf fbb gdddddddddddddcceaccdddddddddddddf bbf gdddddddddddddccccccdddddddddddddf bbd gdddddddddddddaccccedddddddddddddf bbb gdddddddddddddeccccddddddddddddddf gbb gddddddddddddddccccddddddddddddddf dbb gddddddddddddddcccaddddddddddddddf bbf gddddddddddddddaccgddddddddddddddf bbd gdddddddddddddddccdddddddddddddddf bbg gddddddddddddddddddddddddddddddddf gbb gddddddddddddddddddddddddddddddddf dbb gddddddddddddddddddddddddddddddddf bbf dgggggggggggggggggggggggggggggggg bbd bbg gbb dbb bbf bbd bbg gbb dbd ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4d73a7ff b,#86cf80ff c,#1e489aff d,#addea9ff e,#7d95c4ff f,#d8e9e0ff g,#aebdd9ff ``` ```image cca ccc ccc ccc ccc cccg ccce ccca ccccf eccce fcccc ccccf accce gccca fcccc eccce gccca ccccf f ccccg d cccce b ccccc bd acccce bb gcccca bbffccccc bbd ccccc bbb ecccc bbb gcccc bbb acccg bbbf eccce bbbd gcccc bbbbf ccccf dbbbd accce bbbbffcccc dbbbd ccccg fbbbb eccce bbbbfgccca dbbbdfccccf fbbbb acccg bbbbdgcccc bbbbb ccccf bbbbbfccccg dbbbbdcccca fbbbbbccccc bbbbbcccccg bbbbgcccca dbbbdccccc fbbbbacccc bbbbecccc dbbbdcccc fbbbbccccf dbbbbccca fbbbbcccc bbbbacccg dbbbbccce fbbbbccca bbbbaccc bbbbbccce dbbbbaccc fbbbbbcccf d bbbbbcccg fbb dbbbbccca bbb fbbbbcccc fbbb dbbbaccce dbbbbb fbbbbccca bbbbbbd bbbbaccc fbbbbbbd dbbbbcccg bbbbbbf fbbbbccce dbbbbbb bbbbacca dbbbbbbf fbbbbccc fbbbbbbd bbbbacc fbbbbbbf dbbbbcc bbbbbbf bbbbccf dbbbbbb bbbbace bbbbbbd bbbbbca fbbbbbbd dbbbbacg dbbbbbbf fbbbbbce bbbbbbf bbbbbca bbbbbbd dbbbbccf fbbbbbbd fbbbbccg fbbbbbbf bbbbaca dbbbbbbf fea fbbbbccf bbbbbbb gaccccc bbbbace fbbbbbbd ecccccccc dbbbbcafbbbbbbd gecccccccccc fbbbbcabbbbbbf fecccccccccccae dbbbbbbbbbbf fecccccccccccaf bbbbbbbd accccccccccceg dbbbbbb ecccccccccccag fbbbbbg ecccccccccag bbbbce ccccccccaf bbbccc fcccccaef ccccc ecccaf gcccc ccccf fcccc gcccc ccccg ecccc eccce ccccc gcccafccccc ccccecccca eccccccccf gccccccca ccccccce accccccg gcccccc fccccca eccccf gccca ccce ace ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Alright, let's examine the next area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#5275acff b,#86cf7fff c,#1e489aff d,#addea8ff e,#809ac2ff f,#d4e8daff g,#acbcd8ff ``` ```image bbbbb bbbbbf dbbbbf fbbbbd fbbbbb bbbbb bbbbbf dbbbbf fbbbbd fbbbbb bbbbb bbbbbf dbbbbf fbbbbd fbbbbd bbbbb bbbbbf dbbbbf fbbbbd fbbbbd bbbbb bbbbbf gf dbbbbf fecce dbbbbd fecccccc fbbbbd feaccccccccg bbbbb gaccccccccccca bbbbbgaccccccccccccceg dbbbbacccccccccccag febbbbaccccccccag feccabbbbbcccccaef feacccccbbbbbcccef gaccccccccbbbbbef gacccccccccccbbbbbf gacccccccccccccadbbbbd fecccccccccccccag fbbbbd ecccccccccccccaef bbbbb ccccccccccccef bbbbbf cccccccccef dbbbbf cccccceg dbbbbd cccag fbbbbd ag bbbbb bbbbbf dbbbbf dbbbbd fbbbbd bbbbb bbbbbf dbbbbf dbbbbd fbbbbd bbbbb bbbbb dbbbbf dbbbbd fbbbbd bbbbb bbbbb dbbbbf dbbbbd fbbbbd ``` <!-- end of image --> As I suspected, there's 1 intersection within area B. Answer: A: 1; B: 1; 1 + 1 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#4f75a8ff b,#87d080ff c,#1e489aff d,#b4e1b0ff e,#7b95c2ff f,#dae9e1ff g,#a6b7d7ff ``` ```image f ccc ecc ccf cca acc gcc ccg ccc acc fcc cce ccc ecc ccf cca fbb bd ccc dbbb bbb gcc bbbbbf bbf ccg bbbbbbd bbb ccc bbbb bbb dbb acc fbbbd dbb bbffcc dbbbf fbb bbb cce bbbb bbf dbb ccc bbbb bbd bbdecc bbbb bbb bbb ccf fbbbd dbb dbb cca dbbbf fbb bbdccc bbbb bbf bbbgcc bbbb bbd fbb ccg bbbb bbb bbdccc fbbbd dbb bbbacc dbbbf fbb fbbfcc bbbb bbf bbbcce bbbb bbd dbbccc bbbb bbb bbecc fbbbd dbb bbbccf dbbbf fbb dbbcca bbbb bbf f bbacc bbbb bbd eccc bbbcc bbbb bbb gcccccc dbbccg fbbbd dbbccccccg bbacc dbbbf fcabbcccg bbbcc bbbb faccccbbe fbbcc bbbb eccccccabbd bbace bbbb eccccccaf bbb bbbcc fbbbd gcccccccf dbb fbbcc dbbbf gcccccccg fbb bbbcf bbbb fcccccccg bbf bbbca bbbb facccccce bbd bbcc bbbb ecccccca bbb bbbc fbbbd eccccccaf dbb dbbcg dbbbf gcccccccf fbb bbaa bbbb gcccccccg bbf bbbc bbbb fcccccccg bbd dbbc bbbb facccccce bbb bbaefbbbd ecccccca dbb bbbabbbf eccccccaf fbb dbbbbb gcccccccf bbf bbbb cccccccg bbd bbbe cccccg bbb ccc cca dbb gcc ccf fbb ccgecc bb ccaccc bbd accccg bbb fcccc bbb cccc fbb ccca bb eccf bbd cc bbb bbb fbb bb bbd bbb bbb dbb bb bbd bbb bbb dbd ``` <!-- end of image -->
[ "" ]
Let's examine this image for potential line intersections. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#622882ff b,#e877a6ff c,#8c6da0ff d,#f0f0eeff e,#b2d7b1ff f,#d1aac4ff g,#a2cda2ff ``` ```image daa cac aad aa ddddddddddddddddaadddd dgggggggggggggggcacgggg dgeeeeeeeeeeeeeeaageeee af dgeeeeeeeeeeeeeeaaeeeee caaa dgeeeeeeeeeeeeeeaaeeeee daaac dgeeeeeeeeeeeeecaceeeee caaad dgeeeeeeeeeeeeeaageeeee daaac ddddddddddddddddddddddddd dgeeeeeeeeeeeeeaaeeeeee faaad dggggggggggggggggggggggggg dgeeeeeeeeeeeeeaaeeeeee aaac dgeeeeeeeeeeeeeeeeeeeeeeeg dgeeeeeeeeeeeecaaeeeeee faaaf dgeeeeeeeeeeeeeeeeeeeeeeeg dgeeeeeeeeeeeeaageeeeee aaaa dgeeeeeeeeeeeeeeeeeeeeeeeg dgeeeeeeeeeeeeaaeeeeeee faaaf dgeeeeeeeeeeeeeeeeeeeeeeeg dgeeeeeeeeeeeeaaeeeeeee aaaadgeeeeeeeeeeeeeeeeeeeeeeeg dgeeeeeeeeeeegaaeeeeeee daaaceeeeeeeeeeeeeeeeeeeeeeeg dgeeeeeeeeeeeaacffbfeee caaaeeeeeeeeeeeeeeeeeeeeeeg dgeeeeeefbbbbaabbbbbeee daaaceeeeeeeeeeeeeeeeeeeeg dfbbbbbbbbbbbbaabbfeeeee dgcaaaeeeeeeeeeeeeeeeeeeeg dffbbbbbbbbbbbbbbffeegaaeeeeeeee dgeeaaaceeeeeeeeeeeeeeeeeg dfbbbbbbbbbbbbbbbffeeeeeeeeeecaceeeeeeee dgeeecaaageeeeeeeeeffbbbbbbbbbbbbbbbfd dgeeeeeeeeeeaaeeeeeeeee dgeeeeeaaaaefbbbbbbbbbbbbbbbfd dgeeeeeeeeeeaaeeeeeeeee dgeeeeeecaaabbbbbbbbfeeeeg dgeeeeeeeeegaaeeeeeeeee dgeeeeeeeeaaaaeeeeeeeeeeeg dgeeeeeeeeecaceeeeeeeee dgeeeeeeeeecaaageeeeeeeeeg dgeeeeeeeeeaaeeeeeeeeee dgeeeeeeeebbfaaaaeeeeeeeeg dgeeeeeeeeeaaeeeeeeeeee dgeeeeeeefbbeegaaaceeeeeeg dgeeeeeeeegaaeeeeeeeeee dgeeeeeeebbeeeeeaaaaeeeeeg dgeeeeeeeecaceeeeeeeeee dgeeeeeebbbeeeeeegaaaceeeg dgeeeeeeeeaageeeeeeeeee dgeeeeeebbeeeeeeeeecaaaeeg dgeeeeeeeeaaeeeeeeeeeee dgeeeeebbeeeeeeeeeeegaaacg dgeeeeeeeeaaeeeeeeeeeee dgeeeefbbeeeeeeeeeeeeecaaad dgeeeeeeecaceeeeeeeeeee dgeeeebbeeeeeeeeeeeeeeeeaaac dggggggggaagggggggggggg dgeeebbfeeeeeeeeeeeeeeeeecaaf aa dgeeebbeeeeeeeeeeeeeeeeeegdaa aa dgeebbeeeeeeeeeeeeeeeeeeeg aa fac dgebbbeeeeeeeeeeeeeeeeeeeg cac aad dgebbeeeeeeeeeeeeeeeeeeeeg aa aa dgbbfggggggggggggggggggggg aaf aa dbbdddddddddddddddddddddd faa fac bbd aa aaf fbb caf aa bb daa aa bbf aad fac dbb cac caf bbd aa aa fbb aaf aa bb faa faa bbf aa caf dbb cac aa bbd daa aa fbb aad daa d bb fac caf fbb bbf aa aa bb dbb aaf aa fbb bbd faa daa bbd bbb aa cac dbb bb cac aad bbf bbf aa aa dbb dbb aad daa bbfbbd faa cac bbbb aa aad fbb aaf aa bd daa aa aa fac cac aad aa aa aad aa faa fac aa aaf aaf aa daa aa aafac caaaf aaa aaa faa f ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#622782ff b,#e876a7ff c,#aa8abbff d,#f3e0ebff e,#85549cff f,#cfbdd8ff g,#f1aecbff ``` ```image ed aac aaaed aaaaac aaaaaaef deaaaaaac faaaaaaef deaaaaaacd faaaaaaaf dcaaaaaaed feaaaaaaf ddgg caaaaaaed ddgggbbbbbbb feaaaaaac ddgggbbbbbbbbbbbbbbb caaaaaaed dgbbbbbbbbbbbbbbbbbbbbbbb deaaaaaacdbbbbbbbbbbbbbbbbbbbbbbggg caaaaaaabbbbbbbbbbbbbbgggddd deaaaaaaebbbbgggdd faaaaaaaf deaaaaaac dbbaaaaaaaf bbbbeaaaaaaed gbbbbdfeaaaaaaf bbbbg caaaaaaed gbbbbd feaaaaaac dbbbbg caaaaaaed bbbbb deaaaaaac gbbbbd caaaaaaed bbbbg deaaaaaac gbbbbd faaaaaaef dbbbbg deaaaaaac bbbbb faaaaaaaf gbbbbd dcaaaaaac bbbbg faaaaaa gbbbbd caaaa dbbbbg feaa bbbbb ca gbbbbd d bbbbg gbbbb dbbbbg bbbbb gbbbbd dbbbbg gbbbb dbbbbg bbbbb gbbbbd dbbbbg ``` <!-- end of image --> Area A contains 1 intersection. Let's shift our focus to the next area. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#612682ff b,#e875a6ff c,#a07db4ff d,#edd5e5ff e,#834e98ff f,#c3adcfff g,#efa3c4ff ``` ```image aaaad daaaa caaac eaaaf aaaad daaaa faaac eaaaf aaaad daaaa faaae caaac aaaad daaaa faaae caaac eaaaf daaaa faaae caaac eaaaf daaaa faaae caaac eaaaf aaaad faaae caaac eaaafddgggbbg dddgaaaabbbbbbbbg dddgggbbbbbbaaaabbbbbbbbg dddgggbbbbbbbbbbbbbeaaaebbbbbbbbb dggbbbbbbbbbbbbbbbbbbbbbbeaaaebgggddd bbbbbbbbbbbbbbbbbbbbbbbggaaaad bbbbbbbbbbbbbbbgggddd daaaa bbbbbbbgggdd faaac ggdd eaaaf aaaad daaaa faaae caaaf aaaad daaaa faaae caaac eaaaf daaaa faaae caaac eaaaf daaaa faaae caaac eaaaf aaaad faaae caaac eaaaf aaaad faaae caaac ``` <!-- end of image --> Aha! I've found 1 intersection inside area B! Answer: A: 1; B: 1; 1 + 1 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#612782ff b,#e976a6ff c,#a27eb4ff d,#efd9e7ff e,#81539bff f,#c2acceff g,#f0a5c5ff ``` ```image daa cac aad aa aa cac aad ac aa caaa aa daaac fae caaad aad aaae aa caaad aa aaae fae faaad eaf aaae aa faaaf aa eaaa fae daaaf eafdgbg eaaa ddgbbbaabbbbg daaac dggbbbbbbbbbbbaabgdd caaa dggbbbbbbbbbbbbbbgdd daa aaac dggbbbbbbbbbbbbbbgd eaf caaad dgbbbbbbbbbbbbbbbgd aa aaae dbbbbbbbbbbbbbbggd aa faaabbbbbbbggd daa aaaa cac dcaaaf aa bbdeaaa aa gbb daaaf daa bb eaaa cac bbg daaac aad dbb eaaa aa bbd daaac aa gbb caaad cac bb aaae aad bbg faaf aa dbb daa aa bbd aa fae gbb cae aad bb aa aa bbg aad aa dbb faa fae bbd aa eaf gbb eac aa bb daa aa bbg aa fae dbb cae eaf bbd aa aa gbb aaf aa bb faa daa bbg aa eaf dbb eac aa bbd aa aa gbb aad daa bb cae cac gbb bbg aa aa bb dbb aaf aa gbb bbd daa daa bbd gbb aa cac dbb bb eac aad bbd bbg aa aa bb dbb aad aa bbgbbd fae cac bbbb aa aad gbb aaf aa bd daa aa aa fae cac aad aa aa aad aa faa fae aa aaf aaf aa daa aa aafae caaaf aaa aaa fae f ``` <!-- end of image -->
[ "" ]
I'm on the case! Let's uncover any intersections hidden in this image. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#97aefaff b,#c9f3caff c,#c9d4fcff d,#eff6f0ff e,#b1d7b1ff f,#96c996ff g,#a5c5d3ff ``` ```image b dbb bbbb bb bb db bb bb bb bb bbd ffffffffffffbeffe bbd eeeeeeeeeeebbeeef bbd eeeeeeeeeeebbeeef bbd eeeeeeeeeeebeeeef bbd eeeeeeeeeebbeeeef bbd eeeeeeeeeebbeeeef bbd effffffffffffffffffffffffffffffffffffffffffffffffffffffe eeeeeeeeeebbeeeef bbd feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeebeeeeef bbb feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeebbeeeeef bbbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeebbeeeeef bbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeebeeeeeef bbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeebbeeeeeef ebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeebbeeeeeef fbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeebeeeeeeef feebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeebbeeeeeeef feeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeebbeeeeeeef feeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeebeeeeeeeef feeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeebeeeeeeeef feeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeebbeeeeeeeef feeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeebbeeeeeeeef feeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeebeeeeeeeeef feeeeeaaeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeebbeeeeeeeeef feeeeeaaaeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeegebbeeeeeeeeef feeeegaeaaaebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeagbeeeeeeeeeef feeeeaaeeaaaebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeabbeeeeeeeeeef feeeeaaeeeeaagbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeebbeeeeeeeeeef feeeeageeeeeaaabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeebgeeeeeeeeeef feeegaeeeeeeeeaabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeebbageeeeeeeeef feeeaaeeeeeeeeeaabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeebbaaeeeeeeeeef feeeaaeeeeeeeeeeeabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeebbgaeeeeeeeeef feeeageeeeeeeeeeeeabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeaaeeeeeeeef feeeaeeeeeeeeeeeeeegbbgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeegaeeeeeeeef feegaeeeeeeeeeeeeeeeebbgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeaaeeeeeeef feeaaeeeeeeeeeeeeeeeeebbggeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeaaeeeeeeef feeaaeeeeeeeeeeeeeeeeeebbbaeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeageeeeeef feeageeeeeeeeeeeeeeeeeeebbbageeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeaaeeeeeef fegaeeeeeeeeeeeeeeeeeeeeebbbaaeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeageeeeef feaaeeeeeeeeeeeeeeeeeeeeeebbbaageeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeaaeeeeef feaaeeeeeeeeeeeeeeeeeeeeeeebbbaaaeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeegaeeeeef feageeeeeeeeeeeeeeeeeeeeeeeeebbgaageeeeeeeeeeeeeeeeeeeef eeeeeeeeeeaaeeeef fgaeeeeeeeeeeeeeeeeeeeeeeeeeeebbeaaaeeeeeeeeeeeeeeeeeeef eeeeeeeeeegaeeeef faaeeeeeeeeeeeeeeeeeeeeeeeeeeeebbegaageeeeeeeeeeeeeeeeef eeeeeeeeeeeaaeeef faaeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeaaaeeeeeeeeeeeeeeeef eeeeeeeeeeeaaeeef fageeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeegaageeeeeeeeeeeeeef eeeeeeeeeeeeageef faeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeaaaeeeeeeeeeeeeef eeeeeeeeeeeeaaeef gaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeegaageeeeeeeeeeef eeeeeeeeeeeeeagef aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeaaaeeeeeeeeeef eeeeeeeeeeeeeaaef ageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeegaageeeeeeeef eeeeeeeeeeeeegagf ageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeaaaeeeeeeef eeeeeeeeeeeeeeaaf caeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeegaageeeeef eeeeeeeeeeeeeegaf aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeaaaeeeef eeeeeeeeeeeeeeeaa aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeegaageef eeeeeeeeeeeeeeega ageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeaeeef ddddddddddddddddaa cafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeef aa aafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeef ac aafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeef aa acfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeef dac da feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeef aa ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeef cad aa feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeef aa ac feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeef ca ad dddddddddddddddddddddddddddddddddddddddddddddddddddbdddd aa ca aa aa ac aa aa ac ac ca aa aa dad aa aa ac caca aaa caa ac ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#acbff9ff b,#caf4ccff c,#c3d0fbff d,#f1f9f6ff e,#96adfbff f,#e0f8e0ff g,#dbe3fdff ``` ```image fbbf bbbd dbbb fbbf bbbf dbbb fbbb bbbf dbbbd fbbb bbbf dbbbd fbbb fbbf bbbd dbbb fbbf bbbf dbbbd fbbb bbbf dbbbd fbbb bbbf dbbbd fbbb fbbf bbbd dbbb fbbf bbbf dbbbd fbbb bbbf dbbbd fbbb bbbf bbbd fbbb fbbf bbbd dbbb fbbf bbbf dbbbd gc fbbb daeegbbbf aeeabbbd geeabbb aebbbf gebbbd abbb bbbb bbbag dbbbea fbbbeeg bbbceea dbbbgeeeg fbbb aeea bbbf geeed fbbd eeec d ceee deeec ceee deeeg aeea geeeg aeea geeed eeec ceeed eeec ceee deeeg ceea geeeg aeea geeed aeec geeed eeec ceee deeeg ceee deeeg aeea geeeg aeea geeed eeec ceeed deeec ceee deeeg aeea geeeg aeea geeed aeec geee eee cee dee ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Let's move forward and inspect another region. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#aec1f9ff b,#caf4ccff c,#cdd8fbff d,#effbefff e,#96adfbff f,#dbf7dcff g,#e9eefdff ``` ```image f bf bbb bbbb fbbbb fbbbbd fbbbbd fbbbbd fbbbbd dbbbbd dbbbbd dbbbbd dbbbbd dbbbbd dbbbbd dbbbbd dbbbbd dbbbbf dbbbbf dbbbbf bbbbf bbbbf gg bbbbf ceeag fbbbf aeeeec fbbbf eeeeeeag fbbbf geeeeeeeec fbbbf ceeagaeeeeag fbbbb aeec ceeeeec fbbbb eeec gaeeeeagfbbbb geeeg ceeeeecfbbbbd ceee gaeeeeafbbbbd aeea ceeeeefbbbbd aeec gaeeeecbbbbd eeeg ceeeeabbbbd geee gaeeeabbbbd ceea ceeeabbbbd aeec gaeeabbbbd eeeg ceeabbbbd geee gaeabbbbd ceea ceabbbbd aeec gaabbbbf eeec cabbbbf geeeg gabbbbc ceee cbbbbcg aeea gbbbbac eeec dbbbbbeg geeeg bbbbbec geee bbbbbeag ceea fbbbbeec aeec fbbbbeeag eeeg fbbbbeeec geee fbbbbeeeag ceea fbbbbeeeec aeec fbbbbeeeeag eeec fbbbbaeeeec geeeg fbbbbaeeeeag ceee fbbbbceeeeec aeea fbbbbdaeeeeag eeec dbbbbdceeeeec geeeg dbbbbdgaeeeeag ceee dbbbbd ceeeeec ceea dbbbbd gaeeeeag aeec dbbbbd ceeeeec eeeg dbbbbd gaeeeeag geee dbbbbd ceeeeec ceea dbbbbd gaeeeeag aeec dbbbbf ceeeeec eeeg dbbbbf gaeeeeag geee dbbbbf ceeeeec ceea dbbbbf gaeeeeag aeea bbbbf ceeeeec eeec bbbbf gaeeeeag geeeg bbbbf ceeeeec ceee fbbbf gaeeeea ceea fbbbf ceeeeec aeec fbbbf gaeeeea eeeg fbbbf ceeeeeg eee fbbbb gaeeeea eea fbbbb ceeeeeg eec fbbbb gaeeeea eeg fbbbbd ceeeeeg ee fbbbbd gaeeeea ea fbbbbd ceeeeeg ea dbbbbd gaeeec ec dbbbbd cee eg dbbbbd gg e dbbbbd a dbbbbd c dbbbbd g dbbbbd dbbbbd dbbbbf dbbbbf dbbbbf dbbbbf bbbbf bbbbf bbbbf fbbbf fbbbf ``` <!-- end of image --> Area B contains 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#acbffbff b,#caf4ccff c,#c6d3fcff d,#f1f9f5ff e,#96adfcff f,#ddf8ddff g,#dde4fdff ``` ```image f dbb bbbb bf bb dbd bb bb bbd bb bbd bd bbd fb bbd bb bbd bf bbd fb bbf bb bbf bf bbf db bbf bb fbf bf fbf dbd fbb fb fbb bb fbb bd fbb fb dbb bb dbb bf dbb fb dbb bb dbb bf dbb db ea bb bb eeed bb g bb cedeea bb eabd ee aeedbbd abb ee deeabbd bb ec aeebbd ba ge deebbd fbeg ae aebbd bbee ee gebbd bfged ec abbf ee ded gbbb ce ce bbc ea ee bbbc ae ea fbbe ec eg fbbec ee ce fbbee deg ee fbbeec ee ea fbbeee geg eg fbbgeec ee ge dbb eee ce ae dbb geec ea ee dbb eee ae ec dbb geeg ea ged dbb eee ee ae dbb ceeg ec ee bb eee ee ea bb ceeg geg eg bb eee ee ce bbd ceeg ced ee bbd eee ee ea bbd ceeg ce eg bbd e ea ge bbd ae ae bbd ec ee bbf ee ec bbf deg ge bbf ee ae bbf ged ee fbf ee ea fbf ce deg f ea ce ae ee ec ea ee eg dec ge ee ae geg ee ee ec cege eee aee ec ``` <!-- end of image -->
[ "" ]
Time to put on my detective hat and find those intersection points! I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#be6fa2ff b,#4bbfb5ff c,#d1a5c0ff d,#b1d7b1ff e,#81cdbeff f,#95c896ff g,#eaecedff ``` ```image gcc ggccaaaaaaaaaaa ggccaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaac caaaaaaaaaaaaaaaaaaaccgg aaaa bg caaaaaaaaaccgg gaaa bbbg caaa aaac bbbbd aaac caaa bbbbe aaac aaag bbbbe aaac aaaa ebbbb aaac gaaa ebbbb aaac aaac dbbbb aaac caaa gbbbb aaag aaag gbbbb aaag aaaa bbbbg aaag gaaa bbbbg aaag aaac bbbbe aaa caaa bbbbe aaa dffffaaafffffffffffffbbbbb aaa fddddaaaadddddddddddebbbb aaa fddddcaaaddddddddddebbbb aaa fdddddaaacddddddddebbbbf aaa fdddddaaaaddddddddbbbbdf aaa fddddddaaadddddddbbbbddf gaaa fddddddaaaadddddbbbbeddf gaaa fddddddcaaaddddbbbbedddf gaaa fdddddddaaadddbbbbeddddf gaaa fdddddddaaaadbbbbbdddddf caaa fddddddddaaabbbbbddddddf caaa fddddddddaaebbbbdddddddf caaa fddddddddaabbbbddddddddf caaa fdddddddddbbbbdddddddddf caaa fddddddddbbbbaaaaaaaaaaaccgg caaa fdddddddbbbbaaaaaaaaaaaaaaaaaaaaaaaag aaac fddddddbbbbfaaaaaaaaaaaaaaaaaaaaaaaa aaac fdddddbbbbedddddddddccaaaaaaaaaaaaaa aaac fddddbbbbbdddddddddddddf ggccc aaac fdddbbbbbddddddddddddddf aaac fddebbbbdddddddddddddddf aaag fdebbbbddddddddddddddddf e aaag febbbbdddddddddddddddddf gbbb aaag fbbbbddddddddddddddddddf bbbd aaag bbbbdddddddddddddddddddf bbbb aaa bbbbedddddddddddddddddddf gbbb aaa bbbbeddddddddddddddddddddf bbbe aaa bbbbbfffffffffffffffffffffd ebbb aaa bbbbe bbb aaa ebbbb bbbe aaa ebbbb ebbb aaa gbbbb bbbg aaa gbbbb bbbe gaaa gbbbbg dbbb gaaa bbbbg fffffbbbfffffffffaaafff bbbbg gdddddbbbbdddddddcaaadddg bbbbe gdddddebbbdddddddaaaadddg bbbbe gddddddbbbeddddddaaaadddg ebbbb gddddddbbbbdddddaaaaddddg ebbbb gddddddebbbddddcaaadddddg dbbbb gdddddddbbbedddaaaadddddg gbbbb gdddddddbbbbddaaaaddddddg gbbbb gddddddddbbbddaaacddddddg bbbbg gddddddddbbbeaaaadddddddg bbbbg gddddddddbbbbaaaddddddddg bbbbd gdddddddddbbbaaaddddddddg bbbbe gdddddddddbbbbadddddddddg bbbbe gdddddddddebbbddddddddddg ebbbb gdddddddddabbbddddddddddgebbbb gddddddddaabbbbddddddddddbbbb gddddddddaafbbbddddddddfbbbb gdddddddaaaabbbedddddddbbbbg gddddddaaaadbbbbddddddbbbbg gddddddaaaadebbbdddddbbbbg gdddddaaaadddbbbedddbbbbe gddddcaaaddddbbbbddbbbbbg gddddaaaadddddbbbdbbbbbdg gdddaaaaddddddbbbbbbbbddg gdddaaacddddddbbbbbbbdddg gddaaaaddddddddbbbbbddddg gdaaaadddddddddbbbbdddddg faaaafffffffffebbffffff aaa gg ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#be6fa2ff b,#4bbfb5ff c,#e3c0d6ff d,#b3e3dfff e,#7bccc6ff f,#ce92b9ff g,#e9ebefff ``` ```image ebbbbbbg caaaaaac dbbbbbbe caaaaaag gbbbbbbb caaaaaag ebbbbbbd caaaaaag dbbbbbbe faaaaaag bbbbbbb caaaaaaa ebbbbbbd gaaaaaaaf dbbbbbbe faaaaaaag bbbbbbb caaaaaaac ebbbbbbd aaaaaaaf gbbbbbbe caaaaaaag bbbbbbbg gaaaaaaaf dbbbbbbd faaaaaaa gbbbbbbe caaaaaaac ebbbbbbg gaaaaaaaf dbbbbbbd faaaaaaag gbbbbbbb caaaaaaac ebbbbbbg aaaaaaaf dbbbbbbecaaaaaaag gbbbbbbbaaaaaaaf ebbbbbbaaaaaaa dbbbbbbbaaaaac bbbbbbbaaaaf ebbbbbbaaaag dbbbbbbbaac bbbbbbbaf ebbbbbbag gabbbbbbb fabbbbbbbg caaebbbbbbd gaaaabbbbbbe faaaabbbbbbbg gaaaaaebbbbbbd g faaaaaabbbbbbb gb caaaaaaaebbbbbbg eb gaaaaaaafdbbbbbbe ebb faaaaaaag bbbbbbb ebbb caaaaaaac ebbbbbbd ebbbb aaaaaaaf dbbbbbbe dbbbbb faaaaaaag bbbbbbb dbbbbbb gaaaaaaac ebbbbbbd dbbbbbbb faaaaaaa dbbbbbbe gbbbbbbbb caaaaaaag bbbbbbbg gbbbbbbbbe gaaaaaaaf ebbbbbbd gbbbbbbbbe faaaaaaag gbbbbbbe ebbbbbbbbg caaaaaaac bbbbbbbgebbbbbbbbg aaaaaaaf dbbbbbbbbbbbbbbbg faaaaaaag gbbbbbbbbbbbbbbd gaaaaaaac ebbbbbbbbbbbbd faaaaaaa dbbbbbbbbbbbd caaaaaaac gbbbbbbbbbbe gaaaaaaaf ebbbbbbbbe faaaaaaag dbbbbbbbe ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Time for a closer look at another area. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#be6fa2ff b,#4abfb5ff c,#e4c4d9ff d,#a8e0dbff e,#73c8c3ff f,#cf99bcff g,#e3eeefff ``` ```image aaaaaaa ebbb faaaaaac ebbbb gaaaaaaf ebbbbb aaaaaaag dbbbbbb caaaaaaf dbbbbbbb aaaaaaa dbbbbbbbb faaaaaac gbbbbbbbbd caaaaaaf gbbbbbbbbe aaaaaaag gbbbbbbbbe caaaaaaf gebbbbbbbe gaaaaaaa ebbbbbbbbg faaaaaac ebbbbbbbbg caaaaaaf ebbbbbbbbg aaaaaaag dbbbbbbbbd faaaaaac dbbbbbbbbd gaaaaaaa dbbbbbbbbd faaaaaac gbbbbbbbbe caaaaaaf gbbbbbbbbe aaaaaaa gbbbbbbbbe faaaaaac ebbbbbbbeg caaaaaafebbbbbbbbg aaaaaaebbbbbbbbg caaaaebbbbbbbbg gaaaebbbbbbbbd faabbbbbbbbd cabbbbbbbbd gbbbbbbbbegg gbbbbbbbbbaaaaaaffffccccgg gebbbbbbbbaaaaaaaaaaaaaaaaaaaa ebbbbbbbbaaaaaaaaaaaaaaaaaaaaa ebbbbbbbbaaaaaaaaaaaaaaaaaaaaaa ebbbbbbbbaaaaaaaaaaaaaaaaaaaaaaa dbbbbbbbbfaaaaaaaaaaaaaaaaaaaaaaa dbbbbbbbbd gccccffffaaaaaaaaaaaa dbbbbbbbbd ggccccfff gbbbbbbbbe gbbbbbbbbe gbbbbbbbbe ebbbbbbbeg ebbbbbbbbg ebbbbbbbbg dbbbbbbbbg dbbbbbbbbd dbbbbbbbbd gbbbbbbbbd gbbbbbbbbe gbbbbbbbbe gebbbbbbbe ebbbbbbbbg bbbbbbbbg bbbbbbbg bbbbbbd bbbbbd ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 1; B: 1; 1 + 1 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#bf6ea2ff b,#4abfb5ff c,#e1bdd4ff d,#a9e0dbff e,#74c9c4ff f,#cd93b9ff g,#e6e8edff ``` ```image gcc gccfaaaaaaaaaaa gccfaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaac caaaaaaaaaaaaaaaaaaafccg faaa bg faaaaaaaaafccg aaa bbbd faaa aaaf bbbbd faaf caaa bbbbe aaaf aaac bbbbe aaaf aaaa ebbbb aaac gaaa dbbbb aaac aaaf dbbbb aaac faaa gbbbb aaac aaag gbbbb aaag aaaa bbbbg aaag caaa bbbbd aaag aaac bbbbd aaa faaa bbbbe aaa aaa ebbbe aaa aaaf ebbbb aaa caaa dbbbb aaa aaac gbbbb aaa aaaa gbbbb aaa gaaa bbbbg gaaa aaaf bbbbg gaaa faaa bbbbd gaaa aaag bbbbe caaa aaaa bbbbe caaa gaaaebbbb caaa aaebbbb caaa fabbbb faaa gbbbbg faaa gbbbbaaaaaaaaaaffccg faaf bbbbaaaaaaaaaaaaaaaaaaaaaaaag faaf bbbbfaaaaaaaaaaaaaaaaaaaaaaaa aaaf bbbbd gccffaaaaaaaaaaaa aaaf bbbbe gccf aaac ebbbe aaac ebbbb aaac dbbbb e aaag gbbbb gbbb aaag gbbbb bbbd aaag bbbbg ebbb aaa bbbbg gbbb aaa bbbbd bbbd aaa bbbbe ebbb aaa bbbbe bbb aaa ebbbb bbbe aaa dbbbb dbbb aaa dbbbb bbbg aaa gbbbb bbbe gaaa bbbb dbbb gaaa bbbbg bbbg caaa bbbbd bbbb caaa bbbbd dbbb faaa bbbbe bbbd gaaaf ebbbb bbbb aaaa ebbbb gbbb caaag dbbbb bbbd aaaa gbbbb ebbb aaaa gbbbb gbbb gaaac bbbbg bbbdaaaa bbbbg ebbbaaa bbbbd bbbaaf bbbbe bbbba bbbbe ebbbg ebbbb abbbg dbbbb aabbbe dbbbb gaaebbb gbbbb aaaabbbg bbbb faaa bbbb bbbbg aaaf dbbb bbbbd aaaa bbbd bbbbd caaag bbbb bbbbe aaaa gbbb ebbbb aaaa bbbbbbbb gaaac ebbbbbb aaaa gbbbbb faaag bbbb aaaf dbbg aaa gg ``` <!-- end of image -->
[ "" ]
I'm optimistic that I'll find some intersections in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#f339c0ff b,#54c6acff c,#b1d7b2ff d,#faace4ff e,#0eb69cff f,#d582bbff g,#94c99aff ``` ```image da ee aa eec aad ceee aaf becec daaa ee ee aaaa eb ceb aada ec cec ee aa ad bee be ceb ad aa ceee ee ee da aa eeee eb ceb aa aa ee ee ggggggggggggggbebgggggeegggggggggaaggfagggggggggggggggggggg eec ee cccccccccccccceeccccccgeeccccccccafcccafccccccccccccccccccc beb ee cccccccccccccceeccccccceecccccccfafcccaaccccccccccccccccccc cee ee cccccccccccccceecccccccceeccccccfaccccaaccccccccccccccccccc ee ee cccccccccccccgegcccccccceeccccccaaccccfaccccccccccccccccccc ee ee ccccccccccccceecccccccccceecccccaacccccafcccccccccccccccccc eec ee ccccccccccccceecccccccccceecccccafcccccaacccccccccccccccccc cee ee ccccccccccccceeccccccccccceecccfaccccccaacccccccccccccccccc ee ee ccccccccccccgegccccccccccceecccaaccccccaacccccccccccccccccc ee ee cccccccccccceeccccccccccccceeccaaccccccfacccccccccccccccccc eec ee cccccccccccceeccccccccccccceeccaacccccccafccccccccccccccccc beb ee cccccccccccceecccccccccccccceecafcccccccaaccccccccccccccccc cee ee cccccccccccgegcccccccccccccceefaccccccccaaccccccccccccccccc ee ee ccccccccccceecccccccccccccccceaaccccccccfaccccccccccccccccc ee ee ccccccccccceeccccccccccccccccbaacccccccccafcccccccccccccccc eec ee cccccccccccebcccccccccccccccccafcccccccccaacccccccccccccccc beb be ccccccccccbegccccccccccccccccfaegccccccccaacccccccccccccccc ee be cccccccccceecccccccccccccccccaaeeccccccccaacccccccccccccccc ee be cccccccccceecccccccccccccccccaabebcccccccfacccccccccccccccc ee be ccccccccccebcccccccccccccccccaaceeccccccccafccccccccccccccc beb be cccccccccbegcccccccccccccccccafcbebcccccccaaccccccccccccccc cee be ccccccccceecccccccccccccccccfaccceecccccccaaccccccccccccccc ee be ccccccccceecccccccccccccccccaacccbebccccccfaccccccccccccccc ee be cccccccccebcccccccccccccccccaacccceeccccccfafcccccccccccccceec ce ccccccccbegcccccccccccccccccafccccgebccccccafcccccccccccccbeb ce cccccccceecccccccccccccccccfafccccceeccccccaaccccccccccccgee ce cccccccceecccccccccccccccccfaccccccgebcccccaaccccccccccccee ce ccccccccebcccccccccccccccccaaccccccceecccccfaccccccccccceeg ce cccccccbegcccccccccccccccccaacccccccgebcccccafccccccccceebc ce ccccccceeccccccccccccccccccafcccccccceecccccaaccccccccbeecc ce ccccccceecccccccccccccccccfacccccccccceeccccaacccccccgeeccc cec cccccccebcccccccccccccccccaacccccccccceeccccaaccccccceecccc ec ccccccbegccccfafccccccccccaaccccccccccceecccfacccccceegcccc ec cccccceecccccaafccccccccccaaccccccccccceeccccafcccceebccccc ec cccccceecccccaaaccccccccccafcccccccccccceecccaacccbeecccccc ec ccccccebccccfaaacccccccccfaccccccccccccceecccaaccceeccccccc ec cccccbegccccaaaacccccccccaacccccccccccccceeccfacceecccccccc ccccceecccccaaaacccccccccaacccccccccccccceecccafeegcccccccc ccccceeccccfacfacccccccccafccccccccccccccceeccaaebccccccccc cccccebccccaacfaccccccccfacccccccccccccccceegcaaecccccccccc ccccbecccccafccafcccccccaaccccccccccccccccceecaaccccccccccc cccceeccccaacccafcccccccaacccccccccccccccccbeebaccccccccccc cccceeccccaacccaacccccccaacccccccccccccccccceebafcccccccccc ccccebccccafcccaacccccccafccccccccccccccccccbbcaacccccccccc cccbeccccaaccccaaccccccfaccccccccccccccccccccccaacccccccccc ccceeccccaaccccaaccccccaaccccccccccccccccccccccfacccccccccc ccceecccfafccccfaccccccaacccccccccccccccccccccccafccccccccc cccebcccaacccccfaccccccafcccccccccccccccccccccccaaccccccccc ccccccccaaccccccafcccccafcccccccccccccccccccccccaaccccccccc cccccccfacccccccafccccfaccccccccccccccccccccccccaaccccccccc cccccccaacccccccaaccccaaccccccccccccccccccccccccfaccccccccc cccccccafcccccccaaccccaacccccccccccccccccccccccccafcccccccc ccccccfaccccccccaaccccafcccccccccccccccccccccccccaacccccccc ccccccaaccccccccaacccfaccccccccccccccccccccccccccaacccccccc ccccccafccccccccfacccaaccccccccccccccccccccccccccfacccccccc gggggaaggggggggggagggaagggggggggggggggggggggggggggafggggggg aa ad aa af faad dad af ad aa aaaaaf aa aa da aa daaaaaf aa aa aa da daaaaad dad aa aa ad daaaaad aa fa af aa daaaaad aa dadad aa faaaaa d daaa aa aaaaaf aaa daddaaaaad aaa aaaaad aad aad aa aa ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f338c0ff b,#4ec5b5ff c,#8ddcd0ff d,#fabbe9ff e,#0db69cff f,#f577d3ff g,#c9eee9ff ``` ```image geeg eeeb daaa daaad cee beeeg faaa aaad beb geeeb aaaf aaaf eec beeeg aaad faaa geeg geeeb daaad daaa cee beeeg faaa daaad eec ceeec aaaf faaf geeg eeeb aaad faaa cee ceeec daaad daaad bee eeee faaa aaad eee ceeec faaf aaaf geee eeee aaaf faaa ceee ceeec daaad faaa beeb eeee daaa daaad eeec ceeec faaa aaad geeeg eeee aaaf aaaf ceee ceee aaad faaa beeb bee daaad daaa eeec ceec faaa daaad ceee geeb aaaf faaf beeb beegdaaad faaa eeec geebdaaa daaa geeeg eeefaaa aaa ceee eeeaaaf aaa beeb beeaaad faa eeec gebaaad daa ceeeg bbaaa daad beee gaaaa aaf beeb aaafg faf eeec aaabb faa ceeeg daaabeg daad beee faaaeeb aad geeec aaafeeeb faa ceeeg daaadceeec daa beee daaa eeee daad eeeb faaa ceeec aaf geeec aaaf eeee aaf ceeeg aaad ceeec aaa beee aaad eeee aaad eeeb aaa ceee aaad geeec aaf eee aaaf ceeeg aaf ceec faaa beee daad eee daaa eeeb daa ceec daaad eeeg aaf geec aaaf b eee aaf eeeg faaa ce eeb daad eeeb daaa gee geec daa beeeg daaad geee ceeg faa geeeb aaaf beee bee aaf beeeg faaf beeeb eeb aad geeeb faaa ceeee geec daad beeeg daaad eeeeg ceeg faa geeeb aaad eeec bee faa beeeg aaaf beeb eeb aaa geeeb faaa ceeb geec daaa beeeg daaa ceeeg ceeg daaa geeeb daaad geeeg eee aaaf geeeb faaf beeeb geee fa aaad ceeec faaa ceeee ceee daad daaad eeee daaad geeeeg beee faad faaa ceeec aaad geeeec eeeb aaaf faaf eeee aaaf beeec geeec daaaf aaaf ceeec faaa beeeb ceeeg faaaf daaad eeee daaa ceeee beee aaaaa daaa ceee daaad geeeeg eeeb daaaaa faaa eee aaaf eeeec geeec faaaaad aaaf ceec faaf beeeb ceeeg daaafaad aaaf eee faaa ceeeb beee faaadaad daaad ceec daaad eeeeg geeec daaad faf faaa ceec aaafbeec ceeeg faaa faa aaaf eeeg faaaeeb beee aaaf faa aaad eeeb daaaee eeeb daaad daa daaad beeeg daaabg geeec faaa daad faaa geeeb gaaab ceeeg aaaf aad faaf beeeg baaaf beee daaad aad aaaf geeebbefaaa eeeb faaa aaf daaad beeeeebaaa geeec aaaf aaf daaa geeeeeeaaa ceeeg daaad aaa faaa beeeecaaa beee aaaa aaa aaaf geeeb faa eeeb daaad aaa aaad ceb faa geeec faaa aaad daaad daad beeb daaad aaaf faaf aaf eeeb faaa aaaf aaaf faa geeec aaaf faaf daaad daa ceee aaad faaa daaad daad beeb aaa daaa faaa aaf eeec aaf daaad faaf faf cbeg daad daaad aaaf faa faa aaad daaad daad daaf aaaf daaa aad faa faaf faaa aaf aaf faaf aaaf aaa daad faaa aaad aaa faa daaa aaad aaad daaa daaad aaf faaf faaa aaad aaf faaa aaaf aaaf daad daaad daaad faaf daa aaad faaa faaa faa aaaf aaaf faaa aaf faaa ``` <!-- end of image --> My investigation has led me to 2 intersections in area A! Answer: A: 2; 2 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#f337c0ff b,#46c5b3ff c,#8ddcd0ff d,#fab8e8ff e,#0cb69cff f,#f575d3ff g,#c5ede7ff ``` ```image df ee aa eec aad geee aaf becec daaa ee ee faaa eb cec aafa ec geg ee aa ad bee be geb ad aa ceee ee ee fa aa eeee eb geb aa fa ee ee geg ee aa dad eec ee be geb af af beb ee ee ee dad aa gee ee eb geb fa aa ee ee geg ee aa fa eeg ee be ee aa ad bec ee ee ee af aa ceb ee eb ee da aa gee ee geg ee aa aa ee ee be ee aa da eeg ee ee beg af af beb ee eb eedad aa gee ee geg befa aa ee ee be eaa fa ee ee ee baa dad eec be eb af af ceb be ceg dabg aa gee be be faee aa ee be ee aacec da eeg be eb aa ee af bec be ceg ad cec aa cee be ee fa ee aa ee ce ee aa cec fa ee ce eb aa ee dad eeg ce ceg af gec af beb ce ee dad ee aa gee ce ee fa geb aa ee ce eb aa ee fa ee ceg ceg aa geb ad eec geg ee af ee aa ceb geg ee da geb aa gee geg eb aa ee fa ee geg ceg dad aa eb dad eeg geg ee aaf af ee af bec ec ee aaf dad ee aa cee ec eb daaa fa ee aa ee ec ceg aaaa aa ee fa ee g ee afaa aa be adeeg ee fa fa af ee aaeb eb aa da dad beg aae ceg af ad fa ee aa ee fa af aa beeba ee aa aa aa eecaf ec dad aa ad cb aa ce aa aa fa aa ee aa aa aa fa ee dad fa aa dad ec aa da af af aa ad dad aa fa af fa aa aa aa aa da af aa aa af fa aa af aa aa fa da aa af fa aa fa aa dad aa dad aa ad af af faad dad af ad aa faaaaf aa aa fa aa daaaaaf aa aa aa da daaaaad dad aa aa ad daaaaad aa fa af aa faaaaad af dadad aa faaaafd d daaa fa dfaaaaf aaa daddaaaaaf aaa aaaaad aad aad aa aa ``` <!-- end of image -->
[ "" ]
I'm curious to see if this image contains any intersection points. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#92cc99ff b,#26c175ff c,#e4ee0bff d,#b1d8b1ff e,#d2e755ff f,#55ca89ff g,#f5f8a5ff ``` ```image ddd fbbbbbbbbbbbbbbbbbbbbbfffaaddd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbb ddddaafffbbbbbbbbbbbbbbb bbbb bbb bbb bbb bbbf bbb dbbb bbbd aaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbf fbbd dddddddddddddddddddddddddddddfbbb fbba dddddddddddddddddddddddddddddbbbf abbf ddddddddddddddddddddddddddddfbbba dbbb ddddddddddddddddddddddddddddbbbaa bbb dddddddddddddddddddddddddddfbbbda bbb dddddddddddddddddddddddddddbbbadaccg bbb ddddddddddddddddddddddddddbbbbddeccc bbb ddddddddddddddddddddddddddbbbdddcccc bbb dddddddddddddddddddddddddbbbbddccccc bbb ddcccdddddddddddddddddddabbbdddccccc bbb ddcccdddddddddddddddddddbbbbddccccccg ge bbb ddcccedddddddddddddddddabbbddecccecce eccc fbbd ddecccdddddddddddddddddbbbfddcccegccc gcccc fbba dddcccddddddddddddddddfbbbddcccca ccc cccccc abbf dddcccddddddddddddddddbbbfddcccda ccc ccccccce dbbf dddcccdddddddddddddddfbbbddccccda ccc cccc gccc dbbb dddcccdddddddddddddddbbbadecccdda cccg cccc cccc bbb dddeccedddddddddddddfbbbddcccedda ecce ccccg cccg bbb dddecccdddddddddddddbbbadecccddda gccc eccce eccc bbb ddddcccddddddddddddbbbbddccceddda ccc gccce cccc bbb ddddcccddddddddddddbbbddccccdddda ccc cccc gcccg bbb ddddcccdddddddddddbbbbddcccddddda ccc cccc cccc bbb ddddcccedddddddddabbbddccccddddda ccc cccc ccce bbb ddddeccedddddddddbbbfdecccdddddda cccg cccc gccc bbbd ddddecccddddddddabbbddcccedddddda gcce ecccg ccccaaaaabbbfaaaaaa dddddcccddddddddbbbfdccccddddddda gccc eccce ccceddddfbbfdddddd dddddcccdddddddfbbbddcccdddddddda ccc gcccc ecccddddabbbdddddd dddddcccdddddddbbbfdccccdddddddda ccc cccc dccccdddabbbdddddd dddddcccedddddfbbbdecccddddddddda ccc cccc ddcccddddbbbdddddd dddddecccdddddbbbadccceddddddddda cccg cccc ddccccdddbbbdddddd ddddddcccddddfbbbdecccdddddddddda ecce cccc dddccccddbbbdddddd ddddddcccddddbbbadcccedddddddddda gccc ecccg dddecccddbbbdddddd ddddddcccdddbbbbdccccddddddddddda ccc gccce ddddccccdbbbdddddd ddddddcccdddbbbddcccdddddddddddda ccc gcccc dddddcccebbbdddddd ddddddeccedbbbbdccccdddddddddddda ccc cccc dddddecccbbbaddddd ddddddecccdbbbdecccddddddddddddda ccccccc ddddddccccbbaddddd dddddddcccabbbdccceddddddddddddda eccccc dddddddcccfbfddddd dddddddcccfbbfccccdddddddddddddda gccccg dddddddccccbfddddd dddddddcccbbbacccddddddddddddddda cccg ddddddddccccfddddd dddddddcccfbbccccddddddddddddddda cce dddddddddcccbddddd dddddddeccebfcccdddddddddddddddda dddddddddccccddddd dddddddecccbccccdddddddddddddddda ddddddddddcccedddd ddddddddcccecccddddddddddddddddda ddddddddddecccdddd ddddddddcccccceddddddddddddddddda ddddddddddbccccddd ddddddddccccccdddddddddddddddddda ddddddddddbbcccedd ddddddddcccccddddddddddddddddddda ddddddddddbbeccddd ddddddddeccccddddddddddddddddddda ddddddddddbbbedddd ddddddddbcccdddddddddddddddddddda ddddddddddbbbadddd dddddddabccedddddddddddddddddddda ddddddddddbbbadddd dddddddfbbfddddddddddddddddddddda ddddddddddfbbfdddd dddddddbbbaddddddddddddddddddddda ddddddddddfbbfdddd dddddddbbbdddddddddddddddddddddda ddddddddddabbbdddd ddddddabbbdddddddddddddddddddddda aaaaaaaaaaabbbaaaa ddddddfbbfdddddddddddddddddddddda bbb ddddddbbbadddddddddddddddddddddda bbb ddddddbbbddddddddddddddddddddddda bbb dddddabbbddddddddddddddddddddddda bbb aaaaabbbfaaaaaaaaaaaaaaaaaaaaaaad bbb bbb bbb bbb bbbd dbbb fbbd fbba fbba bbb abbf bbb dbbf dbbb bbb fbba bbb bbb bbb bbb bbb dbbb bbb fbba bbb bbb bbb bbb ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#e7f7dbff b,#27c175ff c,#e4ee0bff d,#99e1bdff e,#ebf24fff f,#5fd08aff g,#f3f798ff ``` ```image fbb dbbb bbbb dbbbb bbbbb dbbbbb abbbbbb fbbbbbb abbbbbbb fbbbbbbd abbbbbbf dbbbbbbf fbbbbbba dbbbbbbf bbbbbbba bbbbbbd bbbbbba dbbbbbd g aa abbbbbb c ggecce fbbbbbd gc ecccce abbbbbb acc gccccc fbbbbbd ecc accccca abbbbbf gccc cccccg fbbbbba cccc cccccg dbbbbbf gcccc ecccce fbbbbba accccc gcccce dbbbbbf eccccc gccccc bbbbbba acccccc accccca dbbbbbb ecccccc cccccg bbbbbbb gcccccce eccccg dbbbbbbd ccccccca ecccce abbbbbbb gcccccce gccccc fbbbbbbd accccccca gccccc abbbbbbb eccccccg cccccg abbbbbbf cccccccg ecccce fbbbbbba cccccce ecccce dbbbbbbf acccccca gccccc fbbbbbba eccccce accccca dbbbbbbf acccccc cccccg bbbbbbba ecccccg cccccg dbbbbbbd gccccce ccccce abbbbbbba cccccca ccccce dbbbbbbd gccccce cccccc abbbbbbb acccccca cccccca fbbbbbbd ecccccg ccccccg abbbbbbb gcccccc ecccccg fbbbbbbd ccccccg eccccce abbbbbbf gcccccc gcccccc fbbbbbba accccccc gcccccc dbbbbbbf ecccccce acccccca fbbbbbba accccccc ccccccg dbbbbbbf eccccccg eccccce bbbbbbba gcccccce eccccce dbbbbbbd ccccccca gcccccc bbbbbbba gcccccce acccccca bbbbbbd accccccca ccccccg fbbbbbd gccccccc eccccce abbbbbb eccccccg gccccce fbbbbbd gcccccce gcccccc abbbbbf accccccca acccccca fbbbbba ecccccce ccccccg dbbbbbf accccccc ecccccg fbbbbba eccccccg eccccce dbbbbbf gcccccce gcccccc bbbbbba ccccccca gcccccc dbbbbbd gcccccce acccccca abbbbbba accccccca ccccccg dbbbbbb eccccccg eccccce abbbbbbb gccccccc eccccce dbbbbbbd eccccccg gcccccc fbbbbbb gcccccce acccccca bbbbbbd ccccccca ccccccgabbbbbba cccccce ccccccgdbbbbbb acccccc ecccccefbbbbbf ecccccg gcccccebbbbbbdgccccce gccccccbbbbbbaccccccg accccccbbbbbbgccccce ecccccfbbbbecccccg eccccccbbbfcccccc gccccccbbbccccccg gccccccbbfccccce accccccfbcccccca ccccccfccccccc eccccccccccccc eccccccccccccg gccccccccccce acccccccccccg cccccccccce cccccccccca cccccccccg afcccccccc dfcccccccg fbcccccce bbcccccca abbfccccg dbbbfccg fbbbbbf bbbbbbd abbbbbba dbbbbbb bbbbbbd abbbbbba dbbbbbb fbbbbbf bbbbbbd abbbbbba dbbbbbb fbbbbbf bbbbbbd abbbbbba dbbbbbb ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area A. Right then, let's explore the next spot. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ed939ff b,#27c174ff c,#e4ee0bff d,#aae6c9ff e,#ebf34fff f,#65d29dff g,#f2f7a3ff ``` ```image cccccce fbbbbbd cccccccg fbbbbbd gcccccce fbbbbbf eccccccg fbbbbbf gccccccc dbbbbbf ecccccce dbbbbbf cccccccg dbbbbbb gccccccc dbbbbbb ecccccce bbbbbb cccccccg bbbbbb gccccccc bbbbbbd eccccccg bbbbbbd gccccccc bbbbbbd ecccccce fbbbbbd cccccccg fbbbbbf gccccccc fbbbbbf ecccccce dbbbbbf cccccccg dbbbbbf gccccccc dbbbbbb eccccccedbbbbbb gcccccccgbbbbbb eccccccebbbbbb cccccccabbbbbd gcccccccbbbbbd eccccccabbbbd cccccccabbbd gcccccccbbbf eccccccabbf cccccccbbf gcccccccbf cccccccab gcccccccb ecccccca cccccccg gccccccc acccccce bcccccccg facccccce fbcccccccg fbbccccccc fbbacccccce dbbbcccccccg dbbbacccccce dbbbbaccccg dbbbbbcce bbbbbag bbbbbb bbbbbbd bbbbbbd fbbbbbd fbbbbbd fbbbbbf fbbbbbf dbbbbbf dbbbbbf dbbbbbb dbbbbbb ``` <!-- end of image --> The lines cross each other within area B, forming 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#e7f7e0ff b,#26c175ff c,#e4ee0bff d,#a6e5c6ff e,#ecf354ff f,#63d194ff g,#f4f89eff ``` ```image dddaa fbbbbbbbbbbbbbbbbbbbbbffffddddaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb abbba aaddddffffbbbbbbbbbbbbbbbb bbbb bbb abbb bbb bbbf bbba dbbb bbba bbbf fbbd dbbb fbbf bbbd dbbf fbbb dbbb bbbd abbb fbbb bbb bbba ccg bbb bbbb eccc bbb abbba cccc bbb g bbbb ccccc bbb ccc abbb accccca bbb ccca bbbf ccccccg ge bbba cccg dbbb gcccecce eccc bbbd gcce bbbf cccegccc gcccca fbbd accc dbbb eccc ccc acccccc dbbf ccc bbbd cccg ccc ccccccce dbbb ccc fbbb cccc ccc cccc gccc abbb ccca bbbd gccc cccg cccca cccc bbb ecce fbbb ccce ecce ccccg cccg bbb gccc bbba eccc gccc eccce eccc bbb ccc bbbb cccg ccc gccce cccc bbb ccc abbba cccc ccc acccc accca bbb ccc bbbb accca ccc cccc cccc bbb cccg abbb cccc ccca cccc ccce bbba ecce bbbf gccc eccg cccca gccc bbbd gccc dbbb ccce gcce ecccg cccc fbbd ccc bbbf eccc accc eccce cccg fbbf ccc dbbb cccg ccc gcccc eccc dbbf ccca bbbd cccc ccc acccc cccc dbbb cccg fbbb gccc ccc cccc acccg abbb gcce bbbd ccce cccg cccc eccc bbb accc fbbb eccc ecce cccca ccce bbb ccc bbba cccg gccc ecccg gccca bbb ccc bbbb cccc ccc gccce cccc bbb ccca abbbaaccca ccc acccc cccebbb ecce bbbb cccc ccc cccc ecccbbba gccc bbb gccc ccccccc ccccbbd cccabbb ccce eccccc acccfbd cccfbbfeccc gcccca ecccbf cccbbbacccg acccg ccccf cccfbbcccc cce gcccb ecccbfccc cccc gcccbccce ccce ccccccc fccc ccccccg bcccc cccccc bbcccg ccccca bbccc fcccc bbbg bccc bbba abccg fbbd fbbf fbbf bbba dbbf bbb dbbb abbb abbb fbbf bbb bbba bbb bbb bbb dbbb bbb fbbf bbb bbba bbb bbb bbba dbbb bbbd fbbf fbbd bbba dbbf bbb dbbb dbbb abbb fbbf bbb bbba bbb bbb bbb dbbb bbb fbbf bbb bbba bbb bbb a ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#5dcc8aff b,#686816ff c,#b1d8b2ff d,#7d843fff e,#95cb9aff f,#98a46dff g,#d9eddcff ``` ```image a gag ac cac gac eae gag aaa cag aaa ca aaa ea aaa aa aaa aa aaa aa aaa aa gaaa aa gaeag aa cagag aa ea ac ae aa ae ac aa aa gac eg aa aa gag bb aa aa cag bb aa aa ca gbb aa aa ea ebbc ae aa aa dbbd ac ea aa bbbb gag ca aa bbbb cag cag aa bbfb ca gag aa eeeeeeeebdfbfeeeeeeeeeeeeec aa ac aa cccccccebfcbbccccccccccccce aaa ac aa cccccccfbecbbccccccccccccce eaae ae ae cccccccdbccbbccccccccccccce gaaa aa ac cccccccbbccfbccccccccccccce eaac aa gac cccccccbbccebfccccccccccccegaaa aa gag cccccccbbcccbbccccccccccccaaac aa cag cccccccbdcccbbcccccccccceaaa aa ca ccccccebfcccbbcccccccccaaae ea ea ccccccfbecccfbecccccceaaace ca aa ccccccdbccccebfcccccaaaecce ca aa ccccccbbcccccbbccceaaacccce gag aa ccccccbbcccccbbccaaacccccce gaaaaaaaaaaaaaaaaeeecccccgggggg aa ccccccbbcccccbbeaaaccccccce aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa ccccccbdcccccfbaaccccccccce ggggggcccceeeeaag cccccebfccccaabdcccccccccce cccccfbecccaaabbcccccccccce cccccdbccaaaecbbcccccccccce cccccbbeaaacccdbcccccccccce cccccbbaaeccccfbeccccccccce ccccebbacccccccbdccccccccce cccaabdccccccccbbccccccccce cccaabfccccccccbbccccccccce ccccfbeccccccccdbccccccccce ccccdbcccccccccfbecccccccce ccccbbccccccccccbdcccccccce ccccbbccccccccccbbcccccccce ccccbbccccccccccbbcccccccce ccccbdccccccccccdbcccccccce cccebfccccccccccfbfccccccce cccfbecccccccccccbdccccccce cccdbccccccccccccbbccccccce cccbbccccccccccccbbccccccce cccbbccccccccccccdbccccccce cccbbccccccccccccfbfcccccce eeebdeeeeeeeeeeeeebdeeeeeec bf bb bb fbc fb fbbbd cbc fbb bbbg bd ebb fbbf bb cbb bbb bb cbb dbbg fb cbb cbbd gbc gbb bbb bd gbb fbbc bbgbbg gbbd bbbbg bbbg fbbg ebbf cfbbbbe bg bbb cfbbbbbbbbbfg dbbc gfbbbbbbbbbfc gbbd gfdbbbbbbbbfc bbbedbbbbbbbbdc fbbbbbdeg g ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5fcc8bff b,#686917ff c,#ccccb1ff d,#8a8f50ff e,#aeae82ff f,#9fe0baff g,#e1ebddff ``` ```image bbbd gbbbe bbbe bbbd gbbbe dbbb cbbbc ebbbg ebbbg cbbbc ebbb gbbbe dbbb bbbd bbbd dbbb bbbe ebbbg gbbbe cbbbc cbbbc gbbbe ebbbg bbbd ebbb dbbb dbbb ebbbg f bbbd cbbbc gaa bbbe gbbbe faaa gbbbe bbbd gaaaaa cbbbc dbbb gfaaaaaf ebbbg ebbbg faaaaaag ebbb cbbbc gfaaaaaf dbbb gbbbe faaaaaag dbbd bbbd gaaaaaaf bbbe dbbb faaaaaag gbbbe ebbbg gaaaaaaf cbbbc cbbbc faaaaaag ebbbg gbbbe gaaaaaaf ebbb bbbdfaaaaafg dbbb dbbbaaaaag dbbd ebbbaaaf bbbe fabbbdag gbbbe gfaabbbd cbbbc faaaabbbd cbbbg gaaaaaadbbb ebbb faaaaaagebbbg dbbb gaaaaaaf cbbbc dbbd faaaaaag bbbe bbbegaaaaaaf dbbd gbbbdaaaaafg dbbb cbbbdaaaaf ebbbg ebbbaaaf gbbbc gdbbbaag bbbe gfabbbbf dbbd faaabbbd ebbb gaaaabbbe cbbbc aaaabbbe gbbbe gafcbbbc bbbd cbbbg dbbd ebbb ebbb dbbb cbbbc dbbd gbbbe bbbd bbbd gbbbe dbbb cbbbc ebbbg cbbbg cbbbc ebbbg gbbbe dbbb bbbd dbbd dbbb bbbd ebbbg gbbbe cbbbc cbbbc gbbbe cbbbg bbbd ebbbg dbbb dbbb ebbbg dbbd cbbbc bbbd gbbbe gbbbe bbbd cbbbc dbbb cbbbg ebbbg ebbbg cbbbc dbbb gbbbe ``` <!-- end of image --> Success! This area contains 2 intersections point! Answer: A: 2; 2 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#5dcc8bff b,#686817ff c,#bee0c4ff d,#8e8f52ff e,#b5b58dff f,#8cdaadff g,#dfeddfff ``` ```image a cac af cac gac faf gag aaa cag aaa fa aaa fa aaa aa aaa aa aaa aa aaa aa gaaa aa gafag aa cacac aa fa ac af aa af af aa af gac eg aa aa gag bb aa aa cag bb aa aa fa gbb aa aa fa ebbe af aa aa dbbd ac fa aa bbbb gag fa aa bbbb cag cag aa bbeb fa gag aa bdgbe aa gac aa gbe bb aaa af aa ebg bb faaf af af db bb gaaa aa af bb ebg faaf aa gac bb gbe gaaa aa gag bb bb aaac aa cag bd bb gaaa aa fa gbe bb aaac fa fa ebg ebg caaa fa aa db gbe aaag cag aa bb bb caaf gag aa bb bb aaag gaaaaaaaaaaaaaaaafffffcccccgggg aa bb bbfaaf aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa bd ebaa ggggcccccfffffaac gbe fabd ebg gaaabb db faac bb bbgaaa db bbaac ebg cbba bd aabd bb aabe bb ebg db db ebc bb bd bb bb bb bb bd db gbe cbc ebg bd db bb bb bb bb db bb cbc bd bd be bb bb dbc db dbbbd cbe ebb bbbg bd ebb ebbe bb ebb gbbb bb cbb dbbg db cbb cbbd gbe gbb bbb bd gbb dbbe bbgbbg gbbb bbbbg bbbg ebbg ebbd cdbbbbe gbc bbb cdbbbbbbbbbeg dbbc cebbbbbbbbbdc cbbd gebbbbbbbbbdc bbbedbbbbbbbbde ebbbbbdeg g ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#64f348ff b,#1ffd9eff c,#b2d8b2ff d,#8aee78ff e,#67efaeff f,#ebf8ebff g,#a3d4a2ff ``` ```image daf aaa aaa aaa aaaf aaad aaaa aaaa cad aaaa gaa aaaaf aaa faaaad faaf faadaa aaa caacaa faac caa aa aaa daa aac aad daa aad daa aaa daa aaa aad faa caaf aad aa aaa aag aac faac aac aad aaa aac daa aad aaf faa daa aaf aaf aaa aa aac caaf aa aaa aaa aa gaa faac faa faa aaa faa aaf aad caa aag daa gaa aaa aad daa caa caaf daa faa aaa aaa aaf faaf ffffffffffffffffffffffffffffffffffffffffaadffffffaadffffffffffffff aaagggggggggggggggggggggggggggggggggggggggggaadggggggaaagggggggggggggg e faadccccccccccccccccccccccccccccccccccccccccaadccccccdaacccccccccccccc ebb daaccccccccccccccccccccccccccccccccccccccccaadcccccccaagccccccccccccc fbbb aaacccccccccccccccccccccccccccccccccccccccaagcccccccaaaaagcccccccccc cbbb gaacccccccccccccccccccccccccccccccccccccccaagcccccccgaaaaaadcccccccc ebbe aaaccccccccccccccccccccccccccccccccccccccaagccccccccccdaaaaaadccccc ebbe daagcccccccccccccccccccccccccccccccccccccaaccccccccccccccdaaaaaaccc bbbe gaaacccccccccccccccccccccccccccccccccccccaaccccccccccccccccgaaaaccc bbbc ggaadccccccccccccccccccccccccccccccccccccaaccccccccccccccccccebbccc bbbf gcaaacccccccccccccccccccccccccccccccccccgaacccccccccccccccccebbbccc bbbf gccaadccccccccccccccccccccccccccccccccccgaaccccccccccccccccebbbcccc bbb gccdaaccccccccccccccccccccccccccccccccccdaacccccccccccccccbbbbccccc bbb gcccaaacccccccccccccccccccccccccccccccccdaaccccccccccccccbbbbcccccc fbbb gcccdaagccccccccccccccccccccccccccccccccdaacccccccccccccbbbbccccccc fbbb gccccaaaccccccccccccccccccccccccccccccccaaaccccccccccccbbbecccccccc fbbb gccccgaadcccccccccccccccccccccccccccccccaaaccccccccccgbbbeccccccccc ebbb gcccccaaacccccccccccccccccccccccccccccccaaacccccccccbbbbecccccccccc ebbe gccccccaaagcccccccccccccccccccccccccccccaadcccggeeebbbbgccccccccccc ebbegccccccgaaagcccccccccccccggeeeeebbbbbbbbbbbbbbbbbbbbbeccccccccccccc bbbecccggeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeccccccccccccccc bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeeaagcccccccccccccccccccccccc bbbbbbbbbbbbbbbbeeeeggcccccccccccccccccccaagcccccccccccccccccccccccc gcccccccccccaaaaccccccccccccccccccccccccaaccccccccccccccccccccccccc gccccccccccccdaaacccccccccccccccccccccccaaccccccccccccccccccccccccc gcccccccccccccgaaagcccccccccccccccccccccaaccccccccccccccccccccccccc gccccccccccccccgaaadcccccccccccccccccccgaaccccccccccccccccccccccccc gccccccccccccccccaaadccccccccccccccccccgaaccccccccccccccccccccccccc gcccccccccccccccccaaaacccccccccccccccccgaaccccccccccccccccccccccccc gccccccccccccccccccaaaaccccccccccccccccdaaccccccccccccccccccccccccc gcccccccccccccccccccdaaacccccccccccccccdaaccccccccccccccccccccccccc gccccccccccccccccccccgaaagcccccccccccccdaaccccccccccccccccccccccccc gcccccccccccccccccccccgaaadccccccccccccaaaccccccccccccccccccccccccc gcccccccccccccccccccccccaaadcccccccccccaaaccccccccccccccccccccccccc gccccccccccccccccccccccccaaaaccccccccccaaaccccccccccccccccccccccccc ggggggggggggggggggggggggggaaaagggggggggaadggggggggggggggggggggggggg ffffffffffffffffffffffffffdaaaffffffffaagfffffffffffffffffffffffff faaaf aac faaac aaf aaad aaf aaaa aa daaa aa daaa aa caaaaa faaaa aaa dc ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#64f448ff b,#1efd9eff c,#b7f9aaff d,#8df678ff e,#56fdb6ff f,#d8fcdeff g,#97fdd2ff ``` ```image aaad faaad aaad aaad faaad daaaf c faaac caaac af faaac faaad ad caaac aaaaf aa caaaf caaaaaadc aac caaaf faaaaaaaadc aaa daaaf daaaaaaaaaad aaac daaaf cdaaaaaaaaacf daaad daaa fdaaaaaaaaadf faaaaf daaa cdaaaaaaaaaa daaad aaaa fcaaaaaaaa faaaa aaad fcaaaaaa aaaac aaad bbbe caaaa faaad gbbbb aaaac faaad gbbbbb caaaaf faaac ebbbbbg faaaaf caaac bbbbbf daaad caaac ebbbbf faaaa caaaf febbbbb aaaa caaaf fbbbbbef caaaaf daaaf fbbbbe daaad daaa gbbbbb faaaaf daaa gbbbbbe daaad daaa gbbbbbg caaaa aaad gbbbbbg aaaa aaad gbbbbbbb aaaad aaad fbbbbbbbf daaaad faaad ffffggebbbbbbef faaaaaaf ffffgggbbbbeebbbbbbbbbbbbbbbbf fdaaaac ffffgggggeeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbg g ffffggggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbf bebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeegggggf bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeegggggdaaac bbbbbbbbbbbbbbbbbbbbbbbeegggggfff daaaf bbbeeeeegggggfff aaaaaac daaaf daaaaac daaa daaaaa daaa aaaaadf aaaa faaaaaaf aaad faaaaaa aaad daaaac aaad caaaaad faaac caaaaad faaac faaaaaf faaac faaaaac caaac daaaaad caaaf caaaaa caaaf caaaadf daaaf aaaaaaf daaaf daaaaa daaa daaaad daaa aaaaad aaaa caaaaadf aaaa faaaaaf aaaa faaaaac aaaa ``` <!-- end of image --> I can confirm that 2 intersections exists in area A. Answer: A: 2; 2 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#64f448ff b,#1ffd9eff c,#b4f9a6ff d,#8df678ff e,#5ffdbaff f,#d9fcd7ff g,#9ffed6ff ``` ```image daf aaa aaa aaa aaaf aaad aaaa aaaa cad aaaa caa aaaaf aaa faaaad faaf faadaa aaa caacaa aac caa aa aaa daa aaf aad daa aad daa aaa daa aaa aad faa caaf aad aa aaa aac aac faac aac aad aaa aaf daa aad aaf faa daa aa aa aaa aa aac caa aa aaa aaa aa caa faaf faa faa aaa faa aaf aac caa aac daa caa aaa aad daa caa caa daa aa aaa aaa aaf faaf aad aad aaa aad daa g aac aac caa ebb daa aac aaf gbbb aad aaf aaaad gbbb caa aaf faaaaaad ebbe aaa aa caaaaaac ebbe faaf aa daaaaaa bbbg aaa aa faaaa bbbg aac aa gbe bbbf aaa faa ebbb bbbf aad faa ebbb bbb daa caa ebbb bbb aaa caa bbbb bbb caaf daa bbbe fbbb aaa daa bbbe gbbb faac aaa fbbbg gbbb aaa aad bbbbg ebbe aaa aad fggebbbbf ebbe faaaf fgggeeebbbbbbbbbbbbbbbbbbbbg bbbg ffgggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeegggaaf bbbbbbbbbbbbbbbbegggff aaf daaa aa caaa aa faaaf aa aaac aa aaad faa aaaa faa daaa caa caaa caa faaaf daa aaac daa aaad aaa aaaa aad daaa aad caaa aac faaaf aac faaac aaf aaad aaf aaaa aa daaa aa caaa aa faaaaa faaaa aaa df ``` <!-- end of image -->
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Let's examine this image for potential line intersections. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#ccad0aff b,#77d47aff c,#b2d8b2ff d,#d4cb6cff e,#a2d0a0ff f,#eef6ecff g,#4ecf59ff ``` ```image b ggf bgc cgb fgg ggf bgc cgb fgg ggf ggf ege fgg gg ggf bge cgb fgg ggf bgc cgb fgg ggf bgc egb fgg gg ggf bge ffffffffffffffffffffffffffffffffffffffffffff cgg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee fgg fecccccccccccccccccccccccccccccccccccccccccce ggfecccccccccccccccccccccccccccccccccccccccccce bgbcccccccccccccccccccccccccccccccccccccccccce cggccccccccccccccccccccccccccccccccccccccccce feggcccccccccccccccccccccccccccccccccccccccce fecggecccccccccccccccccccccceaaccccccccccccce feccggecccccccccccccccccceaaaaaccccccccccccce fecccbgbcccccccccccccceaaaadccaccccccccccccce fecccceggcccccccccceaaaadcccccadcccccccccccce feccccccggcccccceaaaadccccccccaacccccccccccce fecccccccggbcdaaaadcccccccccccdacccccccccccce feccccccccbaaaadcccccccccccccccacccccccccccce fecccccdaaaaeggggecccccccccccccadccccccccccce feccdaaaaecccccegggbcccccccccccaaccccccccccce fdaaaaecccccccccccbgggbccccccccdaccccccccccce daaaaecccccccccccccccccbgggeccccccaccccccccccce daaadfecccccccccccccccccccccegggbccccadcccccccccce daaadf feccccccccccccccccccccccccbgggbcaacccccccccce daaadf fecccccccccccccccccccccccccccbggaacccccccccce daaad fecccccccccccccccccccccccccccccegaggcccccccce daaad fecccccccccccccccccccccccccccccccabgggbccccce daaad fecccccccccccccccccccccccccccccccaaccbgggecce daaad fecccccccccccccccccccccccccccccccdacccccgccce fdaaad feccccccccccccccccccccccccccccccceaccccccccce fdaaad feccccccccccccccccccccccccccccccccaecccccccce fdaaad feccccccccccccccccccccccccccccccccadcccccccce fdaaad feccccccccccccccccccccccccccccccccaacccccccce faaaad fecccccccccccccccccccccccccccccccceacccccccce aad fecccccccccccccccccccccccccccccccccacccccccce fecccccccccccccccccccccccccccccccccadccccccce fecccccccccccccccccccccccccccccccccaaccccccce fecccccccccccccccccccccccccccccccccdaccccccce feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeee ad aa da a ac aa da a af ad da fa af ad da fa af ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#cdad07ff b,#78d97eff c,#a8e7acff d,#e8d98fff e,#d8c147ff f,#e6f1d3ff g,#4ecf58ff ``` ```image f gf ggc gggb cgggbf fggggf fbgggc bgggc cgggb fdeae fggggf fdeaaaaaf fbgggc fdeaaaaaaaad bgggc fdeaaaaaaedfaae cgggb fdeaaaaaaed eaa fgggbf fdeaaaaaaed daaf fggggf fdaaaaaaaed daad bgggc fdaaaaaaaed aae cgggb fdaaaaaaaed eaa cgggbf feaaaaaaaed eaaf fggggcf feaaaaaaaef daad bggggeaaaaaaaef faae baaaaaaaaef aaa deaaaaaaaagggcf eaaf deaaaaaaadfcbgggggbcf daad deaaaaaaadf fcggggggbc faae deaaaaaaadf fbggggggbf aaa deaaaaaaedf cbggggggcf eaaf deaaaaaaedf fcggggggbc daad eaaaaaaedf fbggggggbf faae aaaaedf cbggggggcf aae aedf fcbgggggbc eaa f fcggggggbc daad fbggggggcf faad cbgggggbcf aae fcggggggbceaa fbgggggaaaf cbgggaaecf fcgaaaggbc eaagggggbf daacbggggggcf daad fcbgggggbcf aae fcggggggbf eaa fbggggf eaaf cbb daad faae aaa eaaf daad faae aae eaa daad faad aae eaa daaf faad aae eaa daaf daad ``` <!-- end of image --> I've cracked the case! This area contains 2 intersections. Answer: A: 2; 2 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#cdad07ff b,#77d97dff c,#a9e7acff d,#e9da91ff e,#dac248ff f,#e9f2d8ff g,#4ecf59ff ``` ```image b ggf bgc cgb fgg ggf bgc cgb fgg gg ggf cgb fgg gg ggf bgc cgb gg ggf bgc cgb fgg gg bgf cgb fgg gg ggf bgc fgg gg ggf bgc cgb fgg ggf fee bgc feaaaa cgb feaaad a fgg faaaad ad gg faaaad ea ggc faaaad da baaaaf a daaaafbggbf ad daaaaf fgggb aa daaaef cgggc da daaaef bgggf a daaaef fgggb ad daaaef cgggc ae daaae bggaa daaae fgagb eaaae acgggc eaaae ae cgggf eaaad ea b eaaad fa eaaad af feaaad ae feaaad ea feaaad fa aad a ad ea da a ad aa da a ad ae da a af ae da fa af ae ea fa af ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#47b2cfff b,#119fd7ff c,#acdef1ff d,#ecf6f2ff e,#6bc7e7ff f,#b0d7b1ff g,#94c998ff ``` ```image abe bbb bbbbd dbbbbe bbbbbb cbbecbb bbb bbe cbbc bbb bbb ebb ebbc bbe bbb bbb abbd ebb bbb bbc bbb bbb dbba ebb bbb dbbc cbbe bbb bbb abb cbbc dbbc bbb bbb ebbc abb dce bbb dbbd eee abbd bba cee bbb bbb eed bbb cbbd eec dbba bba eee bbb bbb eee cbbe cbbd cee bbb bbe deed cbbc bbb eec bbb cbb eee ebbc dddddbbedddddddddddddddd eee bbb dgffffbbbfffffffffffffffg cee abbd dfffffabbfffffffffffffffg dee bbb dffffffbbaffffffffffffffg eec bbb dffffffbbbffffffffffffffg eee dbba dffffffabbffffffffffffffg dddddeeeddddddddddddddddddddddddddddbbb dfffffffbbafffffffffffffg fffffeeefffffffffffffffffffffffffffgbbad dfffffffbbbfffffffffffffg ffffffeefffffffffffffffffffffffffffbbbfd dfffffffabbfffffffffffffg ffffffeeffffffffffffffffffffffffffebbefd dffffffffbbeffffffffffffg ffffffeeefffffffffffffffffffffffffbbbffd dffffffffbbbffffffffffffg ffffffeeeffffffffffffffffffffffffabbgffd dffffffffabbffffffffffffg ffffffeeeffffffffffffffffffffffffbbbfffd dfffffffffbbgfffffffffffg fffffffeefffffffffffffffffffffffabbffffd dfffffffffbbbfffffffffffg fffffffeefffffffffffffffffffffffbbbffffd dfffffffffabbffffffffeeeg fffffffeeefffffffffffffffffffffbbbfffffd dffffffffffbbeeeeeeeeeeeg fffffffeeeffffffffffffffffffffgbbafffffd dffffffeeeebbbeeeeeeeeeeg fffffffeeeffffffffffffffffgabbbbbffffffd dceeeeeeeeeeebbbeeeeffffffg ffffffffeeffffffffffffgabbbbbbbbaffffffd dceeeeeeeeeeeeeeeeeeebbffffffffffg ffffffffeefffffffffabbbbbbbbbafffffffffd dceeeeeeeeeeeeeeeeeeffffffffbbafffffffffg ffffffffeeeffffabbbbbbbbbaffffffffffffeeeeeeeeeeeeeeeeeecd dfffffffffffbbbfffffffffg ffffffffeeeabbbbbbbbbafffffffffeeeeeeeeeeeeeeeeeecd dfffffffffffgbbfffffffffg fffffffabbbbbbbbbaffffffeeeeeeeeeeeeeeeeeecd dffffffffffffbbaffffffffg fffabbbbbbbbbafffeeeeeeeeeeeeeeeeeeefffd dffffffffffffbbbffffffffg ffbbbbbbbaeeeeeeeeeeeeeeeeeeeffffffffffd dffffffffffffebbffffffffg ffebbafffeeeeeeeeeeeeefffffffffffffffffd dfffffffffffffbbafffffffg fffffffffeeeeeeffffffffffffffffffffffffd dfffffffffffffbbbfffffffg fffffffffffffffffffffffffffffffffffffffd dfffffffffffffabbfffffffg fffffffffffffffffffffffffffffffffffffffd dffffffffffffffbbaffffffg fffffffffffffffffffffffffffffffffffffffd dffffffffffffffbbbffffffg fffffffffffffffffffffffffffffffffffffffd dffffffffffffffabbffffffg fffffffffffffffffffffffffffffffffffffffd dfffffffffffffffbbafffffg fffffffffffffffffffffffffffffffffffffffd dfffffffffffffffbbbfffffg fffffffffffffffffffffffffffffffffffffffd dgggggggggggggggabbgggggf fffffffffffffffffffffffffffffffffffffffd bbc fffffffffffffffffffffffffffffffffffffffd bbb fffffffffffffffffffffffffffffffffffffffd ebb fffffffffffffffffffffffffffffffffffffffd dbbc fffffffffffffffffffffffffffffffffffffffd bbb gggggggggggggggggggggggggggggggggggggggd abb dbbc bbb abb dbbd bba bbb cbbd bba bbb cbe ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#35addcff b,#119fd7ff c,#a9def2ff d,#e3f4faff e,#68c6eaff f,#8dd3eeff g,#c7e9f6ff ``` ```image feeeeg ebbbbb ceeeec gbbbbbe geeeef abbbbbd deeeee cbbbbbf eeeeed abbbbbd eeeeeg fbbbbbf feeeec abbbba ceeeef fbbbbbc geeeee dbbbbba deeeeed ebbbbbg eeeeeg dbbbbbe feeeec ebbbbbg ceeeef gbbbbbe geeeee abbbbbd deeeeed cbbbbbf eeeeeg abbbbbd feeeec cbbbbbf ceeeef abbbba geeeee fbbbbbc deeeee gbbbbba eeeeed gfabbbbbbbg feeeeg gfabbbbbbbbbba ceeeec gfebbbbbbbbbbbbbbg geeeef gfebbbbbbbbbbbbbbbbbf deeeee gfebbbbbbbbbbbbbbbbbbaeg eeeeed gfebbbbbbbbbbbbbbbbbbaecd feeeeg gfebbbbbbbbbbbbbbbbbbaecd ceeeec gfebbbbbbbbbbbbbbbbbbaecd ddgc geeeef dfeabbbbbbbbbbbbbbbbbaecd ddgcffeeeee deeeeefeabbbbbbbbbbbbbbbbbaecd ddgcffeeeeeeeeeeee eaabbbbbbbbbbbbbbbbbbaecd ddgcffeeeeeeeeeeeeeeeeeee dceabbbbbbbbbbbbbbbbbaecd ddgcffeeeeeeeeeeeeeeeeeeeeeeeeee dceabbbbbbbbbbbbbbbbbaecd ddgcffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeff dceabbbbbbbbbbbbbbbbbaecd ddgcffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffcgdd dbbbbbbbbbbbbbbbbbbecgggcffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffcgdd abbbbbbbbbbbbbaaeefeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeffcgdd ebbbbbbbbaefdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefccgdd cbbbbbefg feeeeeeeeeeeeeeeeeeeeeefccgd dbefg ceeeeeeeeeeeeeeefccgd deeeeeeeefccgd dcccgd ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Alright, let's examine the next area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#3aafddff b,#119fd7ff c,#a3dbf0ff d,#def2f9ff e,#68c6eaff f,#87d0ecff g,#bfe6f5ff ``` ```image abbbbe fbbbbb dbbbbbg abbbbe fbbbba dbbbbbg abbbbf fbbbba gbbbbbd abbbbf ebbbba gbbbbbd bbbbbf ebbbba gbbbbbd bbbbbc ebbbba cbbbbbd bbbbbc ebbbbe cbbbbb dbbbbbc abbbbe cbbbbb dbbbbbg abbbbe fbbbbb dbbbbbg dd abbbbe ddgcffeee fbbbba ddgcffeeeeeeeeee dbbbbbfcffeeeeeeeeeeeeeeeee dggcbbbbbaeeeeeeeeeeeeeeeeeeee dggcfeeeeeeabbbbbeeeeeeeeeeeeeeeeeeee dggcfeeeeeeeeeeeeeebbbbbeeeeeeeeeeeeefcggd eeeeeeeeeeeeeeeeeeeeebbbbbaeeeeffcggd eeeeeeeeeeeeeeeeeeeeeabbbbagdd eeeeeeeeeeeeeeeeeffcgcbbbbbd eeeeeeeeeeffcgdd bbbbbf eeeffcgdd ebbbba dd gbbbbbd bbbbbf ebbbba gbbbbbd bbbbbc ebbbba cbbbbbd bbbbbc ebbbbe cbbbbb dbbbbbc abbbbe cbbbbb dbbbbbg abbbbe fbbbbb dbbbbbg abbbbe fbbbba dbbbbbg abbbbf fbbbba gbbbbbd abbbbf ebbbba gbbbbbd ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area B. Answer: A: 1; B: 1; 1 + 1 = 2 I've identified a total of two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#41b2deff b,#119fd7ff c,#a3dbf0ff d,#dcf1f9ff e,#68c6eaff f,#85d0edff g,#bae4f4ff ``` ```image abe bbb bbbb dbbbbe bbbbbb gbbefbb bbb bbe fbbc bbb bbb fbb ebbg bbf bbb bbb abbd ebb bbb bbc bbb bbb dbba ebb bbb bbc gbbe bbb bbb abb fbbc dbbg bbb bbb ebbg abb dce bbb dbbd fee abbd bba gee bbb bbb eed bbb gbbd eec dbba bba eee bbb bbb fee gbbe cbb gee bbb bbe deed cbbc bbb eeg bbb cbb eef ebbg bbe eee bbb bbb cee abbd fbb dee bbb bbf eeg bbb bbb eef dbba ebb eee bbb bbf cee gbbe bbb dee bbb ebb eeg cbbf bbc eef bbb bbb eee ebbg abb fee bbb dbbg dee abbd bbb eed bbb abb dgfee eec bbb dbbffeeeeeeeee eee gbba dgfeeebbbeeeeeeeeef fee gabbbbb dgfeeeeeeeeeebbbeefcd gee dabbbbbbbbf dgfeeeeeeeeeeeeeeefccbbd eed debbbbbbbbbe dgfeeeeeeeeeeeeeeefcd bba eec debbbbbbbbbed dgfeeeeeeeeeeeeeeefcd bbb eeeebbbbbbbbbed dgfeeeeeeeeeeeeeeefcd gbbd debbbbbbbbbed dcfeeeeeeeeeeeeeeefcd bba debbbbbbbbbed dcfeeeeeeeeeeeeeeefcd bbb abbbbbbaefeeeeeeeeeeeeeeefgd cbb cbbed eeeeeeeeeeefgd bbe eeeefgd bbb fbb bbe bbb fbb bbf bbb ebb bbc bbb ebb dbbc bbb abb dbbg bbb abb dbbd bba bbb gbbd bba bbb cbe ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#e0df1cff b,#82346bff c,#b1d7b1ff d,#d8e268ff e,#a0798eff f,#ede4ccff g,#98c696ff ``` ```image df a a fa fa da aa aa aa ad ad gcccccccccccagcccc ccccccccccccaccccc ccccccccccccaccccc cccccccccccdaccccc e cccccccccccdaccccc eb cccccccccccdaccccc bbe cccccccccccaaccccc bbb cccccccccccaaccccc fb bf cccccccccccaaccccc eb be cccccccccccadccccc be eb cccccccccccadccccc bf bf cccccccccccacbcccc eb bb cccccccccccabbcccc bb eb ccccccccccbbbccccc bc bf cccccccccbbacccccc fb bb cccccccebbdacccccc eb eb ccccccbbbaaacccccc be bf cccccbbaaaaacccccc bf bb cccebbdacdaacccccc eb cb ccbbecaaccdccccccc ggggggggbbggggggggbegggggggggggggggg gbbgccaccccccccccc ccccccccbeccccccccbbcccccccccccccccc ebbcccdaccccccccccc cccccccgbcccccccccebcccccccccccccccc bbeccccaaccccccccccc cccccccbbccccccccccbeccccccccccccccc fbbfcccccacccccccccccc cccccccbeccccccccccbbccccccccccccccc ebb ccccaacccccccccccc cccccccbcccccccccccgbccccccccccccccc bbc ccccadcccccccccccc ccccccebccccccccccccbecccccccccccccc cbb cccdaccccccccccccc ccccccbbccccccccccccbbcccccccccccccc bbe cccaaccccccccccccc ccccccbeccccccccccccgbcccccccccccccc bbf cccadccccccccccccc cccccgbccccccccccccccbeccccccccccccc ebb ccdacccccccccccccc cccacbbccccccccccccccbbccccccccccccc bbe ggaagggggggggggggg cccaabeccccccccccccccgbccccccccccccc fbbf a ccccabccccccccccccccccbecccccccccccc ebb aa ccccebccccccccccccccccbbcccccccccccc bbe ad ccccbbdccccccccccccccccbcccccccccccc fbbf fa ccccbeaccccccccccccccccbeccccccccccc ebb aa cccgbcaacccccccccccccccebccccccccccc bbc af cccbbcdaccccccccccccccccbccccccccccc fbb da cccbeccaacccccccccccccccbbcccccccccc bbb aa ccceccccadccccccccccccccebcccccccccc bbf af ccccccccaacccccccccccccccbgccccccccc cbb da cccccccccadccccccccccccccbbccccccccc bbe ad cccccccccdaccccccccccccccebccccccccc fbbf fa ccccccccccaaccccccccccccccbgcccccccc ebb aa ccccccccccdaccccccccccccccbbcccccccc bbe ad cccccccccccaacccccccccccccebcccccccgbbf fa ccccccccccccadcccccccccccccbgcccccebb aa ccccccccccccaacccccccccccccbbccccbbe af cccccccccccccaaccccccccccccebccgbbcc da cccccccccccccdadccccccccccccbebbbccc aa ccccccccccccccaaaaccccccccccbbbecccc a ccccccccccccccccdaaadcccccccgbcccccc aa cccccccccccccccccccaaadccccccccccccc ad cccccccccccccccccccccaaaaccccccccccc fa cccccccccccccccccccccccdaaadcccccccc aa ccccccccccccccccccccccccccaaadcccccc af ccccccccccccccccccccccccccccaaaacccc da ccccccccccccccccccccccccccccccdaaacc aa gggggggggggggggggggggggggggggggggaaad af aaad da daaaf ad faaad fa aaad aa daaaf ad faaad fa aaad aa daaaf af faaada aad ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#e1df19ff b,#82326bff c,#c4a0b9ff d,#e8e654ff e,#a0658cff f,#f1f098ff g,#ece2dcff ``` ```image ebbg gbbb gbbb ebbc cbbe cbbe ebbc gbbb bbbg ebbc gbbe cbbe cbbc bbbg ebbg ebbc gbbb cbbe cbbe bbbg ebbc ebbc bbbg cbbe gbbe bbbg cbbc ebbc ebbg gbbe gbbb bbbg cbbe cbbc ebbc gbbb bbbg bbbg gbbe cbbc cbbc gbbb gdd ebbg bbbg aaafgbbb cbbe faaacbbe gbbb daaebbc ebbg gaabbbg cbbe dabbe gbbb gebbe ebbc bbba cbbe gbbbaf gbbb cbbeaag ebbc ebbdaad cbbe bbbgaaag gbbb gbbe daad ebbc cbbc aaaf cbbe ebbg faaa bbbg gbbb daaf ebbc cbbe faaag cbbe ebbc daad bbbg cebg gaaaf ebbc faaa cbbe aaaf bbbg faaa ebbc daad gbbe gaaag bbbg daad ebbc aaaf gbbb faaa bbbg aaaf cbbc faaag gbbb daad bbbg gaaag cbbc daad gbbb c aaaf ebbg eb faaa cbbe gbbb daaf gbbb cbbbb gaaag ebbc gebbbbg daad cbbe cbbbbe gaaaf gbbb cbbbbc faaadg ebbcgebbbeg aaaaadf cbbebbbbe gdaaaaaaf gbbbbbbc gdaaaaaadg ebbbeg faaaaaadf cbbc fdaaaaaaf gg gdaaaaaadg faaaaaadf fdaaaaaaf gdaaaaaafg faaaaaadf fdaaaaadf gdaaaaaafg faaaaaadg fdaaaaadf gdaaaaaafg gfaaaaaadg fdaaaaad ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Alright, let's concentrate on the next area. I'm going to scrutinize area B for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#e1de19ff b,#82346aff c,#c9a7beff d,#eae85bff e,#a36a86ff f,#f2f19cff g,#f3eed9ff ``` ```image daaf daag daag aaa aaa gaaa gaad faad faad faaf daaf daaf daag aaag aaa aaa gaad gaad faad faaf faaf daaf daag gg daagcbe aaaebbbc aabbbbeg gebbbbc gebbbbg cbbbbe ebbbbad gebbbbaaf cbbbbedaaf ebbbbc daaf gbbbbbad daag cbbbbeaaadaaag gebbbbaadaaaaaa cbbbbeaaa faaaaa cbbbbcfaad faaaa gebbbbg aaaf faad cbbbbe gaaa ffg ebbbbc daad gebbbeg aaag cbbbbe faad bbbbc daaf bbeg aaag bc faad c daaf gaaa faad aaag gaaa daaf aaag faad daaf gaaa faad aaaf gaaa daad aaag ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#e1df18ff b,#82346bff c,#c9a8bfff d,#e8e655ff e,#a56c92ff f,#f2f19cff g,#f0e9deff ``` ```image dg ag a ga fa da da aa ad ad af ag a ga fa e fa cb da bbe aa bbb aa gb bg ad eb be af be eb af bg bg agb cb bb abbg bb eb ebb bc bg bba gb bb cbbda eb cb bbbdda be bc gbbadaaa bg bb cbbfa fad cb cb bbe aa fg bb bc gbbg ag bc bb ebb da gb cb bbe ad eb bc gbbg ga be bb ebb aa bg cb bbc af cb bc cbb fa bb bb bbe aa bc gb gbbc af cb be cbb da d bb bb bbe ad aabe gb gbbg ag gabg be ebb da eb eb bbe ad bbf gb gbbg fa bda be ebb aa cb ad eb bbc af bb fa gbg cbb fa be aa be ebe aa eg gaf eb bbc ag aa bg cbb da ad bb bbe ad da eb gbbg ga aa bg ebb aa fag bb bbe af aa cb gbbg fa af bc ebb aa da bb bbc af ad cb cbbg da fad bcebb ad daaa bbbc ga faaaf cb da gaaad ad daaa fa faaaf aa gaaaf af daad fa faaag aa gaaaf ag daad da daaag ad faaaf ga aaad aa daaag af faaaf fa gaaad aa daaag ag faaada gaad ``` <!-- end of image -->
[ "" ]
This image might have some surprises. Let's look for intersections carefully. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#f89c0bff b,#2c507eff c,#b2d7b2ff d,#e7be65ff e,#f0f4ebff f,#6d838bff g,#a1cca1ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eggggggggggggggggggggggggggggggggggggggggggggggggaagggg egcccccccccccccccccccccccccccccccccccccccccccccccaaadcg egcccccccccccccccccccccccccccccccccccccccccccccccaaaccg egccccccccccccccccccccccccccccccccccccccccccccccdaaafcg egccccccccccccccccccccccccccccccccccccccccccccccaaaaccg egccccccccccccccccccccccccccccccccccccccccccccccaaafccg egccccccccccccccccccccccccccccccccccccccccccccccaaabccg egccccccccccccccccccccccccccccccccccccccccccccccaaafccg egcccccccccccccccccccccccccccccccccccccccccccccdaaagccg egcccccccccccccccccccccccccccccccccccccccccccccaaaacccg egcccccccccccccccccccccccccccccccccccccccccccccaaafcccg egcccccccccccccccccccccccccccccccccccccccccccccaaabcccg egccccccccccccccccccccccccccccccccccccccccccccdaaafcccg ae egccccccccccccccccccccccccccccccccccccccccccccaaaagcccg aaa egccccccccccccccccccccccccccccccccccccccccccccaaafccccg daaaa egccccccccccccccccccccccccccccccccccccccccccccaaabccccg daaaa egcccccccccccccccccccccccccccccccccccccccccccgaaabccccg daaaa egcccccccccccccccccccccccccccccccccccccccccccdaaafccccg daaaa egcccccccccccccccccccccccccccccccccccccccccccaaaagccccg aaaaa egcccccccccccccccccccccccccccccccccccccccccccaaabcccccg aaaaa egcccccccccccccccccccccccccccccccccccccccccccaaabcccccg aaaaa egccccccccccccccccccccccccccccccccccccccccccdaaabcccccg aaaad egccccccccccccccccccccccccccccccccccccccccccaaaafcccccg aaaad egccccccccccccccccccccccccccccccccccccccccccaaafgcccccg aaaad egccccccccccccccccccccccccccccccccccccccccccaaabccccccg aaaad egcccccccccccccccccccccccccccccccccccccccccdaaabccccccg aaaae egcccccccccccccccccccccccccccccccccccccccccaaaabccccccg eaaaae egcccccccccccccccccccccccccccccccccccccccccaaaffccccccg eaaaae egcccccccccccccccccccccccccccccccccccccccccaaabcccccccg eaaaae egcccccccccccccccccccccccccccccccccccccccccaaabcccccccg eaaaa egccccccccccccccccccccccccccccccccccccccccdaaabcccccccg daaaa egccccccccccccccccccccccccccccccccccccccccaaaafcccccccg daaaa egccccccccccccccccccccccccccccccccccccccccaaafgcccccccg daaaa egccccccccccccccccccccccccccccccccccccccccaaabccccccccg daaaa egcccccccccccccccccccccccccccccccccccccccdaaabccccccccg cb aaaaa egcccccccccccccccccccccccccccccccccccccccaaaabccccccccg ebbb aaaaa egcccccccccccccccccccccccccccccccccccccccaaaffccccccccg bbbg aaaaa egcccccccccccccccccccccccccccccccccccccccaaabgccccccccg fbbb aaaad egccccccccccccccccccccccccccccccccccccccgaaabcccccccccg ebbb aaaad egccccccccccccccccccccccccccccccccccccccdaaabcccccccccg bbbc aaaad egccccccccccccccccccccccccccccccccccccccaaaabcccccccccg bbbb aaaad egccccccccccccccccccccccccccccccccccccccaaabfcccccccccg cbbb aaaaeegccccccccccccccccccccccccccccccccccccccaaabgcccccccccg bbbc eaaaaegccccccccccccccccccccccccccccccccccccffaaabccccccccccg bbbb eaaaagccccccccccccccccccccccccccccccccccfbbaaaafccccccccccg cbbb eaaaaccccccccccccccccccccccccccccccccfbbbbaaadcccccccccccg bbbe eaaaacccccccccccccccccccccccccccccfbbbbbbaaaccccccccccccg bbbf daaaaccccccccccccccccccccccccccgbbbbbbbdaaaccccccccccccg gbbb daaaacccccccccccccccccccccccgbbbbbbbccaaaaccccccccccccg bbbe edaaaaccccccccccccccccccccgbbbbbbbgcccaaadccccccccccccg bbbf egdaaaacccccccccccccccccgbbbbbbbgcccccaaacccccccccccccg fbbb egcaaaaacccccccccccccccbbbbbbbgcccccccaaacccccccccccccg bbb egccaaaaaccccccccccccbbbbbbbgccccccccdaaacccccccccccccg bbbf egcccaaaaacccccccccbbbbbbbfccccccccccaaaacccccccccccccg fbbb egccccaaaaaccccccfbbbbbbfccccccccccccaaadcccccccccccccg ebbb egcccccaaaadcccfbbbbbbfccccccccccccccaaaccccccccccccccg bbbg egccccccaaaadfbbbbbbfcccccccccccccccdaaaccccccccccccccg fbbb egcccccccaaaafbbbbfcccccccccccccccccaaaaccccccccccccccg ebbb egcccccccfaaaafbbcccccccccccccccccccaaadccccccccccccccg bbbc egcccccgbbbaaaagccccccccccccccccccccaaacccccccccccccccg bbbb egcccgbbbbbbaaaagccccccccccccccccccgaaacccccccccccccccg cbbb egcgbbbbbbbcgaaaaccccccccccccccccccdaaacccccccccccccccg bbbc egbbbbbbbgcccgaaaacccccccccccccccccaaadcccccccccccccccg bbbb ebbbbbbbgccccccdaaaaccccccccccccccccaaagcccccccccccccccg cbbb bbbbbbbgcccccccccdaaaacccccccccccccccaaaccccccccccccccccg bbbe fbbbbbbgccccccccccccdaaaacccccccccccccdaaaccccccccccccccccg bbbf fbbbbbbfcccccccccccccccdaaaaccccccccccccaaaaccccccccccccccccg gbbb fbbbbbbgegccccccccccccccccaaaaacccccccccccaaadccccccccccccccccg bbbe fbbbbbbf egcccccccccccccccccaaaaaccccccccccaaacccccccccccccccccg bbbf gbbbbbbf egccccccccccccccccccaaaaaccccccccgaaacccccccccccccccccg fbbb cbbbbbbf egcccccccccccccccccccaaaaacccccccdaaacccccccccccccccccg bbbcbbbbbbf egggggggggggggggggggggaaaaaggggggaaadgggggggggggggggggg bbbbbbbbb eeeeeeeeeeeeeeeeeeeeeeaaaadeeeeeaaaeeeeeeeeeeeeeeeeeee fbbbbbbe aaaad eaaa ebbbbe aaaad daaa gbe aaaae aaad eaaaaeaaae eaaaaaaa eaaaaaa eaaaaa daaad daa ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#f99c0aff b,#2d507eff c,#bcc7d6ff d,#fbbb58ff e,#fce0b4ff f,#738aa8ff g,#9a783fff ``` ```image aade eaaaaae daaaaa aaaaaa aaaaagc aaaaabc aaaaab aaaaaf eaaaagc daaaab aaaaab aaaaaf daaaaac daaaaa aaaaag daaaaag daaaaab aaaaaab eaaaaagb daaaaabc aaaaaabc aaaaagb aaaaabf aaaaabc aaaaabc eaaaagb daaaabf aaaaabc aaaaab eaaaaab daaaaaf aaaaagc eaaaaag daaaaab aaaaaab aaaaagb aaaaagb aaaaabf aaaagbc eaaaagbc daaaabb aaaaabf eaaaagbc eaaaagbc aaaaabf aaaaabf eaaaaabc daaaaab aaaaagf eaaaaagf eaaaaagc aaaaaab aaaaagb aaaaagb aaaaabb aaaagbb eaaaagbf daaaabbc daaaabbc eaaaaabf eaaaaabf daaaaabc aaaaagb eaaaaagf daaaaabf daaaaabc faaaaagb fgaaaaagb e fbbgaaaaabb aa cbbbbbaaaaagc aa bbbbbbbaaaaae aad cbbbbbbbbaaaaae aaad cbbbbbbbbbbaaaaa aaaaa cfbbbbbbbbbbceaaaad aaaaad cbbbbbbbbbbb daaaae aaaaaad cfbbbbbbbbbbc daaaa daaaaaad fbbbbbbbbbbf aaaaa aaaaaaa fbbbbbbbbbbf eaaaaa daaaaaae bbbbbbbbbbb daaaaa daaaaaae fbbbbbbbbbbfc aaaaaa aaaaaaae cbbbbbbbbbbfc eaaaaae aaaaaaaa cbbbbbbbbbbfc daaaaae aaaaaaa cbbbbbbbbbbb daaaaa eaaaaaaa cfbbbbbbbbbbc aaaaad eaaaaaad cfbbbbbbbbbbc aaaaae aaaaaaa fbbbbbbbbbbf aaaaa eaaaaaad fbbbbbbbbbbf aaaaa eaaaaaad fbbbbbbbbbbf aaaad daaaaaagbbbbbbbbbfc daaaae aaaaaaabbbbbbbfc daaaa daaaaaagbbbbbf aaaad cbbgaaaaaagb daaaae cfbbbbaaaaaaae daaaa fbbbbbbaaaaaaaa aaaaa cfbbbbbbbbaaaaaaae eaaaaa bbbbbbbbbbb eaaaaaaa daaaaa fbbbbbbbbbbf eaaaaaaa aaaaaa bbbbbbbbbbb aaaaaaa aaaaad bbbbbbbbbfc eaaaaaad daaaaae bbbbbbbbf eaaaaaad daaaaa bbbbbbfc eaaaaaad aaaaad bbbbbc aaaaaaa aaaaad bbc daaaaaae aaaaa bc daaaaaae aaaaa aaaaaaae aaaad daaaaaaa eaaaae aaaaaaae daaaa aaaaaaa aaaaa eaaaaaaa eaaaaa eaaaaaad daaaaa eaaaaaad aaaaad ``` <!-- end of image --> I can confirm that 2 intersections exists in area A. Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#f99c0aff b,#2c507eff c,#b2bfcfff d,#fbbc59ff e,#fcdfb0ff f,#6c84a5ff g,#917443ff ``` ```image ade aaae aaa eaaac daaa aaag aaab aaaf daaac aaag aaag aaab eaaaf d aaaac aaa aaag eaaaa aaab daaaa eaaab daaaa daaaf daaaa aaag aaaaa aaab aaaaa aaab aaaad eaaab aaaad aaaac aaaad aaag aaaad aaab aaaae eaaab aaaae daaaf aaaae aaagc aaaa aaab eaaaa aaab eaaaa daaab eaaaa aaaaf daaaa aaagc daaaa aaab daaaa eaaab cb daaaa aaaab bbb aaaaa aaagf bbbc aaaaa aaabc fbbb aaaad eaaab bbb aaaad daaab bbbc aaaad aaagb bbbb aaaae aaabf cbbb aaaae aaab bbbc aaaae fgaaab bbbb aaaa cbbaaaac cbbb eaaaa cbbbbaaae bbbc eaaaa cbbbbbbaaa bbbf eaaaa cbbbbbbbeaaa cbbb daaaa cbbbbbbb daaa bbb daaaa bbbbbbb aaad bbbf daaaa bbbbbbb aaa fbbb daaaa bbbbbbbc aaa bbb aaaaa bbbbbbbc daaa bbbf aaaaa fbbbbbbc aaad fbbb aaaad fbbbbbbc aaae bbb aaaad fbbbbbbf aaa bbbc aaaadfbbbbbbf eaaa fbbb aaaagbbbbf daaa cbbb caaaagbf aaad bbbc cbbbaaaae aaa bbbb cbbbbbbaaaae eaaa cbbb bbbbbbb eaaaa daaa bbbc bbbbbbb eaaaa aaad bbbb bbbbbbb eaaaa aaae cbbb bbbbbbbc eaaaa aaa bbb fbbbbbbc daaaa eaaa bbbf fbbbbbbc daaaa aaaa cbbb fbbbbbbc daaaa aaae bbb fbbbbbbf aaaaa aaa bbbf cbbbbbbf aaaaa eaaa fbbb cbbbbbbf aaaad daaa bbbcbbbbbbf aaaad aaad bbbbbbbbb aaaad aaa fbbbbbb aaaad aaa bbbb aaaae daaa cb aaaae aaad aaaaeaaae aaaaaaa eaaaaaa eaaaaa eaaad daa ``` <!-- end of image -->
[ "" ]
I'm approaching this image with caution. Intersections might be tricky to spot. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#8faa5eff b,#de26cbff c,#b1d7b1ff d,#dd7ad2ff e,#6f902dff f,#f0e9ecff g,#9cc691ff ``` ```image b db fbf f bd bf bb db db fb fbf b bd bd bb db db fb fbf b bd bd bb db db fb fbf b bd bd bb db db fb fbf b bd bd bb db db b fbf bf bd bd bb db db c b fbf ce bf bd ce gggggggggbdggggggggggggggggggggggggggggc bb cef cccccccccdbccccccccccccccccccccccccccccg db geg ccccccccccbccccccccccccccccccccccccccccg fbf gea ccccccccccbccccccccccccccccccccccccccccg bd aee ccccccccccbccccccccccccccccccccccccccccg bb aae ccccccccccbdcccccccccccccccccccccccccccg db eae ccceccccccbdcccccccccccccccccccccccccccg fbf egef ccceecccccbbcccccccccccccccccccccccccccg bd egeg ccccegccccdbcccccccccccccccccccccccccccg bb ecae ccccaeccccdbcccccccccccccccccccccccccccg db ecce ccccceeacccbcccccccccccccccccccccccccccg fbf ec e ccccccgeeccbcccccccccccccccccccccccccccg bd ef e ccccccccaeebcccccccccccccccccccccccccccg fbb ef ec ccccccccccebgccccccccccccccccccccccccccg dbbd e eg cccccccccccbeecccccccccccccccccccccccccg bbbf e ge cccccccccccbceeacccccccccccccccccccccccg fbbbf e ce cccccccccccbdcgeegcccccccccccccccccccccg dbbd e e cccccccccccbdcccaeeccccccccccccccccccccgbbbf e e cccccccccccbbccccceeaccccccccccccccccdbbb e ec cccccccccccdbccccccgeecccccccccccccdbbdg e ea cccccccccccdbccccccccaeecccccccccbbbcccg fe ge ccccccccccccbcccccccccceegccccdbbbcccccg fe fe ccccccccccccbcccccccccccgeecdbbdcccccccg ce e ccccccccccccbcccccccccccccbbbccccccccccg ce e ccccccccccccbccccccccccdbbbgeegccccccccg ce ec ccccccccccccbccccccccbbbdccccaeecccccccg ge aa ccccccccccccbccccccbbbccccccccceeacccccg ge ge ccccccccccccbdccdbbdccccccccccccgeeccccg ae fe ccccccccccccbdbbbdccccccccccccccccaeeccg aa e ccccccccccccbbbccccccccccccccccccccceegg aa ef cccccccccccccccccccccccccccccccccccccgee eg ec ccccccccccccccccccccccccccccccccccccccceea eg aa cccccccccccccccccccccccccccccccccccccccgfeef ec ce cccccccccccccccccccccccccccccccccccccccg gee ec fe cccccccccccccccccccccccccccccccccccccccg eeg ec e cccccccccccccccccccccccccccccccccccccccg feef ef ef gccccccccccccccccccccccccccccccccccccccg aea ef eg fffffffffffffffffffffffffffffffffffffff eec e aa cee e ce aea e e feef e e gee e c eeg e feef e aea fe eec fe cee ce aea ce feef ge gee ae eeea feg ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a0b174ff b,#de23caff c,#ccd7b4ff d,#ef9ae7ff e,#729130ff f,#f3dbedff g,#e55cd6ff ``` ```image bbg gbb dbbf fbbd bbg gbb dbbf dbbf fbbf fbbd fbbd f bbd cea bbg aeec gbg eeef gbg ceea gbb aeec dbb feee dbb ceea dbbf eeeaf fbbf feeeea fbbd aeeeec fbbd ceeeeaf bbd ceeeec bbg faeeeebbg ceeebbg aebbbc fgbbeaf dbbeeea dbbaeeeec dbbfceeeeaf fbbd ceeeec fbbd faeeeec bbd ceeeea bbd aeeeec bbg faeeeaf f gbg ceeeea dgb gbg aeeeec fdbbbb gbb ceeeeaf fgbbbbbd dbb ceeeec dgbbbbgd dbbf faeeeec fdbbbbbgf dbbf ceeeea fgbbbbbdf fbbf aeeeec dgbbbbgd fbbd faeeeaf fdbbbbbgf fbbd ceeeea fgbbbbbdf bbd aeeabbbbbgd bbg fgbbbbbgf gbg dgbbbbbaeec gbg dbbbbbgdfaeeeec gbb fgbbbbbgf ceeeea dbb dgbbbbbd aeeeec dbb fdbbbbbgf faeeeaf dbbf fgbbbbbdf ceeeea fbbf dgbbbbgd aeeeec fbbd fdbbbbbgf ceeeeaf fbbd fgbbbbbdf ceeeec bbddgbbbbgd faeeeec bbbbbbbgf ceeeea gbbbbdf aeeeec dbgd faeee cee a ``` <!-- end of image --> The lines cross each other within area A, forming 2 intersections. Answer: A: 2; 2 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#92ab60ff b,#df26ccff c,#bbca9bff d,#eb7cdfff e,#6f902cff f,#e1e7d3ff g,#f7cef3ff ``` ```image b db bg g bd bg bb db db gb bg b bd bg bb db db gb bg b bd bd bb db db gb bg b bd bd bb db db gb bg b bd bd bb db db b gbg b bd bd bb db db c b gbg fe bg bd ce bd bb cef db db cec b gbg aea bg bd aee bg bb aae bd db eae a bd gbg ecef ee db bd ecec ef db bb ecae ce gb db ecce eec gb gbg ef e feef b bd ef e aeab gbb e ef ebc dbbd e ea bee bbbg e ae bgaea gbbb e fe bd feef dbbd e e bd cee bbbg e e bd eec gbbb e ef db feef dbbd e ea db aea gbbbg fe ce gb eec dbbb fe fe b cee dbbd fe e b gbbbg ce e b dbbdfeef ce ec b dbbd cee ce aa bg gbbbg eec ce ce bg dbbd feef ae fe bdbbbd aea aa e bbbg eec aa ef cee ea ec aea ec aa feef ec ce cee ec e eec ef e feef ef ef aea ef ec eec e aa cee e ce aea e e feef e e cee e c eec e feef e aea e eec fe cee fe aea ce feef ce cee ae eeea fea ``` <!-- end of image -->
[ "" ]
This image seems promising for intersection detection. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#6964f5ff b,#41a0bfff c,#b5bff3ff d,#b1d7b1ff e,#eef4f1ff f,#88b8c1ff g,#96ca95ff ``` ```image e cbbbb efbbbbbbb fbbbbbbbbbc cbbbbbbbbbfe cbbbbbbbbbfe ccf efbbbbbbbbbc fbb fbbbbbbbbbc eefbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecbbbbbbbbbfe ddfbbddddddddddddddddddddddddddddddddddddddddddddfbbbbbbbbbfe ddfbbdddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbc ddfbbdddddddddddddddddddddddddddddddddddddfbbbbbbbbbfddde ddfbbdddddddddddddddddddddddddddddddddfbbbbbbbaaaddddddde ddfbbdddddddddddddddddddddddddddddfbbbbbbbbbbaaaaadddddde ddfbbddddddddddddddddddddddddddfbbbbbbbbbfdaaaaaaaaddddde ddfbbddddddddddddddddddddddddddbbbbbbfdddfaaaafdaaafdddde ddfbbddddddddddddddddddddddddddbbbddddddaaaaaddddaaafddde ddfbbddddddddddddddddddddddddddbbdddddfaaaafddddddaaaddde ddfbbdddddddddddddddddddddddddfbbddddaaaaaddddddddfaaadde ddfbbdddddddddddddddddddddddddbbbddfaaaafddddddddddfaaade ddfbbdddddddddddddddddddddddddbbbdaaaaadddddddddddddaaaae dddbbdddddddddddddddddddddddddbbbaaaafdddddddddddddddaaac dddbbdddddddddddddddddddddddddbaaaaaddddddddddddddddddaaae dddbbddddddddddddddddddddddddfaaaafddddddddddddddddddddaaa dddbbdddddddddddddddddddddddaaaaaddddddddddddddddddddddfaaa dddbbdddddddddddddddddddddfaaaabddddddddddddddddddddddddaaaa dddbbddddddddddddddddddddaaaaabbddddddddddddddddddddddddeaaac dddbbddddddddddddddddddfaaaafbbbdddddddddddddddddddddddde aaae dddbbdddddddddddddddddaaaaaddbbfdddddddddddddddddddddddde eaaa dddbbfddddddddddddddfaaaafdddbbddddddddddddddddddddddddde caaa dddbbfdddddddddddddaaaaaddddfbbddddddddddddddddddddddddde caaa dddbbfdddddddddddfaaaafdddddbbbddddddddddddddddddddddddde aaac dddbbfddddddddddaaaaadddddddbbbddddddddddddddddddddddddde aaae dddbbfddddddddfaaaafddddddddbbbddddddddddddddddddddddddde aaa dddbbfdddddddaaaaaddddddddddbbfddddddddddddddddddddddddde eaaa dddbbfddddddfaaafdddddddddddbbdddddddddddddddddddddddddde caaa dddbbfddddddaaaddddddddddddfbbdddddddddddddddddddddddddde aaaa dddbbfddddddaaaddddddddddddbbbdddddddddddddddddddddddddde aaac dddbbfddddddaafddddddddddddbbbdddddddddddddddddddddddddde aaae dddbbfdddddfaadddddddddddddbbbdddddddddddddddddddddddddde eaaa dddbbfdddddaaadddddddddddddbbfdddddddddddddddddddddddddde caaa dddbbfdddddaaadddddddddddddbbddddddddddddddddddddddddddde aaaa dddbbbdddddaafddddddddddddfbbddddddddddddddddddddddddddde aaac dddbbbdddddaadddddddddddddbbbddddddddddddddddddddddddddde aaae dddbbbddddfaadddddddddddddbbbddddddddddddddddddddddddddde eaaa dddbbbddddaaadddddddddddddbbbddddddddddddddddddddddddddde caaa dddbbbddddaaadddddddddddddbbfddddddddddddddddddddddddddde caaa dddbbbddddaafddddddddffbbbbbdddddddddddddddddddddddddddde aaac dddbbbdddfaadddfbbbbbbbbbbbbdddddddddddddddddddddddddddde aaae dddbbbdddaaabbbbbbbbbbbbbffddddddddddddddddddddddddddddde aaa dddbbbbbbaaabbbbbbbfdddddddddddddddddddddddddddddddddddde eaaa dddbbbbbbaaabfdddddddddddddddddddddddddddddddddddddddddde caaa dddfbbbffaaddddddddddddddddddddddddddddddddddddddddddddde aaaa ddddddddaaaddddddddddddddddddddddddddddddddddddddddddddde aaac ddddddddaaaddddddddddddddddddddddddddddddddddddddddddddde aaae ddddddddaaaddddddddddddddddddddddddddddddddddddddddddddde eaaa ddddddddaafddddddddddddddddddddddddddddddddddddddddddddde caa dddddddfaadddddddddddddddddddddddddddddddddddddddddddddde c dddddddaaadddddddddddddddddddddddddddddddddddddddddddddde dddddddaaadddddddddddddddddddddddddddddddddddddddddddddde dddddddaafdddddddddddddddddddddddddddddddddddddddddddddde ddddddfaaddddddddddddddddddddddddddddddddddddddddddddddde ddddddaaaddddddddddddddddddddddddddddddddddddddddddddddde ddddddaaaddddddddddddddddddddddddddddddddddddddddddddddde ddddddaaaddddddddddddddddddddddddddddddddddddddddddddddde ddddddaafddddddddddddddddddddddddddddddddddddddddddddddde gggggfaagggggggggggggggggggggggggggggggggggggggggggggggge aaa aaa aac caa aaa aaa aac eaae caa aaa aaa aac caa aaa caa ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#6761f6ff b,#3fa0c0ff c,#9fcfdfff d,#b0aefaff e,#d2dff4ff f,#70b8d0ff g,#8b87f8ff ``` ```image fbbbbc efbbbbbbb fbbbbc ecfbbbbbbbbbb cbbbbc ecfbbbbbbbbbbbbbb cbbbbc ecfbbbbbbbbbbbbbbbbbf cbbbbc efbbbbbbbbbbbbbbbbbbfc cbbbbc ecfbbbbbbbbbbbbbbbbbfce cbbbbf ecfbbbbbbbbbbaaaabbfce cbbbbf ecfbbbbbbbbbbbbbaaaaag cbbbbf efbbbbbbbbbbbbbbbaaaaaaaad cbbbbf ecfbbbbbbbbbbbbbbbbfaaaaaaaaaae cbbbbf ecfbbbbbbbbbbbbbbbbfcegaaaaaaaaaaaae cbbbbf ebbbbbbbbbbbbbbbbbfc eaaaaaaaaaaaaaag cbbbbf ebbbbbbbbbbbbbbbfc gaaaaaaaad gaaaaag cbbbbf cbbbbbbbbbbbfce aaaaaaaage eaaaaaad cbbbbf fbbbbbbbfce gaaaaaaad eaaaaaad cbbbbf fbbbbfe eaaaaaaage daaaaaae cbbbbf bbbbbe gaaaaaaad gaaaaaa ebbbbf ebbbbb eaaaaaaage gaaaaag ebbbbf ebbbbb gaaaaaaad aaaaaag ebbbbf cbbbbf eaaaaaaaae eaaaaaad ebbbbb fbbbbc gaaaaaaaad daaaaaae ebbbbb fbbbbc eaaaaaaaage daaaaaae ebbbbb bbbbbe gaaaaaaaad gaaaaag ebbbbb ebbbbb eaaaaaaaage aaaaaag ebbbbb ebbbbb gaaaaaaaad eaaaaaa ebbbbb cbbbbfaaaaaaaage eaaaaa ebbbbb fbbbaaaaaaaaad daaaa ebbbbb fbbaaaaaaaage gaaa ebbbbb daaaaaaaage eaa bbbbb gaaaaaaaad ea bbbbb eaaaaaaaage d bbbbb gaaaaaaaag bbbbb eaaaaaaaaabc bbbbb gaaaaaaaaabbe bbbbbe eaaaaaaaaabbbb bbbbbe gaaaaaaaagbbbbb bbbbbe eaaaaaaaagecbbbbf bbbbbe gaaaaaaaad fbbbbc bbbbbe eaaaaaaaage fbbbbc bbbbbe gaaaaaaaad bbbbbe bbbbbe eaaaaaaaage ebbbbb bbbbbe gaaaaaaaad ebbbbb bbbbbe eaaaaaaaage cbbbbf bbbbbe gaaaaaaaad fbbbbc fbbbbe eaaaaaaaage fbbbbc fbbbbe gaaaaaaaad bbbbbe fbbbbe eaaaaaaaage ebbbbb fbbbbe gaaaaaaaad ebbbbb fbbbbc eaaaaaaaage cbbbbf fbbbbc gaaaaaaaad fbbbbc fbbbbc aaaaaaaage fbbbbc fbbbbc eaaaaaaad bbbbbe fbbbbc daaaaage ebbbbb fbbbbc gaaaad ebbbbb fbbbbc aaaae cbbbbf fbbbbc eaaaa fbbbbc fbbbbc daaag fbbbbc fbbbbc gaaad bbbbbe cbbbbc aaaae ebbbbb cbbbbc eaaaae ebbbbb cbbbbc daaaa cbbbbf cbbbbc daaag fbbbbc cbbbbf gaaad fbbbbc cbbbbf aaaae bbbbbe cbbbbf eaaaa ebbbbb cbbbbf daaag ebbbbb cbbbbf gaaad cbbbbf cbbbbf aaaae fbbbbc cbbbbf eaaaa fbbbbc cbbbbf daaaa bbbbbe cbbbbf daaaa ebbbbb cbbbbf gaaaa ebbbbb ebbbbf aaaaa cbbbbf ebbbbf eaaaaa fbbbbc ebbbbf daaaag fbbbbc ebbbbf gaaaad eecfbbbbbe ebbbbb aaaaae eecffbbbbbbbbbb ebbbbb eaaaaa eccffbbbbbbbbbbbbbbbb ebbbbb daaaaa eccfbbbbbbbbbbbbbbbbbbbbbbf ebbbbb gaaaagcfbbbbbbbbbbbbbbbbbbbbbbbbbbbf ebbbbb eeaaaaabbbbbbbbbbbbbbbbbbbbbbbbbfcce ebbbbbecffbbbaaaaabbbbbbbbbbbbbbbbbbbfcce ebbbbbbbbbbbbaaaaabbbbbbbbbbbbffcce ebbbbbbbbbbbaaaaaabbbbbbffcee bbbbbbbbbbbaaaaad ebbbbbfcceeaaaaa ee daaaag gaaaag aaaaad aaaaae eaaaaa daaaag gaaaad aaaaae eaaaaa daaaag gaaaad aaaaad aaaaae eaaaaa daaaag gaaaad aaaaae eaaaaa daaaag gaaaad aaaaad eaaaaae eaaaaa daaaag gaaaad aaaaae ``` <!-- end of image --> Case closed! This is definitely 2 intersections point in area A. Answer: A: 2; 2 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#6762f6ff b,#3fa0c0ff c,#a4d2e1ff d,#b3b1faff e,#d6def7ff f,#6cb4cfff g,#8681f8ff ``` ```image e efbbb efbbbbbbb cbbbbbbbbbc cbbbbbbbbbc efbbbbbbbbfe ccc efbbbbbbbbfe fbb cbbbbbbbbbc fbb cbbbbbbbbbc fbb efbbbbbbbbfe cbb efbbbbbbbbfe cbb cbbbbbbbbbc cbb cbbbbbbbaaa cbb efbbbbbbbbfaaaaa cbb cbbbbbbbbfe aaaaaaag cbb bbbbbbc eaaaae aaad cbb bbf aaaag aaae cbb ebb eaaaae aaa ebb cbb aaaag eaaa ebb fbb eaaaae daaa ebb bbb aaaag gaag ebb bbfaaaae aaae ebb baaaag aaa ebb daaaae eaaa bb aaaag daaa bb eaaaab gaag bbe aaaaabb aaad bbe eaaaaebbf aaae bbe aaaag bbc aaa bbe eaaaae ebb eaaa bbe aaaag cbb gaag bbe eaaaae fbb aaad bbc aaaag bbb aaae bbc eaaaae bbf aaa bbc aaaag bbc eaaa bbc daaae ebb daaa bbc aaa cbb gaag bbc aag fbb aaae bbc aad bbb aaa bbc daa bbf eaaa bbf gaa bbc daaa bbf aaa ebb gaag bbf aad cbb aaad bbf eaae fbb aaae bbf daa bbb aaa bbf aaa bbf eaaa bbf aag bbc gaaa bbf aae cfbbbbb aaad bbb daa cfbbbbbbbbbbb aaae bbb eaaabbbbbbbbbbbbbce aaa bbbbbbaaabbbbbbfce eaaa bbbbbbaaafce daaa cbbfceaa gaag gaa aaad aaa aaa aag aaa aae dag daa d aaa aaa aad eaa gaa aaa aag aae daa aaa aaa aad eaa gaa aaa aag aae daa aaa aag aad eaa gaa daa ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#b8a507ff b,#56aaf9ff c,#a7d0a4ff d,#eff6efff e,#b1d7b2ff f,#babe5eff g,#83c0dbff ``` ```image bd bbg bbg bbg bbg bbg bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb gbb gbb gbb gbb dddddddddddddddddddddddddddddddddddddddddddddddddddddddddgbb ccccccccccccccccccccccccccccccccccccccccccccccccccccccccgbbd fae eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbcd faaaa eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbecd faaaf eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbeecd aaaaf eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbeeecd daaaaf eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbeeeecd daaaae eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbeeeeecd daaaae eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbeeeeeecd eaaaad eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegbbeeeeeeecd faaaad eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeecd faaaad eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeeecdfaaaf eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeeeeaaaaf eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeeeaaaaf eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeeaaaafd eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeecaaafecd eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeefaaaeeecd eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeaaafeeeecd eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeeaaaceeeeecd eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeefaaaeeeeeeecd eeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeaaafeeeeeeeecd eeegbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeeeeeaaaceeeeeeeeecd eeegbgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeefaaaeeeeeeeeeeecd eeegbgeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeaaafeeeeeeeeeeeecd eeegbgeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeaaaceeeeeeeeeeeeecd eeegbgeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeefaaaeeeeeeeeeeeeeeecd eeeebgeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeaaafeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeaaaceeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeeeeeeeebbbeecaaaeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeeeeeeebbbeefaafeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeeeeeebbbeeaaaceeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeeeeebbbecaaaeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeeeebbbefaafeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeeebbbeaaaceeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeeebbbcaaaeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeeebbbfaafeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeeebbbaaaceeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeeebbbaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeeebbfaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeeebbaaaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeebbeeeeeeeeeeeebbaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeegbeeeeeeeeeeegfaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeegbgeeeeeeeeegaaafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeegbgeeeeeeeegaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeegbgeeeeeeefaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeegbgeeeeeeaaafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeebgeeeecaaaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeebbeeefaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeebbeeaaaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeebbeaaabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeebcaaabeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeeaaacbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeaaabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eefaaabbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeafbbgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecd ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#b9a406ff b,#56aafaff c,#7da9a1ff d,#cbe4fcff e,#e6dfaaff f,#c4ba50ff g,#89c3fbff ``` ```image gb bb gbbb gbbbg gbbbg bbbb dbbbb dbbbb dbbbb bbbb dbbbbd bbg dbbbbd bbg dbbbbd bbb bbbbd bbb dbbbbd bbb dbbbbd bbb dbbbbd bbb bbbbd bbbd dbbbbd bbbd dbbbbd e bbbd dbbbbd aa bbbd bbbbd eaaa bbbd bbbbd eaaaaaa bbbg bbbbd eaaaaae bbbg bbbbd faaaafe bbbg bbbd aaaaae bbbg gbbbg faaaaf bbbg gbbbg eaaaaae bbbg gbbbg aaaaae bbbb bbbb faaaa bbbb gbbbg eaaaaae bbbb gbbbg aaaaf gbbb gbbbg faaaa gbbb bbbb eaaaaae gbbb gbbbg aaaae gbbb gbbbg eaaaaa gbbb gbbbg faaaaf gbbb bbbb aaaae dbbb gbbbg faaaaf dbbb gbbbg faaaaf dbbb gbbbb eaaaae dbbb bbbb faaaaf dbbb dbbbb aaaaae bbb dbbbb eaaaa bbb dbbbb faaaaf bbb bbbbd eaaaaae bbb dbbbbd faaaa bbb dbbbbd eaaaaae gbb dbbbbd eaaaaf gbb bbbbd aaaaf gbbd dbbbbd eaaaaae gbbd dbbbbd faaaaf gbbd dbbbbd eaaaae gbbd bbbbd eaaaaa dbbd dbbbbdaaaaae dbbg dbbbbdeaaaae dbbg bbbbdfaaaaf dbbg bbbbdfaaaae dbbg bbbbfaaaa bbg bbbbfaaaae bbg bbbcaaaaae bbb gbbbaaaaf bbb gbcaaaaae bbb gbcaaaaf gbb gbbaaaaf gbb gbcaaaaa gbbd gfaaaaf gbbd gcaaaae gbbd gcaaaaf gbbd gfaaaaf dbbd caaaa dbbg faaaaf dbbg eaaaaae dbbg aaaaae dbbg eaaaaac bbg aaaaac bbg faaafb bbb eaaaaab bbb aaaafbb bbbeaaaaabbd gbcaaaaacbd gfaaaafbbd eaaaaabbbd faaaafbbbd faaaacbbbd eaaaacbbbd aaedbbbd fe bbd d ``` <!-- end of image --> My investigation has led me to 2 intersections in area A! Answer: A: 2; 2 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#b9a406ff b,#56aafaff c,#88a985ff d,#cbe4fdff e,#e6dea7ff f,#cdbf4fff g,#87c2fbff ``` ```image bd bbg bbg bbg bbg bbg bbg bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb bbb gbb gbb gbb gbb gbb gbb gbb fae gbb faaaa gbb faaaf dbb aaaaf dbb aaaaf dbb aaaae bg dbbd eaaaae bb dbbd eaaaae bb dbbd eaaaa bb dbbd faaaa bb dbbd faaaf bb dbbd faaaf bb dbbd aaaaf bb bbd aaaae bb bbd aaae bb bbg eaaa bb bbg aaae bb bbg aaa bb bbg eaaa gb bbg faae gbd bbg aaa gbd bbg eaaa gbd bbg faae dbd bbg aaa dbg bbg eaaa dbg bbb faaf bg bbb aaa bb bbb eaaa bb bbb faaf bb bbb aaa bb bbb eaaa bb bbb faaf bb bbb aaae bb bbbeaaa bb bbbfaaf bb bbbaaae bb bbbaaa bb gbcaaf bb gbaaae gb gbaaa gbd gcaaf gbd gaaae gbd gaaa dbd caaf dbg aaae dbg aaa bg eaaa bb aaac bb aaab bcaaabd aaacbd aaabbd eaaabbd aebbd ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#444c72ff b,#3663a8ff c,#b1d6b1ff d,#171a52ff e,#718aa6ff f,#eaf0eeff g,#96c59aff ``` ```image cc ddd ddd ddd cdde add ddd ddd cdde addf ddd ddd cdde gggggggggggggaddgggggg fcccccccccccccdddcccccc fcccccccccccccdddcccccc fccccccccccccgddacccccc fccccccccccccaddgcccccc fccccccccccccdddccccccc fccccccccccccdddccbcccc fcccccccccccgddacbbbgcc fcccccccccccaddgbbbbccc fcccccccccccdddebbbcccc fcccccccccccddabbbccccc fccccccccccgddbbbgccccc fccccccccccadbbbecccccc fccccccccccdbbbbccccccc fccccccccccbbbbcccccccc fcccccccccebbbccccccccc fccccccccebbbeccccccccc fcccccccgbbbdcccccccccc fcccccccbbbadcccccccccc fccccccbbbbdacccccccccc fcccccbbbbddecccccccccc fccccebbbdddccccccccccc fcccebbbcdddccccccccccc fccgbbbgcdddccccccccccc fccbbbeceddeccccccccccc fcbbbbccdddcccccccccccc fbbbbcccdddcccccccccccc ebbbccccdddcccccccccccc cbbbcccceddecccccccccccc fbbbgccccaddccccccccccccc bbbecccccdddccccccccccccc bbbeccccccdddccccccccccccc bbbbfccccceddeccccccccccccc ebbb gggggaddgggggggggggggg cbbb ddd fbbbf ddd bbbc cdde bbbe addf bbbb ddd ebbb ddd cbbb fdde fbbbf addf bbbc ddd bbbe ddd edde ffffffffffffffffffffffff bbbb fdda ddddddc gcccccccccccccccccccccccgebbb eddf cdddddddaf gcccccccccccccccccccccccebbb ddd eddddddda gccccccccccccccccccccccgbbbf ddd addddddde gccccccccccccccccccccccbbbc fdda fadddddddc gcccccccccccccccccccccbbbe eddc cdddddddaf gccccccccccccccccccccbbbbf ddd edddddddacccccccccccccccccccbbbbcf ddd edddddddacccccccccccccccebbbccf fdda fadddddddecccccccccccgbbbgccf eddc eddddddddgccccccccbbbecccf ddd gccedddddddacccebbbbeccccf ddd gcccccadddddbbbbbbbbcccccf dda gcccccccebbbbbbbbbeccccccf eddc gcccgebbbbbbbbbdddddgccccf ddd gebbbbbbbbbeccedddddddaccf ddd ebbbbbbbbbgccccccccaddddddde ddd febbbbbbbbecccccccccccccccadddddddg gddg cbbbbbbbbbeccccccccccccccccccccgddddddddc add febbbbbbbbbf gccccccccccccccccccccccccedddddddaf ddd fbbbbbbbbbef gccccccccccccccccccccccccf eddddddde ddd cbbbbbbbbbc gccccccccccccccccccccccccf faddddddddde ebbbbbbbbef gccccccccccccccccccccccccf cddddddd bbbbbbe gccccccccccccccccccccccccf gdddd cbbc gccccccccccccccccccccccccf c gccccccccccccccccccccccccf cgggggggggggggggggggggggg ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#30386eff b,#3663a9ff c,#a8b4ceff d,#171952ff e,#5f628aff f,#d6dce9ff g,#748cb8ff ``` ```image c cb fbb fbbb gbbb gbbbb cbbbbb cbbbbbb fbbbbbbb f fbbbbbbbf dec gbbbbbbc ddddec gbbbbbbg ddddddagf cbbbbbbg dddddddddagf cbbbbbbb ddddddddddddec fbbbbbbbf addddddddddddddec fbbbbbbbf ceddddddddddddddagf gbbbbbbc ceddddddddddddddagf fgbbbbbbbg fgaddddddddddddddec fcgbbbbbbbbbg fgaddddddddddddddeggbbbbbbbbbbbb cedddddddddaabbbbbbbbbbbbbbbf cedddabbbbbbbbbbbbbbbbbbf fgbbbbbbbbbbbbbbbbbbgc cgbbbbbbbbbbbbbbbbbbaaddec fcgbbbbbbbbbbbbbbbbbbaddddddddaef fgbbbbbbbbbbbbbbbbbbgeddddddddddddddagf fcgbbbbbbbbbbbbbbbbbgcf fgaddddddddddddddec cgbbbbbbbbbbbbbbbbbgcf fgaddddddddddddddec bbbbbbbbbbbbbbbbgf cedddddddddddddd bbbbbbbbbbbbgcf ceddddddddddd bbbbbbbbbgcf fcadddddddd bbbbbbgf fgaddddd bbgcf feddd c ce ``` <!-- end of image --> 1 intersection present within area A. Now, let's scrutinize the next spot. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#30376cff b,#3663a8ff c,#9ea9c6ff d,#171952ff e,#6a6c90ff f,#d7dce8ff g,#5e82b9ff ``` ```image cdddddc edddddf ddddda fddddde cdddddc edddddf ddddda fddddde cdddddc edddddf adddda fddddde cdddddc c edddddf gbg adddda cbbbgf fddddde cbbbbbbf cdddddc fbbbbbbbf edddddffbbbbbbbf addddd gbbbbbbc fdddddegbbbbbbc cdddddgbbbbbbg eddddabbbbbbg adddabbbbbbbf fddddbbbbbbbf cdddbbbbbbbc eddbbbbbbbc adabbbbbbg dabbbbbbg cabbbbbbbf ebbbbbbbf bbbbbbbc gbbbbbbc cbbbbbbb cbbbbbbbc fbbbbbbbd fbbbbbbbaa gbbbbbbade gbbbbbbaddc cbbbbbbbdddf cbbbbbbbddda fbbbbbbbdddde fbbbbbbbaddddc gbbbbbbbdddddf gbbbbbbcddddda cbbbbbbgfddddde cbbbbbbg cdddddc fbbbbbbbf edddddf fbbbbbbbf adddda gbbbbbbc fddddde gbbbbbbc cdddddc cbbbbbbg edddddf cbbbbbbg adddda fbbbbbbbf fddddde fbbbbbbbf cdddddc gbbbbbbc edddddf gbbbbbbc addddd bbbbbbg fddddde bbbbbg cdddddc bbbbbf edddddf bbbbf addddd bbbc fddddde bbc cdddddc bg edddddf g addddd f ddddda cddddde ``` <!-- end of image --> My investigation has led me to 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#363a6dff b,#3663a9ff c,#a3aec9ff d,#171952ff e,#64658bff f,#d3d8e5ff g,#7388b4ff ``` ```image cf add ddd ddd cddc add ddd ddd cddg add ddd ddd fddg edd ddd ddd fdde eddf ddd ddd b fdde bbbf eddfbbbb dddgbbb ddabbb fddbbbf gdbbbg dbbbb bbbb gbbb cbbbc fbbba bbbad bbbbda bbbbddc gbbbddd cbbb ddd fbbbf dda bbbc cddc bbbg add bbbb ddd gbbb ddd cbbb cddg fbbbf add bbbc ddd bbbg ddd bbbb cddg gbbb add cbbb ddd fbbbf ddd bbbc fddg bbbg eddf bbbb ddd gbbb ddd cbbb fdde fbbbf eddf bbbc ddd bbbg ddd gddg bbbb fdde ddddddc gbbb eddf cdddddddaf cbbb ddd gddddddde fbbbf ddd edddddddg bbbc dde fadddddddc bbbg gddf cdddddddaf bbbb ddd gddddddde gbbb ddd edddddddg cbbb dda fadddddddc fbbbf gddc cdddddddaf bbbc ddd gddddddde fgbbbbg ddd eddddabbbbbbbb dda gbbbbbbbbbc cddc fgbbbbbbbbbddddaf ddd cbbbbbbbbbc cddddddda ddd gbbbbbbbbbf eddddddde dda fgbbbbbbbbgf adddddddc cddc cbbbbbbbbbc fddddddddf add gbbbbbbbbbf cdddddddaf ddd fbbbbbbbbbg eddddddde ddd cbbbbbbbbbc adddddddddg gbbbbbbbbgf fadddddd bbbbbbc cdddd cbbc c ``` <!-- end of image -->
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I have an image in front of me. I need to determine if there are any intersection segments. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#88b163ff b,#aacce3ff c,#b1d7b1ff d,#689930ff e,#99c892ff f,#eff5f0ff g,#d8e5d9ff ``` ```image ed ddf dde ddd ddd dddf ddde fdddd gdadd cdedd edcadc ceeeeeeeeeeeddaaddeeeeeeeeeeeeeb ecccccccccccddccddccccccccccccbbb fffffffffgbfff ecccccccccccddccddcccccccccccbbb ccccccccbbbbbe ecccccccccccddccddecccccccccbbbe ccccccbbbbcbbbb ecccccccccccddccedaccccccccbbbce cccccbbbccccbbbbg ecccccccccccddcccddcccccccbbbcce cccbbbbccccccebbbbf ecccccccccccddcccddcccccccbbccce cccbbcccccccce bbbb ecccccccccccddcccddecccccbbcccce ccacdcccccccce fbbbf ecccccccccccddcccadaccccbbccccce cccddcccccccce fbb ecccccccccceddccccddcccbbbccccce cccaddccccccce gbb eccccccccccedaccccddccbbbcccccce ccccddccccccce bbb eccccccccccadaccccddcbbbccccccce ccccaddcccccce bbb eccccccccccadeccccadbbbcccccccce cccccddcccccce bbg eccccccccccddecccccbbbccccccccce ccccceddccccce fbbf eccccccccccddcccccbbbcccccccccce ccccccddecccce gbb eccccccccccddccccbbbdcccccccccce cccccceddcccce bbb eccccccccccddcccbbbadeccccccccce cccccccddeccce bbb eccccccccccddccbbbceddccccccccce ccccccceddccce bbg eccccccccccddcbbbcccddccccccccce ccccccccddecce bbf eccccccccccddbbbccccddccccccccce cccccccceddcce fbb eccccccccccdabbcccccddecccccccce eeeeeeeeeddaec gbb eccccccccccabbccccccedacccccccce fdd bbb eccccccccccbbccccccccddcccccccce ddc bbb ecccccccccbbeccccccccddcccccccce fdd bbf eccccccccbbaaccccccccddeccccccce ddd fbbf ecccccccbbedeccccccccadaccccccce dddf gbb eccccccbbcddecccccccccddccccccce addf bbb ecccccbbccddccccccccccddccccccce addg bbb eccccbbbccddccccccccccddccccccce eddc bbg ecccbbbcccddccccccccccadacccccce cddc bbf eccbbbccccddcccccccccccddcccccce gdde fbb ecbbbcccccddcccccccccccddcccccce gdda gbb ebbbccccccddcccccccccccddcccccce fdda bbb bbbcccccccddcccccccccccadaccccce fddd bbb bbbccccccccddccccccccccceddccccce ddd bbf bbbccccccccedaccccccccccccddccccce ddd fbb bbbeccccccccadaccccccccccccddccccce ddd gbb bbb fffffffffedcffffffffffffadcfffff ddd bbbbbb adg gda addf bbbb ddf dd addg bb dd dd addg dd ddg eddc dd cda cdde dd dd gdda dd dd gdda dd ddf fdda dd ede ddd gda fdd ddd cda dd ddd cde dd ddd edc edc dddf adg gdd addf ddf dd addg dd dd eddg dd adc cddc dd gda cdde dd dd gdda dd dd fdda dd adg fddd fdd cda ddd gda dd ddd cde dd ddd edc ddf ddd adg ede dddf adg fda addfdd adddd eddd cdd gg ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#82ab55ff b,#aacce4ff c,#c7d9b2ff d,#689930ff e,#a6c284ff f,#e7efe7ff g,#cfe2f0ff ``` ```image fbbbbbbg gbbbbbbbbb fbbbbbbbbbbb gbbbbbbggbbbb gbbbbbbbf gbb bbbbbbbg g gbbbbbbg fbbbbbbbg gbbbbbbg fbbbbbf bbbb edbaa fddddc eddda fddddc eddda fddddc edddd fdddde eddddf dddde cddddf addde cddddf addde cddddf addde cddddf addda cddddf addda fddddc addda fddddc eddda fddddc eddda ``` <!-- end of image --> No intersection found in area A, but I won't give up. Okay, let's proceed to the next area. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ab062ff b,#a9cce5ff c,#acc791ff d,#689930ff e,#c6ddecff f,#e9f1ecff g,#ceddbdff ``` ```image adddg cdddc adddg gddda e adddf ddddf fb ddddf adddg fbb dddd cdddc fbbb fdddd gddda fbbbb fddda fdddd bbbbb gddda adddg bbbbbf gddda cdddc ebbbbe gdddc gddda ebbbbe cdddc fdddd ebbbbe cdddc ddddg ebbbbe cdddg adddc ebbbbb adddg gddda fbbbbb adddg fdddd fbbbbbf adddf ddddf fbbbbbf ddddf adddg fbbbbbf dddd cdddc bbbbbf fdddd gddda bbbbbe fddda ddddf ebbbbe gddda adddg ebbbbe gddda cdddc ebbbbe gdddc gddda ebbbbe cdddc fddddfebbbbb cdddc adddgbbbbb adddg cddabbbbbf adddg gdabbbbbf adddf fdbbbbbf ddddf bbbbbf dddd bbbbbg dddd ebbbbca fdddd ebbbbcdd fddda ebbbbcdddf gddda ebbbbeadddg gddda ebbbbb cdddc cdddc ebbbbb gdddd cdddc ebbbbb ddddf cdddg ebbbbb adddg adddg ebbbbb cdddc adddgebbbbbf gddda adddebbbbbf ddddf dddabbbbbf adddg ddabbbbbf cdddc fdabbbbbf gddda fabbbbbf fdddd ebbbbbf adddg fbbbbbf cdddc fbbbbbc gddda fbbbbbac fdddd fbbbbbadc ddddf fbbbbbaddg adddg fbbbbbcdddg cddda fbbbbbfadddg gdddd fbbbbbf adddf ddddf fbbbbbf ddddf adddg fbbbbbe dddd cdddc fbbbbbe fdddd gddda fbbbbbe fddda ddddf bbbbbe gddda adddg bbbbbe gddda cdddc bbbbbe gdddc gddda bbbbbe cdddc fdddd bbbbbe cdddc adddg bbbbbe adddg cdddc ebbbbe adddg gddda ebbbbe adddf fdddd ebbbbe ddddf ddddf ebbbbe dddd adddc bbbbe dddd cddda bbbe fdddd fdddd bbe fddda ddddf be gddda adddg e gddda cdddc cdddc gddda ``` <!-- end of image --> Oh my, look at that! It's 2 intersections in area B! Answer: A: 0; B: 2; 0 + 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#82aa54ff b,#abcde5ff c,#bcd1a2ff d,#68992fff e,#9fbe7fff f,#e0ececff g,#d4e2c6ff ``` ```image ed ddf dde ddd ddd ddd dddc fdddd gdadd cdedd edcadc adggda b adf dd bbb fb dd dd bbb bbbbb dd adg bbb bbbbfbbbb dd cda bbb bbbf fbbbf dd dd fbb bbbb bbbbf dd dd fbb fbbf bbbb dd ddf fbbf eba bbbf dd cde bbf dd fbb fda dd bbf eda fbb gde dd bbb dd bbb cdc dd bbb cdd bbb edc edbbb ddf bbf adg fbbb cdd bb dd bbb ddf fbb dd bbbd gdd bbb dd fbbedc ddg bbb dd fbb gda gdd bbf dd fbb dd ddg bbf ddfbb dd fdd fbb debb adg ddc fbb ebbf gda fdd bbb gbbf dd ddc bbb fbbe dd dd bbf fbbac ddf add bb fbbedg cde add fbb fbbfadf dd addf bbb bbf dd dd eddg bbb bbf dd ddf eddg bbf bbf dd ede cddc bbf bbf dd fdd gdde fbb bbf dd dd fdda bbb bbb dd dd fdda bbb bbb dd edc ddd bbb bbb fda gda ddd bbf bbb gda dd ddd bb bbb cde dd ddd fbb bbb edc adg ddd bbbbbb adg gda addf bbbb adf dd addf bb dd dd eddg dd adg cddc dd cde cddc dd dd gdde dd dd fdda dd ddf fdda dd ede ddd fda dd ddd gde dd ddd cdc dd ddd edc edc ddd adg fdd addf dd dd addf dd dd eddg dd adg cddc dd gda gdde dd dd gdde dd dd fdda dd adg dda dd cde ddd gda dd ddd cde dd ddd edc ddf ddd edg cde add adf da addfdd edddd eddd cdd ff ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for intersections. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#7d6d8bff b,#1f8facff c,#b1d7b2ff d,#5faeb5ff e,#9999a2ff f,#ecf1eeff g,#96c799ff ``` ```image bf bbbf dbdbbc dbb bbc cbb bbc fbb bbd fbb bbd bbf bbd bbf bbd ggggggggggggggggggggggggggggggggggggbbd dbb cccccccccccccccccccccccccccccccccccbbdcf dbb ccccccccccccccccccccccccccccccccccdbbccf dbb cccccccccccccccccccccccccccccccccdbbcccf dbb ccccccccccccccccccccccccccccccccgbbccccf dbbggggggggggggggggggggc ccccccccccccccccccccccccccccccccbbcccccf fcdbbcccccccccccccccccccg cccccccccccccccccccccccccccccccbbccccccf fccdbbccccccccccccccccccg ccccccccccccccccccccccccccccccbbcccccccf fcccgbbcccccccccccccccccg cccccccccccccccccccccccccccccbbgcccccccf fccccgbbccccccccccccccccg ccccccccccccccccccccccccccccbbdcceaccccf fcccccgbbcccccccccccccccg cccccccccccccccccccccccccccbbdcccaaecccf fcccccccbbccccccccccccccg ccccccccccccccccccccccccccdbbccccaaacccf fccccccccbbgccccccccccccg cccccccccccccccccccccccccdbbccccgaaacccf fcccccccccbbccccccccccccg ccccccccccccccccccccccccgbbccccceacaaccf fcccccccccbbccccccccccccg ccccccccccccccccccccccccbbccccccaacaaccf fcccccccccdbccccccccccccg cccaeccccccccccccccccccbbcccccccaeccaecf fccccccccccbdcccccccccccg cccaacccccccccccccccccbbcccccccgagccaacf fccccccccccbbcccccccccccg cccaaccccccccccccccccbbgcccccccaacccgaef fccccccccccbbcccccccccccg cccgagccccccccccccccbbdccccccccaaccccaaf fcccccccccgbbcccccccccccg ccccaecccccccccccccdbdcccccccccaecccceaf fcccccccccaaacccccccccccg ccccaaccccccccccccdbbccccccccceaccccccaa fccccccccgaaaaacccccccccg cccceacccccccccccgbbccccccccccaaccccccaa fccccccccaacbaaaacccccccg cccccaecccccccccgbbcccccccccccaaccccccgae fccccccccaacbbcaaaecccccg cccccaacccccccccbbccccccccccccaecccccccaa fccccccceaccbbcccaaaecccg cccccaaccccccccbbcccccccccccceacccccccccaf fcccccccaaccdbccccgaaagcg ccccceacccccccbbgccccccccccccaaccccccccfaa fcccccccaecccbdccccceaaag ccccccaecccccbbdcccccccccccccaaccccccccfea fccccccaaccccbbccccccceaaa ccccccaaccccbbdccccccccccccccaeccccccccf ae fccccccaaccccbbcccccccccaaae ccccccaacccdbbcccccccccccccceacccccccccf aa fccccceagccccbbcccccccccg aac cccccceaccdbbcccccccccccccccaacccccccccf fac fcccccaacccccdbcccccccccg f cccccccaegbbccccccccccccccccaacccccccccf aa fcccccaaccccccbdccccccccg cccccccaabbcccccccccccccccccaecccccccccf eaf fcccceacccccccbbccccccccg cccccccaabccccccccccccccccceaccccccccccf aa fccccaacccccccbbccccccccg cccccccbagcccccccccccccccccaaccccccccccf aa fccccaecccccccbbccccccccg ccccccbbaacccccccccccccccccaaccccccccccf fae fcccaaccccccccdbccccccccg cccccbbdaaccccccccccccccccgagccccccccccf aa fcccaacccccccccbdcccccccg ccccbbdceacccccccccccccccceacccccccccccf caf ggeaggggggggggbbgggggggc cccdbbcccaecccccccccccccccaacccccccccccf aa aa bb ccgbbccccaacccccccccccccccaecccccccccccf ea ae bb cccdcccccaaccccccccccccccgagcccccccccccf ae ea cb ccccccccceaccccccccccccccaaccccccccccccf aa aa fbc ccccccccccaecccccccccccccaaccccccccccccf fac fac bd ccccccccccaacccccccccccccaeccccccccccccf aa aa bb ccccccccccaacccccccccccceacccccccccccccf caf aa bb cccccccccceaccccccccccccaacccccccccccccf aa caf cb cccccccccccaecccccccccccaacccccccccccccf ea aa fbc cccccccccccaacccccccccccaecccccccccccccf ae ae bd cccccccccccaacccccccccceaccccccccccccccf aa ea bb cccccccccccgagcccccccccaaccccccccccccccf fac aa bb ggggggggggggaagggggggggaagggggggggggggg aa fac cb d aa ac eafaa fbc cbbd ea ea aaae bd fbbbf fac aa aaaf bb bbbc aa aa faa bbdbbd aa fac ac cbbbf ca ea bc ac aa aa ae aa faf caf ea ae aa aa ae ea faf faf ea ae aa aa ae eacaf faaa aaa aae ca f ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#7c6c8bff b,#1d8dacff c,#beb6c6ff d,#4fa6beff e,#9d91a9ff f,#d9e0e7ff g,#91c8d6ff ``` ```image fbbbb fbbbbf fbbbbg dbbbg dbbbd dbbbd gbbbd gbbbbf gbbbbf fbbbbf fbbbbg fbbbbg dbbbg dbbbd dbbbd gbbbd gbbbbf gbbbbf fbbbbf ee fbbbbg caae fbbbbg aaaa dbbbd faaaac dbbbd caaaaa dbbbd eaaaaaf gbbbbf aaaaaae gbbbbf faaaeaaaf fbbbbf caaafaaac fbbbbg eaae eaaa fbbbbg aaac faaac f dbbbg faaaf eaae eaaf dbbbd caaa caaaf aaac dbbbd eaae aaae eaaa gbbbd aaac caaaf caaaf gbbbbf faaaf faaac aaac gbbbbf caaa eaaa eaae fbbbbf eaae faaac caaa fbbbbg aaac aaae faaaf fbbbbg faaaf caaa aaac dbbbd caaa aaa eaae dbbbd eaae eaa caaa dbbbd faaac faa faaaf gbbbbf caaaf ea aaac gbbbbf eaaa ca eaae fbbbbf aaac a caaa fbbbbg faaaf c faaaf fbbbbg caaa f aaae dbbbg eaae eaaa dbbbd aaac caaaf dbbbd faaaf aaac gbbbd caaa eaae gbbbbf eaae caaa gbbbbf aaac faaaf fbbbbf faaaf aaac fbbbbg caaa eaae fbbbbg eaae caaa dbbbg aaac faaaf dbbbd faaaf aaac dbbbd caaa eaae gbbbd eaae caaa gbbbbf aaac faaac gbbbbf faaaf aaae fbbbbf caaa eaaafbbbbg eaae faaadbbbg faaac aaabbbd caaaf eaaabd eaaa eaaad aaac gbaaaf faaaf gbbaaac caaa fbbbaaae eaae fbbbbeaaa aaac fbbbbgfaaaf faaaf dbbbg aaac caaa dbbbd eaae eaae dbbbd caaa aaac gbbbd faaac faaaf gbbbbf aaae caaa fbbbbf caaa eaae gbbf faaaf aaac gg aaac faaaf eaae caaa caaa eaae faaaf aaac aaac faaaf eaae caaa caaa eaae faaaf faaac aaac caaaf eaae eaaa caaaf aaac faaac faaaf eaae caaa caaa eaae faaaf aaac aaac faaaf eaae caaa caaa eaae faaaf aaac ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Now, let's dive into another area. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#7c6d8cff b,#1b8dacff c,#afc4d2ff d,#439fb9ff e,#a195acff f,#d7e0e8ff g,#72b8cbff ``` ```image gbbbbc gbbbbc gbbbbc cbbbbc cbbbbg cbbbbg cbbbbg fbbbbg fbbbbg fbbbbd fbbbbd fdbbbd fdbbbd fdbbbdf dbbbdf dbbbdf dbbbd dbbbf bbbc dbbg gbbd cbbb fbbbf bbbc dbbg gbbd cbbb fbbbf bbbc fcdbbg faaaabd caaaaaaf aaaaaaaac faaaeaaaaaac eaaa daaaaaaaf aaae gbbaaaaaaef caaaf cbbbcaaaaaaef eaae fbbbf caaaaaae faaac bbbc caaaaaac caaa dbbg eaaaaaac aaae gbbd feaaaaaaf faaaf cbbb feaaaaaef eaaa fbbbf faaaaaaef aaac bbbc caaaaaa caaaf dbbg caaaa eaae gbbd eaa faaac cbbb fe eaaa fbbbf aaae bbbc faaaf dbbg eaaa gbbd aaac cbbb caaaf fbbbf aaae bbbc faaac dbbg eaaa gbbd aaae cbbb caaaf fbbbf eaaa bbbc faaac dbbg caaa gbbd aaae cbbb faaaf fbbbf eaaa bbbc ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#7d6c8cff b,#1c8dacff c,#c2bac9ff d,#4aa3bcff e,#9f92aaff f,#dee2e8ff g,#97cad8ff ``` ```image df bbbf dbdbbf gbd bbg gbb bbg fbb bbg bb bbd bb bbd bbf bbd bbg dbd dbg dbb dbd dbb gbb dbb fbb gbb fbb gbb bb gbb bb fbb bbf fbb bbg ca fbb dbd aac fbbf dbd aaa bbf gbb faeaf bb fbb ea aa db bb aa ea gb ae bb ae ae bg aa bbf faf aa bd ea bbf ea fac bb faf bbg aa aa fdb ae dbd ae ea aaaf aa gbd caf aa faeaaa ea gbb aa aa aa baaae fac fbb aa fac ae bb aaae aa bb ac aa ca db faaac aa bb ca caf aa gb faaaf ca bbf aa aa ac bg caaa ac bbg aa ea ea bd eaaa aa dbg ac ae aa bb eaae aa dbd ca aa caf db aac ca gbb aa fac aa gb f aefbb aa aa ae bg aabb fac caf ea bd eab ea aa aa bb baf aa aa fac db bbae ae ae aa gb bbgaa faf aa aa bg dbd ea ea caf caf bd gbd fac aa aa aa bb fbb aa ae ea ae db g aa faf ae ea gb ca ea aa aa bg ac aa fac fac bd aa ae aa aa bb aa caf caf aa db caf aa aa caf gb ae aa ea aa bg aa ac ae ae bd ea ca aa ea bb faf aa fac aa db ae aa aa fac gb d aa ac ea aa bg gbbd ea ca aaae bd fbbbf fac aa aaa bb bbbg aa aa faa dbgbbd aa fac ac gbbb ca ea bg ac aa aa ae aa faf caf ea ae aa aa ae ea faf faf ea ae aa aa ae eacaf aaa aaa aac ca f ``` <!-- end of image -->
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This image looks interesting. I wonder if there are any intersections hidden in there? I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#aac9a9ff b,#d5d45fff c,#dce3c8ff d,#d0d989ff e,#f0f5edff f,#96ca96ff g,#b2d7b2ff ``` ```image de b cb bb bc b cb bd bc b db bd be eb db bd be eb db bd be eb db bc afffffffffffffffffffffffe b fggggggggggggggggggggggae effffffffffffffbffffffffe fggggggggggggggggggggggaeeeccccgggaaaaaaaaaaaac eaggggggggggggbbgggggggae fggggggggggggaaaaaaaaaaaaaaaaaaaaaggcccceeeeegaaage eaggggggggggggbdgggggggae fggggggggggggaaggggggggae caaaac eaggggggggggggbggggggggae fggbdggggggggagggggggggae egaaage eagggggggggggdbggggggggae fggdbbgggggggagggggggggae caaaaceagggggggggggbbggggggggae fggggbbgggggaagggggggggae egaaaaggggggggggbdggggggggae fgggggbbdgggaagggggggggae eaaaaaaggggggbgggggggggae fggggggdbbggaggggggggggae eagggaaaaaggdbgggggggggae fggggggggbbgaggggggggggae eaggggggaaaabbgggggggggae fgggggggggbbdggggggggggae eagggggggggabdgggggggggae fggggggggggdbbgggggggggae eagggggggggabggggggggggae fggggggggggagbbggggggggae eagggggggggdbggggggggggae fggggggggggaggbbdggggggae eagggggggggbbggggggggggae fgggggggggaagggdbbgggggae eagggggggggbaagggggggggae fgggggggggaagggggbbggggae eagggggggggbaagggggggggae fgggggggggagggggggbbdggae eaggggggggdbaagggggggggae fgggggggggaggggggggdbbgae cbbd eaggggggggbdgagggggggggae fggggggggaaggggggggggbbae edbbbbcbb eaggggggggbggagggggggggae fggggggggaagggggggggggbbc edbbbbc bb eaggggggggbggagggggggggae fggggggggagggggggggggggdbb cbbbbde bb eagggggggdbggaaggggggggae fgggggggaagggggggggggggaebb cbbbbde bbe eagggggggbdggaaggggggggae faaaaaaaaaaaaaaaaaaaaaafe bbc edbbbbc bbe eagggggggbgggaaggggggggae eeeeeeeeaceeeeeeeeeeeeee cbbbbbc dbceagggggggbggggaggggggggae a ede cbdaggggggbbggggaggggggggae ca cbbggggggbdggggaagggggggae ag ebbgggggbgggggaagggggggae ae eabbgggdbgggggaagggggggae ea eagbbggbbggggggagggggggae ca efaabbabdaaaaaaaaaaaaaafe ag eeeebbbeeeeeeeaceeeeeee ae db ac ea ga ga ca ac a ae ae ge ea ac a ga ag a ac ca a a ea ea ea a ca ga ae ca ac ac ga e ga ag ca ac a ac aeae acae aga caa eaa aa aa aa ga ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#acc3aaff b,#d6d45fff c,#d5e0d5ff d,#dfde89ff e,#eff2e2ff f,#ebeab2ff g,#bed0beff ``` ```image ecccccccgggggggaaaa caaaaaaaaaaaaaaaaaaa gaaaaaaaaaaaaaaggggg aageeeeee de eaac fbbf caae dbbbde gaa fbbbbe aag edbbbf eaac dbbbde caae fbbbbe gaa edbbbf aag dbbbde caac fbbbbe gaae ebbbbf aaa dbbbdeaag fbbbbaac ebbbbde dbbbde eabbbbe caabbbbf gaaedbbbd aag fbbbbe eaac ebbbbf caae dbbbd gaa fbbbbe aag ebbbbf eaac dbbbd caae fbbbbe gaa ebbbbf aag dbbbd eaac fbbbbe caae ebbbbf gaa dbbbd aag fbbb caac ebb gaae d aaa eaag caac gaae ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Let's shift our focus to the next area. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#acc3aaff b,#d6d45fff c,#d4dfd3ff d,#dfdf8cff e,#f1f4e7ff f,#edecbbff g,#bdcfbbff ``` ```image ebbd fbbf dbbe bbb ebbd fbbf dbbe bbb ebbd fbbf dbbe bbb gce ebbd aaaagce fbbf aaaaaaagce dbbe ecgaaaaaaagce bbb ecgaaaaaaagce ebbd ecgaaaaaaagce fbbf ecgaaaaaaagcedbbe ecgaaaaaabbd ecgaaabbd gdbbf cbbb cbbb fbbd dbbg dbba bbba fbbdae dbbaac bbbaac ebbdaag fbbfgaa dbbecaae bbb caac ebbd eaac fbbf aag dbbe gaa bbb gaa ebbd caae fbbf eaac dbbe eaac bbb aag ebbd gaa fbbf caae dbbe caac bbd eaac ebbd aag fbbf gaa d dbb gaa bd bbd caae bbde fbbf eaac bbbbe fbbf eaac ebbbbe dbb aag dbbbf bbd gaa dbbbf fbbf caae dbbbf dbbe caac fbbbd dbb eaac fbbbd ebbd aag ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#acc3abff b,#d6d45fff c,#d5e0d5ff d,#dfde87ff e,#f1f4e9ff f,#ebebb5ff g,#bed0bdff ``` ```image de b fb bb bf b fb bd bf b fb bd be eb db bd be eb db bd be eb db bf b fb eeeccccgggaaaaaaaaaaaac bb caaaaaaaaaaaaaaaaaaaagggcccceeeegaaage bf ageee caaaac b bf ae egaaage fb fbb a caaaac bb bbe ca egaaage bf dbf ag caaaac b fbb ae egaaage fb bbea caaabd bbd gbf abb cb aebbe fb ea bbf bbe ga fbb bac ac bbe ebag a bbf dbca ca fbb fbbd bdea ga ebbe edbbbbfbb be a ac bbf edbbbbf bb eb ae a fbb fbbbbde bb db ag ca ebb fbbbbde bbe bd ga aa bbf edbbbbf bbe be ca ac fbbbbbf dbf eb a a ede fbd db ae ca fbd bf ac ag ebb b ag ae bb fb ca a bb db ea ca bbebf a ag dbb ae ae db ag ea ga ga ca ac a ae ae ge ea ac a ga ag a ac ca a a ea ea ca a ca ga ae ca ac ag ga e ga ag ca ag a ac aeae acae aga caa eaa aa aa aa ga ``` <!-- end of image -->
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I'm approaching this image with caution. Intersections might be tricky to spot. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#16ef51ff b,#ed93e8ff c,#7bef98ff d,#eef4efff e,#48ee74ff f,#a0cfa0ff g,#b2d8b2ff ``` ```image aad aac aac daac gaac caac eaac aaae aaae aaae aaae aaae daaae caaaa eaaaa aaaaa aaaaa aaaaa aaaaa aaaaa daaeaa gaaeaa caaeaa eaaeaa aaaeaa aaecaa aaccaa aagcaa aadcaa daa caa caa caa d eaa gaa dddddddddddddddddddddddd bbb aaa gaa fffffffffffffffffffffffbd dbbb aae gaa fgggggggggggggggggggggbbb bbbd aac gaa fggggggggggggggggggggbbbb bbb aag gaa fgggggggggggggggggggbbbbd bbb aad daa fggggggggggggggggggbbbbfd dbbb daa daa fgggggggggggggggggbbbbgfd bbbb gaa daa fggggggggggggggggbbbbggfd bbb caa daa fggggggggggggggggbbbgggfd bbb eaa daa fgggggggggggggggbbbggggfd dbbb aaa daaeccgd fggggggggggggggbbbgggggfd bbbbddddddddddaaedddaaaaaaaaaaaaaeecgd fgggggggggggggbbbggggggfd bbbgfffffffffaaefffeaaaaaaaaaaaaaaaaaaaaaaaeecgd fggggggggggggbbbgggggggfd dbbbgggggggggaacgggggggfd dgcceaaaaaaaaaaaaaaaaaaaaaaaaeecfggbbbggggggggfd dgbbbggggggggaaggggggggfd dgcceaaaaaaaaaaaaaaaaaaaaaaaaeecfggfd dfbbbbggggggfaaggggggggfd dcceeaaaaaaaaaaaaaaaaaaaaa dfgbbbggggggcaaggggggggfd fggggggggbbgceeaaaaaaaaaa dfggbbbgggggeaaggggggggfd fgggggggbbbgggggggggggfcc dfgggbbbggggaaaggggggggfd fggggggbbbbggggggggggggfd dfggggbbbgggaaaggggggggfd fgggggbbbbgggggggggggggfd dfggggbbbgggaaeggggggggfd fggggbbbbggggggggggggggfd dfgggggbbbggaacggggggggfd fgggbbbbgggggggggggggggfd dfggggggbbbgaafggggggggfd fggbbbbggggggggggggggggfd dfgggggggbbbaagggggggggfd fgbbbbgggggggggggggggggfd dfgggggggbbfaagggggggggfd fbbbbggggggggggggggggggfd dfgggggfceaaaagggggggggfd bbbbgggggggggggggggggggfd dceaaaaaaaaaaagggggggggfd bbbbggggggggggggggggggggfd dceaaaaaaaaaaaaaaefbbggggggggfd dbbbgggggggggggggggggggggfd eaaaaaaaaaaaaecgggggbbbbgggggggfd dbbbggggggggggggggggggggggfd caaaaacgdfgggggggggggbbbgggggggfd dbbbffffffffffffffffffffffffd dd dfggggggggggggbbbggggggfd dbbb dfgggggggggggggbbbgggggfd bbb dfgggggggggggggbbbbggggfd bbb dfggggggggggggggbbbggggfd bbb dfgggggggggggggggbbbgggfd bbbd dfggggggggggggggggbbbggfd bbbd dfgggggggggggggggggbbbgfd bbbd dfgggggggggggggggggbbbgfd bbbd dfggggggggggggggggggbbbfd bbbb dfgggggggggggggggggggbbbd bbbb dffffffffffffffffffffgbbb bbbb bbbd bbbb bbb bbbb bbb bbbb dbbb bbbb bbbb bbbb bbbbbbb bbbbb bbb db ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#16f051ff b,#ee91e9ff c,#69ee8eff d,#cafbd7ff e,#3ff170ff f,#f5c8f3ff g,#97f2b0ff ``` ```image bbbbbf gaaaac caaaaaaaaa bbbbbb gaaaag ceaaaaaaa fbbbbbb caaaag ddggg fbbbbbf eaaaad bbbbbbf eaaaad bbbbbbf aaaaa fbbbbbb aaaaa fbbbbbb daaaae bbbbbbf gaaaac bbbbbbf gaaaac fbbbbbb caaaag fbbbbbb caaaag fbbbbbf eaaaad bbbbbbf aaaaad bbbbbb aaaaa fbbbbbb daaaae fbbbbbf daaaae bbbbbbf gaaaac bbbbbb gaaaag fbbbbbb caaaag fbbbbbf eaaaad bbbbbbf eaaaad bbbbbbfaaaaa fbbbbbbaaaaa fbbbbbaaaae bbbbgaaaac bbbcaaaac ddgceeaaaaaaag dggceaaaaaaaaaaaaaag ddgceaaaaaaaaaaaaaaaaaaaaaf aaaaaaaaaaaaaaaaaaaaaaaaaacbf aaaaaaaaaaaaaaaaaaaaaeecgbbbb aaaaaaaaaaaaaaaecggd fbbbbbb aaaaaaaaecggd fbbbbbf aeecgdd bbbbbbf bbbbbb fbbbbbb fbbbbbf bbbbbbf bbbbbb fbbbbbb fbbbbbb bbbbbbf bbbbbbf fbbbbbb fbbbbbb bbbbbbf bbbbbbf bbbbbb fbbbbbb fbbbbbf bbbbbbf bbbbbb fbbbbbb fbbbbbf bbbbbb bbbbb ``` <!-- end of image --> My analysis confirms the presence of 1 intersection in area A. Let's inspect the next region. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#16ef51ff b,#ef91eaff c,#85f3a3ff d,#c5fad3ff e,#4cee78ff f,#f7cbf4ff g,#a8afb7ff ``` ```image b bb bbb bbbb bbbbb bbbbbb bbbbbbb fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf bbbbbbb bbbbbbb bbbbbbb bbbbbbb eecccddd bbbbbbb aaaaaaaaaaaeecccddd bbbbbbb aaaaaaaaaaaaaaaaaaaaaaeeecgggd aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeecccddd aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaee ddccceeeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa dddccceeeaaaaaaaaaaaaaaaaaaaaaaaaaaa fbbbbggccceeeaaaaaaaaaaaaaaaa fbbbbbbf dddccceeeaaaaa fbbbbbbf ddd fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf bbbbbbb bbbbbbb bbbbbbb bbbbbbb bbbbbbb bbbbbbb bbbbbbb bbbbbbb bbbbbbbf fbbbbbbf bbbbbbf bbbbbf bbbbf bbbf bbf bf f ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area B. Answer: A: 1; B: 1; 1 + 1 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#16f051ff b,#ee91eaff c,#79f49aff d,#d4fbdfff e,#48f276ff f,#f6c6f4ff g,#a5f5bbff ``` ```image aa aag aac daac gaac caac eaac aaae aaae aaae aaae aaae daaae caaaa eaaaa aaaaa aaaaa aaaaa aaaaa aaaaa daaeaa gaaeaa caaeaa eaaeaa aaaeaa aaecaa aaccaa aagcaa aa caa daa caa gaa gaa f eaa gaa bbb aaa gaa b fbbb aae gaa bbb bbbf aac gaa bbbb bbb aag daa bbbb bbb aad daa fbbb fbbb daa daa fbbb bbbf gaa daa fbbb bbb caa daa fbbb bbb eaa daa fbbb bbb aaa aaeccgd bbb fbbf aae aaaaaaaaaaaaaeecgd bbb bbb aac caaaaaaaaaaaaaaaaaaaaaaaeecgd bbb bbb aag ddgceaaaaaaaaaaaaaaaaaaaaaaaaecgd bbb bbb aa dgceaaaaaaaaaaaaaaaaaaaaaaaaecgd fbbb daa dgceaaaaaaaaaaaaaaaaaaaaa bbbf gaa bbbgceaaaaaaaaaa bbb eaa bbbf dgc bbb aaa bbbf fbbb aae bbbf bbbf aac bbbf bbb aag bbbb bbb aad bbbb fbbbaa bbbb bbgaa bbbb dgeaaaa fbbb gcaaaaaaaaaaa fbbb dceaaaaaaaaaaaaaaecbb fbbb eaaaaaaaaaaaecd fbbf fbbb caaaaacg bbb fbbb dd bbb bbb bbb bbb fbbb bbb bbbf bbb bbb bbb bbb bbbf fbbb bbbf bbbf bbbf bbb bbbf bbb bbbf fbbb bbbf bbbf bbbb bbb bbbb bbb bbbb bbb bbbb fbbf fbbb bbbfbbb bbbbb bbb fb ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#c17986ff b,#78bfa5ff c,#ded2d3ff d,#95c999ff e,#c1a39fff f,#eff4efff g,#b1d7b1ff ``` ```image faa ffffffffffffffffffffffffffffffffffffffffeaefff dgggggggggggggggggggggggggggggggggggggggaadggd dgggggggggggggggggggggggggggggggggggggggaagggd dgggggggggggggggggggggggggggggggggggggggaagggd dggggggggggggggggggggggggggggggggggggggeaebggd dggggggggggggggggggggggggggggggggggggggaabdggd dggggggggggggggggggggggggggggggggggggggaabgggd dgggggggggggggggggggggggggggggggggggggeaabgggd f dgggggggggggggggggggggggggggggggggggggaadbgggd fae dgggggggggggggggggggggggggggggggggggggaabbgggd faae dgggggggggggggggggggggggggggggggggggggaabdgggd faae dggggggggggggggggggggggggggggggggggggeaabggggd caac dggggggggggggggggggggggggggggggggggggaabbggggd caac dggggggggggggggggggggggggggggggggggggaabbggggd caac dggggggggggggggggggggggggggggggggggggaabbggggd eaaf dgggggggggggggggggggggggggggggggggggeaabdggggd eaaf dgggggggggggggggggggggggggggggggggggaabbgggggd eaa dgggggggggggggggggggggggggggggggggggaabbgggggd aaa dgggggggggggggggggggggggggggggggggggaabbgggggd aaa dggggggggggggggggggggggggggggggggggeaebbgggggd aaa dggggggggggggggggggggggggggggggggggaabbggggggd aaa dggggggggggggggggggggggggggggggggggaabbggggggd aaa dggggggggggggggggggggggggggggggggggaabbggggggd aaa dgggggggggggggggggggggggggggggggggaaebbggggggd aaa dgggggggggggggggggggggggggggggggggaadbdggggggd aae dgggggggggggggggggggggggggggggggggaabbgggggggd faae dggggggggggggggggggggggggggggggggeaabbgggggggd faae dggggggggggggggggggggggggggggggggaaebbgggggggd caac dggggggggggggggggggggggggggggggggaadbbgggggggd caac dggggggggggggggggggggggggggggggggaabbdgggggggd caaf dgggggggggggggggggggggggggggggggeaabbggggggggd eaaf dgggggggggggggggggggggggggggggggaaebbggggggggd eaaf dgggggggggggggggggggggggggggggggaagbbggggggggd eaa dgggggggggggggggggggggggggggggggaadbbggggggggd aaa dggggggggggggggggggggggggggggggeaebbdggggggggd aaa dggggggggggggggggggggggggggggggaagbbgggggggggd aaa dggggggggggggggggggggggggggggggaagbbgggggggggd aaa dggggggggggggggggggggggggggggggaagbbgggggggggd aaa dgggggggggggggggggggggggggggggeaedbdgggggggggd aaa dgggggggggggggggggggggggggggggaagbbggggggggggd aae dgggggggggggggggggggggggggggggaagbbggggggggggd faae dgggggggggggggggggggggggggggggaagbbggggggggggd faae dggggggggggggggggggggggggggggaaegbbggggggggggd faac dggggggggggggggggggggggggggggaagbbdggggggggggd caac dggggggggggggggggggggggggggggaagbbgggggggggggd caac dgggggggggggggggggggggggggggeaagbbgggggggggggd caaf dgggggggggggggggggggggggggggaaegbbgggggggggggd eaafdgggggggggggggggggggggggggggaagdbbgggggggggggd eaadgggggggggggggggggggggggggggaagbbdgggggggggggd eaaggggggggggggggggggggggggggeaagbbggggggggggggd aaagggggggggggggggggggggggggaaegbbggggggggggggd aaaggggggggggggggggggggggggaaggbbggggggggggggd daaagggggggggggggggggggggggaagdbbggggggggggggd dgaaagggggggggggggggggggggeaegbbgggggggggggggd dggaaaggggggggggggggggggggaaggbbgggggggggggggd dgggaaagggggggggggggggggggaaggbbgggggggggggggd dggggaaaggggggggggggggggggaaggbbgggggggggggggd dgggggaaeggggggggggggggggeaebbbdgggggggggggggd dggggggaaegggggggggggggggaabbbbggggggggggggggd dgggggggaaeggggggggggdbbbaabdggggggggggggggggd dgggggggeaaeggggggdbbbbbbaaggggggggggggggggggd dggggggggeaagggbbbbbbbggaaeggggggggggggggggggd dgggggggggeaabbbbbbgggggaagggggggggggggggggggd dgggggggdbbaaabdggggggggaagggggggggggggggggggd dggggbbbbbbbaaaggggggggeaagggggggggggggggggggd dgbbbbbbbggggaaagggggggaaegggggggggggggggggggd cbbbbbbdggggggggaaaggggggaaggggggggggggggggggggd gbbbbbbdggggggggggggaaagggggaaggggggggggggggggggggd fdbbbbbbfdgggggggggggggggaaagggeaaggggggggggggggggggggd cbbbbbbgf dggggggggggggggggaaaggaaeggggggggggggggggggggd gbbbbbbg dgggggggggggggggggaaagaagggggggggggggggggggggd fgbbbbbbc dggggggggggggggggggaaaaagggggggggggggggggggggd fbbbbbbdf dgggggggggggggggggggaaaegggggggggggggggggggggd cbbbbbbg dggggggggggggggggggggaaggggggggggggggggggggggd gbbbbbbc dgggggggggggggggggggggeggggggggggggggggggggggd fdbbbbbbf dggggggggggggggggggggggggggggggggggggggggggggd cbbbbbbgf dggggggggggggggggggggggggggggggggggggggggggggd gbbbbbbg ffffffffffffffffffffffffffffffffffffffffffffff fbbbbc df ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#c17986ff b,#78bea5ff c,#dfbbc2ff d,#bee0d4ff e,#cf97a2ff f,#e8e6e5ff g,#9dcfbdff ``` ```image aaa faaa caae eaac faaa caaad eaaab faaabb caaabb eaabbb aaabbg aaabbd aaabbd caaabb eaaabg faaabbf caaabb eaaabb aaabbd aaabbf aaabb faabbb caabbb eaabbb faaabbg caaebbd eaabbbf caaabbb eaaebbg aaabbbf aaabbb aaabbg faaabbd caaebbf eaacbb faaagbb caaebbb eaacbbb faaadbbg caaegbbd eaacbbbf aaadbbb aaadbbg faaabbbf caaebbb eaacbbb faaa bbb caae bbb eaacfbbb faaa gbbd caae bbbf eaacfbbb aaa dbbg aaa gbbd aaa bbbf caaadbbg eaaegbbg faaafbbbf caae bbb eaac bbb aaa bbb aae bbb aac fbbb faa gbbd caa bbbf eaa fbbb faaa dbbg caae gbbd eaac bbbf caaa dbbg eaae gbbd e aaaf bbbf a aaa bbb ae aaa bbb aaac faaa bbb aaaa caae fbbb faaac eaac dbbb caaaaf faaa gbbd caaaa caae bbbf caaaf eaac fbbb caaaaf faaa gbbg eaaaa caae gbbd eaaa eaac bbbf eaaae aaa bbg eaaa aaadgbbbd faaac fgaaabbbbb aaaac dbbbaaabbbgd faaaa fdbbbbaaaabgf aaaac gbbbbbbbbbaaa caaaaf dgbbbbbbbbbdcaae caaaa dgbbbbbbbbbf eaac aaaabbbbbbbgd faaa fdaaaaabbbbgf caae fgbbbaaaaagd eaac gbbbbbbbbbgaaae aaa dgbbbbbbbbbf eaaae aaa fdbbbbbbbbbdf eaaa aaa bbbbbbbgf faaac caaa bbbbgdf aaaac eaae g faaac faaaf aaaac caae caaaaf eaac caaaf aaa aaaaf aae eaaaafaac eaaaaa aaaaa eaaaa faae fcf ``` <!-- end of image --> Wow! I can see 2 intersections so clearly in area A! Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#c27987ff b,#78bea5ff c,#e4c5cbff d,#bfe0d4ff e,#d19ca6ff f,#ecebeaff g,#9dd0beff ``` ```image faa eae aaf aa faa eaab aabg aabf caab f eabb fae aabb faae aabd faae caab faac aabb caac aabb caaf aabg eaaf caabd eaaf aabb eaa aabb aaa faabb aaa eaebg aaa aabbf aaa aabb aaa faabb aaa eaebb aaa aagbd aae aabbf faae caabb faac eacbb faac aadbb caac aagbd caaf caebb eaaf aacbb eaa aa bb eaa aadbg aaa caebbd aaa aafbb aaa aa bb aaa faafbb aaa eaegbg aaa aafbbf aae aa bb aae faa bb faae eacfbb faac aa gbd caac aa bb caac caa bb caaf aac bb eaaf aa dbg eaa aa bbd eaa cae bb aaa aac bb aaa aa fbb aaa aa dbg aaa cae bbf aaa aaf bb aaa aa bb aae faa fbb aae eaegbbd faae faabbbb faac dbbbaabg caac gbbbbbbaa caaf fgbbbbbbf eac caabbbbbgf aa dbbaaabd aa fgbbbbbbeaa caa fbbbbbbgf aaa aac dbbbbbbg aaa aa gbbbbbbd aaa aa fgbbbbbbf aaa cae dbbbbbbgf aaa aac dbbbbbbd aaa aa fgbbbbbbd aaaaa fbbbbbbgf aaae dbbbbbbg faaf gbbbbbbd fe fgbbbbbbf dbbbbbbgf dbbbbbbd fbbbbd gf ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#b10646ff b,#85c95fff c,#dc92aeff d,#9aca93ff e,#ba5675ff f,#ebdedcff g,#b1d7b1ff ``` ```image dgggggggggggggggggggggggggggggggggggggggg dgggggggggggggggggggggggggggggggggggggggg dgggggggggggggggggggggggggggggggggggggggg fgdb dgggggggggggggggggggggggggggggggggggggggg fgdbbbbbbbb dgggggggggggggggggggggggggggggggggggggggg fgdbbbbbbbbbbbbbbbbf dgggggggggggggggggggggggggggggggggggggdbbbbbbbbbbbbbbbbbbbbbbbbbf dgggggggggggggggggggggggggggggddbbbbbbbbbbbbbbbbbbbbbbbbdgf dggggggggggdaaaaegggggddbbbbbbbbbbbbbbbbbbbbbbbbdgf dggggggggggaaaaaebbbbbbbbbbbbbbbbbbbbbbbbgf dggggggggddbbbbbbbbbbbbbbbbbbbbbbddgggggg dggddbbbbbbbbbbbbbbbbbbbbbedggggggggggggg fgdbbbbbbbbbbbbbbbbbbbbeaaaaaaaaaaegggggggggg fgbbbbbbbbbbbbbbbbbbbbbdgggggggeaaaaaaaaaaaedgggggg gdbbbbbbbbbbbbbbbbbbbbddgaaaagggggggggggdeaaaaaaaaaaaeggg bbbbbbbbbbbbbbbbbddggggggggaaaegggggggggggggggeaaaaaaaaaaaef bbbbbbbbbbbgf dgggggggeaaagggggggggggggggggggdeaaaaaaaaaaac bbbbdgf dgggggggaaaagggggggggggggggggggggggeaaaaaaaaaaaef dggggggdaaaggggggggggggggggggggggggggggeaaaaaaaaaaac dggggggaaaagggggggggggggggggggggggggggggg caaaaaaaaaaaef dggggggaaaegggggggggggggggggggggggggggggg feaaaaaaaaaaac dgggggeaaaggggggggggggggggggggggggggggggg caaaaaaaaaaaef dgggggaaaaggggggggggggggggggggggggggggggg feaaaaaaaaaae dggggdaaagggggggggggggggggggggggggggggggg caaaaaaaf dggggaaaagggggggggggggggggggggggggggggggg feaaa dggggaaaegggggggggggggggggggggggggggggggg c gdddeaaaddddddddddddddddddddddddddddddddd aaaa faaaf aaaa aaac caaa aaaa faaaf aaaa aaac caaa aaaa faaaf aaaa aaae caaa aaaa aaaf eaaa aaae caaa aaaa aaaf eaaa aaae caaa aaaa aaac eaaa aaae caaa aaaa aaac eaaa aaae caaa aaaa aaac eaaa aaae faaa aaaa aaac eaaa aaae faaa aaaa aaac eaaa aaaa faaaf aaaa aaac caaa aaaa faaaf aaaa aaac faaa e ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#b10546ff b,#85c95fff c,#d680a0ff d,#aedb96ff e,#bd3867ff f,#e1dacfff g,#987c57ff ``` ```image fffdddb ffdddbbbbbbbbb f ffdddbbbbbbbbbbbbbbbbb feaaecf fffddbbbbbbbbbbbbbbbbbbbbbbbbb faaaaaaaaecf ffdddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb eaaaaaaaaaaaecfffdddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb aaaaaaaaaegggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb caaaegggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdddff ffdgbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdddff ffddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddfff ffdddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggcf fddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggeaaaaaaaaecf bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbggeaaaaaaaaaaaaaaaaaaaecf bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddff fceaaaaaaaaaaaaaaaaaaaaaecf bbbbbbbbbbbbbbbbbbbbbbbbggff fceaaaaaaaaaaaaaaaaaaaaaaecf bbbbbbbbbbbbbbbbbdggeaaaac fceaaaaaaaaaaaaaaaaaaaaaecf bbbbbbbbbbbddff aaaaaaaf fceaaaaaaaaaaaaaaaaaaaaaaecf bbbbdddff caaaaaae fceaaaaaaaaaaaaaaaaaaaaaecf ff eaaaaaac fceaaaaaaaaaaaaaaaaaaaaaae faaaaaaa fceaaaaaaaaaaaaaaaaaaa caaaaaac fceaaaaaaaaaaaaaaaa aaaaaaaf fceaaaaaaaaaaaa caaaaaae fceaaaaaaaaa eaaaaaac fceaaaaa faaaaaaa fceaa caaaaaac f aaaaaaaf caaaaaae eaaaaaac faaaaaaa caaaaaae aaaaaaaf caaaaaae eaaaaaac faaaaaaa caaaaaae aaaaaaaf caaaaaae eaaaaaac ``` <!-- end of image --> As I suspected, there's 2 intersections within area A. Answer: A: 2; 2 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#b10646ff b,#85c95fff c,#db8dabff d,#aedb95ff e,#c24b75ff f,#f0d2ddff g,#d8eccbff ``` ```image gdb gdbbbbbbbbb gddbbbbbbbbbbbbbbbbg ggdbbbbbbbbbbbbbbbbbbbbbbbbg gdbbbbbbbbbbbbbbbbbbbbbbbbdgg faaaac gddbbbbbbbbbbbbbbbbbbbbbbbddg aaaaaebbbbbbbbbbbbbbbbbbbbbbbbdg gdbbbbbbbbbbbbbbbbbbbbbbdg gdbbbbbbbbbbbbbbbbbbbbbeg ggdbbbbbbbbbbbbbbbbbbbbeaaaaaaaaaac gdbbbbbbbbbbbbbbbbbbbbbg caaaaaaaaaaaef gdbbbbbbbbbbbbbbbbbbbbdg aaaa feaaaaaaaaaaac bbbbbbbbbbbbbbbbbdg aaac caaaaaaaaaaaef bbbbbbbbbbbdg eaaa feaaaaaaaaaaac bbbbdgg aaae caaaaaaaaaaaef faaa feaaaaaaaaaaac aaaa caaaaaaaaaaaef aaac feaaaaaaaaaaac caaa caaaaaaaaaaaef aaaa feaaaaaaaaaae faaaf caaaaaaaf aaaa eaaa aaac c caaa aaaa faaaf aaaa aaac caaa aaaa faaaf aaaa aaac caaa aaaa aaaf eaaa aaae caaa aaaa aaaf eaaa aaae caaa aaaa aaaf eaaa aaae caaa aaaa aaaf eaaa aaae caaa aaaa aaac eaaa aaae faaa aaaa aaac eaaa aaae faaa aaaa aaac eaaa aaae faaa aaaa aaac eaaa aaae faaaf aaaa aaac caaa aaaa faaaf aaaa aaac faaa e ``` <!-- end of image -->
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This is the image I'm working with. The goal is to count the intersections. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#c6f087ff b,#83c8e7ff c,#dff7b6ff d,#eef7edff e,#b1d8b1ff f,#95c996ff g,#a6d1a7ff ``` ```image a dad a a a a a a cd c cd a c a a a c cd a c a dd a c a c c a c a c a dc c dc a a d a a a dbd a dd dd db b dc a dffffffafffffffffffffffffffffbfffbffffffffffffffffffffffffffaffd a dgeeeeeaeeeeeeeeeeeeeeeeeeeebeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeaegd cd dgeeeeeaeeeeeeeeeeeeeeeeeeebeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeegd a dgeeeeeeaeeeeeeeeeeeeeeeeebeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeaeegd c dgeeeeeeaeeeeeeeeeeeeeeeebeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeaeegd c dgeeeeeeaeeeeeeeeeeeeeeebeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeaeeegd a dgeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeaeeegd dc dgeeeeeeeaeeeeeeeeeeeebeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeaeeegd a dgeeeeeeeaeeeeeeeeeeebeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeaeeeegd a dgeeeeeeeaeeeeeeeeeebeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeaeeeegd dc dgeeeeeeeeaeeeeeeeebeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeaeeeegd a dgeeeeeeeeaeeeeeeebeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeaeeeeegd a dgeeeeeeeeaeeeeeebeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeaeeeeegd cd dgeeeeeeeeeaeeeebbeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeaeeeeegd a dgeeeeeeeeeaeeebbeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeaeeeeeegd a dgeeeeeeeeeaeebbeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeaeeeeeegd cd dgeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeaeeeeeegd a dgeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeaeeeeeeegd c dgeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeaeeeeeeegd c dgeeeeeeeeebaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeeeegd a dgeeeeeeeebeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeaeeeeeeeegd dc dgeeeeeeebeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeaeeeeeeeegd a dgeeeeeebeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeeeeegd a dgeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeaeeeeeeeeegd dd dgeeeebeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeaeeeeeeeeegd a dgeeebeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeaeeeeeeeeeegd a dgeebeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebaeeeeeeeeeegd cd dgebeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebaeeeeeeeeeegd c dgbeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeabeeeeeeeeeegd dbeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaebeeeeeeeeegd bbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaebeeeeeeeeegd bbgeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeebeeeeeeeegd dbdgeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeebeeeeeeeegd db dgeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeebeeeeeeegd db dgeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeebeeeeeegd db dgeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeebeeeeeegd db dgeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeegd b dgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeebeeeegd b dgeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeebeeeegd b dgeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeegd b dgeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeebeegd b dgeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeebeegd b dgeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeebegd b dgeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeebgd bd dgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeebgd bd dgeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeebd dfffffffffffffffffffafffffffffffffffffffffffafffffffffffffffffgb a c b ad c b ac a dd cc c b ca a da a a dc ad a ad a cc dc ca a da a a cd a a ada ad ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#c8f383ff b,#a4d7f4ff c,#e7f9cbff d,#cce8f8ff e,#7fc7efff f,#f0f9f4ff g,#d7f5a6ff ``` ```image ag deef bef gaf ga feef feb ag caf feef ded cac fac feef bef ga ag feef feb ag fac eed bef a ag ed feb g ga bd ded cc ca be eef g fa bed feb fa g beb be ca cf beb e ga fc deb db fac g deb ed caf a deb ee ag ac deb deb fac ga eef fee ag caf fef ded cac fac fef bef ga ag fee feb ag ga feef ded cac cac feed bef ga ag bed feb ag ga bed ded cac caf bed bef ga fac bed feb fag ga beb ef ga cac deb fb fac ag eb ed caf ga db ee gg caf de deb fac facdeb bed caf ageef ee ag ceef deb ac feec bef af feeag fee g feefga ded cc bed fac feb a bed gg ded ca ed caf bef ga bd fac feb ag be ag ded cac beb ga ee ga deb ca fe fag deb fa bd caf deb g e ga deb cf eb fac deef g ee ag feef a debfac eef ac becaf fef ag feeg fef ga deb fee caf geef bed fac ageb bed ag cacded bed ga ga bef ed cac ag feb d ag cac ded caf fag fe fac caf dd ag ga ef ga ac eb cac af bed ag a ee ga fc deb caf cf bed fac a ee ag fa deb fac ag fee ag cac ded ga ga bef caf ag feb fac cac ded gg ga be caf ag fe fac cac dd ag ga ef ga fag eb cac caf bed ga fac deb ca caf bed fa ag ee a fac de g caf b ``` <!-- end of image --> Gotcha! I've found 2 intersections hiding in area A! Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#c8f383ff b,#a6d8f4ff c,#e3f8c1ff d,#d7edfaff e,#80c7f0ff f,#f1fbe1ff g,#d5f5a2ff ``` ```image a fgf a g a a a a cf g cf a c a g a g cf a g a ff a g a g g a g a c a fc c fc a a d g a a ded a ff ff db e fc a a de e a a a de bd a cf c e e ff a g e db a g a e e a g g e e cf a fc e db a c a e e g g a e e c a cf e db a fc g ed e g a a ed e g a g bd dd a cf fc bd e c a a bb e g g a db bd a cf cfdb e fc a ge e a g de bd a g eg e fc a e c b a fc e a b a a e a e cf a e cf db a ff e g e a a e a e cf a e g dba cf ed c eg c ed a ge bd a add bd ff g e bb a g e db a a bd db c fc e de g g e de a a bd e g fc e e fc a e e a a bd e a ff e e cf a db e g a e e a cf e e g a db ed fc g e ed a cf e a a db a g e af g e ac a dd gg c e ca g fa a a fc af a af a gc fc cg a fa a a cf a a afa gf ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#628a5aff b,#2de628ff c,#b1d8b1ff d,#64e661ff e,#80a27aff f,#e6f3e6ff g,#96c895ff ``` ```image fccccccgggeeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaag faaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaef gaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeeeegggggaaaaaaaaag gaaffff feaaaaaaaaec gaa caaaaaaaaag gaa feaaaaaaaaac eaa caaaaaaaaagf eaa geaaaaaaaagggggggggggggggc eaa gcccgaaaaaaccccccccccccccg fffeaaffffffffff gcccccccaaaccccccccccccccg cccaaaccccccccccg gcccccccaaaccccccccccccccg cccaaaccccccccccg gccccccceaaccccccccccccccg cccaaaccccccccccg gcccccccdaagcccccccccccccg cccaaaccccccccccg gccccccdbaaecccccccccccccg cccaaaccccccccccg gccccccbbaaacccccccccccccg cccaaaccccccccccg gcccccbbbaaacccccccccccccg cccaaaccccccccccg gccccgbbbaaacccccccccccccg cccaaaccccccccccg gccccbbbcbaagccccccccccccg cccaaaccccccccccg gcccdbbbcbaaeccccccccccccg cccaaaccccccccccg gcccbbbccgaaaccccccccccccg cccaaaccccccccccg gccbbbdcccaaaccccccccccccg ccgaaaccccccccccg gcgbbbccccaaagcccccccccccg ccbaaaccccccccccg gcbbbgccccgaabcccccccccccg cccaaagcccccccccg gdbbbccccccaaacccccccccccg cccaaabcccccccccg gbbbcccccccaaadccccccccccg cccaaabbccccccccg bbbdcccccccaaabccccccccccg cccaaabbbcccccccg fbbbccccccccaaabccccccccccg cccaaabbbdccccccg bbbgccccccccgaabbcccccccccg cccaaagbbbccccccg cbbbccccccccccaaabcccccccccg cccaaacdbbbcccccg bbbcccccccccccaaabdccccccccg cccaaaccbbbbccccg dbbdcccccccccccaaabbccccccccg cccaaacccbbbdcccg bbbgcccccccccccaaabbccccccccg cccaaaccccbbbgccg bbbcgccccccccccceaabbdcccccccg cccaaaccccgbbbccg fbbb gccccccccccccaabbbcccccccg cccaaacccccdbbbcg bbbf gccccccccccccaaabbgccccccg cccaaaccccccbbbbg dbbd gccccccccccccaaabbbccccccg cccaaacccccccbbbd bbb gccccccccccccaaabbbccccccg gggaaaggggggggbbbf bbbc gcccccccccccceaagbbdcccccg aae cbbb fbbb gccccccccccccgaagbbbcccccg aae dbbb bbbf gcccccccccccccaaadbbgccccg aae bbbd gbbb gcccccccccccccaaacbbbccccg aae bbbc bbb gcccccccccccccaaacbbbccccg aae fbbbf dbbg gccccccccccccceaacgbbdcccg aae cbbb fbbb gcccccccccccccgaagcbbbcccg aae dbbb bbbf gccccccccccccccaaecdbbgccg aag bbbd cbbb gccccccccccccccaaaccbbbccg aag bbbc bbb gccccccccccccccaaaccbbbccg aag fbbb dbbd gcccccccccccccceaaccdbdccg aag dbbb bbb gccccccccccccccgaagccccccg aag bbbb bbbc gcccccccccccccccaaeccccccg aac bbbd cbbb gcccccccccccccccaaaccccccg aac bbbf bbb fffffffffffffffaaaffffff aac cbbb bbb eaa faac dbbb bbd caaf faac bbbd fbbc aag faac bbbc gbbf aaa faac fbbbf dbb aaa faac cbbb bbb eaa faaf dbbb bbb caaf faaf bbbd bbb aag caaf bbbc bbd aaa caaf fbbb fbbc aaa caaf gbbb cbbf eaa caaf bbbb dbb caaf caaf bbbd bbb faac caaf bbbf bbb aaa caa cbbb bbb aaa caa dbbb bbd aaa gaa bbbc fbbc gaaf gaa bbb cbbf faac gaa bbb dbb aae gaa cbbcbbb aaa gaa bbbbbb aaa eaa bbbbbb gec eaa gbbbbd eaa bbbbg eaa bbbbf eaa dbbb eaa bbb eaa bbb aaa cbc ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#628a5aff b,#2ee529ff c,#bfd7bcff d,#5fea5cff e,#9fb89aff f,#def2ddff g,#97f295ff ``` ```image eaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaae aaaaac aaaaac aaaaac aaaaac aaaaac faaaaac faaaaac cbaaaaac gbbaaaaac gbbaaaaac dbaaaaae daaaaabf caaaaabd faaaaabbd faaaaabbbg faaaaabbbbc faaaaabbbbbf caaaaabbbbbd caaaaabbbbbbd caaaaadbbbbbbg caaaaafdbbbbbbf caaaaaffbbbbbbbf caaaaaf cbbbbbbd caaaaaf gbbbbbbg caaaaaf dbbbbbbc caaaaaf dbbbbbbf caaaaaf fbbbbbbd caaaaa cbbbbbbd caaaaa gbbbbbbg caaaaa dbbbbbbc caaaaa fbbbbbbbf eaaaaa fbbbbbbd eaaaaa gbbbbbbd eaaaaa gbbbbbbg eaaaaa dbbbbbbf eaaaaa fbbbbbbb eaaaaa fbbbbbb eaaaaa gbbbbb ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Now, let's turn our attention to the next spot. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#628b5aff b,#2ce627ff c,#b2dfb0ff d,#7cee79ff e,#8cab86ff f,#dcf0dbff g,#4ada45ff ``` ```image fceaaaaaaaaaaaaaaaaa fceaaaaaaaaaaaaac fceaaaaaaaaaae fceaaaaaaa feaaaaaf faaaaac aaaaae eaaaae eaaaaa caaaaaf fdaaaaac fgbaaaaac dbbaaaaae fbbbaaaaaa gbbbgaaaaaf cbbbbgaaaaac fbbbbbbaaaaac dbbbbbbaaaaae fbbbbbbbaaaaaa gbbbbbgbgaaaaaf cbbbbbbfggaaaaaf bbbbbbc dbaaaaac dbbbbbg fbaaaaae fbbbbbbf daaaaaa gbbbbbd cgaaaaa cbbbbbbf gaaaaaf gbbbbbd daaaaae dbbbbbg faaaaaa fbbbbbbc aaaaaaf dbbbbbd eaaaaad cbbbbbbf caaaaag gbbbbbd faaaaagc cbbbbbg aaaaaad fbbbbbbc eaaaaabf dbbbbbg eaaaaabd fbbbbbbf caaaaabg gbbbbbd faaaaagbc cbbbbbb aaaaagbd bbbbbbc eaaaaabbf bbbbbg eaaaaabbc bbbbbf caaaaabbg bbbbd faaaaagbbf bbbbf aaaaagbbd bbbc aaaaaabbb bbg eaaaaabbbc bbc caaaaabbbg bd faaaaagbbbf bf aaaaagbbbd d aaaaaabbbb eaaaaabbbbc caaaaabbbbg faaaaagbbbbf faaaaagbbbbd aaaaaabbbbb eaaaaabbbbbc caaaaabbbbbd caaaaagbbbbbf faaaaaebbbbbd aaaaaebbbbbg eaaaaadbbbbbc eaaaaacbbbbbd caaaaafgbbbbbf faaaaaccbbbbbc aaaaaefbbbbbg eaaaae dbbbbbf eaaaaa cbbbbbd caaaaaf gbbbbb faaaaac dbbbbbc aaaaae fbbbbbg eaaaae dbbbbbf eaaaaa cbbbbbd caaaaaf bbbbbb faaaaac dbbbbbc aaaaae fbbbbbg aaaaae gbbbbbf eaaaaa cbbbbbd caaaaaf bbbbbb faaaaac dbbbbbc aaaaac fbbbbbd aaaaae gbbbbbf eaaaaa cbbbdf caaaaaf gc faaaaaf faaaaac aaaaae eaaaaa caaaaa ``` <!-- end of image --> Incredible, there's actually 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#628a5aff b,#2de628ff c,#b1c5adff d,#68ed65ff e,#8aa884ff f,#d9eed8ff g,#a5f4a3ff ``` ```image ffcccccceeeeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaac faaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaef caaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeeeeeecccaaaaaaaaac caafff feaaaaaaaaaf eaa caaaaaaaaac eaa feaaaaaaaaaf eaa caaaaaaaaae eaa feaaaaaaaa eaa caaaaae eaa faaa eaa aaa eaa eaa aaa eaac aaa dbaae aaa bbaaa aaa bbbaaa aaa fbbbaaa aaa bbbfbaaf aaa dbbd baae aaa bbb gaaa aaa bbbg aaa gaaa fbbb aaaf baaa bbbf caab aaaf gbbb aaa aaab bbb aaag aaabb dbbd aaab aaabbd bbb eaabf aaabbbg bbbf caabb aaafbbbf gbbb aaab aaa gbbb bbb aaabg aaa dbbb dbbd aaabb aaa bbbd bbb aaabb aaa bbbf bbbg caabbd aaa fbbb fbbb faabbb aaa dbbb bbb aaabbg aaa bbbb dbbd aaabbb aaa bbbd bbb aaabbb aaa bbbf bbbg caafbbd aaa gbbb fbbb faacbbb aae dbbb bbbf aaedbbf aae bbbd gbbb aaa bbb aae bbbg bbb aaa bbb aae fbbbf dbbg eaa gbbd aae gbbb fbbb faac bbb aae dbbb bbbf aae dbbf aae bbbd gbbb aaa bbb aae bbbg bbb aaa bbb aac fbbb dbbd eaa gbd aac dbbb bbb faaf aac bbbb bbbg aae aac bbbd fbbb aaa aac bbbf bbb aaa aac fbbb bbb eaa aac dbbb bbd caaf faac bbbd fbbg aae faac bbbg gbb aaa faaf fbbbf dbb aaa faaf gbbb bbb eaa faaf dbbb bbb caaf faaf bbbd bbb aac faaf bbbg bbd aaa faaf fbbb fbbg aaa caaf gbbb gbbf aaa caaf bbbb dbb caaf caa bbbd bbb faac caa bbbf bbb aaa caa fbbb bbb aaa caa dbbb bbd aaa caa bbbg fbbg caa caa bbb gbbf faac caa bbb dbb aae eaa gbbgbbb aaa eaa bbbbbb aaa eaa bbbbbb eac eaa gbbbbd eaa bbbbg eaa bbbbf eaa dbbb eaa bbb aaa bbb aaa fbg ``` <!-- end of image -->
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This image seems promising for intersection detection. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#68e46bff b,#54d406ff c,#cbf4c3ff d,#95db8cff e,#edf8ecff f,#79da41ff g,#b0d8afff ``` ```image gg bbbe bbb ebbb fbbg bbb bbb dbbd bbbe eeeeeeeeeeeeeee bbb ggggggggggggggd cbbf ggggggggggggggd fbbc ggggggggggggggd ff bbb ggggggggggggggfbbbd bbb gggggggggggggbbbbbb dbbd gggggggggggfbbbbbbbb bbb gggggggggdbbbbbe bbbg bbb ggggggggbbbbbfd cbbb cbbf ggggggdbbbbbggd bbbb fbbc gggggbbbbbagggd bbbc bbb gggfbbbbbgggggd gbbb ebbb ggbbbbbdggggggd bbbb dbbd ggbbbbggggggggd bbbc bbb gggbdgggggggggd gbbb bbb ggaaagggggggggd bbbf gbbf ggaaagggggggggd bbbc bbbe ggaaagggggggggd dbbb bbb ggaaagggggggggd bbbf ebbb ggdaadggggggggd bbbe fbbg ggdaadggggggggd dbbb bbb ggdaadggggggggd bbbf bbb eecaadeeeeeeeee ebbbe dbbf eaad dbbb bbbe aaa bbbf bbb aaa ebbbe cbbb aaa fbbb fbbc aaa bbbf bbb aaa ebbbe bbb aaa fbbb dbbd aaa bbbd bbb aaa ebbbe bbb daa fbbb cbbf daae bbbd fbbc gaac cbbb bbb caac fbbb ebbb caag bbbd dbbd eaad cbbb bbb aad fbbb bbb aaa bbbg cbbf aaa cbbb bbbe aaa bbbb bbb aaa bbbc ebbb aaa cbbb fbbg aaa bbbf bbb aaa bbbe bbb aaa dbbb gbbf daa bbbf bbbe daae ebbb bbb gaac fbbb ebbb caac bbbg fbbc caag cbbb bbb eaad bbbf bbb aad bbbceeeeeeeeeeeedbbdeeeee aaa fbbbggggggggggggbbbgggggde aaa dbbbfgggggggggggbbbgggggge aaa dgbbbggggggggggdbbbgggggge aaa dgfbbbgggggggggbbbdgggggge aaa dggbbbdggggggggbbbggggggge aaa dggdbbbggggggggbbbggggggge aaa dgggbbbfggggggfbbfggggggge aaa dggggbbbggggggbbbgggggggge daae dggggfbbbgggggbbbgggggggge daae dgggggbbbfgggdbbfgggggggge gaac dgggggdbbbgggbbbdgggggggge caac dggggggbbbbggbbbggggggggge caaaggccccee dgggggggbbbdgbbbggggggggge eaaaaaaaaaaaaaaaaaaaaaaaaaaaaadddggccceee dgggggggdbbbfbbaggggggggge aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadddddddcee eeecccggdddaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa eeccccggdddaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa dggggggggggbbbggggggdddddddddaaaaaaaa dgggggggggggbbggggggggggge dgggggggggggggggggggggggge dgggggggggggggggggggggggge ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#69e56cff b,#54d405ff c,#c4f2b8ff d,#9eea89ff e,#e6f8dfff f,#69d824ff g,#84df4cff ``` ```image cf egbb cbbbb egbbbbb dbbbbbbb efbbbbbbbb dbbbbbbbbbf cfbbbbbbbbbge egbbbbbbbbbfc cfbbbbbbbbbd egbbbbbbbbbfe dbbbbbbbbbbd egbbbbbbbbbge dbbbbbbbbbfc cfbbbbbbbbbge dbbbbbbbbbfc gbbbbbbbbd ebbbbbbfc dbbbbd gbge edaaaad eaaaaad aaaaad aaaaaa aaaaaa aaaaaa daaaaa daaaaae daaaaae daaaaae caaaaac caaaaac caaaaac caaaaac ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Hmm, interesting. Let's check out another area. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#68e56bff b,#54d405ff c,#bcf0b0ff d,#9de984ff e,#def7d7ff f,#7ddf4aff g,#64d821ff ``` ```image ebbbbbbf fbbbbbc dbbbbbbc ebbbbbb gbbbbbg cbbbbbf cbbbbbbd fbbbbbc fbbbbbbe gbbbbbe ebbbbbbg ebbbbbg dbbbbbbd dbbbbbd fbbbbbbe gbbbbbc ebbbbbbf ebbbbbb dbbbbbbc cbbbbbf gbbbbbg fbbbbbc cbbbbbbd bbbbbbe fbbbbbbe cbbbbbf ebbbbbbf dbbbbbd dbbbbbbc gbbbbbe gbbbbbbe ebbbbbg ebbbbbbf dbbbbbf dbbbbbbc fbbbbbc gbbbbbg bbbbbb cbbbbbbd cbbbbbf fbbbbbbe dbbbbbd ebbbbbbf gbbbbbe dbbbbbbc ebbbbbg gbbbbbge dbbbbbd ebbbbbbf fbbbbbc dbbbbbbc bbbbbb gbbbbbg cbbbbbf cbbbbbbdfbbbbbd aaaaaddddddcccccccfgggggggbbbbbe aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadddddddccccccceee aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa eeeeeeeccccccdffffaaaaaaaaaaaaaaaaaaaaaaaa cbbbbbbe eeeeeeecccccc fbbbbf egbbge cc ``` <!-- end of image --> My investigation has led me to 2 intersections in area B! Answer: A: 0; B: 2; 0 + 2 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#68e56bff b,#54d405ff c,#c1f1b5ff d,#90e674ff e,#e0f8dbff f,#74db34ff g,#a3ec98ff ``` ```image cc bbbe bbb ebbb fbbc bbb bbb gbbd bbb bbb ebbf fbbc fd bbb dbbbg bbb ebbbbbb dbbd fbbbbbbbb bbb ebbbbbe bbbc bbb fbbbbd cbbb cbbf cbbbbb bbbb fbbe bbbbbg bbbc bbb dbbbbb cbbb bbb bbbbbc bbbf dbbg bbbf bbbc bbb be gbbb bbb aaa bbbf cbbf aaa bbbe bbbe daa gbbb bbb gaae bbbf ebbb gaae bbbe fbbc caac dbbb bbb eaac bbbf bbb eaag bbbe gbbd aad dbbb bbb aaa bbbf bbb aaa bbbe ebbf aaa dbbb fbbc aaa bbbd bbb aaa ebbb bbb aaa fbbb dbbd aaa bbbd bbb aaa ebbb bbb daa fbbb cbbf gaae bbbd fbbc gaae ebbb bbb caac fbbb bbb eaag bbbg dbbg eaag ebbb bbb aad fbbb bbb aaa bbbg cbbf aaa cbbb bbbe aaa fbbb bbb aaa bbbc ebbb aaa cbbb dbbg aaa bbbf bbb aaa bbbe bbb aaa gbbb gbbd daa bbbd bbbe gaae ebbb bbb gaae fbbb ebbb caac bbbc fbbc eaag cbbb bbb eaag bbbf bbb aad bbbe gbbd aaa dbbb bbb aaa bbbd bbb aaa ebbb cbbf aaa fbbb fbbc aaa bbbc bbb aaa cbbb bbb aaa bbbf dbbd aaa bbbe bbb daa dbbb bbb gaae bbbd cbbf caae ebbb fbbe caac fbbb bbb eaadgccceeee bbbc bbb eaaaaaaaaaaaaaaaaaaaaaaaaaaaaddgggccceee cbbbdbbg aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaddgggccceee eeecccgggddaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa eeeecccgggdaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa bbbe eeecccgggddaaaaaaaa ebb ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#15f85fff b,#677533ff c,#62f591ff d,#b0d8b1ff e,#889763ff f,#99c694ff g,#e6f7e9ff ``` ```image cac aaag aaaa aaaaa gaacaac caa aaag aaa aaa aaa gaaa aad caaaacd aag aaaaaaaaacd be daa gcaaaaaaaaaaacd bbb caa gcaaaaaaaaaaaacg fffbbefffffaaaffffffff gcaaaaaaaaaaaacg dddbbbdddddaacddddddddg gdaaaaaaaaaaaacg dddfbbfddddaacddddddddg dcaaaaaaaaaaacd ddddbbbddddaadddddddddg dcaaaaaaaaaaacd ddddfbbfddcaadddddddddg gcaaaaaaaaaaaadg dddddbbbddaaadddddddddg gcaaaaaaaaaaaacg dddddebbddaaadddddddddg gdaaaaaaaaaaaacg ddddddbbbdaacdddddddddg dcaaaaaaaaa ddddddebbdaafdddddddddg dcaaaa dddddddbbbaaddddddddddg gaa dddddddbbbaaddddddddddg aag ddddddddbbbaddddddddddg aad ddddddddbbbaddddddddddg aac dddddddddbbeddddddddddg aac dddddddddbbbddddddddddg aaa ddddddddcabbfdddddddddg aaa ddddddddcabbbdddddddddg caa ddddddddaaabbfddddddddg caa ddddddddaacbbbddddddddg daa ddddddddaacebbddddddddg gaa ddddddddaaddbbbdddddddg aag dddddddcaaddebbdddddddg aag dddddddaaadddbbeddddddg aad dddddddaaadddbbbddddddg aac dddddddaacddddbbedddddg aaa dddddddaafddddbbbdddddg aaa ddddddfaadddddfbbedddfg caa ggggggcaaggggggbbbgggg caa aaa gbbd daa aac bbb gaa aad dbbg aa aag bbb aag daa fbbg aad caa bbb aac aaa ebb aac aac bbe aaa aad ebb aaa gaa bbe caa daa ebb daa caa bbe gaa aaa ebb gaa aac bbe aag aag ebb aad gaa bbe aac caa ebbg aac aaa bbb aaa aac gbbb aaa aad dbbb caa aag ebbe caa daa bbbbd daa caa bbbbbbeg gaa gca ebbbbbbbbf gggggggggaaggggg dbbbbbbbbed fdddddddddaacdddd fbbbbbbbbeg fdddddddddaacdddd gebbbbbbbbd fdddddddddaacdddd dbbbbbbbbeg fdddddddddaaadddd gebbbbbbbbf fdddddddddaaadddd debbbbbbbbd fdddddddddaaadddd fbbbbbbbbeg fdddddddddcaadddd gebbbbbbbbf fdddddddddcaadddd dbbbbbbbbbfddddddddfaadddd gfbbbbbbbbeddddddaadddd debbbbbbbbfddaafddd fdebbbbbbbbbacddd fddddfebbbbbbbddd fddddddddfbbbbddd fddddddddddaaaddd fddddddddddaaaddd fddddddddddcaaddd fdddddddddddddddd fdddddddddddddddd ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#14f75eff b,#667533ff c,#94fbb6ff d,#bac0a3ff e,#879662ff f,#4cf984ff g,#d9f1dbff ``` ```image dbbbbb faaaag bbbbbd aaaaa dbbbbb gaaaaa gbbbbbd caaaaf ebbbbe caaaac gbbbbbd faaaac ebbbbe aaaaag gbbbbbg aaaaa ebbbbe gaaaaf dbbbbbg caaaaf ebbbbe faaaac dbbbbbg faaaag bbbbbd aaaaag dbbbbb gaaaaa bbbbbd caaaaf dbbbbb caaaac gbbbbbd faaaac ebbbbe faaaag gbbbbbdaaaaa ebbbbeaaaaf gbbbbbaaaaf ebbbbbaaac dbbbbbaaac ebbbbbaag dbbbbbaa bbbbbbf dbbbbbf bbbbbe ebbbbb abbbbbd gabbbbbe caabbbbbd caabbbbbe faaabbbbbg faaabbbbbe aaaaabbbbbg gaaaafebbbbe caaaafdbbbbbg caaaac bbbbbd faaaac dbbbbb aaaaag bbbbbd gaaaaa dbbbbb gaaaaf gbbbbbd caaaaf ebbbbe faaaac gbbbbbd faaaag ebbbbe aaaaag gbbbbbg gaaaaa ebbbbe caaaaf dbbbbbg caaaac ebbbbe faaaac dbbbbbg faaaag bbbbbd aaaaa dbbbbb gaaaaf bbbbbd ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Let's move forward and inspect another region. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#15f75eff b,#677533ff c,#99fbb9ff d,#bdc3a7ff e,#919d6dff f,#55fa8aff g,#d4f1d9ff ``` ```image faaaag faaaag faaaac caaaac caaaaf caaaaf gaaaaf gaaaaa aaaaa aaaaa aaaaag faaaag faaaac caaaac caaaac caaaaf gaaaaf edg gaaaaa bbbbedg aaaaa bbbbbbbbed aaaaa bbbbbbbbbbbedg aaaaag bbbbbbbbbbbbbbbedg faaaag debbbbbbbbbbbbbbbbedgfaaaac gdebbbbbbbbbbbbbbbbbaaac debbbbbbbbbbbbbbbbbeg gdebbbbbbbbbbbbbbe gdebbbbbbbbbbd debbbbbbb gabbbb aaaaa aaaaag faaaag faaaac faaaac gg ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#14f85eff b,#677533ff c,#89fbaeff d,#bec4a8ff e,#8d9866ff f,#4cf985ff g,#cef6d9ff ``` ```image caf aaag aaaa aaaaa gaacaac caa aaag aaa aaa aaf gaaa aac faaaafg aag aaaaaaaaafc be gaa gfaaaaaaaaaaafc bbb faa gcaaaaaaaaaaaacg bbd aaa gcaaaaaaaaaaaacg bbb aaf cfaaaaaaaaaaafg gbbd aac cfaaaaaaaaaaafg bbb aa gfaaaaaaaaaaafc dbbg caa gcaaaaaaaaaaafc bbb faa gcaaaaaaaaaaaacg dbb aaa cfaaaaaaaaaaacg bbb aac cfaaaaaaaaa ebb aag gfaaaa bbeaa gaa ebbaa aag bbba aag bbbf aac bbe aaf bbb aaa gabbd aaa fabbb faa aaabbg caa aafbbb caa aagdbb gaa aa bbb aa caa ebb aag faa bbe aac aaa ebb aaf aac bbe aaf aag bbb aaa gaa bbd faa caa bbb caa aaa gbbd caa aaf bbb gaa aac dbbg aa aa bbb aag gaa dbb aac faa bbb aac aaa ebb aaf aaf bbe aaa aag ebb faa gaa bbe faa caa ebb caa faa bbe gaa aaa ebb aa aac bbe aag aag ebb aag gaa bbe aac caa ebbg aaf aaa bbb aaa aaf gbbb aaa aac dbbb faa aa ebbe caa caa bbbbd gaa faa bbbbbbeg gaa gca ebbbbbbbbd aa dbbbbbbbbbd aag dbbbbbbbbe aac gebbbbbbbbd aaf dbbbbbbbbeg aaa ebbbbbbbbd aaa debbbbbbbbd faa dbbbbbbbbeg caa gebbbbbbbbd caa dbbbbbbbbeg gaa ebbbbbbbbe aa gebbbbbbbbd aag dbbbbbbbbbac gebbbbbbb dbbbb aaa faa caf ``` <!-- end of image -->
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I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#562577ff b,#ba8977ff c,#8c75a0ff d,#ad4b3cff e,#b1d7b1ff f,#d3bfceff g,#9bc298ff ``` ```image c a a a a a a a a fffffcccccaaaaaaa a aaaaaaaaaaaaaaaaacccccffffa a fa a a ac af a a ac a ac ca a a a fa ca a fa a a fa ca ac fa af ca fa fa fa fa ac a fa a a ca ac af ca a cc ca ca fa cc a a cc ca a cc d af af cc dd fa ac ac ddb af fa ac fd df a a ac bb fd ac a af db bd a a af df dd aa ac af d db a ca af eeeeeeeedeeeeegdgeeeeeeeeeeeeeeecaeeeeeg fa af eeeeeeeedeeeeeegdeeeeeeeeeeeeeeeageeeeeg a af eeeeeeeedeeeeeeebdeeeeeeeeeeeeecaeeeeeeg a af eeeeeeegdeeeeeeeeddeeeeeeeeeeeeaceeeeeeg af a eeeeeeebdeeeeeeeeedbeeeeeeeeeegaeeeeeeeg cc a eeeeeeedbeeeeeeeeeedgeeeeeeeeeaceeeeeeeg fa a eeeeeeedbeeeeeeeeeebdeeeeeeeeeaeeeeeeeeg a a eeeeeeedgeeeeeeeeeeeddeeeeeeeaaeeeeeeeeg a a eeeeeeedeeeeeeeeeeeeeddeeeeeeaeeeeeeeeeg af a eeeeeeedeeeeeeeeeeeeeedbeeeecaeeeeeeeeeg cc a eeeeeeedeeeeeeeeeeeeeeedgeeeaeeeeeeeeeeg fa a eeeeeegdeeeeeeeeeeeeeeegddecaeeeeeeeeeeg a a eeeeeebdeeeeeeeeeeeeeeeeeddageeeeeeeeeeg a a eeeeeebdeeeeeeeeeeeeeeeeeegddeeeeeeeeeeg a a eeeeeedbeeeeeeeeeeeeeeeeeeacbdbeeeeeeeeg ac a eeeeeedgeeeeeeeeeeeeeeeeeeaeeeddeeeeeeeg ca a eeeeeedeeeeeeeeeeeeeeeeeeaceeeebddeeeeeg fa a eeeeeedeeeeeeeeeeeeeeeeeeaeeeeeeeddgeeeg a a eeeeeedeeeeeeeeeeeeeeeeeaaeeeeeeeebddeeg a a eeeeeedeeeeeeeeeeeeeeeeeaeeeeeeeeeeeddbg af a eeeeebdeeeeeeeeeeeeeeeecaeeeeeeeeeeeegdd gggggaagaggggg eeeeebdeeeeeeeeeeeeeeeeageeeeeeeeeeeeeeddb eeeeegagaeeeee eeeeedbeeeeeeeeeeeeeeegaeeeeeeeeeeeeeeeg dd eeeeeeagaeeeee eeecedbeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeg bdb eeeeeeagaeeeee eeeaadeeeeeeeeeeeeeeegaeeeeeeeeeeeeeeeeg ddf eeeeeeacaeeeee eeeeadeeeeeeeeeeeeeeeaceeeeeeeeeeeeeeeeg fdd eeeeeeaaaeeeee eeeeedceeeeeeeeeeeeeeaeeeeeeeeeeeeeeeeeg ddf eeeeeecaaeeeee eeeeedaceeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeg fdd eeeeeeeaaeeeee eeeegdgageeeeeeeeeeeaeeeeeeeeeeeeeeeeeeg bdb eeeeeeeaaeeeee eeeebdecaeeeeeeeeeecaeeeeeeeeeeeeeeeeeeg dd eeeeeeeaaeeeee eeeedbeecaeeeeeeeeeageeeeeeeeeeeeeeeeeeg bdb eeeeeeeaaeeeee eeeedbeeeaaeeeeeeecaeeeeeeeeeeeeeeeeeeeg dd eeeeeeecceeeee eeeedgeeeeaaeeeeeeaceeeeeeeeeeeeeeeeeeeg fdb eeeeeeeeeeeeee eeeedeeeeeeaceeeegaeeeeeeeeeeeeeeeeeeeeg ddf eeeeeeeeeeeeee eeeedeeeeeeeaceeeaceeeeeeeeeeeeeeeeeeeeg fdd eeeeeeeeeeeeee eeeedeeeeeeegageeaeeeeeeeeeeeeeeeeeeeeeg ddf eeeeeeeeeeeeee eeegdeeeeeeeecaeaaeeeeeeeeeeeeeeeeeeeeeg fdd eeeeeeeddeeeee eeebdeeeeeeeeecaaeeeeeeeeeeeeeeeeeeeeeeg bdb eeeeeedddeeeee eeebdeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeeeeg dd gggggddgdbgggg eeedbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg bdb bd fd df ddf fd d d fdd df f ddfdb fdb ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#562377ff b,#c1756aff c,#ad95bdff d,#ad483bff e,#805b99ff f,#e3d0d7ff g,#d5a39dff ``` ```image fdd gddb eaa gdd gddg faac gdb bddf eaa bdb dddf aac bdg fddb caaf ddg gddb aae ddg bddg caaf fddf bddf eae fddf fddd faac gdd fddb eaa gdd gddg faac bdb bddg eaa bdb bddf aac ddg fddd caaf ddg fddb aae fddf gddg caaf fddf bddf aae gdd dddf faaf gdd fddb eae gdb gddb faac bdb gddg eaa bdg bddf faac ddg dddf caa ddf fdddb aae fddf fddddg caaf fdd gdddbfaae gdd fbdddaaf gdb gddddf bdb gddddg bdb eaadddbf ddg faac bdddg ddg caa fddddf fddf aac gdddb fddf caaf fbdddg gdd aae gdddbf gdd caaf fbdddg bdb eae gdddbf bdb faac fbdddg ddg eaa fddddf ddg faac bdddb ddf eaa fddddg fddf aac gddd fdd caaf fbd gdd aae g gdb caaf bdb aae bdg faaf ddg eaa ec ddf faac caacfddf eaa eaagdd faac faaadd caa faddd aae fddd caaf ddde aae ddaac caaf ddeaac eae fddfeaaf faac fddffaaaf eaa gdd faaa faac gdd caae caa bdb caae aac bdb eaac caaf ddg eaac aae ddg eaaf caaf ddf faaaf eae fddf faaa faac fdd caae eaa gdd caae faac gdb eaac eaa bdb eaac aac bdg aaaf caaf ddg faaaf aae ddf faae caaf fddf caae eae fdd caaefaaf gdd eaaaaa gdd eaaac bdb aaa bdb fef ``` <!-- end of image --> Case closed! This is definitely 2 intersections point in area A. Now, let's dive into another area. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#532076ff b,#cf938bff c,#9c7fb0ff d,#af4a3dff e,#754d91ff f,#e7dde7ff g,#cab6cdff ``` ```image eac aag cae faag caa faag gaaffaag faagfaag aacfaaf eaefaaf caafaaf gaagaaf faacaaf aaeaaf eaaaaf caaaa gaaaa faaaa aaaa eaaa caaa caaa gaaa faae aae eae gac f f bdb gddd fddddg fdddddb dddfbddf ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area B. Answer: A: 2; B: 0; 2 + 0 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#542176ff b,#c47c72ff c,#9f83b2ff d,#ae493bff e,#785193ff f,#e5d7deff g,#ccadbaff ``` ```image c a a a a a a a a ffgggccceeeaaaaaa a aaaaaaaaaaaaaaaaeeecccggffa a fa a a ac af a a ec a ee ca fa a fa fa ea a fa a af fa ca ac ga af ce ga fa fa ga ac a ca fa a ca ae ag ce a ee ce ee ga ce a a ee ca a ee d af af ec dd ga ec ec fddb ag ca ec gd dg fa a ac bb fd ac a ag db gd a af ag dg dd ee ac ag d db a ce ag d df ca fa af d fd af a af d bd ga a af fd dd ag ag af gd db fa ee a bb df ac ga a dg gd a a a df bd ee a a d db a af a d dg ea ec a d fdf af ga a fd fdd ca a a gd bdaf a a bb gdd af a dg acbdb ac a df a ddf ca a d ae gdb fa a d a ddf a a d ea gdd a a fd a ddg ag a gd ca fdd ee a bb af bdb gafa bb ga dd afa e dg ag bdb afa eadf fa ddf aca ad ac gdd eaa de a ddg gaa dag ee fdd aa fdfaf a bdg aa gd ga ca fdd aa bb ca af bdb ae dg ea ga ddf gc df ae ag gdb d ac fa ddf d ag ac fdd d faf a bdg fd ga ee fdd dd gd eaa bdb ddd bb aa ddf bd dg dg gdb gd gd df ddf fd d d gdd df g ddgdg fdb ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#ef7b85ff b,#d80ab3ff c,#f1f3eeff d,#cd53b5ff e,#c8a3aaff f,#b1d7b1ff g,#96ca96ff ``` ```image a aae caac eaa aac caa aaa caac ea ac ea ae ca aa ca aa ac aa ccccacccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc cgfffeaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg cfffffaefffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg cfffffeafffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffg cffffffaefffffffffebeffffffffffffffffffffffffffffffffffffffffffffffffffg cffffffeaffffffffebbbffffffffffffffffffffffffffffffffffffffffffffffffffg cfffffffaafffffffbdfbffffffffffffffffffffffffffffffffffffffffffffffffffg cffffffffaffffffbbffbefffffffffffffffffffffffffffffffffffffffffffffffffg cffffffffaaffffbbfffbbfffffffffffffffffffffffffffffffffffffffffffffffffg cfffffffffafffbbffffebfffffffffffffffffffffffffffffffffffffffffffffffffg cfffffffffaafdbffffffbeffffffffffffffffffffffffffffffffffffffffffffffffg cffffffffffaebeffffffbbffffffffffffffffffffffffffffffffffffffffffffffffg cffffffffffabdfffffffebffffffffffffffffffffffffffffffffffffffffffffffffg cffffffffffbbeffffffffbefffffffffffffffffffffffffffffffffffffffffffffffg cfffffffffbbeaffffffffbbfffffffffffffffffffffffffffffffffffffffffffffffg cffffffffbbffaefffffffebfffffffffffffffffffffffffffffffffffffffffffffffg cfffffffdbfffeaffffffffbfffffffffffffffffffffffffffffffffffffffffffffffg cffffffebfffffaafffffffbdffffffffffffffffffffffffffffffffffffffffffffffg cfffffebeffffffafffffffebffffffffffffffffffffffffffffffffffffffffffffffg cfffffbdfffffffaafffffffbffffffffffffffffffffffffffffffffffffffffffffffg cffffbbfffffffffafffffffbdfffffffffffffffffffffffffffffffffffffffffffffg cfffbbffffffffffaaffffffebfffffffffffffffffffffffffffffffffffffffffffffg cffbbffffffffffffafffffffbfffffffffffffffffffffffffffffffffffffffffffffg cfdbfffffffffffffeaffffffbdffffffffffffffffffffffffffffffffffffffffffffg cebeffffffffffffffaefffffdbffffffffffffffffffffffffffffffffffffffffffffg cbdfffffffffffffffeaffffffbffffffffffffffffffffffffffffffffffffffffffffg bdfffffffffffffffffaefffffbdfffffffffffffffffffffffffffffffffffffffffffg bbffffffffffffffffffeafffffdbfffffffffffffffffffffffffffffffffffffffffffg bbcfffffffffffffffffffaafffffbfffffffffffffffffffffffffffffffffffffffffffg db cffffffffffffffffffffafffffbdffffffffffffffffffffffffffffffffffffffffffg ebc cffffffffffffffffffffaaffffdbffffffffffffffffffffffffffffffffffffffffffg cbc cfffffffffffffffffffffafffffbffffffffffffffffffffffffffffffffffffffffffg bd cfffffffffffffffffffffaaffffbdfffffffffffffffffffffffffffffffffffffffffg bb cffffffffffffffffffffffaffffdbfffffffffffffffffffffffffffffffffffffefffg bb cffffffffffffffffffffffaaffffbffffffffffffffffffffffffffffffffffffaaeffg db cfffffffffffffffffffffffaefffbefffffffffffffffffffffffffffffffffaaaffffg db cfffffffffffffffffffffffeafffdbfffffffffffffffffffffffffffffffaaaffffffg cbc cffffffffffffffffffffffffaefffbfffffffffffffffffffffffffffffaaaffffefffg cbe cffffffffffffffffffffffffeafffbeffffffffffffffffffffffffffaaafffffdbeffg bd cfffffffffffffffffffffffffaaffdbffffffffffffffffffffffffaaaffffffbbffffg bb cffffffffffffffffffffffffffafffbffffffffffffffffffffffaaafffffffbbfffffg e cffffffffffffffffffffffffffaaffbefffffffffffffffffffaaafffffffebdffffffg cfffffffffffffffffffffffffffaffdbfffffffffffffffffaaaffffffffbbefffffffg cfffffffffffffffffffffffffffaafebfffffffffffffffaaafffffffffbbfffffffffg cffffffffffffffffffffffffffffaffbeffffffffffffaaafffffffffebbffffffffffg cffffffffffffffffffffffffffffaafbbffffffffffaaaffffffffffdbdfffffffffffg cfffffffffffffffffffffffffffffaeebffffffffeaaeffffffffffbbeffffffffffffg cfffffffffffffffffffffffffffffeafbefffffeaaefffffffffffbbffffffffffffffg cffffffffffffffffffffffffffffffaebbfffeaaefffffffffffebbfffffffffffffffg cffffffffffffffffffffffffffffffeaebfeaaeffffffffffffdbdffffffffffffffffg cfffffffffffffffffffffffffffffffaabaaefffffffffffffbbefffffffffffffffffg cffffffffffffffffffffffffffffffffabbffffffffffffffbbfffffffffffffffffffg cfffffffffffffffffffffffffffffffffebffffffffffffebdffffffffffffffffffffg cffffffffffffffffffffffffffffffffffbfffffffffffdbefffffffffffffffffffffg cffffffffffffffffffffffffffffffffffbdfffffffffbbfffffffffffffffffffffffg cffffffffffffffffffffffffffffffffffebffffffffbbffffffffffffffffffffffffg cfffffffffffffffffffffffffffffffffffbffffffdbdfffffffffffffffffffffffffg cfffffffffffffffffffffffffffffffffffbdffffbbeffffffffffffffffffffffffffg cfffffffffffffffffffffffffffffffffffebfffbbffffffffffffffffffffffffffffg cffffffffffffffffffffffffffffffffffffbfebbfffffffffffffffffffffffffffffg cffffffffffffffffffffffffffffffffffffbbbdffffffffffffffffffffffffffffffg cffffffffffffffffffffffffffffffffffffdbefffffffffffffffffffffffffffffffg cffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg cggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggf ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f27985ff b,#d905b4ff c,#f9d7e6ff d,#df2fbfff e,#f6aab1ff f,#ef98dfff g,#e661cfff ``` ```image eac cae caa aac aaa eaae cc caa fbbb aac bbbb cae cbbbb cae dbg cbg aac gbb db aaa fbbd fbc eaac bbbc cbg eaa cdbf bbc aa dbg bbg cae gbb dbd cae fbbc cbb aafbbc db aabbf gbc ebbb cbf bbba gbc fbdaa cbf fbbceae bd cbbc aa bbc dbbg aac bbd bbg aae gbbc gbd eaa fbbf cbbc eac gbb cbbb caa fbb dbbf eac bb bbg aa gb fbd aaa bg fbbc caae gb bbb aaa fbf cbbf caa bg gbg cae bbf gbb eac bbg fbbd caa dbb cbbf aaa cbbg dbf eaae dbb dbg aaa fbb bb caa cbb bc cae fbc c eac cbg cae dd aac gbc eaa bd aa bbc eae bbf cae gbbc aac cbbf aae bbd eaac gbb c eaa bb eaaac caa gbc ceaaac eac fbf ceaaaec aa bd caaaac aa fbf eaaaec aae bg eaaae c aaac bb eaaaac fd caae bbf aaaac gbbc caa dbb aaaac fbbd eac fbb eaaaa gbbg caa cbb caaaae cdbbf aa fbf caaaae fbbd aae cbg aaaae gbbg aaa db caaaae cdbbf caae fbf aaaae bbbd caa bb ceaaaec gbbf eac bbc caaaac cdbbf cae bbg ceaaaec bbbd eac dbd eaaaec gbbg aaccbbg ceaaaec dbbc aaa dbd aaaac fbbd eaa gbb eaaaac gbbg cae db eaaaa bbbd aacgbc eaaaac fbbg caecbf eaaaa gbbf aacbdeaaaac cdbbf eaaabdae fbbg caaabd gbbf eaabbc dbbc c bbf fbbd gbbc cdbbf fbbf dbbd bbd fbbd fbb cdbbf bb bbbd gb fbbg fbf gbbf db bbbd fbf gbbg cbg dbbf bb dbbc bbbbbg dbbbf fbbd ``` <!-- end of image --> Case closed! This is definitely 2 intersections point in area A. Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#f27783ff b,#d908b5ff c,#f5bad9ff d,#e245c7ff e,#f59ca5ff f,#ec86daff g,#faddebff ``` ```image e aae gaag eaa aac caa eae gaag ea ac ca ae ga ae ga aa a ea ag ea ac ca g ae fbc ga gbbb ae bdgb ga bb bc aa bb db a db gb ea fb bg acbg bb ebf cb bbc bg bbca bd bb ae cb db ga bg fbg ae bd gbc ga cb bd aa b bb a bd bb ea fb db ag b fb ea bd cbg ac fb gbf ca b bd ae bf bb ga fb bb ae b db ga bf fbg aa fb gbc a b bd ea bf bb ag db g bb ea b gaag db ac bf gaae fb ca db gaae cbg ae b aae c gbf ga bc aae dbc bd ae db aaa bbg bb ga gb aaa gbb f aa bc aaa fbd a db eaa dbc ea gb eaag bb ag bc eaag gbb ea db eaag fbd acgb eaag bbc ca bg eaag bb aebd caac cbb gacb caac dbf aebaac bbg gabb bb gcb cbd bg dbf bd bbg cb gbb b fbd bd dbc fb bb b gbb bbbf fbg ``` <!-- end of image -->
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This is the image I'm working with. The goal is to count the intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#b230a8ff b,#55927dff c,#dfaadbff d,#b1d6b1ff e,#b56bafff f,#92c299ff g,#edf0efff ``` ```image gf bbb bbbg dbbd gbbb bbb bbb bbbg dbbd gbbb bbb bbb bbbg dbbd bbb gccccec bbb caaaaaaaaaa bbb caaaaaaaaaaac fbbg caaaaeeecccaae dbbf caaae aaa bbb caaae aaa bbb caaae aaa bbb caaae eaag fbbg caaae caac dbbf caaae gaae bbb caaaa aaa bbb caaaa aaa bbb gaaaa aaa fbbg gaaaa eaag dbbf gaaaa caac bbb gaaaa gaae bbb gaaaa aaa bbb gaaaa dfffffffffaaaffffffff fbbd gaaaa fdddddddddaaadddddddd gbbf gaaaa fdddddddddeaadddddddd bbb gaaaa fdddddddddeaaeddddddd bbb gaaaa fddddddddddaaaddddddd bbb aaaa fddddddddddaaaddddddd fbbd aaaa fddddddddddaaaddddddd gbbf aaaa fddddddddddaaaddfdddd bbb aaaa fddddddddddeaadfbbddd bbb aaaa fddddddddddeaaebbbfdd bbb aaaa fdddddddddddaaabbbddd dbbd aaaa fdddddddddddaaabbdddd gbbb aaaa fdddddddddddaaabddddd bbb aaaa fddddddddddbaaadddddd bbb aaaa fdddddddddbbaaadddddd bbbg aaaa fddddddddfbbbaaeddddd dbbd aaaa fdddddddfbbbfaaaddddd gbbb aaaag fdddddddbbbbdaaaddddd bbb aaaag fddddddbbbbddaaaddddd bbb aaaag fddfbbbbbbdddaaaddddd bbbg aaaag gbbbbbbbbbddddaaaddddd dbbd aaaag gfbbbbbbbbbbfdddddeaaedddd ggggggbbbggggggggggggaaaag dbbbbbbbbbbfddddddddddaaedddd fddddddbbbdddddddddddaaaaffg dbbbbbbbbbbffdddddddddddddaaadddd fddddddbbbddddddddddaaaadddg gfbbbbbbbbbbd fdddddddddddddaaadddd fddddddbbbdddddddddaaaaddddg dbbbbbbbbbbfg dfffffffffffffaaaffff fddddddfbbfdddddddaaaadddddg dbbbbbbbbbbfg aaa fdddddddbbbddddddaaaaddddddg gfbbbbbbbbbbd eaac fdddddddbbbdddddaaaafddddddg dbbbbbbbbbbf caae fdddddddbbbddddaaaafddddddfbbbbbbbbbbfg aaa fdddddddbbbfddaaaaedddfbbbbbbbbbbbd aaa fdddddddfbbfdeaaaedfbbbbbbbbbbd aaa fddddddddbbbeaaabbbbbbbbbbbg aaa fddddddddbbaaaabbbbbbbbfdddg ecg fddddddddbaaaaebbbbfdddddddg fddddddddeaaaebbdddddddddddg fdddddddeaaaeddddddddddddddg fddddddeaaaedddddddddddddddg fdddddeaaaeddddddddddddddddg fddddeaaaedddddddddddddddddg fdddeaaaeddddddddddddddddddg fddeaaaedddddddddddddddddddg fdeaaaeddddddddddddddddddddg feaaaedddddddddddddddddddddg eaaaeddddddddddddddddddddddg caaaedddddddddddddddddddddddg caaaaddddddddddddddddddddddddg caaaaddddddddddddddddddddddddfg caaaagggggggggggggggggggggggggg gaaaa caa c ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#b330a8ff b,#54927cff c,#cb74c4ff d,#b8d1c8ff e,#8b5a95ff f,#87b2a3ff g,#e8d6e9ff ``` ```image bbbbbb gaaaaaaaag bbbbbbg gaaaaaaaag fbbbbbd gaaaaaaaag dbbbbbd gaaaaaaaag gbbbbbf gaaaaaaaag bbbbbb gaaaaaaaag fbbbbbg gaaaaaaaag fbbbbbd gaaaaaaaag dbbbbbf gaaaaaaaag gbbbbbf gaaaaaaaag bbbbbb gaaaaaaaag fbbbbbg gaaaaaaaag fbbbbbd gaaaaaaaag dbbbbbf gaaaaaaaag gbbbbbf aaaaaaaag d bbbbbb aaaaaaaag dffbb fbbbbbg caaaaaaag gdfbbbbbb fbbbbbd caaaaaaag gdfbbbbbbbbbb dbbbbbf caaaaaaag dfbbbbbbbbbbbbbb gbbbbbf caaaaaaacdfbbbbbbbbbbbbbbbbb bbbbbb caaaaaaaebbbbbbbbbbbbbbbbbbbf fbbbbbcaaaaaaaebbbbbbbbbbbbbbbbfdg fbbbbeaaaaaaaebbbbbbbbbbbbbbfd dbbbeaaaaaaaebbbbbbbbbbbfdg gbbeaaaaaaaebbbbbbbbfdg beaaaaaaaebbbbbbfd eaaaaaaaebbbfdg caaaaaaaefdg caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac gaaaaaaac gaaaaaaac gaaaaaaac aaaaaaac aaaaaac aaaaac aaaaa aaaa ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Right then, let's explore the next spot. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#b230a7ff b,#55917cff c,#dea6d9ff d,#aac8beff e,#c86ec1ff f,#7fad9dff g,#e6e1e9ff ``` ```image caaaaac caaaaae gaaaaae aaaaaa eaaaaag eaaaaac caaaaac caaaaae gaaaaae aaaaaa eaaaaag eaaaaac caaaaac gaaaaae gaaaaaa d aaaaaa fbf eaaaaag dbbbfg eaaaaacdbbbbbbg caaaaaebbbbbbbd gaaaaaabbbbbbf gaaaaaabbbbbf aaaaaabbbbb eaaaaabbbbg eaaaaabbbg eaaaaaabd gbaaaaaad gbbaaaaaa fbbaaaaaa fbbbaaaaaag dbbbbaaaaaac dbbbbbbaaaaac gbbbbbbbaaaaae gbbbbbbbdaaaaaa gbbbbbbbf aaaaaa fbbbbbbf eaaaaag fbbbbbbbg eaaaaac gdbbbbbbbg caaaaac gdfbbbbbbbbg gaaaaae gdfbbbbbbbbbbbd gaaaaae gdfbbbbbbbbbbbbbbd aaaaaa dfbbbbbbbbbbbbbbbbf eaaaaag bbbbbbbbbbbbbbbbbf eaaaaag bbbbbbbbbbbbbbfdg caaaaac bbbbbbbbbbfdg caaaaae bbbbbbbfd gaaaaae bbbfdg aaaaaa dg aaaaaa eaaaaag eaaaaac caaaaac ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#b230a8ff b,#55927cff c,#da9cd5ff d,#b0ccc2ff e,#c25dbaff f,#82af9fff g,#e8ddeaff ``` ```image gf bbb bbb dbbd gbbb bbb bbb bbb dbbd bbb bbb bbb fbbg dbbd bbb ggcccec bbb caaaaaaaaaa bbb caaaaaaaaaaac fbbg caaaaeeecccaae dbbf caaae aaa bbb caaae aaa bbb caaae aaa bbb caaae eaag fbbg caaae caac dbbf gaaae gaae bbb gaaae aaa bbb gaaaa aaa bbb gaaaa aaa fbbg gaaaa eaag gbbf gaaaa caac bbb gaaaa gaae bbb gaaaa aaa bbb gaaaa aaa fbbd gaaaa aaa gbbf aaaa eaag bbb aaaa caac bbb aaaa gaae bbb aaaa aaa fbbd aaaa aaa gbbf aaaa aaa d bbb aaaa eaagdbf bbb aaaa caacbbbd bbb aaaa gaaabbf dbbd aaaa aaabb gbbf aaaa aaab bbb aaaa baaa bbb aaaa fbaaag bbb aaaa dbbbaac dbbd aaaa gbbbfaae gbbb aaaa bbbf aaa bbb aaaa bbbb aaa bbb aaaa dbbbbbb aaa bbbg aaaag gfbbbbbbbb eaag dbbd aaaag gfbbbbbbbbbbd caac bbb aaaag dbbbbbbbbbbf gaae bbb aaaag dbbbbbbbbbbfg aaa bbb aaaag gfbbbbbbbbbbd aaa fbbg aaaag dbbbbbbbbbbf aaa dbbd aaaag dbbbbbbbbbbfg aaa bbb eaaag gfbbbbbbbbbbd eaag bbb eaaag dbbbbbbbbbbd caac bbb eaaag dbbbbbbbbbbfg aaa fbbg eaaac gfbbbbbbbbbbd aaa dbbf eaaac dbbbbbbbbbbd aaa bbbeaaabbbbbbbbbbfg aaa bbaaaabbbbbbbbd ecg baaaabbbbbd eaaaabfg eaaae eaaac caaac caaae caaae caaae caaae caaae caaae caaae caaae gaaae gaaae aaaa gaa g ``` <!-- end of image -->
[ "" ]
I have a feeling there might be some intersections in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#7a729cff b,#d3a3a3ff c,#d5cbd5ff d,#9c9bb1ff e,#eff0efff f,#b1d7b1ff g,#96c997ff ``` ```image c aaa aaae caaad dde aaaaa caaaad aaaaa aaaaaaaad caaaaa aaaaaaaaaaac aaaaaa aaa caaaaaaaaac aaaaaac eaaa caaaaaaaaac caaadaad daaa caaaaaaaaae aaadcaaa aaac daaaaaaaade aaa aaa aaa daaaaaaaade caaa aaa aaa edaaaaaaaad aaad aaac caaa eaaaaaaaaad aaae daad daad caaaaaaaaac caaa caaa aaac caaaaaaaaac aaad eaaa aaa caaaaaaaaac aaae aaa aaa caaaaaaaaae caaa aaae eeeeeecaaaeeeeeeee daaaaaaaad aaad aaac ffffffaaadfffffffg daaaaaaa aaae daad ffffffaaaffffffffg edaaaa eaaa caaa ffffffaaaffffffffg aaa aaad aaa ffffffaaaffffffffg aaa aaae aaa fffffdaaaffffffffg aaa eaaa aaac fffffaaadffffffffg aaa aaad daad fffffaaafffffffffg aaa aaae caaa fffffaaafffffffffg aaa eaaa aaa fffbdaaafffffffffg aaa daad aaa ffbbdaaafffffffffg aaa aaae aaae ffbbaaadfffffffffg aaa eaaa aaac fffbaaaffffffffffg aaa daaa daaa fffbaaaffffffffffg aaa aaae eaaa fffgaaabfffffffffg aaaeaaa aaa fffaaaabbffffffffg aaadaaa aaa fffaaadbbbfffffffg aaaaaae aaac fffaaafbbbbffffffg aaaaaa daad fffaaafbbbbffffffg aaaaaa caaa ffdaaaffbbbbfffffg aaaaac eeeeeeeeeaaaeeeeeeeeee ffaaadfffbbbbffffg aaaaa gffffffffaaaffffffffff ffaaafffffbbbbfffg aaaaa gffffffffaaaffffffffff ffaaafffffbbbbfffg aaaac gffffffffaaadfffffffff ffffdffffffbbbbffg aaaa gffffffffdaaafffffffff ffffffffffffbbbbfg aaaa gfffffffffaaafffffffff fffffffffffffbbbbg aaac gfffffffffaaafffffffff gggggggggggggbbbbf caa gfffffffffaaaffffbffff bbbb gfffffffffaaadffbbbfff bbbb gfffffffffdaadfbbbbbff bbbb gfffffffffdaaabbbbbfff cbbbc gffffffffffaaabbbbffff bbbbe gffffffffffaaabbffffff bbbb gfffffffffbaaabfffffff bbbb gffffffffbbaaadfffffff ebbbc gfffffffbbbdaaafffffff cbbbe gfffffbbbbbbaaafffffff bbbb gffffbbbbbffaaafffffff bbbb gfffbbbbbfffaaafffffff ebbbb gffbbbbbffffaaadffffff cbbbc gfbbbbbfffffdaaaffffff bbbb bbbbbfffffffgaaaffffff bbbb bbbbbfffffffffaaaffffff bbbb bbbbbffffffffffaaaffffff cbbbc ebbbbbfffffffffffaaagfffff bbbbe cbbbbbffffffffffffaaadfffff bbbb bbbbbeeeeeeeeeeeeeecaaaeeeee bbbb bbbbb eaaa ebbbc bbbbb aaa cbbbe ebbbbb aaae bbbb cbbbbc aaac bbbb bbbbbe daad ebbbb bbbbb caaa cbbbc bbbbb aaa bbbb ebbbbc aaa bbbb cbbbbe aaac bbbb bbbbb daad cbbbc bbbbb caaa bbbbe ebbbbb eaaa bbbb cbbbbc aaa bbbbbbbbe aaae ebbbbbb adc bbbbb bbb ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#7a729cff b,#d4a2a3ff c,#cac6d6ff d,#ada8c2ff e,#ece3e7ff f,#998aa8ff g,#e3c3c3ff ``` ```image daaaaaf faaaaad aaaaaac eaaaaaae caaaaaa daaaaaf faaaaad aaaaaac caaaaaae daaaaaa faaaaaf aaaaaad eaaaaaac caaaaaae daaaaaa faaaaad e aaaaaac gbcaaaaaae ebbbfaaaaaa gbbbbfaaaaaf ebbbbbaaaaaad gbbbbaaaaaac bbbbaaaaaae ebbfaaaaaa ebfaaaaaf gaaaaaafe eaaaaaafbe caaaaaabbb daaaaaabbbg faaaaafbbbbg aaaaaafbbbbbe eaaaaaafbbbbbb caaaaaabbbbbbbg daaaaafebbbbbbbg faaaaad gbbbbbbbe aaaaaac bbbbbbbbe eaaaaaae ebbbbbbbb caaaaaa ebbbbbbbg daaaaaf gbbbbbbbe faaaaad gbbbbbbbe aaaaaac bbbbbbbb eaaaaaae ebbbbbbbg caaaaaa gbbbbbbbg daaaaaf gbbbbbbbe cdfaaad bbbbbbbb ece ebbbbbbbg ebbbbbbbg gbbbbbbbe bbbbbbbbe ebbbbbbbb ``` <!-- end of image --> Success! This area contains 1 intersection point! Onward to the next region of interest. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#7a729cff b,#d3a2a3ff c,#dbced7ff d,#b5afc6ff e,#f0e7e9ff f,#9b8fadff g,#debabaff ``` ```image faaaaad daaaaaf daaaaaa caaaaaae eaaaaaac aaaaaad faaaaaf daaaaaa caaaaaae eaaaaaac aaaaaad faaaaad daaaaaf daaaaaa gg caaaaaae gbbc aaaaaac ebbbbbe aaaaaad ebbbbbbbe faaaaaf cbbbbbbbbb daaaaaa gbbbbbbbbbe caaaaaabbbbbbbbbge eaaaaaabbbbbbbbg aaaaaafbbbbbbc faaaaafbbbbbe daaaaaabbbbe efaaaaaabbg ebbaaaaaabg cbbbaaaaaad gbbbbaaaaaad gbbbbbfaaaaaf ebbbbbbbfaaaaaa ebbbbbbbbfaaaaaae cbbbbbbbbbcaaaaaac gbbbbbbbbbe aaaaaad egbbbbbbbbge faaaaaf ebbbbbbbbbg daaaaaf cbbbbbbbbbc caaaaaa gbbbbbbbbbe eaaaaaae gbbbbbbbbbe aaaaaac ebbbbbbbbbg faaaaad ebbbbbbbbbg daaaaaf cbbbbbbbbbc daaaaaa gbbbbbbbbbe caaaaaae gbbbbbbbbbe eaaaaaac bbbbbbbbg aaaaaad bbbbbbbg faaaaaf bbbbbbc daaaaaf bbbbbe caaaaaa bbbge eaaaaaae bbg aaaaaac bc faaaaad ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#7a729cff b,#d4a2a3ff c,#cdcad9ff d,#aca7c1ff e,#ece4e8ff f,#938cadff g,#e2c2c3ff ``` ```image c aaa aaae caaad df aaaaa caaaad aaaaa aaaaaaaad caaaaa aaaaaaaaaaad aaaaaa aaa caaaaaaaaac aaaaaac eaaa caaaaaaaaac caaadaaf daaf daaaaaaaaae aaadcaaa aaac daaaaaaaafe aaa aaa aaa daaaaaaaaf caaa aaa aaa efaaaaaaaad aaad aaae caaa efaaaaaaaad aaa faad daaf eaaaaaaaaac caaa caaa aaac caaaaaaaaac aaaf aaa aaa caaaaaaaaac aaa aaa aaa daaaaaaaafe eaaa aaa caaa daaaaaaaaf aaaf aaac faad faaaaaaa aaae daaf aaae efaaaa eaaa eaaa aaa aaa faaf aaa aaa aaa aaae aaa daaa aaa eaaa aaac aaad aaa faaf faad aaae aaa aaae caaa aaa aaa eaaa aaa gcaaa aaa faaf aaa bbfaaf aaa aaae aaae bbaaac aaa eaaa aaac ebaaa aaa faaf daaf gaaae aaa aaae eaaa caaab aaaeaaa aaa faafbb aaafaaf aaa aaabbbb aaaaaae aaac aaaebbbg aaaaaa faad aaa bbbbe aaaaaa caaa caaa bbbb aaaaae aaa faad bbbb aaaaa aaa aaae ebbbg aaaaa aaae aaa gbbbe aaaac aaad c bbbb aaaa daaf bbbb aaaa eaaa ebbbb aaac aaa gbbbe caa aaa g bbbb aaac bbb bbbb daaf bbbbb bbbb caaabbbbb ebbbg aaabbbg bbbbe aaabbe bbbb baaab bbbb bbaaad ebbbg ebbbfaaa gbbbe gbbbbgaaa bbbb bbbbbe aaa bbbb bbbbb aaa ebbbb bbbbb aaac gbbbe ebbbbg daaf bbbb gbbbbe caaa bbbb bbbbb aaa bbbb bbbbb aaa ebbbg ebbbbb aaae bbbbe ebbbbg faad bbbb gbbbbe caaa bbbb bbbbb eaaa ebbbg bbbbb aaa gbbbe ebbbbg aaa bbbb gbbbbe aaac bbbb bbbbbe daaf ebbbg bbbbb eaaa gbbbe bbbbb aaa bbbb ebbbbg aaa bbbb gbbbbe aaac bbbb bbbbb faad ebbbg bbbbb caaa bbbb ebbbbb aaa bbbb ebbbbg aaa bbbbbbbbe aaae ebbbbbb afc gbbbb bbg ``` <!-- end of image -->
[ "" ]
I'm optimistic that I'll find some intersections in this image. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#3ba266ff b,#909ed1ff c,#b1d7b1ff d,#92c899ff e,#5b64ceff f,#d1e0e3ff g,#63b582ff ``` ```image f fa afg af a gd dc ca a a a a fg a af a a gg gc fg fa a gf a a a a cdddggddddddddddddddddddddddddddddddddddaddddd ac dccccacccccccccccccebccccccccccccccccccggccccc dg dccccgdcccccccccccbeeecccccccccccccccccacccccc fa dcccccaccccccccccceccbebcccccccccccccccacccccc a dcccccaccccccccccbecccceecccccccccccccdacccccc af dcccccdgccccccccceccccccbebcccccccccccgdcccccc gd dccccccaccccccccdecccccccceeccccccccccaccccccc cg dccccccadccccccceccccccccccdebccccccccaccccccc fa dcccccccacccccccecccccccccccceeccccccdgccccccc a dcccccccaccccccecccccccccccccccebccccacccccccc af dcccccccggcccccecccccccccccccccceecccacccccccc gd dccccccccaccccecccccccccccccccccccebcacccccccc ca dccccccccadcccecccccccccccccccccccceadcccccccc a dcccccccccacceccccccccccccccccccccccaebccccccc a dcccccccccacceccccccccccccccccccccccaceecccccc ac dcccccccccggeccccccccccccccccccccccdgcccebcccc dg dccccccccccaeccccccccccccccccccccccgdccccbcccc fa dccccccccccadccccccccccccccccccccccacccccccccc a dcccccccccceaccccccccccccccccccccccacccccccccc af dcccccccccedacccccccccccccccccccccggcccccccccc ac dcccccccccecgdccccccccccccccccccccaccccccccccc dg dccccccccebccaccccccccccccccccccccaccccccccccc fa dccccccccecccaccccccccccccccccccccaccccccccccc a dcccccccebcccdaccccccccccccccccccgdccccccccccc af dcccccccecccccaccccccccccccccccccacccccccccccc gd dccccccebcccccgdcccccccccccccccccacccccccccccc ca dccccccecccccccaccccccccccccccccdgcccccccccccc a dcccccbbcccccccaccccccccccccccccaccccccccccccc a dccccceccccccccdgcccccccccccccccaccccccccccccc af dccccbbcccccccccacccccccccccccccaccccccccccccc gg e gc dc fa bb a a a e a a a bb cd fg ac e a gf dg fb gf a fa e a a g fb a cd e cd a fe a a e gf a beee a dc beeeb a a fbeeef dd a fbeebf a fg feeebf af gf beeeb fa a beeeb a a eef dc dc bb a a e a a fe fag e af e f bb e fe e e bf e fe e e bf e fb e ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3ba267ff b,#858adcff c,#a8d5bbff d,#b6baeaff e,#5962cfff f,#dae5eaff g,#72bc90ff ``` ```image cag aa aaf f fag gac deef cac faa eeeeb gaf gaf debdeeed aa cag eef beeb cag aa deb deeed gac gac bef beeb aaf faa deb feeed faa gaf bed beebf cag cag feb feeed gaf aa bed beebf aa gac fee feeed fag fag bed deebf cac aaf fee feeed gaf cag bed deebf aa aa fee fbeed cag gac bed deebf gac fag fee fbeed aa aaf bed deebf fag cac fee fbeed cac faa bed deebf gaf gac fee fbeed aa cag bed deeecag aaf fee fbeaac cac ded daaef faa ee faaeeb gac deb cagdeeef cag eef gac fbeeb aaf deb aa deeef cac eef fag beeb faadeb cac deeb gaeef gaf bf caab aa aaf cag daac gac eeaa aaf debgaf fag eefcag cac deb aa gaf eef gac aa deb fag fag bef gaf cac deb cag gaf bed aa faa feb gac cag bed fag gac fee aaf aa bed cag fag fee faa cac bed gac gaf fee fag aa bed aaf cag fee cac gac bed faa aaf fee gac fag bed cag cac fee aaf gaf bed cac aa ``` <!-- end of image --> There is 2 intersections point visible in this close-up of area A. Answer: A: 2; 2 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#3ca267ff b,#7e84daff c,#a2d3b6ff d,#aeb2e8ff e,#5860cfff f,#d4e4e4ff g,#6dba8dff ``` ```image f fa afg af a gc gc ca a a a a fg a af a a gg gc fg fa a gf a a a a cg a ac a ef cc gg gf dbee a fa a e fed a a a fb ee fg af cg e fed gf ac a fb be a ca gf e fed a fa a fe be cg a a e fed a af cc fe be a gg a e fed a ca af e bac a fa e aed a a e a be ac ccef fg eb gg ae gf b fa af a a ea a af bfa cc ac e gc a cg bf a a fa e a fa a bd fg gf af e a a gc bd gc a ca e a fg a bd a af a e fg a af dd a a gg e gf cc fa dd a a a e a a a db cg fg ac e a gf gg db gf a fa e a a g db a cc e cg a fb a a e af a deeb a gc deeed a a fbeeed cc a fbeebf a fg dbeebf af af deeed fa a fdeeed a a ebd cc cc dd a a e a a fe fag e af e f dd e fb e e bd e fb e e bd e fb e ``` <!-- end of image -->
[ "" ]
Here's an image. My task is to find intersections or areas where lines come close together. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#feffffff a,#12533eff b,#6de963ff c,#eff6efff d,#79a888ff e,#43805fff f,#b1d8b1ff g,#a1d4a1ff ``` ```image cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaafff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaafff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaafff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaafff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaafff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaafff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaafff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeaefff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbfffeaefff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbbffaaefff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbbgfaaefff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbbbbgaaefff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgbbffbbbaaefff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffbbbaefff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffbbbefff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbgfffffgbbbfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffebbfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgbbgfffffffaeefff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffaadfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgbbfffffffffaadfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffaadfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffaadfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbgffffffffffaadfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffaadfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgbbgfffffffffffaadfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffaadfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgbbfffffffffffffaadfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffaadfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffaagfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbgffffffffffffffaagfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffffaagfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffgbbffffffffffffffffaagfff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffaagfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffffffaagfff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbgfffffffffffffffffaaffff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffgbbgffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffffffffaaffff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffgbbffffffffffffffffffffaaffff cgfffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffbbgfffffffffffffffffffffaaffff cgfffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffffgbbgffffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffffffffffffaaffff cgfffffffffffffffffffffffffffffffffffffffffffffffffgbbffffffffffffffffffffffffaaffff cgfffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffffbbgfffffffffffffffffffffffffaaffff cgfffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffgbbfffffffffffffffffffffffffffaaffff cgffffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffffffffffffgaaffff cgfffffffffffffffffffffffffffffffffffffffffffffgbbfffffffffffffffffffffffffffgaaffff cgfffffffffffffffffffffffffffffffffffffffffffffbbbfffffffffffffffffffffffdeaaaaaffff cgffffffffffffffffffffffffffffffffffffffffffffbbbffffffffffffffffffdeaaaaaaaaaaaffff cgffffffffffffffffffffffffffffffffffffffffffffbbgffffffffffffgdaaaaaaaaaaaaedfffffff cgfffffffffffffffffffffffffffffffffffffffffffbbbffffffffdeaaaaaaaaaaaedgffffffffffff adffffffffffffffffffffffffffffffffffffffffffgbbffffeaaaaaaaaaaaadgffffffffffffffffff aaaffffffffffffffffffffffffffffffffffffffffffbbbffeaaaaaaaaedffffffffffffffffffffffff aaaffffffffffffffffffffffffffffffffffffffffbbbfdaaaaedffffffffffffffffffffffffffffff caaafffffffffffffffffffffffffffffffffffffffbbbaaaaefffffffffffffffffffffffffffffffff cdaaefffffffffffffffffffffffffffffffffffffbbbaaaefffffffffffffffffffffffffffffffffff cgeaadfffffffffffffffffffffffffffffffffffgbbaaafffffffffffffffffffffffffffffffffffff cgfaaaffffffffffffffffffffffffffffffffffabbbagffffffffffffffffffffffffffffffffffffff cgffaaafffffffffffffffffffffffffffffffeaebbgffffffffffffffffffffffffffffffffffffffff bgfffaaaffffffffffffffffffffffffffffeaaabbbfffffffffffffffffffffffffffffffffffffffff fbbbgfdaaefffffffffffffffffffffffffdaaaabbbffffffffffffffffffffffffffffffffffffffffff fbbbbbbeaadffffffffffffffffffffffdaaaaefbbgffffffffffffffffffffffffffffffffffffffffff cgbbbbbbeagfffffffffffffffffffgaaaaeffbbbfffffffffffffffffffffffffffffffffffffffffff cgffgbbbbbbaaegffffffffffffffaaaaafffgbbgfffffffffffffffffffffffffffffffffffffffffff cgfffffbbbbbbeaaaaedgffffffeaaaagffffbbbffffffffffffffffffffffffffffffffffffffffffff cgfffffffgbbbbbbaaaaaaaaeeaaaagfffffgbbfffffffffffffffffffffffffffffffffffffffffffff cgffffffffffbbbbbbeaaaaaaaaadfffffffbbbfffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffgbbbbbbgdeaadffffffffbbbffffffffffffffffffffffffffffffffffffffffffffff cgfffffffffffffffbbbbbbbfffffffffffbbgffffffffffffffffffffffffffffffffffffffffffffff cgfffffffffffffffffgbbbbbbgfffffffbbbfffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffgbbbbbbffffgbbffffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffffgbbbbbbgfbbbffffffffffffffffffffffffffffffffffffffffffffffff cgfffffffffffffffffffffffffgbbbbbbbfffffffffffffffffffffffffffffffffffffffffffffffff cgfffffffffffffffffffffffffffgbbbbgfffffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffffffffffffgbffffffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#12523dff b,#6cea62ff c,#d3ead6ff d,#699284ff e,#3d785eff f,#99b5abff g,#a7f2a1ff ``` ```image aaa aaa aaa aaa aaa aaa aae aae aae aae bb aae cbbg aae gbbbbg aae bbbbbbb aae cbbbcbbb aad bbb cbbbgaad bbb bbbbaad bbbc gbbbad bbb bbbbd bbb cbbbb bbbc bbb bbb ebd gbbg caaf bbbg caaf bbb caaf gbbg caaf gbbb caaf bbbb caaf gbbb caaf bbbc caaf cbbb caaf cbbb faac bbbc faac bbb faac gbbg faac bbbb faac bbbc faac gbbg faac bbb faac cbbb faac gbbb faac bbb daa cbbb daa bbb daa gbbb daa bbbc daa bbb daa bbb daa bbbc dae bbbb eae bbbg eae bbbg eae bbb eae gbbg eae gbbg eae bbb eae gbbb ead gbbb aad bbbb aad cbbb aad bbbc aad bbb aad cbbb aad bbbg aad bbb caaf gbbg caaf bbb ffeaaaaaf bbbg cdaaaaaaaaaaaaa gbbb cddaaaaaaaaaaaaaaef bbb cfeaaaaaaaaaaaaaedfc cbbb fdaaaaaaaaaaaaaaedc ac cbbb cdaaaaaaaaaaaaaaefc aa bbbb aaaaaaaaaaefc aad bbbc faaaaaaaedcc eaaa bbb faaaaaf aaae cbbbaaaaac faaad bbbeaaaec daaac bbbaaae eaaa fbbbaaf aaad eabbbec daaa caaaabbb b aaac aaaaebbg bbbb caaad faaaaabbbg bbbbbg aaaa eaaaaadbbb cbbbbbbbbaaa cdaaaaac gbbb bbbbbbbbef aaaaae gbbb cbbbbbbbeadfc faaaaaf bbbb cbbbbbbbeaaaaaedc eaaaaad cbbb cbbbbbbbeaaaaaaaaaefdaaaaac bbb gbbbbbbbeaaaaaaaaaaaaaec bbb gbbbbbbbfeaaaaaaaf cbbb cgbbbbbbgcfdeaaf bbbg cgbbbbbbgc bbb gbbbbbbbc cbbbc cgbbbbbbg gbbb cgbbbbbbb bbbg gbbbbbbbc gbbb gbbbbbbbbb bbbbbg gbbb ``` <!-- end of image --> Area A contains 2 intersections. Answer: A: 2; 2 = 2 I've identified a total of two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#12533dff b,#6cea62ff c,#d2efd3ff d,#6a9385ff e,#3d7a5dff f,#a6beb6ff g,#9ef097ff ``` ```image daa daa daa daa daa eae eae eae bg eae bbbg eae bbbbc eae bbbbbb aad cbb bbbaad bbg bbbad gbb bbbd bbg cbbb bbb ebb cbbc aed bbb aad cbb aaf bbg aaf gbb aaf bbc aaf bbb aaf cbb aaf bbb aaf gbb aaf bbg aac bbb aac bbc aac bbb aac cbb aac bbb aa gbb aa bbg aa bbb aa bbc aa bbb aa cbb aa bbg aa gbb aa bbc aa bbb aa cbbc aa bbb aa gbb aa bbg aa gbb aa bbc aa bbb aa cbb aa bbb aa gbb caa bbg fdaaaaa bbb cdaaaaaaaaaae bbc cfeaaaaaaaaaaadf bbb feaaaaaaaaaaaef ac cbb daaaaaaaaaaaedc aaa bbg daaaaaaaadc aaa gbb faaaadf aae bbgaaaad faad bbbaaae daac cbbaae aaa ebbba aaa daebbc g aaa daaabbg cbbbc caad faaaabbb cbbbbbbdaaf caaaad bbc gbbbbbea caaaae bbb cbbbbbbaedc aaaaa cbb gbbbbbeaaaaef eaaaa bbb cbbbbbbaaaaaaaaddaaaac gbb gbbbbbeaaaaaaaaaf bbg cbbbbbbcfdaaf bbb gbbbbbg bbc cbbbbbbc bbb gbbbbbg cbb bbbbbbc bbb gbbbbbbb bbbbg cg ``` <!-- end of image -->
[ "" ]
This image might have some surprises. Let's look for intersections carefully. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#411838ff b,#34a422ff c,#715f6bff d,#b1d7b1ff e,#65b859ff f,#ecf2ecff g,#97b994ff ``` ```image ff daad aaaa aaaa aaaa aaaa aaaa aaaa bd aaaad fbbb daaaag ebbbbe gaaaac bbbbbd caaaaa dbbbbb aaaaaa bbbbbg aaaaaa fbbbbbf aaaaaa ebbbbe aaaaaaf fbbbbbf aaaaaad gbbbbb aaacaac bbbbbd faaagaaa dbbbbb gggggggggcaaagaaaggggggggggggggggg ebbbbe dddddddddcaacdaaadddddddddddddddddf fbbbbbf dddddddddcaacdaaadddddddddddddddddf ebbbbe dddddddddaaagdaaadddddddddddddddddf bbbbbd dddddddddaaaddaaagddddddddddddddddf dbbbbb dddddddddaaaddaaacddddddddddddddddf bbbbbg dddddddddaaaddcaacddddddddddddddddf fbbbbbf dddddddddaaaddgaaaddddddddddddddddf ebbbbe dddddddddaaadddaaaddddddddddddddddf fbbbbbd ddddddddgaaadddaaaddddddddddddddddf gbbbbb ddddddddcaaadddaaaddddddddddddddddf bbbbbg ddddddddcaacdddaaaddddddddddddddddf dbbbbb ddddddddaaacdddaaagdddddddddddddddf ebbbbe dddddddgaaaddddcaacdddddddddddddddf fbbbbbf dddddddaaacddddcaacdddddddddddddddf gbbbbb ddddedgaaadddddgaaadddddddddddddddf bbbbbd ddbbbdaaaaddddddaaadddddddddddddddf dbbbbb ddbbbeaaadddddddaaadddddddddddddddf ebbbbe ddebbbaaadddddddaaadddddddddddddddf fbbbbbf dddbbbaaddddddddaaadddddddddddddddf ebbbbe dddebbbaddddddddaaagddddddddddddddf bbbbbd ddddbbbdddddddddcaacddddddddddddddfdbbbbb dddabbbbddddddddcaaaddddddddddddddbbbbbg dddaabbbddddddddgaaaddddddddddddgbbbbbf ddaaabbbeddddddddaaadddddddddddebbbbe ddaaagbbbddddddddaaaddddddddddbbbbbf dddaadbbbgdddddddaaaddddddddebbbbbf ddddddebbbdddddddaaagddddddbbbbbedf dddddddbbbgddddddaaacddddgbbbbbdddf dddddddebbbddddddcaacdddbbbbbeddddf ddddddddbbbddddddgaaaddbbbbbgdddddf ddddddddbbbbddddddaaaebbbbbdddddddf dddddddddbbbddddddaabbbbbgddddddddf dddddddddbbbedddddabbbbbddddddddddf dddddddddgbbbddddbbbbbbaacddddddddf ddddddddddbbbedgbbbbbaaaaaaaddddddf ddddddddddebbbebbbbbddcaaaaaaagdddf dddddddddddbbbbbbbgdddddgaaaaaaagdf dddddddddddebbbbbdddddddddgaaaaaaac ddddddddddddbbbedddddddddddddcaaaaaac ddddddddddddgedddddddddddddddddcaaaaaaaf dddddddddddddddddddddddddddddddddgaaaaaaag ddddddddddddddddddddddddddddddddddffaaaaaaac ddddddddddddddddddddddddddddddddddf caaaaaac ddddddddddddddddddddddddddddddddddf gaaaaaaaf ddddddddddddddddddddddddddddddddddf daaaaaaag ddddddddddddddddddddddddddddddddddf faaaaaaac ddddddddddddddddddddddddddddddddddf caaaaaacf ddddddddddddddddddddddddddddddddddf gaaaaaaaf ddddddddddddddddddddddddddddddddddf daaaaaaag ddddddddddddddddddddddddddddddddddf faaaaaaac ddddddddddddddddddddddddddddddddddf caaaaaacf ddddddddddddddddddddddddddddddddddf gaaaaaaaf ddddddddddddddddddddddddddddddddddf daaaaaaag dddddddddddddddddddddddddddddddddgf faaaaaaac ffffffffffffffffffffffffffffffffff caaaaaacf gaaaaaaaf daaaaaaag faaaaaaac caaaaaaaf gaaaaaaaf daaaaaf faaa d ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#411838ff b,#34a322ff c,#a693a2ff d,#a1d498ff e,#67ba5aff f,#d3d6d0ff g,#74566eff ``` ```image caaaaaa faaaaaaf caaaaag aaaaaaf caaaaag aaaaaac gaaaaag gaaaaac gaaaaac gaaaaag aaaaaac caaaaag aaaaaaf caaaaaa aaaaaaf faaaaaa faaaaaa aaaaaaf faaaaaa aaaaaaf caaaaaa gaaaaac caaaaag gaaaaac gaaaaag caaaaag gaaaaac caaaaag gaaaaac faaaaaa aaaaaac faaaaaa aaaaaaf aaaaaaf faaaaaaf aaaaaac faaaaaa gaaaaac caaaaaa gaaaaag caaaaag caaaaag caaaaag caaaaaa gaaaaag faaaaaa gaaaaac faaaaaaf faaaaaac aaaaaaf gaaaaaaf aaaaaac faaaaaag gaaaaac gaaaaaaf gaaaaag faaaaaag caaaaag gaaaaaaf caaaaaa dd faaaaaag faaaaaa dbbb gaaaaaaf aaaaaaf dbbbbbd faaaaaag aaaaaaf bbbbbbb gaaaaaaf gaaaaac dbbbbbbdaaaaaag gaaaaac bbbbbbbaaaaaac caaaaag dbbbbbbaaaaag caaaaag bbbbbbbaaaac faaaaaa ebbbbbbaaag faaaaaa fbbbbbbbaac aaaaaaf ebbbbbbaa aaaaaac fbbbbbbac gaaaaac bbbbbbb gaaaaag cabbbbbbd caaaaag aabbbbbbe caaaaaa caabbbbbbbf faaaaaa aaaabbbbbbe faaaaaaf fe caaaabbbbbbbf aaaaaaf dbb aaaaaabbbbbbe aaaaaac ebbb caaaaaabbbbbbb gaaaaac dbbbbb aaaaaaadbbbbbbd gaaaaag ebbbbbb caaaaac ebbbbbb caaaaag fbbbbbbbb caaa dbbbbbbd caaaaaa dbbbbbbbbb cc bbbbbbe faaaaaa febbbbbbbbbe dbbbbbbf aaaaaaf dbbbbbbbbbbd bbbbbbe aaaaaaf ebbbbbbbbbef ebbbbbbf gaaaaac fbbbbbbbbbbd fbbbbbbe gaaaaac dbbbbbbbbbbf ebbbbbb caaaaag febbbbbbbbbe fbbbbbbd caaaaag dbbbbbbbbbbd ebbbbbb faaaaaa ebbbbbbbbbef dbbbbbbd faaaaaa fbbbbbbbbbbd bbbbbbe aaaaaafebbbbbbbbbbf dbbbbbbf aaaaaabbbbbbbbbbe bbbbbbe gaaaabbbbbbbbbbd ebbbbbbf gaabbbbbbbbbbef fbbbbbbe cabbbbbbbbbbd ebbbbbb ebbbbbbbbbbaac fbbbbbbd fbbbbbbbbbbbaaaaagf ebbbbbb dbbbbbbbbbbaaaaaaaaagf dbbbbbbd febbbbbbbbbbaaaaaaaaaaaagc bbbbbbe dbbbbbbbbbbdfgaaaaaaaaaaaaaac dbbbbbbdebbbbbbbbbef fcaaaaaaaaaaaaaagf bbbbbbbbbbbbbbbbd caaaaaaaaaaaaaagf ebbbbbbbbbbbbbbf fgaaaaaaaaaaaaagc fbbbbbbbbbbbbe fgaaaaaaaaaaaaaa ebbbbbbbbbbd fcaaaaaaaaaaaa fbbbbbbbbef caaaaaaaaaa ebbbbbbd fgaaaaaaa fbbbbbf fgaaaaa feed fcaaa ca ``` <!-- end of image --> Incredible, there's actually 2 intersections in area A! Answer: A: 2; 2 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#411738ff b,#34a422ff c,#90788bff d,#b1bdacff e,#70bf63ff f,#dce2d9ff g,#66455fff ``` ```image ff daaf aaaa aaaa aaaa aaaa aaaa aaaa bf aaaaf fbbb faaaac ebbbbe daaaag bbbbbf caaaaa dbbbbb gaaaaa bbbbbd aaaaaa fbbbbb aaaaaa ebbbbe aaaaaaf bbbbbf aaaaaad ebbbbb aaacaac bbbbbd faaadaag fbbbbb daaafaaa bbbbbe caag aaa fbbbbbf gaac aaa ebbbbb aaad aaa bbbbbd aaaf aaaf dbbbbb aaa gaad bbbbbe aaa caag fbbbbb aaa daaa ebbbbe aaa aaa bbbbbf faaa aaa dbbbbb daag aaa bbbbbd caac aaa fbbbbb aaad aaad ebbbbe faaa gaac bbbbbf aaag caag ebbbbb d faaa faaa bbbbbd bbb aaag aaa dbbbbb bbbdaaa aaa bbbbbe ebbbaag aaa fbbbbbf bbbaa aaaf ebbbbb ebbbg aaad bbbbbf fbbb caac dbbbbb abbbe daag bbbbbe aabbb faaa fbbbbb aaabbbe aaa ebbbbe aaadbbb aaa bbbbbf aa bbbd aaa dbbbbb dbbb aaaf bbbbbd bbbf gaad fbbbbb ebbb caag ebbbbe bbb daaa fbbbbbf bbbb aaaebbbbb fbbb aabbbbbd bbbe abbbbb fbbb bbbbbbaac bbbd fbbbbbaaaaaag dbbbebbbbe caaaaaaaf bbbbbbbf daaaaaaad ebbbbb faaaaaaac bbbd gaaaaaag fe caaaaaaaf daaaaaaad faaaaaaac gaaaaaag caaaaaaaf daaaaaaad faaaaaaac gaaaaaag caaaaaaaf daaaaaaad faaaaaaac gaaaaaag caaaaaaaf daaaaaaad faaaaaaac gaaaaaag caaaaaaaf daaaaaaad faaaaaaac gaaaaaag caaaaaaaf daaaaaf faaa f ``` <!-- end of image -->
[ "" ]
I'm analyzing this image to identify any points where lines intersect. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#b41c7cff b,#614c03ff c,#ba6e99ff d,#9bc295ff e,#e6b5d3ff f,#85864dff g,#b1d7b1ff ``` ```image gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg bbdgggggggggggggggggggggggggggggggggggggggggggggggggggcggggggggggggggggggg fbbbbfggggggggggggggggggggggggggggggggggggggggggggcaaaaaagggggggggggggggggg fbbbbbfgggggggggggggggggggggggggggggggggggdcaaaaaaaaaaagggggggggggggggggg gdbbbbbbdgggggggggggggggggggggggggggcaaaaaaaaaaacdggaacggggggggggggggggg ggggfbbbbbfgggggggggggggggggggdcaaaaaaaaaaccggggggggdaaggggggggggggggggg gggggggfbbbbbdgggggggggggcaaaaaaaaaaacdggggggggggggggaaggggggggggggggggg gggggggggdbbbbbbdggdcaaaaaaaaaaacggggggggggggggggggggaacgggggggggggggggg ggggggggggggfbbaaaaaaaaaaacdgggggggggggggggggggggggggcaagggggggggggggggg gggggggggcaaaaaaaaaaacggggggggggggggggggggggggggggggggaagggggggggggggggg gggdcaaaaaaaaaaccdbbbbbfggggggggggggggggggggggggggggggaacggggggggggggggg ecaaaaaaaaaacdggggggggfbbbbbfgggggggggggggggggggggggggggcaaggggggggggggggg eaaaaaaccggggggggggggggggdbbbbbbdgggggggggggggggggggggggggaaggggggggggggggg acdggggggggggggggggggggggggfbbbbbfgggggggggggggggggggggggaacgggggggggggggg ggggggggggggggggggggggggggggfbbbbbfggggggggggggggggggggcaagggggggggggggg ggggggggggggggggggggggggggggggdbbbbbbdggggggggggggggggggaagggggggggggggg gggggggggggggggggggggggggggggggggfbbbbbfggggggggggggggggaadggggggggggggg ggggggggggggggggggggggggggggggggggggfbbbbbdgggggggggggggcaaggggggggggggg ggggggggggggggggggggggggggggggggggggggdbbbbbbggggggggggggaaggggggggggggg gggggggggggggggggggggggggggggggggggggggggfbbbbbfgggggggggaadgggggggggggg gggggggggggggggggggggggggggggggggggggggggggdbbbbbbdggggggcaagggggggggggg ggggggggggggggggggggggggggggggggggggggggggggggdbbbbbfgggggaagggggggggggg gggggggggggggggggggggggggggggggggggggggggggggggggfbbbbbfggaagggggggggggg gggggggggggggggggggggggggggggggggggggggggggggggggggdbbbbbbaacggggggggggg ggggggggggggggggggggggggggggggggggggggggggggggggggggggfbbbbaaggggggggggg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggfbaabbfgggggggg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaaabbbdgggggg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggdaafbbbdggggg ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaaggbbbggggg ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaacggbbbgggg ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcaagggbbbggg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaaggggbbbgg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaacggggbbbg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcaagggggbbb ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaagggggdbbf ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaacgggggdbbf ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcaaggggggfbbd gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaagggggggfbbg gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaadgggggg fbbe gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcaagggggg bbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddaadddddd bbb aae bbb caa b aa aa cac eaa aa aac eaa aa aac eaa aa aae eaa aa aae caa aa aae caa aa aae cac aa aa aac eaa aa aac eaa aa aac eaa aa aae eaa aa aae caa ae ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#b51b7cff b,#604b02ff c,#c7569dff d,#ada37dff e,#e3cad1ff f,#7f6832ff g,#d98abcff ``` ```image de eee bbbbf egcaaaaaaaaa bbbbbbde egcaaaaaaaaaaaaa bbbbbbbbf egcaaaaaaaaaaaaaaaaa edbbbbbbbbfe egccaaaaaaaaaaaaaaacge aaac fbbbbbbbbfd egcaaaaaaaaaaaaaaaccge gaaa dfbbbbbbbde egcaaaaaaaaaaaaaaaagee eaaae dbbbbbbbbfd eecaaaaaaaaaaaaaaaacge aaac dfbbbbbbbbe egcaaaaaaaaaaaaaaaacg eaaae ebbbbbbbbfd egcaaaaaaaaaaaaaaacgg aaag dfbbbbbbbbcccaaaaaaaaaaaaaaacgee caaa efbbfaaaaaaaaaaaaaaaaacge eaaae egaaaaaaaaaaaaaaaaaae aaac eggcaaaaaaaaaaaaaaaaafbbbfde aaaa egccaaaaaaaaaaaaaaacgeefbbbbbbbbf aaaa aaaaaaaaaaaaaaaagee edbbbbbbbbfe gaaa aaaaaaaaaaacce fbbbbbbbbfe aaag aaaaaaacge edfbbbbbbbde caac aaccg dbbbbbbbbfd gaaa dfbbbbbbbbe caac ebbbbbbbbfd gaaa dfbbbbbbbbe eaaae ebbbbbbbbfde aaac dfbbbbbbbbd eaaa edbbbbbbbfd aaa dfbbbbbbbbf aaa edbbbbbbbbd aaag fbbbbbbbbfe caaa edbbbbbbbbde eaaae fbbbbbbbbfd aaag edbbbbbbbbfe gaaae ebbbbbbbbfd aaag edfbbbbbbbbe caac ebbbbbbbbfd gaaa dfbbbbbbbbdaaac edbbbbbbbaaaa dfbbbbbaaaa efbfaaabbbd faaafbbbbde aaaabbbbbb gaaabbbbbbe aaag efbbbfe caaa fbbbf eaaae ebbbbf aaag ebbbb eaaa ebbbbd aaa dbbbbd aaa dbbbb aaag bbbbe caac fbbbb gaaa fbbb aaag fbb gaaa bb eaaae eb caac e gaaa aaac aaaa aaaa caaa eaaae ``` <!-- end of image --> I've cracked the case! This area contains 2 intersections. Answer: A: 2; 2 = 2 After a thorough search, I conclude that there are two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#b51b7cff b,#614c03ff c,#c8599fff d,#bab192ff e,#e9d2daff f,#8e7f4bff g,#dc95c2ff ``` ```image bbe g fbbbbf egaaaaaa fbbbbbd ecaaaaaaaaaaa ebbbbbbe gcaaaaaaaaaage aac dbbbbbf ecaaaaaaaaaacg eaa fbbbbbd gcaaaaaaaaaage aa ebbbbbfe egaaaaaaaaaacg aag dbbaaaaaaaaaaace gaa egaaaaaaaaaaace aa ecaaaaaaaaaacedbbbbbf aag gcaaaaaaaaaage fbbbbbd gaa gaaaaaacg ebbbbbbe aa ace dbbbbbf aag fbbbbbd gaa ebbbbbbe aa dbbbbbf aae fbbbbbd caa ebbbbbf aa dbbbbbd aae fbbbbbe cac dbbbbbf aa fbbbbbd aae ebbbbbbcac dbbbbaa fbaabbd aaabbbd eaadbbbe aa bbb aag bbb gaa bbb aa bbb aag bbb gaa bbb aa ebbf aag ebbf gaa dbbd aa fbbe aae fbbe caa bbb aa bbb aae bbb cac b aa aa cac eaa aa aac eaa aa aag gaa aa aag gaa aa aag gaa aa aae caa aa aae cac eaa aa cac eaa aa aac eaa aa aag gaa aa aag gaa aa aag gaa ae ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#e0f56dff b,#826ceeff c,#ddf729ff d,#f3fcb5ff e,#b0abe7ff f,#b1d7b1ff g,#97c795ff ``` ```image bbb ebb gggbbggggggggggggggggggggf fffbbefffffffffffffffffffg fffbbbfffffffffffffffffffg fffebbfffffffffffffffffffg ffffbbfffffffffffffffffffg ffffbbeffffffffffffffffffg fffcbbbffffffffffffffffffg ffccgbbffffffffffffffffffg fffccbbffffffffffffffffffg ffffcbbffffffffffffffffffg ffffabbbfffffffffffffffffg fffffgbbfffffffffffffffffg ffffffbbcffffffffffffffffg ffffffbbaafffffffffffffffg ffffffbbgcfffffbbbeffffffg ffffffebbccfffebbbbbbffffg fffffffbbcccffbbbbbbbbbbfg fffffffbbfccafbbfffebbbbbbe fffffffbbecccbbbffffffebbbbbbe fffffffbbbfccbbefffffffffbbbbbbb ffffffffbbffgbbffffffffffg bbbbbbb ffffffffbbffbbeafffffffffg bbbbbbe ffffffffbbefbbccfffffffffg ebbbbbbe ffffffffbbbbbbcccffffffffg ebbbbbbe ffffffffebbbbffcccfffffffg ebbbbbb fffffffffbbbbffaccaffffffg bbbbbbe fffffffffbbbefffcccffffffg ebbbbbbe fffffffffbbbfffffcccfffffg ebbbbbbe ffffffffffbbffffffcccffffg ebbbbbb ffffffffffffffffffaccafffg bbbbbbb fffffffffffffffffffcccfffg bbbbbbe ffffffffffffffffffffcccffg ebbbbbbe ffffffffffffffffffffgcccfg ebbbbbbe accd ebbbbbb ccc bbbbbbe ccc ebbbbbbe cca ebbbbbbe accd ebbbbbb ccc bbbbbb ccc bbe dcca accd ccc ccc dcca acc ccc ccc dcca acc ccc ccc dccd acc cd ccc ccc ccc ccc dccd dccc ccc ccccd ccc ccccc ccc accdcc dccd accd cc ccc cccc cc ccc ccca cca cca acccd acc dccd cccc dcc ccc ccca cc ccc dcccd ccd cca accc cca accd cccc acc ccc dccca cc ccc accc cc cca cccc ccd accd ccca ccc ccc dcccd dcc ccccccc cc dccccc ccd accd cca d acc dca ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#e0f165ff b,#826beeff c,#def729ff d,#eff7b4ff e,#d2caf8ff f,#aa9af3ff g,#a6a2a0ff ``` ```image bbbbf bbbbb fbbbbe ebbbbe bbbbf bbbbb fbbbb ebbbbe bbbbf bbbbb fbbbb ebbbbe dbbbbf dccbbbbb dcccgbbbb ccccgbbbbe dcccabbbbf acccbbbbf cccgbbbb dccgbbbbe dcabbbbf acbbbbf cgbbbb dgbbbbd dbbbbgd bbbbgc bbbbbca fbbbbaca ebbbbgccd fbfe bbbbgccc ebbbbbfe bbbbbccca bbbbbbbbbfe fbbbbacccd ebbbbbbbbbbbbfe ebbbbgccccd fbbbbbbbbbbbbbbfe bbbbgccccc bbbbbfbbbbbbbbbbbbfe bbbbbccccca fbbbbe efbbbbbbbbbbbb fbbbbdcccccd bbbbb efbbbbbbbbb ebbbbeacccccdebbbbf efbbbbbb ebbbbf acccccfbbbbe ebbbb bbbbb ccccabbbbf efb fbbbb dcccgbbbbe ebbbbe accbbbbb ebbbbf agbbbbf bbbbf bbbbba fbbbb ebbbbgcd ebbbbe fbbbbaccd ebbbbf bbbbbcccc bbbbf fbbbbgcccca fbbbb bbbbbdcccccd fbbbbfbbbbf acccccd ebbbbbbbbbe cccccc bbbbbbbbb dccccca fbbbbbbbe dcccccd fbbbbbbb accccc ebbbbbbf ccccca bbbbbbe dccccca bbbbbf dcccccd fbbbbe accccc ebbbb ccccca ebfe dccccca dcccccd accccc ccccca dccccca dcccccd accccc ``` <!-- end of image --> The close-up clearly shows 2 intersections point in area A. Answer: A: 2; 2 = 2 I've identified a total of two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#e4f858ff b,#816befff c,#def728ff d,#eaf793ff e,#d3ccf9ff f,#a595ecff g,#f6fcceff ``` ```image fbb ebb bb bbe bbb ebb bb bbe abbf ccdbb ccbb gcbbe abbf fbb bbc bbad bbfcg bbbe fbbcc ebbbbbbe bbccc bbbbbbbbbf bbgccd bb ebbbbbbf bbfaccfbb ebbbbbbe fbb ccbbe fbbbbbbe ebb dbb fbbbbbf bb bbfd ebbbbbbf bbf bbcc ebbbbbbe fbbbbbccc fbbbbbbe ebbbbe cca fbbbbbbe bbbb dccd ebbbbbbf bbbf acc ebbbbbbf bbb ccc ebbbbbbe ebb cca fbbbbbbe dccg fbbbbbf ccc ebbbbbbf ccc ebbbbbbe gcca fbbbbbbe dccg fbbbbbbe ccc bbbbbbf ccc ebbbbbbf gcca ebbbbbbe dccg fbbbbbbe ccc fbbbbb ccc ebbf gcca accg ccc ccc gccd accg ccc ccc gccd acc ccc ccc gccd acc cg ccc ccc cca ccc dccd dccc acc ccccd ccc cccca cca accdcc dccd accd cc ccc cccc ccg ccc gccca ccd cca dcccg acc dccg cccc gcc ccc ccca cc ccc gcccd ccg gcca accc cca dccg cccc dcc ccc gcccd gcc ccc dcccg cc gcca cccc ccd dccg ccca acc ccc dcccg dcc cccaccc cc gcccca ccg accd cca d acc gcd ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#918fc7ff b,#0a9eceff c,#60bdd1ff d,#bdcbe5ff e,#a1cea7ff f,#eef5f1ff g,#b1d7b2ff ``` ```image cbb cbbb dbbbb fbbbbb fbbbbbb bbbccbb bbbc cbb bbbb cbb ffbbbbfffcbbffffffffffffffffffffffff febbbbeeeecbbeeeeeeeeeeeeeeeeeeeeeeee fbbbbgggggcbbeggggggggggggggggggggggg cbbbggggggcbbeggggggggggggggggggggggg cbbbeggggggebbeggggggggggggggggggggggg dbbbegggggggebbeggggggggggggeaaaggggggg dbbbcggggggggebbcggggggggggaaaaaaagggggg fbbbceggggggggebbcggggggggaaaaaaaaaaggggg fbbbcfeggggggggebbcggggggaaaaaaaggaaaggggg bbbc fegggggggggbbcggggaaaaaaeggggeaaagggg bbbb fegggggggggbbcgeaaaaaaegggggggaaaaggg bbbb fegggggggggbbcaaaaaagggggggggggaaaegg bbbb fegggggggggcaaaaaagggggggggggggcabegg bbbb feggggggggaaaaaagggggggggggggggbbbggg cbbb fegggggggaaaaaggggggggggggggggebbbggg cbbbf feggggggeaaabbggggggggggggggggbbbgggg dbbbf feggggggaaabbbggggggggggggggggbbbgggg dbbbd fegggggaaaabbbgggggggggggggggbbbegggg daa fbbbd fegggggaaagbbbgggggggggggggggbbbggggg aaaf fbbbc feggggaaaegbbbggggggggggggggcbbcggggg aaa bbbc feggggaaaggbbbggggggggggggggbbbgggggg aaad bbbb fegggaaagggbbbgggggggggggggcbbbgggggg aaa bbbb feggeaaagggbbbggggggggggggebbbggggggg daaa bbbb feggaaaggggbbbggggggggggggbbbeggggggg aaad bbbb fegaaaaggggbbbgggggggggggbbbcgggggggg aaa cbbb fegaaagggggbbbggggggggggbbbbggggggggg daaa cbbbf feaaaegggggbbbgggggggggcbbbgggggggggg aaa dbbbf feaaaeeeeeebbbeeeeeeeeebbbeeeeeeeeeee fdaaaffffffffffffffffdbbbd aaa bbb bbbc feeaaaeeeeeeeeeeeeeeeebbbd daaa bbb bbbb feggaaagggggggggggggebbbc aaa bbb cbbb feggaaaaggggggggggggbbbbf aaad bbb fbbbf fegggaaagggggggggggbbbbef faaa bbb bbbd fegggeaaagggggggggbbbbgef aaaf bbb bbbc feggggaaaegggggggbbbbggef daaa bbb cbbb fegggggaaaggggggbbbbgggef aaa bbb dbbb fegggggaaaaggggbbbbggggef daad cbb bbbd feggggggaaagggcbbbgggggef aaa cbb bbbc fegggggggaaagcbbbegggggef aaad cbbcbbb fegggggggaaaabbbeggggggef faaa cbbbbb feggggggggaaabbcgggggggef aaaf cbbbbf feggggggggaaaacggggggggef daaa cbbbc feggggggggbaaagggggggggef aaa cbbb fegggggggbbbaaaggggggggef aaad bb feggggggbbbbaaaagggggggef aaa fegggggbbbbggaaagggggggef aaaf feggggbbbbgggeaaaggggggef faaa c fegggbbbbgggggaaaegggggef aaa cbbfeggcbbbgggggggaaagggggef daaa bbbbegcbbbegggggggaaaaggggef aaa bbbbcbbbegggggggggaaaggggef aaad bbbbbbcggggggggggeaaagggef faaa bbbbcggggggggggggaaagggef aaaf fbbcgggggggggggggeaaeggef daaa feeeeeeeeeeeeeeeeeaaaeeef aaa fffffffffffffffffaaafff aaad aaa aaa daa aaaf faad faaa aaa aaa aaa daaa aaa aaa daa aaad faad faaa aaa aaaf aaa daaa aaa aaa daadaad faaaaa aaaad aaaa aaaf fad ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#908dc8ff b,#099ecfff c,#89d0e7ff d,#c8daecff e,#45b3d9ff f,#e6eef6ff g,#afaed7ff ``` ```image gaaaaag dbbb faaaaaad fbbbb daaaaaa fbbbbb gaaaaag febbbbb faaaaaaf ebbbbbb gaaaaag ebbbbbbe faaaaaad ebbbbbbe daaaaaa cbbbbbbef gaaaaag cbbbbbbbf faaaaaaf cbbbbbbbf gaaaaag dbbbbbbbd aaaaaad dbbbbbbbd daaaaaaf fbbbbbbbc gaaaaag fbbbbbbbc faaaaaaf febbbbbbc gaaaaag ebbbbbbe aaaaaad ebbbbbbe daaaaaaf ebbbbbbe gaaaaag cbbbbbbef faaaaaad cbbbbbbbf gaaaaaa cbbbbbbbf aaaaaagbbbbbbbd daaaaaabbbbbbd gaaaaaabbbbd faaaaaaebbc gaaaaaabc feaaaaaaa ebeaaaaaaf ebbbaaaaaag cbbbbbaaaaaad cbbbbbbeaaaaaa cbbbbbbbfaaaaaag dbbbbbbbd faaaaaaf dbbbbbbbd gaaaaag dbbbbbbbd faaaaaad fbbbbbbbc daaaaaa fbbbbbbbc gaaaaag febbbbbbc faaaaaaf ebbbbbbe gaaaaag ebbbbbbe faaaaaad c ebbbbbbe daaaaaaf bd cbbbbbbef gaaaaag bbd cbbbbbbbf faaaaaaf bbbfcbbbbbbbf gaaaaag bbbbbbbbbbbd aaaaaad bbbbbbbbbbd daaaaaaf bbbbbbbbbc gaaaaag bbbbbbbbc faaaaaa ebbbbbbc gaaaaaf febbbbe daaaaad febbc faaaaad ff aaaaag ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Right then, let's explore the next spot. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#908dc8ff b,#089ecfff c,#6dc3e1ff d,#d8e5f2ff e,#3aabd5ff f,#a0d9ecff g,#b6b4daff ``` ```image fbbbbbbbd fbbbbb dbbbbbbbf fbbbbb dbbbbbbbf fbbbbb debbbbbbf fbbbbbd ebbbbbbc fbbbbbd ebbbbbbc fbbbbbd ebbbbbbe fbbbbbd bbbbbbe fbbbbbd bbbbbe fbbbbbd bbbbed dbbbbbd dgaag bbbbd dbbbbbd daaaaaag bbbd dbbbbbf gaaaaaaaaad bbf dbbbbbf gaaaaaaaaaaaad bf dbbbbbf dgaaaaaaaaaaaaaaa f dbbbbbf dgaaaaaaaaaaaaaaaaag dbbbbbf dgaaaaaaaaaaagdgaaaaaad dbbbbbf daaaaaaaaaaaagd gaaaaaad bbbbbf gaaaaaaaaaaaag aaaaaaa bbbbbf dgaaaaaaaaaaaag daaaaaag bbbbbf dgaaaaaaaaaaaad gaaaaaad bbbbbc dgaaaaaaaaaaagd gaaaaaad bbbbbc daaaaaaaaaaaagd aaaaaag bbbbbcaaaaaaaaaaaagd daaaaaad bbbeaaaaaaaaaaaag gaaaad eeaaaaaaaaaaaag caaabcd gaaaaaaaaaaaad bbebbb aaaaaaaaaaagd fbbbbbc gaaaaaaaaagd ebbbbbd daaaaaaaaad dbbbbbe gaaaaaaebe cbbbbbf daaaaaabbbe dbbbbbe aaaaaaebbbe cbbbbbf daaaaaabbbbe bbbbbb aaaaaacbbbbe fbbbbbc gaaaaagcbbbbe ebbbbbd daaaaaadcbbbbe dbbbbbe gaaaaag cbbbbe cbbbbbf daaaaaa cbbbbb dbbbbbe aaaaaad cbbbbb cbbbbbf gaaaaaa cbbbbb bbbbbb aaaaaad cbbbbb fbbbbbc gaaaaag cbbbbb ebbbbbd daaaaaad cbbbbb cbbbbbe aaaaaag fbbbbb fbbbbbbf daaaaaa fbbbbb dbbbbbbe aaaaaad fbbbbbd ebbbbbe gaaaaag fbbbbbd ebbbbbbd daaaaaad fbbbbbd cbbbbbbf gaaaaag fbbbbbd fbbbbbbc daaaaaa fbbbbbd dbbbbbbe aaaaaag fbbbbbd ebbbbbbd gaaaaaa fbbbbbd cbbbbbbf aaaaaad dbbbbbd fbbbbbbc ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#908dc8ff b,#099ecfff c,#85cde6ff d,#c4d9ecff e,#48b5daff f,#e3eaf4ff g,#b1b0d8ff ``` ```image ebb cbbb dbbbb dbbbbb fbbbbbb bbbeebb bbbe cbb bbbb cbb bbbb cbb bbbb cbbf ebbb cbbf ebbb dbbf cbbbf dbbd cbbbf dbbd daaa dbbbd fbbd gaaaaaa fbbbc fbbd gaaaaaaaag bbbe fbbc aaaaaag aaaf bbbe bbc faaaaaad faaa bbbb bbc faaaaaad gaaa bbbb bbcaaaaaaf aaaf bbbb eaaaaaa cabf ebbb aaaaag bbb ebbb aaaaa dbbe cbbb faaabe bbb cbbbf aaabbe bbb dbbbd gaagbbe ebbf daa fbbbc aaa bbb bbb aaaf bbbc aaad bbb cbbc aaa bbbe faaa bbb bbb gaag bbbe aaaf bbb ebbe aaa bbbb daaa bbb dbbb daaa bbbb aaa bbb bbbd aaaf bbbb gaag bbb bbbe aaa ebbb aaa bbb ebbb gaag ebbb aaaf bbb cbbb aaa cbbbf faaa bbb bbbf faaa dbbbd aaa bbb bbbc aaad fbbbc gaag bbb bbbb aaa fbbbc aaa bbb cbbb gaag bbbe aaad bbb fbbb aaa bbbe aaa bbb bbbd faaa bbbb aaaf bbb bbbe aaad bbbb daaa bbb ebbb aaa bbbb aaa ebb dbbb gaaa ebbb gaag ebb bbbd aaaf ebbb aaa ebb bbbe faaa cbbbf aaad ebbebbb aaagbbbd faaa ebbbbb aaabbd aaa cbbbbf gaaac daaa cbbbc baaaf aaa cbbb bbbaaa gaag bb bbbbaaag aaa bbbb aaa aaaf bbbb daaa faaa e ebbb aaaf aaa ebb ebbb aaa gaag bbbb cbbbf gaag aaa bbbbdbbbf aaa aaad bbbbbbd daaa faaa bbbbc aaa aaaf fbbe faaf daaa f aag aaa aaa gaag aaa aaa gaa aaaf faad faaa aag aaa aaa gaag aaa aaa gaa aaad faad aaa aag aaaf aaa daaa aaa aaa gaagaag faaaaa aaaad aaaa aaa fag ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#7ed1baff b,#2b964bff c,#b4e3d5ff d,#8fc795ff e,#b0d7b1ff f,#54ab6dff g,#ecf6efff ``` ```image geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg geeeeeeeeeeeefeeeeeeeeeeeeeeeeeeeeeeeg geaeeeeeeeeedbbbeeeeeeeeeeeeeeeeeeeeeg geaaaeeeeeeefbdbbbdeeeeeeeeeeeeeeeeeeg geeeaaaeeeeebbeedbbbdeeeeeeeeeeeeeeeeg geeeeeaaaeeebfeeeedbbbdeeeeeeeeeeeeeeg geeeeeeeaaaabeeeeeeedbbbdeeeeeeeeeeeeg geeeeeeeeeafbaeeeeeeeedbbbdeeeeeeeeeeg geeeeeeeeeebbaaaeeeeeeeedbbbdeeeeeeeeg ag geeeeeeeeeebfeaaaaeeeeeeeeebbbdeeeeeeg ga geeeeeeeeeebdeeeaaaaeeeeeeeeebbbdeeefbd aa geeeeeeeeedbeeeeeeaaaaeeeeeeeeebbbfbbfbbg aa geeeeeeeeebbeeeeeeeeeaaaeeeeeeeeebbfeggbbf ag geeeeeeeeebbeeeeeeeeeeeaaaeeeeeeeeeeeg ebbe ga geeeeeeeeebdeeeeeeeeeeeeeaaaeeeeeeeeeg fbbg aa geeeeeeeedbeeeeeeeeeeeeeeeeaaaeeeeeeeg gbbf aa geeeeeeeefbeeeeeeeeeeeeeeeeeeaaaaeeeeg dbbc ag geeeeeeeebbeeeeeeeeeeeeeeeeeeeeaaaeeeg bbb ga geeeeeeeebfeeeeeeeeeeeeeeeeeeeeeeaaeeg ebbd gddddddddddddddaadddddd geeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeaaeg fbbg geeeeeeeeeeeeeeaaeeeeee geeeeeeefbeeeeeeeeeeeeeeeeeeeeeeeeeaag gbbf geeeeeeeeeeeeeeaeeeeeee geeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeag dbbc geeeeeeeeeeeeeeaeeeeeee geeeeeeebfeeeeeeeeeeeeeeeeeeeeeeeeeeaa bbb geeeeeeeeeeeeeaaeeeeeee gdeeeeeebdeeeeeeeeeeeeeeeeeeeeeeeeeeda cbbd geeeeeeeeeeeeeaaeeeeeee ggggggebggggggggggggggggggggggggggggaa fbbg geeeeeeeeeeeeeaeeeeeeee fb ca gbbfgeeeeeeeeeeeeeaeeeeeeee bf aa dbbdeeeeeeeeeeeaaeeeeeeee be ca bbbeeeeeeeeeeaaeeeeeeee cb ac gdbbfeeeeeeeeaeeeeeeeee fb aa geefbbdeeeeeeaeeeeeeeee bb ac geeeebbbeeeeaaeeeeeeeee bd aa geeeeedbbdeeaaeeeeeeeee gbg ag geeeeeeebbbeaeeeeeeeeee db aa geeeeeeeedbbfeeeeeeeeee bb gag geeeeeeeeeefbbdeeeeeeee bd aa geeeeeeeeeeaabbbeeeeeee bg ga geeeeeeeeeeaeedbbfeeeee eb aa geeeeeeeeeeaeeeebbbeeee fb ca geeeeeeeeeaaeeeeedbeeee bf aa geeeeeeeeeaaeeeeeeeeeee bc ca geeeeeeeeeaaeeeeeeeeeee cb ac geeeeeeeeeaeeeeeeeeeeee fb ca geeeeeeeeaaeeeeeeeeeeee bb ac geeeeeeeeaaeeeeeeeeeeee be aa geeeeeeeeaaeeeeeeeeeeee gb ac geeeeeeeeaeeeeeeeeeeeee db aa geeeeeeeaaeeeeeeeeeeeee bb gag geeeeeeeaaeeeeeeeeeeeee bd aa geeeeeeeaaeeeeeeeeeeeee dg gag geeeeeeeaeeeeeeeeeeeeee aa gddddddaadddddddddddddd ca aa aa ac ca ga ac ca ca aa ac ac aa a ac ca aa aa gag ac aa ag gag ca aa aa ca ac aa ag ca ca ac aa ca ac ac ag aa ca ac aa aa ac gag ag aa ca gag aa aa ac ga ag aaa caa ac ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#7cd1baff b,#2b964bff c,#c3e6d8ff d,#7fc093ff e,#a0d9c2ff f,#57ad72ff g,#e3f3edff ``` ```image cfdg bbbbdg gac cbbbbbbdg eaaacg ebbbbbbbbdg aaaaaaeg dbbdefbbbbbdg ceaaaaaeg bbbc efbbbbbdg geaaaaaeg gbbb efbbbbbdg geaaaaaeg ebbf cfbbbbbdc geaaaaaec dbbd cfbbbbbfc geaaaaaac fbbc cfbbbbbfc gcaaaaaacbbbg cfbbbbbfc caaaadbbf cfbbbbbfc caafbbfcg cdbbbbbfc cfbbfaaeg gdbbbbbfe bbbaaaaaeg gdbbbbbfe cbbbceaaaaaeg gdbbbbbfe ebbf geaaaaaeg gdbbbbbfe dbbe geaaaaaec gdbbbbbbe bbbc geaaaaaac gdbbbbbbe cf gbbb gcaaaaaac gdbbbbbbe cfbb ebbf gcaaaaaac gdbbbbbbfbbbb dbbd caaaaaac ebbbbbbbbd fbbc caaaaaacg ebbbbfc gbbbg caaaaaaeg edc cbbf ceaaaaaeg dbbd geaaaaaeg fbbe geaaaaaeg bbbg geaaaaaec cbbb geaaaaaac ebbd gcaaaaaac fbbe caaaaaac bbbc caaaaaac gbbb caaaaae ebbf ceaaae dbbd caaae fbbc caaae gbbbg caaae cbbf caaae dbbd caaa fbbe eaa bbbg gaa cbbb ea ebbd ga fbbe e bbbc c ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Alright, let's examine the next area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#7cd1baff b,#2c974bff c,#c5e9ddff d,#82c297ff e,#a5dcc9ff f,#53aa6eff g,#e6f5efff ``` ```image caae eaac aaag gaaa caae eaac aaag gaaa caae eaac aaag gaaa caae eaac aaag gaaa dg caae bbe eaac bbbfg aaag bbbbbd gaaa gdbbbbfc caae cfbbbbdg eaac dbbbbbe aaag gfbbbbfc gaaa ebbbbbd caae gdbbbbfc eaac cfbbbbdg aaag ebbbbbe gaaa gdbbbbfc caae efbbbbdgeaac dbbbbbdaag cfbbbbfa ebbbbbd gfbbbbfc adbbbbbdg gaaadbbbbbe caae gfbbbbfg eaac ebbbbbd aaag gdbbbbfc gaaa cfbbbbdg caae dbbbbd eaac gfbbg aaag ee gaaa caae eaac aaag gaaa caae eaac aaag gaaa caae eaac aaag gaaa caae eaac aaag gaaa caae eaac aaag gaaa caae ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area B. Answer: A: 1; B: 1; 1 + 1 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#7cd1baff b,#2b964bff c,#c9e9ddff d,#83c196ff e,#a8dcc8ff f,#55ab70ff g,#e7f5f0ff ``` ```image fg ag cbbbg aaag dbebbbg caaag bb ebbbc gaaac bd cbbbc gaaaebg cbbbc afbe cbbbe bbaae gbbbe ac bf eaae gbbbe ca bc eaaa gbbbe fbd aa eb eaaa gbbbfbbfbbc ae fb caaag bbf gbbf ac bf caaag ebbe ca be gaaac fbbg ea cb gaaac cbbf aa fb aaac dbbc ac bb aaa bbb ga bd aa ebbd ea gbg aa fbbg aa db aa gbbf ac bb gag dbbe ga bd aa bbb ea bc ca ebbd aa eb aa fbbg ac fb ca gbbf ga bf ae dbbe ea be ea bbb aa cb ae cbbd ac fb ea fbbc ga bb ac gbbf ea bd aa ebbe aa gb ac fbbgac db aa cbbf bb gag fbbc bd aa aabbb bc ca ac ebbd eb aa ga fbbg bb ca ea gbg bf ae aa be ea ac cb ae ga fb ea ea bb ac aa bd aa ac gb ac ga db aa ea bb gag aa bd aa ac dg gag ga aa ea ca aa aa ac ea ga ae ea ea aa ae ae aa a ac ea aa aa gag ae aa ag gag ca aa aa ca ae aa ag ca ca ae aa ea ae ae ag aa ca ac aa aa ae gac ag aa ca gag aa aa ae ca ag aaa caa ae ``` <!-- end of image -->
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Time to put on my detective hat and find those intersection points! These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#4a223eff b,#e5dac3ff c,#99be98ff d,#b0d7b0ff e,#d8c27aff f,#f1f5eeff g,#7a6571ff ``` ```image f a cab afg bg a a a a gb gb fg a a cc a a gb bg fg a a a a gb gb a bg cc a b a a fe bg gb e a bg ef a a be e gb a e fb a gb e e cc bg eb bb a a be e bg a e e a gf ef fe a bg eb e gb gg fe bb a accccccccccccccccccccccccf e e cc agddddddddddddddddddddddf ef e a facdddddddddddddddddddddf bb fe bg fdacddddddddddddddddddddffe ffffffefffffffffffffafff fddacdddddddddddddddddddfe cdddddeeddddddddddddaddcf fdddacddddddddddddddddddef cddddddedddddddddddgcdddf fddddadddddddddddddddddee cddddddedddddddddddaddddf fdddddaddddddddddddddddef cdddddddedddddddddggddddf fddddddaddddddddddddddedf cdddddddedddddddddadddddf fdddddddaddddddddddddeddf cddddddddedddddddcadddddf fdddddddcadddddddddddeddf cddddddddedddddddaddddddf ef fddddddddcadddddddddedddf cddddddddedddddddaddddddf eee fdddddddddcaddddddeeddddf cdddddddddedddddadddddddf bb ee fdddddddddegaeeeeeddddddf cdddddddddeddddaddddddddf e feb fdeeeeeeeeddgaddddddddddf cddddddddddeddadddddddddf e beeeeedddddddddddgadddddddddf cddddddddddecaddddddddddf e fdddddddddddddggddddddddf cddddddddddeadddddddddddf fe fddddddddddddddggdddddddf cdddddddddcaedddddddddddf bb fdddddddddddddddagddddddf cddddddddcadedddddddddddf e fddddddddddddddddagdddddf cdddddddcadddeddddddddddf e fdddddddddddddddddagddddf cddddddcaddddeddddddddddf e fddddddddddddddddddacdddf cdddddcadddddeddddddddddf fb fdddddddddddddddddddacddf cddddcadddddddedddddddddf bf fddddddddddddddddddddacdf cdddgaddddddddedddddddddf e fdddddddddddddddddddddacf cddgaddddddddddeddddddddf e fddddddddddddddddddddddaf cdgadddddddddddeddddddddf e fcdddddddddddddddddddddca cgaddddddddddddeddddddddf fb ffffffffffffffffffffffffa ccddddddddddddddedddddddf bf fa cdddddddddddddddedddddddf e fa cddddddddddddddddeddddddf e ba dcccccccccccccccceccccccf e ba bb bb da e ef ca e e gg fe e gg e e gg bb bb gg e e ac ef e ac e e a e fe bb bb e e ef e e e e fb bbbf ee ee e ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#4c243fff b,#e8d9abff c,#a995a3ff d,#ccc1c9ff e,#dbc177ff f,#eee8dcff g,#78596cff ``` ```image feb aa ee cac beb aaf ee dag bef gad feb fag ee cac beb aa ee cac bef gaf feb dag ee gad beb fag ee cac bef aa feb cac eef gaf feb gag ee gag bef gag feb gag eef fgag feb fgag ee fgag beffgag feeaag eaac faag faage faacbef faac ee daac bef daac feb daac ee daac beb daad ee daad bef daad feb daad ee daad beb caad ee caad bef caad feb caad ee caaf feb caaf ee caaf bef faaf feb df eef feb ee bef fee ``` <!-- end of image --> Success! This area contains 1 intersection point! Now, let's turn our attention to the next spot. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#4a213dff b,#e8d9abff c,#967d8bff d,#c3b5bdff e,#dac074ff f,#ede6ddff g,#6a485fff ``` ```image d ad aad daad daad daaf daaf daaf cagf cagf cagf cag b cag fe gag ee gac beb gac fee fgac feef fgac eef fgac beb faad fee faad eef faad beb daad beb daad ffbbee daaf ffbbbeeeeeeeef fffbbcaaeeeeeeeebbbff ffbbbeeeeeeeeecaadbff ffbbbeeeeeeeeeebbbfff cagf eeeeeeebbbff cagf bbff cagf cag cag gag gac gac fgac fgac fgac faad faad faad daad daad daaf daaf daaf cagf cagf cag ca c ``` <!-- end of image --> I observe 1 intersection inside area B. Answer: A: 1; B: 1; 1 + 1 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#4b223eff b,#e8d8a8ff c,#a6929fff d,#d5cbd2ff e,#dbc176ff f,#f0e9daff g,#77596eff ``` ```image f a cad afg dg a a a a gd gd fg a a cc a a gd dg fg a a a a gd gd a fg cc a f a a e dg gd e a dg ef a a bb e gd a e fb a gf e e cc dg ef bf a a fe e dg a e e a gf e fb a dg bb e gd gc fe bf a ac e e cc ac ef e a ad bb e fg ad e e a af e bb a af ef e gd a bb e a a e e cc a e e a fa ef fb fg fa fe e a ef da e ef a eee da fbe e a ff ee fbcaeeeebf e a e feb fbeeeeebbf ca fb fa e beeebbf cg efa e gg ea b gg fae bf gc da e e ac da fb e ac da e e ad da bf fb ad da e bf af ca e e af ca fb e a ca e e a ca bf fb a d e bf fa e e fa fe e da e e da bf fb ca e b ca e e cg e e gg e e gg bb ff gc e e ac e e ac e e a e b fb bf e e bf e e e e fb fbbf ee be e ``` <!-- end of image -->
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Let's examine this image for potential line intersections. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#945b0dff b,#f362e5ff c,#aea36fff d,#b2d7b1ff e,#e095d8ff f,#a37e3eff g,#99c895ff ``` ```image faf e aaa ebbe caaa bbbbb aaaa ebbbbb daaaa ebbbbb aaaaa bbbbbb dggggggggggggggggaaaaagggggggggggggggggggggggggggggggggggggggg bbbbbe gdddddddddddddddfaafaadddddddddddddddddddddddddddddddddddddddd bbbbbe gdddddddddddddddaaafaadddddddddddddddddddddddddddddddddddddddd bbbbbe gddddddddddddddcaacfaadddddddddddddddddddddddddddddddddddddddd bbbbb gddddddddddddddaaadcaadddddddddddddddddddddddddddddddddddddddd ebbbbb gdddddddddddddgaafdcaadddddddddddddddddddddddddddddddddddddddd ebbbbb gdddddddddddddaaaddcaadddddddddddddddddddddddddddddddddddddddd bbbbbbdddddddddddddaaaddgaadddddddddddddddddddddddddddddddddddddddd bbbbbeddddddddddfaadddgaagddddddddddddddddddddddddddddddddddddddd bbbbbeddddddddaaaddddaagddddddddddddddddddddddddddddddddddddddd gbbbbbedddddcaacddddaacddddddddddddddddddddddddddddddddddbdddd gdebbbbbddddaaadddddaacdddddddddddddddddddddddddddddddddbbbddd gdddebbbbbddaafdddddaacdddddddddddddddddddddddddddddddebbbbddd gdddddebbbbbaaddddddaafddddddddddddddddddddddddddddddbbbbedddd gdddddddbbbbbbddddddaafddddddddddddddddddddddddddddebbbbdddddd gdddddddddbbbbbeddddaafdddddddddddddddddddddddddddbbbbeddddddd gdddddddddaabbbbbeddaafdddddddddddddddddddddddddebbbbddddddddd gddddddddgaacdbbbbbeaaaddddddddddddddddddddddddbbbbedddddddddd gddddddddaaadddebbbbbfaddddddddddddddddddddddebbbbdddddddcdddd gddddddddaaadddddebbbbbdddddddddddddddddddddbbbbedddddddcaaddd gdddddddfaaddddddddebbbbbdddddddddddddddddebbbbdddddddddaaaddd gdddddddaaadddddddddabbbbbbddddddddddddddbbbbedddddddddaaagddd gddddddcaacdddddddddaaabbbbbbedddddddddebbbbddddddddddfaafdddd gddddddaaaddddddddddaaaddbbbbbbbedddddbbbbeddddddddddcaaaddddd gdddddgaafddddddddddaaaddddebbbbbbbeebbbbddddddddddddaaadddddd gdddddaaadddddddddddfaadddddddebbbbbbbbeddddddddddddaaacdddddd gdddddaaadddddddddddfaaddddddddddebbbbdddddddddddddfaafddddddd gddddfaagdddddddddddfaadddddddddddddedddddddddddddgaaadddddddd gddddaaaddddddddddddfaadddddddddddddddddddddddddddaaaddddddddd gdddcaacddddddddddddcaaddddddddddddddddddddddddddaaacddddddddd gdddaaadddddddddddddcaadddddddddddddddddddddddddfaaadddddddddd gdddaafdddddddddddddcaadddddddddddddddddddddddddaaaddddddddddd gddfaaddddddddddddddgaaddddddddddddddddddddddddaaagddddddddddd gddaaaddddddddddddddgaagddddddddddddddddddddddaaafdddddddddddd gdcaacddddddddddddddgaagdddddddddddddddddddddcaaaddddddddddddd aaa aad aaa aac aad aaad aaa aac faaf aaa aac daaa faa aac aaa aaa aaf aaad daad aaf dcfaaaaaaaaf aaa aaafaaaaaaaaaaaaaaaaaa aaf aaaaaaaaaaaaaaaaafcd faa aaaaaaafcd aaa caa aaa daac aaa aaf faa aaa caad aaa aac aaa aaa aaa aaaa aaaa aaaa aaaa aaaa aaaa aaaf aaaf aaaf aaaf aaaf aaaf aaaf aaaf aaac ac ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#945b0cff b,#f362e5ff c,#c09d70ff d,#dac7acff e,#f797eeff f,#a8743cff g,#f6d9ecff ``` ```image aaaaaaaac daaaaaaaac faaaafaaac caaaagcaaac gaaaaf caaaf caaaad caaaf faaaf caaaf daaaad caaaf gaaaac daaaa caaaag daaaa aaaaa daaaa aaaaa daaaa bg aaaaa daaaag bbbeg caaaag gaaaag bbbbbe gaaaac gaaaag bbbbbbbe caaaad gaaaad bbbbbbbbe aaaaf aaaad g gebbbbbbbbg daaaad aaaad geb gbbbbbbbbbg gaaaac aaaad gebbbbg gbbbbbbbbeg caaaag aaaad ebbbbbbb ebbbbbbbbe aaaaf aaaac gebbbbbbbe ebbbbbbbbbdaaaad aaaac bbbbbbbbg gebbbbbbbbfaaa aaaac gebbbbbbe gebbbbbbbbfa aaaac gbbbbbbbg gbbbbbbbbeg aaaac bbbbbbbbg gbbbbbbbbeg aaaaf ebbbbbbe fbbbbbbbbbe aaaaf gbbbbbbbg daacbbbbbbbbe aaaaf ebbbbbbbe faaafebbbbbbbbe aaaaf bbbbbbbbg caaaag gebbbbbbbbfaaaa gbbbbbbbg gaaaac gbbbbbbbbbfaa ebbbbbbbe gd caaaad gbbbbbbbbbf bbbbbbbbg facg faaaf ebbbbbbbbb ebbbbbbe aaafd daaaad ebbbbbbbbe gbbbbbbbg daaaaa aaaaa bbbbbbbbbb bbbbbbbbg caaaaf aaaaa afbbbbbbbbeg ebbbbbbe daaaaag aaaaf aaafbbbbbbbbbeg gbbbbbbbg gaaaaad daaaad aaaaabbbbbbbbbbeg ebbbbbbbe faaaaf faaaf aaaaa ebbbbbbbbbbbeg bbbbbbbbg caaaaag daaaac aaaaa ebbbbbbbbbbbeg ebbbbbbeg aaaaad gaaaac faaaa gebbbbbbbbbbbbbgebbbbbbbe faaaaf caaaad faaaa gbbbbbbbbbbbbbbbbbbbg caaaaag aaaaf faaaa gebbbbbbbbbbbbbbeg daaaaad daaaad faaaa gbbbbbbbbbbbe gfaaaac faaaa faaaa gebbbbbbbe faaaaf caaaag caaaa gg aaaaad aaaaa caaaa aaaaa aaaaa caaaa caaaaf aaaaf caaaa daaaaad daaaac caaaa gaaaaac gaaaac daaaa caaaaag caaaag daaaa daaaaad aaaaf daaaa aaaaac daaaad daaaa aaaaa faaaa daaaa caaaaa caaaag gaaaag faaaac gaaaac gaaaag caaaaf caaaad gaaaad daaaaag ``` <!-- end of image --> 2 intersections present within area A. Answer: A: 2; 2 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#945b0dff b,#f362e5ff c,#c2a275ff d,#dac7acff e,#f79eefff f,#aa7d40ff g,#f4e5e6ff ``` ```image faf e aaa ebbe caaa bbbbbg aaaa ebbbbb daaaa ebbbbb aaaaa ebbbbb aaaaa bbbbbe faafaa bbbbbe aaacaa gbbbbbe caadcaa gbbbbbg aaa caa ebbbbb gaac daa ebbbbb aaa daa bbbbbb aaa daag bbbbbe faag gaag bbbbbe aaa gaad gbbbbbe daad aad b gbbbbbg aaa aad gbbb ebbbbb gaaf aac ebbbb ebbbbbaa aac gbbbbe bbbbbb aac ebbbb bbbbbe aaf bbbbe aabbbbbe aaf ebbbb daacgbbbbbeaaf bbbbe aaa gbbbbbfa ebbbb d aaf ebbbbb bbbbe caa faag ebbbbb ebbbb gaaa aaa abbbbbb bbbbe aaag daad aaabbbbbbe ebbbb faaf aaa aaa bbbbbbbe bbbbe daaa gaac aaa ebbbbbbbeebbbbg aaa aaa faa ebbbbbbbbe aaad aaa faa ebbbbg faaf caag caa e gaaa aaa caa aaag daac caa aaac aaa daa caaa aaf daa gaaa faa daag aaag aaa gaag faac caad gaag daaa aaa aad aaa gaac aad aaad aaa aac faaf aaa aac daaa faag aac aaa aaa aaf aaad daad aaf gdcfaaaaaaaaf aaa aaafaaaaaaaaaaaaaaaaaa gaaf aaaaaaaaaaaaaaaaafcdg faa aaaaaaafcdg aaa caag aaa daac aaa aaf faa aaa daad aaa gaac aaa aaa aaag aaaa aaaa aaaa aaaa aaaa aaaa aaaf aaaf aaaf aaaf aaaf aaaf aaaf gaaaf aaaf gac g ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#52d290ff b,#9ec084ff c,#b1d7b1ff d,#76d59fff e,#edf6eeff f,#99cb98ff g,#cce8d0ff ``` ```image e aaa cbe caaa bbbc aaaag gbbbbb eeeeeeeeeeeeeeeeeedaaaaaeeeeeeeeeeeeeeeeeeeeee cbbbbbbe efccccccccccccccccfaaaaaacccccccccccccccccccccf bbbgbbbbg ecccccccccccccccccaaaaaaadccccccccccccccccccccf bbb ebbbbf ecccccccccccccccccaaaccaaaccccccccccccccccccccf bbb bbbbb eccccccccccccccccaaadccaaaccccccccccccccccccccf gbbc cbbbbgcccccccccccccccfaaacccaaadcccccccccccccccccccf cbbg ebbbbbccccccccccccccaaadccccaaacccccccccccccccccccf bbb bbbbbccccccccccccdaaacccccaaacccccccccccccccccccf bbb cbbbbcccccccccccaaaccccccaaadccccccccccccccccccf bbb gbbbbfccccccccaaaacccccccaaaccccccccccccccccccf gbbc ecbbbbbcccccccaaaccccccccaaaccccccccccccccccccf fbbg eccbbbbbcccccaaaaccccccccdaadcccccccccccccccccf bbb ecccfbbbbfcccaaaccccccccccaaacccccccccccccccccf bbb ecccccbbbbbcaaadccccccccccaaacccccccccccccccccf ebbb eccccccbbbbdaaacccccccccccdaadccccccccccccccccf gbbc ecccccccfbbaaafccccccccccccaaaccccccccccccccccf bbbe ecccccccccdaaabccccccccccccaaaccccccccccccccccf bbb ecccccccccaaabbbcccccccccccdaadcccccccccccccccf bbb eccccccccaaaabbbbcccccccccccaaacccccccccccccccf ebbb eccccccccaaaccbbbbfcccccccccaaacccccccccccccccf gbbc ecccccccaaaacccbbbbbccccccccdaadccccccccccccccf bbbe eccccccfaaacccccbbbbbccccccccaaaccccccccccccccf bbb eccccccaaadccccccfbbbbfccccccaaaccccccccccccccf bbb ecccccdaaacccccccccbbbbbcccccdaaacccccccccccccf ebbb ecccccaaafccccccccccbbbbbcccccaaacccccccccccccf cbbc eccccdaaaccccccccccccfbbbbccccaaacccccccccccccf bbbe eccccaaacccccccccccccccbbbbbccdaaaccccccccccccf bbb ecccaaaaccccccccccccccccbbbbbccaaaccccccccccccf bbb ecccaaaccccccccccccccccccbbbbbcaaafcccccccccccf ebbb eccaaadccccccccccccccccccccbbbbdaaacccccccccccf cbbg ecfaaaccccccccccccccccccccccbbbbaaacccccccccccf bbbe ecaaadcccccccccccccccccccccccbbbaaafccccccccccf bbb edaaacccccccccccccccccccccccccfbdaaaccccccccccf bbb eaaafcccccccccccccccccccccccccccbaaabcccccccccf gbbf daaacccccccccccccccccccccccccccccaaabbccccccccf cbbg aaaccccccccccccccccccccccccccccccfaaabbcccccccf bbb aaaacccccccccccccccccccccccccccccccaaabbbbcccccf bbb eaaaccccccccccccccccccccccccccccccccaaafbbbbccccf bbb aaadccccccccccccccccccccccccccccccccfaaabbbbbcccf gbbf gaaaccccccccccccccccccccccccccccccccccaaaccbbbbfcf cbbg aaacccccccccccccccccccccccccccccccccccaaadccbbbbbf bbb caaaeccccccccccccccccccccccccccccccccccfaaacccbbbbbe bbb aaagecccccccccccccccccccccccccccccccccccaaaccccfbbbbg bbb daaa ecccccccccccccccccccccccccccccccccccaaadcccccbbbbf gbbc aaae ecccccccccccccccccccccccccccccccccccfaaaccccccbbbbb fbbg aaad eccccccccccccccccccccccccccccccccccccaaaccccccfcbbbbg bbb eaaa eccccccccccccccccccccccccccccccccccccaaadcccccf ebbbbc bbb aaad ecccccccccccccccccccccccccccccccccccccaaacccccf bbbbb bbb gaaa ecccccccccccccccccccccccccccccccccccccaaacccccf cbbbbe gbbc aaag efffffffffffffffffffffffffffffffffffffaaadffffc gbbbbc fbbe caaa eaaa bbbbb bbb aaae aaag fbbbg bbb daaa caaa gbf ebbb aaae aaaa e gbbc aaad aaac bbbe eaaa gaaa bbb aaad aaaa gcb gaaa aaac aaag gaaa caaa aaaa aaae aaac daaa gaaae aaa daaa aaad aaad eaaa gaaae aaac daaa gaaa aaad aaag eaaae caaa daaa aaae aaad daaa eaaae eaaa daaa aaad aaad eaaa eaaag aaac daaa gaaa aaaa aaag eaaag caa cad e g ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#52d290ff b,#9ec084ff c,#9de5c0ff d,#73d8a3ff e,#e6f5eaff f,#b8d1a5ff g,#caead2ff ``` ```image gaaaaaaaaaaac daaaaaaaaaaad caaaaaacaaaaaae eaaaaaad daaaaac caaaaaag caaaaad eaaaaaad eaaaaaae daaaaaae daaaaac gaaaaaac caaaaad daaaaaae eaaaaaae e gaaaaaac daaaaac bg aaaaaaa caaaaad bbf caaaaaag eaaaaaae bbbbe eaaaaaad daaaaac bbbbbg caaaaaag caaaaad bbbbbbf eaaaaaad eaaaaaae bbbbbbbfe daaaaaae daaaaac bbbbbbbbbg gaaaaaac caaaaaa gbbbbbbbbbf daaaaaae eaaaaaag efbbbbbbbbfe gaaaaaac daaaaac fbbbbbbbbbe aaaaaaa gaaaaaa gbbbbbbbbbg caaaaaag eaaaaaag ebbbbbbbbbf eaaaaaad daaaaac fbbbbbbbbbe caaaaaag gaaaaaa gbbbbbbbbbg eaaaaaad eaaaaaag ebbbbbbbbbf daaaaaae daaaaac efbbbbbbbbfe gaaaaaac gaaaaaa fbbbbbbbbbgdaaaaaae aaaaaag gbbbbbbbbdaaaaaac daaaaac efbbbbbbaaaaaad gaaaaaa fbbbbdaaaaaag aaaaaag gbbbaaaaaad caaaaad ebaaaaaaabf gaaaaaa gaaaaaaabbbe aaaaaag daaaaaabbbbbg caaaaad gaaaaaadbbbbbbf gaaaaaae daaaaaabbbbbbbbfe aaaaaag caaaaaacfbbbbbbbbbg caaaaad aaaaaad gbbbbbbbbbf gaaaaaae caaaaaag efbbbbbbbbfe aaaaaag eaaaaaad fbbbbbbbbbe caaaaad caaaaaae gbbbbbbbbbg gaaaaaae eaaaaaac ebbbbbbbbbf aaaaaac daaaaaae fbbbbbbbbbe caaaaad gaaaaaac gbbbbbbbbbg eaaaaaae daaaaaa ebbbbbbbbbf daaaaac caaaaaac efbbbbbbbbfe caaaaad aaaaaad fbbbbbbbbbg eaaaaaae caaaaaag gbbbbbbbbbf daaaaac eaaaaaad efbbbbbbbbfe caaaaad daaaaaae fbbbbbbbbbe eaaaaaae eaaaaaac gbbbbbbbbbg daaaaac daaaaaae ebbbbbbbbbf caaaaad gaaaaaac fbbbbbbbbbe eaaaaaae daaaaaa gbbbbbbbbbg daaaaac caaaaaag ebbbbbbbbbf caaaaad eaaaaaad efbbbbbbbbfeeaaaaaae caaaaaag fbbbbbbbbbgdaaaaac eaaaaaad gbbbbbbbbbdaaaaad daaaaaae efbbbbbbbbaaaaaae gaaaaaac fbbbbbbbaaaaaac daaaaaae gbbbbbbdaaaaaa gaaaaaac ebbbbbbaaaaaag daaaaaa fbbbbaaaaaac caaaaaag gbbbdaaaaaa eaaaaaad ebbbaaaaaaf caaaaaag efbaaaaaaabe eaaaaaad gbaaaaaabbg daaaaaae gaaaaaabbbf aaaaaac daaaaaabbbfe aaaaaae gaaaaaabbbbbe aaaaac aaaaaabbbbbbg aaaaa daaaaaabbbbbbf aaaag gaaaaaabbbbbbbbe aaad aaaaaabbbbbbbbbg aaag caaaaadbbbbbbbbbf aad gaaaaaaefbbbbbbbbbe aae aaaaaag gbbbbbbbbbg ac caaaaad gbbbbbbbbbf ae gaaaaaae efbbbbbbbbfe c aaaaaag fbbbbbbbbb caaaaad gbbbbbbbb gaaaaaae ebbbbbbb aaaaaag fbbbbb caaaaad gbbbb gaaaaaae ebbb aaaaaac efb caaaaad g eaaaaaae daaaaac caaaaad eaaaaaae daaaaac caaaaad eaaaaaae daaaaac caaaaad eaaaaaae ``` <!-- end of image --> There's no doubt about it - I see 2 intersections in area A. Answer: A: 2; 2 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#52d290ff b,#9ec084ff c,#9fe5c1ff d,#74daa5ff e,#e7f5ebff f,#b9d1a7ff g,#cfe9d1ff ``` ```image e aaa fbe caaa bbbf aaaac gbbbbb daaaaa fbbbbbb aaaaaa bbbgbbbbg aaaddaac bbb ebbbbf eaaa eaaa bbb bbbbb aaac aaa gbbf fbbbbe gaaa daac fbbg ebbbbf aaag eaaa bbb bbbbb caaa aaa bbb fbbbbe aaae daac bbb gbbbbf daaa eaaa gbbf bbbbb aaa aaa fbbg bbbbb aaad daac bbb gbbbbg eaaa eaaa bbb ebbbbf aaac aaa bbb bbbbbaaa daad gbbf fbbaaag aaa bbbe eaaaaf aaa bbb aaabbb caad bbb daaabbbbe aaa ebbb aaa gbbbbf aaae gbbf aaad bbbbb caad bbbe eaaa bbbbb aaa bbb aaac gbbbbg aaae bbb caaa ebbbbb caad ebbb aaag bbbbb aaa fbbf daaa fbbbbg aaae bbbe aaae ebbbbf caad bbb daaa bbbbb aaa bbb eaaa fbbbbeaaae ebbb aaad gbbbbdaaa fbbg gaaa bbbbaaa bbbe aaac bbbaaag bbb caaa gbbaaa bbb aaag ebaaab gbbb daaa aaabb fbbg aaae gaaabbg bbb aaaa aaabbbf bbb eaaa aaabbbbb bbb aaad gaaafbbbbe gbbf gaaa aaa gbbbbf fbbg aaac aaag bbbbb bbb caaa gaaa bbbbbe bbb aaag aaa gbbbbg bbb daaa aaac ebbbbb gbbf aaae eaaa bbbbb fbbg aaad aaa fbbbbg bbb eaaa daac ebbbbf bbb aaad eaaa bbbbb bbb gaaa aaa fbbbbe gbbf aaac daac gbbbbf bbbe caaa eaaa bbbbb bbb aaae aaac bbbbg bbb daaa caaa gbf ebbb aaa aaaa e gbbf aaad aaac bbbe eaaa caaa bbb aaac aaaa gfb gaaa aaac aaac gaaa caaa aaaa aaae aaac daaa gaaae aaa daaa aaad aaad eaaa gaaae aaac daaa gaaa aaad aaag eaaae caaa daaa aaae aaad daaa eaaae aaa daaa aaad aaad eaaa eaaag aaac caaa caaa aaaa aaag aaag caa cad e g ``` <!-- end of image -->
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I'm on the case! Let's uncover any intersections hidden in this image. I've noticed 2 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#0cd41cff b,#c454a7ff c,#93cd94ff d,#d19cc1ff e,#4dd456ff f,#edf0ecff g,#b1d7b1ff ``` ```image fffffffffffffffggffff fcggggggggggggggaaacgg fgggggggggggggggaaaggg fgggggggggggggggaaaggg fggggggggggggggeaacggg fggggggggggggggaaagggg fggggggggggggggaaagggg fgggggggggggggcaaegggg fgggggggggggggaaaggggg fgggggggggggggaaaggggg fggggggggggggcaaeggggg fggggggggggggeaacggggg fggggggggggggaaagggggg fggggggggggggaaagggggg fgggggggggggeaaegggggg fggggggggggbbaaggggggg fggggggggbbbbbaggggggg fggggggdbbbbbbeggggggg fgggggbbbbbbbbcggggggg fgggbbbbbbgbbbgggggggg fgdbbbbbgggbbbgggggggg fbbbbbdgggebbbgggggggg bbbbbbgggggaebbgggggggg dbbbbbgggggggaebbdggggggg bbbbbdgggggggcaabbdggggggg dbbbbdfggggggggaaabbbggggggg dbbbbb fggggggggaaabbbggggggg bbbbbd fggggggggaaabbbggggggg dbbbbb fgggggggeaacbbbggggggg fbbbbbf fgggggggaaagbbbggggggg bbbbbd fgggggggaaagdbbggggggg dbbbbb fggggggcaaegdbbggggggg fbbbbbf fggggggaaagggbbdgggggg bbbbbd fggggggaaagggbbbgggggg gccccccccccccccccccccccg dbbbbb fggggggaaegggbbbgggggg cggggggggggggggggggggggc fbbbbbf fgggggeaacgggbbbgggggg cggggggggggggggggggggggc bbbbbd fgggggaaaggggbbbgggggg cggggggggggggggggggggggc dbbbbb fgggggaaaggggbbbgggggg cggggggggggggggggggggggc fbbbbbf cccceaaeccccbbbcccccc cggggggggggggggggggggggc bbbbbd aaa dbbf cggggggggggggggggggggggc dbbbbb aaa fbbd cggggggggggggggggggggggc fbbbbbf faae bbd cggggggggggggggggggggggc bbbbbd eaaf bbb faccggggggggggggggggggggggcdbbbbb aaa bbb aaaaggggggggggggggggggggggbbbbbf aaa bbb eaaaaeggggggggggggggggggbbbbbd caag bbb faaaaagggggggggggggggdbbbbb aaa bbb eaaaaeggggggggggggbbbbbc aaa dbb cgaaaaacggggggggbbbbbbgc gaae dbbf cggeaaaaagggggdbbbbbgggc eaaf fbbd cggggaaaaacggbbbbbdggggc aaa bbd cgggggcaaaabbbbbbggggggc aaa bbb cgggggggeebbbbbggggggggc caag bbb cgggggggbbbbbeaggggggggc aaa bbb cgggggbbbbbbaaaaeggggggc aaa bbb cgggdbbbbbgggaaaaacggggc gaac bbb cggbbbbbdgggggeaaaaagggc aaa dbbf cbbbbbbgggggggggaaaaacgc aaa fbbf fbbbbbggggggggggggcaaaaac faae fbbd bbbbbdgggggggggggggggaaaaac eaag bbb bbbbbggggggggggggggggggcaaaaaf aaa bbb dbbcgggggggggggggggggggggeaaaae aaa bbb d cggggggggggggggggggggggcaaaaaf gaac bbb cggggggggggggggggggggggc caaaae aaa bbb cggggggggggggggggggggggc aaaaag aaa cggggggggggggggggggggggc gaaaaa faae cggggggggggggggggggggggc eaaaac eaaf cggggggggggggggggggggggc faaaaa aaa cggggggggggggggggggggggc eaaaae aaa cggggggggggggggggggggggc faaaaaf caac cggggggggggggggggggggggc caaaae aaa gccccccccccccccccccccccg aaaaag aaa gaaaaa faae aaaaag eaaf faaaaa aaa eaaaac aaa faaaaaf caag caaaae aaa aaaaaaaa gaaaaae aaaa gae ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0cd41bff b,#c554a7ff c,#74dd7cff d,#dd9bccff e,#3cd547ff f,#ebe6e8ff g,#b4efb8ff ``` ```image ef aac f aaaeg db aaaaac fbbb aaaaaaeg fdbbbb aaaaaaaacf dbbbbbb eaaaaaaaaag fbbbbbbbb caaaaaaaaaef dbbbbbbbbb geaaaaaaaaac dbbbbbbbbbbd caaaaaaaaaeg fbbbbbbbbbbdf feaaaaaaaaac dbbbbbbbbbbf gaaaaaaaaaeg dbbbbbbbbbbd fcaaaaaaaaacf fbbbbbbbbbbdf geaaaaaaaaag dbbbbbbbbbbf caaaaaaaaaefdbbbbbbbbbbd geaaaaaaaebbbbbbbbbbdf caaaaacbbbbbbbbbbd feaebbbbbbbbbbd fbbbbbbbbbbbg dbbbbbbbbbbeaacf fbbbbbbbbbbcaaaaaag fdbbbbbbbbbbeaaaaaaaaef dbbbbbbbbbbd geaaaaaaaaag fbbbbbbbbbbd caaaaaaaaaef fdbbbbbbbbbbf feaaaaaaaaac dbbbbbbbbbbd gaaaaaaaaaeg fbbbbbbbbbbdf feaaaaaaaaac fdbbbbbbbbbbf gaaaaaaaaaag dbbbbbbbbbbd fcaaaaaaaaaef bbbbbbbbbbdf geaaaaaaaaa bbbbbbbbbf caaaaaaaa bbbbbbbd geaaaaaa bbbbbdf caaaaa bbbbf feaaa bbd gaa df fc ``` <!-- end of image --> I observe 1 intersection inside area A. Alright, let's examine the next area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#0bd41bff b,#c453a7ff c,#a4ebaaff d,#d997c8ff e,#30d33cff f,#e7e1e3ff g,#69d66fff ``` ```image gaaagc eaaaaa faaaaag caaaaac eaaaaaf aaaaae caaaaag gaaaaac eaaaaa faaaaag caaaaac eaaaaaf faaaaae caaaaag gaaaaaf aaaaae caaaaag gaaaaac eaaaaa faaaaae caaaaac gaaaaaf aaaaae caaaaag gaaaaac eaaaaa faaaaag caaaaac fdgeaaaaf fdbbbbeaae dbbbbbbgaag fbbbbbbbbbaac fdbbbbbbbbbbaa dbbbbbbbbbbbbag fbbbbbbbbbbbbbbec fdbbbbbbbbbbbbbbbef dbbbbbbbbbbdfbbbbbg fbbbbbbbbbbd cbbbbbc dbbbbbbbbbbf gbbbbbd dbbbbbbbbbbd abbbbbd fbbbbbbbbbbdf fabbbbbb dbbbbbbbbbbf gabbbbbb bbbbbbbbbd eagbbbbb bbbbbbbdf faagbbbbbf bbbbbbf caagbbbbbf bbbbd gaaebbbbbd bbdf aaaebbbbbd bf caaaabbbbbd gaaaabbbbbd eaaaabbbbbb faaaaabbbbbb caaaaadbbbbb gaaaaadbbbbbf aaaaaefbbbbbf caaaaagfbbbbbd gaaaaac bbbbbd eaaaaa bbbbbd faaaaag bbbbbb caaaaac dbbbbb eaaaaaf dbbbbb aaaaae dbbbbbf caaaaag dbbbbbf gaaaaac fbbbbbf eaaaaa fbbbbbd faaaaag bbbbbd gaaaaac bbbbbd eaaaaaf bbbbbb faaaaae dbbbbb caaaaac dbbbbb gaaaaaf dbbbbbf aaaaae fbbbbbf caaaaag fbbbbbd gaaaaac fbbbbbd eaaaaa bbbbbd ``` <!-- end of image --> As I suspected, there's 1 intersection within area B. Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#0cd41cff b,#c453a7ff c,#8aea91ff d,#d98fc5ff e,#49d854ff f,#ecc9e3ff g,#c7f4caff ``` ```image gg aaa aaa aae eaag aaa aaa caac aaa aaa gaae eaag aaa aaa caac fbbaa bbbbba dbbbbbbe bbbbbbbb bbbbbd bbb fbbbbb bbb bbbbbf cbbb bbbbbd aebbf fbbbbb aebbf bbbbbf gaabbd dbbbbd eaabbb fbbbbb aaabbb bbbbbf aaebbb dbbbbd caagbbb fbbbbb aaa bbb bbbbbf aaa dbb dbbbbb gaac fbbf fbbbbb aaa fbbd bbbbbd aaa bbd dbbbbb aae bbb fbbbbb eaag bbb bbbbbd aaa bbb dbbbbb aaa bbb fbbbbbf caac dbb bbbbbd aaa dbb dbbbbb aaa fbbf fbbbbbf gaae bbd bbbbbd eaag bbb ac dbbbbb aaa bbb aaaa bbbbbf aaa bbb eaaaac bbbbbd caac bbb aaaaa fbbbbb aaa bbb caaaae bbbbbf aaa dbb aaaaag dbbbbd gaae fbbf caaaaa fbbbbb eaa fbbd aaaaac bbbbbf aaa bbd gaaaabbbbbd aaa bbb eebbbbb caag bbb bbbbbea aaa bbb dbbbbbaaaae aaa bbb fbbbbb aaaaag gaac dbb bbbbbf caaaae aaa dbb dbbbbb aaaaag aaa fbbf fbbbbb gaaaaa aae bbd bbbbbd eaaaac eaag bbb bbbbb gaaaaa aaa bbb dbbf eaaaae aaa bbb d aaaaag caac bbb caaaae aaa bbb aaaaag aaa gaaaaa gaae eaaaac eaag gaaaaa aaa eaaaae aaa aaaaag caac caaaae aaa aaaaag aaa caaaaa gaae aaaaac eaa gaaaaa aaa eaaaac aaa aaaaa caag caaaae aaa aaaaaaaa caaaaac aaaa gae ``` <!-- end of image -->
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This is the image I'm working with. The goal is to count the intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#b8ec2fff b,#daf4a4ff c,#99e035ff d,#f0f9e4ff e,#b9e867ff f,#b1d7b1ff g,#97cb95ff ``` ```image bccccccccccccccccccceeeed bcccccccccccccccccccccccc ddddbbbbbbbeeeeeeccccccccd cce ecc gggggggggggggggggggggggggggggggggggggggf dcc dfffffffffffffffffffffffffffffffffffffffg cce dffffffffffffffffffffffffaafffffffffffffg ecc dffffffffffffffffffffffffaaeffffffffffffg dcc dfffffffffffffffffffffffaaaaffffffffffffg cce dffffffffffffffffffffffeaaaaffffffffffffg ccc dffffffffffffffffffffffaaaaaffffffffffffg dcc dfffffffffffffffffffffeaafaagfffffffffffg ccb dfffffffffffffffffffffaaafaaefffffffffffg ccc dffffffffffffffffffffaaaffaaafffffffffffg bcc dffffffffffffffffffffaaeffeaafffffffffffg ccb dfffffffffffffffffffaaaffffaafffffffffffg ccc dfffffffffffffffffffaaeffffaagffffffffffg bcc dffffffffffffffffffaaafffffaaeffffffffffg bd ccb dfffffffffffffffffeaaffffffaaacgffffffffg aaa ccc dfffffffffffffffffaaafffffgaaaccffffffffg daae bcc dffffffffffffffffeaafffffcccaacccfffffffg eaad ccb dffffffffffffffffaaafffcccccaaecccffffffg aaa ccc dfffffffffffffffaaaffeccccgfaaeeccefffffg daaa bcc dfffffffffffffffaaefccccefffaaafcccfffffg baab ccd dffffffffffffffaaacccccfffffeaaffcccffffg aaa cce dfffffffffffffgaaccccffffffffaafffcccfffg aaa ecc dfffffffffffffaaaccefffffffffaafffecceffg baab ccd dffffffffffffaaaccfffffffffffaaefffcccgfg aaa cce dffffffffffccaaafffffffffffffaaaffffcccfg aaa ecc dffffffffeccaaaffffffffffffffeaafffffcccg daae dccd dfffffffccccaaefffffffffffffffaafffffgccc eaad cce dfffffcccccaaaffffffffffffffffaaffffffcccb aaa ecc dfffeccccgfaaeffffffffffffffffaaeffffffccc daae dcc dfgcccceffaaafffffffffffffffffaaafffffffcd eaad cce dcccccfffeaaffffffffffffffffffeaafffffffg aaa ccc eccccfffffaaafffffffffffffffffffaafffffffg daaa dcc bccccefffffeaaffffffffffffffffffffaafffffffg baab ccccccefffffffaaaffffffffffffffffffffaaeffffffg aaa cccccddffffffaaafffffffffffffffffffffaaaffffffg aaa dccb dffffffaaefffffffffffffffffffffeaaffffffg baab dfffffaaafffffffffffffffffffffffaaffffffg aaa dfffffaaefffffffffffffffffffffffaaffffffg aaa dffffeaaffffffffffffffffffffffffaaefffffg daae ggggaaaggggggggggggggggggggggggaaagggggf eaad baa eaa aaa aaa daa daae daad aad eaad aaa aab aaa aab aaa aaa eaa eaa baab aae daa aaa baa aad aaa aaa aab baab baad aaa aaa aaa eaa aaa daad daa daae aaa aad eaad aab aab aaa eaa aaa daae aae eaa eaad baa baa aaa aaa aad aaa daad aab baab aaa aaa aaa daab eaa aaaaaa baa baaaab aa aaaa aab aae aae e eaa baa aa aab aae eaa baa aa aab aae eaa bae ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#b8ec2eff b,#ccf180ff c,#99e135ff d,#f4fbe4ff e,#dbf5a6ff f,#bbec58ff g,#e8f8c8ff ``` ```image eed faaad eaaaae daaaaab baaaaaa gaaaaaaad faaaaaaag gaaaaaaaae faaaaaaaab eaaaaaaaaaf daaaaabfaaaad baaaaadbaaaag daaaaae eaaaae baaaaf gaaaab gaaaaag daaaaf faaaaf aaaaad eaaaaag baaaag aaaaab eaaaae eaaaaad gaaaab daaaaab daaaaf baaaaa aaaaad daaaaae baaaag faaaaf eaaaae gaaaaag gaaaabgd faaaaf daaaaaccb eaaaaad aaaaaccce daaaaab dfaaaaccccg baaaaad ecaaaaacccccd daaaaae gfcccaaaaaccccf baaaaf dbcccccaaaaaccccce gaaaaae ecccccccaaaaafcccccg faaaaf gfccccccccfaaaaeccccccd eaaaaag dfccccccccbdbaaaaeecccccf faaaab bccccccccfg gaaaab bcccccb eaaaaad eccccccccce daaaaf fcccccg daaaaab dfccccccccbd aaaaa dccccccd baaaaadbccccccccfg faaaag gcccccf daaaaabccccccccce baaaae bcccccb faaaaaccccccccb eaaaab fccccce gaaaaacccccccfd daaaaf dccccccd faaaaacccccfg aaaaa gcccccf eaaaaaccccce faaaag ecccccb gaaaaaacccbd baaaae fccccce baaaaaaccfg eaaaab dccccccg eccaaaaacce daaaaf gccccccd gfccaaaaaabd aaaaa ecccccf dbccccaaaaae faaaag bccccce ecccccaaaaaf baaaae fcccccg gfccccccaaaaag eaaaab dcccccc dbcccccccaaaaab daaaaf eccccc eccccccccaaaaaad aaaaa bcccc gfccccccccbaaaaab faaaad fccc dfccccccccbdbaaaaad baaaae dccc bccccccccfg daaaaae eaaaab gcc eccccccccce faaaaf daaaaf bc gfccccccccbd gaaaaag aaaaa f dbccccccccfd faaaaf faaaad d eccccccccce eaaaaag baaaae fccccccccb aaaaab eaaaab cccccccfd baaaaad daaaaf cccccfg daaaaae aaaaa cccce baaaaa faaaad ccbd gaaaaae baaaae fg faaaaf eaaaab gaaaaag gaaaaf faaaab aaaaa eaaaaad faaaad faaaab baaaae gaaaaad eaaaab faaaab gaaaaf gaaaaad aaaaa baaaab faaaad daaaaag baaaae baaaaf eaaaab ``` <!-- end of image --> Bingo! This close-up reveals 2 intersections in area A! Answer: A: 2; 2 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#b8ec2eff b,#d3f291ff c,#99e134ff d,#f1faddff e,#c7ef72ff f,#b8eb52ff g,#e2f6b7ff ``` ```image bcccccccccccccccccccfffed bcccccccccccccccccccccccc dddggggbbbeeeffffcccccccd ccf ecc dcc cce fa fcc daae dcc aaaa cce gaaaa fcc aaaaa dcc baadaag ccb aaf aae ccc faa faa gcc aae baa ccb aaa daa ccc daag aag gcc aaa aaed bd ccg gaad aaacg aaa ccc aaa gaaacc daaf bcc eaa dcccaaccc eaad ccg aaf fccccaagccc aaa ccc faa bccccg aaeeccb daaf bcc daabdcccce aaa cccd baag ccd aaaccccc baa ccc aaa ccf gaaccccd daa dccc aaa ecc aaaccb aad bcce baab ccd aaacf aae fccd aaa ccf fcaaad aaa ccc aaa ecc gccaaa baa ccc gaae dcc dccccaae daa gccf faad cce fccccaaa aad fccg aaa fcc bccccddaab aab ccc daaf dcc dccccb aaa aaa cd eaad cce ccccc gaad baa aaa fcc eccccd aaa daa aaf dcc gccccb eaa aad baag ccccccf aaf aab aaa ccccc faa aaa aaa dccg aab eaa gaab faa daa aaa aae aad aaa baa aab gaae aaf aaa faad gaa eaa aaa aaa daa daaf daad aad eaad aaa aab aaa aab aaa aaa eaa eaa baag aae gaa aaa baa aad aaa aaf aab gaab gaa aaf aaa aaa eaa aaa daag gaa daae aaa aad faad aab aab aaa eaa aaf daaf aae eaa eaad baa gaa aaa aaa aa aaa gaad aab baag aaa aaf aaa aag eaa aaafaa gaa gaaaab aa aaaa aab aae aaf e eaa gaa aa aag aaf faa gaa aa aag aaf faa gae ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#f1f2efff b,#eb0ebbff c,#63638cff d,#b1d7b1ff e,#d86ebeff f,#2b3d74ff g,#90bb9aff ``` ```image bea bbba bbb abbb ebbb bbbe bbba bbb abbb ebbb bbbe bbba bbb abbb ebbb bbbe bbba ebb bbb bbbb abbb aaaaaaaaaaabbbbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaebbbaaaaa agdddddddddgbbbbbedddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbeddddg addddddddddebbbbbbeddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbdddddg addddddddddbbbebbbbddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbdddddg addddddddddbbbddbbbbddddddddddddddddddddddddddddddddddddddddddddddddddddddddebbbdddddg addddddddddbbbdddbbbbdddddddddddddddddddddddddddddddddddddddddddddddddddddddebbbdddddg adddddddddebbbdddebbbbddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbedddddg adddddddddebbbdddcffbbbdddddddddddddddddddddddddddddddddddddddddddddddddddddbbbddddddg adddddddddbbbedddfffcbbeddddddddddddddddddddddddddddddddddddddddddddddddddddbbbddddddg adddddddddbbbdddgffffbbbeddddddddddddddddddddddddddddddddddddddddddddddddddebbbddddddg adddddddddbbbdddfffffbbbbddddddddddddddddddddddddddddddddddddddddddddddddddebbbddddddg addddddddebbbdddfffffdbbbbdddddddddddddddddddddddddddddddddddddddddddddddddbbbeddddddg addddddddbbbbddgfffffddbbbbddddddddddddddddddddddddddddddddddddddddddddddddbbbdddddddg addddddddbbbeddffffffgdebbbbdddddddddddddddddddddddddddddddddddddddddddddddbbbdddddddg addddddddbbbdddffffffcddebbbbdddddddddddddddddddddddddddddddddddddddddddddebbbdddddddg addddddddbbbddgfffcfffdddbbbbeddddddddddddddddddddddddddddddddddddddddddddebbbdddddddg adddddddebbbddfffcgfffddddbbbbedddddddddddddddddddddddddddddddddddddddddddbbbedddddddg adddddddbbbeddfffddfffdddddbbbbdddddddddddddddddddddddddddddddddddddddddddbbbddddddddg adddddddbbbedcfffddfffddddddbbbbddddddddddddddddddddddddddddddddddddddddddbbbddddddddg adddddddbbbddfffcddfffgddddddbbbbddddddddddddddddddddddddddddddddddddddddebbbddddddddg adddddddbbbddfffdddfffcddddddebbbbdddddddddddddddddddddddddddddddddddddddebbbddddddddg addddddebbbdcfffdddcfffdddddddebbbbddddddddddddddddddddddddddddddddddddddbbbeddddddddg addddddbbbedfffcdddgfffddddddddbbbbedddddddddddddddddddddddddddddddddddddbbbdddddddddg addddddbbbddfffdddddfffdddddddddbbbbeddddddddddddddddddddddddddddddddddddbbbdddddddddg addddddbbbdcfffdddddfffddddddddddbbbbdddddddddddddddddddddddddddddddddddebbbdddddddddg adddddebbbdfffcdddddfffgddddddddddbbbbddddddddddddddddddddddddddddddddddbbbbdddddddddg adddddbbbbdfffddddddfffcdddddddddddbbbbdddddddddddddddddddddddddddddddggcfffffffffdddg adddddbbbecfffddddddcfffdddddddddddebbbbddddddddddddddddddddgccffffffffffffffffffffddg adddddbbbdfffcddddddgfffddddddddddddebbbbddddddddggccffffffffffffffffffffffffffffffcdg adddddbbbdfffddddddddfffdddddddddddddbbbccffffffffffffffffffffffffffffffffcggdddffffdg addddebbbcfffddddddddfffddddggccfffffffffffffffffffffffffffffffccgdddddbbbbddddddffffg addddbbbbfffgddddddddfffffffffffffffffffffffffffffffccggdddddddddddddddbbbeddddddgfgdg addddbbbefffdddddddddfffffffffffffffffffffccgddddddddddddddddddddddddddbbbdddddddddddg addddbbbffffdddddddddgfffffffffccggddddddbbbbddddddddddddddddddddddddddbbbdddddddddddg addddbbbfffgdddddddddddgdddddddddddddddddebbbbddddddddddddddddddddddddebbbdddddddddddg adddebbbfffdddddddddddddddddddddddddddddddebbbbdddddddddddddddddddddddbbbbdddddddddddg adddbbbffffddddddddddddddddddddddddddddddddbbbbeddddddddddddddddddddddbbbedddddddddddg adddbbbfffgdddddddddddddddddddddddddddddddddbbbbddddddddddddddddddddddbbbddddddddddddg adddbbbfffdddddddddddddddddddddddddddddddddddbbbbdddddddddddddddddddddbbbddddddddddddg addebbffffddddddddddddddddddddddddddddddddddddbbbbdddddddddddddddddddebbbddddddddddddg addebbfffgdddddddddddddddddddddddddddddddddddddbbbbddddddddddddddddddbbbbddddddddddddg addbbbfffddddddddddddddddddddddddddddddddddddddebbbbdddddddddddddddddbbbeddddddddddddg addbbffffdddddddddddddddddddddddddddddddddddddddbbbbbddddddddddddddddbbbdddddddddddddg addbbfffgddddddddddddddddddddddddddddddddddddddddbbbbedddddddddddddddbbbdddddddddddddg adebcfffddddddddddddddddddddddddddddddddddddddddddbbbbddddddddddddddebbbdddddddddddddg adbbfffcdddddddddddddddddddddddddddddddddddddddddddbbbbdddddddddddddbbbbdddddddddddddg agbbfffgddddddddddddddddddddddddddddddddddddddddddddbbbbddddddddddddbbbedddddddddddddg abcfffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbaaaaaaaaaaabbbaaaaaaaaaaaaaaa afffc ebbbb abbb fffa bbbbe ebbb gfff bbbbe bbbe fffc bbbba bbbe fff bbbb bbb acf abbbb abbb abbbb ebbb ebbbb bbbe bbbbe bbba bbbbebbb bbbbbbb bbbbbb abbbbe abbba ebb ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#ead1eaff b,#ec0cbcff c,#626a96ff d,#a1a9c1ff e,#ef42caff f,#2b3d74ff g,#f58cdeff ``` ```image ebbbbbe ebbbb bbbbbbbb bbbbg bbbbbbbbg abbbbg bbbbbbbbbb ebbbb bbbbgbbbbba ebbbe gbbbb bbbbbe bbbbg ebbbb ebbbbb bbbba bbbbg abbbbb bbbb abbbbg bbbbba bbbb ebbbb ffffbbe gbbbb bbbbe affffbbb ebbbb bbbba fffffbbbbg bbbbg bbbb dfffffbbbbb abbbbg bbbb ffffffgbbbbba ebbbb abbbb ffffffdbbbbbe bbbbe ebbbb ffffffc ebbbbe bbbbg ebbbe dffffffc abbbbbg bbbba abbbbg ffffffff gbbbbba bbbb gbbbba dffffffff gbbbbba abbbb bbbbe ffffcffff ebbbbb gbbbb bbbbg ffffdcfff ebbbbe ebbbb bbbba affff dfffa bbbbbb abbbbg bbbb dffff afffd gbbbbba gbbbbg abbbb affffc fffc bbbbbe ebbbb gbbbb dffffd ffff ebbbbb bbbbe ebbbe ffffc ffffa abbbbbg bbbba bbbbe ffffd ffffd bbbbbb bbbba gbbbba affff cfffc gbbbbba bbbb ebbbb dffff cffff bbbbbe abbbb bbbbg affffc dffff bbbbbg gbbbb bbbbg cffffd affff abbbbbg ebbbb bbbb ffffc cfff gbbbbba abbbbg bbbb ffffa cfff gbbbbba gbbbba gbbbb dffff afffd ebbbbb ebbbb gbbbb cffff afffd abbbbbg bbbbeaddccffd bbbbedffffd ffff bbbbbb aaddccffffffffffffffffff abbbbgcffffa ffff gbbbbba aaddccfffffffffffffffffffffffffa ebbbb ffffd ffffd bbbbbe aaddccffffffffffffffffffffffffffffffffffffffffd ebbbe ffffa ffffd ebbbbb addccffffffffffffffffffffffffffffffffffffffffcccfffff bbbbgdffff cffff addccffffffffffffffffffffffffffffffffffffffffccddaebbbb dffffc bbbbacffff dffff aaddccfffffffffffffffffffffffffffffffffffffffffcddda ebbbe fffff bbbbdffffd affffffffffffffffffffffffffffffffffffffffccddda abbbbg affd abbbbcffffa ffffffffffffffffffffffffffffffffffccdda gbbbba da gbbbbffffd ffffffffffffffffffffccddabbbbbg ebbbe ebbbbffff ffffffffffffccddaa abbbbbg bbbbe abbbbcffff aaa gbbbbba bbbba gbbbbfffff ebbbbe bbbb ebbbcffffd ebbbbb bbbb bbbbfffff abbbbbg abbbb bbbbffffd bbbbbb ebbbb bbbbffff gbbbbba ebbbe bbbcffff bbbbbe abbbbg abbbfffff ebbbbb gbbbba ebbcffffa abbbbbg ebbbe bbbfffff bbbbbb bbbbg gbbbffffa ebbbbe bbbba gbbbffff bbbbbe bbbb bbbfffff abbbbbg bbbb bbbffffc abbbbbg abbbb bbfffffa gbbbbba ebbbb bbffffc ebbbbe ebbbe abbffffa ebbbbb abbbbg ``` <!-- end of image --> Eureka! There's definitely 2 intersections in area A! Answer: A: 2; 2 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#f8b0e8ff b,#ec0dbcff c,#92229aff d,#bdc3d3ff e,#f259d1ff f,#2c3d74ff g,#737ea3ff ``` ```image bea bbba bbb abbb ebbb bbbe bbba bbb abbb ebbb bbbe bbba bbb abbb ebbb bbbe bbba abb bbb bbbb abbb bbbbb ebbb abbbbbe bbbe ebbbbbba bbba bbbebbbba bbb bbba bbbb abbb bbb bbbb ebbb abbb acbbb bbbe ebbb gffbbb bbba bbbe fffcbbe bbb bbb dffffbbba abbb bbb fffffbbbb ebbb abbb fffff bbbb bbbe bbbe dfffff abbbb bbb bbba ffffffd abbbb bbb bbb ffffffg ebbbb abbb bbb dfffgfff bbbbe ebbb ebbb fffgdfff bbbba bbbe bbbe fff fff bbbb bbb bbba gfff fff bbbb bbb bbb fffg fffd abbbb abbb abbb fff fffg abbbb ebbb ebbb gfff gfff ebbbe bbbe bbbe fffg dfff bbbbe bbb bbba fff fff bbbba bbb bbb gfff fff bbbb abbb abbb fffg fffd bbbb ebbb ebbb fff fffg abbbb ddcfffffffff bbbagfff gfff abbbb dggffffffffffffffffffff bbb fffg dfff ebbbe ddggffffffffffffffffffffffffffffffg bbb fff fff bbccgffffffffffffffffffffffffffffffffcdd ffff abbbgfff fff ddggfffffffffffffffffffffffffffffffggd ebbb ffff bbbefffd fffffffffffffffffffffffffffffffggdd bbba dfd bbbafff fffffffffffffffffffffccd bbb bbbffff dfffffffffggdd abbbb bbb abbbfffd d abbbb abbb ebbbfff ebbbe ebbb bbbffff bbbbe bbba bbbfffd bbbba bbb bbcfff bbbb bbb abbffff bbbb abbb ebbfffd abbbb bbbe bbcfff ebbbb bbba bbffff ebbbe bbb bbfffd bbbba bbb abcfff bbbba abbb bbfffg bbbb bbbe bbfff bbbb bbba bcfff abbbb bbb afffg ebbbb bbb fff ebbbe abbb gfff bbbba bbbe fffg bbbba bbba fff bbbb bbb gf bbbb bbb abbbb ebbb ebbbb bbbe ebbbe bbba bbbbabbb bbbbbbb bbbbbb bbbbe abbba ebb ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f10f8ff b,#e2e0a6ff c,#a89ce4ff d,#744deeff e,#eff3efff f,#a4d0a5ff g,#b2d7b1ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeee ffffffffffffffffffffffffe ebbe fggggggggggggggggggggggfe bbbbbbbbggggggggggggggggggggggfe bb ebbbbbbbbbbggggggggggggggggfe bb fggbbbbbgggggggggggggggfe bb fgggggbbgggggggggggggggfe ebe fggggggbgggggggggggggdafe bb fggggggbbgggggggggggaaade eac bb fggggggbbggggggggggaaaaae aa bb fgggggggbbggggggggaaagdae eaa bb fgggggggbbgggggggaadggcac dae ebe fggggggggbbgggggaadggggaa aa bb fggggggggbbggggaadgggggaa cad ebe fgggggggggbgggaadggggggdae aa bb fgggggggggbbgaadgggggggfad eaa bb fgggggggggbbaadggggggggfaa dac bb fggggggggggaacgggggggggfaa aa bb fgggggggggaacggggggggggfcae ead ebe fggggggggaacbbgggggggggfead aae bb fgggggggaacgbbgggggggggfeaa aa bb fggggggaacgggbgggggggggfeda cac bb fggggfaafggggbbggggggggfeeac aa bb fgggfaafgggggbbggggggggfe aa beeeeeeeeaaeeeeeeeeeeeeeeeeeeeeeeebe fggfaafgggggggbbgggggggfe aa bbfffffffaacfffffffffffffffffffffbbfe fggaagggggggggbbgggggggfe cae ebbgggggggaagggggggggggggggggggggbbfe fgcacggggggggggbbggggggfe ad ebbbggggggcadgggggggggggggggggggbbgfe fgaagggggggggggbbggggggfe aa efbbgggggggaagggggggggggggggggggbbgfe fgaaggggggggggggbggggggfe aa efgbbgggggggaaggggggggggggggggggbggfe fdacggggggggggggbbgggggfe cac efggbbggggggdacggggggggggggggggbbggfe faagggggggggggggbbgggggfe ad efggbbgggggggaaggggggggggggggggbbggfe fadggggggggggggggbbggggfe aa efgggbbggggggcaaggggggggggggggbbgggfe dagggggggggggggggbbggggfe da efggggbbggggggaafgggggggggggggbbgggfe aaggggggggggggggggbbgggfe eac efggggbbgggggggaaggggggggggggbbggggfe eadffffffffffffffffbbffffe aa efgggggbbggggggdadgggggggggggbbggggfe aaeeeeeeeeeeeeeeeeeebeeee aa efggggggbbggggggaagggggggggggbbggggfe aa bb cae efggggggbbbgggggfaagggggggggbbgggggfe cae bbe ad efgggggggbbggggggdacggggggggbbgggggfe aa bb efggggggggbbggggggaagggggggbbggggggfe ad bb efgggggggggbbgggggcadggggggbbggggggfe dae bb efgggggggggbbggggggaaggggggbbggggggfe aa bb efggggggggggbbggggggaaggggbbgggggggfe eac ebe efgggggggggggbbgggggdacgggbbgggggggfe aa bb efgggggggggggbbbgggggaaggbbggggggggfe aa bbe efggggggggggggbbgggggcaagbbggggggggfe cac bb efgggggggggggggbbgggggaagbgggggggggfe aa bb efgggggggggggggbbbggggcagbgggggggggfe ad bb efggggggggggggggbbgggggadbgggggggggfe dae bb efgggggggggggggggbbggggaaggggggggggfe aa ebe efggggggggggggggggbbgggaaggggggggggfe eac bb efggggggggggggggggbbgggcacgggggggggfe aa bbe efgggggggggggggggggbbgbbadgggggggggfe aa bb efggggggggggggggggggbbbbaagggggggggfe cac bb efggggggggggggggggggbbbgaagggggggggfe aa bb efgggggggggggggggggggbbgcacggggggggfe ad bb efgggggggggggggggggggggggadggggggggfe dae ebe efgggggggggggggggggggggggaaggggggggfe aa bb efgggggggggggggggggggggggaaggggggggfe eac bbe efgggggggggggggggggggggggcacgggggggfe aa bb efggggggggggggggggggggggggadgggggggfe aa bb efggggggggggggggggggggggggaagggggggfe cac bb efggggggggggggggggggggggggaagggggggfe aa e efggggggggggggggggggggggggcacggggggfe ad efgggggggggggggggggggggggggadggggggfedae efgggggggggggggggggggggggggaaggggggfeaa effffffffffffffffffffffffffdafffffffead eeeeeeeeeeeeeeeeeeeeeeeeeecaceeeeeeda ad aa aa cac da aa cac aa ad dae aa aa da ead cac da ad aa aacac daaa caaa aae aa ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#4f0ff8ff b,#e4e0a5ff c,#cbb9fcff d,#7442f8ff e,#f4f2edff f,#eeebc7ff g,#9f7df8ff ``` ```image bbbe gaaag fbbb bbbf daaac ebbbf fbbbf caaad fbbbe ebbbbe gaaag bbbf ebbbb eaaaae fbbbe fbbbf caaad bbbb bbbbe daaac ebbbf ebbbb caaaae fbbbe fbbbf gaaag bbbf bbbbf daaac fbbbe ebbbbe caaad bbbb fbbbb daaag ebbbf fbbbf eaaaae fbbb bbbbe gaaag bbbf ebbbb daaac fbbbe fbbbf caaad bbbb bbbbe gaaag ebbbf ebbbb eaaaae fbbb fbbbf caaad ebbbf fbbbf daaac fbbbe ebbbbe eaaaae bbbb ebbbb gaaag ebbbf fbbbf daaac fbbb bbbbe caaad ebbbf ebbbb daaag fbbbe fbbbf eaaaae bbbf bbbbe gaaad ebbbe ebbbbe daaac bbbb fbbbf caaad ebbbf fbbbf gaaag fbbbe ebbbbe eaaaae bbbf ebbbb caaad fbbbe fbbbf daaac bbbb bbbbe eaaaae ebbbf ebbbb gaaag fbbb fbbbf daaac bbbf bbbbf caaad fbbbe ebbbbe gaaag bbbb fbbbb eaaaae ebbbf fbbbf gaaad fbbb bbbbe daaac ebbbf ebbbb caaad fbbbe fbbbf gaaag bbbb bbbbe eaaadebbbf ebbbb gaaafbbb fbbbf caaabbbf bbbbf eaaagbbe ebbbbe aaadbf ebbbb gaaabe fbbbf caaab bbbbe eaaag ebbbb faaad fbbbf bdaaa bbbbe fbgaaac ebbbbe bbbaaag fbbbf ebbbdaad fbbbffbbbgaaa ebbbbbbbfcaaac ebbbbbbeeaaag fbbbbb daad bbbbf gaaa ebbb caaac efe eaaag daad gaaa caaac eaaag daad gaaa caaac eaaag daad gaaa caaac eaaag daad gaaa caaac eaaag daad gaaa caaac eaaag daad ``` <!-- end of image --> Success! This area contains 1 intersection point! Alright, let's examine the next area. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#4e0ff8ff b,#e4e0a6ff c,#b398f5ff d,#6a35f9ff e,#e1d6fdff f,#f2f0d4ff g,#8c63f5ff ``` ```image bfff bbbbbbfff bbbbbbbbbbbbff bbbbbbbbbbbbbbf fffbbbbbbbbb ffbbbb bbbf bbbb gag fbbbf daaa bbbb edaaaa fbbbf edaaaaa bbbb edaaaaaa fbbb edaaadcaa bbbf edaaade aa bbbb edaaade da fbbbf eaaaade ca bbbb eaaaad ea fbbbf eaaaad a bbbb eaaaad g fbbb eaaaag c bbbf caaaag e bbbb caaaag fbbbf caaaag bbbb caaaag fbbbf caaaag bbbbcaaaag fbbgaaaac bgaaaac gaaaac gaaaac gaaaacb gaaaacbbf gaaaacbbbb gaaaae fbbb daaaae bbbf daaaae bbbb daaaae fbbbf edaaaae bbbb edaaade fbbbf edaaade bbbb edaaade fbbb edaaade bbbf edaaade bbbb eaaaad fbbbf caaad bbbb daad fbbbf eaaac bbbb gaaae fbbb aaag bbbf caaac bbbb daaa fbbbf eaaag bbbb caaae fbbbf daad bbbb eaaac fbbb gaaae bbbf aaag bbbb caaac fbbbf daaa bbbb aaag fbbbf aaae bbbb aad fbbb ``` <!-- end of image --> I observe 1 intersection inside area B. Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#4f0ff8ff b,#e4e0a6ff c,#b9a1f8ff d,#723ff9ff e,#dacdfdff f,#f1efd3ff g,#9771faff ``` ```image bff bbbbbbbbf bb ffbbbbbbbbf bb fbbbbb bb bb fbf fbf dae bb bb daad eag bf fb dadaa aa bb bb aad da eaa bb bb aad eac dae fb bb aad aa aa bb bb aad aa cad bf fbf aag ga aa bb bb aag ag aa bb fbaag aa dac fb aac aa aa bb aac cae ead fbf aacbb ad aae bb aae bb aa aa bb aae fbf da gag bb eaae bb eac aa bb eaae fb aa bf eaa fbf eaa bb aa bb dae bb aa bb ga bb aa bb eac bb ag fbf cad bb aa bb aa bb aa bb aa fbf aa bb aa fbf gae bb cae fbb gac bb aa fb ad bbf aa bf ad bb aa bb ead bb da bb da bb aae bb aa bb eac bbf aa fb eac bb aa bb gag bb aa fbf aa bb aa bf aa bb ga fbf eaa bb cae fb ag bb dae bb aa bb bb aa fb ad bb fbb cad bb da bb bbf aa fbf aa bb bb aa bb eag fbf bb gac bb aa bb bbf aa fb aa fb bb ead bb cae bb bb aafbf aa bb fbb cabb ad bb bb adb ga bb bb aa aa fbf fbb aa eag bb bbf fcae aa fb bb bbad aa bb bbbfaa cac bb fbb da aa bb bb cae ad bb ad ga fbf aa aa bb da eag fb cae da bb ad aa bb aa cac bb da aa cae ad ad gae aa aa da eag cae da ad aa aa cac da aa eac ad ad gae aa aa da ag eac da ad aa aacac daaa eaaa aae aa ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#675ddbff b,#9e9ac7ff c,#3118e0ff d,#c7c2e5ff e,#b0d6b1ff f,#96c996ff g,#eef3f2ff ``` ```image a accg gccc cccd accc gccc cccd bccc gbbg ccc dbbbg cccb bbbbbd bccc bbbbbbd ccc bbbgdbbbd ccca bbb gbbbb dccc dbbd gbbbb gggggggggggggggggggcccg bbb bbbbgfeeeeeeeeeeeeeeeeecccafg dbbd bbbbeeeeeeeeeeeeeeeeebccceeg bbb bbbbeeeeeeeeeeeeeeeeccceeeg gbbd bbbbeeeeeeeeeeeeeeaccceeeg bbb bbbbeeeeeeeeeeeeeccceeeeg gbbb gbbbbeeeeeeeeeeecccbeeeeg bbb gebbbbeeeeeeeeeaccceeeeeg gbbb geebbbbbeeeeeeeccceeeeeeg bbbg geeeebbbbeeeeecccbeeeeeeg bbb geeeeebbbbeeeaccceeeeeeeg bbbg geeeeeebbbbeeccceeeeeeeeg bbb geeeeeeebbbbcccaeeeeeeeeg dbbd geeeeeeeebbaccceeeeeeeeeg bbb geeeeeeeeebccceeeeeeeeeeg dbbd geeeeeeeeecccabeeeeeeeeeg bbb geeeeeeeebcccbbbeeeeeeeeg dbbd geeeeeeeecccebbbbeeeeeeeg bbb geeeeeeecccaeebbbbeeeeeeg gbbb geeeeeeeccceeeebbbbbeeeeg bbb geeeeeecccbeeeeeebbbbeeeg gbbb geeeeeaccceeeeeeeebbbbeeg bbb geeeeeccceeeeeeeeeebbbbeg bbb geeeecccbeeeeeeeeeeebbbbg bbbg geeeaccceeeeeeeeeeeeebbbb bbb geeeccceeeeeeeeeeeeeeebbbb dbbg geecccbeeeeeeeeeeeeeeeebbbbg gcc bbb geaccceeeeeeeeeeeeeeeeeebbbbg cccc dbbd gfccceeeeeeeeeeeeeeeeeefgbbbbg dcccca bbb cccbggggggggggggggggggg dbbbd ccccccg dbbd dccc dbbbg bccadccc bbb cccg dbd ccc ccccfffffffffffffbbbfffe ccca g acca fcccbeeeeeeeeeeebbbeeeef dccc ccc feccceeeeeeeeeeebbbeeeef cccg cccd feaccceeeeeeeeebbbeeeeef acca acc feecccaeeeeeeeebbbeeeeef gccc g feeeccceeeeeeebbbeeeeeef cccd feeebccceeeeeebbbeeeeeef accc feeeecccaeeeebbbeeeeeeef gccc feeeeecccbeeebbbeeeeeeef cccd feeeeebccceebbbeeeeeeeef bccc feeeeeeacccebbbeeeeeeeef ccc feeeeeeecccabbbeeeeeeeef cccb feeeeeeeecccbbeeeeeeeeef bccc feeeeeeeeacccbeeeeeeeeef ccc feeeeeeeeecccaeeeeeeeeef ccca feeeeeeeeebcccbeeeeeeeef dccc feeeeeeeebbbccceeeeeeeef cccg feeeeeeeebbbaccceeeeeeef acca feeeeeeebbbeecccbeeeeeef dccc feeeeeeebbbeeeccceeeeeef cccg feeeeeebbbeeeeaccceeeeef acca feeeeeebbbeeeeecccaeeeef gccc feeeeebbbeeeeeeeccceeeef cccd feeeeebbbeeeeeeebccceeef accc feeeebbbeeeeeeeeecccceef gccc feeeebbbeeeeeeeeeecccbef cccd feeeebbbeeeeeeeeeeecccef bccc feeebbbeeeeeeeeeeeeacccf ccc effbbbbfffffffffffffccca cccb bbbb cccbccc d bbbb dcccccg dbbd bbbb accca bbbbbddbbb ccc dbbbbbbbg b dbbbbg dbg ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#5440e4ff b,#9f99c7ff c,#3017e0ff d,#cecaeaff e,#b4aee1ff f,#8375e8ff g,#e9e7f6ff ``` ```image fccccccg bbbbbbg gaccccca gbbbbbe dccccccf ebbbbbg fccccccd gbbbbbe acccccag ebbbbbd gccccccf gbbbbbb ecccccce ebbbbbd fccccccg gbbbbbb gaccccca dbbbbbd dccccccf bbbbbb fccccccd dbbbbbd acccccag bbbbbbg gccccccf dbbbbbe ecccccce bbbbbbg fccccccg dbbbbbe gaccccca ebbbbbg dccccccf gbbbbbe fccccccd ebbbbbg accccca gbbbbbb dccccccf ebbbbbd ecccccce gbbbbbb accccccg dbbbbbd gccccccagbbbbbb eccccccfbbbbbd fccccccfbbbb accccccbbbd dccccccabbg eccccccfe accccccd dcccccca efcccccce gbbaccccccd ebbbcccccca gbbbbfccccccf ebbbbbfccccccd gbbbbbb acccccag dbbbbbd gccccccf bbbbbb ecccccce dbbbbbd fccccccg bbbbbbg gaccccca dbbbbbe dccccccf bbbbbbg fccccccd dbbbbbe acccccag ebbbbbg gccccccf gbbbbbe ecccccce ebbbbbg fccccccg gbbbbbb gaccccca ebbbbbd dccccccf gbbbbbb fccccccd dbbbbbd acccccag bbbbbb gccccccf dbbbbbd ecccccce bbbbbbg fccccccg dbbbbbd gaccccca bbbbbbg dccccccf dbbbbbe fccccccd ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Okay, let's proceed to the next area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#5642e4ff b,#9f99c7ff c,#3017e1ff d,#e0ddf3ff e,#bdb8deff f,#a094f0ff g,#7b6ce6ff ``` ```image dcccccce acccccg fccccccd e dccccccf be accccca bbe fccccccd bbbe dccccccf bbbbe accccca bbbbbb fccccccd bbbbbbbd dccccccf bbbbbbbbd gccccca ebbbbbbbd eccccccd ebbbbbbbd ccccccg ebbbbbbbd gccccca ebbbbbbbe ecccccce ebbbbbbbe acccccg dbbbbbbbe gccccccd dbbbbbbbe dcccccce dbbbbbbbe acccccg dbbbbbbbb fccccccd dbbbbbbbbd dccccccf bbbbbbbbd accccca ebbbbbbbd fccccccd ebbbbbbbeccccccf ebbbbbbaccccca ebbbbgccccccd ebbbccccccg dbacccccc fccccccge acccccabbe gccccccbbbbb eccccccgbbbbbbd acccccgbbbbbbbbd fccccccd ebbbbbbbd dccccccf ebbbbbbbd accccca ebbbbbbbd fccccccd ebbbbbbbe dccccccf ebbbbbbbe accccca dbbbbbbbe fccccccd dbbbbbbbe dccccccf dbbbbbbbe gccccca dbbbbbbbb eccccccd dbbbbbbbbd dccccccg bbbbbbbbd gccccca ebbbbbbbd ecccccce ebbbbbbb acccccg ebbbbbb gccccccd ebbbbb dcccccce ebbbb acccccg dbbb fccccccd dbb dccccccf db accccca d fccccccd dccccccf accccca ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#604de6ff b,#9f99c7ff c,#3118e1ff d,#d3cfecff e,#b8b3dfff f,#9083ecff g,#eae8f6ff ``` ```image a accg gccc cccd acca gccc ccce fccc bbg ccc ebbbg cccf bbbbbd eccc bbbbbbe ccc ebbgdbbbe cccf bbb gbbbb eccc ebbd gbbbb cccg bbb bbbb acca dbbe bbbb dccc bbb bbbb cccg dbbe bbbb acca bbb bbbbg gccc gbbb ebbbg cccd bbb ebbbd fccc bbb dbbbe ccc bbbg dbbbe ccce bbb gbbbb fccc bbbg gbbbb ccc bbb bbbbcccf ebbd bbaccc bbb bcccg dbbd cccab bbb dcccbbbg dbbe cccgebbbg bbb acca ebbbd gbbe gccc dbbbe bbb cccd dbbbe gbbb acca gbbbb bbb gccc gbbbb bbb cccd bbbb bbbg fccc bbbb bbb ccc bbbb ebbg ccce bbbb cc bbb fccc bbbbg cccc ebbd ccc ebbbg dccccf bbb cccf ebbbd ccccccg dbbe eccc dbbbd fccaeccc bbb cccg dbe ccc acca dbbe acca g accf cccd bbb dccc ccc gccc gbbb cccg ccce accc bbb acca acc cccf bbb gccc g cccg bbbg cccd eccc bbb acca ccca ebbg gccc cccd bbb ccce dccc ebbd fccc accc bbb ccc cccfbbd cccf cccbb eccc fccce ccc ccca cccf gbcccd dccc bbfccc cccg gbbbaccc acca bbb ccce dccc bbb gccc cccg bbbg fccc acca bbb ccca gccc ebbd cccg cccd bbb dccc fccc ebbd acca ccc bbb ccce ccce dbbe gccc fccc bbb fccc ccc bbbe cccf cccf bbbb cccfccc d bbbb eccccc dbbd ebbb acccf bbbbbdebbb ccc ebbbbbbb f ebbbbg ebg ``` <!-- end of image -->
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This image seems promising for intersection detection. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#6bc2d7ff b,#9dd8eaff c,#94c99bff d,#4e90d7ff e,#b1d7b1ff f,#29c2d3ff g,#d0ecf4ff ``` ```image b adda adda bddag bdddg bdddg gdddb gdddb gaddb adda adda bddag bdddg bdddg gdddb gdddb gaddb adda adda bddag ecccccccccccccccccc bdddg ceeeeeeeeeeeeeeeeee bdddceeeeeeeeeeeeeeeee cdddaeeaddeeeeeeeee ceecdddaedeeeeeeeee ceeeeeeeedeeeeeeeee ceeeeeeeedeeeeeeeee ceeeeeeeeaaeeeeeeee ceeeeeeeecdeeeeeeee ceeeeeeeeedeeeeeeee ceeeeeeeeedeeeeeeee ceeeeeeeeedeeeeeeee ceeeeeeeeeaaeeeeeee ceeeeeeeeecdeeeeeee ceeeeeeeeeedfeeeeee ceeeeeeeeeedfeeeeee ceeeeeeeeeeffeeeeee ceeeeeeeeeeffeeeeee ceeeeeeeeeeffeeeeee ceeeeeeeeeeffeeeeee ceeeeeeeeeeffeeeeee ceeeeeeeeeeffeeeeee ceeeeeeeeeaffaeeeee ceeeeeeeeeaafdeeeee ceeeeeeeeefcfdeeeee ceeeeeeeeefefdeeeee ceeeeeeeeefefdeeeee ceeeeeeeeefeafaeeee ceeeeeeeeefeaadeeee ceeeeeeeecfeaadeeee ceeeeeeeeaaeafdeeee ceeeeeeeefaecfceeee ceeeeeeeefeeefeeeee ceeeeeeeefeeefeeeee ceeeeeeeefeeefeeeee ceeeeeeeefeeefeeeee gf f ba f ab f fg f f f f f fffabg f f gbafffffab gf f gbffffffbg ba fg bafffffabg ab fg gbafffffab fg ab gbffffffbg f ab bafffffabg f aa gbafffffag f ba gbfffffabg gf ba bafffffabg ba gf gbafffffaab gf gaf f f f f f f f f ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5bceddff b,#bfe1f1ff c,#80aee2ff d,#4f91d8ff e,#96d3e8ff f,#28c1d3ff g,#e2f2f8ff ``` ```image dcb ddddcb gbg bcdddddcbg gbcdddd bcdddddccdddddddg beddddddcbgddb geeg cde edc bdd ddg ddb cde edc bdd gddg ddb cde edc bdd gddg ddb cde edc bdd gddaf ddffg cdffb edffb bfffb gfffb fffe fffe gfffe bfffe bfffa efffa afffa affff ffaff ffeffg gffbffb bffgffe efagffc efegffd afe ffdg ffb ffdb ffg ffde gff ffdc bff afdd efa afddg efa afddb afe afade afb afadc ffg efadd gffg efaddg bff efaddb efa efacde efa efaedc afe bfabdd afb bffgbg ffb bff gffg gff bff gff bfa gffg efa ffg afe ffg afe ffb ``` <!-- end of image --> Gotcha! I've found 2 intersections hiding in area A! Answer: A: 2; 2 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#55cedcff b,#b0ddeeff c,#86b2e4ff d,#4f90d8ff e,#82dbe5ff f,#28c2d3ff g,#dbeff7ff ``` ```image b cddc cddcg cddcg bdddg bdddb bdddb gdddb gcddc gcddc cddcg cddcg bdddg bdddb bdddb gdddb gcddc gcddc cddcg cddcg bdddg bdddb bdddb cdd gdddcgd d dg cc gd d d dg cc gd df df ff ff ff ff ff ffg bafc eefd fbfd f fd f adg f aab f ead bf ead ee bad ab bfg fg gf f gf f f f f gf f ea f ab f fg f f f f f fffaeg f f gbafffffeb gf fg geaffffaeg ba fg befffffabg ae fb gbafffffeb fg ab geaffffaeg f ae befffffabg f ee geafffffeb f ea befffffaeg gf ba gbafffffabg ba bf geafffffeae gf befg gf f f f f f f f ``` <!-- end of image -->
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I have an image in front of me. I need to determine if there are any intersection segments. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#ba64e9ff b,#aec8d8ff c,#d29bf1ff d,#e6dbf5ff e,#b1d7b1ff f,#96c996ff g,#b29acdff ``` ```image bbb aa bbbbd aaac dbbbbbb aaaaa bbbbbbbb aaaaaaa bbb dbbbb effffffffffffffffffffffe daaaa aaa bbbd bbbbd feeeeeeeeeeeeeeeeeeeeeefdaaaa caaa bbb bbbbb feeeeeeeeeeeeeeeeeeeeeegaaaa aaa bbb bbbbb feeeeeeeeeeeeeeeeeeeeegaaaa caaa bbb dbbbbfeeeeeeeeeeeeeeeeeeeegaaac aaad bbb bbbbbeeeeeeeeeeeeeeeeeeaaaac daaa dbbb bbbbbeeeeeeeeeeeeeeeeaaaag aaad bbb bbbbbeeeeeeeeeeeeeeaaaagf daaa bbb fbbbbeeeeeeeeeeeeaaaaeef aaad dbbd febbbbbeeeeeeeeeaaaaeeef daaa bbb feebbbbbeeeeeeeaaaaeeeef aaac bbb feeebbbbbeeeeeaaaaeeeeef aaa bbbd feeeeebbbbeebaaaaeeeeeef aaac bbb feeeeeebbbbgaaaaeeeeeeef aaa db feeeeeeebbgaaaaeeeeeeeef aaac feeeeeeeeaaaaaeeeeeeeeef aaa feeeeeeegaaagbbbeeeeeeef caac feeeeeeeaaagbbbbbeeeeeef aaa feeeeeeeaaaeebbbbbeeeeef caaa feeeeeegaageeeebbbbeeeef aaa feeeeeeaaaeeeeeebbbbbeef caaa feeeeeeaaaeeeeeeebbbbbef aaa feeeeeeaaaeeeeeeeebbbbbf daaa feeeeegaageeeeeeeeeebbbbd aaad feeeeeaaaeeeeeeeeeeeebbbbb daaa feeeeeaaaeeeeeeeeeeeeebbbbb aaad feeeeeaaaeeeeeeeeeeeeeeebbbb daaa feeeeaaabeeeeeeeeeeeeeef bbbbd aaad feeeeaaaeeeeeeeeeeeeeeef bbbbb aaa feeeeaaaeeeeeeeeeeeeeeef bbbbb aaac efffgaagfffffffffffffffe dbbbbd aaa aaa bbbbb aaac aaa bbbbb aaa aaa dbbbb caac caad bbbbd aaa aaa bbbbb caaa aaa bbbbbeffffffffaaafffffffffffff daac dbbbbeeeeeeeegaaaeeeeeeeeeeee aaa bbbbbeeeeeeeaaaeeeeeeeeeeee aaa bbbbbeeeeeegaaaeeeeeeeeeee aaa bbbbbeeeeeeaaaeeeeeeeeeee caac febbbbeeeeegaaaeeeeeeeeee aaa feebbbbbeeeeaaabeeeeeeeee aaa feeebbbbbeeebaaaeeeeeeeee daac feeeebbbbbeeeaaageeeeeeee caad feeeeeebbbbeeeaaaeeeeeeee aaa feeeeeeebbbbbeaaageeeeeee aaa feeeeeeeebbbbbeaaaeeeeeee caac feeeeeeeeeebbbbaaageeeeee aaa feeeeeeeeeeebbbbaaaeeeeee aaa feeeeeeeeeeeebbbaaageeeee daaa feeeeeeeeeeeeebbbaaaeeeee ac caad feeeeeeeeeeeeeeebaaaaeeee aaa aaa feeeeeeeeeeeeeeeebaaabeee aaa aaa feeeeeeeeeeeeeeeeegaaaeee aaaa daac feeeeeeeeeeeeeeeeeeaaaeee aaaad aaa feeeeeeeeeeeeeeeeeegaaeee caaaad aaa feeeeeeeeeeeeeeeeeeeeeeee aaaaac aaa feeeeeeeeeeeeeeeeeeeeeeee caaaaac caad feeeeeeeeeeeeeeeeeeeeeeee aaa aac aaa feeeeeeeeeeeeeeeeeeeeeeee caaa aac aaa feeeeeeeeeeeeeeeeeeeeeeee aaa aaadaac feeeeeeeeeeeeeeeeeeeeeeee daaa aaaaaad feeeeeeeeeeeeeeeeeeeeeeee aaad aaaaaa feeeeeeeeeeeeeeeeeeeeeeee daaa aaaaaa feeeeeeeeeeeeeeeeeeeeeeee aaad aaaaac feeeeeeeeeeeeeeeeeeeeeeee aaa aaaaa feeeeeeeeeeeeeeeeeeeeeeee aaac aaaaa feeeeeeeeeeeeeeeeeeeeeeee aaa aaaaa caac aaaad aaa aaaa caaa caaa aaa caac daaa daa aaa d caa ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ba63eaff b,#adc8d9ff c,#d6a6f2ff d,#eeedf7ff e,#e7caf7ff f,#c383ebff g,#cadbe6ff ``` ```image c ca caa bd faaa bbd faaaa bbbg dfaaaaa bbbbg dfaaaaaa bbbbbbd daaaaaaaa bbbbbbbd eaaaaaaaae bbbbbbbbg eaaaaaaaae gbbbbbbbbgd eaaaaaaaae dbbbbbbbbbd caaaaaaaad dgbbbbbbbbg caaaaaaafd gbbbbbbbbg caaaaaaafd dbbbbbbbbbd faaaaaaaf dbbbbbbbbbd dfaaaaaaac gbbbbbbbbg dfaaaaaaac gbbbbbbbbg dfaaaaaaac dbbbbbbbbbd daaaaaaaae dbbbbbbbbbd eaaaaaaaae gbbbbbbbbg eaaaaaaaae gbbbbbbbbcaaaaaaaad dbbbbbbfaaaaaaafd dgbbbfaaaaaaafd gbfaaaaaaafd faaaaaaafbd faaaaaaafbbbd caaaaaaafbbbbbg aaaaaaafbbbbbbbg daaaaaaedbbbbbbbbbd caaaaac dbbbbbbbbbd faaaaae gbbbbbbbbg aaaaaa gbbbbbbbbgd eaaaaaf dbbbbbbbbbd caaaaae dgbbbbbbbbg faaaaad gbbbbbbbbg daaaaaf dbbbbbbbbbd eaaaaac dbbbbbbbbbd faaaaae gbbbbbbbbg aaaaaa gbbbbbbbbg eaaaaaf dbbbbbbbb caaaaac dbbbbbbb faaaaad gbbbbb daaaaaa gbbbb eaaaaac dbbb caaaaae dgb aaaaaad g daaaaaf caaaaac faaaaae aaaaaa eaaaaac caaaaae faaaaad daaaaaf ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Time to investigate another area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#ba63eaff b,#adc8d9ff c,#cd9fedff d,#ebeaf6ff e,#e1bff5ff f,#bf78eaff g,#c9dae5ff ``` ```image g caaaaaf bg daaaaaae bbbd caaaaaf bbbbd daaaaaae bbbbbg caaaaaa bbbbbbg aaaaaac bbbbbbbbd eaaaaaad bbbbbbbbbd faaaaac gbbbbbbbbg eaaaaaad dbbbbbbbbg faaaaac dbbbbbbbbbd eaaaaaad gbbbbbbbbg faaaaac gbbbbbbbbg eaaaaaad dbbbbbbbbbd faaaaaf dbbbbbbbbbd daaaaaae gbbbbbbbbg caaaaaf gbbbbbbbbg daaaaaae dbbbbbbbbbd caaaaaf dbbbbbbbbbd daaaaaae gbbbbbbbbg caaaaaf dbbbbbbbbg daaaaaae dbbbbbbbbbd caaaaaf gbbbbbbbbgdaaaaaae gbbbbbbbbgcaaaaaa dbbbbbbbbbaaaaaac dbbbbbbbbcaaaaaad gbbbbbbbaaaaaac gbbbbbbcaaaaaad dbbbbbbfaaaaac dbbbbbcaaaaaad gbbbbfaaaaac dbbbbaaaaaad dbbbfaaaaaf gbbaaaaaae gbfaaaaafg dbaaaaaacbd dfaaaaafbd daaaaaac caaaaaf daaaaaae caaafe afe d ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#ba63eaff b,#adc8d9ff c,#d7a8f2ff d,#eeecf7ff e,#e8cdf7ff f,#c582ecff g,#c7d9e5ff ``` ```image bbb fa bbbbd aaaf gbbbbbg aaaaa bbbbbbbb aaaaaaf bbb gbbbb daaaa aaa gbbd dbbbbd eaaaa caaa bbb bbbbg eaaaa aaad dbbb gbbbb caaaf caaa bbbd dbbbbd faaaf aaad bbb bbbbg faaac eaaa dbbg bbbbb aaaac aaae bbb gbbbb aaaae eaaa bbb dbbbbd aaaad aaae gbbg bbbbg aaaad daaa bbb bbbbb aaaa aaac bbb gbbbb daaaa daaa gbbd dbbbbd eaaaa aaac bbb bbbbcaaaa aaa gb gbfaaaf faaf faaafd aaa caaafbbg faaf aaaebbbbb aaa aaa gbbbb caaf eaaf dbbbbd aaa faad bbbbg caaa aaa bbbbb aaad aaa gbbbb eaaa caac dbbbbd aaad aaa bbbbg eaaa aaa gbbbb aaae daaf dbbbbd daaa faae bbbbg aaae aaa bbbbb daaa aaa gbbbb aaac caac dbbbbd aaa aaa bbbbg faac aaa bbbbb aaa daaf gbbbb faaf caae dbbbbd aaa aaa bbbbg faaf aaa gbbbb aaa eaac dbbbbd caaa faad bbbbg aaa aaa bbbbb caaa aaa gbbbb aaad caac dbbbbd eaaa aaa bbbbg aaae aaa bbbbb eaaa eaaf gbbbb aaae faad dbbbbd daaa aaa bbbbg aaac aaa gbbbbdaaa caac dbbbbaaac aaa bbbbaaa aaa bbbaaac daaf gbbaaa af faae dbfaaf aaa aaa baaag daaa aaa faaad aaaad eaac aaa aaaae aaad caf faaaae aaa aaaaac aaa caaaaac caae aaadaaf aaa caaf aaf aaa aaa aaaeaaf eaaa aaafaad aaad aaaaaa daaa aaaaaa aaae aaaaac aaa aaaaa faac aaaaa aaa aaaaf faac aaaae aaa faaa caaf faaa aaa caac eaaa eaa aaad dd caa d ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#dc740cff b,#1335e9ff c,#e3d7d8ff d,#6381d9ff e,#97c897ff f,#d9a561ff g,#b1d7b1ff ``` ```image ffc aaa aaa aaa aaa aaa aaa aaa caaa caaa caaa faaa faaf faaf faaf aaaf aaac aaac aaac aaa aaa aaa aaa aaa cbbbc aaa bbbbbbd aaa bbbbbbbbb aaa dbbbbbbbbbbbc caaa bbbc dbbbbbbbd caaa dbbb cbbbbbbbbc eggggggggggggfaaagggg bbbd dbbbbbbbc eggggggggggggfaaagggg bbb dbbbbbbb eggggggggggggfaaagggg bbbb bbbbbbb eggggggggggggfaafgggg bbbc bbbbbbb eggggggggggggaaafgggg dbbb bbbbbbb eggggggggggggaaafgggg bbbd cbbbbbbb eggggggggggggaaafgggg cbbb cbbbbbbb eggggggggggggaaaegggg bbbb cbbbbbbbggggggggggggaaaegggg eeeeeeeeeeeeeeeeebbbeeeg cbbbbbbdggggggggggaaaggggg ggggggggggggggggdbbbggge cbbbbbbdggggggggaaaggggg ggggggggggggggggbbbdggge cbbbbbbdggggggaaaggggg gggggggggggggggebbbgggge edbbbbbbdggggaaaggggg gggggggggggggggbbbbgggge eggdbbbbbbdggaaaggggg gggggggggggggggbbbggggge eggggdbbbbbbdaaaggggg ggggggggggggggdbbbggggge eggggggdbbbbbaaaggggg ggggggggggggggbbbdggggge eggggggggdbbbaaadgggg gggggggggggggdbbbgggggge eggggggggggdbaaabbdgg gggggggggggggbbbbgggggge egggggggggggeaaabbegg gggggggggggggbbbggggggge egggggggggggfaaabbggg fafc ggggggggggggbbbbggggggge egggggggggggfaaaggggg aaaaaafc ggggggggggggbbbdggggggge egggggggggggfaaaggggg aaaaaaaaaaafggggggggggdbbbgggggggge egggggggggggfaafggggg faaaaaaaaaaaaafggggggbbbdgggggggge egggggggggggaaafggggg cfaaaaaaaaaaaaafgbbbggggggggge egggggggggggaaafggggg cfaaaaaaaaaaaaadggggggggge egggggggggggaaafggggg gggfaaaaaaaaaaaaafggggge egggggggggggaaaeggggg gggggggfaaaaaaaaaaaaaafe egggggggggggaaaeggggg gggggggggbbbfaaaaaaaaaaaaaf egggggggggggaaagggggg gggggggggbbbggggfaaaaaaaaaaaaafc egggggggggggaaagggggg ggggggggbbbbggggggggfaaaaaaaaaaaaafc egggggggggggaaagggggg ggggggggbbbegggggggggggecfaaaaaaaaaaaaaf egggggggggggaaagggggg gggggggdbbbgggggggggggge faaaaaaaaaaaaafc egggggggggggaaagggggg gggggggbbbdgggggggggggge cfaaaaaaaaaaaafc egggggggggggaaagggggg ggggggebbbggggggggggggge cfaaaaaaaaaaaaafegggggggggggaaagggggg ggggggbbbbggggggggggggge faaaaaaaaaaaaafc caaa ggggggbbbgggggggggggggge cfaaaaaaaaaaaafc caaa gggggdbbbgggggggggggggge cfaaaaaaaaaaaaaaaa gggggbbbdgggggggggggggge faaaaaaaaaaaa ggggebbbggggggggggggggge cfaaaaaaa ggggbbbbggggggggggggggge cfaa ggggbbbgggggggggggggggge gggdbbbgggggggggggggggge gggbbbdgggggggggggggggge eedbbbeeeeeeeeeeeeeeeeeg bbbd bbb dbbb bbbc cddbbbbbbbb bbbbbbbbbbbbbbd bbbbbbbbbbbbbb bbbbbbddc ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#dc740cff b,#1235e9ff c,#f2d1afff d,#6279efff e,#845a70ff f,#e8a25dff g,#b5c0f8ff ``` ```image dbbbbbb gbbbbbbd dbbbbbbg bbbbbbb gbbbbbbd dbbbbbb gbbbbbbd dbbbbbbg bbbbbbb gbbbbbbg bbbbbbb gbbbbbbd dbbbbbbg bbbbbbd dbbbbbbg bbbbbbb gbbbbbbd dbbbbbbg bbbbbbd dbbbbbbg bbbbbbb gbbbbbbd dbbbbbb gbbbbbbd dbbbbbbg bbbbbbb fcc gbbbbbbd aaaaffc dbbbbbb aaaaaaaaafc gbbbbbbd aaaaaaaaaaaaafcc dbbbbbbg aaaaaaaaaaaaaaaaaffc bbbbbbb aaaaaaaaaaaaaaaaaaaaaaeebbbbg aaaaaaaaaaaaaaaaaaaaaaaaaaeec cffaaaaaaaaaaaaaaaaaaaaaaaaaffc ccfaaaaaaaaaaaaaaaaaaaaaaaaaafc ccfaaaaaaaaaaaaaaaaaaaaaaaaaafcc cffaaaaaaaaaaaaaaaaaaaaaaaaaffc deeaaaaaaaaaaaaaaaaaaaaaaaa gbbbbbeeaaaaaaaaaaaaaaaaaaaa dbbbbbbg cffaaaaaaaaaaaaaaa bbbbbbd ccfaaaaaaaaaaa dbbbbbbg ccfaaaaaaa bbbbbbb cffaa gbbbbbbd c dbbbbbbg bbbbbbd dbbbbbbg bbbbbbb gbbbbbbd dbbbbbb gbbbbbbd dbbbbbbg bbbbbbb gbbbbbbd dbbbbbb gbbbbbbd dbbbbbbg bbbbbbb gbbbbbbg bbbbbbb gbbbbbbd dbbbbbbg bbbbbbd dbbbbbbg bbbbbbb gbbbbbbd dbbbbbbg bbbbbbd dbbbbbbg ``` <!-- end of image --> My analysis confirms the presence of 1 intersection in area A. Hmm, interesting. Let's check out another area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#dc740bff b,#1335e8ff c,#f4d6b8ff d,#6d80edff e,#ecb57eff f,#e49445ff g,#c5cdf9ff ``` ```image caaaaaa caaaaaa eaaaaaa eaaaaaa eaaaaaf eaaaaaf eaaaaaf faaaaaf faaaaaf faaaaae faaaaae aaaaaae aaaaaae aaaaaac aaaaaac aaaaaac g caaaaaac bdg caaaaaac bbbdg caaaaaa bbbbbdg caaaaaa bbbbbbbdg caaaaaa bbbbbbbbbdg eaaaaaa bbbbbbbbbbbdg eaaaaaa bbbbbbbbbbbbbdg eaaaaaf gbbbbbbbbbbbbbd eaaaaaf gbbbbbbbbbbbbbd eaaaaaf dbbbbbbbbbbbbbd faaaaaf dbbbbbbbbbbbbbd faaaaaf dbbbbbbbbbbbbbd faaaaae dbbbbbbbbbbbbbdfaaaaae dbbbbbbbbbbbbaaaaaae dbbbbbbbbbbaaaaaae dbbbbbbbbaaaaaac gdbbbbbbaaaaaadg gdbbbbaaaaaabbbg gdbbaaaaaabbbbbg gdaaaaaabbbbbd caaaaaabbbbbg caaaaaabbbbd caaaaaabbbbg eaaaaaagdbd eaaaaaa gg eaaaaaf eaaaaaf eaaaaaf faaaaaf faaaaaf faaaaae faaaaae aaaaaae aaaaaae aaaaaac aaaaaac aaaaaac caaaaaac caaaaaac caaaaaa caaaaaa caaaaaa eaaaaaa eaaaaaa eaaaaaf eaaaaaf eaaaaaf faaaaaf faaaaaf faaaaae faaaaae aaaaaae ``` <!-- end of image --> Area B contains 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#dd740bff b,#1235e9ff c,#f1c9a0ff d,#5b71ecff e,#e8e4ecff f,#e59c54ff g,#a2aff6ff ``` ```image fcc aaa aaa aaa aaa aaa aaa aaa eaaa caaa caaa caaa faaf faaf faaf aaac aaac aaac aaae aaa aaa aaa aaa aaa ebbbe aaa bbbbbbg aaa bbbbbbbbd aaa dbbbbbbbbbbbg eaaa bbbg dbbbbbbbd caaa gbbb gbbbbbbbbe caaa bbbd dbbbbbbbe caaa ebbb gbbbbbbbe faaf bbbb ebbbbbbbe faaf bbbe ebbbbbbb faaf gbbb ebbbbbbb aaac bbbd ebbbbbbb aaac ebbb ebbbbbbd aaac bbbb ebbbbbbd aaae bbbe gbbbbbbd aaa dbbb gbbbbbbd aaa bbbg gbbbbbbd aaa ebbb gbbbbbbd aaa bbbb gbbbbbbg aaa bbbe gbbbbbbgaaa dbbb dbbbbbaaa bbbg dbbbaaag gbbb dbaaabbg bbbd caaabbe bbb caaabb fafe dbbb caaa e aaaaaafc bbbg faaf aaaaaaaaaaac gbbb faaf caaaaaaaaaaaaafe bbbd faaf cfaaaaaaaaaaaafc bbb aaac efaaaaaaaaaaaaad aaac caaaaaaaaaaaaafe aaac cfaaaaaaaaaaaafc aaae bbbfaaaaaaaaaaaaac aaa ebbb caaaaaaaaaaaaafe aaa bbbb cfaaaaaaaaaaaafc aaa bbbe efaaaaaaaaaaaaac aaa dbbb caaaaaaaaaaaaafe aaa bbbg cfaaaaaaaaaaaafc aaa ebbb efaaaaaaaaaaaaac aaa bbbb caaaaaaaaaaaaafe aaa bbbe cfaaaaaaaaaaaafc eaaa dbbb efaaaaaaaaaaaaaaaa bbbg caaaaaaaaaaaa gbbb cfaaaaaaa bbbd efaa bbb dbbb bbbg gbbb bbbd bbb dbbb bbbg ggdbbbbbbbb bbbbbbbbbbbbbbd bbbbbbbbbbbbbb bbbbbbdgge ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#c46995ff b,#dcbecfff c,#978399ff d,#a3cba2ff e,#c696abff f,#b1d7b1ff g,#f0efeeff ``` ```image e ba aag aae aaa gaba ea a aa ab ab aa ag ea ba ga ea ab ggggggggggggaegggaegggggggggggggg ddddddddddddaedddaaddddddddddddddg ffffffffffffaffffeafffffffffffffdg fffffffffffeafffffafffffffffffffdg fffffffffffaafffffaeffffffffffffdg gbccg fffffffffffaefffffaaffffffffffffdg gbccccccceg fffffffffffadfffffeaffffffffffffdgeeeebbbbbbbbbbbgggggggg gbcccccccebg fffffffffffafffffffaffffffffffffccccccccccccccccccccccccccccccccccccccebg ffffffffffeafffffffaefffffffffcccb ggg ffffffffffaafffffffaafffffffcccddg ffffffffffaefffffffeafffffdcccffdg ffffffffffaffffffffdafffdcccffffdg fffffffffdafffffffffadfcccffffffdg fffffffffeafffffffffacccffffffffdg fffffffffaaffffffffcccdfffffffffdg fffffffffaeffffffccccaffffffffffdg fffffffffadffffdcccffaffffffffffdg fffffffffafffdcccffffaefffffffffdg ffffffffeaffcccffffffaafffffffffdg ffffffffeacccffffffffeafffffffffdg ffffffffcccdfffffffffdafffffffffdg ffffffccccffffffffffffadffffffffdg ffffdcccaeffffffffffffaeffffffffdg fffcccffafffffffffffffaaffffffffdg fffcfffdafffffffffffffeaffffffffdg fffffffeaffffffffffffffaffffffffdg fffffffaaffffffffffffffaefffffffdg fffffffaeffffffffffffffaafffffffdg fffffffaeffffffffffffffeafffffffdg fffffffaffffffffffffffffafffffffdg ffffffdaffffffffffffffffaeffffffdg ffffffeaffffffffffffffffaaffffffdg ffffffaaffffffffffffffffeaffffffdg ffffffaaffffffffffffffffdaffffffdg ddddddacdddddddddddddddddaddddddd ag ae ga aa ba ba ea a aa ab ae aa ab ea a ga ba ag ea ae aa eag ae aab ab eab ag eae ga bae ba gaa ea gaa aa aa ab aag gaab ag aag gaaab aab baaag eae baaag bae baaa baa eaae gaa eaae aa aaab aag gaaab aag gaaag aab baaag eab baaa bae eaae baaeaae gaab ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#c46995ff b,#d4b1c5ff c,#968098ff d,#e6ccdaff e,#d18caeff f,#aa97abff g,#f2e6edff ``` ```image daab aaa eaad eaag eaag baab aaa daae daae gaaa baab aaag eaad eaad aaag daab gaaa gaae daae aaa baab eaad eaad baab aaa daae gaae gaaa b daae eaag dfc baad baad dfccc eaag daab gfccccf aaa gaae gbcccccb gaae aaag bcccccb daab eaad bcccccbg eaad baab dfccccfg eaag daae dfccccfd aaa aaa gfccccfd daae eaag gbcccccb baab baabbcccccb eaad daacccccbg aaag bcccccfg gaaa dfccccfd daae gfcccccad baab gbcccccfaab baad bcccccb gaae eaag bcccccbg aaa aaa dfccccfg eaad gaaa dfccccfd baab gaae gfccccfd daae daab gbcccccb gaaa baad bcccccb aaag eaabcccccbg eaad aacccccfg daab dcccccfd gaae gfccccfd aaa gbcccccf eaad bccccccab baab bcccccbeaad daae dfccccfg eaag aaa fccccfd aaa eaag bccfd gaae baad gfb daae daae baab gaaa baad aaag eaag eaad aaa baab gaaa gaae gaae aaa daab eaag baad baab eaad daae aaag gaaa aaa aaag gaae eaad daae daab baab gaae eaad aaa eaag eaad aaa baab gaae daae daae aaa ``` <!-- end of image --> I observe 2 intersections inside area A. Answer: A: 2; 2 = 2 I've identified a total of two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#c46995ff b,#d9b2c7ff c,#968098ff d,#e8d0dcff e,#d08badff f,#b4a3b5ff g,#f2e8eeff ``` ```image b ba aad aae aaa daba ea a aa ab ab aa ag ba da ga ea ad ae ae ad ea a da ba ag aa ab gbccg ae aa gbcccccccfg ad ba gfffffbbbbbbddddddgggggg gbcccccccfbg ga ga ccccccccccccccccccccccccccccccccccccccfbg ba ad fccd ggg aa ae fccb ab ea bccf ag da dccf da aggccc ea acccg aa fccd ab fccfa ag bccf a ga dccf ab da gccc aa eacccg ea cccd ga fcce ad bccfad ae ccf a ea c da da ba ag aa ab ae aa ab ba ag ga ga ad ba ae ea ea ae da ab ag ag ae ga aa da ba ea a aa ab ae aa ad ea a ga da ad ba ae aa eag ae aad ab eab ag eae ga bae ba daa ea gaa ae aa ab aag gaad ag aad gaaad eab daaag eae baaag bae baae daa eaae gaa eaab aa aaab aag gaaad aag daaad aad daaag eab baaa bae baae daaeaae gaab ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#f52d7cff b,#cd0dd0ff c,#d97fa1ff d,#f5a8d7ff e,#cd52cfff f,#b1d7b1ff g,#f1f3efff ``` ```image aaag aaaaaad aaaaaaaaac aa gcaaaaaacg gaa daaaaaaad daa daaaaaaac caa gcaaaaaacg aac daaaaaaad aad daaaaaaad aad gcaaaaaacg aag caaaaaaad aa daaaaaaad aa gcaaaaaa gaa caac daa g daa caa aac aad aag aa aa aa gaa daa caa aac aad aad gggggggggggggggggggggggggggggggggggggggaagggggggg fffffffffffffffffffffffffffffffffffffffaaffffffffg fffffffffffffffffffffffffffffffffffffffaaffffffffg fffffffffffffffffffffffffffffffffffffffaaffffffffg ffffffffffffffffffffffffffffffffffffffcaaffffffffg ffffffffffffffffffffffffffffffffffffffcaaffffffffg ffffffffffffffffffffffffffffffffffffffaacffffffffg ffffffffffffffffffffffffffffffffffffffaafffffffffg ffffffffffffffffffffffffffffffffffffffaafffffffffg ffffffffffffffffffffffffffffffffffffffaafffffffffg fffffffffffffffffffffffffffffffffffffcaafffffffffg fffffffffffffffffffffffffffffffffffffaacfffffffffg gdd fffffffffffffffffffffffffffffffffffffaaffffffffffg gdeebbbbbbbbbb fffffffffffffffffffffffffffffffffffffaaffffffffffg gddebbbbbbbbbbbbbbbbbbbbb fffffffffffffffffffffffffffffffffffffaaffffffffffddeebbbbbbbbbbbbbbbbbbbbeedg ffffffffffffffffffffffffffffffffffffcaaceebbbbbbbbbbbbbbbbbbbbeedd ffffffffffffffffffffffffffffceebbbbbaaabbbbbbbbbbbbeeddg fffffffffffffffffceebbbbbbbbbbbbbbbbaabbbeecfffffg ffffffffffffbbbbbbbbbbbbbbbbbbeecfffaafffffffffffg fffffffffffbbbbbbbbeecffffffffffffffaafffffffffffg fffffffffffbbffffffffffffffffffffffcaafffffffffffg ffffffffffcbbffffffffffffffffffffffaacfffffffffffg ffffffffffbbeffffffffffffffffffffffaacfffffffffffg ffffffffffbbfffffffffffffffffffffffaaffffffffffffg fffffffffebbfffffffffffffffffffffffaaffffffffffffg fffffffffbbcffffffffffffffffffffffcaaffffffffffffg fffffffffbbfffffffffffffffffffffffaacffffffffffffg ffffffffbbbfffffffffffffffffffffffaacffffffffffffg ffffffffbbffffffffffffffffffffffffaafffffffffffffg fffffffcbbffffffffffffffffffffffffaafffffffffffffg fffffffbbefffffffffffffffffffffffcaafffffffffffffg fffffffbbffffffffffffffffffffffffaaafffffffffffffg ffffffebbffffffffffffffffffffffffaacfffffffffffffg ffffffbbcffffffffffffffffffffffffaaffffffffffffffg ffffffbbfffffffffffffffffffffffffaaffffffffffffffg fffffbbbffffffffffffffffffffffffcaaffffffffffffffg fffffbbfffffffffffffffffffffffffaaaffffffffffffffg fffaabbfffffffffffffffffffffffffaacffffffffffffffg ffaaaaacffffffffffffffffffffffffaafffffffffffffffg ffffaaaaacffffffffffffffffffffffaafffffffffffffffg fffebbcaaaacfffffffffffffffffffcaafffffffffffffffg fffbbcffcaaaaafffffffffffffffffcaafffffffffffffffg fffbbfffffcaaaaafffffffffffffffaacfffffffffffffffg ffebbffffffffaaaaafffffffffffffaaffffffffffffffffg fffffffffffffffaaaaacffffffffffaaffffffffffffffffg fffffffffffffffffaaaaacfffffffcaaffffffffffffffffg fffffffffffffffffffcaaaacfffffcaaffffffffffffffffg fffffffffffffffffffffcaaaaafffaacffffffffffffffffg fffffffffffffffffffffffcaaaaafaafffffffffffffffffg ffffffffffffffffffffffffffaaaaaafffffffffffffffffg ffffffffffffffffffffffffffffaaaafffffffffffffffffg ffffffffffffffffffffffffffffffcffffffffffffffffffg fffffffffffffffffffffffffffffffffffffffffffffffffg fffffffffffffffffffffffffffffffffffffffffffffffffg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#f52c7bff b,#ce0cd0ff c,#f992bbff d,#f8c6e6ff e,#d946dbff f,#f75c9aff g,#e583e7ff ``` ```image caaaa caaaa faaaf faaaf faaac aaaac aaaac daaaad daaaad caaaa caaaa faaaf aaaac daaaad caaaad caaaa faaaf aaaac daaaac daaaad caaaa faaaf aaaac daaaac daaaad caaaa faaaf aaaac daaaac daaaad dddggeeebbb caaaadgggeebbbbbbbbbbbbbb dddgggeeaaaaabbbbbbbbbbbbbbbbbbbb ddgggeeebbbbbbbbbbaaaaabbbbbbbbbbbbbbbbbbbb ddgggeeebbbbbbbbbbbbbbbbbbbbbaaaabbbbbbbbbbbbbbbeeeggg dddggeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbaaaabbbbeeegggddd gggeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbefaaaadd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeegggddd faaaf gbbbbbbbbbbbbbbbbbbbbbbbbbeeegggdd aaaaf bbbbbbbbbbbbbbbeeegggdd aaaac dbbbbbeegggddd daaaad ebbbb caaaa bbbbe faaaa gbbbbd faaaf ebbbb aaaac dbbbbg daaaad gbbbbd caaaa bbbbe faaaa dbbbbg faaaf ebbbb aaaac bbbbe daaaad gbbbbd caaaa ebbbb caaaa dbbbbg faaaf gbbbbd aaaac bbbbe daaaad dbbbbg caaaad ebbbb caaaa bbbbe faaaf gbbbbd aaaac ebbbb daaaad dbbbbg caaaad gbbbbd caaaa bbbbe faaaf dbbbbg aaaac ebbbb daaaad bbbbe caaaad gbbbbd caaaa ebbbb faaaf dbbbbg aaaac gbbbbd daaaac bbbbe daaaad dbbbbg caaaa ebbbb faaaf cacdbbbbe aaaac aaaaabbbd daaaac caaaaaaab daaaad faaaaaaaafd caaaa caaaaaaaaafc faaaf baaaaaaaaaac aaaac dbbbaaaaaaaaaac aaaac ebbbbdfaaaaaaaaafd daaaad bbbbe dcaaaaaaaaafd caaaa gbbbbd caaaaaaaaafd faaaf ebbbb caaaaaaaaafc aaaaf dbbbbg dfaaaaaaaaac aaaac gbbbbd dfaaaaaaaaacd daaaad ebbbe dfaaaaaaaaafd caaaa dgbg dcaaaaaaaaafd faaaf caaaaaaaaafc aaaaf cfaaaaaaaaac aaaac dfaaaaaaaaac daaaad dfaaaaaaaaacd caaaa dcaaaaaaaaafd faaaa caaaaaaaaafd faaaf caaaaaaaaafc aaaac cfaaaaaaaaac daaaad dfaaaaaaaaacdcaaaa dfaaaaaaaaaaaaaa dcaaaaaaaaaaaf caaaaaaaaac caaaaaaad dfaaaa dccd ``` <!-- end of image --> Gotcha! I've found 2 intersections hiding in area A! Answer: A: 2; 2 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#f52c7bff b,#ce0dd1ff c,#f98cb7ff d,#f4addeff e,#de5fe0ff f,#f75c99ff g,#faddf0ff ``` ```image aafg aaaaaad aafaaaaaac aa gfaaaaaafg gaa caaaaaaad daa daaaaaaac caa gfaaaaaafg faf caaaaaaad aac daaaaaaac aad gfaaaaaafg aa caaaaaaad aa daaaaaaac aa gfaaaaaa aa caaf daa caa faf aac aad aag aa aa aa gaa daa caa faf aac aad aa aa aa gaa daa caa aac aag aa gaa caa aac gdd aag gdeebbbbbbbbbb aa gdeebbbbbbbbbbbbbbbbbbbbb gaa gddebbbbbbbbbbbbbbbbbbbbbeedg caadeebbbbbbbbbbbbbbbbbbbbeedg gdeebbbbbaaabbbbbbbbbbbbbeddg gdeebbbbbbbbbbbbbbbbaabbbeedg gbbbbbbbbbbbbbbbbbbeedg aa bbbbbbbbeedg gaa bbg caa dbb faf bbe aad bb aa ebb aa bbd caa gbb faf bbb aad bbg aa dbb aa bbe daa bb faf ebb aad bbd aa gbb aa bbb daa bbg faf gaabb aad faaaad aa aaaaac aa ebbfaaaac daa bbd caaaaf faf gbb daaaaag aac ebb gaaaaag aa gaaaaad aa faaaac daa caaaaf faa caaaaf aac daaaaagaag gaaaaaa aaaa cg ``` <!-- end of image -->
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I'm analyzing this image to identify any points where lines intersect. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#69b5dcff b,#859383ff c,#b2d7b2ff d,#b2d8eaff e,#edf5f0ff f,#98ba98ff g,#a5cfaaff ``` ```image dd aaa aaaa aaae eaaaa eebbaaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ggbbbaaaggggggggggggggggggggggggggggggge ccfbbaaaacccccccccccccccccccccccccccccge dad ccgbbbaaagccccccccccccccccccccccccccccge aaa cccbbbgaaaccccccccccccccccccccccccccccge daaa cccbbbcaaaacccccccccccccccccccccccccccge aaaa cccbbbgcaaacccccccccccccccccccccccccccge eaaaa cccfbbfcaaaaccccccccccccccccccfbgcccccge aaaaa cccgbbbccaaagccccccccccccccccgbbbbccccge aaaaa ccccbbbccgaaaccccccccccccccccfbbbbbbccge daaaaa ccccbbbcccaaaacccccccccccccccbbbbbbbbbge aaaaaa ccccbbbccccaaacccccccccccccccbbbcfbbbbbg daaaaaae ccccfbbfcccaaaaccccccccccccccbbbcccbbbbbbc aaaedaae ccccgbbbccccaaaacccccccccccccbbbcccccbbbbbbd aaa daad cccccbbbccccgaaacccccccccccccbbbccccccgbbbbbbe aaad daad cccccbbbcccccaaaacccccccccccfbbfccccccgeebbbbbbe aaa daad cccccbbbccccccaaagccccccccccbbbgccccccge ebbbbbbe eeeeeeeeeeeeeeedaaaeedaad cccccfbbfcccccgaaaccccccccccbbbcccccccge cbbbbbb fggggggggggggggaaaggggaad cccccgbbbccccccaaaacccccccccbbbcccccccge cbbbbbf fccccccccccccccaaaccccaaa ccccccbbbcccccccaaacccccccccbbbcccccccge gbbbbbg fcccccccccccccaaaaccccaaa ccccccbbbcccccccaaaaccccccccbbbcccccccge fbbbbbc fcccccccccccccaaacccccaaa ccccccbbbccccccccaaagccccccfbbfcccccccge bbbbbbcfccccccccccccgaaacccccaaa ccccccfbbfcccccccgaaaccccccfbbgcccccccge bbbbbbgcccccccccccaaaccccccaaa ccccccgbbbccccccccaaaacccccbbbccccccccge ebbbbbbgcccccccccaaaccccccaaa cccccccbbbcccccccccaaagccccbbbccccccccge ebbbbbbcccccccaaagccccccaaa cccccccbbbcccccccccaaaaccccbbbccccccccge fbbbbbbcccccaaacccccccaaa cccccccbbbccccccccccaaaacccbbbccccccccge fcfbbbbbbccaaaacccccccaaa cccccccfbbfccccccccccaaaccfbbfccccccccge fcccfbbbbbfaaaccccccccaaa cccccccgbbbccccccccccaaaacfbbfccccccccge fcccccbbbbbaaaccccccccaad ccccccccbbbcccccccccccaaagbbbcccccccccge fcccccccbbaaabfccccccccf ccccccccbbbcccccccccccgaaabbbcccccccccge fcccccccccaaabbbfccccccf ccccccccbbbccccccccccccaaaabbcccccccccge fccccccccaaaabbbbbgccccf ccccccccfbbfccccccccccccaaabbcccccccccge fccccccccaaacgbbbbbbgccf ccccccccgbbbccccccccccccaaaafcccccccccge fcccccccgaaacccgbbbbbbcf cccccccccbbbcccccccccccccaaafcccccccccge fcccccccaaagcccccfbbbbbf cccccccccbbbcccccccccccccbaaacccccccccge fcccccccaaaccccccccfbbbf cccccccccbbbcccccccccccccbaaaaccccccccge fccccccaaaacccccccccbbbf cccccccccfbbfccccccccccccbbaaagcccccccge fccccccaaaccccccccccbbbf cccccccccgbbbccccccccccccbbaaaacccccccge fcccccgaaaccccccccccbbbf ccccccccccbbbcccccccccccgbbbaaaaccccccge fcccccaaagccccccccccbbbf ccccccccccbbbcccccccccccfbbfcaaaccccccge fcccccaaacccccccccccbbbf ccccccccccbbbcccccccccccbbbccaaaacccccge fccccaaaacccccccccccfbbf ccccccccccfbbfccccccccccbbbcccaaagccccge fggggaaaggggggggggggfbbf ccccccccccgbbbccccccccccbbbcccgaaaccccge eeeedaaaeeeeeeeeeeeeebbf cccccccccccbbbccccccccccbbbccccaaaacccge aaae bbb cccccccccccbbbcccccccccgbbbcccccaaacccge eaaa bbb cccccccccccbbbcccccccccfbbfcccccaaaaccge aaad bbb gggggggggggbbbfggggggggbbbgggggggaaaagge aaa bbb eeeeeeeeeeedbbfeeeeeeeebbbeeeeeeeeaaaee daaa bbb bbb bbb aaaa aaa bbb bbb bbb aaae eaaa bbbe bbb ebbf daaa aaad gbbe fbbd cbbc aaad aaa cbbc ebbbb fbbe eaaa daaa ebbg bbbbbb bbb aaaa aaa ebbf cbbbbbf bbb aaad eaaa bbb gbbbbbbbb daaa aaad bbb fbbbbbf aaaa aaa bbb bbbbc aaae daad bbb bb daaa aaa bbb aaad daaa ee eaaa aaae aaaa aaa aaae aaad daaa aaa aaad daaa eaaa aaae aaaa eaaa aaad aaad eaaa aaa aaaa daaa aaaeaaae daaaaaa aaaaad eaaaa aaaa aa ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#68b5dcff b,#859383ff c,#ccd2cbff d,#9ecfe8ff e,#dee9ecff f,#9aa79cff g,#b4bdb3ff ``` ```image ebbbbaaaaaaae bbbbbaaaaaad fbbbbaaaaaaae gbbbbbaaaaaaa cbbbbbfaaaaaad ebbbbbbdaaaaaae bbbbbbeaaaaaaa fbbbbbcdaaaaaad gbbbbbc aaaaaaae cbbbbbg eaaaaaad ebbbbbb daaaaaae bbbbbb aaaaaaa fbbbbbe eaaaaaad gbbbbbc daaaaaae fbbg cbbbbbg eaaaaaad fbbbbbg ebbbbbf daaaaaae bbbbbbbbc bbbbbb aaaaaaa ebbbbbbbbbbc fbbbbbe eaaaaaad cbbbbbbbbbbbfc gbbbbbc daaaaaae gbbbbbbbbbbbbbfe cbbbbbg aaaaaaa fbbbbbbbbbbbbbbbfe ebbbbbf daaaaaad bbbbbbgbbbbbbbbbbb bbbbbb aaaaaaae bbbbbf egbbbbbbbbb fbbbbbe eaaaaaad ebbbbbf efbbbbbbb gbbbbbc daaaaaae cbbbbbg efbbbbb cbbbbbg aaaaaaa gbbbbbc cfbbb ebbbbbf eaaaaaad fbbbbbe cbb bbbbbb daaaaaae bbbbbb c fbbbbbe eaaaaaad bbbbbb gbbbbbc daaaaaae ebbbbbf cbbbbbg aaaaaaa cbbbbbg ebbbbbf eaaaaaad gbbbbbc bbbbbb daaaaaae fbbbbbe fbbbbbe aaaaaaa bbbbbb gbbbbbc daaaaaad bbbbbb cbbbbbg daaaaaae ebbbbbf ebbbbbf eaaaaaad cbbbbbg bbbbbb daaaaaae gbbbbbc fbbbbbe aaaaaaa fbbbbbe gbbbbbc eaaaaaad fbbbbbe cbbbbbg daaaaaae bbbbbb ebbbbbf eaaaaaaa ebbbbbf bbbbbb daaaaaad cbbbbbg fbbbbbe aaaaaaa gbbbbbc gbbbbbc eaaaaaad gbbbbbe cbbbbbg daaaaaae fbbbbbe ebbbbbf aaaaaaa bbbbbb bbbbbb eaaaaaad ebbbbbf fbbbbbe daaaaaae cbbbbbg gbbbbbc eaaaaaad gbbbbbc cbbbbbg daaaaaae gbbbbbc ebbbbbf aaaaaaa fbbbbbe bbbbbb eaaaaaad bbbbbb fbbbbbe daaaaaae ebbbbbf gbbbbbc eaaaaaaa cbbbbbg cbbbbbg daaaaaad cbbbbbc ebbbbbf aaaaaaae gbbbbbc bbbbbb eaaaaaad fbbbbbe fbbbbbe daaaaaae bbbbbb gbbbbbc aaaaaaaebbbbbf cbbbbbg eaaaaaadbbbbbg ebbbbbf daaaaaabbbbbg bbbbbb eaaaaaaabbbbc fbbbbbe daaaaaafbbbe gbbbbbc aaaaaaabbb cbbbbbg eaaaaaaabf ebbbbbf daaaaaabg bbbbbb eaaaaaaag fbbbbbe daaaaaad gbbbbbc aaaaaaae cbbbbbg faaaaaad ebbbbbf ebaaaaaaae bbbbbb ebbaaaaaaa fbbbbbe cbbfaaaaaad gbbbbbc gbbbaaaaaaae cbbbbbg fbbbbaaaaaad ebbbbbf bbbbbfaaaaaae bbbbbb bbbbbfaaaaaaa fbbbbbe ebbbbbfeaaaaaad gbbbbbc cbbbbbg daaaaaae cbbbbbg gbbbbbc aaaaaaa ebbbbbf fbbbbbe daaaaaad bbbbbb bbbbbb aaaaaaae fbbbbbe bbbbbb eaaaaaad gbbbbbc ebbbbbf daaaaaae cbbbbbg cbbbbbg aaaaaaa ebbbbbf gbbbbbc eaaaaaad bbbbbb fbbbbbe daaaaaae fbbbbbe fbbbbb eaaaaaad gbbbbbc bbbbbb daaaaaad cbbbbbg ebbbbbf aaaaaaa ebbbbbf cbbbbbg eaaaaaad bbbbbb gbbbbbc daaaaaae fbbbbbe fbbbbbe aaaaaaa ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Now, let's scrutinize the next spot. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#67b5dcff b,#859383ff c,#c8cec7ff d,#b3d9edff e,#e0ebefff f,#a4aea2ff g,#8bc6e4ff ``` ```image gaaaaad eaaa eaaaaaae eaaa daaaaag eaaa aaaaaad aaa daaaaaa aaa gaaaaad aaa eaaaaaae aaa gaaaaag aaa aaaaaae gaa daaaaaa gaa fc aaaaaad gaa bbfe eaaaaaa gaa bbbbfe gaaaaag gaa bbbbbbfe eaaaaaae daa bbbbbbbbfe daaaaag daa bbbbbbbbbbc aaaaaad daa fbbbbbbbbbbbc eaaaaaa daa cbbbbbbbbbbbbc gaaaaag daa cbbbbbbbbbbbbc eaaaaaae daa cbbbbbbbbbbbfe daaaaag eaa cbbbbbbbbbbbfe aaaaaad eaa efbbbbbbbbbbbfdaaaaaa eaa efbbbbbbbbbbaaaaaad eaa efbbbbbbbbaaaaaae gg efbbbbbaaaaaaa cfbbbaaaaaabbc cbbaaaaaabbbbc aaaaaaabbbbbfc eaaaaaabbbbbbbbfe gaaaaaabbbbbbbbbbfe aaaaaadfbbbbbbbbbbbfe daaaaaa efbbbbbbbbbbbfe gaaaaad efbbbbbbbbbbbc eaaaaaae cfbbbbbbbbbbbc gaaaaag cbbbbbbbbbbbc eaaaaaae cbbbbbbbbbb daaaaag cbbbbbbbb aaaaaad cbbbbbbe eaaaaaa fbbbbbe gaaaaag cbbbbbc eaaaaaae cbbbbbc daaaaag cbbbbbc aaaaaad ebbbbbf daaaaaa ebbbbbf gaaaaad ebbbbbf eaaaaaae bbbbbb daaaaag bbbbbb aaaaaad fbbbbb daaaaaa fbbbbb gaaaaad fbbbbb eaaaaaae cbbbbb ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area B. Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#67b5dcff b,#859383ff c,#c8cec7ff d,#b2d9edff e,#e1ebeeff f,#a6b0a4ff g,#89c5e3ff ``` ```image dd aaa aaag aaae egaaa bbaaad bbbaaa cbbaaaa dad ebbbaaae aaa bbbdaaa daaa bbb aaag aaaa bbbe aaa eaaaa cbbc gaaa fbe aaaaa ebbb aaad ebbbb aaaaa bbb eaaa cbbbbbb gaaaaa bbb aaag fbbbbbbbf aaaaaa bbb aaae bbb fbbbbbf eaaagaae cbbc daaa bbb fbbbbbc aaaegaae ebbb aaad bbb bbbbbbc aaa daae bbb eaaa bbb bbbbbbe gaad daad bbb gaaa cbbf ebbbbbbe aaa daad bbb aaae fbbe ebbbbbb daaa eaad cbbc daaa bbb cbbbbbb aaae eaag ebbf aaag bbb cbbbbbf aaa aag bbb aaa bbb fbbbbbf gaad aaa bbb gaaa bbb fbbbbbc aaa aaa bbb aaad cbbf bbbbbbc daaa aaa fbbc eaaa fbbe bbbbbbe aaa aaa ebbf aaag bbb ebbbbbbe eaaa aaa bbb aaae bbb ebbbbbb aaad aaa bbb daaa bbb cbbbbbb aaa aaa bbb aaad bbb cbbbbbf daag aaa fbbc eaaa cbbf fbbbbbfaaa aaa ebbf gaaa fbbc fbbbbaaa ggd bbb aaaebbb fbaaabc bbb daaabbb aaabbbc bbb aaaabb gaaabbbbbe fbbc aaabb aaa ebbbbbbe ebbf gaaaf eaaa cbbbbbb bbb aaag aaae cbbbbb bbb baaa aaa cbbb bbb baaaa gaag bbb fbbc bbaaae aaa bbb ebbf bbaaaa daaa bbb bbb ebbfaaag aaae bbb bbb fbbceaaa aaa fbbe bbb bbb gaaa gaad fbbc fbbc bbb aaae aaa cbbc ebbf bbb daaa daaa ebbf bbb bbb aaag aaae bbb bbb ebbf aaa aaa bbb bbb cbbc gaaa aaad bbb fbbc bbbe aaad aaa bbb ebbf bbb eaaa daag bbb bbb bbb aaaa aaa bbb bbb bbb aaae eaaa bbb bbb ebbf daaa aaad fbbe fbbc cbbc aaag aaa cbbc ebbbb fbbe aaa daag ebbf bbbbbb bbb gaaa aaa ebbf cbbbbbf bbb aaad eaaa bbb fbbbbbbbb eaaa aaae bbb fbbbbbf aaag aaa bbb bbbbc aaae gaag bbb bb daaa aaa bbb aaad eaaa e eaaa aaae aaaa aaa aaae gaad daaa aaa aaag daaa aaa aaae gaaa aaa aaad gaad eaaa aaa aaag daag aaaeaaa daaaaaa aaaaad eaaaa gaag aa ``` <!-- end of image -->
[ "" ]
This image looks interesting. I wonder if there are any intersections hidden in there? Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#a26cabff b,#24e455ff c,#b1d8b2ff d,#8a2896ff e,#94cc97ff f,#5be27bff g,#d9baddff ``` ```image f bbbc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeec bbbc ccccccccccccccccccccccccccccccccce cbbb ccccccccccccccccccccccccccccccccce ebbf ccccccccccccccccccccccccccccccccce fbbf ccccccccccccccccccccccccccccccccce bbbc ccccccccccccccccccccccccccccccccce bbbc ccccccccccccccccccccccccccccccccce cbbb ccccccccccccccccccccccccccccccccce ebbf ccccccccccccccccccccccccccccccccce fbbf ccccccccccccccccccccccccccccccccce fbbe ccccccccccccccccccccccccccccccccce bbbc ccceccccccccccccccccccccccccccccce cbbb cccbecccccccccccccccccccccccccccce cbbb cccdfcccccccccccccccccccccccccccce fbbf cccddcccccccccccccccccccccccccccce fbbe cccedaccccccccccccccccccccccccccce bbbc ccccadccccccccccccccccccccccccccce cbbb ccccbddcccccccccccccccccccccccccce cbbb ccccbfdcccccccccccccccccccccccccce fbbf ccccbbddccccccccccccccccccccccccce fbbe ccccfbcdaccccccccccccccccccccccccebbbc cccccbcadccccccccccccccccccccccebbbc cccccbecdacccccccccccccccccccfbbbe cccccbfcadcccccccccccccccccfbbfcce cccccbbccddccccccccccccccfbbfcccce cccccfbcccdeccccccccccccbbfcccccce ccccccbcccddccccccccccccbcccccccce ccccccbecccdaccccccccccfbcccccccce ccccccbfcccadccccccccccfbcccccccce ccccccbbccccddcccccccccbfcccccccce ccccccfbcccccdcccccccccbfcccccccce ccccccebcccccddccccccccbccccccccce cccccccbccccccdacccccccbccccccccce cccccccbfcccccadccccccfbccccccccce cccccccbbccccccdacccccfbccccccccce cccccccfbccccccadcccccbfccccccccce gdg cccccccebcccccccddccccbfccccccccce dddg ccccccccbccccccccdecccbcccccccccce dgadg ccccccccbfcccccccddcccbcccccccccce d ad ccccccccbbccccccccdacfbcccccccccce ad dd ccccccccfbccccccccadcfbcccccccccce da dd ccccccccebcccccccccddbfcccccccccce d dd cccccccccbccccccccccdbfcccccccccce gd dd cccccccccbecccccccccddccccccccccce dd dd cccccccccbfccccccccccdacccccccccce dg dd cccccccccfbcccccccccfddcccccccccce gd dd cccccccccebcccccccccfbddccccccccce dd dd ccccccccccbcccccccccbfadccccccccce dg dd ccccccccccbeccccccccbfcddcccccccce d dd ccccccccccbfccccccccbcccdeccccccce ad dd ccccccccccbbccccccccbcccddccccccce da dd ccccccccccfbcccccccfbccccdacccccce d da cccccccccccbcccccccfbccccadcccccce ad gda cccccccccccbeccccccbfcccccddccccce da gda cccccccccccbfccccccbfccccccdccccce dg gda cccccccccccbbccccccbcccccccddcccce gd gda cccccccccccfbccccccbccccccccdaccce dd gdg cccccccccccebcccccfbccccccccadccce dg adg eeeeeeeeeeeebeeeeebbeeeeeeeeeddeecgd adg be bf gd ad adg bb bc dd da adg fb b dg d ad cb b adad dd b cb dda dd bc fb gd dd bf bf g dd fb bc dd cb b dd b b dd bccb dd bffb dd fbbf dd cbbc dd bb dd bb da bb gda fb gda gdg g ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#b273baff b,#24e455ff c,#8df0a7ff d,#8a2a96ff e,#c6f7d2ff f,#55e67bff g,#d8b9dcff ``` ```image ec fbbe cbbc efdc addf gddd dddg cddd eddda ebdddg bddda fbdddg cbfddd ebbddda ebbfddd bbbadda fbbedddg cbbegddd cbbc dddg ebbf gddd e bbf adda efb cbbe adda cfbbbbb cbbc dddg cbbbbbfc ebbc gddd ecbbbbbfe bbf adda fbbbbbfe fbb gddd efbbbbce fbbe adda efbbbbc cbbc dddg fbbbc ebbc gddd bbbe bbf dddg bbf bbb gddd ebbc fbbe add cbbc cbbe ddg cbbe ebbc ada fbb bbf ddg bbb bbb gdd bbf fbbe dda ebbc cbbe ddd cbbc ebbc adda cbbe ebbf dddg fbb bbb gddd bbb fbb dddg bbf cbbe gddd ebbc cbbc adda cbbc ebbf dddg cbbe bbf adda fbb fbb dddg bbb cbbe gddd bbf cbbc adda ebbc bbf adda cbbe fbb dddg fbb fbbe gddd bbb cbbc dddg bbf ebbc gddd ebbc bbf adda cbbc bbb dddg cbbe fbbe adda fbb cbbe dddg bbb ebbc gddd bbf bbf addabbc bbb gdddbbc fbbe adddbe cbbe dddb ebbc gddd ebbf dddg bbb ebddd fbb cbddda cbbe cbbdddg ebbc fbbadda ebbf bbb dddg bbb bbf gddd fbb ebbc adda cbbe cbbc gddd cbbc cbbe adda ebbf fbb dddg bbf bbb gddd fbb bbf ddd cbbc cbbc ada ebbc cbbe ddg bbf fbb ada fbb bbb ddg fbb bbf ddd cbb ebbc adda ebb cbbc gddd bb cbbe adda bb fbb dddg fbe bbb gddd cbe bbf dddg ebc ebbc gddd ebf cbbc adda bb cbbe dddg ``` <!-- end of image --> Eureka! There's definitely 2 intersections in area A! Answer: A: 2; 2 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#a45caeff b,#23e555ff c,#a1f3b6ff d,#8a2796ff e,#e5ece9ff f,#5ae97fff g,#cda2d2ff ``` ```image f bbbc ebbbc cbbbe cbbf fbbf bbbc ebbbc cbbbe cbbf fbbf fbbc ebbbc e cbbbe bc cbbb df fbbf dd fbbc cdg ebbbc ad cbbbe bdd cbbb bfde fbbf fbdd fbbc cb dg ebbbc b ad ebbbe be da cbbbe bf gd fbbf fb dd fbbf cb ede bbc eb ad eb be dg cb bc gd fb bb dd bf cb ede bc eb dd be be dg eb bc ad cb bb da fb fb gd bf edg eb dd bc adde b ede be dgade bc ad eb ed ade bf da cb ad dde fb gd fb da dd cb ddbf de dd b edbc gd dd bc dde da dd bf edg de dd fb cdd gd dd cb fbda dd dd b bfgd dg dd be bc dd ed dd bf be dg ad dd fb eb ad da eda cb cb da d eda b fb gd gd eda be bf dd da eda bc bc ede de gda bb be dd gd gdg cb eb dg dd gdg eb cb ad dg gdg be fb da ed adg bc bf gd ad ade bb bc dd dg ade fb be dg d ade eb eb adad dde b cb dda dd bc fb gde dd bf bf g dd fb bc dd cb be dd b eb dd bccb dd bffb dd fbbf dd cbbc dd bbe edd bb eda bb eda fb eda gdg e ``` <!-- end of image -->
[ "" ]
This is the image I'm working with. The goal is to count the intersections. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#a97136ff b,#15dcbeff c,#b1d7b1ff d,#5fdcbdff e,#b19b6aff f,#eef5eeff g,#98c996ff ``` ```image f fggggggggggggggggggggggggggggggggggggggc ea fccccccccccccccccccccccccccccccccccccccg caef fccccccccccccccccccccccccccccccccccccccg ca a fccccccccccccccccccccccccccccccccccccccg fa a fccccccccccccccccccccccccccccccccccccccg fa ef fccccccccccccccccccccccccccccccccccccccg fa fe fccccccccccccccccccccccccccccccccccccccg fa a fccccccccccccccccccccccccccccccccccccccg a ef fccccccccccccccccccccccccccccccccccccccg a fe fccccccccccccccccccccccccccccccccccccccg af a fccccccccccccccccccccccccccccccccccccccg af e fccccccccccccccccccccccccccccccccccccccg af fe fccccccccccccccccccccccccccccccccccccccg af a fccccccccccccccccccccccccccccccccccccccg ac a fccccccccccccccccccccccccccccccccccccccgac fe fccccccccccccccccccccccccccccccccccccccac a fcccccccccccccccccccccccccccccccccccccae a fcccccccccccccccccccccccccccccccccccceeg cc fccccccccccccccccccccccccccccccccccceacg a fcccccccccccccccccccccccccccccccccceaccg a fccccccccccccccccccccccccccccccccceacccg cc fccccccccccccccccccccccccccccccccgaccccg a fcccccccccccccccccccccccccccccccgacccccg a fcccccccccccccccccccccccccccccccaccccccg cc fccccccccccccccccccccccccccccccacccccccg ffafffffffffffffffffffff fcccccccccccccccccccccccccccccaccccccccg gcaccccccccccccccccccccg fccccccccccccccccccccccccccccacccccccccg gcegcccccccccccccccccccg fcccccccccccccccccccccccccccacdbcccccccg gccacccccccccccccccccccg fccccccccccccccccccccccccccabbdcbccccccg gccacccccccccccccccccccg fccccccccccccccccccccccccdbdccccddcccccg gccegccccccccccccccccccg fcccccccccccccccccccccdbbagccccccbcccccg gcccaccccccccccccccccccg fcccccccccccccccccccbbdcagccccccccbccccg gcccaccccccccccccccccccg fccccccccccccccccdbbcccaecccccccccgbcccg gccceccccccccccccccccccg fcccccccccccccdbbdccccaecccccccccccbdccg gccccacccccccccccccccccg fcccccccccccbbdccccccaecccccccccccccbccg gccccacccccccccccccccccg fccccccccdbbcccccccceecccccccccccccccbcg gccccacccccccccccccccccg fcccccgbbdccccccccceaccccccccccccccccddg gccccgeccccccccccccbcccg fcccdbdccccccccccceaccccccccccccccccccbg gcccccacccccccccccgdcccg fdbbccccccccccccceaccccccccccccccccccccb gcccccacccccccccccbccccg bdccccccccccccccgacccccccccccccccccccccdb gcccccgeccccccccccbccccg fccccccccccccccgaccccccccccccccccccccccgbf gccccccacccccccccbcccccg fcccccccccccccgacccccccccccccccccccccccg b gccccccacccccccccbcccccg fcccccccccccccaccccccccccccccccccccccccg fb gccccccgecccccccddcccccg fccccccccccccacccccccccccccccccccccccccg dd gcccccccacccccccbccccccg fcccccccccccaccccccccccccccccccccccccccg bf gcccccccaccccccddccccccg fccccccccccacccccccccccccccccccccccccccg b gccccccceecccccbcccccccg fcccccccccaccccccccccccccccccccccccccccg fb gccccccccacccccbcccccccg fccccccccacccccccccccccccccccccccccccccg bf gccccccccaccccbccccccccg fcccccccagcccccccccccccccccccccccccccccg b gcccccccceecccbccccccccg fccccccagccccccccccccccccccccccccccccccg fb gcccccccccaccbcccccccccg fcccccagcccccccccccccccccccccccccccccccg dd gcccccccccaccbcccccccccg fccccaeccccccccccccccccccccccccccccccccg bf gcccccccccegddcccccccccg fcccaecccccccccccccccccccccccccccccccccg b gccccccccccabccccccccccg fccaeccccccccccccccccccccccccccccccccccg cd gccccccccccadccccccccccg fceecccccccccccccccccccccccccccccccccccg bf gccccccccccbgccccccccccg feaccccccccccccccccccccccccccccccccccccg b gccccccccccbaccccccccccg cacccccccccccccccccccccccccccccccccccccg fb gcccccccccbcaccccccccccg cccccccccccccccccccccccccccccccccccccccg dd gcccccccccbcegcccccccccg fgcccccccccccccccccccccccccccccccccccccg bf gccccccccddccacccccccccg fffffffffffffffffffffffffffffffffffffff b gccccccccbcccacccccccccg cd gcccccccddcccacccccccccg bf gcccccccbccccceccccccccg b gcccccccbcccccaccccccccg fb gccccccbccccccaccccccccg dd gccccccbccccccgecccccccg b gcccccbccccccccacccccccg bgcccccbccccccccacccccccg cbccccddccccccccgeccccccg bccccbccccccccccaccccccg gbccgdccccccccccaccccccg gcbcbccccccccccceecccccg gcddbccccccccccccacccccg gccbcccccccccccccacccccg gcccccccccccccccceeccccg gcccccccccccccccccaccccg gcccccccccccccccccaccccg gcccccccccccccccccegcccg gccccccccccccccccccacccg gccccccccccccccccccacccg gccccccccccccccccccccccg gccccccccccccccccccccccg gccccccccccccccccccccccg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ac6f35ff b,#14ddc0ff c,#d8bca1ff d,#5ae5d0ff e,#bf9367ff f,#e9e8dfff g,#a4f1e6ff ``` ```image e ea eae eae cae cae caaf caaf caaf aaf faf faf faa faac faac faac eac eac eae eae eae f eae gbbd caegdbbbbbg cadbbbdg bbg dbbbbdf gbb gdbbbdg gbd fdbbbef db gdbbdaaf fb gdbbbdgaaf gd gbbbbg faf bg gdbbbdg fac bbf fdbbbdg faa gbb gbbbbgf faac dbd dbbbdg faac dbg gdbbbf eac gbd gdbbbdg eae dbg fgbbbbg eae bbf gdbbbdg eae gbb gdbbbdg eae dbd gbbbbgf cae db gdbbdg cae fb fdbbbg caaf g gdbbbdf caaf dbbbdg caaf bbg caaf faaf faaf faaf aac fac fac fea eac eae eae eae eae cae cae caaf caaf caaf faaf faaf faaf faac faac aac fac ec ea eae eae eae cae cae caaf aaf ff ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Alright, let's examine the next area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ab6e34ff b,#17dec1ff c,#d8bba0ff d,#6bead7ff e,#c3966cff f,#ecddd0ff g,#b5f4ebff ``` ```image caf fae aa caf fae aa eaf fac aa eaf fac eaf cac ae ea ca a e cc fe a ac dg ae gbd ea bb caf gbd fae dbg aa bb caf dbg fae bb aa bd eaf b fac gd aa dg eaf gb aa bb eaf dbg cac bb ae gbd eaf bb cac gbd ae dbg ea bb cac dbg ae bb ea gbd cac bb fae gbd ea dbg cac gbd fae dbg aa bb caf dbg fae bb aagbd cabb fabd bbf dbac bbaa gbdeaf bb fac gbd ae dbg eaf gbd cac dbg ae bb eaf dbg cac bb ae gbd ea bb cac gbd fae dbg ea bb cac dbg fae bb aa gbd caf bb fae gbd aa gbd fae g dbg aa b bb eaf bd bg fac dbd b aa bbg gd eaf gbb b fac dbd gb aa bbg db ea gbb bb ca gbd dbg a dbdbb ef bbbd cc gbb e gg a ac ae ea cac fae ea caf fae caf fae cf ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area B. Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#ab6f35ff b,#17dec1ff c,#d7ba9eff d,#6be9d7ff e,#c19367ff f,#ecded1ff g,#b5f4ebff ``` ```image ca caef fa a fa a fa ef fa e a a a e a fe a a a e af fe af a af a ac fc ec a ee a ee cc ce a ca a ca cc fa a fa a fa cc a a a a a cf a db a abbg b a dbd dd ef gbbaf b e bbd af b a dbd ac gb ef gbbg ac bg e bbd ec b a dbb ee b e gbbg ee dd fe b dbd ce b a gd gbbg ca b a b bg fa gb fe b fa bg a b fa b a b fa b fc dg a dd a b a b a gd a b cc b a gb a b a bg a b af b cc b af b a dg af dd a b ac b cfdg ec b ab ee gb ad ee bg bf ce b ba ca b b a f dd b ef b dg e b b a gd gd e bg b fe b b a b b e dd b fe b dg a b b a gd dg fc bg b a b gd a gb b cc ddb a b a cc a a cf a a ``` <!-- end of image -->
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I'm optimistic that I'll find some intersections in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#897549ff b,#a8d2a3ff c,#9dda74ff d,#eff6eeff e,#97c895ff f,#97986eff g,#b2d8b1ff ``` ```image ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd ebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbe eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbcggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggccfggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggccfgggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcffggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcffgggggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcffggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcffgggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbcffggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbcffgggggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggccffggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcbffgggggggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcbffggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcgffgggggggggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcgffggggggggggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggggbcgffgggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggggggggbcgffggggggggggggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggggbcgffgggggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggggggccgffggggggggggggggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggggcbgffgggggggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggggcbgffggggggggggggggggggggge eggggggggggggggggggggggggggggggggggggggggggggggggggcggffgggggggggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggggcggffggggggggggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggggbcggefgggggggggggggggggggggggge eggggggggggggggggggggggggggggggggggggggggggggggbcgggaggggggggggggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggggccgggfeggggggggggggggggggggggggge eggggggggggggggggggggggggggggggggggggggggggggcbggggagggggggggggggggggggggggggge egggggggggggggggggggggggggggggggggggggggggggcbggggaggggggggggggggggggggggggggge eggggggggggggggggggggggggggggggggggggggggggcbggggbfggggggggggggggggggggggggggge eggggggggggggggggggggggggfggggggggggggggggcggggggagggggggggggggggggggggggggggge eggggggggggggggggggggggggagggggggggggggggcggggggfegggggggggggggggggggggggggggge eggggggggggggggggggggggggagggggggggggggbcgggggggaggggggggggggggggggggggggggggge eggggggggggggggggggggggggabgggggggggggbcgggggggabggggggggggggggggggggggggggggge eggggggggggggggggggggggggafggggggggggccgggggggbagggggggggggggggggggggggggggggge eggggggggggggggggggggggggaagggggggggcbggggggggaggggggggggggggggggggggggggggggge eggggggggggggggggggggggggfaggggggggcbggggggggefggggggggggggggggggggggggggggggge eggggggggggggggggggggggggfagggggggcggggggggggagggggggggggggggggggggggggggggggge egggggggggggggggggggggggbffggggggcggggggggggfbgggggggggggggggggggggggggggggggge egggggggggggggggggggggggbfeeggggcgggggggggggaggggggggggggggggggggggggggggggggge egggggggggggggggggggggggeegfggbcgggggggggggagggggggggggggggggggggggggggggggggge egggggggggggggggggggggggeegagbcgggggggggggefgggggggggggggggggggggggggggggggggge egggggggggggggggggggggggfbgaccggggggggggggaggggggggggggggggggggggggggggggggggge egggggggggggggggggggggggfggcbggggggggggggfeggggggggggggggggggggggggggggggggggge egggggggggggggggggggggggfgcfgggggggggggggagggggggggggggggggggggggggggggggggggge egggggggggggggggggggggggfcgeegggggggggggaggggggggggggggggggggggggggggggggggggge egggggggggggggggggggggggcgggfggggggggggbfggggggggggggggggggggggggggggggggggggge c egggggggggggggggggggggbcagggaggggggggggagggggggggggggggggggggggggggggggggggggge dg eggggggggggggggggggggbcaggggagggggggggfegggggggggggggggggggggggggggggggggggggge c egggggggggggggggggggccagggggagggggggggaggggggggggggggggggggggggggggggggggggggge c eggggggggggggggggggccaggggggfggggggggabggggggggggggggggggggggggggggggggggggggge gd egggggggggggggggggcbabggggggbeggggggbagggggggggggggggggggggggggggggggggggggggge c eggggggggggggggggcbfeggggggggfggggggaggggggggggggggggggggggggggggggggggggggggge c egggggggggggggggcgffgggggggggagggggefggggggggggggggggggggggggggggggggggggggggge g eggggggggggggggcgeaggggggggggagggggagggggggggggggggggggggggggggggggggggggggggge dg eggggggggggggbcgbagggggggggggaggggfbgggggggggggggggggggggggggggggggggggggggggge c egggggggggggbcggaggggggggggggfbgggaggggggggggggggggggggggggggggggggggggggggggge c eggggggggggccggagggggggggggggbfggagggggggggggggggggggggggggggggggggggggggggggge ddegggggggggcbggabggggggggggggggagefgggggggggggggggggggggggggggggggggggggggggggge ceggggggggcbggaegggggggggggggggagaggggggggggggggggggggggggggggggggggggggggggggge cegggggggcgggffggggggggggggggggafeggggggggggggggggggggggggggggggggggggggggggggge geggggggcgggefgggggggggggggggggaagggggggggggggggggggggggggggggggggggggggggggggge cgggggcgggbaggggggggggggggggggeggggggggggggggggggggggggggggggggggggggggggggggge cgggbcggggaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge cggbcggggagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge eeccggggaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge ecbggggabggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge egggggfegggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge eggggffggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge egggbagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge egggaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge eggagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge egaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge eabggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge aegggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggge bfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeb df da a a ad ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#8a7348ff b,#baad94ff c,#9fdb71ff d,#ebefe2ff e,#b7e595ff f,#a39270ff g,#d4ddbeff ``` ```image cg gcd eccf cca ecaf dcbb dcba cebb eeba ecbab dcgbb dcdba gedab gc bb eceba dcg bb cc ba dcdbab gce bb ce ba ec bb dcg fa dcd fab ccd fb ge fa ce fb eg fa dcc fab dcd fb gcd fa ee fb ec fa ecg bab dcd ad gcc gg ee ba ec ab cg ad dcc a ccd ba gc fad df ce ab ga ee a ba ccg da ba dcd ba bad cc fad bag ge ag fab ec f ffa dcg da ffa dcg fa abag gcd a abab gcd bg abff ece da dabba eg gab dagga cc fa dagda dcd ag gag f gcc bd gad b ce da bad ggec ab bad dccg f ba dcg bg ba cca fa fagcdad gab cce ab ag cc af df defb ff fd dcfd gad fa dcfa gag ag cebb af bd eeba fa da ecgaf ba fa dcddad da af dccdfd a ag ge ab f fd ec bb bd ga ce ga gg aa dcc aad b df ccd dad f fd gcd fa ad fa ce ab ag bag ee gb ab af ecg daf ff db dcg aad ba fd dcc fg gagaf ccd ba dabag ge ab aff g ce da ba e deg daa gb c dcc fad c gcd bb e gcd ba dg ee af cec dad ccg dad ag bb gaf aad dad fa ab ga daf aad fg ``` <!-- end of image --> Gotcha! I've found 2 intersections hiding in area A! Answer: A: 2; 2 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#8a7349ff b,#bbaf96ff c,#9fdc71ff d,#edf2e4ff e,#b9e698ff f,#a89777ff g,#d7dfc3ff ``` ```image d gc ecf ecf cbf cbf cbf dcbb dcbb gcbb eebb cgbb cdfb cdfb c fb dc fb dc fb ge fb ee fb cg fb cd fb c fb c fb dc gb gc a ee bg eg a cd a cd df f c a a dc bg a dc a ad gc fd ab ee df fa eg a fa cd gb ba cd a dbf c fd dggg dc a gg b dc a gg a ge gb bd aee a b cg bg f cb a fc gg a c f df c dca a a dg gca a bg c eea a a c eea b fd gd cgad dg df e cdfg f a c c bb a gb e c gf a a e dc da f fd c gc a bd a c ee a db a dg eg ad f gb c cd fg a a c cd bb abg gd c gf fa e dc da g c dc a e ge a dgee a cg ad fg gf da a a a ad fg bb gf da a a ad ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#cf819bff b,#69d044ff c,#b2d8b1ff d,#a3d0a1ff e,#d7377cff f,#88d06dff g,#eff1ebff ``` ```image dddddddddddddddddddd dccccccccccccccccccc dccccccccccccccccccc dcccccccccccccbbfccc dccccccccccccbbbbccc dccccccccccccbbdcccc dcccccccccccdbbccccc dcccccccccccfbbccccc dcccccccccccbbfccccc dcccccccccccbbdccccc dcccccccccccbbcccccc dcccccccccccbbcccccc dccccccccccfbbcccccc dccccccccccfbbcccccc dccccccccccbbfcccccc dccccccdcccbbdcccccc dccccdeeeeefbaeeaccc dcccaeeeeeeeeeeeeccc dccaeeeccaeeeeaacccc dcaeeeccccbbfccccccc daeeacccccbbdccccccc eeeaccccccbbcccccccc eeeacccccccbbcccccccc eeeacccccccdbbcccccccc eeedccccccccfbbcccccccc eeegdccccccccbbfcccccccc eeeg dccccccccbbdcccccccc eee dccccccccbbccccccccc geee dccccccccbbccccccccc geee dcccccccdbbccccccccc geee dcccccccfbbccccccccc geee dcccccccbbfccccccccc aeee dcccccccbbdccccccccc aeee dcccccccbbcccccccccc aeea dcccccccbbcccccccccc aeea dddddddfbbdddddddddd eeea ggggggfbfgggggggggg eeea bbc eeeg bbg eeeg bb eeeg gbb eeeg cbb eee fbf geee bbc geee bb geee bb geee gbb aeee dbb aeee gbbd aeea bbbbg eeea fbbbb eeea dbbbbg eeeg cbbbbg eeeg gbbbbc eeeg gbbbbd eeeg bbbbf eee fbbbb gggggggggggggggggggggggggggggeee dbbbbg ddddddddddddddddddddddddddddeeeg cbbbbg dcccccccccccccccccccccccccdeeedg gbbbbc dccccccccccccccccccccccccaeeecdg gbbbbd dcccccccccccccccccccccccaeeeccdg bbbbf dccccccccccccccccccccccaeeecccdg fbbbb dcccccccccccccccccccccaeeeccccdg dbbbbg dcccccccccccccccccccceeeacccccdg cbbbbg dccccccccccccccccccceeeaccccccdg gbbbbc dcccccccccccccccccceeeacccccccdg gbbbbd dccccccccccccccccceeeaccccccccdg bbbbf dcccccccccccccccceeedcccccccccdg fbbbb dccccccccccccccceeecccccccccccdggdbbbbg dcccccccccccccceeeccccccccccdbbbbbbbg dccccccccccccceeeccccccdfbbbbbbbbbc dcccccccccccceeecccfbbbbbbbbbffg dccccccccccdeeefbbbbbbbbbfdcccdg dcccccccccfeeebbbbbbfdccccccccdg dccccdfbbfeeebbbfcccccccccccccdg dcfbbbbbaeeedcccccccccccccccccdg dcdbbbbaeeecccccccccccccccccccdg dccdcceeeaccccccccccccccccccccdg dcccceeeacccccccccccccccccccccdg dccceeeaccccccccccccccccccccccdg dcceeeacccccccccccccccccccccccdg dceeedccccccccccccccccccccccccdg dccedcccccccccccccccccccccccccdg dcccccccccccccccccccccccccccccdg dcccccccccccccccccccccccccccccdg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#e275a3ff b,#69d044ff c,#cdeec1ff d,#f3c6daff e,#d8367cff f,#9cde83ff g,#939258ff ``` ```image aee eeee deeeee deeeeee deeeeeed deeeeeed deeeeeed deeeeeed deeeeeed aeeeeeed aeeeeee aeeeeea aeeeeea aeeeeea aeeeeea eeeeeea deeeeeea deeeeeed deeeeeed deeeeeed deeeeeed deeeeeed deeeeeed aeeeeeed aeeeeee aeeeeea aeeeeea cffb aeeeeea cffbbbbbb aeeeeea ccfbbbbbbbbbbb aeeeeea cffbbbbbbbbbbbbbbb eeeeeea ccfbbbbbbbbbbbbbbbbbbff deeeeeea cffbbbbbbbbbbbbbbbbbbfcc deeeeeeafbbbbbbbbbbbbbbbbbbffc deeeeeegbbbbbbbbbbbbbbbbfcc cfeeeeeegbbbbbbbbbbbbfcc ccfbbgeeeeeegbbbbbbbbffc cffbbbbbgeeeeeegbbbbbfcc ccfbbbbbbbbbgeeeeeebbffc fbbbbbbbbbbbgeeeeeecc cbbbbbbbbbbgeeeeee cbbbbbbbffaeeeeea bbbfcc aeeeeea c aeeeeea aeeeeea eeeeeea deeeeeea deeeeeed deeeeeed deeeeeed deeeeeed eeeeeed deeeed deed d ``` <!-- end of image --> 1 intersection present within area A. Now, let's dive into another area. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#e47fa9ff b,#68cf43ff c,#b2e69fff d,#f3c4d8ff e,#d8367cff f,#8cd26dff g,#d8f2cfff ``` ```image gcbg cfbbbc bbbbbbb cbbbbbbbc fbbbbbfc bbbbfg bbbbc gbbbbg cbbbb cbbbb fbbbf bbbbc gbbbbc gbbbbg cbbbb fbbbf fbbbf bbbbc gbbbbg cbbbbg cbbbb fbbbf bbbbc bbbbc gbbbbg dd cbbbb deeeeaad cbbbb ddd deeeeeeeeeeafbbfaaeeeea deeeeeeeeeeeeeeeeeeeeeee deeeeeeeeeeeeeeeeeeeeeeee deeeeeeaaeeeeeeeeeeeeeeeeed aeeeeeed daeeeeeeeeaadd aeeeeee fbbffd aeeeeee fbbbf aeeeeea bbbbc aeeeeea gbbbbg aeeeeea gbbbbg eeeeeea cbbbb eeeeeea fbbbf eeeeea fbbbf eeeed bbbbc eeed gbbbbg eed cbbbbg ed cbbbb d fbbbf bbbbc bbbbc gbbbbg cbbbb cbbbb fbbbf bbbbc gbbbbc gbbbbg cbbbb fbbbf fbbbf bbbbc gbbbbg gbbbbg cbbbb fbbbf bbbbf bbbbc gbbbbg ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 1; B: 1; 1 + 1 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#de6698ff b,#69cf44ff c,#c1e9b1ff d,#eea9c7ff e,#d8357bff f,#95dd7bff g,#eceae1ff ``` ```image fbf bbbb bbg cbb fbb bbf bbg bb bb cbb fbf bbc g bbg geeeeabbdaea deeeeeeeeeeee deee daeeead aeea fbf aeea bbc aeea bb eeed bb eeed gbb eeed fbb eeeg bbf eeeg bbg eee bb eee bb geee cbb geee fbb deee bbc deee bbg deea bb aeea bb aeea cbb aeed fbf eeed bbc eeed bb eeeg bb eeeg gbb eee cbb eee bbf geee bbc geee bb deee bb deee gbb deee fbb aeea gbbf aeea bbbbg aeea fbbbb eeed fbbbb eeed cbbbbg eeeg gbbbbc eeeg gbbbbf eeeg bbbbf eee fbbbb eee fbbbbg geee cbbbbg geee gbbbbc deee gbbbbf deee bbbbf deea fbbbb aeea fbbbbg aeea cbbbbg aeed gbbbbc eeed bbbbf eeed bbbbf eeeg fbbbb eeeg gfbbbbg eee cfbbbbbbg eee gfbbbbbbbbbc geee cbbbbbbbbbfc geeefbbbbbbbbbc ceeebbbbbbfg cfbbbeeebbbc fbbbbbaeeeg gbbbfaeea g aeea aeed eeed eeed eeeg eg ``` <!-- end of image -->
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I have an image in front of me. I need to determine if there are any intersection segments. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#b1d7b1ff b,#87608aff c,#a3a375ff d,#6d2f73ff e,#dbd5d0ff f,#a1c295ff g,#aa92adff ``` ```image e ffffffffffffffffffffff egddddd aaaaaaaaaaaaaaaaaaaaaa egdddbg dg aaaaaaaaaaaaaaaaaaaaaa ebdddbg d aaaaaaaaaaaaaaaaaagbdddbe ed aaaaaaaaaaaaagbdddbgaa dg aaaaaaaaaaaabbgaaaaaaa d aaaaaaaaaaaadaaaaaaaaa ed aaaaaaaaaaaadaaaaaaaaa bg aaaaaaaaaaabbaaaaaaaaa d aaaaaaaaaaadaaaaaaaaaa ed aaaaaaaaaaadaaaaaaaaaa bg aaaaaaaaaagbaaaaaaaaaa d aaaaaaaaaadaaaaaaaaaaa ed aaaffffffadaaaaaaaaaaa bg aaafffffccdccccccccccccccccccf d aaaaaaaaadfaaaaaaaaaaa ec ed aaaaaaaaadaaaaaaaaaaaa c bb aaaaaaaaadaaaaaaaaaaaa ef d aaaaaaaabgaaaaaaaaaaaa c d aaaaaaaadaaaaaaaaaaaaa ce bb aaaaaaaadaaaaaaaaaaaaa c de aaaaaaabbaaaaaaaaaaaaa c d aaaaaaadaaaaaaaaaaaaaa ef gb aaaaaaadaaaaaaaaaaaaaa c de aaaaaagbaaaaaaaaaaaaaa ce d aaaaaadfaaaaaaaaaaaaaa c gb aaaaaadaaaaaaaaaaaaaaa c de aaaaafdaaaaaaaaaaaaaaa ef d fffffdcfffffffffffffff c gd d ce de d c d gg c gd d ef de d c d gg ce ed d c dg c d ef ed c dg fe d c ed c bg e ef d c c ed c fe bg c c d c c ed c ef bb ef c fadfaaaaaaaaffaaaa fe fafdaaaaaaaacfaaaa c faabbaaaaaaacaaaaa c faaadfaaaaaacaaaaa ef faaaadaaaaaacaaaaa c faaaabbaaaaacaaaaa fe faaaaadfaaaacaaaaa c faaaaaadaaaacaaaaa c faaaaaabdaaacaaaaa ef faaaaaaadfafcaaaaa c faaaaaaaadaffaaaaa fe faaaaaaaabdcfaaaaa c faaaaaaaaadcaaaaaa c faaaaaaaaaadaaaaaa ef faaaaaaaaacbdaaaaa c faaaaaaaccaadgaaaa fe faaaaaaccaaaadaaaa c faaaaccaaaaaaaaaaa c faaacfaaaaaaaaaaaa ef faccaaaaaaaaaaaaaa c fcfaaaaaaaaaaaaaaa fe fcaaaaaaaaaaaaaaaaa c ecafaaaaaaaaaaaaaaaaa c fc faaaaaaaaaaaaaaaaa ef eca faaaaaaaaaaaaaaaaa c cc faaaaaaaaaaaaaaaaa fe ece faaaaaaaaaaaaaaaaa c cc faaaaaaaaaaaaaaaaa c ece efcc ce ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#eae4e7ff b,#916195ff c,#a4a274ff d,#6d2e73ff e,#d3c9caff f,#c4c3a5ff g,#b393b6ff ``` ```image aeg aegbdddd aegbdddddddbg aegbdddddddbgea gddddddbgea bdbgea add gdb bdg dda edb gdg dda edd gdg bde add gdb bde adda edb ffffeeeeeaaaabdg acccccccccccccddcccccccccffffffffeeeee eeeeffffffffcddcccccccccccccccccccccc gdg aaaaaaeeeeeeffff dda add gdg bde add gdb bde dda edb bdg dda edb gdg bde add gdb bde add edb bdg dda edb gdg dda add ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Alright, let's concentrate on the next area. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#efecebff b,#8e5f91ff c,#a4a375ff d,#6e2f73ff e,#d8d3cbff f,#bebd9cff g,#b696b9ff ``` ```image adde ecf gdda fce bdb fce addg fca gdda cca bdb cc addg cc edda acc bdb acf addg ecf edda ecf bdb ece addg fce edda fce gdb fca addg cca edde cc gdb acc bdg acf edde ecf gdb ecf bdg ece edde fce gdd fce bdgfca addcca gddc bdb ecdde afccbdda eccce bdb afccfa adde eccce gdda afccfa bdb eccce adg afccfa a eccce afccfa eccce afccfa eccce afccf eccce ccf ca ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 1; B: 1; 1 + 1 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#f1eeeeff b,#936597ff c,#a3a273ff d,#6e2f73ff e,#d9d3cbff f,#b9b894ff g,#b99cbcff ``` ```image a egddddd ebddddga dg ebdddbga d ebdddbg ed gbdddbe dg bbe d d ed ad dg bg d d ed d bg gb da da ad feeeeeada bb eeefffcdccccccccccccccccccfa da de aac ad d c bb ad ef da bg c ad d fe bb d ac da gg c ad d ef bb d c de gb fe ad da ac gb d c de ed ef d be c gd d fe de ad ac d bg c gd d ef dg d c d gb fe gd da ac dg c d ef ed c dg fe d c ed c bg e ef da c c ed c fe bb c c da c c ad af ef bb ef c da ee fe ad fe c bb ca c da c ef ad c c bb c fe da c c ad c c gb ac ef de ef c d ee fe gdfe c dca c d ef acbd c fca de fe acf d c fca a c acf ef fca c acf fe fc c acf c fc ef ace c fc fe ece c cc c ece efcc ce ``` <!-- end of image -->
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Let's examine this image for potential line intersections. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0e2b88ff b,#bf44bbff c,#b0d6b1ff d,#c979c7ff e,#5d77a5ff f,#d8cde7ff g,#95c797ff ``` ```image f db fbdd b b bf dd bd b db dd fb b b dd bf b bd dd db b fb dd b b bf dd bd b db dd fb b b dd bf b bd dd db b gccccccccccccccccccdbccg gccccccddccccccccc cccccccccccccccccccbcccg gcccccccbccccccccc ccccccccccccccccccbccccg gcccccccddcccccccc cccccceacccccccccbdccccg gccccccccbcccccccc cccgaaeeacccccccdbcccccg gccccccccddccccccc ceaaecccaccccccdbccccccg gcccccccccbccccccc eaagccccceacccccbcccccccg gcccccccccddcccccc faaecccccccccaccccbccccccccg gccccccccccbcccccc gaac ccccccccceaccbdccccccccg gccccccccccddccccc eaa ccccccccccacdbcccccccccg gcccccccccccbccccc faae cccccccccceabccccccccccg gcccccccccccdacccc eaaf cccccccccccacccccccccccg gccccccccccceacccc eaa ccccccccccbeaccccccccccg gcccccccccccaccccc faae cccccccccbdcaccccccccccg gccccccccccaeccccc eaaf ccccccccdbcceacccccccccg gccccccccceacccccc aae ccccccccbccccacccccccccg gcccccccccaccccccc faae cccccccbccccceaccccccccg gccccccccaeccccccc aaf ccccccbcccccccaccccccccg gcccccccgacccccccc cccccbdccccccceacccccccg gcccccccaccccccccc ccccdbcccccccccacccccccg gccccccaeccccccccc ccccbcccccccccceaccccccg gcccccgacccccccccc cccbccccccccccccaccccccg gcccccaccccccccccc ccbccccccccccccceacccccg gccccaeccccccccccc gbdggggggggggggggagggggc ca db fa a fb af ae b fa fa bf af a bd fa ae db af fa fb fa a b af ae bf fa fa bd af a db fa ae fb af fa b fa af bf af ae bd fa fa db af af fb fa ae b ac fa bf a af bd ac ae db a fa fb acaf b ae bf e bd db fb b bf bd db fb b bf ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#334599ff b,#c045bcff c,#a0abd0ff d,#d481d1ff e,#7686bbff f,#e6cfebff g,#0c2887ff ``` ```image dbbf fbbf fbbd bbd dbb dbbf fcf fbbf fegga fbbd cagggggc bbd feagggacega dbb feggggef fggc dbbf cagggac ega fbbf feggggef fggc fbbd ggggef ega bbd gac fggc dbb f ega dbbf fggc fbbf ega fbbd fggc bbd ega dbb ggcdbbf egabbf ggad agg dbggc dbbega fbbf ggc fbbd ega bbd ggc dbb cgg dbbf ggc fbbf cgg fbbd age bbd cgg dbb age dbbf cgg fbbf age fbbd cgg bbd age dbb cgg dbbf age fbbf cgg fbbd age bbd cggf dbb age dbbf cggf ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Let's shift our focus to the next area. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#263992ff b,#bd41baff c,#b4bcdaff d,#d179ceff e,#6476b3ff f,#efdff2ff g,#072586ff ``` ```image dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbd fbbf dbac faga cggb fagad egaf cggc fage ega cggc fage ega cggc fage ega cggc fage egaf cggc fage egaf cggc fage egaf cggc fage ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area B. Answer: A: 1; B: 1; 1 + 1 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#284095ff b,#c044bcff c,#afb8d7ff d,#d27ccfff e,#6577b3ff f,#e4d3ecff g,#092686ff ``` ```image f db fbdd b b bf dd bd b db dd fb b b dd bf b bd dd db b fb dd b b bf dd bd b db dd fb b b dd bf b bd dd db b fb dd b b bf dd eg bd b fageea db dd cggc g fb b egaf ea b dd fgge g bf b cggc ea bd dd egaf g db b fgge eab da eggc g cg aga bea gf cgge bd g ae eggc db ca cg aga fb g g cgge b ca ae ggf bf g cg bd cg g db g ae fb cg cg b gf g bf cg ae bd gf cg db cg g fb gf ae b cg cg bf gf g bd cg ae db gf cg fb cg gf b gf ae bf fg cg bd gf gf db fg ae fb gc cg b fg gf bf gc ae bd fg fg db gc gf fb fg ae b gc fg bf fg gf bd gc ae db fg fg fb gcgf b ge bf e bd db fb b bf bd db fb b bf ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#8a12c9ff b,#3ffdebff c,#ad77d0ff d,#a2cda3ff e,#ecf3f1ff f,#b1d7b2ff g,#82f5e3ff ``` ```image ae aa eaa caa aaceeeeeeeeeeeeeeeeeeeeee eaadddddddddddddddddddddd edaaffffffffffffffffffffd edcaafffffffffffffffffffd edfaacffffffffffffffffffd edffaadfffffffffffffffffd edfffaafffffffffffffffffd edfffcaaffffffffffffffffd edffffaacfffffffffffffffd edfffffaadffffffffffffffd edffffffaaffffffffffffffd edffffffcaafffffffffffffd edfffffffaaaffffffffffffd edffffffffaacfffffffffffd edfbbbbbbbbaabbbbbbbbbbbb edbbbbbbbbbbaabbbbbbbbbbbb edbbffffffffcaafffffffffbbg edbbfffffffffaacffffffffdbbg edbbffffffffffaaffffffffd bbe edbbffffffffffdaafffffffd bbe edbgfffffffffffcaaffffffd ebb egbfffffffffffffaacfffffd ebb egbffffffffffffffaadffffd gbb ebbfffffffffffffffaaffffd gbb ebbfffffffffffffffcaafffd bbg ebbffffffffffffffffaacffd bbg cce ebbfffffffffffffffffaadfd bbe caaaaaaaacce ebgffffffffffffffffffaafd bbe aaeccaaaaaaaaaaaaac ebgffffffffffffffffffdaad ebb aa eccaaaaac gbddddddddddddddddddddaaa ebb ac bbeeeeeeeeeeeeeeeeeeeeeaac gbb cae bb aae gbb aa bb eaa bbb aa bb caa bbg aa bg aac bbg eac ebg aae bbe cae gbe eaa bbeeeeeeeeeeeeeeaaeeeeeeee gb caa ebbdddddddddddddaadddddddde bb aac ebbffffffffffffaafffffffde bb aae gbbffffffffffcacfffffffde bb aa dbbbfffffffffaaffffffffde bb eaa dfbbbffffffffaaffffffffde ebg cac dffbbgfffffffaaffffffffde gbe aae dfffbbfffffffacffffffffde gb aa dffffbbfffffcadffffffffde bb eaa dfffffbbffffaafffffffffde bb caa dfffffgbbfffaafffffffffde bb aac dffffffgbbffaafffffffffde bb aae dfffffffbbbcacfffffffffde bg eaa dffffffffbbaaffffffffffde caa dfffffffffbaaffffffffffde aac dffffffffffaagfffffffffde aae dffffffffffacbfffffffffde eaa dfffffffffcadbbffffffffde caadfffffffffaaffbbfffffffde aaafffffffffaaffgbbffffffde aadffffffffaafffgbbfffffde aafffffffdacffffbbbffffde daaffffffcaffffffbbbfffde dcaafffffaafffffffbbgffde dfaacffffaaffffffffbbgfde dffaaffffaafffffffffbbfde dffdaaffcacffffffffffbbde dfffcaafaaffffffffffffbbe dffffaacaaffffffffffffgbb ddddddaaaadddddddddddddgbb eeeeeeeaaceeeeeeeeeeeeeegbb cae bbg bbg bbg bbe bbe ebb ebb gbb gbb b ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#890fcaff b,#3dfdebff c,#c084e3ff d,#9f45d5ff e,#c8fef9ff f,#e2c5f2ff g,#8efdf3ff ``` ```image aaaf aaaaf daaad daaad faaaac faaaaf caaaa daaad faaaac faaaaf caaaa daaad aaaac faaaaf caaaaf daaad daaac faaaac caaaaf caaad daaad faaaac faaaaf caaaa daaad aaaac faaaaf caaaaf bbbbbbbbbbbbbbbbdaaadbbbbbbbbbbbbbbbbbbbbb gbbbbbbbbbbbbbbbbbaaaadbbbbbbbbbbbbbbbbbbbb gbbbbbbbbbbbbbbbbbbaaaabbbbbbbbbbbbbbbbbbbb bbbbgggggggggggggggcaaaaggggggggggggggggggg bbbg daaad ebbbg daaad ebbbe faaaac gbbbe faaaaf gbbb caaaa gbbb daaad bbbb faaaac bbbg faaaaf bbbg caaaa ebbbe daaad ebbbe aaaac gbbb faaaaf gbbb caaaaf bbbb daaad bbbg daaac bbbg faaaac ebbbg caaaaf ebbbe caaad gbbbe daaad gbbb faaaac gbbb faaaaf bbbg caaaa bbbg daaad bbbg aaaac bbbe faaaa bbbe caaa ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Alright, let's examine the next area. I'm going to scrutinize area B for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#890ecaff b,#3ffdecff c,#c48ae5ff d,#a34ed7ff e,#c2fdf8ff f,#e2c5f2ff g,#7afdf1ff ``` ```image aaad g faaac bg caaaf bbg daaa bbbe aaad bbbbe faaac gbbbbe caaaf gbbbb caaa gbbbb daaa bbbbg aaad ebbbbg faaac ebbbbg caaaf ebbbbe daaa ebbbbe aaad gbbbbe aaac gbbbbe faaac gbbbb caaaf bbbbg daaa bbbbg aaad ebbbbg faaac ebbbbg caaaf ebbbbe daaa gbbbbe daad gbbbbe aaad gbbbb faaac bbbbbcaaaf bbbbdaaa ebbbaaad ebbaaac ebaaac daaabe daaabbe aaadbbbe faaadbbbb caaafbbbbg daaa bbbbg aaad ebbbbg aaac ebbbbg d faaac ebbbbe ac caaaf gbbbbe aaf daaa gbbbbe aaa aaad gbbbbe aaad faaac gbbbb aaaac caaaf bbbbb faaaaf daaa bbbbg caaaaf daad ebbbbg daaad aaad ebbbbg aaaac faaac ebbbbe faaaac caaaf ebbbbe caaaaf daaa gbbbbe daaad aaad gbbbbe daaad faaac gbbbb faaaac caaaf bbbbb faaaaf caaa bbbb caaaa daaa ebbb daaad aaad ebb faaaacfaaac eb faaaadaaaf e caaaaaaa ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area B! Answer: A: 1; B: 1; 1 + 1 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#890fcaff b,#3efdecff c,#c78de5ff d,#a44bd7ff e,#c3fef8ff f,#e4caf2ff g,#7bfef1ff ``` ```image af aa faa dad aac aa faa caa aac aaf aa caa dad aaf aa faa dad aaf bbbbbbbbaabbbbbbbbbbbb gbbbbbbbbbaabbbbbbbbbbbb bb dad bbg bb aac bbg bb aa bbe bg faa bb bg caa bb ebe aac ebb gb aaf gbb bb aa gbb bb caa bbg bb dad bbg dcf bb aaf bbe daaaaaaaadcf bg aa bbe aafcdaaaaaaaaaaaadc ebe faa bb aa fcdaaaaac gb dad ebb ad bb aac ebb caf bb aa gbb aa bb faa bbb aa bb caa bbg aa bg aac bbe fac ebe aaf bbe da ebe aa bb aa gb caa ebb aa bb dad ebb ad bb aaf gbb caf bb aa gbb da bg faa bbg aa bg dad bbe aa ebe aaf bbe ac gb aa bb caf bb faa bb aa bb dad ebb aa bb aac gbb ad bb aa gbbfac bg faa bbda caa baa aac aae aaf adbe aa cafbb caa aa ebb dad aa ebb aaf aa gbb aa fac gbb faa da bbg dad aa bbg aac aa bbe aa ad bbe faa caf bb caa da ebb aacaa ebb aaaa gbb aac gbb caf bbg bbg bbe bbe bb ebb ebb gbb gbb g ``` <!-- end of image -->
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Let's examine this image for potential line intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#9e488dff b,#f5a971ff c,#d3accbff d,#f5d9cdff e,#ad80a0ff f,#b1d7b1ff g,#98c797ff ``` ```image gfffffffffffffffffffffffffffffffffff gfffffffffffffffffffffffffffffffffff gfffffffffffffffffffffffffffffffffff bbb gffffffffffffffffffffffffffeffffffff dbb gfffffffffffffffffffffffffaaefffffff bb gffffffffffffffffffffffffaaaefffffff bbd gfffffffffffffffffffffffaaaaaffbffff bbb gffffffffffffffffffffffeaaaaafbbbfff dbb gffffffffffffffffffffffaaaeabbbbffff bb gfffffffffffffffffffffaaafgbbbbfffff bbd gffffffffffffffffffffaaafbbbbbffffff bbd gfffffffffffffffffffaaagbbbbafffffff bbb gffffffffffffffffffeaaebbbbaafffffff dbb gffffffffffffffffffaabbbbffaafffffff bb gfffffffffffffffffaabbbbfffaaeffffff bbd gffffffffffffffffaabbbbffffaaeffffff bbb gfffffffffffffffebbbbffffffaaeffffff dbb gffffffffffffffebbbbfffffffaaaffffff bb gffffffffffffffbbbbffffffffeaaffffff bbd gffffffffffffbbbbffffffffffeaaffffff bbb gfffffffffffbbbbfffffffffffeaaffffff bbb gffffffffffbbbeeffffffffffffaaffffff dbb gffffffffbbbbaafffffffffffffaaffffff bb gfffffffbbbbaaffffffffffffffaaffffff bbd gfffffbbbbeaafffffffffffffffaaffffff bbb gffffbbbbaaaffffffffffffffffaagfffff dbb gfffbbbbeaaeffffffffffffffffaaefffff bb gfbbbbffaaafffffffffffffffffaaefffff bbd gbbbbffaaaffffffffffffffffffaaafffff bbb bbbbbffaaafffffffffffffffffffeaafffff dbb dbbbbbbfffaaagfffffffffffffffffffeaafffff dbb dbbbbbbbbfffeaaeffffffffffffffffffffeaafffff fffeeffffbbbffg dbbbbbbbd gfffaaafffffffffffffffffffffgaafffff ffaaafffffbbffg bbbbbbbbd gffaaafffffffffffffffffffffffaafffff fffaagffffbbbfg dbbbbbbb gfaaaffffffffffffffffffffffffaafffff fffaaafffffbbbg dbbbbd geaagffffffffffffffffffffffffaafffff ffffaafffffbbbg dbbb eaaefffffffffffffffffffffffffaagffff ffffaaafffffbbb dbbb aaaffffffffffffffffffffffffffaaeffff ffffgaaffffffbbd dbbb aaafffffffffffffffffffffffffffaaeffff fffffaaafffffbbb dbbb aaaggggggggggggggggggggggggggggaaagggg fffffeaaffffffbbd dbbb eaac eaa ffffffaaefffffbbb dbbb daae eaa ffffffeaafffffgbbb dbbb aaa caa fffffffaaeffffgdbb dbbb aaa daa fffffffaaaffffg bbb dbbb aaa aa ffffffffaagfffg bbd dbbb caac aa ffffffffaaafffg bbb dbbb daae aa fffffffffaafffg bbbdbbb aaa aad fffffffffaaaffg dbbbbb aaa aac caa bbbb eaad aac aae dbb caac aae caa aaa aaa aac aaa eaa eaa aaa caa aac eaad aaa caae aa aaa aaa aaa daa aaa aae eaac caa caae aae aaa eaa eaa aac aac eaa aa aad eaa aaa aac daa daa aaa aaa caa aac aae daa caa aaa aac aac eaa caa aac aaa aaa aac aad caa aaa aaa daa aad aaaaa caaaa aaad eaa ed ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#9e478dff b,#f7a971ff c,#c592bbff d,#f9c8a4ff e,#b16ca4ff f,#f4e2e2ff g,#d8b6d2ff ``` ```image fbbbbb f bbbbbd feag fbbbbbf eaaaa dbbbbd eaaaag fbbbbbf gaaaae dbbbbb eaaaag bbbbbd gaaaae fbbbbbf aaaaaf bbbbbd caaaac fbbbbbf faaaaaf dbbbbb caaaac bbbbb faaaaa dbbbb eaaaag bbbb gaaaae fbbb eaaaag dbb gaaaae fbb aaaaaf db caaaae b aaaaaf f caaaac faaaaa eaaaac faaaaa eaaaag gaaaae eaaaag gaaaae aaaaaf caaaac faaaaaf caaaac faaaaa eaaaag ``` <!-- end of image --> Area A does not contain any intersection points. Now, let's dive into another area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#9e478dff b,#f5a770ff c,#c38db7ff d,#f9c7a3ff e,#b36999ff f,#f2e0e2ff g,#d8b6d1ff ``` ```image fccg feaaaf eaaaac caaaaac gaaaaaae faaaaaaae fd eaaaaaaaa dbbf caaaaaaaaa fbbbbb caaaaaaaaaaffbbbbbbd gaaaaaecaaaadbbbbbbbf faaaaae gaaebbbbbbbdf eaaaaaf gaebbbbbbbd caaaaag gbbbbbbbbf gaaaaac fbbbbbbbd faaaaae dbbbbbbbd faaaaaef dbbbbbbbc eaaaaaffbbbbbbbbae caaaaagdbbbbbbbeaae gaaaaacdbbbbbbbeaaaa faaaaaebbbbbbbd caaaa faaaaabbbbbbbbf caaaaf eaaaabbbbbbbbf caaaaf caaaebbbbbbbd gaaaag gaaabbbbbbbbf gaaaag faaebbbbbbbd faaaac eaebbbbbbbd faaaac eabbbbbbbbf aaaac cebbbbbbbd aaaae gebbbbbbbd eaaae fbbbbbbbbf eaaaa fbbbbbbbd caaaa dbbbbbbbf caaaaf fbbbbbbbbf caaaaf fbbbbbbbb gaaaag dbbbbbbbe gaaaag fbbbbbbbbaf faaaag dbbbbbbbeag faaaac dbbbbbbbeac aaaac fbbbbbbbbaae aaaae dbbbbbbbeaaaf aaaae dbbbbbbbeaaaf eaaaa fbbbbbbbbaaaag eaaaa dbbbbbbbeaaaac caaaaf fdbbbbbbbeaaaae caaaaf fbbbbbbbdeaaaaaf gaaaag dbbbbbbbfeaaaaag gaaaag fbbbbbbbbfcaaaaag gaaaag fbbbbbbbd gaaaaac faaaac dbbbbbbbf faaaaae faaaac fbbbbbbbd eaaaaaf aaaae dbbbbbbbd caaaaag aaaae dbbbbbbbf gaaaaac eaaaa bbbbbbbd gaaaaae eaaaa bbbbbbd faaaaae caaaa bbbbbf eaaaaaf caaaaf bbbd caaaaag gaaaaf bdf gaaaaac gaaaag faaaaae gaaaag faaaaaaf faaaac eaaaaaf faaaac caaaaag aaaac gaaaaac aaaae faaaaae eaaae feaaaaaf eaaaa eaaaaaf caaaa caaaaag caaaaf gaaaaac caaaaf faaaaae gaaaag eaaaaaf gaaaag aaaaag faaaag aaaac faaaac ``` <!-- end of image --> Case closed! This is definitely 2 intersections point in area B. Answer: A: 0; B: 2; 0 + 2 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#9e488dff b,#f6a871ff c,#ca9bc0ff d,#fad4b9ff e,#b36ea3ff f,#f5e7e8ff g,#dfc3d9ff ``` ```image bbb fe dbb aac bb aaae bbd eaaaa bf bbb caaaaadbbb dbb faaecabbbbf fbb aaa gbbbb bbf aaa dbbbd bbd eaagbbbba bbb gaacbbbbaa fbb faabbbbd aaf bb aabbbb aag bbd aabbbb aac bbb ebbbbf aae dbb gbbbb aae bb dbbbd eaa bbf bbbbf caa bbd bbbbf gaa dbb dbbbeg faa fbb bbbbae aa bb fbbbbaa aa bbd dbbbeaa aaf bbb bbbbeaaf aag dbb fbbbbcaac aac bb dbbbdfaae aac bbd bbbb aaa aae bbb fbbbbb aaa eaa dbb fbbbbbbf eaaf caa fbb dbbbbbbbd caac gaa ec bbb dbbbbbbbd faaa gaa eaa fbbd dbbbbbbbf aaa aa aag bbb dbbbbbbbf aaa aa aaa bbd dbbbbd eaag aa faaf dbb dbbb gaae aag aaa bbb dbbb faaa aag gaa fbbf dbbb aaa aac aae bbb dbbb aaaf aae caa bbd dbbb eaag eaa aac bbb dbbb gaae caa eaa bbb dbbb aaa caa aag dbb dbbb aaa gaa eaa bbb dbbb aaaf faa aaf fbbd dbbb caac aa aaa bbb dbbb faae aa faa bbddbbb aaa aaf aaa dbbbbb aaa aag gaa bbbb eaaf aac aae fbb caac aae caa faaa eaa aac aaa eaa eaa aaa cae aag eaag aaa gaac faaf faaa aaa aaa gaa aaa aae eaag caa gaae aac aaa eaa eaa aac aac eaa faa aag eaa aaa aac faaf faa aaa eaa gaa aac aae gaa caa aaa aac aag eaa gaa aag aaa aaa aag faaf gaa aaa aaa gaa aag aaaaa caaae aaaf caa eg ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#5a5175ff b,#bbf451ff c,#b1d7b1ff d,#eff7ebff e,#7c8588ff f,#b8e77cff g,#97c597ff ``` ```image bbd bbbf bbbbf bbbbbb bbbbbbb bbbb bbb ggggggggggggggggggggggggggggggggggggggggggggbbbbggbbbggggggggggggggggggggggggggggc cccccccccccccccccccccccccccccccccccccccccccbbbbagcbbbccccccccccccccccccccccccccccg ccccccccccccccccccccccccccccccccccccccccccfbbbaaacbbbccccccccccccccccccccccccccccg cccccccccccccccccccccccccccccccccccccccccfbbbaaaacfbbccccccccccccccccccccccccccccg ccccfcccccccccccccccccccccccccccccccccccfbbbaaaaaafbbccccccccccccccccccccccccccccg ccbbbccccccccccccccccccccccccccccccccccfbbbaaacaaafbbccccccccccccccccccccccccccccg ccfbbcccccccccccccccccccccccccccccccccfbbbeaaeccaaebbccccccccccccccccccccccccccccg cccbbfcccccccccccccccccccccccccccccccfbbbcaaacccaaebbccccccccccccccccccccccccccccg cccbbbcccccccccccccccccccccccccccccccbbbcaaaccccgaabbccccccccccccccccccccccccccccg cccbbbccccccccccccccccccccccccccccccbbbceaaecccccaabbccccccccccccccccccccccccccccg cccfbbcccccccccccccccccccccccccccccbbbfcaaaccccccgabbfcccccccccccccccccccccccccccg ccccbbfcccccccccccccccccccccccccccbbbfcaaagcccccccabbfcccccccccccccccccccccccccccg ccaabbbccccccccccccccccccccccccccbbbfceaaaccccccccebbfcccccccccccccccccccccccccccg cceagbbcccccccccccccccccccccccccbbbfccaaaccccccccccbbfcccccccccccccccccccccccccccg ccgaabbfcccccccccccccccccccccccbbbfccaaagccccccccccbbbgccccccccccccccccccccccccccg cccaabbbccccccccccccccccccccccbbbfccgaaacccccccccccbbbaccccccccccccccccccccccccccg cccaabbbcccccccccccccccccccccbbbbcccaaaccccccccccccbbbaccccccccccccccccccccccccccg cccaaebbccccccccccccccccccccbbbbcccaaaeccccccccccccbbbaacccccccccccccccccccccccccg ccceaabbfccccccccccccccccccbbbbcccgaaacccccccccccccbbbaacccccccccccccccccccccccccg ccccaabbbcccccccccccccccccbbbbccccaaaccccccccccccccbbbaaaccccccccccccccccccccccccgd ccccaafbbccccccccccccccccbbbbcccceaaeccccccccccccccbbbaaaccccccccccccccccccccccccfbb ccccaaabbfccccccccccccccbbbbcccccaaacccccccccccccccfbbgaaecccccccccccccccccccccccbbb cccceaabbbcccccccccccccbbbbcccccaaaccccccccccccccccfbbcaaaccccccccccccccccccccccfbbd ccccgaabbbccccccccccccbbbbccccceaaeccccccccccccccccfbbcgaaecccccccccccccccccccccbbb cccccaagbbcccccccccccfbbbccccccaaacccccccccccccccccfbbccaaaccccccccccccccccccccfbbd cccccaaabbfcccccccccfbbbccccccaaaccccccccccccccccccfbbcceaagcccccccccccccccccccbbb cccccaaabbbccccccccfbbbcccccceaaecccccccccccccccccccbbcccaaaccccccccccccccccccfbbg ccccceaafbbcccccccfbbbcccccccaaaccccccccccccccccccccbbccceaagcccccccccccccccccbbbg cccccgaagbbfcccccfbbbcccccccaaagccccccccccccccccccccbbfcccaaaccccccccccccccccbbbcg ccccccaaebbbccccfbbbccccccceaaacccccccccccccccccccccbbfccceaaccccccccccccccccbbbcg ccccccaaabbbccccbbbccccccccaaaccccccccccccccccccccccbbfccccaaaccccccccccccccbbbccg ccccccaaafbbcccbbbccccccccaaagccccccccccccccccccccccbbfccccaaaccccccccccccccbbbccg cccccceaacbbfcbbbccccccccgaaacccccccccccccccccccccccbbfcccccaaaccccccccccccbbbcccg cccccccaaebbbbbbfccccccccaaaccccccccccccccccccccccccbbbcccccaaaccccccccccccbbbcccg cccccccaaafbbbbfccccccccaaagccccccccccccccccccccccccbbbccccccaaeccccccccccbbbccccg cccccccaaacbbbfccccccccgaaacccccccccccccccccccccccccbbbccccccaaaccccccccccbbbccccg ccccccceaacbbfcccccccccaaaccccccccccccccccccccccccccbbbccccccgaaeccccccccbbbcccccg cccccccgaagccccccccccceaaeccccccccccccccccccccccccccbbbcccccccaaaccccccccbbbcccccg ccccccccaaeccccccccccgaaacccccccccccccccccccccccccccbbbcccccccgaaeccccccbbbccccccg ccccccccaaaccccccccccaaaccccccccccccccccccccccccccccbbbccccccccaaaccccccbbbccccccg ccccccccaaaccccccccceaaeccccccccccccccccccccccccccccfbbcccccccceaaaccccbbbcccccccg cccccccceaacccccccccaaacccccccccccccccccccccccccccccfbbcccccccccaaaacccbbfcccccccg cccccccccaagcccccccaaaccccccccccccccccccccccccccccccfbbccccccccccaaaecbbbccccccccg cccccccccaaecccccceaaeccccccccccccccccccccccccccccccfbbcccccccccccaaagbbfccccccccg cccccccccaaaccceaaaaaccccccccccccccccccccccccccccccccbbccccccccccccaabbbcccccccccg ccccccccceaaaaaaaaaagccccccccccccccccccccccccccccccccbbccccccccccccgebbfcccccccccg cccccccccgaaaaaaaegccccccccccccccccccccccccccccccccccbbcccccccccccccbbbacccccccccg ccccccccccaaaagccccccccccccccccccccccccccccccccccccccbbfcccccccccccfbbeaaccccccccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbfcccccccccccbbbeaaacccccccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbfccccccccccfbbfcaaaaccccccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbfccccccccccbbbcccaaaecccccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbbcccccccccfbbfccccaaaeccccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbbcccccccccbbbccccccaaagcccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbbccccccccfbbccccccccaaacccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbbccccccccbbbccccccccgaaaccg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbbcccccccfbbcccccccccceaaacg cccccccccccccccccccccccccccccccccccccccccccccccccccccbbbcccccccbbbccccccccccceaaag cccccccccccccccccccccccccccccccccccccccccccccccccccccbbbccccccbbbcccccccccccccaaaa cccccccccccccccccccccccccccccccccccccccccccccccccccccfbbccccccbbbccccccccccccccaaae dddddddddddddddddddddddddddddddddddddddddddddddddddddfbbdddddbbbddddddddddddddddaaag cbb bbb aaad dbb bbb dac dbb dbbb dbbd bbb dbbd dbbb bbd bbb bbcdbbf bbfbbb bbbbbf bbbbb bbbbf bbbb bbbf bbb dbd ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#5b5175ff b,#bcf451ff c,#b8b4c3ff d,#e2fab4ff e,#858191ff f,#cef683ff g,#ebefe2ff ``` ```image fbbbbd bbbg fbbbbeag bbbd fbbbbeaae bbbd fbbbbeaaaa bbbd fbbbbbaaaaa bbbf dd dbbbbaaaaaaaa bbbf dbbb dbbbbbaaaecaaacbbbf bbbb dbbbbaaaaa aaaabbbb fbbb dbbbbfaaaae aaaabbbb dbbbg bbbbbcaaaag eaaabbbb bbbf gbbbbbcaaae eaabbbb bbbb bbbbbgaaaag gaabbbb bbbbf gbbbbb caaae aabbbb fbbbb gbbbbbggaaaag eabbbb bbbb gbbbbb aaaa abbbb fbbb fbbbbd gaaaa cbbbb gaaabbbd bbbbb caaae bbbb aaabbbf fbbbbd aaaag bbbb caaebbbg bbbbf caaaa fbbbe gaaabbbd fbbbb gaaaac dbbbag aaabbbb bbbbf aaaag dbbbaa aaabbbb dbbbb aaaa dbbbaa aaabbbb bbbbf gaaaag gbbbaac aaaebbbg dbbbb eaaac gbbbaaa eaaabbbd dbbbbb caaaa gbbbaaac caaaebbb dbbbbg aaaac bbbeaaac gaaaabbbg gbbbbb caaae bbbeaaae eaaabbbf gbbbbg eaaaa fbbdaaaa caaabbbb gbbbbb aaaae fbbdeaaag aaabbbb bbbbbd eaaae fbbf aaaag b eaafbbb bbbbb caaaa fbbf aaaae b caaabbbd fbbbbd aaaa dbbf caaaa fb gaaafbbf bbbbb caaaa dbbf eaaa gbb aaaebbbd fbbbbf eaaae dbbb aaaa bbb aaaabbbf bbbbf aaaag dbbb caaac bbb aaaabbbb fbbbbf caaae gbbb aaaa fbbb eaaabbbb bbbbf gaaaag gbbbg aaaa gbbbf caaadbbbg dbbbbf aaaa bbbg gaaae bbbb gaaagbbbd bbbbf gaaaa bbbd eaaag bbbb eaaedbbb dbbbbb caaae bbbd aaaa fbbbg caaagbbbg bbbbbg aaaag bbbd aaaa dbbbf caaagbbbd gbbbbg aaaa bbbd eaaag fbbbg aaacbbbb gbbbbbg gaaaac bbbf aaaa bbbbb aaaebbbb bbbbbg eaaae bbbf caaac bbbbd aaaadbbbgbbbbbd aaaa bbbf aaaa dbbbd aaaagbbbbbbbbd eaaae bbbb aaaa bbbb caaa fbbbbbbd aaaac bbbb gaaae bbbbb caaagdbbbbbd caaaa bbbb eaaag bbbbd aaac bbbb aaaac bbbb aaaa dbbbd eaae bbbf caaae bbbb aaaa gbbbb gaaag eaaaa bbbb caaac bbbb aaac aaaae bbbb eaaa bbbb aaae eaaac fbbb aaaa fbbbd aaaa caaaa fbbb aaaac gbbbf aaaa aaaa fbbb caaaag bbbb eaaa caaaa fbbb gaaaaag bbbb caaa gaaaac fbbb gaaaae gbbbf aaac aaaag dbbb caaaae dbbbf eaac aaaa dbbb caaaacfbbbg caaa gcaaaaag dbbb aaaabbbb gaaag gceaaaaaac gbbb eaaebbbf aaaaaaaaaaaaaaa gbbbg gebbbf aaaaaaaaaaaaaeg bbbg bbbbe aaaaaaaaec bbbd bbbbaa eaaaaecg bbbd dbbbeaac fbbd dbbbdeaaaa fbbd bbbb gaaaag fbbf bbbb gaaaae fbbf fbbbd caaaa dbbf fbbbd caaaac dbbb gbbbb eaaaac dbbb fbbbb aaaaa gbbb bbbbg gaaaaag gbbb gbbbf gaaaae bbbg gbbbb caaaae bbbg fbbbb caaaac bbbd bbbbg aaaac bbbd dbbbf eaaaa bbbd dbbbf gaaa ``` <!-- end of image --> Success! This area contains 2 intersections point! Answer: A: 2; 2 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#5b5175ff b,#bcf451ff c,#bcb9c4ff d,#e2fab6ff e,#8a8598ff f,#cff784ff g,#edf2e3ff ``` ```image bbd bbbf bbbbf bbbbbb bbbbbbb bbbb bbb fbbb bbb fbbbag bbb fbbbaaa fbb fbbbaaaa fbb d fbbbaaaaaafbb bbb dbbbaaa aaadbb fbb dbbbeaae gaaebb bbd dbbbgaaa aaabb bbb gbbbgaaag gaabbg bbb gbbbgcaae aabbg dbbg gbbbd aaa cabbd bbf bbbd aaag abbd aabbb bbbd caaa cbbf eabbb bbbf aaa bbb caabbd bbbf aaac bbbg aabbb bbbf caaa bbba aabbb bbbf aaa bbbag aaebbg bbbf aaac bbbaa caabbf bbbb gaaa bbbaa gaabbb bbbb aaa bbbaae g aabbb bbbb eaac bbbaaa dbb aaabbd bbbb gaaa fbbgaae bbb eaabbb bbbb aaa fbb aaa fbbd caabbb fbbb eaae dbb caac bbb aacbbg fbbb aaa dbb aaa fbbd aaabbf fbbb aaag dbb caac bbb aaabbb fbbb caae gbbg aaa fbbg eaafbb dbbb aaa bbg eaag bbb gaacbbd dbbb aaag bbd aaa fbbg aaebbb dbbbg caae bbd eaag bbb aaabbb gbbbg aaa bbd aaa bbbg aaadbbg gbbbg aaac bbf aaa bbb caa bbfgbbbg caaa bbf aaa bbb aacbbbbbbd aaa bbb aaa bbb aaafbbbbd aaac bbb gaae bbb aaagbbbd gaaa bbb aaa bbb eaa bbf aaa bbb gaae bbb gaag eaac bbb aaa gbbf aae gaaa bbb caac bbb aaa aaa fbb aaa gbbf aaa eaae fbb caaa bbb caa gaaa fbb aaae gbbf gaac aaag dbb aaae bbb aae eaae dbb aaacbbf aaa geaaaaa gbb aabbb eaaaaaaaaaag gbbg gebbf caaaaaaaec bbg bbba aaaac bbd dbbeaa bbd bbbeaaa bbf dbbd aaaa bbf bbb aaae bbf fbbd aaac bbb bbb aaac bbb fbbg gaaag bbb bbb caaa bbb fbbg caaa bbb bbb eaaa fbb fbbg aaaa fbb bbb aaae fbb bbb aaae dbb bbb aaag dbb bbb gac dbb bbb gbbg bbb bbg gbbb bbd bbb bbdgbbf bbdbbb bbbbbf bbbbb bbbbf bbbb bbbf bbb gbg ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for intersections. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#c03bb9ff b,#9a2cd7ff c,#daa9e9ff d,#b1d7b1ff e,#b36bcaff f,#b0aeb6ff g,#f0f0f2ff ``` ```image ae caaa gaaac aaaa caaag aaac eaaa gaaag aaae gbg caaa bbe gaaac bbb eaaa bbb caaag cbbb aaae bbbb caaa bbbb gaaac bbbbg aaae cbbbbc caaag ebcebc aaac bb cbe eaaa bb gbb gaaag cbb bb aaae ebc bb caaa bb bb gaaac bb bb eaaa gggggggggggggggcbbgggbbcggggggggg caaag gdddddddddddddddbbedddebeddddddddd b aaac gdddddddddddddddbbddddebeddddddddd ebb eaaa gdddddddddddddddbbddddfbbddddddddd bbb gaaag gddddddddddddddfbbdddddbbddddafddd bbbg aaae gddddddddddddddebedddddbbdddeaaddd bbbg caaa gddddddddddddddbbddddddbbdddaafddd bbbg aaac gddddddddddddddbbddddddbbdddaadddd bbbg eaaa gdddddddddddddfbbddddddbbfdeaadddd ebbg gaaag gdddddddddddddebeddddddbbfdaafdddd ebbg aaae gdddddddddddddbbdddddddebedaaddddd ebbc caaagdddddddddddddbbdddddddfbbeaaddddd ebbc gaaafdddddddddddfbbddddddddbbaafddddd ebbc aaaaddddddddddebeddddddddbbaadddddd ebbc caaadddddddddbbdddddddddbbaedddddd cbbc gdaaaedddddddbbdddddddddbbaddddddd cbbc gddeaaadddddfbbdddddddddbbaddddddd cbbc gdddfaaafdddebedddddddddbbaddddddd cbbe gdddddaaaeddbbddddddddddbbeddddddd cbbe gddddddeaaadbbddddddddddabeddddddd cbbe gddddddddaaabbdddddddddeabbddddddd cbbe gdddddddddabbbdddddddddaabbddddddd gbbe gddddddddddbbafddddddddaabbddddddd gbbe gddddddddddbbafdddddddeaebbddddddd gbbe gdddddddddfbbafdddddddaadbbddddddd gbbb gdddddddddebbafdddddddaadbbfdddddd gbbb gdddddddddbbeaeddddddeaedebedddddd gbbb gdddddddddbbeaeddddddaaddebedddddd gbbb gddddddddfbbeaeddddddaaddfbbdddddd bbb gddddddddebeeaedddddeaedddbbdddddd bbb gddddddddbbffaedddddaaddddbbdddddd bbb gddddddddbbdfaedddddaaddddbbdddddd bbb gddddddddbbdfaaddddeaeddddbbdddddd bbb gdddddddebedfaaddddaadddddbbdddddd bbb gdddddddbbfdfaaddddaadddddbbfddddd bbb gdddddddbbddfaadddeaedddddebeddddd bbb gdddddddbbdddaadddaaddddddfbbddddd bbb gddddddebedddaaddfaaddddddfbbddddd bbb gddddddbbfdddaaddaaedddddddbbddddd bbb gddddddbbddddaaddaaddddddddbbddddd bbb gddddddbbddddaadfaaddddddddbbddddd bbbg gdddddebeddddaadaaeddddddddbbddddd bbbg gdddddbbfddddaadaadddddddddbbfdddd bbbg gdddddbbdddddaafaadddddddddebedddd bbbg gdddddbbdddddaaaaedddddddddebedddd ebbg gddddebedddddaaaaddddddddddfbbdddd ebbg gddddbbfdddddaaaadddddddddddbbdddd ebbg gddddbbddddddaaaedddddddddddbbdddd ebbc ggggbbggggggaaaggggggggggggbbgggg ebbc cbe aaa bb ebbc bbc aac bbg cbbc bb aa ebc cbbc bb cbe cbbbbe cbb cbbbc cbb gc ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#c039b9ff b,#9a2ad7ff c,#d18ee1ff d,#e1b5ebff e,#cd62c7ff f,#b15ce0ff g,#f0dbf5ff ``` ```image dbbbb bbbbg cbbbf fbbbd fbbbc fbbbc bbbbd cbbbc dbbbb cbbbf cbbbf dbbbf fbbbc gbbbb bbbbd gbbbb g dbbbb bbbbg eecg cbbbf bbbbd gaaaag fbbbc fbbbd caaae bbbbd fbbbc eaaac dbbbb cbbbf gaaaag cbbbf dbbbf caaae fbbbc dbbbb eaaac bbbbd gbbbb gaaaag gbbbb bbbbg caaae cbbbf bbbbd eaaac fbbbc fbbbd gaaaag bbbbd fbbbc caaae gbbbb cbbbc aaaac cbbbf cbbbf gaaaag fbbbc dbbbf caaae g bbbbd gbbbb aaaac ad gbbbb gbbbbdaaaag aac cbbbf bbbbeaaae aaaeg fbbbc fbbbaaaad aaaaad bbbbd fbbbaaaag aaaaaaeg gbbbbg cbbbbaae geaaaaaag cbbbf cbbbbaad caaaaaac fbbbc dbbbbaag gaaaaaaeg bbbbd dbbbbae eaaaaaad gbbbbg gbbbbad daaaaaac cbbbf bbbbag geaaaaaeg fbbbc bbbbe caaaaaac bbbbd bbbbc daaaaaaeg gbbbbg dbbbbc geaaaaaad cbbbf cbbbbf caaaaaac fbbbc aabbbf geaaaaaebbbbd daabbbb caaaaabbbbg caabbbb daaaabbbf aaabbbbg geabbbbbg daaabbbbg cbbbbaa eaaabbbbd gbbbbaad aaaafbbbc dbbbbaad daaaacbbbc fbbbbaad eaaaecbbbf bbbbaaad aaaaddbbbf gbbbbaaad daaaa gbbbb dbbbbaaad eaaae gbbbb fbbbfaaad aaaad bbbbg bbbbfaaac daaaa fbbbd gbbbbeaaac eaaae fbbbc dbbbbcaaac aaaad cbbbc fbbbfcaaac daaaa cbbbf bbbbdcaaac eaaae dbbbf gbbbbgcaaac aaaad dbbbb dbbbb caaac daaaa gbbbb cbbbf caaae eaaac bbbbg fbbbd daaae gaaaad bbbbd gbbbbg daaae daaaa fbbbd dbbbb daaae eaaac fbbbc cbbbf daaae gaaaad cbbbc fbbbd daaae daaaa cbbbf gbbbbg daaae eaaac dbbbf dbbbb daaae gaaaad gbbbb cbbbf gaaaa daaaa gbbbbg fbbbc gaaaa eaaac bbbbg gbbbbg gaaaa gaaaad fbbbd dbbbb gaaaa daaaa fbbbc cbbbf gaaaa eaaac cbbbc fbbbc gaaaa gaaaag cbbbf gbbbbg gaaaa daaaa dbbbf dbbbb aaaa eaaac gbbbb cbbbf aaaag gaaaag gbbbb fbbbc aaaag caaaa bbbbg gbbbbg aaaag eaaac bbbbd dbbbb aaaag gaaaag fbbbd cbbbf aaaag caaaa fbbbc fbbbc aaaag eaaac cbbbf bbbbg aaaag gaaaag dbbbf dbbbb eaaad caaae dbbbb cbbbf eaaad eaaac gbbbb fbbbc eaaad gaaaag bbbbg bbbbg eaaad caaae bbbbd dbbbb eaaad eaaac fbbbd cbbbf eaaadgaaaag fbbbc fbbbc eaaadcaaae cbbbc bbbbg eaaaceaaac cbbbf dbbbb caaaeaaaag dbbbf cbbbf caaaaaaae gbbbb fbbbc caaaaaaac gbbbbg bbbbd caaaaaaag bbbbg dbbbb caaaaaae fbbbd cbbbf caaaaaac fbbbc ``` <!-- end of image --> My investigation has led me to 2 intersections in area A! Answer: A: 2; 2 = 2 There's for sure two intersections on the image you sent me.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#c139b9ff b,#9a2ad8ff c,#d08ce1ff d,#e1b8edff e,#cd63c8ff f,#b15ae0ff g,#f1dff6ff ``` ```image ae caaa gaaad eaae daaag aaac eaaa gaaag aaae gbg caaa fbc aaad bbb eaaa bbb daaag dbbb aaac fbbb caaa bbbb gaaad bbbbg eaae dbbfbd daaa fbccbc aaac bb dbf eaaa bb gbb gaaag dbb bb aaae fbc bb caaa bb bb aaad bb bb eaae dbb bbg daaag fbc fbc f aaac bb cbf fbb caaa bb dbb bbb gaaag dbb bb eg bbbg aaae fbc bb cae bbbg daaa bb bb aag fbbg aaad bb bb aa fbbg eaaa dbb bbg cae fbbg gaaag fbc fbd aag fbbg aaae bb cbc aa fbbd caaa bb dbfcae fbbd gaaad gbb gbbaag fbbd eaae fbc bbaa cbbd daaag bbg bbae cbbd aaac bb bbag cbbc eaaa gbb bba cbbc gaaag fbc bbe dbbc aaae bbg bbc dbbc caaa bb abf dbbf aaabb cabb dbbf ebbb aabb gbbf bbad aabb gbbf bbad eaebb gbbf gbbad aa bb gbbf fbfad aa bbg gbbf bbeac eae fbc gbbb bbcac aa cbf bbb gbbcac gaa dbb bbb cbfcae eac bb bbb bbgdae aa bb bbb bb dae gaa bb bbb gbb dae eac bb bbb cbf daa aa bbg bbb bbg gaa gaa fbd bbb bb gaa eac cbc bbb gbb gaa aa dbf bbb cbf aa gaa gbb bbb bbg aa eac bb bbb bb aa aa bb bbb gbb aa gaa bb bbb cbf aa eac bb bbbg bbg aa aa bbd fbbg bb aagaa fbc fbbg bb aaeac cbf fbbg cbf aaaa gbb fbbg bbd aaaa bb fbbg bb aaac bb fbbd bb aaa bb fbbd cbf aaa bb cbbd bbd aac bbg cbbd bb aa fbd cbbc bb cbf cbbfbf dbb dbbbd dbb gd ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#51a918ff b,#abe7c6ff c,#96ca8eff d,#cbeed5ff e,#b1d7b1ff f,#edf7efff g,#76bb4dff ``` ```image fbf bbbb bbbbbd bbfdbbbf bbf bbbb bbf fbbbd bbf dbbbf bbf bbbb bbf fbbbd bbf bbbbf bbf fbbbb bbf dbbbd bbf bbbbf bbf fbbbb bb dbbbd bb bbd bb f bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bbb bbbbf dbbbd dbbbb fbbbb fbbbbf bbbbf bbbbd e dbbbd faaa dbbbb gaaae fbbbbf eaaag bbbbf faaaaf bbbbd gaaae dbbbd eaaag cccccccccccccccccccccccccccccf dbbbb faaaaf eeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbbb gaaae eeeeeeeeeeeeeeeeeeeeeeeeeeeebbbbf eaaag eeeeeeeeeeeeeeeeeeeeeeeeeebbbbf aaaaf eeeeeeeeeeeeeeeeeeeeeeeebbbbef gaaae eeeeeeeeeeeeeeeeeeeeeebbbbbeef daaag eeeeeeeeeeeeeeeeeeeeebbbbeeeef aaaaf eeeeeeeeeeeeeeeeeeebbbbeeeeeef caaac eeeeeeeeeeeeeeeeebbbbeeeeeeeef daaag eeeeeeeeeeeeeeebbbbeeeeeeeeeef decgaaaaaaaaaf eeeeeeeeeeeeeebbbbeeeeeeeeeeef decgaaaaaaaaaaaaaaaaac eeeeeeeeeeeeebbbeeeeeeeeeeecgcgaaaaaaaaaaaaaaaaagced eeeeeeeeeeeeebbbeccggaaaaaaaaaaaaaaaaagcedf eeeeeeeccggaaaaaaaaaaaaaaaaaagedf eecaaaaaaaaaaaaaaaaggceeeeeeef eecaaaaaaggcebbeeeeeeeeeeeeeef eeeebbeeeeeeebbeeeeeeeeeeeeeef eeeebbbeeeeeebbeeeeeeeeeeeeeef eeeeebbeeeeeebbeeeeeeeeeeeeeef eeeeeebbeeeeebbeeeeeeeeeeeeeef eeeeeebbbeeeebbeeeeeeeeeeeeeef eeeeeeebbeeeebbeeeeeeeeeeeeeef eeeeeeebbbeeebbeeeeeeeeeeeeeef eeeeeeeebbbeebbeeeeeeeeeeeeeef eeeeeeeeebbeebbeeeeeeeeeeeeeef eeeeeeeeebbbebbeeeeeeeeeeeeeef eeeeeeeeeebbebbeeeeeeeeeeeeeef eeeeeeeeeeebbbbeeeeeeeeeeeeeef eeeeeeeeeeebbbbeeeeeeeeeeeeecf ffffffffffffbbbffffffffffffff dbb d ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#51a918ff b,#abe8c6ff c,#89c76cff d,#c9edd4ff e,#afd99aff f,#e3f6e9ff g,#6bb73fff ``` ```image f db dbbb fbbbbb fbbbbbbb fbbbbbbbbd fdbbbbbbbd dbbbbbbbdf dbbbbbbbbf fbbbbbbbbf fbbbbbbbbd fdbbbbbbbd dbbbbbbbdf dbbbbbbbbf fbbbbbbbbf fbbbbbbbbf fbbbbbbbbd fbbbbbbbd dbbbbbdf dbbbbf fdde dbbbd fddeeccggaaaaa dbbbd fddeeccggaaaaaaaaaaaaaaa fddeccgggaaaaaaaaaaaaaaaaaaaaaaaaa fb fddeeccggaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaag feccccggaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaggcceedf eaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaggcceedf daaaaaaaaaaaaaaaaaaaaagggceedf faaaaaaaaaaaggcceedff bbbbf fagggccedff bbbbf fbbbbd bbbbf dbbbbf bbbbf bbbbb bbbb fbbbbd bbbb dbbbbf bbbb bbbbb fbbbb fbbbbd fbbbb dbbbbf fbbbb fbbbbd fbbbb dbbbbf fbbbb bbbbb fbbbb fbbbbd fbbbd dbbbbf fbbbd bbbbb dbbbd fbbbbd dbbbd dbbbbf dbbbd bbbbb dbbbd fbbbbd dbbbd bbbbbf dbbbd fbbbbd dbbbf dbbbbfdbbbf bbbbbbbbbf fbbbbbbbbf dbbbbbbbf ``` <!-- end of image --> I've cracked the case! This area contains 2 intersections. Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#51a918ff b,#abe8c6ff c,#8ec669ff d,#cbedd3ff e,#b3d99cff f,#e7f7edff g,#6fb740ff ``` ```image fbf bbbb bbbbbd bbfdbbbf bbf bbbb bbf fbbbd bbf dbbbf bbf bbbb bbf fbbbd bbf bbbbf bbf bbbb bbf dbbbd bbf bbbbf bb fbbbb bb dbbbd bb bbd bb f bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb bbb bbbbf dbbbd dbbbb fbbbb fbbbbf bbbbf bbbbd e dbbbd faag fbbbb gaaad fbbbb eaaac bbbbf faaaa bbbbd gaaae dbbbd eaaag dbbbb aaaaf fbbbb caaae fbbbbf daaag bbbbf aaaaf bbbbd caaae dbbbd daaag fbbbb aaaaf fbbbb caaae bbbbf daaag bbbbd decgaaaaaaaaaf fbbbd decgaaaaaaaaaaaaaaaaae dbb decgaaaaaaaaaaaaaaaaagced dbd decgaaaaaaaaaaaaaaaaagced f decgaaaaaaaaaaaaaaaaagced eaaaaaaaaaaaaaaagced faaaaagcedfbbf fbb bbf bbb bbf bbf bb fbb bb bbd bb bb bb dbb bb bbd bb fbb bb bbb bb bbfbb fbbbb bbbb bbb dbb d ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#50904eff b,#dfabaeff c,#96c695ff d,#b1d7b1ff e,#eef0eaff f,#2d792bff g,#7baf7aff ``` ```image ffe effg fffa effff fffff efffff fffcff effcdff fff effe e dffc ffd bbb fff ffc bbbb dffc ffg ebbbb fff ffa bbbbe dffc fff bbbb fff aff ebbbb dffc gff bbbbe fff cff bbbb dffc dff ebbbb fff eff bbbbe dffc ffd bbbb fff ffc ebbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedffceeeeeeeeeffgeeeeeeeeeebbbbe ecddddddddddddddddddddddddddddddddddddfffddddddddddffadddddddddbbbb eddddddddddddddddddddddddddddddddddddcffgddddddddddfffddddddddbbbb eddddddddddddddddddddddddddddddddddddfffdddddddddddfffddddddbbbbdc edddddddddddddddddddddddddddddddddddcffgdddddddddddaffdddddbbbbddc edddddddddddddddddddddddddddddddddddfffddddddddddddgffddddbbbbdddc eddddddddddddddddddddddddddddddddddcffgddddddddddddgffddbbbbdddddc eddddddddddddddddddddddddddddddddddfffdddddddddddddcffdbbbbddddddc edddddddddddddddddddddddddddddddddcffgddddddddddddddffcbbbdddddddc edddddddddddddddddddddddddddddddddfffdddddddddddddddffbbbddddddddc eddddddddddddddddddddddddddddddddcffgdddddddddddddddffbbbddddddddc eddddddddddddddddddddddddddddddddfffddddddddddddddddfgbbdddddddddc edddddddddddddddddddddddddddddddcffgddddddddddddddddfbbbdddddddddc edddddddddddddddddddddddddddddddfffdddddddddddddddddfbbddddddddddc edbbdddddddddddgdddddddddddddddcffgdddddddddddddddddcbbddddddddddc ebbbbdddddddddfffddddddddddddddfffddddddddddddddddddbbbddddddddddc edbbbdddddddddfffcddddddddddddgffgddddddddddddddddddbbaddddddddddc eddbbbdddddddcffffddddddddddddfffddddddddddddddddddbbbfddddddddddc edddbbbddddddfffffgddddddddddgffgddddddddddddddddddbbbfcdddddddddc edddbbbbdddddffafffddddddddddfffdddddddddddddddddddbbffffddddddddc eddddbbbbddddffccffaddddddddgffgddddddddddddddddddbbbcffffgddddddc edddddbbbdddaffddfffddddddddfffdddddddddddddddddddbbbddaffffdddddc eddddddbbbddfffdddffaddddddgffgddddddddddddddddddbbbdddddffffadddc edddddddbbbdffgdddfffddddddfffdddddddddddddddddddbbbddddddgffffgdc eddddddddbbbffdddddfffddddgffgdddddddddddddddddddbbdddddddddfffffc eddddddddbbbbfdddddaffcdddfffdddddddddddddddddddbbbddddddddddcffffg edddddddddbbbcddddddfffddgffgdddddddddddddddddddbbbddddddddddddaffffe edddddddddcbbbddddddgffgdfffddddddddddddddddddddbbdddddddddddddddffffa edddddddddafbbbddddddfffgffgdddddddddddddddddddbbbdddddddddddddddcdffffc edddddddddffabbbdddddcfffffddddddddddddddddddddbbbdddddddddddddddc affffe edddddddddffcdbbbdddddffffgddddddddddddddddddddbbddddddddddddddddc effffa eddddddddaffddbbbbdddddfffddddddddddddddddddddbbbddddddddddddddddc cffffd eddddddddfffdddbbbbddddafcddddddddddddddddddddbbbddddddddddddddddc fffff eddddddddffgddddbbbddddddddddddddddddddddddddbbbdddddddddddddddddc effffg edddddddgffddddddbbbdddddddddddddddddddddddddbbbdddddddddddddddddc gffffe edddddddfffdddddddbbbddddddddddddddddddddddddbbddddddddddddddddddc ffffa edddddddffadddddddbbbbddddddddddddddddddddddbbbddddddddddddddddddc dfff eddddddcffcddddddddbbbbdddddddddddddddddddddbbbddddddddddddddddddc ae eddddddaffddddddddddbbbdddddddddddddddddddddbbdddddddddddddddddddc eddddddfffdddddddddddbbbdddddddddddddddddddbbbdddddddddddddddddddc ccccccffgccccccccccccbbbccccccccccccccccccbbbcccccccccccccccccccd gff ebbb ebb fff bbbb bbb ffc bbbb bbb dff bbbe ebb fff bbb bbb ffg ebbb bbe effe ebbb bbb aff bbbb bbb fff bbbe ebbe ffd bbbe bbb gff bbb bbb fff ebbb ebb ffc ebbb bbb dff bbbb bbb fff bbbbbb ffa bbbbb effe bbbe aff ebb cff ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f8d4cff b,#e0aaafff c,#a5c3a2ff d,#c2d7c1ff e,#eddeddff f,#2d792bff g,#7ca576ff ``` ```image dfffffc cfffg ebb affffa cfffg bbb fffffc dfffa bbbb dffffc effff ebbbbbb afffa ffffe bbbbbbbe dffffc afffd bbbbbbbe afffa afffd ebbbbbb dffffc gfffc bbbbbbbe afffa gfffc ebbbbbbbe afffa cfffg bbbbbbbe dffffc dfffa bbbbbbbe affff dfffa ebbbbbbb dfffff effff ebbbbbbe affffa ffffebbbbbbe fffffc afffdbbbbb dffffc gfffbbbbe afffa gffgbbbb dffffc cffcbbbe afffa cfabbbbe dffffc dfgbbbb afffa dfbbbbb dffffc eabbbbb dffffc bbbbbe bb affff bbbbb ebbb dcd dfffff bbbbb ebbbbb cfff affffa bbbbc bbbbbe effffe fffffc ebbbbg ebbbbbe cffffg ffffa bbbbgg ebbbbb ffffffg afffa ebbbbfa bbbbbb dfffffffd dffffc bbbbgff bbbbbe gfffffffa afffa ebbbbaffe bbbbbe affffffffc dffffc ebbbbfffd ebbbbbe fffffafffa afffa bbbbgffff ebbbbb ffffadffffc dffffc ebbbbfffffad bbbbbb effffd fffffg dffffc bbbbedafffffffc bbbbbbe cffff gfffff affff ebbbb gfffffffad ebbbbbb gfffg efffff dfffff bbbbb eafffffffe ebbbbbe ffffd gffffd affffa bbbbb ffffffffc ebbbbb dffff ffffa fffffc ebbbbb egfffffffae bbbbbb gfffa cffffc ffffa bbbbbe dafffffffg bbbbbdffffe dffffc afffa bbbbb egffffffge ebbbbbaffa affffe dffffc bbbbe afffffffc ebbbbbafg dffffg afffa ebbbb gfffffff bbbbbbfd gffffe dffffc bbbbb eafffff bbbbbbf effffg afffa bbbbe cffff bbbbbc fffffd dffffc ebbbb efff dabbbbbe cfffff dffffd bbbbe c gfgbbbbb affff affff ebbbb affgbbbbb dffffcdfffff bbbbe effffbbbbbb affffaffffa ebbbb cffffabbbbbe dfffffffffd ebbbb affffgbbbbbb gfffffffa bbbbe fffffdebbbbbe efffffffd ebbbb ffffg bbbbbb fffffd bbbbb ffffc bbbbbe cfffa ebbbbb dffffe bbbbbe fffd bbbbbe gfffa ebbbbbe cce bbbbbe afffc ebbbbb bbbbb effffe bbbbbb bbbbe gfffg bbbbbe ebbbb ffffd bbbbbe bbbbe dffff ebbbbbe ebbbb gfffg ebbbbb bbbbb ffffc ebbbbb bbbbe dffffe bbbbbb ebbbb afffc bbbbbb bbbbe effffe ebbbbbe ebbbb cffff ebbbbb bbbbe ``` <!-- end of image --> The close-up clearly shows 2 intersections point in area A. Answer: A: 2; 2 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#4d8c4bff b,#e0aaafff c,#a3c2a1ff d,#c6dac5ff e,#eeddddff f,#2d792bff g,#75a572ff ``` ```image ffd dffg fffa dffff fffff dfffff fffcff dffcdff fff ff e dffc ffd bbb fff ffc bbbb dffc ffg ebbbb fff ffa bbbbe dffc fff bbbb fff aff ebbbb dffc gff bbbbe fff cff bbbb dffc dff ebbbb fff eff bbbbe dffc ffd bbbb fff ffc ebbbb dffc ffg bbbbe fff ffa bbbb dffc fff ebbbb fff aff bbbbe dffc gff bbbb fff cff ebbbb dffc dff bbbbe fff eff bbbb dffc ffdbbb fff ffbbb dffc ffbbe fff fgbb dffc fbbb fff abbe ebb c dffc cbb bbbe fff fff bbb bbbe fffe dffc bba bbb dffff fff bbbf bbb affffc dffc bbbfd ebbb ffafff fff ebbfffa bbbb effddffg dffc bbbdffffc bbbe gff fff fff bbe affffe bbb fff ffa dffc ebb effffa bbb ffc aff fff bbb cffffd ebbbff fff dffc bbe affff ebbbf gffe fff bbb dffffg bbbc fff dffc bbb gffffe dbbbe cffc fff bbe ffffa afbbb fffdffd bbb dffffc ffabbb dfffff bbb affffe ffdebbb ffffd ebb effffa gff bbbb fff bbb cffffd fff bbbe afd bbe affff ffc bbb ebb dffffg cff bbb bbb gffffe fff bbb bbe ffffa ffg ebbb bbb cfff dffe bbbb bbb ae aff bbbe bbe ffa bbb bbb ffd bbb bbb gff ebbb ebb fff ebbb bbb ffc bbbe bbe cff bbbe ebb fff bbb bbb ffg bbb bbe dffe ebbb bbb aff bbbb bbb ffa bbbe bbe ffd bbb bbb gff bbb bbb fff ebbb ebb ffc ebbb bbb cff bbbb bbe fff bbbbbb ffg bbbbb effe bbbe aff ebb cff ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#73e464ff b,#c1bf80ff c,#dae8c1ff d,#b6a449ff e,#b1d7b0ff f,#eff6edff g,#96d791ff ``` ```image d d d d d d b b c c cc fc ag cf ga c g a c a a b fc a b a g b g c d e fc d a e d fe g d a a d a a d cf a d a g b g e b g cf b a fc c fc e fc a g ff g a cf e a c a a b fe g b a e b a cf d cf c d a g d g a d g a d a a d fc a d b a g b b g c b d e ff b fc a e c d fe g fc cf a a fc d a a cf b cf a ffffffffffffffcfffffff b a a geeeeeeeeeeeeebeeeeeee d e e geeeeeeeeeeeeebeeeeeee cc g c geeeeeeeeeeeeedeeeeeee d a fc geeeeeeeeeeeeedeeeeeee b fc e geeeeeeeeeeeeedeeeeeee b a g geeeeeeeeeeeeedeeeeeee d g a geeeeeeeeeeeeedeeeeeee fc e a geeeeeeeeeeeeedeeeeeee d a a geeeeeeeeeeeeedeeeeeee bfffffffffffffffffffffffffffeffffff g geeeeeeeeeeeeedeeeeeee fgdeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeegf e geeeeeeeeeeeeedeeeeeee fedeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeef cf geeeeeeeeeeeeedeegeeee feebeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeef fc geeeeeeeeeeeeedaaeeeee feedeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeef e geeeeeeeeegaagbeeeeeee feebeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeef a geeeeeegaageeebeeeeeee feeedeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeef a geeeaaaeeeeeeebeeeeeee feeedeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeef a gaageeeeeeeeebeeeeeeee feeeedeeeeeeeeeeeeeeeeeeeggeeeeeeeeef aageeeeeeeeeeeebeeeeeeee feeeedeeeeeeeeeeeeeeeeeeeaeeeeeeeeeef geeeeeeeeeeeebeeeeeeee feeeeebeeeeeeeeeeeeeeeeeeaeeeeeeeeeef geeeeeeeeeeeebeeeeeeee feeeeedeeeeeeeeeeeeeeeeegeeeeeeeeeeef geeeeeeeeeeeedeeeeeeee feeeeeebdddddbbeeeeeeeeeaeeeeeeeeeeef geeeeeeeeeeeedeeeeeeee feeeeeeeeeeeeeebbdddddbbgeeeeeeeeeeef geeeeeeeeeeeedeeeeeeee feeeeeeeeeeeeeeeeeeeeeeabbdddddbbeeef geeeeeeeeeeeedeeeeeeee feeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeebbddddbbcf geeeeeeeeeeeedeeeeeeee ccf feeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeef fcbbdddbbcf geeeeeeeeeeeedeeeeeeee fcegaaaaaggeeeeeeeeeeeeeeeeaeeeeeeeeeeeeef fcbbddddbggggggggggdgggggggg feeeeeggaaaaaagggeeeeegeeeeeeeeeeeeef fcbddddbccd feeeeeeeeeeeeeeegggaaaeeeeeeeeeeeeeef ff feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#70e560ff b,#cbbb78ff c,#baf2b3ff d,#b9a347ff e,#ded4abff f,#e7f3dcff g,#94eb88ff ``` ```image de ca bd gg fdf faf bb ga edf ac de caf bd gg fde fac bb ca edf ac db faf ed gg fde ac bd ca fdf ag db faf edf ga de ac bd caf fde gg bb fac edf ca dddbbeeeff ac feebbdddddddbbeeeff faf ffeebbdddddddbbeeeff gg ffeebbdddddddbbeeeac feeebbdddddddbbeeef ageeebbdddddddbbeeef faf ffeeebbdddddddb ga ffeeeb ac caf fff gg aaaaagggcccff fac ffcccggaaaaaaaaggcccff ca ffcccgggaaaaaaagggccfff ac ffcccgggaaaaaaagggccccaf fffcccggaaaag f ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Let's inspect the next region. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#73e664ff b,#c9b973ff c,#c5f4bfff d,#b7a346ff e,#dcd2a5ff f,#eaf0d9ff g,#a1ee98ff ``` ```image ed ed ed bb bb bb bb be de de de de df fdf fdf fdf fd ed ed ed ed eb bb bb fcf bb fgaaac dbaaagc fcgaddgf fgaaagcde cgaaagc de fcgaaagf de fgaaagcf df cgaaagc fdf fcgaaagf fdf fgaaagcf fdf aagc fdf f ed ed ed ed eb bb bb bb bb be de de de de fdf fdf fdf ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#72e663ff b,#c7b66eff c,#bff3b8ff d,#b7a143ff e,#dacfa1ff f,#e7f0d7ff g,#9bed90ff ``` ```image d d d d d b b e e e cc ff ag ff ga e g a e a a e ff a b a g b g c d c ff d a c d c g d a a d a a d cf a b a g b g c b g c e a c e ff g f a g ff g a f c a e a a e c g b a c b a ff b cf c d a g d g a d g a d a a d ff a d e a g b b g c b d c ff e fe a c e d c g f e a a ff d a a ff b cf a e e a a e d g g e ff g c b d a ff b b ff c d b a g d d g a d fe c a d d a a d e c g d b a c b b a ff b c e cf c bag d a g faace ff g g caaf e d g a gag ff b a a faac ff b ff aaf e d a e ff g e d c b febdddbeff a b febdddbeec d afebdddbef d a febdddbef d cf cf ffebdddbef d fccgaaaagccf a feebdddbef d fcgaaaaggcf g feebdddbefd fcggaa ff ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#646276ff b,#a62fccff c,#34334cff d,#bd75d6ff e,#b0d6b0ff f,#dec2e8ff g,#9abe9eff ``` ```image fcc cca fcc cca fcc ccc geeeeeeeeeeeeeegccgeeeeg eeeeeeeeeeeeeeeccceeeeeg eeeeeeeeeeeeeegcceeeeeeg eeeeeeeeeeeeeeccceeeeeeg eeeeeeeeeeeeegcceeeeeeeg eeeeeeeeeeeeeccceeeeeeeg eeeeeeeeeeeegcceeeeeeeeg fbbddff eeeeeeeeeeeeccceeeeeeeeg bbbbbbbbbbbbbbddff eeeeeeeeeeegcceeeeeeeeeg bbddbbbbbbbbbbbbbbbbbbbbbbddgeeeeeeeccceeeeeeeeeg bb ffddbbbbbbbbbbbbbbbbbbbbbbbdgeeeeeeeeg fbb ffdbbbbbbbbbbbbbbbbeeeeeeeg fc dbb eeeeeeeegdabbbbbeeeeeeeg ccc bbd eeeeeeeeeccceebbeeeeeeeg cccc bbf eeeeeeeeecceeebbeeeeeeeg cccca bb eeeeeeeeccceeebbgeeeeeeg gccgcce bb eeeeeeeecceeeebbdeeeeeeg aca acc bb eeeeeeeccceeeebbdeeeeeeg ccg ccc fbb eeeeeeeccgeeeebbdeeeeeeg cc ccc dbb eeeeeeccceeeeedbbeeeeeeg fcc cca bbd eeeeeeccgeeeeedbbeeeeeeg gcc eccg bbf eeeeeccceeeeeedbbeeeeeeg cca accf bb eeeeeccgeeeeeegbbeeeeeeg ccf ccc bb ggggcccggggggggbbgggggge cc ccc fbb ccf bb ecc ccc dbb ccc bb acc fcca bbd ccf bb gcce bbf ccc bb acc bb ccf bbf ccc bb ccc bbf ccc bb ccf bbd fcca fbb acc bbd gccg dbb ccf dbd bd accf bbd acc dbb dbb ccc bbf ccf fbb bbb gccceeeeeeeebbeeeeeeeeg acc fbb bbd eeccceeeeeeebbeeeeeeeee ccf bb dbb eegccaeeeeegbbeeeeeeeee acc bb bbb eeeaccgeeeedbbeeeeeeeee ccf bb bbf eeeeccceeeebbdeeeeeeeee acc bb dbb eeeeeccceeebbdeeeeeeeee ccf bb bbb eeeeeeccceebbeeeeeeeeee acc bbf bbf eeeeeegccaebbeeeeeeeeee ccf bbf dbb eeeeeeeaccabbeeeeeeeeee acc bbf bbb eeeeeeeeacabbeeeeeeeeee cce bbd bbf eeeeeeeeecbbbeeeeeeeeee acc dbd dbb eeeeeeeeeebbaeeeeeeeeee cce dbb bbb eeeeeeeeeebbcceeeeeeeee acc fbb fbbf eeeeeeeeeebbccaeeeeeeee cce fbb dbb eeeeeeeeeebbaccgeeeeeee acc fbb bbb eeeeeeeeegbbeccceeeeeee cce bb fbbf eeeeeeeeedbbeeccceeeeee acc bb bbb eeeeeeeeebbdeeeccceeeee cce bb bbb eeeeeeeeebbgeeegccaeeee acc bb fbbf eeeeeeeeebbeeeeeaccgeee ccg bb bbb eeeeeeeeebbeeeeeecccgee acc bbf bbd eeeeeeeeebbeeeeeeecccee ccg bbf fbb eeeeeeeedbbeeeeeeeeccce acc bbd bbb ggggggggbbbgggggggggccc ccg bbd bbd bbf eccg acc dbb fbb bbf accf ccg dbb bbb bb ccc acc fbb bbd bb cccccg fbb fbb fbb cccc bb bbb dbb fccg bb bbd bbd ga bb fbb bbf bb bbb bb bb bbd bb bbf dbbfbb bbf bbbbb bbd bbbd bbd dbbf dbb bb dbb fdd ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#5a4f70ff b,#a630cdff c,#34324bff d,#ca83e1ff e,#848392ff f,#e0d0e7ff g,#b3b1bcff ``` ```image gccccce dbbbb ecccccg dbbbb ecccccf bbbbd accccaf bbbbd fccccca fbbbbd fccccce fbbbbf gcccccg dbbbbf ecccccf dbbbb acccccf dbbbb facccca bbbbd fccccce bbbbd gccccce fbbbbf ecccccg fbbbbf acccccf dbbbb acccca dbbbb fccccca bbbbd gccccce bbbbd gcccccgbbbbd eccccabbbbf acccabbbb fcccabbbb fccbbbbb gcbbbbb ebbbbag fbbbbacf fbbbbcca dbbbbccca dbbbbcccce bbbbbcccccg bbbbdecccccf fbbbbd accccaf fbbbbf fccccca dbbbb fccccce dbbbb gcccccg bbbbb ecccccg bbbbd acccccf bbbbd acccca fbbbbf fccccce dbbbbf gccccce dbbbb ecccccg dbbbb ecccccf bbbbd accccaf bbbbd fccccca fbbbbf gccccce fbbbbf gcccccg dbbbb ecccccf ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area A. Time to investigate another area. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#7d309fff b,#a62ecdff c,#35344cff d,#d8a5e8ff e,#bd64d9ff f,#ebe1efff g,#91919eff ``` ```image gccccg fccccc gccccg fccccc gccccg fccccc gccccg fccccc gccccg fccccc gccccg fccccc gccccg fccccc gccccg fccccc gccccg fccccc gccccg beeedddff fccccc bbbbbbbbbbbbeeedddff gccccg bbbbbbbbbbbbbbbbbbbbbbbaaaaddff bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbef eeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbd ffddddeeebbbbbbbbbbbbbbbbbbe ffddaaaabbbbbbbbe gccccg febbbb fcccccf ebbbb gccccg dbbbb fcccccf dbbbbf gccccg dbbbbf fcccccf dbbbbf gccccg fbbbbd fcccccf fbbbbd gccccg bbbbd fcccccf bbbbd gccccg bbbbe fcccccf ebbbe gccccg ebbbe fcccccf ebbbe gccccg ebbbb fcccccf dbbbb gccccg dbbbbf fcccccf dbbbbf gccccg dbbbbf cccccf fbbbbd ``` <!-- end of image --> I observe 1 intersection inside area B. Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#655e78ff b,#a62eccff c,#34334cff d,#d298e5ff e,#bb60d8ff f,#e3d4e9ff g,#a9a8b3ff ``` ```image fcc cca fcc cca fcc cca fcc ccc fcc ccc fcc ccc fcc dbbeddf ccc bbbbbbbbbbbbbbeddf fcc bbdebbbbbbbbbbbbbbbbbbbbbeddf ccc bb fddebbbbbbbbbbbbbbbbbbbbbbadf fbb fddebbbbbbbbbbbbbbb fc dbb fdabbbbb ccc ebe ccc bb cccc bbd fcc bb cccca bbf ccc bbf gccgccg bb ccf bbd aca accf bb ccc bbd ccg ccc dbb ccf ebe cc ccc ebb ccc ebe fcc fcca bbd ccf dbb gcc gccg bbf ccc dbb cca accf bb ccf fbb ccf ccc bb ccc bb cc ccc fbb ccf bb gcc ccc dbb ccc bb acc fcca bbe ccf bb gccg bbd ccc bb acc bb ccf bbf ccc bb ccc bbd ccc fbb ccf bbd fcca dbb acc bbe gccg ebe ccf ebe bd accf bbd acc dbb dbb ccc bbf ccf dbb bbb ccc bb acc fbb bbd ccc bb ccf fbb ebb fcca fbb acc bb bbb accf dbb ccf bb bbd ccc bbe acc bb ebb ccc bbd ccf bb bbb ccc bb acc bbf bbd fcca bb ccf bbf ebb gccgbb acc bbd bbb acabb ccg bbd fbbf cbbe acc ebe ebb bba ccg ebb bbb bbca acc dbb fbbf bbccg ccg fbb ebb bbaccf acc fbb bbe fbb ccc ccg bb fbbf ebb ccc acc bb ebb bbe ccc ccg bb bbe bbf fcca acc bb fbbf bb gccg ccg bbf bbb bb accf acc bbf bbe fbb ccc ccg bbd fbbf dbb ccc acc bbd bbb ebe fcca ccg ebe bbe bbd gccg acc ebe dbb bbf accf ccg dbb bbb bb ccc acc dbb bbe bb cccccg fbb dbb dbb cccc bb bbb ebb fccg bb bbe bbd ga bb dbb bbf bb bbb bb bb bbd bb bbf dbbfbb bbd bbbbb bbd bbbe ebe dbbd ebe bb dbb dee ``` <!-- end of image -->
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This image looks interesting. I wonder if there are any intersections hidden in there? These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#745507ff b,#f58971ff c,#f2cfc3ff d,#998a52ff e,#b1d7b0ff f,#98c794ff g,#d1b192ff ``` ```image cb bbb bbbc cbbb bbb bbbc cbbb bbb bbbc cbbb bbb bbbc cbbb bbb bbbc cbbb bbb bbbc cbbb bbb bbbc cbbb bbb bbbc feeeeeeeeeeeeeeeeeeeeeef cbbb feeeeeeeeeeeeeeeeeeeeeef bg bbb feeeeeeeeeeeeeeeeeeeeeef bbbb bbbc feeeeeeeeeeeeeeeeeeeeeef gbbbbbg cbbb feeeeeeeeeeeeeeeeeeeeeef cbbbbbb bbb feeeeeeefaaaeeeeeeeeeeegbbbbbb fffffbbbgfffffffffffffffffff feeeefaaaaaaeeeeeeeeegbbbbbbc eeeeegbbbeeeeeeeeeeeeeeeeeee fedaaaaaaaaadeeeeeeebbbbbbc eeeeeebbbeeeeeeeeeeeeeeeeeee daaaaaaaaaaaadeeeeebbbbbbc eeeeeebbbgeeeeeeeeeeeeeeeeee cdaaaaaaaaadeefaaaeeebbbbbbgf eeeeeegbbbeeeeeeeeeeeeeeeeee caaaaaaaaaadeeeeeeaaaebbbbbbbeef eeeeeeebbbeeeeeeeeeeeeeeeeee gaaaaaaaaaadeeeeeeeeeaaabbbbbbeeeef eeeeeeebbbgeeeeeeeeeeeeeeeee daaaaaaaaadc feeeeeeeeeaaabbbbeeeeeef eeeeeeegbbbeeeeeeeeeeeeeeeefdaaaaaaaaad feeeeeeegbaaadbeeeeeeeef eeeeeeeebbbeeeeeeeeeeeeefaaaaaaaaaag feeeeegbbbdaaaddfeeeeeef eeeeeeeebbbgeeeeeeeeedaaaaaaaaaac feeeebbbbbbaaaaaaaaaaaaaddgc eeeeeeeegbbbeeeeeedaaaaaaaaadc feebbbbbbgeaaaaaaaaaaaaaaaaaa eeeeeeeeebbbeefdaaaaaaaaadee fbbbbbbgeeeefddaaaaaaaaaaaaaa eeeeeeeeebbbaaaaaaaaaadeeeee bbbbbbbeeeeeeeeeeeeeeeeefgdaaa eeeeeeeedaaaaaaaaaafeeeeeeee gbbbbbbeeeeeeeeeeeeeeeeeeef aaa eeeeedaaaaaaaaaafeeeeeeeeeee cbbbbbbeeeeeeeeeeeeeeeeeeeeef aaa efdaaaaaaaaadgeeeeeeeeeeeeee cbbbbbbfeeeeeeeeeeeeeeeeeeeeeef aaac caaaaaaaaaadgbbbeeeeeeeeeeeeee ccgbbbbbbbbc feeeeeeeeeeeeeeeeeeeeeef daag aaaaaaaaaafeeeebbbeeeeeeeeeeggbbbbbbbbbbbbbbbc feeeeeeeeeeeeeeeeeeeeeef daad aaaaaaafeeeeeeebbbgggbbbbbbbbbbbbbbbbbbbbbbc feeeeeeeeeeeeeeeeeeeeeef gaaa daadfeeeeeeeeeeebbbbbbbbbbbbbbbbbbbbbbcc feeeeeeeeeeeeeeeeeeeeeef caaa eeeeeeeeeeeebbbbbbbbbbbbbgge feeeeeeeeeeeeeeeeeeeeeef aaa eeeeeeeeeeeegbbbggeeeeeeeeee effffffffffffffffffffffe aaa eeeeeeeeeeeeeeeeeeeeeeeeeeee aaa eeeeeeeeeeeeeeeeeeeeeeeeeeee aaa eeeeeeeeeeeeeeeeeeeeeeeeeeee aaac eeeeeeeeeeeeeeeeeeeeeeeeeeee aaag eeeeeeeeeeeeeeeeeeeeeeeeeeee daad feeeeeeeeeeeeeeeeeeeeeeeeeef gaad caaa aaa aaa aaa aaa aaa aaac daag daad gaaa caaa aaa aaa aaa aaa aaac aaag daad gaad caaa aaa aaa aaa aaa aaa ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#745406ff b,#f58971ff c,#f5dfd6ff d,#9a783eff e,#b3a177ff f,#f8b4a5ff g,#cdc2a7ff ``` ```image bbbbbbf fbbbbbb cbbbbbbc bbbbbbf fbbbbbb cbbbbbbc bbbbbbf fbbbbbb cbbbbbbc bbbbbbf fbbbbbb cbbbbbbc bbbbbbf fbbbbbb cbbbbbbc bbbbbbf ced fbbbbbb geaaaa cbbbbbbc gdaaaaaaa bbbbbbf cgdaaaaaaaaaa fbbbbbb cedaaaaaaaaaaaaa cbbbbbbc geaaaaaaaaaaaaaaaaa bbbbbbf gdaaaaaaaaaaaaaaaaaaad fbbbbbb cgdaaaaaaaaaaaaaaaaaaaeg cbbbbbbccedaaaaaaaaaaaaaaaaaadec bbbbbdaaaaaaaaaaaaaaaaaaadec fddaaaaaaaaaaaaaaaaaaadgc cgdaaaaaaaaaaaaaaaaaaaeg cedaaaaaaaaaaaaaaaaaadec gedaaaaaaaaaaaaaaaaaadec geaaaaaaaaaaaaaaaaaaadgc cgdaaaaaaaaaaaaaaaaaaaddf cedaaaaaaaaaaaaaaaaaaadbbbbb aaaaaaaaaaaaaaaaaadeccbbbbbbc aaaaaaaaaaaaaaadgc bbbbbbf aaaaaaaaaaaaeg fbbbbbb cccfffbb aaaaaaaadeg cbbbbbbc cccfffbbbbbbbbbbb aaaaadec bbbbbbfccfffbbbbbbbbbbbbbbbbbbbb aadgc fbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb g cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb fbbbbbbbbbbbbbbbbbbbbbbbbbfffcc cbbbbbbbbbbbbbbbbfffccc cbbbbbbfffccc cc ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Okay, let's direct our attention to the next zone. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#745407ff b,#f58971ff c,#e9cfbfff d,#9e814aff e,#f6eae4ff f,#f8ad9dff g,#bfb08cff ``` ```image ecc egdaaaae cgdaaaaaaad cb cdaaaaaaaaaaaa cbbb egdaaaaaaaaaaaaaaac efbbbb egdaaaaaaaaaaaaaaaaaag efbbbbbb cgdaaaaaaaaaaaaaaaaaaaaag efbbbbbbbb aaaaaaaaaaaaaaaaaaaaaaaad efbbbbbbbbbb aaaaaaaaaaaaaaadgegaaaaaa fbbbbbbbbbbbb aaaaaaaaaaaadc caaaaaae cbbbbbbbbbbbbfe aaaaaaaadgc eaaaaaac cbbbbbbbbbbbbfe aaaaadge aaaaaag cbbbbbbbbbbbbfe aadge daaaaadfbbbbbbbbbbbfe c gaaaaaabbbbbbbbbbbc gaaaaaabbbbbbbbbc caaaaaabbbbbbbc fbaaaaaabbbbbf cbbbaaaaaadbbfe cbbbbbaaaaaadfe cbbbbbbbdaaaaaaddgggcce efbbbbbbbbdaaaaaaaaaaaaaaaadddgggcce efbbbbbbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaa efbbbbbbbbbbbbcaaaaaaaaaaaaaaaaaaaaaaaaa efbbbbbbbbbbbbc daaaaaaaaaaaaaaaaaaaaaaaa fbbbbbbbbbbbbf edaaaaaaaaaaaaaaaaaaaaaaa cbbbbbbbbbbbbfe eccggdddaaaaaaaaaaaaaaa bbbbbbbbbbbbfe eeccggdddaaaa bbbbbbbbbbfe ee bbbbbbbbfe bbbbbbbc bbbbbc bbbc bf e ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area B. Answer: A: 1; B: 1; 1 + 1 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#745406ff b,#f58971ff c,#f0d8cdff d,#94763aff e,#a89464ff f,#f9b8aaff g,#c5b797ff ``` ```image cb bbb bbbc fbbb bbb bbbc cbbb bbb bbbf cbbb bbb bbbf cbbb bbb bbbf cbbb bbb bbbf cbbb bbb bbbf cbbb bbb bbbf cbbb bf bbb bbbb bbbf fbbbbbf cbbb fbbbbbb bbb cdad fbbbbbb bbbf gaaaaaa cbbbbbbc cbbb gaaaaaaaaag cbbbbbbc bbb eaaaaaaaaaaaad bbbbbbf bbbf cdaaaaaaaaae caaa bbbbbbf cbbb caaaaaaaaaag aaa bbbbbbf bbb gaaaaaaaaaac aaabbbbbb bbbf eaaaaaaaaadc aaabbbb cbbb cdaaaaaaaaae fbaaadb bbb caaaaaaaaaag cbbbdaaaegc bbbf gaaaaaaaaaag cbbbbbbaaaaaaaaaaaaadegc cbbb eaaaaaaaaadc bbbbbbf aaaaaaaaaaaaaaaaaa bbb cdaaaaaaaaae bbbbbbf cgedaaaaaaaaaaaaa bbbaaaaaaaaaag bbbbbbf cgeaaa gaaaaaaaaaag fbbbbbb aaa eaaaaaaaaadc fbbbbbb aaa cdaaaaaaaaadf fbbbbbb aaac cdaaaaaaaaagcbbb cffbbbbbbbbc daag aaaaaaaaaag bbb ccfbbbbbbbbbbbbbbbc eaae aaaaaadc bbbfcfbbbbbbbbbbbbbbbbbbbbbbf gaad daae cbbbbbbbbbbbbbbbbbbbbbbfc caaa bbbbbbbbbbbbbfc aaa cbbbfcc aaa aaa aaa aaac aaag eaae gaad caaa aaa aaa aaa aaa aaa aaac daag eaae gaad caaa aaa aaa aaa aaa aaac aaag eaae gaad caaa aaa aaa aaa aaa aaa ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#549c64ff b,#17a0f0ff c,#278039ff d,#e8f3edff e,#b0d6b0ff f,#66bfeaff g,#8dc193ff ``` ```image eeeeeeeeeeeeeeeed eeeeeeeeeeeeeeeed eeegaeeeeeeeeeeed eecbaeeeeeeeeeeed eebbbbfeeeeeeeeed eebbbbbbbeeeeeeed eeecbbbbbbbeeeeed eeeaccbbbbbbbeeed eeeecccefbbbbbbgd eeeeccceeefbbbbbbf eeeegccaeeeeebbbbbbf dcd eeeeeccceeeeeeebbbbbbf ccce eeeeecccgeeeeeeedbbbbbbf accc eeeeeeccceeeeeeed fbbbbbb dccc eeeeeeccceeeeeeed fbbbbbbd ddddddddddddddddddddddcccg eeeeeeaccaeeeeeed fbbbbbbd geeeeeeeeeeeeeeeeeeeeecccc eeeeeeeccceeeeeed dbbbbbbf geeeeeeeeeeeeeeeeeeeegccc eeeeeeeccceeeeeed dbbbbbbf geeeeeeeeeeeeeeeeeeeeccce eeeeeeegccaeeeeed dbbbbbbf geeeeeeeeeeeeeeeeeeeccccd eeeeeeeeccceeeeed bbbbbbb geeeeeeeeeeeeeeeeeeaccced eeeeeeeecccgeeeed fbbbbbbd geeeeeeeeeeeeeeeeeeccceed eeeeeeeeeccceeeed fbbbbbbd geeeeeeeeeeeeeeeeecccaeed eeeeeeeeeccceeegd fbbbbbbf geeeeeeeeeeeeeeeeaccceeed dddddddddgccgddd dbbbbbbbf geeeeeeeeeeeeeeegccceeeed ccc fbbbbbbf geeeeeeeeeeeeeeecccgeeeed ccc fbbbbbbbf geeeeeeeeeeeeeecccceeeeed ecca fbbbbbbbgeeeeeeeeeeeeegccceeeeeed ccc dbbbbbbbfeeeeeeeeeeecccgeeeeeed accd fbbbbbbbeeeeeeeecccaeeeeeeed dccc dbbbbbbbfeeeeaccceeeeeeeed ccc gefbbbbbbbeeccceeeeeeeeed gccg geeeebbbbbbbbcaeeeeeeeeed ccc geeeeeefbbbbbbbeeeeeeeeed ccc geeeeeeeegbbbbbbbfeeeeeed ecca geeeeeeeecccfbbbbbbbeeeed ccc geeeeeeecccceeebbbbbbbfed accd geeeeeegccceeeeeefbbbbbbbd dccc geeeeeecccgeeeeeeeeebbbbbbbf ccc geeeeecccaeeeeeeeeeeeefbbbbb gccg geeeeaccceeeeeeeeeeeeeeedfbb ccc geeeeccceeeeeeeeeeeeeeeed d ccc geeecccaeeeeeeeeeeeeeeeed ecca geeaccceeeeeeeeeeeeeeeeed ccc gegccceeeeeeeeeeeeeeeeeed accd gecccgeeeeeeeeeeeeeeeeeed dccc gcccceeeeeeeeeeeeeeeeeeed ccc accceeeeeeeeeeeeeeeeeeeed gccg cccgeeeeeeeeeeeeeeeeeeeed ccc cccaeeeeeeeeeeeeeeeeeeeeed ccc gccceeeeeeeeeeeeeeeeeeeeeed ecca dcccgeeeeeeeeeeeeeeeeeeeeegd ccc cccgddddddddddddddddddddddd accd accc dccc dccc ccc ccce gccg cccc ccc eccc ccc cccd ecca ccca ccc gccc accd dcccd dccc cccg ccc accc gccg dccc ccc ccce ccc cccc ecca eccc ccc cccd accd ccca dccc gccc ccc dcccd gccg cccg ccc accc ccc dccc ecca ccce ccc cccc accd eccc dccc cccd ccc ccca gcccccc cccccd ccccg eccc cc ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#70ab7cff b,#18a0f1ff c,#27813aff d,#d5e9e7ff e,#a2c8abff f,#7ac8f7ff g,#25949cff ``` ```image daa eggccd acbbbge dgbbbbbfd bbbbbbbbfd fbbbbbbbbbbfd fbbbbbbbbbbbbfd gbbbbbbbbbbbbbf ecgbbbbbbbbbbbbbf ccccgbbbbbbbbbbbbf acccccbbbbbbbbbbbbbfd dccccccdfbbbbbbbbbbbbfd ccccccd fbbbbbbbbbbbbf eccccca fbbbbbbbbbbb dcccccc fbbbbbbbbb accccce dbbbbbbb eccccca dfbbbb ccccccd dfbb accccce df dcccccc ccccccd eccccca dcccccc accccce eccccca ccccccd accccce dcccccc ccccccd eccccca dcccccc accccce eccccca ccccccd accccce dcccccc ccccccd eccccca dcccccc accccce ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Hmm, interesting. Let's check out another area. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#4e9861ff b,#17a0f0ff c,#268038ff d,#c7decdff e,#89ba95ff f,#58baf3ff g,#a8dbf9ff ``` ```image dc ac ecc dccc cccc acccc eccccc dcccccc acccccc ecccccce dcccccca acccccc eccccccd dcccccce cccccca accccccd ecccccce dcccccca accccccd ecccccce dcccccca acccccc eccccccd dcccccce bfg cccccca bbbbg accccccd bbbbbbfg ecccccce bbbbbbbbbg dcccccca bbbbbbbbbbbfg accccccd bbbbbbbbbbbbbbg ecccccce gbbbbbbbbbbbbbbfg dcccccca gfbbbbbbbbbbbbbbf acccccc gfbbbbbbbbbbbbbfeccccccd gfbbbbbbbbbbbbbbbccce gfbbbbbbbbbbbbbba gfbbbbbbbbbbbbbbfg gfbbbbbbbbbbbbbfg dbbbbbbbbbbbbbbbfg accabbbbbbbbbbbbbbfg eccccccfbbbbbbbbbbbbbbfg dcccccca gfbbbbbbbbbbbbbbg acccccc gbbbbbbbbbbbbbbfg eccccccd gfbbbbbbbbbbbbb dcccccce gbbbbbbbbbbb cccccca gfbbbbbbbb accccccd gbbbbbb ecccccce gfbbb dcccccca gf accccccd ecccccce dcccccca acccccc eccccccd dcccccce cccccca accccccd ecccccce dcccccca accccccd ecccccce dcccccca acccccc eccccccd dcccccce cccccca ccccccd ccccce cccca ccccd ccce cca ``` <!-- end of image --> I can confirm that 1 intersection exists in area B. Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#68a777ff b,#17a0f1ff c,#278139ff d,#d6e9e4ff e,#a4c9abff f,#51b7f2ff g,#9ad5f9ff ``` ```image da cba bbbbf bbbbbbf cbbbbbbb accfbbbbbbd ccc gbbbbbbd ccc gbbbbbbg ecca dbbbbbbg cd ccc dbbbbbbf ccce cccd bbbbbbf accc dccc fbbbbbb dccc ccc fbbbbbbd ccce acce gbbbbbbg cccc ccc gbbbbbbg eccc ccc dbbbbbbg cccd ecca bbbbbbf ccca ccc fbbbbbf eccc cccd fbbbbbb cccd dccc gbbbbbbg ccca ccc gbbbbbbf accc acce gbbbbbbbg dccc ccc fbbbbbbf ccce ccc gbbbbbbbg cccc ecca fbbbbbbf eccc ccc gbbbbbbbg cccd cccd fbbbbbbbd ccca dccc dbbbbbbbg eccc ccc fbbbbbbbd cccd acce dbbbbbbbbca ccc fbbbbbbbd ccc dbbbbbbbf ecca cccfbbbbbbbd ccc cccc dbbbbbbbf cccd eccc gbbbbbbbg dccc cccd fbbbbbbf ccc ccca gbbbbb acce eccc fbb ccc cccd ccc ccca ecca accc ccc dccc cccd ccce dccc cccc ccc eccc acce cccd ccc ccca ccc eccc ecca cccd ccc ccca cccd accc dccc dccc ccc ccce acce cccc ccc eccc ccc cccd ecca ccca ccc accc cccd cccd dccc ccca ccc accc acce dccc ccc ccce ccc cccc ecca eccc ccc cccd cccd ccca dccc accc ccc cccd acce ccca ccc accc ccc dccc ecca ccce ccc cccc cccd eccc dccc cccd ccc ccca acccccc ccccc cccca eccc cc ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#74483bff b,#e19295ff c,#5e1e15ff d,#eccdceff e,#8e7c68ff f,#97c795ff g,#b1d7b1ff ``` ```image b bbb dbbd bbb dbbd bbb dbbd bbb dbbb bbbd bbb dbbd bbb dbbd bbb dbbd bbb bbb gfffffffffffffffffffffffffffffffffffffffffffffffg bbbd fgggggggggggggggggggggggggggggggggggggggggggggggf bbb fgggggggggggggggggggggggggggggggggggggggggggggggf dbbd fgggggggggggggggggggggggggggggggggggggggggggggggf bbb fgggggggggggggggggggggggggggggggggggggggggggggggf dbbbgggggggggggggggggggggggggggggggggggggggggggggggf bbbggggggggggggggggggggggggggggggggggggggggggggggf fbbbggggggggggggggcfggggggggggggggggggggggggggggf fgbbbgggggggggggfcceggggggggggggggggggggggggggggf fgggbbbggggggggecccaggggggggggggggggggggggggggggf fggggbbbggggggaccgccggggggggggggggggggggggggggggf fggggggbbbgggccaggccggggggggggggggggggggggggggggf fgggggggbbbbccegggccggggggggggggggggggggggggggggf fgggggggggbccfggggacggggggggggggggggggggggggggggf fggggggggfccbbbgggacggggggggggggggggggggggggggggf fgggggggeccggbbbggecggggggggggggggggggggggggggggf fggggggaccgggggbbbecggggggggggggggggggggggggggggf fgggggccagggggggbbbcggggggggggggggggggggggggggggf fggggcceggggggggggbcbgggggggggggggggggggggggggggf fggfccfggggggggggggcebggggggggggggggggggggggggggf fgeccggggggggggggggcebbbggggggggggggggggggggggggf feccgggggggggggggggcagbbbbggggggggggggggggggggggf accggggggggggggggggcagggbbbgggggggggggggggggggggf ccagggggggggggggggggccgggggbbbgggggggggggggggggggf cceggggggggggggggggggccggggggbbbggggggggggggggggggf dccdfggggggggggggggggggccggggggggbbgggggggggggggggggf gcc fggggggggggggggggggacgggggggggbbggggggggggggggggf ecc fggggggggggggggggggacggeagggggbbggggggggggggggggf aca fggggggggggggggggggecggccfgggggbbgggggggggggggggf cce fggggggggggggggggggecggcccgggggbbgggggggggggggggf ccb fggggggggggggggggggfcgacfcegggggbgggggggggggggggf dccd fgggggggggggggggggggcfccgccgggggbbggggggggggggggf bcc fgggggggggggggggggggceceggccggggbbggggggggggggggf ecc fgggggggggggggggggggcccgggacfggggbbgggggggggggggf aca fgggggggggggggggggggcccggggccggggbbgggggggggggggf cce fgggggggggggggggggggcceggggfceggggbbggggggggggggf ccg fgggggggggggggggggggccggggggccggggbbggggggggggggf dccd fgggggggggggggggggggccgggggggcaggggbggggggggggggf bcc fggggggggggggggggggggggggggggacfgggbbgggggggggggf ecc fgggggggggggggggggggggggggggggccgggbbgggggggggggf aca fgggggggggggggggggggggggggggggecegggbbggggggggggf cce fggggggggggggggggggggggggggggggccgggbbggggggggggf ccd fgggggggggggggggggggggggggggggggcagggbggggggggggf dcc fgggggggggggggggggggggggggggggggacgggbbgggggggggf bcc fggggggggggggggggggggggggggggggggccggbbgggggggggf acc fggggggggggggggggggggggggggggggggeceggbbggggggggf cca fgggggggggggggggggggggggggggggggggccggbbggggggggf cce fgggggggggggggggggggggggggggggggggfcaggbggggggggf ccd fggggggggggggggggggggggggggggggggggacggbbgggggggf dcc fgggggggggggggggggggggggggggggggggggccgbbgggggggf ecc fgggggggggggggggggggggggggggggggggggecegbbggggggf acc fggggggggggggggggggggggggggggggggggggccgbbggggggf cca fggggggggggggggggggggggggggggggggggggfcagbggggggf cb fgggggggggggggggggggggggggggggggggggggacgbbgggggf fggggggggggggggggggggggggggggggggggggggccbbgggggf fggggggggggggggggggggggggggggggggggggggecfbbggggf fgggggggggggggggggggggggggggggggggggggggccbbggggf fgggggggggggggggggggggggggggggggggggggggfcabggggf fggggggggggggggggggggggggggggggggggggggggccbbgggf fgggggggggggggggggggggggggggggggggggggggggccbgggf fgggggggggggggggggggggggggggggggggggggggggecbbggf fggggggggggggggggggggggggggggggggggggggggggccgggf fggggggggggggggggggggggggggggggggggggggggggfceggf fgggggggggggggggggggggggggggggggggggggggggggegggf fgggggggggggggggggggggggggggggggggggggggggggggggf ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#773e37ff b,#e68e94ff c,#5e1d14ff d,#e2b9baff e,#936862ff f,#b3928eff g,#f0ddddff ``` ```image g bd bbbd dbbbbg dg gbbbbd geccd bbbbbg gacccf gbbbbbb acccce dbbbbd dccccce gbbbbd ecccffcca bbbbbg gacccd dcca gbbbbb gaccca dccc dbbbbg ccccag gcccg gbbbbdg fccce gcccg dbbbbdfcccf cccd bbbbacccd cccd gacccabg accf dccccabbbd eccf ccccegdbbbbg ecce fcccf bbbbbd fcce ecccd dbbbbg fcca gaccad gbbbbdgfcca gacccg dbbbbfccc cccce gbbbccc fcccf dbcccg ecccd gcccbd gaccag cccbbbg gacccg accbbbbd dcccce accdbbbbb ccccf ecc dbbbbd ecccd fcc gdbbbbg gaccag fcc bbbbbd accag fcc dbbbbg ccc dcc gbbbbd ccf dcc dbbbbg cf gccg gbbbbd ccd gbbbbb acd gbbb acf gbbg ecf bbd ece fag dbb ece cce bbg fca eccca gbbg dca cccccd bbd dcc dccacca bbb gcc eccdcccf bbbg gccg ccc ecccg dbbb ccddccc gccce gbbbg ccdecca fccc bbbd acecccg dccf bbbg ecccca eccg dbbb eccccf gcce gbbb eccccg fccd bbb fccca cca gbb fcccf cccf bbg dcccg ecccg dbb gccf fcccd bbd gccg acca gbb af dcccf bbd eccc bbb gccc bbbg fccd bbbd dccf bbbd eccg dbbb gcce gbbbg cccd bbbd acca gbbb fcccf bbbd acccg dbbb eccc dbb gccc gbb fccf bbd acag dbb dcce gbbg eccg dbd cccd bbd acca bbb dcccf bbbg ecccg dbbd gccce gbbbg fcccd bbbd acca dbbb eccg dbbd gcce gbbb fccd bbb aca dbb dccf bbg cccgdbb cccegbbg accadbb dcccfbbg ecccbbb gcccbbbg fccfbbd acabbb accbbb gccabbg cccfbd accad fcccf acccg gccce gf ``` <!-- end of image --> I've cracked the case! This area contains 2 intersections. Answer: A: 2; 2 = 2 Two intersections have been found!
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#7e4a43ff b,#e68f95ff c,#5f1e15ff d,#e6c0c2ff e,#a0726dff f,#b69995ff g,#f4e3e4ff ``` ```image bg bbb dbbg bbb dbbd bbb gbbd bbbg gbbb bbbg gbbb dbbg bbb dbbd bbb gbbd bbbg gbbb dbbg bbb dbbd bbb dbbd bbb gbbd gcd bbbg dcce gbbb fccca dbbg acc cc bbb cca cc dbbdccf cc bccd ac dccbbd ac ecc bbb ec acc gbbbfc cca bbec ccf gbcb gccd cebg dcc cfbbb ecc ce dbbd aca ca bbb cce cc gbbd ccf cc bbbg gccg cc gbbg fcc ac bb ecc ec fa db aca fc ccd bb cce fc ccc bb ccf dcgecdce bd gccg cdcc cc bb fcc cfcf ca db ecc ccc ecg bb aca ccc cc bb cce ccf dcf bd ccd cc cc bb dccg cc ca db fcc acg bb acc cc bb cca fcf bd cce cc bb gccd gca gbg dccg acg bb fcc cc bb acc fcf bd cca cc bb ccf gca gbg gccd ac bb dccg cc db fcc fcd bd acc cc bb cca gcagbg cf ac bb ccdb fcdbd ccbb gcebg ccbb ccb eced cc dce f ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#b38389ff b,#931fbeff c,#ddb9d4ff d,#a94a65ff e,#b0d6b0ff f,#ac78c3ff g,#f0f5f0ff ``` ```image g cd dac aa d d dg dg ga cd d d ac ac d d d dg ca cd d d ac ggggggggggggggggggggaaggg d geeeeeeeeeeeeeeeeeeeedeeeeg d geeeeeeeeeeeeeeeeeeedeeeeeg ca geeeeeeeeeeeeeeeeeeedeeeeeg d geeeeeeeeeeeeeeeeeedeeeeeeg g geeeeeeeeeeeeeeeeeaaeeeeeeg geeeeeeeeeeeeeeeeedeeeeeeeg geeeeeeeeeeeeeeeedeeeeeeeeg geeeeeeeeeeeeeeeadeeeeeeeeg geeeeeeeeeeeeeeedeeeeeeeeeg geeeeeeeeeeeeeeaaeebeeeeeeg geeeeeeeeeeeeeedefbbfeeeeeg geeeeeeeeeeeeedfbfeebeeeeeg geeeeeeeeeeeeadfeeeebeeeeeg geeeeeeeeeefbdeeeeeebeeeeeg geeeeeeeeebbaaeeeeeeffeeeeg geeeeeeebbeedeeeeeeeebeeeeg geeeeebbeeedeeeeeeeeebeeeeg geeebbeeeeadeeeeeeeeeffeeeg gebbeeeeeedeeeeeeeeeeebeeeg fbfeeeeeeaaeeeeeeeeeeebeeeg fbceeeeeeeedeeeeeeeeeeeebeeeg fbf geeeeeeedeeeeeeeeeeeeeffeeg cbf geeeeeeadeeeeeeeeeeeeeebeeg gggggggggggggggggggggggggggg cbf geeeeeedeeeeeeeeeeeeeeebeeg eeeedeeeeeeeeeeeeeeeeeeeeeeeg gbb geeeeeaaeeeeeeeeeeeeeeeffeg eeeeddeeeeeeeeeeeeeeeeeeeeeeg gbb geeeeedeeeeeeeeeeeeeeeeebeg eeeededeeeeeeeeeeeeeeeeeeeeeg bbg ggggdggggggggggggggggggbg eeeedeedeeeeeeeeeeeeeeeeeeeeg bbg ca bg eeeedeeedeeeeeeeeeeeeeeeeeeeg fbc d cf eeeedeeeedeeeeeeeeeeeeeeeeeefbc ac b eeeedeeeeadeeeeeeeeeeeeeeefbf gd b eeeedeeeeeadeeeeeeeeeeeefbfeg dg fc eeeedeeeeeeadeeeeeeeeefbbeeeg ca gb eeeedeeeeeeeadeeeeeeebbeeeeeg d b eeeeaeeeeeeeeadeeeebbeeeeeeeg ac bg eeeeaeeeeeeeeeadebbeeeeeeeeeg gd cf eeeaaeeeeeeeeeeadeeeeeeeeeeeg dg b eeeaaeeeeeeeeeebadeeeeeeeeeeg ca b eeeaaeeeeeeeeefbeadeeeeeeeeeg d fc eeeaaeeeeeeeeebeeeadeeeeeeeeg ac gb eeeaaeeeeeeeebeeeeedaeeeeeeeg gd b eeeaeeeeeeeefbeeeeeedaeeeeeeg dg b eeeaeeeeeeeebeeeeeeeedaeeeeeg ca cf eeedeeeeeeebeeeeeeeeeedaeeeeg d b eeedeeeeeefbeeeeeeeeeeedaeeeg ac b eeedeeeeeebeeeeeeeeeeeeedaeeg gd fc eeedeeeeebfeeeeeeeeeeeeeedaeg dg gb eeedeeeefbeeeeeeeeeeeeeeeedag ca b eeeeeeeebeeeeeeeeeeeeeeeeeedc d b eeeeeeebfeeeeeeeeeeeeeeeeeeedc ac cf eeeeeeebeeeeeeeeeeeeeeeeeeeegdc gd b eeeeeebeeeeeeeeeeeeeeeeeeeeeg dc dg b eeeeebfeeeeeeeeeeeeeeeeeeeeeg dc ca fc eeeeebeeeeeeeeeeeeeeeeeeeeeeg dg d gb eeeebeeeeeeeeeeeeeeeeeeeeeeeg dgac b eeeffeeeeeeeeeeeeeeeeeeeeeeeg dd b gggcgggggggggggggggggggggggg cf b b fc gb b b cf b b ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#be748aff b,#921abfff c,#d4a3b2ff d,#aa4866ff e,#ca90e0ff f,#ab4fcdff g,#ebd4e4ff ``` ```image g cdc cddc cdddc cdcddc adggddc adg gddc adg gddc adg gddc adg gddc ad gddc ad gddc dd gddg e dd gddg ebb dd gddg ebbbe dd cddg ebbbeg dd cddg efbbfg da cddg gfbbfg da cddg gfbbfg da cddg gfbbfg gda cddg gfbbbe gda cddg ebbbe gda cddg ebbbe gda cddg ebbbe gdc cddbbbe gdc addfg gdc edddg cdc gbbada cdc fbe ada cdc ebf ada cdc gbbg ada cdc fbe ada cdg ebf ada cdg gbbg ada cdg fbe ada adg ebf ada adg gbbg ada adg fbe ada adg ebf ada ad bbg gdda ad fbe gddc ad ebf gddc dd bbg gddc dd fbe gddc dd gbb gddc dd bbg gddc dd ebf gddc da gbb gddc ac bbe gdd ebf gd gbb g fbe ebf gbbg fbe ebf gbbg fbe ebf gbbg fbe ebf bbg fbe ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Let's continue our search in the next region. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#bf768cff b,#931bbeff c,#d5a4b2ff d,#ab4967ff e,#d19fe4ff f,#b25ed0ff g,#ebd4e6ff ``` ```image gdd adg cda gddg adc gdd adg cda gddg adc gdd ddg cda gddg adc gdd ddg cda gddg adc gff gdd gfbbbg ddg gfbbbfbe cdagfbbbe gbf gddfbbbe bb adbbbe fbg fddbf ebe ebddfg gbf ebbbda bb gfbbfddg fbe gfbbfgadc gbf gfbbbe gda bb gfbbbe ddg fbg fbbbe cda ebe ebbbe gddg gbf ebbbe adc bb ebbbfg gda fbe ebbbfg ddg ebf gfbbfg cda bb gfbbfg gddg fbg fbbfe adc ebe bbe gda gbf e ddg bb cda fbe gddg ebf adc bb gda fbg ddg ebe cda gbf gdd bb adc fbe gda ebf ddg bb ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#be7389ff b,#941dc0ff c,#d9adbaff d,#aa4765ff e,#d6aae7ff f,#b869d4ff g,#ecd7e6ff ``` ```image g gd dcc ac d d d dg ga gd d d ac ac d d d dg ga gd d d ac ac d d d dg ca gd d d g ac d dg ga d ac f d fbfe dfbe b fdf b ebd b gbfac ef gbb d b bb dg b bbg ga fe bbg d b fbe ac b fbe d b ebf dg ef ebf ca b gbf d b d gbb ac fe dd bb d b dgd bb d b d gd bbg ca b d gd fbg d ef d gd fbe ac b d cd fbe d b d cd ebf d fe a cd ebf ca b a cd gbb d b ga cd gbb ac b ga cd bb d ef gc adg d b cc baa ca b cc ff aa d fe cc b aa ac b cg bg aa d b ag ef aa d b ag b aa ca ef ag bg aa d b a eb dc ac b d b dc d fe d be dc d b d gb dc ca b b dc d b be dc ac ef gb dg d b b dg d b fe dg ca fe gb dg d gb b dgac b ff dd b g ef b b fg gb b b ef b b ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#203e78ff b,#d3ec84ff c,#8098a9ff d,#b2d7b2ff e,#4c688eff f,#edf3ebff g,#a1cea2ff ``` ```image fgdddddddddddddddddd fgdddddddddddddddddd fgddddddddddddgcdddd fgddddddddddddeaagdd fgddddddddddddaaaddd fgdddddddddddcaaeddd fgdddddddddddaaadddd fgdddddddddddaaadddd fgddddddddddeaacdddd fgddddddddddaaadbddd fgdddddddddbbbbbbddd fgddddbbbbbbbbbbbddd fdbbbbbbbbbbbbbddddd fbbbbbbbbbbbbbgaaedddddd fbbbbbbbbbbbbbbddddaaaddddddd fbbbbbbbbbbbbbbgddddddddaaaddddddd fbbbbbbbbbbbbbbf fgdddddddeaacddddddd ffbbbbbbbbbbbbbf fgdddddddaaadddddddd fbbbbbbbbbbbbbf fgddddddgaaedddddddd fbbbbbbbbbbbbbf fgddddddaaaddddddddd ffffffffffffffffffffffbbbbbbbbbbbff fgddddddaaaddddddddd ggggggggggggggggggggggbbbbbbbbf fgdddddcaacddddddddd a gddddddddddddddddddddbbbbf fgdddddaaadddddddddd eaac gdddddddddddddddddddbbbbf fgdddddaaadddddddddd aaaaaf gdddddddddddddddddddbbbgf fgddddeaagdddddddddd daaaaegddddddddddddddddddbbbdgf fgddddaaaddddddddddd eaaaacddddddddddddddddbbbbdgf ggggcaaeggggggggggg faaaaaddddddddddddddbbbbddgf aaa caaaaedddddddddddbbbbdddgf aaa gaaaaagddddddddbbbbddddgf caad gdcaaaaeddddddbbbbdddddgf aaa gdddaaaaacdddbbbbddddddgf faae gddddgaaaaadbbbbdddddddgf eaaf gddddddeaaagbbbddddddddgf aaa gdddddddgacbbbgddddddddgf daac gdddddddddbbbeaedddddddgf aaa gddddddddbbbeaaaacdddddgf aaa gdddddddbbbbdcaaaaaddddgf caad gddddddbbbbddddeaaaacddgf aaa gdddddbbbbddddddgaaaaaggf aaa gddddbbbbdddddddddcaaaaef aae gdddbbbbddddddddddddaaaaaf caaf gddbbbbddddddddddddddcaaaaa aaa gdbbbbdddddddddddddddddeaaaac aaa gbbbbddddddddddddddddddgfaaaaaf aae bbbbdddddddddddddddddddgf caaaae daad fbbbddddddddddddddddddddgf aaaaaaf eaa fbbbdddddddddddddddddddddgf daaaaaaef aaa bbbbggggggggggggggggggggggf caaaaaaac aae bbbbfffffffffffffffffffffff caaaaaaad daad bbbb feaaaaaaaf eaa bbbb daaaaaac aaa bbbb caaaa aae bbbb aaa daad bbb eaa eaa b caaf aaa faad aaa aae faac aaa eaa aaa aaa aaa aaa eaa faac daaf caaf faac aaa aae aaa aaa faac aaa caaf eaa aaa caa aaa daad faac aac caaf aaa aaa aaa aaa aaa aae eaacaad gaaaaa faaaaa aaaae aaaad aaaa eaaa caae daad aa ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#203e78ff b,#d4ec81ff c,#8496abff d,#bbc4d6ff e,#4c648fff f,#edf3e1ff g,#e1f2a9ff ``` ```image b gb gbb gbbb gbbbb gbbbbb fbbbbbb fbbbbbbb fbbbbbbbf fbbbbbbbf cf fbbbbbbbf aad bbbbbbbg aaaef gbbbbbbg aaaaac gbbbbbbg aaaaaaed gbbbbbbg aaaaaaaac gbbbbbbg eaaaaaaaaed gbbbbbbb caaaaaaaaaef fbbbbbbbf deaaaaaaaaac fbbbbbbbf caaaaaaaaaed fbbbbbbbf feaaaaaaaaac fbbbbbbbf deaaaaaaaaed fbbbbbbbf caaaaaaaaacf bbbbbbbg deaaaaaaaaad gbbbbbbg caaaaaaaaaegbbbbbbg feaaaaaaacbbbbbbg daaaaacbbbbbbg caacbbbbbbbf dcbbbbbbbaad fbbbbbbbeaaaef fbbbbbbbeaaaaaac fbbbbbbbeaaaaaaaaed fbbbbbbbffcaaaaaaaaacf bbbbbbbg deaaaaaaaaad gbbbbbbg caaaaaaaaaef gbbbbbbg feaaaaaaaaac gbbbbbbg daaaaaaaaaed gbbbbbbg fcaaaaaaaaacf gbbbbbbb deaaaaaaaaad fbbbbbbb caaaaaaaaa fbbbbbbbf feaaaaaaa fbbbbbbbf daaaaaa fbbbbbbbf fcaaaa fbbbbbbbf deaa bbbbbbbg ca gbbbbbbg f gbbbbbbg gbbbbbbg gbbbbbbg gbbbbbbb bbbbbbb bbbbbbf bbbbbf bbbbf bbbf ``` <!-- end of image --> I observe 1 intersection inside area A. Let's shift our focus to the next area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#203e78ff b,#d3ec81ff c,#8496adff d,#b2bdceff e,#546c91ff f,#e9eee2ff g,#e3f3b0ff ``` ```image ed daaacf eaaaaaf faaaaae caaaaad aaaaaa daaaaac eaaaaad faaaaae daaaaac eaaaaaf faaaaae caaaaad aaaaaa daaaaacfgg eaeecbbbbb ffgbbbbbbbbbbf fggbbbbbbbbbbbbbbg fggbbbbbbbbbbbbbbbbbbbg fggbbbbbbbbbbbbbbbbbbbbbbbbg fggbbbbbbbbbbbbbbbbbbbbbbbbbgff bbbbbbbbbbbbbbbbbbbbbbbbcee bbbbbbbbbbbbbbbbbbbgdeaaaac bbbbbbbbbbbbbbggf eaaaaaf bbbbbbbbbggf faaaaae bbbbggff caaaaad gff eaaaaa daaaaac caaaaad aaaaae daaaaac eaaaaaf faaaaae caaaaad aaaaaa daaaaac eaaaaad faaaaae daaaaac eaaaaaf faaaaae caaaaad aaaaaa daaaaac eaaaaaf faaaaae caaaaad ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#213e78ff b,#d4ed82ff c,#8a9ab4ff d,#bcc5d5ff e,#576e98ff f,#edf1e7ff g,#e5f3b6ff ``` ```image fd eaaf aaa daac aaa aaa caad aaafg fgbbbbb gbbbbbbbbbb gbbbbbbbbbbbbbg fbbbbbbbbbbbbbdaac fgbbbbbbbbbbbbgf aaa fgbbbbbbbbbbbbgf aaa fgbbbbbbbbbbbbgf eaad gbbbbbbbbbbbbgf aaa gbbbbbbbbbbbbbg faae gbbbbbbbbbbbbbg aaa bbbbbbbbbbbg aaa bbbbbbbgf caac a gbbbf aaa eaac gbbb aaa aaaaaf fbbbf eaad daaaae fbbbf aaa eaaaad bbbg daae faaaaa bbbg aaa eaaaac bbbb aaa aaaaaf bbbb caad caaaae bbbb aaa aaaaad bbbb faaa daaaaa bbbb eaaf eaaacbbb aaa facbbbf daac fbbbeae aaa fbbbeaaaad aaa bbbg daaaaa caad bbbg eaaaac aaa bbbb faaaaaf aaa bbbb caaaae aae bbbb aaaaad caad bbbb daaaaa aaa bbbb eaaaac aaa gbbb faaaaaf aae gbbb caaaae daad fbbbf aaaaaad aaa fbbbf daaaaaaef aaa bbbg caaaaaaac aae bbbg eaaaaaaad daad bbbb feaaaaaaad eaa bbbb daaaaaae aaa bbbb caaaa aaa bbbb aaa daad bbb eaa eaa g caaf aaa daad aaa aae daac aaa eaa aaa aaa aaa aaa eaa faac daad eaaf faac aaa aae aaa aaa faac aaa caaf eaa aaa caa aaa daad aae aae caaf aaa aaa aaa aaa aaa aae eaacaad caaaaa faaaaa aaaae aaaad aaaa aaaa caae daad aa ``` <!-- end of image -->
[ "" ]
I'm optimistic that I'll find some intersections in this image. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#3484f3ff b,#a09334ff c,#6fa9dbff d,#b1d7b0ff e,#acccf9ff f,#b0b370ff g,#eef4eeff ``` ```image f bb ae bg bb aag b bf acag gb gbd a ca db dbg a ca fb fbg a aa bf fb a aa bd bb a aa b bb ga aa b bf ga ag gb gbd ea ca fb dbg ea ag bf fbg ea aa bd fb ea a bg bb ea aa b bb ca ga b bf ca aa db gbd ca ga fb gbg ca ac bf fbg ac ga bd fb ac ac bg bb ac ea b bb ae ae gb bf ae ea db gbd ae ae fb gbg ae ea bf fbg ae ae bd fb ag ca b bb ag ag b ae bb a ca gb caae bf a ag db eaac ggggbfgggggggggggggaggggggggggggggggggaagggggggggggfbgggggggg eaac gddddfbfddddddddddddadddddddddddddddddddadddddddddddbfdddddddd gaaa gdddddfbddddddddddddadddddddddddddddddddaaddddddddddbddddddddd gaaag gddddddbbdddddddddddaddddddddddddddddddddaddddddddddbddddddddd aaae gdddddddbbddddddddddaddddddddddddddddddddaadddddddddbddddddddd caae gddddddddbbdddddddddadddddddddddddddddddddaddddddddfbddddddddd caae gdddddddddbbddddddddadddddddddddddddddddddacdddddddfbddddddddd eaac gddddddddddbfdddddddaddddddddddddddddddddddadddddddbbddddddddd eaaadddddddddddbfdddddcaddddddddddddddddddddddacddddddbfddddddddd gaaadddddddddfbdddddcaddddddddddddddddddddddcaddddddbdddddddddd gdaaaddddddddbbddddcadddddddddddddddddddddddacdddddbdddddddddd gdddaaacddddddbbdddcadddddddddddddddddddddddcadddddbdddddddddd gdddddcaacdddddbbddcaddddddddddddddddddddddddacdddfbdddddddddd gdddddddcaacddddbbdcaddddddddddddddddddddddddcadddfbdddddddddd gdddddddddcaacdddbfcadddddddddddddddddddddddddacddbfdddddddddd gdddddddddddcaddddbcadddddddddddddddddddddddddcaddbfdddddddddd gddddddddddddaddddfbcddddddddddddddddddddddddddaddbddddddddddd gddddddddddddacddddbbddddddddddddddddddddddddddaadbddddddddddd gddddddddddddcaddddabbddddddddddddddddddddddddddadbddddddddddd gdddddddddddddaddddacbbdddddddddddddddddddddddddacbddddddddddd gdddddddddddddacdddacdbbdddddddddddddddddddddddddbbddddddddddd gdddddddddddddaadddacddbfddddddddddddddddddddddddbfddddddddddd gddddddddddddddadddacdddbfdddddddddddddddddddddddbcddddddddddd gddddddddddddddadddacdddfbdddddddddddddddddddddddbaadddddddddd gddddddddddddddaaddadddddbbddddddddddddddddddddddbdadddddddddd gddddddddddddddcaddaddddddbbddddddddddddddddddddfbdacddddddddd gdddddddddddddddaddadddddddbbdddddddddddddddddddfbddaddddddddd gdddddddddddddddacdaddddddddbbddddddddddddddddddbbddacdddddddd gdddddddddddddddcadadddddddddbfdddddddddddddddddbfddcadddddddd gddddddddddddddddadaddddddddddbfddddddddddddddddbddddacddddddd gddddddddddddddddacaddddddddddfbddddddddddddddddbddddcaddddddd gddddddddddddddddaaadddddddddddfbdddddddddddddddbdddddacdddddd gdddddddddddddddddaaddddddddddddbbdddddddddddddfbdddddcadddddd gdddddddddddddddddaadddddddddddddbbddddddddddddfbddddddacddddd gdddddddddddddddddaaddddddddddddddbbdddddddddddbfddddddcaddddd gdddddddddddddddddcadddddddddddddddbfddddddddddbfdddddddaddddd gddddddddddddddddddcddddddddddddddddbfdddddddddbddddddddaadddd gdddddddddddddddddddddddddddddddddddfbdddddddddbdddddddddadddd ggggggggggggggggggggggggggggggggggggfbggggggggbgggggggggegggg bb db bb fb bb bf bf bd gbd b dbg b fbgb bbb bf ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3483f3ff b,#a09333ff c,#6ca5f4ff d,#d6d0a7ff e,#a7c9f9ff f,#b6ad68ff g,#e3e9ecff ``` ```image gbbbd caa aaag fbf gbbbd caa eaae bbf gbbbg caa aaa gbbd dbbbg cac eaae gbbd dbbbg aac aaa dbbg fbbf aac eaae dbbg bbbd aac eaae bbf gbbbd aac gaac bbf gbbbg aac caae gbbd dbbb aac gaac dbbd dbbg gaae caag dbbg fbf gaae gaac fbb fbf gaae caag fbb bbd gaae gaac bbf bbbd gaae caa bbf e gbbbd eaae eaa bbd aae dbbbg eaae cag bbd eaaaaag fbbf eaag aag bb eaaaacg fbbf eaag eae bb eaaaacg fbbd eaag aa bf caaaace gbbbd eaag aae gbd gcaaaace gbbbd eaag aaa gbd gcaaaaae dbbbg eaa eaae dbg gcaaaaae dbbb caa aaa dbg geaaaacg fbb caa eaae fb eaaaacg fbf caa gaac ff eaaaac fbd caa caae bf ecaaag gbbdcaa gaac gbd eaae bbbcaa caag dbd caa dbbbc caag fb eaae fbbb gaac fb gaac bbbf caag bb caa abbbd eaac bb eaag aabbbd caagbb gaae aacbbbd eaacbb aac aacdbbbg aafbb caag aae dbbbg eafbb eaae gaae fbbf abbb aac gaae fbbf ebbf caa gaae fbb gbbf gaac gaae gbbd dbba aaa eaae dbbg dbbae caag eaae bbbg fbbac eaae eaae fbbf fbfcae aac eaag fbbf bbfgac caa eaag fbbf gbbd aag eaae eaag gbbbd dbbd aac gaac eaag gbbbd dbbg caag caa eaag dbbbg dbbg gaac eaa caa dbbbg fbb caag gaa caa fbbf bbf eaac aa caa fbbf bbf caag eae caa gbbb dbbd aaag ac caa gbbd dbbg eaae ca caa dbbg fbb aaa eaecac dbbg fbb eaae gacaac bbf bbf aaa aaaac fbbf bbf eaae aaaac fbbf gbbd aaa aaaac gbbbd dbbd eaae aaaac gbbbd dbbg gaac caaac dbbbg fbb caae eaaac dbbbg fbf gaac caae fbbf gbbd gaac eaae fbbf gbbd caag gaae gbbbd dbbg gaac ee gbbb dbbg caa dbbg fbb eaa dbbg fbf cag ``` <!-- end of image --> The evidence is clear: there's 2 intersections in area A. Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#3484f3ff b,#a09332ff c,#7caff6ff d,#cdc693ff e,#bed7fbff f,#b1a962ff g,#e6e2caff ``` ```image f bb ae b bb aae b bf aca gb bd a ca db gbg a aa fb db a aa bd fb a aa bg bb a aa b bb a aa b bf ea ae gb bd ea ca db gbg ea a ff db ea aa bd fb ea a bg bb ca aa b bb ca a b bf ca aa gb bd ca a fb gbg aa ac bf db ac ea bd fb ac ac b bb ac ea b bb ac ac gb bf ac ea db bd ae ae fb gbg ae ca bd db ae ae bg fb ae ca b bb a ae b ae bb a ca gb caac bf a a db caac bd a aa ff eaac gbg a a bd eaaa db a aa bg aaa fb a a b aaae bb a aa b caae bb a a gb caac bf a ac db eaac bd ea ea bf eaaa gbg ea ac bd eaaa db ea ea bg aaae fb ea ac b caae bb ca ea b caae bb ca ae db caac bf ca ca fb eaac bdca ae bf ea gbca ca bg a dbc ae b ac fb ca b ca abb agb a acbb afb ae ac bf bb ca ae bd bf ea ae gbg ba ae ae db baa ac ae fb b a ea ae bb gb ac a a bb db ea ac a bf ff ac ca a bd bd ea a a gbg bg ac aea db b ea aaa fb b ae eaa bb gb ca aa bb fb ae aa bf bf ca ca bd bd ae c gbg b ca dbg b a fb gb e bb db bb fb bf bd bd bg gbg b dbg b fbgb bbb bf ``` <!-- end of image -->
[ "" ]
I'm ready to tackle this image and find those intersections! My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#514191ff b,#c121c3ff c,#dec4e7ff d,#be88c9ff e,#7f7da8ff f,#a0cca1ff g,#b1d7b1ff ``` ```image dee aaac aaac aaac aaac aaac aaac aaac aaac aaac aaac aaad aaad aaad dbbc aaad dbbbbb aaad dbbbbbbb aaad cbbbbbbbbb aaad cbbbbbbb bbbd aaad cbbbbbbb dbbb aaad cbbbbbbb cbbb aaae cbbbbbbb bbb aaae cbbbbbbb bbbd aaae bbbbbbbc bbbb aaae bbbbbbbc cbbb aaae bbbbbbbc bbb aaae bbbbbbbc bbbc aaae bbbbbbbc bbbb eac aaae bbbbbbbc dbbb aaae ffaaaaffffffffff dbbbbbbd bbb caaa ggaaaagggggggggf dbbbbbbd bbbc aaaa ggaaaagggggggggf dbbbbbbd fffffbbbbfffffffaaaefff ggaaaagggggggggf dbbbbbbd fggggdbbbggggggeaaagggf ggaaaagggggggggf dbbbbbbb fgggggbbbggggggaaaagggf ggeaaagggggggggf cbbbbbbb fgggggbbbggggggaaafgggf ggeaaagggggggggf cbbbbbbb fgggggbbbdggggeaaaggggf ggeaaagggggggggf cbbbbbbb fgggggbbbbggggaaaaggggf ggeaaagggggggggf cbbbbbbb fgggggdbbbggggaaagggggf ggeaaagggggggggf cbbbbbbb fggggggbbbgggeaaagggggf ggeaaagggggggggfcbbbbbbb fggggggbbbdggaaaegggggf ggeaaagggggggggbbbbbbbc fggggggbbbbgfaaaggggggf ggeaaagggggggbbbbbbbc fggggggdbbbgaaaaggggggf ggeaaagggggbbbbbbbc fgggggggbbbgaaaeggggggf ggeaaagggbbbbbbbc fgggggggbbbeaaagggggggf ggeaaagbbbbbbbdf fgggggggbbbaaaagggggggf ggeaaabbbbbbdggf fgggggggdbbaaafgggggggf ggeaaabbbbdggggf fggggggggbaaaaggggggggf gdbaaabbdggggggf fggggggggbaaaeggggggggf ggbaaadggggggggf fggggggggbaaagggggggggf ggeaaagggggggggf fggggggggaaaagggggggggf ggeaaagggggggggf fggggggggaaaagggggggggf ggeaaagggggggggf fgggggggaaaabgggggggggf ggeaaagggggggggf fggggggaaaaabdggggggggf ggeaaagggggggggf fgggggaaaaabbbggggggggf ggeaaagggggggggf fggggeaaaadbbbggggggggf ggfaaagggggggggf fgggeaaaaggbbbggggggggf ggfaaagggggggggf fggfaaaagggbbbdgggggggf ggfaaagggggggggf fgfaaaaggggbbbbgggggggf ggfaaagggggggggf fgaaaafggggdbbbgggggggf ggfaaagggggggggf faaaaeggggggbbbgggggggf ggfaaagggggggggf aaaaegggggggbbbdggggggf ggfaaagggggggggf aaaaaggggggggbbbbggggggf ggfaaagggggggggf eaaaagggggggggdbbbggggggf ggfaaagggggggggf daaaagggggggggggbbbggggggf ggfaaagggggggggf caaaaggggggggggggbbbggggggf ggfaaagggggggggf caaaafggggggggggggbbbdgggggf fffaaaffffffffff aaaacfggggggggggggbbbbgggggf aaa aaaac fggggggggggggdbbbgggggf aaa aaaad ffffffffffffffbbbffffff aaa aaaae bbbd aaa eaaaa bbbb aaa eaaaa cbbb aaa daaaa bbb aaa caaaa bbbc aaadc aaaa bbbb aaaaaaaaaaec aaaac dbbb aaaaaaaaaaaaaaaaaedc aaaac bbb eaaaaaaaaaaaaaaaaaaaaaaaedc aaaae bbbc cdeaaaaaaaaaaaaaaaaaaaaaaaedc aaaae bbbd ceaaaaaaaaaaaaaaaaaaaaaaaaedceaaaa dbbb cdeaaaaaaaaaaaaaaaaaaaaaaa cbbb cdeaaaaaaaaaaaaaa bbb cdeaaaaa bbbd c ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#504091ff b,#c121c3ff c,#beb7d6ff d,#df8ce0ff e,#755ea6ff f,#dfd3e9ff g,#9a8fbfff ``` ```image eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaae eaaaaaa eaaaaaa eaaaaaa eaaaaaa gaaaaaa gaaaaaa gaaaaaa gaaaaaa gaaaaaa gaaaaaa db gaaaaaa dbbb gaaaaaa dbbbbb gaaaaaa dbbbbbbb gaaaaaa dbbbbbbbbb gaaaaaa dbbbbbbbbbbb gaaaaaa dbbbbbbbbbbbbb gaaaaaa fbbbbbbbbbbbbbbd gaaaaaa fbbbbbbbbbbbbbbd gaaaaaafbbbbbbbbbbbbbbd gaaaaaabbbbbbbbbbbbbd gaaaaaabbbbbbbbbbbd gaaaaaabbbbbbbbbd feaaaaaabbbbbbbd fbeaaaaaabbbbbdf beaaaaaabbbdf deaaaaaabdf eaaaaaac gaaaaaaf caaaaaaf caaaaaaf caaaaaaf caaaaaaf caaaaaaf caaaaaaf caaaaaaf caaaaaaf caaaaaac caaaaaac caaaaaac caaaaaac caaaaaac caaaaaac caaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaac faaaaaag faaaaaag faaaaaag faaaaaag faaaaaag faaaaaag aaaaaag ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Time to investigate another area. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#514091ff b,#c11fc2ff c,#afa6ccff d,#e299e3ff e,#7d71adff f,#e5d3ecff g,#d25dd2ff ``` ```image dbbbbbbd faaaaaae fbbbbbbg eaaaaaac bbbbbbb aaaaaaa gbbbbbbf caaaaaae dbbbbbbd eaaaaaac fbbbbbbg faaaaaaa bbbbbbg caaaaaae gbbbbbb eaaaaaaf dbbbbbbf faaaaaaa fbbbbbbd caaaaaac bbbbbbg aaaaaaaf gbbbbbb faaaaaae dbbbbbbf eaaaaaac fbbbbbbd aaaaaaa bbbbbbg caaaaaae gbbbbbb eaaaaaac gbbbbbbf faaaaaaa dbbbbbbd caaaaaac fbbbbbbg eaaaaaaf bbbbbbb faaaaaae gbbbbbbf caaaaaac dbbbbbbd aaaaaaaf fbbbbbbg faaaaaae bbbbbbg eaaaaaac gbbbbbbfaaaaaaa dbbbbbbcaaaaaae fbbbbbbeaaaaaaf bbbbbbaaaaaaa gbbbbaaaaaaac dbbbbaaaaaaaf dbbbbaaaaaae bbbaaaaaaac bbbaaaaaaaf gbbaaaaaae dbaaaaaaac fbaaaaaaa baaaaaae aaaaaaac faaaaaaad eaaaaaaad caaaaaaabg caaaaaaaabb faaaaaaaabbbf faaaaaaaaabbbd faaaaaaaaabbbbg eaaaaaaaabbbbbb eaaaaaaaagbbbbbbf eaaaaaaaafdbbbbbbd caaaaaaaaf fbbbbbbg caaaaaaaac bbbbbbb caaaaaaaac gbbbbbbf faaaaaaaae dbbbbbbd faaaaaaaae fbbbbbbg faaaaaaaae bbbbbbb eaaaaaaaaf gbbbbbb eaaaaaaaaf dbbbbbbd eaaaaaaaaf fbbbbbbd caaaaaaaac bbbbbbg caaaaaaaac gbbbbbb faaaaaaaac dbbbbbbf faaaaaaaae fbbbbbbd aaaaaaaae bbbbbbg aaaaaaae gbbbbbb aaaaaaaf gbbbbbbf aaaaaaf dbbbbbbd aaaaaf fbbbbbbg aaaac bbbbbbb aaac gbbbbbbf aae dbbbbbbd ae fbbbbbbg e bbbbbbg f gbbbbbb dbbbbbbf fbbbbbbd ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area B. Answer: A: 1; B: 1; 1 + 1 = 2 There are precisely two intersections present in the image.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#504091ff b,#c220c3ff c,#bbb5d4ff d,#db7cdbff e,#7460a6ff f,#e4cbebff g,#968bbcff ``` ```image gggf aaaf aaaf aaaf aaaf aaaf aaac aaac aaac aaac aaac aaac aaac aaac dbbf aaac dbbbbb aaag dbbbbbbb aaag dbbbbbbbbb aaag fbbbbbbb bbbd aaag fbbbbbbb dbbb aaag fbbbbbbb fbbb aaag fbbbbbbb bbb aaag fbbbbbbb bbbd aaag bbbbbbbf bbbb aaag bbbbbbbf dbbb aaag bbbbbbbf bbb aaae bbbbbbbf bbbf aaae bbbbbbbf bbbb eac eaae bbbbbbbd dbbb aaag eaae dbbbbbbd bbb faaa eaae dbbbbbbd bbbf eaaa eaae dbbbbbbd bbbd aaac eaae dbbbbbbd dbbb caaa eaae dbbbbbbd fbbb aaaa eaae dbbbbbbb bbb aaaf eaae fbbbbbbb bbbd gaaa eaaa fbbbbbbb bbbb aaae gaaa fbbbbbbb fbbb aaa gaaa fbbbbbbb bbb eaaa gaaa bbbbbbbf bbbd aaag gaaa bbbbbbbf bbbb faaa gaaa bbbbbbbf dbbb aaaa gaaa bbbbbbbf bbb aaac gaaa bbbbbbbf bbbgaaa gaaa bbbbbbbd bbbaaaa gaaabbbbbbd dbbaaaf gaaabbbbd beaaa feaaabbd baaae eaaad baaa gaaa eaaa caaa aaae caaa aaaab caaa aaaaabd caaa eaaaabbb caaa gaaaafbbb caaa caaaa bbb caaa faaaa bbbf faaa aaaa bbbb faaa aaaaf dbbb faaa aaaac bbb faaa aaaag bbbf faaa aaaae bbbd faaa eaaaa dbbb faaa gaaaa fbbb faaa caaaa bbbf aaa faaaa bbbd aaa aaaa dbbb aaa aaaaf fbbb aaa aaaac bbb aaa aaaag bbbd aaa eaaae bbbb aaa gaaaa fbbb aaa caaaa bbb aaa faaaa bbbf aaacf aaaa bbbb aaaaaaaaaegc aaaaf dbbb aaaaaaaaaaaaaaaaaegc aaaac bbb eaaaaaaaaaaaaaaaaaaaaaaaegf aaaag bbbf cgeaaaaaaaaaaaaaaaaaaaaaaaecf aaaae bbbd cgeaaaaaaaaaaaaaaaaaaaaaaagcfeaaaa dbbb fcgaaaaaaaaaaaaaaaaaaaaaaa fbbb fceaaaaaaaaaaaaaa bbb fgeaaaaa bbbd f ``` <!-- end of image -->
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Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#4edee8ff b,#58f8b0ff c,#b7f2f3ff d,#24f899ff e,#b0d7b1ff f,#7de5e4ff g,#93cd98ff ``` ```image eeeeeeeeeeeeeeeeg eeeeeeeeeeeeeeeeg eeeeeeeeeeeeeeeeg eeefeeeeeeeeeeeeg eeeaeeeeeeeeeeeeg eeeafeeeeeeeeeeeg eeefaeeeeeeeeeeeg eeeeaeeeeeeeeeeeg eeegaeeeeeeeeeeeg eeedddeeeeeeeeeeg eeeeadddbeeeeeeeg eeeeafegdddgeeeeg eeeefaeeeebdddeeg eeeefaeeeeeeedddb eeeeeaeeeeeeeeegdddc eeeeeaeeeeeeeeeeg bddb eeeeeaeeeeeeeeeeg dddf eeeeeafeeeeeeeeeg cdddc eeeeeaaeeeeeeeeeg bddb eeeeefaeeeeeeeeeg cdddf eeeeeeaeeeeeeeeeg fdddc eeeeeeaeeeeeeeeeg bddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb a cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbd ac bd ff dc ca fd a geeeedbeeeeeeeeee a eeeeegdeeeeeeeeee a eeeeeedbeeeeeeeee ac eeeeeegdeeeeeeeee af eeeeeeeddeeeeeeee fa eeeeeeeedeeeeeeee ca eeeeeeeeddeeaeeee a eeeeeeeeedeeaeeee a eeeeeeeeebdeaeeee ac eeeeeeeeeedbaeeee af eeeeeeeeeebdfeeee fa eeeeeeeeeeedbeeee ca eeeeeeeeeeeadeeee a eeeeeeeeeeeadeeee a eeeeeeeeeeeaeeeee a eeeeeeeeeefaeeeee ac eeeeeeeeeeafeeeee ff eeeeeeeeeeaeeeeee ca eeeeeeeeeeaeeeeee a eeeeeeeeeeaeeeeee a eeeeeeeeeeaeeeeee a eeeeeeeeefaeeeeee ac eeeeeeeeeafeeeeee ff eeeeeeeeeaeeeeeee ca gggggggggaggggggg a a a ca a fa ac ac af a ca a ca a a ca aac ff caaac ac faaf a aaac a caaac a faaf ca aaac ff caaac ac faaf a aaac a caaac a faaf ca aaac ff caaac ac faaf a aaac a caaac a faaf ca aaac af caaac ac faaf a aaac a caaaca faa ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4edee8ff b,#55f9b1ff c,#b3f3eeff d,#23f899ff e,#d9f9f5ff f,#85e8efff g,#8efbcaff ``` ```image ecf caae eaae aac aaf faf faa caa eaae eaac gaaf eddda gdddddge cbdddddbg caabdddddbc eaacegddddddge aac cbdddddbc aaf gbdddddge faa egdddddbge caa cbdddddbc caae egbdddd eaac egdd aac c aaf faf faa caae eaae aac aaf faf faa caae eaae eaac aaf ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Okay, let's proceed to the next area. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#4edee8ff b,#4af7aeff c,#abf2ecff d,#22f899ff e,#d6f9f4ff f,#7fe7edff g,#85fac8ff ``` ```image gddc ddb gddg bdd cddg bdde eddg bdde eddb gdde eddb gddc ddb gddc ee bdd caa cddg faa bdd faf cddg aac bddeeaac eddgeaae gddfaa eddbaa gddaf edddc gddg cddd cbddg faddd aaadbe aace eaae caae caa faf aaf aac eaae caae caa faf aaf aac eaae caa faa faf aaf eaac eaae caa ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area B. Answer: A: 1; B: 1; 1 + 1 = 2 After a long analysis, I found two intersections.
2
<!-- image --> ```palette Key,Color ,#fefefeff a,#4edee8ff b,#56f9b0ff c,#abf0f0ff d,#23f999ff e,#d7f8f6ff f,#7ee7eeff g,#83fac7ff ``` ```image c ae af fa ea ca ddde abddg ac cdddc fa gddbe ca ebddg a cdddc a gddb ae edddg ac cddde ff bddb ca edddg ea gddde a bddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbg a ebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbde ac bd ff de ca gd ea dg a cd a dg ae ed af db ca d ea dd a a d a a bdea ae dfa ac gdf fa dg ea ad a ade a ea ae ca ac af ff ae ca a a a a ea ae fa ac af ff ae ca a ea a a ea a fa ac ac af ae ca a ea a a ca aac ff caaae ac faaf ae eaaac a caaae a faaf ca eaaac ff caaae ac faaf a eaaac a caaae ea faaf ca eaaac ff caaae ac faaf a eaaac a caaae ea faaf ca eaaac af caaae ae faaf a eaaac a caaaca faa ``` <!-- end of image -->
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