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oliveirabruno01
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intersection-count-pixmap-CoT

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Time to put on my detective hat and find those intersection points! These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#aa7160ff b,#de38dfff c,#952d1dff d,#d09bc3ff e,#b1d7b1ff f,#9ac595ff g,#f0f0eeff ``` ```image cg acc ccc accc ccgca ccg cc gcc cc ccg acg gcc gca ccg cc gcc cc cc dcd dca cc cc cc dca acg cc gca aca cc cc cc d acd acg dcc cc gca cca acd efffccfffffffffffffffff ccd cc feeecceeeeeeeeeeeeeeeee ccg ccd feeeacaeeeeeeeeeeeeeeee gcc cc feeeecceeeeeeeeeeeeeeee dcc ccg feeeecceeeeeeeeeeeeeeee aca gcc feeeeaceeeeeeeeeeeeeeee cca ccg feeeefcaeeeeeeeeeeeeeee ccg gcc feeeeecceeeeeeeeeeeeeee gcc cc feeeeecceeeeeeeeeeeeeee dcc dcc feeeeeacfeeeeeeeeeeeeee acc cc feeeeeecceeeeeeeeeeeeee cca dca feeeeeecceeeeeeeeeeeeee ccd cc feeeeeecceeeeeeeeeeeeee ccg dca feeeeeefcaeeeeeeeeeeeee d gcc cc feeeeeeecceeeeeeeedeeee gbbffffffffffaccffffffffffffffffffffffg aca feeeeeeecceeeeeeedbbeee bbbeeeeeeeeeeacceeeeeeeeeeeeeeeeeeeeeg cc feeeeeeeaceeeeeeebbeeee gbbbeeeeeeeeeeccaeeeeeeeeeeeeeeeeeeeeg acd feeeeeeefcaeeeeebbdeeee gedbbeeeeeeeeeeccfeeeeeeeeeeeeeeeeeeeg cc feeeeeeeecceeeedbbeeeee geedbbeeeeeeeeeecceeeeeeeeeeeeeeeeeeeg acd feeeeeeeecceeeebbeeeeee geeedbbdeeeeeeeefcceeeeeeeeeeeeeeeeeeg cc feeeeeeeeacfeebbdeeeeee geeeeebbdeeeeeeeeacceeeeeeeeeeeeeeeeegccg feeeeeeeeeccedbbeeeeeee geeeeeebbdeeeeeeeeccceeeeeeeeeeeeeeeegcc feeeeeeeeeccebbeeeeeeee geeeeeeebbbeeeeeeeeccaeeeeeeeeeeeeeeeccg feeeeeeeeeccbbeeeeeeeee geeeeeeeebbbeeeeeeeeccfeeeeeeeeeeeeefcc feeeeeeeeefcadeeeeeeeee geeeeeeeeebbbeeeeeeeecceeeeeeeeeeeeeccg feeeeeeeeedcceeeeeeeeee geeeeeeeeeebbbeeeeeeefcceeeeeeeeeeefcc feeeeeeeeebcceeeeeeeeee geeeeeeeeeeebbbeeeeeeeacceeeeeeeeeeccg feeeeeeeebbacfeeeeeeeee geeeeeeeeeeeedbbeeeeeeeccaeeeeeeeefccg feeeeeeedbbecaeeeeeeeee geeeeeeeeeeeeedbbeeeeeeeccaeeeeeeecceg feeeeeeebbeecceeeeeeeee geeeeeeeeeeeeeedbbdeeeeeeccfeeeeeacaeg feeeeeebbdeecceeeeeeeee geeeeeeeeeeeeeeeebbdeeeeefcceeeeecceeg feeeeedbbeeeacfeeeeeeee geeeeeeeeeeeeeeeeebbbeeeeeacceeeacaeeg feeeeebbeeeeecceeeeeeee geeeeeeeeeeeeeeeeeebbbeeeeeacceecceeeg feeeebbeeeeeecceeeeeeee geeeeeeeeeeeeeeeeeeebbbeeeeeccaacaeeeg feeebbbeeeeeecceeeeeeee geeeeeeeeeeeeeeeeeeeebbbeeeeecccceeeeg feeebbeeeeeeefcaeeeeeee geeeeeeeeeeeeeeeeeeeeebbbeeeeeccfeeeeg feebbeeeeeeeeecceeeeeee geeeeeeeeeeeeeeeeeeeeeedbbeeeefaeeeeeg febbdeeeeeeeeecceeeeeee geeeeeeeeeeeeeeeeeeeeeeedbbeeeeeeeeeeg fdbbeeeeeeeeeeacfeeeeee geeeeeeeeeeeeeeeeeeeeeeeedbbdeeeeeeeeg fbbeeeeeeeeeeeecaeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeebbdeeeeeeeg bbdeeeeeeeeeeeecceeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeebbdeeeeeeg dbbeeeeeeeeeeeeecceeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeg bbeeeeeeeeeeeeeeacaeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeg bbfeeeeeeeeeeeeeeecceeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeg bbbfeeeeeeeeeeeeeeecceeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeg gbb feeeeeeeeeeeeeeecceeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeg bb feeeeeeeeeeeeeeefcaeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbg bbd feeeeeeeeeeeeeeeecceeee gfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbg gbb feeeeeeeeeeeeeeeecceeee ggggggggggggggggggggggggggggggggggggbbg bb feeeeeeeeeeeeeeeeacfeee gbbd bbg feeeeeeeeeeeeeeeefcaeee bbd dbb ggggggggggggggggggggggg bbb bb bbb bbg bbb dbb bbb gbb bbb bbg dbb bbd gbbbb gbb g ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#b2655bff b,#df34e0ff c,#962c1dff d,#d1a39cff e,#e768e7ff f,#f0a3f0ff g,#f2d8e8ff ``` ```image bbg gccccd bbbg dccccd bbbbf dccccg bbbbbf accccg ebbbbf accca ebbbbe gcccca ebbbbe gccccd fbbbbe dccccd fbbbbe accccg fbbbbbg accccg fbbbbbg gcccca gbbbbbg gcccca gbbbbbf dccccd gebbbbf dccccg ebbbbf accccg ebbbbe accca ebbbbe gcccca fbbbbe gccccd fbbbbeg dccccd fbbbbbg dccccg g gbbbbbg accccg a gbbbbbf accca gc gbbbbbf gcccca ac ebbbbf gccccd gcc ebbbbf dccccd acc ebbbbe accccg dccc ebbbbe accccg accc fbbbbe gcccca dccca fbbbbbg gcccca ccccg fbbbbbg dccccd dccca gbbbbbg dccccg ccccg gbbbbbf accccg dccca gbbbbbf accca ccccg ebbbbf gcccca dccca ebbbbe gccccd gccccg ebbbbe dccccd dcccd ebbbbe dccccg gccccg fbbbbe accccg acccd fbbbbbg accca gcccc fbbbbbg gcccca acccd gbbbbbg gccccacccc gbbbbbf dcccccccd gebbbbf accccca ebbbbf accccd ebbbbe gccca ebbbbe gaag fbbbbe fbbbbeg fbbbbbg gbbbbbg gbbbbbg gbbbbbf gebbbbf ebbbbf ebbbbe ebbbbe fbbbbe fbbbbeg fbbbbbg gbbbbbg gbbbbbf gbbbbbf ebbbbf ebbbbe ebbbbe ebbbb fbbb fbb ``` <!-- end of image --> No intersection found in area A, but I won't give up. Alright, let's examine the next area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#a94f4aff b,#df35e0ff c,#952a1bff d,#d8b1acff e,#ea80ebff f,#bf8077ff g,#f1d2e8ff ``` ```image accc dcccd gcccf ccca fcccg dcccd gcccf accc fcccg dcccf ccca accc dcccd gcccf acca fcccg dcccd ccca accc fcccd dcccf ccca fcccg dcccd gcccf acca fcccg dcccd ccca accc e fcccd ebbg gcccf gbbbb ccca bbbbe fcccg ebbbe dcccd gbbbbg gcccf bbbbg accc ebbbe fcccg ebbbb dcccd gbbbbg ccca bbbbe accc ebbbb fcccd gbbbbg gcccf bbbbe ccca ebbbe fcccg gbbbbg dcccd bbbbg gcccfebbbe acccbbbb fcccbbbg dcccabe cccab gacccg bacccd ebbcccf gbbbccca bbbbacccg ebbbedcccd gbbbb gcccf gbbbbg accc ebbbe fcccg ebbbb dcccf gbbbbg ccca bbbbe accc ebbbb dcccd gbbbbg gcccf bbbbe ccca ebbbe fcccg gbbbb dcccd bbbbg gcccf ebbbe accc ebbbb fcccg gbbbbg dcccf bbbbe ccca ebbbb accc gbbbbg dcccd bbbbe gcccf ebbbe acca gbbbbg fcccg bbbbg dcccd ebbbe ccca ebbbb accc gbbbbg fcccd bbbbe gcccf bbbb ccca bbbg fcccg bbe dcccd bb gcccf bg acca e fcccg dcccd ccca accc fcccd gcccf ccca fcccg dcccd gcccf accc fcccg dcccd ``` <!-- end of image --> Area B contains 1 intersection. Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#ab544cff b,#df36e0ff c,#952b1cff d,#d9b4afff e,#eb85ecff f,#c08279ff g,#f2d4e8ff ``` ```image cg fcc ccc accc ccgcf acg cc cc cc ccg fcg gcc ca cc cc gcc cc cc dcd dca cc cc cc dca ac cc gcf fcf cc cc cc d fcf fcg dcc cc ca ccf acd cc ccd cc cc cc acd dcd gcc cc cc fcc ccg cc aca gcc ac ccf ccg gcf ccg gcc cc cc cc cc dcc dca fcd fcc cc ca aca dca cc ccd cc ac ccg fcf dcd g gcc cc cc e gbb dcc fcf cc gbb bbb acc cc fcg bb ebb ccf acd gcf bbg ebb ccd cc cc ebb ebbg ccg acd cc bb gbbg gcc cc fcd bbg gbbe fcc ccg ca ebb bbe aca cc cc bb bbb ccf ccg acbb bbb ccg gcc dcae bbb cc cc gcc bbb dcc gca bcc ebb fcc cc bbacg ebb aca dca ebbgcf gbbg ccd cc bb cc gbbg ccg dcf bbg cc bbe gcc cc ebb dcd bbe dcc fcf bb ca bbb acc cc bbg cc bbb ccffcd ebe ac bbb cccc gbb dcf bbb ccd bb cc ebb gf bbe cc ebb gbb fcg gbbg bb gca gbbg bbg cc bbe ebb cc bbe bb dcd bbb bbg cc bbb ebe cc bbb gbb ac ebb bb gcf ebb bbe cc ebbg gbb cc gbbg bb fcg gbbe bbg ca bbe ebb bbe bb bbb bbg bbb ebb bbb bb ebb bb ebb bbe gbbbb gbb ``` <!-- 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,#0c1d11ff b,#202eb3ff c,#6371c3ff d,#b0d6b0ff e,#4e5e51ff f,#e8eeeeff g,#919eb9ff ``` ```image fc bbbg bbb cbbb bbbf fbbb bbbg bbb cbbb bbbf fbbb bbbg bbb cbbb bbbf fbbb f bbbg dae bbb faaae cbbb eaaae bbbf eaaae fbbb eaaae bbbg eaaae bbb eaaae cbbb eaaae bbbf eaaae fbbb eaaae ffffffffffffffffbbbgfff aaaag fddddddddddddddddbbbddddf aaaag fdddddddddddddddcbbbddddf aaaag fdddddddddddddddbbbdddddf aaaag fddddddddddddddgbbbdddddf aaaag fddddddddddddddbbbcdddddf aaaag fddddddddddddddbbbddddddf aaaad fdddddddddddddcbbbddddddf aaaad fdddddddddddddbbbdddddddf gaa aaaad fddddddddddddgbbbdddddddfeaaaa aaaad fddddddddddddbbbcddddddaaaaaaag aaaad fddddddddddddbbbddddgaaaaaaad aaaaf fdddddddddddcbbbddeaaaaaaaf aaaaf fdddddddddddbbbdeaaaaaaef aaaaf fddddddddddgbbbaaaaaaeddf aaaaf fddddddddddbbbaaaaagddddf aaaaf fddddddddeabbbaaadddddddf aaaaf fddddddeaabbbbedddddddddf aaaaf fddddaaaaabbbdddddddddddf aaaaf fdgaaaaaaabbbdddddddddddf aaaaf gaaaaaaadbbbcdddddddddddf aaaa eaaaaaaedddbbbddddddddddddf aaaa faaaaaaaeddddcbbbddddddddddddf faaaa daaaaaaagddddddbbbdddddddddddddf faaaa gaaaaaaaffddddddgbbbdddddddddddddf faaaa eaaaaaae fddddddbbbcdddddddddddddf faaaa faaaaaaag fddddddbbbddddddddddddddf faaaaaaaaaad fdddddcbbbddddddddddddddf faaaaaaaf fdddddbbbdddddddddddddddf faaae fddddgbbbdddddddddddddddf d fddddbbbcdddddddddddddddf fddddbbbddddddddddddddddf fdddcbbbddddddddddddddddf fffbbbfffffffffffffffff fbbb bbbg bbb cbbb dc bbbf bbbbcf fbbb bbbbbbbbd bbbg fcbbbbbbbbbg bbb cbbbbbbbbbcf cbbb gbbbbbbbbbbf bbbf fcbbbbbbbbbg fbbb fcbbbbbbbbbcf bbbg gbbbbbbbbbcf bbb fbbbbbbbbbbg cbbb fcbbbbbbbbbc bbbf gbbbbbbbbbcf fbbb dbbbbbbbbbbg bbbg fcbbbbbbbbbg bbb gbbbbbbbbbccbbb gbbbbbbbbbbf fcbbbbbb cbbf ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0c1d11ff b,#202db2ff c,#5b66c6ff d,#c9cce0ff e,#3d4a4aff f,#9ba2ceff g,#7e8781ff ``` ```image fbbbbbb cbbbbbc dbbbbbbd cbbbbbb bbbbbbf fbbbbbb cbbbbbc dbbbbbbd cbbbbbb bbbbbbf fbbbbbb cbbbbbc dbbbbbbd cbbbbbb bbbbbbf fbbbbbb cbbbbbc dbbbbbbd cbbbbbb bbbbbbf ge fbbbbbb dgaaa cbbbbbc deaaaaa dbbbbbbd feaaaaaaa cbbbbbb geaaaaaaaaa bbbbbbf dgaaaaaaaaaaaa fbbbbbb deaaaaaaaaaaaaae cbbbbbceaaaaaaaaaaaaagd dbbbbbbaaaaaaaaaaaaagd cbbbbbbaaaaaaaaaaeg bbbbbbeaaaaaaaaef febbbbbbaaaaaaagd gaabbbbbbbaaaaagd dgaaaabbbbbbaaaeg deaaaaabbbbbbbaef feaaaaaaabbbbbbbd gaaaaaaaaaebbbbbb dgaaaaaaaaaaabbbbbbc deaaaaaaaaaaaaabbbbbbd feaaaaaaaaaaaaagcbbbbbb gaaaaaaaaaaaaaag bbbbbbf aaaaaaaaaaaaef fbbbbbb aaaaaaaaaaed cbbbbbc aaaaaaaagd dbbbbbbd aaaaaag cbbbbbb aaaef bbbbbbf aed fbbbbbb d cbbbbbc dbbbbbbd cbbbbbb bbbbbbf fbbbbbb cbbbbbc dbbbbbbd cbbbbbb bbbbbbf fbbbbbb cbbbbbc dbbbbbbd cbbbbbb bbbbbbf fbbbbbb cbbbbbc dbbbbbbd cbbbbbb ``` <!-- end of image --> 1 intersection present within area A. Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#0c1d11ff b,#202eb3ff c,#7a82d1ff d,#c1c5dbff e,#4c5950ff f,#e6e8efff g,#8c948fff ``` ```image dc bbbc bbb cbbb bbbf dbbb bbbc bbb cbbb bbbf dbbb bbbc bbb cbbb bbbf dbbb d bbbc dae bbb faaae cbbb eaaae bbbf eaaae dbbb eaaae bbbc eaaae bbb eaaae cbbb eaaae bbbf eaaag dbbb eaaag bbbc aaaag bbb aaaag cbbb aaaag bbbf aaaag dbbb aaaag bbbc aaaag bbb aaaad cbbb aaaad bbbf gaa aaaad dbbb eaaaa aaaad bbbc faaaaaaag aaaad bbb daaaaaaad aaaad cbbb gaaaaaaaf aaaad bbbfeaaaaaae aaaaf dbbbaaaaaag aaaaf bbbaaaaad aaaaf gabbbaaaf aaaaf eaabbbbe aaaaf faaaaabbbf aaaaf daaaaaaabbb aaaaf gaaaaaaafbbbc aaaa eaaaaaae bbb aaaa faaaaaaag cbbb faaaa daaaaaaad bbbf faaaa gaaaaaaaf dbbb faaaa eaaaaaae bbbc faaaa faaaaaaag bbb faaaaaaaaaad cbbb faaaaaaaf bbbf faaae dbbb d bbbc bbb cbbb bbbf dbbb bbbc bbb cbbb dc bbbf bbbbcf dbbb bbbbbbbbd bbbc fcbbbbbbbbbc bbb cbbbbbbbbbcf cbbb dbbbbbbbbbbd bbbf dbbbbbbbbbbc dbbb fcbbbbbbbbbcf bbbc cbbbbbbbbbbd bbb dbbbbbbbbbbd cbbb fcbbbbbbbbbc bbbf cbbbbbbbbbcf dbbb dbbbbbbbbbbd bbbc fcbbbbbbbbbc bbb cbbbbbbbbbccbbb dbbbbbbbbbbf fbbbbbbb cbbd ``` <!-- 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,#a92a5bff b,#be5c93ff c,#ca91abff d,#a00643ff e,#ebcddcff f,#b1d7b1ff g,#96c896ff ``` ```image cdde addd dddda dddddc dddddde ebe eddbaddd bbb bddc ddda bbb ddd dddc cbbc ddd cddd bbb ddd addd ebbb ddd ddda bbbe cddb dddc bbb bdde cddd cbbc ddd addd bbb ddd ddda ebbb ddd dddc bbbe edda cddd bbb cddc addd cbbc adde ddda bbb ddd dddc ebbb ddd cddd bbbe ddd addd bbb edda ddda cbbc bddc edddc bbb ddd cddd ebbb ddd addd bbbe ddd ddda bbb ddd edddc cbbc cddb bddd bbb bdde dddd bbb ddd ddda bbbe ddd eddde bbb ddd bddd ebbb ddd dddd fgggggggggggggggggbbbggg ddd ddda gfffffffffffffffffbbbfff ddd eddde gffffffffffffffffbbbcfff ddd bddd gffffffffffffffffbbbffff ddd dddd gfffffffffffffffcbbbffff ddd dddb gfffffffffffffffbbbfffff dda eddde gfffffffffffffffbbbfffff ffgddafffffg bddd gffffffffffffffbbbcfffff ffgddafffffg dddd gffffffffffffffbbbffffff ffcddafffffg dddb gfffffffffffffcbbbffffff ffcddbfffffg edddc gfffffffffffffbbbfffffff ffcddbfffffg bdddda gfffffffffffffbbbfffffff ffbddbfffffg dddddddc gffffffffffffcbbcfffffff ffbddbfffffg eadddddda gffffffffffffbbbffffffff ffbddcfffffg cdddddddbfffffffffffbbbffffffff ffaddcfffffg eaddddddaffffffffbbbfffffffff ffaddgfffffg cdddddddbfffffbbbfffffffff ffaddgfffffg gaddddddaffcbbcfffffffff ffaddffffffg gffbdddddddbbbffffffffff ffdddffffffg gfffffadddabbbffffffffff ffdddffffffg gfffffffbdbbbaddbfffffff ffdddffffffg gfffffffffbbbdddddafffff ffdddffffffg gffffffffcbbbbdddddddbff fffffffffffg gffffffffbbbffffaddddddae fffffffffffg gffffffffbbbffffffbdddddddc fffffffffffg gfffffffbbbcfffffffffadddddda fffffffffffg gfffffffbbbffffffffffffbdddddddc fffffffffffg gffffffcbbbfffffffffffff eaddddde fffffffffffg gffffffbbbffffffffffffff cddd fffffffffffg gffffffbbbffffffffffffff ec ffcbcffffffg gfffffbbbcffffffffffffff ffbbbbbbfffg gfffffbbbfffffffffffffff ffbbbbbbbbbc gffffcbbbfffffffffffffff ffffcbbbbbbbbbc gffffbbbffffffffffffffff ebbbbbbbbbbe gffffbbbffffffffffffffff cbbbbbbbbbc gfffbbbcffffffffffffffff ebbbbbbbbbce gfffbbbfffffffffffffffff ebbbbbbbbbbe gffcbbbfffffffffffffffff cbbbbbbbbbc gffbbbffffffffffffffffff ebbbbbbbbbce gffbbbffffffffffffffffff ecbbbbbbbbbe fgbbbcgggggggggggggggggg cbbbbbbbbbc bbb ebbbbbbbbbbe ebbb cbbbbbbbbbc bbbe ebbbbbbbbbcebbb ecbbbbbbbbbc cbbbbbb ebbc ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#ad295dff b,#c05c94ff c,#d490b0ff d,#a00643ff e,#f4e3ebff f,#b94976ff g,#e5bccfff ``` ```image ddddda eddddda eddddda edddddf edddddf gdddddf gdddddf gdddddb gdddddb gdddddb cdddddb cdddddc cdddddc cdddddc cdddddc bdddddc bdddddg bdddddg bdddddg fdddddg fdddddg fddddde fddddde addddde addddde addddd addddd dddddd ddddda ddddda ddddda eddddda eddddda eaaaadf ege gbbbce cbbbbbbcge bbbbbbbbbbcge gbbbbbbbbbbbbbbcg cbbbbbbbbbbbbbbbbbc egcbbbbbbbbbbbbbbbb ``` <!-- end of image --> It's a shame, but area A doesn't contain an intersection. I'm ready to analyze the next area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#ac275eff b,#bf5a94ff c,#d79bbeff d,#a00643ff e,#f3e1ebff f,#cd7ea8ff g,#e4bbd0ff ``` ```image fbbbbbg ebbbbbbe cbbbbbc bbbbbbe gbbbbbf fbbbbbg ebbbbbbe cbbbbbf bbbbbbg gbbbbbb fbbbbbc ebbbbbbe cbbbbbf bbbbbbg gbbbbbb fbbbbbc ebbbbbbe cbbbbbf bbbbbbg gbbbbbb fbbbbbc ebbbbbbe cbbbbbf bbbbbbg gbbbbbb fbbbbbc ebbbbbbe gbbbbbf g fbbbbbg dafe ebbbbbb ddddbg cbbbbbc ddddddafe ebbbbbbe dddddddddbg gbbbbbf dddddddddddafe fbbbbbg ddddddddddddddbg ebbbbbbe efadddddddddddddafe cbbbbbf gbddddddddddddddbg bbbbbbg efadddddddddddddabbbbbb gbdddddddddddbbbbbbc efadddddddabbbbbbfe gbdddddabbbbbbddbg efaddbbbbbbaddddafe gbbbbbbbddddddddbg fbbbbbaddddddddddafe ebbbbbbddddddddddddddbg cbbbbbfefadddddddddddddafe bbbbbbg gbddddddddddddddbg gbbbbbb efaddddddddddddd fbbbbbc gbddddddddddd ebbbbbbe efadddddddd cbbbbbf gbdddddd bbbbbbg efaddd gbbbbbb gbd fbbbbbc e ebbbbbbe cbbbbbf bbbbbbg gbbbbbb fbbbbbc ebbbbbbe gbbbbbf fbbbbbg ebbbbbbe cbbbbbc ebbbbbbe gbbbbbf fbbbbbg ebbbbbbe cbbbbbf bbbbbbg gbbbbbb fbbbbbc ebbbbbbe cbbbbbf bbbbbbg gbbbbbb fbbbbbc ebbbbbbe cbbbbbf bbbbbbg gbbbbbb ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 0; B: 1; 0 + 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#ad295dff b,#bf5a94ff c,#d99ebcff d,#a00643ff e,#f4e3ebff f,#ce82a7ff g,#e5bed3ff ``` ```image e cdde addd dddda dddddf dddddde gbg gddbaddd bbbe bddc ddda bbb ddd dddf fbbc ddd cddde bbb ddd addd gbbb ddd ddda bbbe cddb edddf bbb bddg cddde fbbc ddd addd bbb ddd ddda gbbb ddd edddc bbbe edda fddde bbb fddf addd cbbc adde ddda bbb ddd edddc ebbb ddd fddd bbbg ddd addd bbb gdda ddda cbbf bddc edddc bbb ddd fddd ebbb ddd addd bbbg ddd ddda bbb ddd edddc cbbf cddb fddd bbb bddg dddd ebbb ddd ddda bbbg ddd edddg bbb ddd bddd gbbf ddd dddd bbbe ddd ddda bbb ddd edddg fbbc ddd bddd bbb ddd dddd gbbb ddd dddb bbbe dda edddg bbb edda bddd fbbc edda dddd bbb gddb dddb gbbb gddb gdddf bbbe cddf bddddae bbb fddf dddddddf fbbc fddc eaddddddae bbb bddc fdddddddf gbbb bddg eaddddddae bbbe bddg fdddddddf bbb adde eaddddddae cbbf adde fdddddddbbb add eadddabbbe ddd fdbbbaddf ddd bbbdddddae ddd cbbffdddddddf bbb eaddddddae ebbb fdddddddf bbbg eaddddddae bbb fdddddddf cbbf eaddddde bbb fddd ebbb ec gbc fbbg bbbbbfe bbb bbbbbbbbbg gbbb cbbbbbbbbbc bbbe gbbbbbbbbbbg bbb efbbbbbbbbbc fbbc cbbbbbbbbbfe bbb efbbbbbbbbbg gbbb cbbbbbbbbbc bbbe gbbbbbbbbbfe bbb efbbbbbbbbbg fbbc cbbbbbbbbbfe bbb gbbbbbbbbbbg gbbb ecbbbbbbbbbc bbbe gbbbbbbbbbfebbb efbbbbbbbbbc cbbbbbb gbbf ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#77ac69ff b,#9e7bbcff c,#ccb5ddff d,#b2d7b2ff e,#ecf2ecff f,#7b3fa9ff g,#a4cda2ff ``` ```image bff fff ffb ffc ffe eff cff bff fff ffb ffc ffe eff cff bff ad fff gaaag ffb eaaaaaae ffc gaaaaag ff daaaaaae cff eaaaaaad bff gaaaaag fff eaaaaaae fff aaaaaag ffb daaaaaae ffc eaaaaaad eff gaaaaag cff eaaaaaae bff aaaaaag fff daaaaaae eedd ffb eaaaaaaaaaaaaaaaaaad ffc gaaaaaaaaaaaaaaag ffe daaaggddeeeeaaaeeeeeeeeeeee eff eggggggggaaagggggggggggge cff egdddddddgaadddddddddddge bff e egdddddddgaadddddddddddge fff cffffc egddddddddaadddddddddddge ffb fffffffffbc egddddddddaagddddddddddge ffc cbffffffffffbe egddddddddaagddddddddddge ffe ecfffffffffffc egddddddddaaaddddddddddge cff cbffffffffffbc egddddddddaaaddddddddddge bff cbffffffffffbe egddddddddaaaddddddddddge fff ebffffffffffbc egddddddddgaaddddddddddge fff cbffffffffffbcegddddddddgaadgbfffffbdge ffb cfffffffffffbddddddbffffffffffffffbe ffc ebffffffffffffffffffffbgbfffffffffbc ff cffffffffffffbdddddddddbffffffffffff egdddbffbgdaaadddddddddge cffffffff egdddddddddaaadddddddddge cbffb egdddddddddaaadddddddddge egdddddddddgaadddddddddge egdddddddddgaadddddddddge egddddddddddaadddddddddge egddddddddddaagddddddddge egddddddddddaagddddddddge egddddddddddaaaddddddddge egddddddddddaaaddddddddge egggggggggggaaaggggggggge eeeeeeeeeeegaaeeeeeeeee daa eaa aa aae aad aag aaa aaa gaa daa eaaaad aaaaaaae daaaaaag gaaaaaad eaaaaaaae daaaaaag gaaaaaad eaaaaaaae daaaaaag gaaaaaad eaaaaa dag ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#76ac69ff b,#9f76beff c,#c6addaff d,#c0d8baff e,#e3e5e5ff f,#7b3fa9ff g,#9dc393ff ``` ```image aaaaae gaaaae gaaaad daaaad daaaag eaaaag eaaaaa aaaaa aaaaae gaaaae gaaaad daaaad daaaag eaaaag eaaaaa aaaaa aaaaae gaaaae gaaaad daaaad daaaag eccbbbce eaaaag ecbffffffffffbce bbce eaaaabbffffffffffffffffffb fffffbcc ecfffffffffffffffffffffffff ffffffffffbce ccbffffffffffffffffffffffffffff fffffffffffffffffffffffffffffffffbbcecbfffffff fffffffffffffffffffffffffffffbce ecbfff ccbfffffffffffffffffffffffbe ec ecbbffffffffffffbbaaaag ecbfffbbce eaaaag eaaaaa aaaaa aaaaae gaaaae gaaaad daaaad daaaag eaaaag eaaaaa aaaaa aaaaae gaaaae gaaaad gaaaad daaaad daaaag eaaaag eaaaaa aaaaa aaaaae ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#76ac68ff b,#9a6dbdff c,#bda0d3ff d,#bfd8b9ff e,#e0e0e3ff f,#7b3ea9ff g,#9ac190ff ``` ```image bff fff ffb ffc ffe eff cff bff fff ffb ffc ffe eff cff bff ad fff gaaag ffb eaaaaaae ffc gaaaaag ff daaaaaae eff eaaaaaad cff gaaaaag fff eaaaaaae ffb gaaaaag ffc daaaaaa ffe eaaaaaad ff gaaaaag cff eaaaaaae bff gaaaaad fff daaaaaa eedd ffb eaaaaaaaaaaaaaaaaaad ffc gaaaaaaaaaaaaaaag ffe daaggddee aaa eff gaa cff daa bff e eaa fff cffffc aa ffb fffffffffbe aae ffc cbffffffffffce aad ff cffffffffffbc aag eff ebffffffffffbe aaa cff cbffffffffffce gaa bff ecffffffffffbc daa fff ebffffffffffbe eaa ebfffffc ffc cbffffffffffc cffffffffffffffbe ffe ecffffffffffffffffffffcebfffffffffbc ff ebfffffffffffc cffffffffffff cffce aag cbfffffff aaa ebffb gaa daa eaa aa aae aad aag aaa aaa gaa daa eaa aa aae aad aag aaa aaa gaa daa eaaaad gaaaaaae daaaaaag gaaaaaad egaaaaaae daaaaaag gaaaaaad eaaaaaaae daaaaaag gaaaaaad egaaaa dag ``` <!-- end of image -->
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I'm optimistic that I'll find some intersections in this image. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#90a8dcff b,#85e2c6ff c,#bcd1e9ff d,#95c996ff e,#e5eff3ff f,#b1d7b1ff g,#54debdff ``` ```image ae caa caa caa caac caaa aaaa aa aaaa aaa aacac caaae aa aa aaeaa aa aa aa aaa aa aa cac aae aa cac aa eaa aa aa eaa aaa aa aa aac aae aa aae aa eaa aa cac eaa aaa aa aa aae aae aa aa aa eaa aa aae cac aaa aa eaa aa aae aa aa aa eaa aa aa cac aaa aa aae aa aae eaa eaa eaa eaa eaa aa aae aac eac aa aa aaeeeeeeeeeeeeeeeeeeeeeeee eac cac caa dfaafffffffffffffffffffffffd cac eaa aa dfaaaffffffffffffffffffffffd cac aa aa dffaaffffffffffffffffffffffd cac aa cac dfffaafffffffffffffffffffffd cae cac aa dfffaaaffffffffffffffffffffd cae aa eaa dffffaaffffffffffffffffffffd aae aa aac dffffaaafffffffffffffffffffd aa aae aa dfffffaaaffffffffffffffffffd aa cac eaa dffffffaaffffffffffffffffffd aa aa aae dffffffaaafffffffbggfffffffd aa aa aa dfffffffaaafffffggggfffffffd aa aae cac dffffffffaafffggggggbffffffd aa cac aa dffffffffaaabgggbffggffffffd aa aa aa dfffffffffaggggffffggffffffd aa aa cac dffffffffggggffffffggbfffffd eaa aae aa dffffffggggaaaffffffggfffffd aae eaa eaa dffffbgggbffaaffffffggfffffd caa aa aae dfffggggfffffaafffffggfffffd aa aa aa dfggggfffffffaaaffffbggffffd aaa caaaa ggggffffffffffaafffffggffffd aa eaaae cgggbffffffffffffaaffffggffffd aac aaa eggggffffffffffffffaaafffbgbfffd caa aac gggg dfffffffffffffffaaffffggfffd aae ca bggge dffffffffffffffffaafffggfffd caa cgggb dffffffffffffffffaaaffbgbffd aa egggb dfffffffffffffffffaafffggffd aac gggg dffffffffffffffffffaaffffffd eaa bggge dffffffffffffffffffaaafffffd aae cgggb dfffffffffffffffffffaafffffd caa egggg dffffffffffffffffffffaaffffd aa gggg dffffffffffffffffffffaaafffd aac bggge dfffffffffffffffffffffaafffd eaa cgggb dffffffffffffffffffffffaaffd aae egggg dffffffffffffffffffffffffffd caa gggge dffffffffffffffffffffffffffd aa bgggc dffffffffffffffffffffffffffd aac cgggb dffffffffffffffffffffffffffd eaa egggg fddddddddddddddddddddddddddf aae gggge caa bgggc c cgggb egggg gggge bgggc egggb egggg gggge bgggc egggb gggg bggge bgggc cggb g ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#8fa7ddff b,#7de5cdff c,#c5d1edff d,#aeefdfff e,#e0f0f4ff f,#a5b9e3ff g,#53debdff ``` ```image faaaa eaaaaf caaaac faaaa eaaaaf caaaae faaaa eaaaaf caaaae faaaa eaaaac caaaae faaaa eaaaac caaaae faaaf eaaaac caaaae faaaf eaaaac dde caaaae ebggge faaaf ebgggggd eaaaac dgggggggg caaaae dgggggggggge faaaf ebggggggbbgggd eaaaac ebgggggggd dgggb caaaaedgggggggd gggge aaaagggggggbe bgggd eagggggggbe dgggb ebgggggggd egggg dgggggggb bgggd dggggggggaac dgggb ebggggggbfaaaae egggg ebgggggggd aaaaf gggge dgggggggd eaaaac dgggd dgggggggbe faaaae egggg ebggggggbe aaaaf gggge ebgggggggd caaaac bgggd dgggggggd faaaae dgggb dgggggggbe aaaaf gggge ebggggggbe caaaac bgggd gggggggd faaaa dgggb gggggd eaaaaf egggg gggbe caaaac bgggd gbe faaaa dgggb d eaaaaf egggg caaaae gggge faaaa dgggb eaaaaf egggg caaaae gggge faaaa bgggd eaaaac dgggb caaaae gggg faaaa dde eaaaac caaaae faaaf eaaaac caaaae faaaf eaaaac caaaae faaaf eaaaac caaaae faaaf eaaaae cafe c ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#8fa7ddff b,#7ce5cdff c,#c7d3edff d,#afefe0ff e,#e2edf5ff f,#a8bbe4ff g,#53debdff ``` ```image ae caa caa caa faac faaa faaa fa aaaa aaa aafac caaae aa aa aaeaa aa aa aa faa aa aa fac aae aa caf aa eaa aa aa eaa faa aa aa fac aae aa aae aa eaa aa caf eaa faf aa aa aae aae aa aa aa eaa aa fae caf aaf aa eaf aa aae aa aa aa eaa aa aa fac aaf aa fac aa aae eaf eaa eaa caa eaf aa aae aaf eaf aa aa aa caf fac caf caa cac eaa aa aaf cac aa aa aa cac aa fac caa fae cac aa aaf fae aa eaa aa fae aa fac caa aa aae aa aac aa caf eaa aa aa aa aae caa egg aa aa aa aac gggg aa aae caf aa bgggbgd aa caf aa caadgggd gg aa aa aa agggb gg aa aa fac gggg bgd eaa fae aa bgggfaa egg aae eaf eaa dgggd aac gg caa aa aae egggb aa gge aa aa aa gggg faa dgb faf fafaf bggge aac gg aa eaaa dgggd eaa gg aac aaa egggb faa dgb caa aaf gggg aae gg aae ca bggge eaa gg faf dgggd faa bgd aa egggb aae gg aac gggg eaa eaa bggge faa aae dgggd aae faa egggb eaa aa gggg faf aac bgggd aae eaa dgggb eaa aae egggg c caa gggge aa bgggd aaf dgggb eaa egggg aae gggge caa bgggd c dgggb egggg gggge bgggd dgggb gggg bggge dgggd egggb gggg bggge dgggd dggb g ``` <!-- 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 regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#bab1bfff b,#c45d93ff c,#ddc7d6ff d,#d390b3ff e,#b1d7b1ff f,#efedeeff g,#96c996ff ``` ```image bd cbbbbf cbdbbbbd cbc dbbbbc cbc cbbbbd cbc dbbbbc cbf fbbbbbf dbf dbbbbd dbf fbbbbbf fac dbf cbbbbd aa dbf dbbbbc cac db cbbbbd aa db dbbbbc aaf db fbbbbbf aa db dbbbbd aa db fbbbbbf fac bb cbbd aa bb cac bb aa bb aaf bb aa bb aa bb faa bb aa bb cac bb aa bb caf bb aa bb aa bb faa bb aa bb cac bb aa bb caf bb aa bb aa bb faa bb aa bb fac bb aa fffffffffffffffffffffbb caf fgeeeeeeeeeeeeeeeeeeeebbg aa feeeeeeeeeeeeeeeeeeeeebbg aaffeeeeeeeeeeeeeeeeeeeebbbg aafeeeeeeeeeeeeeeeeeeebbbeg aafeeeeeeeeeeeeeeeeeebbbeeg faceeeeeeeeeeeeeeeeebbbeeeg aaeeeeeeeeeeeeeeeebbbeeeeg caeeeeeeeeeeeeeeebbdeeeeeg aaeeeeeeeeeeeeebbdeeeeeeg aaeeeeeeeeeeeebbaeeeeeeeg faaeeeeeeeeeabdaaaaaaeeeg faaeeeeeeaaaaaaaaaaaaaaaaaaaaccf feaaaaaaaaaaaaeeeeeeeeaaaaaaaaaaaaaaaaccf feaaaaaaedbbeeeeeeeeeeeeg fccaaaaaaaaaaaaaaacff feeeeeeebbbeeeeeeeeeeeeeg ffcaaaaaaaaaaaaaaacff feeeeeebbbeeeeeeeeeeeeeeg ffcaaaaaaaaaaaac feeeeebbbeeeeeeeeeeeeeeeg ffccaac feeeebbbeeeeeeeeeeeeeeeeg feeebbbeeeeeeeeeeeeeeeeeg feebbbeeeeeeeeeeeeeeeeeeg febbdeeeeeeeeeeeeeeeeeeeg fbbaeeeeeeeeeeeeeeeeeeeeg cbbaeeeeeeeeeeeeeeeeeeeeeg cbbgeeeeeeeeeeeeeeeeeeeeeeg dbbfggggggggggggggggggggggge dbb dbb bbb bbb bbb bbb bbd fbbd fbbc fbbc cbbf cbbf dbb cbb d ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#bab0c0ff b,#c45b92ff c,#e4d3dfff d,#ca71a0ff e,#d38eb3ff f,#f1eaefff g,#d4becfff ``` ```image ebbb ebbb ebbb dbbb dbbd fdbbd fdbbbd fdbbbbc fdbbbbc cbbbbbc cbbbbbc gbbbbdf gbbbbdf f gbbbbdf c ebbbbdf a ebbbbe ac ebbbbe aa fdbbbbe aaf fdbbbbg aag fdbbbbg aaaf fdbbbbg aaac cbbbbbc fff aaaa cbbddegaaaaaaaaggccfff caaac ffgeaaaaaaaaaaaaaaaaaaaaaa faaaa ffcggaaaaaaaaaaaaaaaaaaaaaaaaaaa gaaaf ffcggaaaaaaaaaaaaaaaaaagcccggaaaaaaaaa faaaagaaaaaaaaaaaaaaaaaagccf ffccgg aaaaaaaaaaaaaaaaaaedde caaaaaaaaaaggcfebbbbe gaaaggcff ebbbbe ff fdbbbbe fdbbbbg fdbbbbg cbbbbbc cbbbbbc cbbbbbc gbbbbdf gbbbbdf ebbbbdf ebbbbe ebbbbe ebbbbe fdbbbbe fdbbbbg dbbbbg bbbbc bbbc bbc df ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#bab0c0ff b,#c45b92ff c,#e5d3dfff d,#ce7aa6ff e,#dc9fbfff f,#f1e9efff g,#d3c2d1ff ``` ```image be cbbbbf cbdbbbbe cbc dbbbbc gbc cbbbbd gbc ebbbbg ebc cbbbbdf ebf ebbbbe ebf fdbbbbf fag ebf gbbbbe aa ebf dbbbbc gac eb cbbbbd aa db ebbbbg aaf db cbbbbdf aa db ebbbbe aa db fdbbbbf fag db gbbe aa db cac bb aa bb gaf bb aa bb aa bb fag bb aa bb cac bb aa bb gaf bb aa bb aa bb faa bb aa bb cag bb aa bb gaf bb aa bb aa bb faa bb aa bb cag bb aa bb gac bb aa bb aaf dbd aa bbb aa bbb fag bbd aa bbd gac bbe aa fbbe aaf fbbg aa cbdaaaaagcf aa fgaaaaaaaaaaaaaaaaaaagcf faaaaaaaaaaagc fcgaaaaaaaaaaaaaagcf aaaaagcdbb fcgaaaaaaaaaaaaaagcff f dbb fcgaaaaaaaaaaaaaaggcf bbb fcggaaaaaaaaaaag bbb ffcgaac bbd bbd bbd fbbe fbbg cbbc gbbf ebbf ebb dbb dbb bbb bbb bbd bbd fbbe fbbe cbbc cbbc ebbf ebb ebb d ``` <!-- end of image -->
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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,#5e07f0ff b,#b62e20ff c,#dcbad9ff d,#b1d7b1ff e,#8349ecff f,#c37868ff g,#99c497ff ``` ```image ec aa aa aa c aa ae aa aa aa eac aa aa aa aa caa gdddddddgaedddddd caa ddddddddaaddddddd caa dddddddaadddddddd eaa dddddddaedddddddd eaa ddddddaaddddddddd eaa dddddeagddddfdddd eaa dddddaadddddbfddd gdddddddddddddddddddddddddddg aaa ddddaadddddfbdddd gdddddddddddddddddddddddddddd aaa dddeaedddddbbdddd gdddddddddddddddddddddddddddd aaac dddaaddddddbbdddd gdddddddddddddddddddddddddddd aaac ddaaddddddgbgdddd gdddddddddddddddddddddddddddd aaac dgaeddddddfbddddd gdddddddddddddddddddddddddddd aeac daadddddddbbddddd gdddddddddddddddddddddddddddd aeae eaddddddddbfddddd gdddddddddddddddddddddddddddd aaacae caadddddddgbgddddd gdddddddddddddddddddddddddddd aaae ae aaddddddddfbdddddd gdddddddddddddddddddddddddddd aaae ae eagddddddddbbdddddd bbbfc gddddddddddddddddddddddddddddaaae ae aadddddddddbfdddddd cbbbbbbbf gddddddddddddddddddddddddddaaae ae aa ddddddddgbddddddd fbbbbbbfcgddddddddddddddddddddddddaaae aa cae ddddddddbbddddddd cfbbbbbbfgddddddddddddddddddaaaedd aa aa ddddddddbbddddddd fbbbbbbbfddddddddddddaaaedddd aa ea ddddddddbfddddddd gdddgfbbbbbbfgdddddaaaedddddd aa cae dddddddfbdddddddd gddddddddfbbbbbbbaaaedddddddd aa aa gggggggbbgggggggg gdddddddddddddfaaaedddddddddd aa eac bb gddddddddddddaaaebbdddddddddd aa aa bf gddddddddddaaaeddfbfddddddddd aa aa cb gddddddddaaaedddddbbddddddddd ea cac bb gddddddaaaeddddddddbbdddddddd ea aa bb gddddaaaeddddddddddfbfddddddd ea aa bc gddaaaedddddddddddddbbddddddd ea cae fb gaaaeddddddddddddddddbbdddddd ea aa bb aaaeddddddddddddddddddgbfddddd caea bb aaaedddddddddddddddddddddbbgdddd caae bc aaae gddddddddddddddddddddddbbdddd caa fb aaae gddddddddddddddddddddddgbbddd cac bb aaae gdddddddddddddddddddddddfbgdd bf aaae gddddddddddddddddddddddddbbdd bc aaae gdddddddddddddddddddddddddbbd fb aae gdddddddddddddddddddddddddfbf bb e gddddddddddddddddddddddddddbb bf gdddddddddddddddddddddddddddbb cbc dgggggggggggggggggggggggggggfbf fb bb bb bb bf cbf cb fbc fb bb bb bb bf fbc cb bb bb bb bb fbf bf bb cb bb bb cbf bb bb bc bb fb cbf bb fbc bb bb bc bb fb fbc bb bb bf bb bc fbf fb bb bb bb bf cbfbc bbb bb ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5c03f0ff b,#b62c1fff c,#da9690ff d,#c9acfaff e,#7930f2ff f,#c25756ff g,#eed1ceff ``` ```image d dea deaaa g deaaaaa bbfcg deaaaaaed bbbbbbfccg deaaaaaed bbbbbbbbbbbfcg deaaaaaed gcfbbbbbbbbbbbbffcg deaaaaaed gcfbbbbbbbbbbbbfcgg deaaaaaed gccfbbbbbbbbbbbbfcg deaaaaaed gcfbbbbbbbbbbbbfccg deaaaaaed ggcfbbbbbbbbbbbbfeaaaaaed gcffbbbbbfaaaaaaed gcfaaaaaaed deaaaaaabc deaaaaaefbbbg deaaaaaed gbbbf deaaaaaed cbbbc deaaaaaed fbbbg deaaaaaed gbbbf deaaaaaed cbbbc deaaaaaed fbbbg deaaaaaed gbbbf deaaaaaed cbbbc deaaaaaed fbbbg deaaaaaed bbbb deaaaaaed gbbbf deaaaaaed cbbbc deaaaaaed fbbbg aaaaaed gbbbf aaaed cbbbc aed fbbbg d gbbbf cbbbc fbbbg gbbbf cbbbc fbbbg bbbb gbbbf cbbbc fbbbg gbbbf cbbb fbb gbb cb f g ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Right then, let's explore the next spot. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#5e06f1ff b,#b62c1eff c,#e1a8a3ff d,#b892f8ff e,#894af4ff f,#ca685eff g,#e8d5efff ``` ```image gaaae eaaag daaad aaaa eaaag gaaae eaaag daaad gaaae eaaag daaad gaaae eaaag ccg gaaae fbbf aaaa bbbc daaad cbbb gaaae fbbf eaaag fbbc daaad gbbbc gaaae cbbb eaaag fbbf daaad bbbc aaaa gbbbg eaaag cbbb gaaae fbbf eaaag bbbc daaad gbbbg gaaae cbbb eaaag fbbf daaad bbbc gaaae gbbbg eaaag cbbb aaae fbbf aaa bbbc aad gbbbg ae cbbb ag fbbf d bbbc cbbbg cbbf fbbf bbbc cbbb fbbf fbbc gbbbc cbbb fbbf ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area B. Answer: A: 1; B: 0; 1 + 0 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#5c04f0ff b,#b62d1fff c,#dea09aff d,#b994f8ff e,#7d37f3ff f,#ca665cff g,#ebd4dfff ``` ```image dd aa aa aa g aa ae aa aa aa dad aa aa aa aa gaa dad daa aa daa ea daa gae eaa aa eaa eag c eaa aa bc aaa aa cb aaag dad bb aaag aa bf aaad aa gbg aaad gae fb aead aa bb aead eag bf eaadad ae gbg eaae ae aa fb eaae ae dad bb bbbfg eaae ae aa bf cfbbbbbbc eaae ae aa gbg gcbbbbbbfc eaae aa dad fb gfbbbbbbfg eaae aa aa bb cbbbbbbbc eaae aa ea bc gfbbbbbbfg eaae aa gae cb cfbbbbbbeaae aa aa bb caaae aa eag bb eaaebb aa aa bc eaae cbc ea aa cb eaae bb ea dad bb eaae bb ea aa bb eaae cbf ea aa bc eaae bb da gae cb eaae bb da aa bb eaae gbf daeag bf eaae fbg daae bc eaae bb daa cb eaae gbb gad bb eaae fbg bf eaae bb gbg eaae bb fb aae cbc bb e bb bf bb gbg cbf fb bb bb bb bf gbf gbg fbg fb bb bb gbb bc fbc cb bb bb bb bb cbc bc bb cb bb bb cbf bb bbg bc bb cb gbf bb fbg bf bb bc gbb cb fbc bb bb bf bb gbg cbc fb bb bb bb bf cbfbg bbb bb ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for intersections. 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,#b55ca8ff b,#bbb106ff c,#e7cfd7ff d,#b2d7b1ff e,#99c895ff f,#c090b8ff g,#c5c758ff ``` ```image bgggdc bbbbbbbbbbbbbbbgggdc ccgggbbbbbbbbbbbbbbbbbbgggdc eddddddddddddddddddd ccgggbbbbbbbbbbbbbbbbbbgggdc eddddddddddddddafddd ccgggbbbbbbbbbbbbbbbbbbgggdc eddddddddddddddadddd ccgggbbbbbbbbbbbbbbbbbbbggdddddadddd ccggbbbbbbbbdddddadddd eddddddddbedddfadddd eddddddddbgdddfadddd eddddddddbbdddfadddd eddddddddbbdddaadddd eddddddddbbdddaadddd eddddddddgbdddaadddd eddddddddgbdddaadddd eddddddddebdddaadddd edddddddddbgddaadddd edddddddddbgddafdddd edddddddddbbddafdddd edddddddddbbddafdddd edddddddddbbddafdddd edddddddddgbddaddddd edddddddddgbddaddddd eddddddddddbefaddddd eddddddddddbgfaddddd aaf eddddddddddbgfaddddd caaaa eddddddddddbbfaddddd aa caaa eddddddddddbbaaddddd fa faac eddddddddddbbaaddddd aa aaa eddddddddddgbaaddddd aa caaf eddddddddddebaaddddd caf aaac edddddddddddbaaddddd aa aaa edddddddddddbaaddddd cac faaf edddddddddddbafddddd aa aaa edddddddddddbafddddd fa caaf edddddddddddbafddddd aa faac edddddddddddbafddddd aa aaa edddddddddddgadddddd af caaf edddddddddddeadddddd aa aaac edddddddddddfagddddd cac caaa edddddddddddfagddddd aa faac edddddddddddfabddddd fa aaa edddddddddddfabddddd aa caaf edddddddddddaabddddd aa faaedddddddddddaabddddd af aaaddddddddddaabddddd aa fafdddddddddaabedddd cac eaadddddddddaabgdddd aa efadddddddddaabgdddd fa edafddddddddafbbdddd aa edaaddddddddafbbdddd aa edaaddddddddafbbdddd af eddaddddddddadgbdddd aa eddaadddddddadgbdddd cac eddaadddddddaddbeddd aa eddfaddddddfaddbgddd fa edddafdddddfaddddddd aa edddaadddddfaddddddd aa edddfadddddaaddddddd af deeeeaeeeeeaaeeeeeee aa aa aa cac aa aa aa ca aa fac af aa aa aa af aa fa af af ac ac aa aa ac cac fa ac aa cac a fac afca aa aaca aa cafa af aaa aa aaa cac faa aa aa fac aa aa fc fa af c ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#b55ca7ff b,#bbb104ff c,#e4c5e0ff d,#dad57aff e,#ebe8b9ff f,#cc8fc4ff g,#c6b73fff ``` ```image fffc aaac aaac aaac ggggdddeeee aaac bbbbbbbbbbbbbbggggdd aaa bbbbbbbbbbbbbbbbbbbbg caaa ddddgggbbbbbbbbbbbbbb caaa eeedddgbbbe caaa bbbe caaa bbbd caaf gbbd faaf dbbg faaf dbbg faaf ebbb faaf ebbb faac bbbe aaac bbbe aaac gbbd aaac gbbd aaac dbbg aaa dbbg caaa ebbb caaa ebbb caaa bbbe caaa bbbe caaa gbbd caaf gbbd faaf dbbg faaf dbbb faaf ebbb faaf ebbbe faac bbbe aaac bbbd aaac gbbd aaac dbbg aaac dbbg aaa ebbb caaa ebbb caaa bbbe caaa bbbe caaa gbbd caaa gbbd caaf dbbg faaf dbbg faaf ebbb faaf ebbb faaf bbbefaac bbbeaaac gbbdaaac gbbdaaac dbbgaaac dbbgaaa ebbbaaa bbgaaa bbgaaa gbgaaf dbgaaf dbgaaf ebaaaf ebaaaf baaac baaac gaaac gaaac daaac daaac eaaa eaaa caaae caaae caaad caaad faaag faaag faaab faagb faagbe aaagbe aaagbd ac aaagbd aaf aaagbg aaaac aaabbb aaaaac caaabbb faaaf caaabbbe caaa caaabbbe aaac caaabbbd aaaf caaagbbd faaa caafdbbg caaa faafdbbg aaac faafebbb faaf faafebbb caaa faaf bbbe aaac faac bbbe faaf aaac gbbd caaa aaac gbbd caaac aaac dbbg aaac aaac dbbg faaf aaa ebbb caaa caaa ebbb aaac caaa bbbe faaf caaa bbbe caaa caaa gbbd aaac caaa e aaaf caaf faaa faaf caaa faaf aaac faaf faaf faaf caaa faac ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Answer: A: 1; 1 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#b55ba8ff b,#bbb105ff c,#dfb8d8ff d,#e1dd93ff e,#f1e6e5ff f,#ca8ac1ff g,#cdc64aff ``` ```image bggddee bbbbbbbbbbbbbbbggddee eddggbbbbbbbbbbbbbbbbbbggddee eddggbbbbbbbbbbbbbbbbbbggddee ac eddggbbbbbbbbbbbbbbbbbbggddee ae eddggbbbbbbbbbbbbbbbbbbggd eae eddggbbbbbbb ea bd ca bd ca bg fa bb fa bb aa gb aa db aa ebe aa bd aa bg af bb af bb ac bb ac gb ae db ea ebeca bdca aaf bgfa caaaae bbfa aa eaaa bbfa fa faac gbaa aa aaa dbaa aa caaf dbaa eaf aaae baa aa eaaa baf cac faac baf aa aaae baf fae caaf bac aa faac gac aa aaa dae eaf caaf cae aa aaae cad cac eaaa cag aa faac fab fae aaa fab aa caaf aab aa faac aab eaf eaaa aab aa caf aabe cac aa aabd aa ca afbg fae ac afbb aa aa acbb aa fa acgb eaf eae aegb aa af eaedb cac aa ea be aa ca ca bd fae ac ca aa aa fa aa fa fa eaf eac aa aa aa aa cac aa aa aa ca aa fae af aa aa aa af aa fa af af ac ac aa aa ac cac fa ae aa eaeeae fae afea aa aaca aa caca af aaa aa aaa eac faa aa eaa cae aa aa cc fa af e ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for 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,#0cbe57ff b,#cafcd1ff c,#8ad09aff d,#44ca7bff e,#b1d8b2ff f,#edf8eeff g,#a5d3a7ff ``` ```image geeeeeeeeeeeeeec geeeeeeeeeeeeeec geeeeeeeeeeeeeec geebbeeeeeeeeeec gebbbbeeeeeeeeec fac geeebbbbeeeeeeec aad geeeebbbbeeeeeec baa gecaaeebbbbeeeec aac gecaaeeebbbbeeec caa gecaaeeeeebbbbec aae gecaaeeeeeebbbbc daa gecaaeeeeeeeebbbf faaf gecaaeeeeeeeeebbbb aaa gegaaeeeeeeeeeegbbbf aaa gegaaeeeeeeeeeec bbbb aaa gegaaeeeeeeeeeec fbbbf aaaf gegaaeeeeeeeeeec bbbb daaf cccaaccccccccccg fbbbf caab aa bbbb eaac aa fbbbf baad aa bbbb faad aa fbbbf aaa aa bbbb aaa aa fbbbf aaa aa bbbb aaa aa fbbbf daaf aa bbbb fffffffffffffffffffffff caab aa fbbbggggggggggggggggggggggggaae aa bbbeeeeeeeeeeeeeeeeeeeeecaac aa bbbeeeeeeeeeeeeeeeeeeegaad aa fbbbeeeeeeeeeeeeeeeeeeaaa aa fgbbbeeeeeeeeeeeeeeeeaaaf aa fgebbeeeeeeeeeeeeeeeaaagf aa fgeebbeeeeeeeeeeeeeaaaegf aa fgeebbbeeeeeeeeeeeaaagegf aa fgeeebbbeeeeeeeeedaaceegf aa fgeeeebbbeeeeeeedaaceeegf aa fgeeeeebbeeeeeecaadeeeegf aa fgeeeeebbbeeeegaadeeeeegf aa fgeeeeeebbbeegaaaeeeeeegf aa fgeeeeeeebbbeaaaeeeeeeegf aa fgeeeeeeeebbaaaeeeeeeeegf aa fgeeeeeeeeeaaaeeeeeeeeegf aa fgeeeeeeeeaaabeeeeeeeeegf aa fgeeeeeeedaaebbeeeeeeeegf aa fgeeeeeedaacebbbeeeeeeegf aa fgeeeeecaadeeebbbeeeeeegf aaf fgeeeecaadeeeeebbeeeeeegf aaf fgeeegaaaeeeeeebbbeeeeegf aaf fgeeeaaaeeeeeeeebbbeeeegf aaf caaadcb fgeeaaaeeeeeeeeeebbbeeegf aaf eaaaaaaaaaaaadgf fgeaaaeeeeeeeeeeeebbeeegf aab baadfbcdaaaaaaaaaaaaaddaaaeeeeeeeeeeeeeebbeegf aab baad bgdaaaaaaaaaageeeeeeeeeeeeeebbbegf aab faad bcaaceeeeeeeeeeeeeeeebbbgf aab faaa fgeeeeeeeeeeeeeeeeeeebbbf aab aaa fgeeeeeeeeeeeeeeeeeeeebbf aab aaa fgeeeeeeeeeeeeeeeeeeeebbb aae aaa fggggggggggggggggggggggbbb aae aaa fffffffffffffffffffffffbbb aae aaa bbb aae aaaf fbbf aag aaaf fbb dag daaf bbb dac daab bbb daccaae bbf daaaag fbbf daaac bbb daad bbb cad bbb bbf fbb bbb bbb bbb bbf fbb bbb bbb bbb fbbf fbb bbb b ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0abd57ff b,#c2eed4ff c,#d6f9deff d,#1fc365ff e,#cbfed2ff f,#e5fbeaff g,#f4fdf6ff ``` ```image g gef eeecg feeeeef ceeeeeecg feeeeeeef gceeeeeecg feeeeeeef gceeeeeecg feeeeeeef bddddg gceeeeeecg baaaag feeeeeeef baaaag gceeeeeecg baaaag feeeeeeef baaaaf gceeeeeec baaaaf feeeeeeeg baaaaf gceeeeeec baaaaf feeeeee caaaaf geeeee caaaac feee caaaac gee caaaac f caaaac faaaac faaaab faaaab faaaab faaaab gaaaab gaaaab ``` <!-- end of image --> After careful examination, I've determined that there's no intersection in area A. Now, let's scrutinize the next spot. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0bbe57ff b,#a1e6bdff c,#7bdca3ff d,#51d087ff e,#cbfdd3ff f,#e7fcebff g,#2cc66dff ``` ```image f eef eeef eeee e eeeee fa eeeeee fga eeeeef fgaa feeeeef daaa feeeee daaaa feeeee caaaaa eeeeef baaaaab eeeeef baaaaac feeeeef eaaaaac feeeee eaaaaad feeeee fgaaaad eeeeef fgaaaagf eeeeef daaaagf feeeeef daaaaae feeeee caaaaae eeeeee caaaaab eeeeef baaaaab eeeeef eaaaaac feeeee eaaaaad feeeee fgaaaad eeeeee fgaaaagf eeeeef gaaaagf feeeeef daaaagf feeeee caaaaae feeeeecaaaaab eeeecaaaaab eecaaaaac fbaaaaac faaaaadf fgaaaagee fgaaaageeef daaaagbeeeef daaaaaefeeeeef caaaaae feeeee baaaaab eeeeee baaaaac eeeeef eaaaaac eeeeef eaaaaad feeeee fgaaaad feeeee fgaaaagf eeeeee daaaagf eeeeef daaaaae feeeeef caaaaae feeeee caaaaab feeeee baaaaab eeeeef eaaaaac eeeeef eaaaaad feeeeef gdcbgaaaad feeeee aaaaaaaagf feeeee aaaaaaagf eeeeef aaaaaaaf eeeeef cdgaage feeeeef feeeee eeeeee eeeee eeee feee fee ee e ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 0; B: 1; 0 + 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#0bbe57ff b,#b4ebcaff c,#87deacff d,#58d28cff e,#ccfdd3ff f,#e5fbeaff g,#30c770ff ``` ```image ee eeee fad eeee aag eeee baa bga eeee aad baa eeee caa baa eeef aab eaa eeee daa eaa eeef aaf eaa eeee aaa faa feeef aaa faa eeee aaa faa feeef gaa faa eeee daaf aa feeef caab aa eeee baac aa feeef eaad aa eeee faag aa feeef aaa aa eeee aaa aa feeef aaa aa eeee gaa aa feeef gaaf aa eeee daae aa feeef caac aa eee eaad aa eee faag aa eee aag aa eee aaa aa eef aaa aa fee aaa aa eee gaaf aa eee daae aa eee caab aa eef baac aa fee faad aa eee aag aa eee aaa aa eeaaa aa faaa aa gaae aa daabee aa caab eee aa baac eef aa eaad fee aaf faag eee aaf aaa eee aaf caaagcb aaa eee aaf baaaaaaaaaaaadcf aaa eef aae baad bcgaaaaaaaaaaaaagcgaa fee aae eaag fcdaaaaaaaaaaf eee aae faag bcgae eee aab faaa eee aab aaa eef aab aaa fee aab aaa eee aab aaa eee aab aaa eef aac aaa feef gac gaaf fee gac gaaf eee gac daae eee gacdaab eef gagaac fee gaaac eee daad eee cag eee eef fee eee eee eee eef fee eee eee eef feef fee eee 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,#2a14f1ff b,#a6c48dff c,#b2abf7ff d,#b49940ff e,#695cefff f,#e3d9b8ff g,#b0d7b1ff ``` ```image fff ddddddddddddddddddddddddddbbbffffff ffffffbbbdddddddddddd d d df bbbbbbbbdbbbbbbbbbbbbbbg ggggggggdggggggggggggggb ggggggggdggggggggggggggb ggggggggdbgggggggggggggb ggggggggbdgggggggggggggb gggggggggdgggggggggggggb gggggggggdgggggggggggggb gggggggggbdggggggggggggb ggggggggggdggggggggggggb ggggggggggdggggggggggggb ggggggggggdbgggggggggggb cceeaaa e ggggggggggbdgggggggggggb cceeaaaaaaaaaecc ee gggggggggggdgggceeaaaaaaaaaeecc a ggggeeeaaaadaaaaeecggggb ca gggaeeeggggdbggggggggggb a gggagggggggbdggggggggggb ca gggaggggggggdggggggggggb ac gggaggggggggdggggggggggb a gggaggggggggdbgggggggggb ac gggaggggggggbdgggggggggb a gggagggggggggdgggggggggb ee gggagggggggggdgggggggggb a gggagggggggggdbggggggggb ea gggaggggggggggdggggggggb a gggaggggggggggdggggggggb ca gggaggggggggggdbgggggggb ac bggaggggggggggbdgggggggb a a d ac a d bf a ca df ddb ee ca fd fdffb a ce d dd fd ee ce d fdf d a ce df dd d ca ce fdfdf d a ee dd d ca ee f d ac ec d a ec d ae ec d a ec d ee ac d a ac df ca a bf a a bf ca a fb ac a fd a a fd ae a d a a d f ee a d fbddddb a a d fbdddddf ca a ddddbf a a ca a ac a a a ac a a a ee a a a ea a a a ca a ac a a a ac ca a ca ee ce a ce ea ce a a caac ac ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#2812f2ff b,#c9b67dff c,#988df7ff d,#b3973dff e,#6251f2ff f,#e4dbbbff g,#cdc8fbff ``` ```image bdb fdd ddf bdf fdb fdd ddf bdb fdb dd ddf bdb fdd dd ddf bdb fdd dd bdf bdb fdd ddf bdf fdb fdd ggccc ddf gggccceeeaaaaaaaa ggccbdbeaaaaaaaaaaaaaaaaaeee ggccceeeaaaaaaaeddaaaaaaeeecccggg gaaaaaaaaaaaaaeecddcgg caaeecccggg ddf cae bdb cae fdd cae dd cae bdf cae bdb cac fdd cac ddf eac bdf eac fdb eac fdd eac ddf eac bdb eac fdb eac dd eag ddf eag bdb eag fdd aag dd aag ddf aag bdb aag fdd aag dd aag bdf aa bdb ``` <!-- end of image --> 1 intersection present within area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#2912f2ff b,#c9b576ff c,#978cf8ff d,#b3963bff e,#5e4df4ff f,#e3d9b9ff g,#cdc8fbff ``` ```image fff bdddddddddddddddddddddddbbbbbffffff ffffffbbbbbdddddddddb d d bf fd d d bf d d d bb d d df ggceeaaa e fb gcceaaaaaaaaeecgg ee d ggceeaaaaaaaaeccg a gcceaaaadaaaeecgg ca aeccg df a a fd ga a d ag a d ga a bf ac a fd a a d ee a d a a bb ca a d a a d ga a d ag a fb ga a d ac ga d bf a ga df ddb ee ga fb bdffb a ge d dd fd ce ce d fdf d a ce bf dd d ca ce fdfdf d ag ce dd d ga cc f d ac ec d a ec d ec ec d a eg d ee eg d a ag df ca ag bf ag ag bb ga a fb ag a fb a a fd ac a d a a d f ee a d fbddddb a a d fbddddbf ca a ddddbf a a ga a ag a a a ac a a a ee a a a ca a a a ga a ag a ga ga ac ga a ga ee ge a ce ce ce a a caag ac ``` <!-- end of image -->
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I'm approaching this image with caution. Intersections might be tricky to spot. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#a27a46ff b,#dcc0baff c,#b3416aff d,#ba8b80ff e,#f2efebff f,#9ac797ff g,#b1d7b1ff ``` ```image b da da bae bae eab eab ad ad aa aa ab da aae da aba bae a da bae ea ad eab ba ab eab bd eae ad dd ba ad db da aa ab ad aa ae ab da a eae da a ba bae a da bae a ad eab a ab eab ea eae adba ba aaa da ad ad ab fafffffffffffffffffffffg fdaggggggggggggggggggggf fgaagggggggggggggggggggf ed fggadggggggggggggggggggf edcccd fgggafggggggggggggggggdcccde fgggfaggggggggggggggfccf fggggdaggggggggggggdcfgf fgggggaaggggggggggccgggf fggggggadggggggggccggggf fgggggggafgggggfcdgggggf fgggggggfaggggdcfggggggf fggggggggdaggccggggggggf fgggggggggaaccgggggggggf fgggggggggfcdggggggggggf fggggggggdcfafgggggggggf fgggggggccggfagggggggggf fggggggccggggdaggggggggf fggggfcdggggggaagggggggf fgggdcgggggggggadggggggf fggccgggggggggggafgggggf fgccggggggggggggfagggggf dcdggggggggggggggdaggggf dcgggggggggggggggggaagggf ccfggggggggggggggggggadggf ecd fgggggggggggggggggggaggf bcb fgggggggggggggggggggfagf dce fggggggggggggggggggggdaf cc eeeeeeeeeeeeeeeeeeeeead ecd ab bcb ae dce ba cd cc da bcc ecd ad c dc bcb ab cd ce dce eae bc bc cc ba ce cb ecd da cc ec bcb a ec dc dce cb ce cc dc bc ecd c cb bcb cb ec cc bc cdcc ce cd cd bc ccece dcc ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#a27a46ff b,#dec4bfff c,#b33f69ff d,#c26788ff e,#f0e4e2ff f,#b79870ff g,#d09fa3ff ``` ```image eaaf baaf baab faae faae eaaf baaf gaab faae bgd faae dccc eaaf edccdg baag bcccb gaab gccce faae dccde faae edccg eaaf bcccb baag gccce gaab edccde faae ecccg aaae bcccb eaaf gccce baag edccde gaab ecccg faae bcccb eaaagccde eacccd ecccd bcccaab gccdefaae edccd eaaa ecccg eaaf bcccb baag gccde gaab edccd faae ecccg eaaf gcccb eaaf gccde baag edccd gaab bcccg faae gcccb eaaf dccde eaaf edccd baag bcccg faab gcccb faae ccde eaaf cg eaaf b baab faab faae eaaf baaf baab ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#a27a46ff b,#e2cbc7ff c,#b33f69ff d,#c56e8dff e,#f2e8e6ff f,#b99b74ff g,#d2aba7ff ``` ```image g fa fa gae bae eab eag af af aa aa ab fa aae fa aba gae a fa bae ea af eab ba ab eag gf eae af ff ba af fg fa aa ab af aa ae ab fa a eae fa a ba gae a fa bae a af eab a ab eag ea ea afba ga aaa fa af af ab ea ga fa ed af edcccd ab gcccde ea ecdb ga gcb aa cc ag cc ae ecg ea gce ga cc aacc bcd dceae cc ea cd ga bcg aa dce ag cc ae cd ba bcg fa dce af cc ag cd ae bcg ba dce fa cc af ecd ag bcb ae dce ba cg cc fa gcc ecd af c dc bcb ab cd ce dce ae bc bc cc ba ce cg ecd fa dd ec gcb a ec dd dc cb ce cc dc gc ecd c cb gcb cg ec dc gc cdcc c cd cd bc cdece gcd ``` <!-- 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. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#675ab3ff b,#a67058ff c,#3b24a7ff d,#d9cedbff e,#b1d7b1ff f,#a1be96ff g,#9f96d1ff ``` ```image bfed bbbbbbbbbbbfdd fb dfbbbbbbbbbbbbbfed bb defbbbbbbbbbbbbbfdd bf dfbbbbbbbbbbbbbfed feeeeeeeeeeeeeee db defbbbbbbbbbbbbbfdd eeeeeeeeeeeeeeee fb dfbbbbbbbbbbbbbbffeeeeeeeee bb debbbbbbbbbbbbfeee bf eeeeeeeeffbbfeee db eeeeeeeeeeeeeeee fb eeeeeeeeeeeeeeee bb eeeeeeeeeeeafeee be eeeeeeeeeeecfeee db eeeeeeeeeefceeee bb eeeeeeeeeegceeee bb eeeeeeeeeeaceeee be eeeeeeeeeecceeee db eeeeeeeeeecceeee bb eeeeeeeeeecaeeee bb eeeeeeeeeecaeeee bd eeeeeeeeeecgeeee db eeeeeeeeeeceeeee bb eeeeeeeeegceeeee bb eeeeeeeeeaceeeee bd eeeeeeeeecceeeee eb eeeeeeeeecceeeee bb eeeeeeeeecceeeee bb eeeeeeeeecaeeeee ffffffffffbffffffe fffffffffcafffff eeeeeeeeefbeeeeeef cd eeeeeeeeebbeeeeeef dc eeeeeeeeebbeeeeeef gc eeeeeeeeebfeeeeeef ac eeeeeeeefbeeeeeeef cc eeeeeeeebbeeeeeeef cc eeeeeeeebbeeeeeeef ca eeeeeeeebfeeeeeeef cg eeeeeeebbeeeeeeeef cd eeeeeeebbeeeeeeeef dc eeeeeeebbeeeeeeeef gc eeeeeefbeeeeeeeeef ac eeeeeebbeeeeeeeeef cc eeeeeebbeeeeeeeeef cc eeeeeebfeeeeeeeeef ca eeeeefbeeeeeeeeeef cg eeefebbeeeeeeeeeef cd eeeccbbfeeeeeeeeef dc eeeeabacccaeeeeeef gc eeeefbefacccccaeef ac eeeebbeeeeefacccccg cc eeeebbeeeeeeeeefacccccg cc eeeebfeeeeeeeeeeef dacccccg ca eeefbeeeeeeeeeeeef dacccccg cg eeebbeeeeeeeeeeeef gcccccad cg eeebbeeeeeeeeeeeef gcccccad c eeebfeeeeeeeeeeeef gcccccad dc eeeeeeeeeeeeeeeeef gcccccg gc eeeeeeeeeeeeeeeeef gccc ac eeeeeeeeeeeeeeeeef gccd cc eeeeeeeeeeeeeeeeef ccg cc eeeeeeeeeeeeeeeeef acc ca eeeeeeeeeeeeeeeeef gcc cg eeeeeeeeeeeeeeeeef ccg cd eeeeeeeeeeeeeeeeef cca dc eeeeeeeeeeeeeeeeef gcc gc eeeeeeeeeeeeeeeeef dccg ac cca cc acc cc dccd ca cca cg acc cd dccd dc cca gc acc ac gccd cc ccg cc acc ca gcc cg cccd cc ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7460b7ff b,#a56c55ff c,#3c24a7ff d,#d4b9aeff e,#e7dee0ff f,#bb917fff g,#ada3d9ff ``` ```image bbbe ebbb dbbf fbbd bbbe ebbb dbbf fbbd bbbe ebbb dbbf fbbd bbbe dbbb dbbf fbbd ebbbe dbbb fbbf bbbd ebbbe dbbb fbbf bbbd ebbbe dbbf fbbd bbbd ebbb dbbf fbbd bbbe ebbb dbbf ee fbbd gccagbbbe accccbbbge acccabbbcccage egabbbacccccccage bbbaccccccccccaag ebbb egaccccccccccagg dbbf egaccccccccccagg fbbd egaccccccccc bbbe egaccccc ebbb egac dbbf fbbd bbbe dbbb dbbf fbbd ebbbe dbbb fbbf bbbd edfe ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Now, let's turn our attention to the next spot. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#6f5ebeff b,#a56d55ff c,#3b23a7ff d,#d4b9adff e,#ded5e2ff f,#bd9482ff g,#a59ad6ff ``` ```image ffddee bbbbbbbbbffdddee bbbbbbbbbbbbbbbbbbfffddee ddffbbbbbbbbbbbbbbbbbbbbbbd eeddfffbbbbbbbbbbbbe eedddffbbbe ggge accg ccce ccce eccc eccc gcca gcca accg accg ccce ccce eccc eccc gcca gcca accg accg cccg ccce eccc eccc gcca gcca acca accg accg ccce ccce eccc gccc gcca gcca accg ``` <!-- end of image --> No intersection found in area B, but I won't give up. Answer: A: 1; B: 0; 1 + 0 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#6956baff b,#a56d55ff c,#3b23a7ff d,#cdbeccff e,#e7e0e7ff f,#c19a8aff g,#9a8ed2ff ``` ```image ffde ebbbbbbbbbbffde fb edffbbbbbbbbbbbbfde bb edfbbbbbbbbbbbbffde bf edffbbbbbbbbbbbbfde ebe edfbbbbbbbbbbbbffde fb edffbbbbbbbbbbbbfde bb edfbbbbbbbbbbbd bf edffbe eb fb bb ge bf cd eb ec fb gc bb ac bd cc db cc bb ca bb cg bd cd db ece bb dc bb gc bd ac db cc bb cc bf ca be cg db ce bb dc bf gc be ac fb cc bb cc bf ca ebe cg fb ce bb ec bf gc ebe ac fb cc bb cc bf ca eb cg e fb cd ccbbe ec egbacccge gc eb eacccccg ac fb eacccccg cc bb dacccccg cc bd dacccccg ca db dacccccd cg bb dcccccad cd bb gcccccad ece bd gcccccad dc gcccccg gc gccc ac dcce cc ccg cc acc ca gcce cg eccg ce cca dc gcc gc eccd ac cca cc acc cc eccd ca cca cg acc cd dcce ec cca gc acc ac dcce cc ccg cc acc ca gccecg ecccd cc ``` <!-- end of image -->
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This image looks interesting. I wonder if there are any intersections hidden in there? It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#e151f9ff b,#abc9abff c,#f1a8fdff d,#b2d7b2ff e,#96ca96ff f,#f0f3f0ff g,#c695d2ff ``` ```image f fb b b bf df dd fd b b b fffffffffffffffffffffffffffbf febbbbbbbbbbbbbbbbbbbbbbbbbbf fbdddddgaaddddddddddddddddbb fbdddgagdggdddddddddddddddbe fbdbagddddaddddddddddddddbde fbaaddddddgbddddddddddddbdde aadddddddddadddddddddddbddde aafbdddddddddaddddddddddbdddde caf fbdddddddddbgddddddddbbdddde cac fbddddddddddaddddddddbddddde cac fbddddddddddggddddddbdddddde fac fbdddddbdddddadddddbddddddde aa fbdddddbdddddaddddbdddddddde aa fbddddbbddddddaddbddddddddde aa fbddddbbddddddadbbddddddddde caf fbddddbbddddddbgbdddddddddde cac fbddddbbdddddddbddddddddddde fffffffffffffff cac fbdddbdbddddddbggdddddddddde bbbbbbbbbbbbbbe fac fbdddbdbdddddbddadddddddddde dddddddddddddde aa fbdddbdbddddbdddadddddddddde dddddddddddddde aa fbdddbdbdddbdddddaddddddddde dddddddddddddde aa fbddbddbddbbdddddaddddddddde ddddddddddddddecaf fbddbddbdbbddddddggdddddddde dddddddddddddgac fbddbddbdbddddddddadddddddde dddddddddddgage fbddbddbbdddddddddggddddddde dddddddddbagdde fbdbdddddddddddddddaddddddde ddddddddaadddde fbdbdddddddddddddddaddddddde ddddddaadddddde fbdbddddddddddddddddadddddde ddddaadddddddde fbdbddddddddddddddddadddddde dddabddddddddde fbbdddddddddddddddddggddddde dddddddddddddde fbbddddddddddddddddddaddddde dddddddddddddde febbbbbbbbbbbbbbbbbbbgbbbbbe dddddddddddddde fdfffffffffffffffffffafffff dddddddddddddde df a dddbbddddddddde b a dddddbbddddddde b a dddddddbbbdddde fd cc dddddddddbbbdde df a eeeeeeeeeeeebbb b cf dbf b a dbf fd a fbd df fc fbb b a dbf b cc dbf fd a fbd df af fbbf b a dbf b a fbd fd fc fbd df a dbfb cc db a a a a fc a cc a a a a cc a cf a a a a ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#e76cfcff b,#b2c4b1ff c,#ed94fdff d,#d5dfd4ff e,#e247fcff f,#f6eaf8ff g,#f5c1fdff ``` ```image g gae gaeec faeecf fceecf fceeaf ceeag geeag gaeeg gaeec faeecf ceecf aaf f df bbbd fdbbbd dbbbdf dbbbdf fdbbbd fdbbbd dbbbdf ``` <!-- end of image --> This isn't an intersection in area A, but I'm not discouraged. Onward to the next region of interest. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#e771fbff b,#b1c3b1ff c,#f0a3fcff d,#cad6caff e,#e248fcff f,#e4eae4ff g,#f8d5fdff ``` ```image gg ceeg ceeaec f ceeag ae fb gaeec cec fbb gaeec ea bbf gaeec ceg dbf gaeeag gea dbd ceeag aeg dbd ceeag gec fbd eeag ae fbb ec cec bbf ea bbf ceg dbf gea dbd aeg fbd gec fbb ae fbb cec bbf fd ea bbf dbf ceg dbf bbf gea dbd bbf ae fbd fbbf gec fbb dbbf ee fbb bbbf ceg bbf bbbf ea dbf fbdbf cegdbd dbfbf gedbd bbfbf abb bdfbd fbbc fbf bd bbae db bd bbfceg bb bd dbf ea bd bd dbd aeg fbf bd fbd gec db bd fbb ae bb bd fbb cec bd bd bbf ea fbf bd bbf ceg db bd dbd gea bb bb dbd aeg bd bb fbd gec fbf bb fbb ae db dbfbb cec bb dbbbf ea bd dbbf ceg fbf dbd gea db fd aeg bb gec bd ae fbf cec db ea bb ceg bd gea fbf ae db gec bb ee bd ceg fbf ea ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area B! Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#e86ffcff b,#b0c2afff c,#f0a2fdff d,#ccd7cbff e,#e248fcff f,#eff2efff g,#f8d4feff ``` ```image f fb b b bf bf dd fb b b b bf g dd cee dd gec cc fb gec e b ea ag b ea e bf ae e bf ceg ga dd ceg e fb gec cc fb gec b e b ea fb a b ee db e bf ae bb e df ceg bb gdd ceg fdb fb gec dfb bcg gec b b b e ea b b b a ae fd b bf a ae df b dd e ceg b b fd gc ceg b dfb e gec fd db cg gea df f e ea b a ae b a ae fd e ag df gc b e b cg fd e df e bd b a bbf b e dbf fd cc dbd df e fbb b ag bbf b e dbd fd e fbd df ga fbb b e dbf b cc dbd fd e fbd df a bbf b e dbf b e dbd fd ga fbb df e bbfb cg db e a a e gc e cg e a a e gc e cg e e a e ``` <!-- end of image -->
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I'm approaching this image with caution. Intersections might be tricky to spot. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5b3e57ff b,#c5efa9ff c,#98c497ff d,#30042bff e,#b2d7b2ff f,#8a7887ff g,#e2e9dbff ``` ```image eeeeeeeeeeeeeeeeeeec eeeeeeeeeeeeeeeeeeec eeeeeeeeeeeeeeeeeeec eefdaeeeeeeeeeeeeeec eecddeeeeeeeeeeeeeec eeeddceeeeeeeeeeeeec eeeaddeeeeeeeeeeeeec eeeeddeeeeeeeeeeeeec eeeeddaeeeeeeeeeeeec eeeecddeeeeeeeeeeeec eeeeeddceeeeeeeeeeec eeeeeaddeeeeeeeeeeec gggbbbbbbbbbbbbbbbbg eeeeeeddeeeeeeeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgg eeebbbbbbbbbbbbbbbbbbbbbbbbbbbbggg ggbbbbbbbbbbbbbbbg eeebbbbbbbbbbbbbbbec ggbbbbbbbbbbbbbbgg eeebbeeddeeeeeeeeeec ggbbbbbbbbbbbbbbbg eeeeeeeadaeeeeeeeeec gbbbbbbbbbbbbbbb eeeeeeeeddeeeeeeeeec ggbbbbbbb eeeeeeeeddfeeeeeeeec g eeeeeeeefddeeeeeeeec eeeeeeeeeddeeeeeeeec eeeeeeeeeddaeeeeeeec eeeeeeeeecddeeeeeeec eeeeeeeeeeddceeeeeec eeeeeeeeeeaddeeeeeec eeeeeeeeeeeddeeeeeec eeeeeeeeeeeddfeeeeec eeeeeeeeeeefddeeeeec eeeeeeeeeeeeddeeeeec eeeeeeeeeeeeadaeeeec eeeeeeeeeeeeeddeeeec eeeeeeeeeeeeeddfeeec eeeeeeeeeeeeefddeeec eeeeeeeeeeeeeeddeeec eeeeeeeeeeeeeeddaeec cccccccccccccccddcce ddg fdd dd ddf edd ddg ada dd ddc cdd dd ada gdd dde fdd dd fdd ddf gdddddd gdd fdddddgddf ddg adddda eddg ada eddddde add dd fdddda ddd ddf gdddddf dda edd fdddddg gdde dd addddf fdd ada eddddde ddd gdd fdddda dda dde gdddddf ddf fddfdddddg cddg dddddf add ddde ddd ddf gddg fdd ddd dda gddc fdd add ddd ddf eddg add ddd dda gdde fdd ddd d ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f2b4aff b,#c6f0a9ff c,#73556fff d,#2f042aff e,#c0b3bfff f,#998496ff g,#e2eed9ff ``` ```image fae fdddc fddddg gddddf cddda edddde adddc fdddd gddddf addda eddddg ddddf cdddd edddde adddc fddddg gddddf cddda edddde adddc ggggggbb fddaaggggggbbbbbbbbbbbbbbb gggbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggg bbbbbbbbbbbbbbbgggggg bgggggggfdddd gdddde adddc fddddg gddddf cddda edddde adddc fddddg gddddf cddda edddde ddddc fdddd gdddde addda fddddg ddddf cddda edddde adddc fddddg gddddf cddda edddde adddc fdddd gddddf addda eddddg ddddf cdddd edddde adddc fddddg gddddf cddda edddde adddc ``` <!-- end of image --> My analysis confirms the presence of 1 intersection in area A. Answer: A: 1; 1 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#4b2546ff b,#c6f0aaff c,#6f516cff d,#2f032aff e,#c3b6c1ff f,#957f93ff g,#e5eeddff ``` ```image fdc gdd dde fdd dd ddf edd ddg cda gggbbbbbbbbbbbbbbbbgg dd gggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgg gbbbbbbbbbbbbbbbbbbbbbbbbbbbggg ggbbbbbbbbbbbbbbbg gbbbbbbbbbbbbbbggg gbbbbbbbbbbbbbbbgg bgggad ggbbbbbbbbbbbbbbbg adc gbbbbbbbbbbbbbbb gdd ggbbbbbbb dde g fdd dd adc gdd ddg cda dd ddf edd dd cda dd dde fdd dd adc gdd dde fdd dd ddf edd ddg cda dd dde fdd dd adc gdd dde fdd dd fdd ddf gadddda edd fdddddeddf ddg cddddc eddg cda eddddde cdd dd cdddda ddd ddf gaddddf ddc edd fdddddg gdde dd addddc fdd adc eddddde add gdd cdddda dda dde gdddddf ddf fddfdddddg eddg dddddc add adde ddd ddc edde cdd ddd dda gdde fddg add dda ddf eddg cdd ddd ddc gdde fdd add d ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#bc748fff b,#e060d3ff c,#a93565ff d,#dea5cfff e,#f2ecefff f,#9bc397ff g,#b1d7b1ff ``` ```image e c c c c c c e ea db da ebe dd bd ad bb ae db ae ebe c bd c bb c db c ebe c bd c bb c db c ebe ea bd ea bb dd db dd ebe ae bd ae bb c eb c be c bd c db c eb c be c bd c db c eb ea be da bb dd db ad ebe ae b c be c eb c b ffffffffffffffffffffffffffffcfffffff b eggggggggggggggggggggggggggggcggggggg dd eggggggggggggggggggggggggggggcggggggg b eggggggggggggggggggggggggggggcggggggg b eggggggggggggggggggggggggggggcggggggg dd eggggggggggggggggggggggggggggcggggggg e b eggggggggggggggggggggggggggggcggggggg ac b egggggggggggggggggggggggggggfaggggggg eca deegggggggggggggggggggggggggggaaggggggg ace ebegggggggggggggggggggggggggggafggggggg eca begggggggggggggggggggggggggggafgdbgggg ace begggggggggggggggggggggggggggcdbdggggg ca edggggggggggggggggggggggggggdbbggggggg dce bgggggggggggggggggggggggggbbggggggggg ca bgggggggggggggggggggggggbbcgggggggggg dce ddggggggggggggggggggggbbcaggggggggggg cc ebggggggggggggggggggbbacggggggggggggg dcd ebggggggggggggggggbbgcagggggggggggggg cc eddgggggggggggggbbgfcfggggggggggggggg dcd egbgggggggggggbbggccggggggggggggggggg cc egbgggggggggbbgggcagggggggggggggggggg ecd egbgggggggbbgggacgggggggggggggggggggg ac eggbggggbbdgggccggggggggggggggggggggg ecd eggbggdbdggggcfgggggggggggggggggggggg ac eggbdbdggggacgggggggggggggggggggggggg eca egggdgggggcaggggggggggggggggggggggggg ace egggggggfcfgggggggggggggggggggggggggg eca eggggggccgggggggggggggggggggggggggggg ace egggggcaggggggggggggggggggggggggggggg ca egggacggggggggggggggggggggggggggggggg dce eggccgggggggggggggggggggggggggggggggg ca efcfggggggggggggggggggggggggggggggggg dce acggggggggggggggggggggggggggggggggggg cc caeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee dcddce cc ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#be618aff b,#e15cd3ff c,#aa3365ff d,#ebbbdeff e,#f6def0ff f,#ea8de1ff g,#d397b0ff ``` ```image dca dcg dcg gcg gcg gcd acd ace ace ac cc cc ca eca eca dcg dcg gcg gcg gcd gcd de ace dbbf ace dbbbfe acdbbbfe abbbfe dbbbfe ebbbbd e efbbbae f efbbbcg b efbbbccd be efbbbaca bd efbbbaccg bf efbbbfccae bbe efbbbdgccg fbd fbbbdeaccd ebf dbbbd gccae bb dbbbd accg fbe dbbbf dcccd ebf dbbbfe gcca bb dbbbfe eaccd fbe dbbbfe dccae dbf dbbbfe gccg ebb efbbfe eaccd fbe efbbfe gccae dbd efbbfe eaccg ebf efbbbe dccae bb efbbbd gccg fbd efbbbd eaccd ebf efbbbd dccae bbfbbbd accg fbbbd eaccd ebd gccae eaccg dccae gccg eaccd gccae accg dcccd gcca eaccd dccae gccg eaccd gccae ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#bb5d85ff b,#e15ed4ff c,#a93264ff d,#e0b6c8ff e,#f4d8edff f,#ec99e4ff g,#cd88a5ff ``` ```image e c c c c c c e ea fb dg eb dg bf gd bb ae fb a ebe c bf c bb c fb c ebe c bf c bb c fb c be a bf eg fb dg eb gd be ge bf ae fb c eb c be c bf c fb c eb c be c bf c fb a eb ea be dg bf dd fb gd eb ae b a b c ef c b c b c ef c b c b c fe c e b ea ac b dg ecg fe dg gc b gd cg b ae fb gce b afbf ca ef ebf gce b ebbe ca b ebbc dce ff ebbcd ca b bbgc dcd b bb ca cc fe bb ece dcd b bbe ac ac b bbe cg ecd be fbe dce ac ef fbe ca ecg b fbe ecd ac bfbf gc ecg ef ca gc dce cg ac gce cg ca gc gce ca ca ecd dce ac ca cg dcddce cc ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#396688ff b,#fd6362ff c,#b1d7b2ff d,#efd8daff e,#e8958bff f,#96c49dff g,#6e91a1ff ``` ```image ffffffffffffffffffffffffffffffffffffffff cccccccccccccccccccccccccccccccccccccccc cccccccccccccccccccccccccccccccccccbcccc ccccccccccccccccccccccccccccccccccbbbfcc cccccccccccccccccccccccccccccccccbbbbecc ccccccccccccccccccccccccccccccccbbbbbccc cccccccccccccccccccccccccccccccbbbbbaccc ccccccccccccccccccccccccccccccbbbbbaaccc cccccccccccccccccccccccccccccbbbbeaaaccc ccccccccccccccccccccccccccccbbbbecaaaccc cg cccccccccccccccccccccccccccbbbbecfaaaccc caaaagd ccccccccccccccccccccccccccbbbbeccfaaaccc gaaaaaaaac cccccccccccccccccccccccccbbbbecccfaaaccc aaaaaaaaaaaaf ccccccccccccccccccccccccbbbbeccccgaaaccc aaacfaaaaaaaaaag cccccccccccccccccccccccbbbbecccccgaaaccc aaa caaaaaaaaaagd ccccccccccccccccccccccbbbbeccccccgaaaccc aaa daaaaaaaaaaac cccccccccccccccccccccbbbbecccccccgaaaccc caaa dgaaaaaaaaaac ccccccccccccccccccccbbbbeccccccccgaaaccc gaaa gaaaaaaaaaag cccccccccccccccccccbbbbecccccccccaaaaccc aaag caaaaaaaaaagd ccccccccccccccccccbbbbeccccccccccaaagccc aaaf caaaaaaaaaaad cccccccccccccccccbbbbecccccccccccaaagccc aaad dgaaaaaaaaaac ccccccccccccccccbbbbeccccccccccccaaagccc aaa gaaaaaaaaaagcccccccccccccbbbbecccccccccccccaaagccc daaa caaaaaaaaaagfccccccccbbbbeccccccccccccccaaagccc caaa caaaaaaaaaaafccccbbbbecccccccccccccccaaafccc gaaa daaaaaaaaaaafbbbbeccccccccccccccccaaafccc aaag cccgaaaaaaabbbbecccccccccccccccccaaafccc aaac ccccccgaaabbbbeccccccccccccccccccaaacccc aaad cccccccccbbbbecccccccccccccccccccaaacccc aaa ccccccccbbbbeagccccccccccccccccccaaacccc daaa cccccccbbbbgaaafcccccccccccccccccaaacccc faaa ccccccbbbbecaaaacccccccccccccccccaaacccc gaaa cccccbbbbeccfaaaaccccccccccccccccaaacccc aaag ccccbbbbeccccgaaagccccccccccccccfaaacccc aaac cccbbbbeccccccaaaafcccccccccccccfaaacccc aaa ccbbbbeccccccccaaaacccccccccccccfaaacccc aaa fbbbbecccccccccfaaaaccccccccccccgaaacccc caaa dbbbbecccccccccccgaaaacccccccccccgaaacccc gaaa dbbbbecccccccccccccaaaagccccccccccgaaacccc aaag dbbbbecccccccccccccccaaaaccccccccccgaaacccc aaaf dbbbbecccccccccccccccccaaaacccccccccaaaacccc aaad dbbbbeccccccccccccccccccfaaaaccccccccaaaacccc aaa dbbbbdffffffffffffffffffffaaaagfffffffaaaaffff daaa dbbbbd aaaad aaag caaa dbbbbd aaaa aaaf gaaa dbbbbd daaaa aaac aaag dbbbbd gaaag aaac aaac dbbbbd aaaa aaad aaad dbbbbd aaa aaad cga dbbbbd aaaf aaa dbbbbd aaaa aaa dbbbbd caaa aaa dbbbbd aaa aaa dbbbbd aaac aaa dbbbbd aaag aaa dbbbbd gaaa daaa dbbbbd daaa daaa dbbbbd aaadcaaa dbbbbd aaagcaaa dbbbbd gaaafaaa dbbbbd caaagaaa ebbbbd aaagaaa ebbbbd aaaaaaa ebbbb aaaaaag ebbbb faaaaag ebbbb aaaaag ebbbb aaaaag ebbbb aaaaaf ebbbb gaaaac ebbbb daaaac ebbbb aaaad ebbbb aaaad ebbbb aaaa ebbbb caaa ebbbb aaa ebbbb aaa ebbbb ebbbb ebbbb ebbbb ebbbb ebbbb ebbbb ebb e ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#396688ff b,#fc6362ff c,#9bb1c2ff d,#d1d9e1ff e,#fea7a6ff f,#fd8180ff g,#6b89a3ff ``` ```image fd fbbd fbbbbd fbbbbbbd fbbbbbbbb fbbbbbbbbf fbbbbbbbbb fbbbbbbbbba fbbbbbbbbbaa fbbbbbbbbbaaa fbbbbbbbbbaaaa fbbbbbbbbbaaaag fbbbbbbbbbaaaaag fbbbbbbbbeaaaaaag fbbbbbbbbe aaaaaag fbbbbbbbbe aaaaaag fbbbbbbbbe aaaaaac fbbbbbbbbe daaaaaac fbbbbbbbbe daaaaaac fbbbbbbbbe daaaaaac fbbbbbbbbe daaaaaac fbbbbbbbbe daaaaaac fbbbbbbbbe daaaaaad fbbbbbbbbe caaaaaad fbbbbbbbbe caaaaaad fbbbbbbbbe caaaaaad fbbbbbbbbe caaaaaad fbbbbbbbbe caaaaaad fbbbbbbbbe caaaaaa fbbbbbbbbe gaaaaaa fbbbbbbbbe gaaaaaa fbbbbbbbbe gaaaaaa fbbbbbbbbe gaaaaaa fbbbbbbbbe gaaaaag fbbbbbbbbe aaaaaag fbbbbbbbbe aaaaaag fbbbbbbbbe aaaaaag fbbbbbbbbe aaaaaag fbbbbbbbbe aaaaaag fbbbbbbbbe aaaaaac cd fbbbbbbbbe daaaaaac aaacd fbbbbbbbbe daaaaaac aaaaaagd fbbbbbbbbe daaaaaac aaaaaaaaagcd fbbbbbbbbe daaaaaac aaaaaaaaaaaagcd fbbbbbbbbe daaaaaac aaaaaaaaaaaaaaaacd fbbbbbbbbe caaaaaad aaaaaaaaaaaaaaaaaaagd fbbbbbbbbe caaaaaad cgaaaaaaaaaaaaaaaaaaaagdfbbbbbbbbe caaaaaad cgaaaaaaaaaaaaaaaaaabbbbbbbbbe caaaaaad dgaaaaaaaaaaaaaabbbbbbbbbe caaaaaad dcaaaaaaaaaabbbbbbbbbe caaaaaa dcgaaaaabbbbbbbbbe gaaaaaa dcgabbbbbbbbbe gaaaaaa fbbbbbbbbb gaaaaaa fbbbbbbbbbag gaaaaaa fbbbbbbbbbaaac gaaaaaa fbbbbbbbbgaaaaad gaaaaag fbbbbbbbbgaaaaaaad aaaaaag fbbbbbbbbecaaaaaaag aaaaaag fbbbbbbbbe gaaaaaaag aaaaaag fbbbbbbbbe daaaaaaaac aaaaaag fbbbbbbbbe daaaaaaaad aaaaaac fbbbbbbbbe caaaaaaaa daaaaaac fbbbbbbbbe gaaaaaaag daaaaaac fbbbbbbbbe aaaaaaaac daaaaaac fbbbbbbbbe daaaaaaaad daaaaaac fbbbbbbbbe caaaaaaaad daaaaaac bbbbbbbbbe gaaaaaaag daaaaaad bbbbbbbbbe gaaaaaaac caaaaaad bbbbbbbbbe daaaaaaaad caaaaaad bbbbbbbbbe daaaaaaaad caaaaaad bbbbbbbbbe caaaaaaag caaaaaad bbbbbbbbe gaaaaaaag caaaaaad bbbbbbbe aaaaaaaac caaaaaa bbbbbbe daaaaaaaad gaaaaaa bbbbbe caaaaaaaa gaaaaaa bbbbe gaaaaaaag gaaaaaa bbbe gaaaaaaac gaaaaaa bbe daaaaaaaad gaaaaag be caaaaaaaad aaaaaag ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Answer: A: 1; 1 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#396688ff b,#fc6362ff c,#9fb5c5ff d,#d2dce3ff e,#fd9f9eff f,#fdd2d2ff g,#6e8da6ff ``` ```image bf bbbf bbbbe bbbbb bbbbba bbbbbaa bbbbeaaa bbbbe aaa cg bbbbe daaa caaaagd bbbbe daaa gaaaaaaaac bbbbe daaa aaaaaaaaaaaac bbbbe caaa aaaccaaaaaaaaaag bbbbe caaa aaa caaaaaaaaaagd bbbbe caaa aaa daaaaaaaaaaad bbbbe gaaa daaa dgaaaaaaaaaac bbbbe gaaa gaaa caaaaaaaaaag bbbbe gaaa aaag caaaaaaaaaagd bbbbe aaag aaac daaaaaaaaaaad bbbbe aaag aaad dgaaaaaaaaaac bbbbe aaac aaa gaaaaaaaaaac bbbbe aaac daaa caaaaaaaaaagd bbbbe aaac caaa daaaaaaaaaaad bbbbe aaad gaaa dgaaaaaaaaaadbbbbe aaad aaag gaaaaaaabbbbe aaad aaac caaabbbbe aaa aaad bbbbb aaa aaa bbbbbac aaa daaa bbbbgaaad aaa caaa bbbbe aaaa aaa gaaa bbbbe daaaa aaa aaag bbbbe gaaag daaa aaad fbbbbe aaaad daaa aaa fbbbbe aaaa caaa aaa fbbbbe daaaa caaa daaa fbbbbf caaag caaa gaaa fbbbbf aaaac gaaa aaag fbbbbf aaaa gaaa aaac fbbbbf aaaa gaaa aaad fbbbbf caaaa aaag aaa fbbbbf gaaag aaag daaa fbbbbf aaaad aaag caaa fbbbbf aaaa aaac gaaa fbbbbf daaaa aaac aaag fbbbbf gaaag aaac aaac fbbbbf aaaa aaad aaad fbbbbf aaa aaad cga fbbbbf aaac aaa fbbbbf aaaa aaa fbbbbf caaa aaa fbbbbf aaa aaa fbbbbf aaad aaa fbbbbf aaag aaa fbbbbf gaaa daaa fbbbbf daaa daaa fbbbbf aaaddaaa fbbbbf aaaccaaa ebbbbf gaaacaaa ebbbbf caaacaaa ebbbb aaagaaa ebbbb aaaaaaa ebbbb aaaaaag ebbbb caaaaag ebbbb aaaaag ebbbb aaaaac ebbbb aaaaac ebbbb gaaaac ebbbb daaaad ebbbb aaaad ebbbb aaaad ebbbb aaaa ebbbb caaa ebbbb aaa ebbbb aaa ebbbb ebbbb ebbbb ebbbb ebbbb ebbbb ebbbb ebb b ``` <!-- 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,#ae6cadff b,#285761ff c,#b1d7b1ff d,#5c8183ff e,#dacfdeff f,#a6a2b1ff g,#95c796ff ``` ```image gcccccccccccccccccccccccccccccccccccccccccccccg gcccccccccccccccccccccccccccccccccccccccccccccg e gcccccccccccccccccccccccccccccccccccccccccccccg eaa gcccccccccccccccccccccccccccccccccccccccccbcccg aaaa gccccccccccccccccccccccccccccccccccccccccdaaccg eaaa gcccccccccccccccccccccccccccccccccccccccdaaaccg eaaae gccccccccccccccccccccccccccccccccccccccgbaacccg aaaf gccccccccccccccccccccccccccccccccccccccbaaacccg aaaa gcccccccccccccccccccccccccccccccccccccbbaafcccg aaaa gccccccccccccccccccccccccccccccccccccbbdaaccccg eaaa gcccccccccccccccccccccccccccccccccccdbbaaaccccg eaaae gccccccccccccccccccccccccccccccccccgbbbaacccccg aaaf gccccccccccccccccccccccccccccccccccbbbaaacccccg aaaa gcccccccccccccccccccccccccccccccccbbbcaafcccccg aaaa gccccccccccccccccccccccccccccccccdbbgfaaccccccg fbd eaaae gcccccccccccccccccccccccccccccccgbbdcaaaccccccg fbb eaaae gcccccccccccccccccccccccccccccccbbbccaacccccccg bbc aaaa gccccccccccccccccccccccccccccccbbbccaaacccccccg bbb aaaa gcccccccccccccccccccccccccccccbbbgccaafcccccccg cbb faaa gccccccccccccccccccccccccccccdbbdccfaaccccccccg bbf eaaae gcccccccccccccccccccccccccccgbbbcccaaaccccccccg dbb aaae gcccccccccccccccccccccccccccbbbccccaacccccccccg ebb aaaa gccccccccccccccccccccccccccbbbccccaaacccccccccg bbd aaaa gcccccccccccccccccccccccccdbbgccccaafcccccccccg dbb faaa gccccccccccccccccccccccccgbbdccccfaaccccccccccg bbc eaaae gccccccccccccccccccccccccbbbcccccaaaccccccccccg bbb aaaf gcccccccccccccccccccccccbbbccccccaacccccccccccg cbb aaaa gccccccccccccccccccccccbbbgcccccaaacccccccccccg bbf aaaa gcccccccccccccccccccccdbbdccccccaafcccccccccccg dbb faaa gccccccccccccccccccccgbbbccccccfaaccccccccccccg ebb eaaae gccccccccccccccccccccbbbcccccccaaaccccccccccccg bbd aaaf gcccccccccccccccccccbbbccccccccaacccccccccccccg dbb aaaagccccccccccccccccccbbbgcccccccaaacccccccccccccg bbe aaaacccccccccccccccccdbbdccccccccaafcccccccccccccg bbb eaaaccccccccccccccccbbbccccccccfaaccccccccccccccg cbb eaaafcccccccccccccbbbcccccccccaaaccccccccccccccg bbf gaaaacccccccccccbbbgcccccccccaacccccccccccccccg bbb gcaaaacccccccccdbbdcccccccccaaacccccccccccccccg ebb gccaaaacccccccgbbbccccccccccaafcccccccccccccccg bbd gcccfaaaccccccbbbccccccccccfaaccccccccccccccccg dbb gcccccaaafcccbbbcccccccccccaaaccccccccccccccccg bbe gccccccaaaacbbbgcccccccccccaacccccccccccccccccg bbb gcccccccaaaabbdcccccccccccaaacccccccccccccccccg fbb gccccccccaaaabccccccccccccaafcccccccccccccccccg bbf gcccccccccdaaafccccccccccfaaccccccccccccccccccg bbb gccccccccbbbaaaccccccccccaaaccccccccccccccccccg ebb gcccccccdbbdcaafcccccccccaacccccccccccccccccccg bbd gccccccgbbbccaaaccccccccaaacccccccccccccccccccg dbb gccccccbbbcccfaaccccccccaafcccccccccccccccccccg bbe gcccccbbbcccccaacccccccfaaccccccccccccccccccccg bbb gccccbbbgcccccaafccccccaaaccccccccccccccccccccg fbb gcccdbbdccccccaaaccccccaacccccccccccccccccccccg bbf gccgbbbcccccccfaacccccaaacccccccccccccccccccccg bbb gccbbbcccccccccaafccccaafcccccccccccccccccccccg fbb gcbbbccccccccccaaacccfaaccccccccccccccccccccccg fbb gdbbdccccccccccfaacccaaaccccccccccccccccccccccg ebb dbbbccccccccccccaacccaacccccccccccccccccccccccg bb bbbcccccccccccccaafcaaacccccccccccccccccccccccg bb bbbccccccccccccccaaacaafcccccccccccccccccccccccg bb bbbe eaafaa bbe fbbd aaaaa bbc ebbb aaaa bbf bbb faaa bbd bbb eaae bbb dbbf aa fbb cbbd ebb bbb bb bbb bbf bbbe bbd fbbf dbb ebbb cbb bbb bb bbb bbc dbbc bbd cbbd dbb bbb fbb bbb bb bbbe bbefbbf bbdbbb bbbbb fbbb ebbc df ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#ae6cadff b,#285761ff c,#cabcd1ff d,#5a7984ff e,#e5dce8ff f,#8fa7acff g,#c392c2ff ``` ```image f fbde caaaaa ebaaaac dbaaaa fbdaaac cbbaaaae ebbdaaag dbbaaaac dbbbaaaa fbbbdaaac cbbbbaaaae ebbbbdaaag dbbbbaaaae fbbbbbaaaa cbbbbbaaaaa ebbbbbbaaaaa dbbbbbgaaaag dbbbbbfgaaaae fbbbbbdeaaaaa cbbbbbd gaaaac dbbbbbc caaaag fbbbbbf gaaaae bbbbbd eaaaaa ebbbbbe gaaaac dbbbbc aaaaae dbbbbf caaaag fbbbbd aaaaae cbbbbd eaaaaa ebbbbbe gaaaac dbbbbc aaaaae fbbbbb caaaag cbbbbbd aaaaae ebbbbbbe eaaaaa dbbbbbc gaaaac dbbbbbf aaaaae fbbbbbd caaaag cbbbbbd aaaaae ebbbbbbe eaaaaa dbbbbbc gaaaac cbbbbbd caaaag ebbbbbbe aaaaae dbbbbbe eaaaaa dbbbbbf gaaaac fbbbbbf aaaaae cbbbbbd aaaag bbbbbbe aaaae bbbbbc eaaaa fbbbbf gaaac fbbbbd aaaae ebbbbbe caaag ebbbbbe aaaae dbbbbf eaaaa fbbbbf gaaac cbbbbb aaaae ebbbbbb caaag dbbbbbc aaaae c fbbbbbf eaaaa aag ebbbbbd aaaaa aaaae ebbbbbbe caaaag aaaaae dbbbbbc aaaaae aaaaaac fbbbbbf eaaaaa gaaaaaag cbbbbbd gaaaac gaaaaaag ebbbbbbe aaaaa caaaaaae dbbbbbc caaaag eaaaaaae dbbbbbf aaaaae eaaaaaac fbbbbbd eaaaaa gaaaaag cbbbbbd gaaaac gaaaaag bbbbbbe eaaaaa caaaaaae bbbbbc caaaag aaaaaaae fbbbbf aaaaae eaaaaaaac cbbbbd eaaaaa gaaaaaag ebbbbbe gaaaac gaaaaaage dbbbbc eaaaaa caaaaaaaedbbbbf caaaag eaaaaaaadbbbd aaaaae eaaaaaaadbb eaaaaa caaaaaaa eaaaaa fdaaaaaae caaaag cbbbaaaaaae aaaaae ebbbbbaaaaag eaaaaa dbbbbbcgaaaa gaaaac dbbbbbf gaaae eaaaaa fbbbbbd eaaag caaaag cbbbbbd aaaa aaaaae ebbbbbbe gaaae eaaaaa dbbbbbc caaac gaaaac fbbbbbf eaaag eaaaaa cbbbbbd aaaa caaaag ebbbbbbe aaaae aaaaae dbbbbbc aaaag aaaaa bbbbbf aaaaa aaaac fbbbbd aaaaae eaaaa cbbbbd caaaac caaag ebbbbbe eaaaag aaaae dbbbbc aaaaa eaaaa cbbbbd caaaac eaaaa ebbbbbe eaaaag caaag dbbbbb aaaaa aaaae dbbbbbf gaaaae eaaaa fbbbbbd eaaaag gaaac cbbbbbd aaaaa eaaaa bbbbbbe gaaaae caaaa bbbbbc caaaac aaaaa bbbbf eaaaag eaaaag ``` <!-- end of image --> Yes! I knew it! There's 1 intersection right here in area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#af6daeff b,#285660ff c,#b6c6c9ff d,#537680ff e,#e7e3ebff f,#859fa5ff g,#d2aed2ff ``` ```image g eaa be aaaa daa gaaae daaa eaaae cbaae aaag baaa aaaa bbaag aaaa bbdaa gaaae fbbaaa eaaag ebbdaae aaag bbbaaa aaaa bbb aag aaaa dbbcgaa fbd gaaae cbbd aaa fbb eaaag bbb aae bbc aaaa bbb aaa bbb aaaa bbbe aag cbb gaaa fbbf gaa bbf gaaae ebbb aaa dbb eaaag bbb aae ebbe aaaa bbb aaa bbd aaaa dbbc aag fbb gaaa cbbd gaa bbc eaaae ebbb aaa bbb eaaag bbb aae cbb aaaa bbbe aaa bbf aaaa fbbf aag dbb gaaae ebbd gaa ebbe eaaag bbb aaa bbd aaag bbb eaae fbb aaaa dbbc aaa bbc aaaa cbbd aag bbb gaaae ebbb gaa cbb eaaag bbb aaa bbf aaaa bbbe eaae dbb aaaa fbbf aaa ebbe aaaa cbbd aag bbd gaaae bbb gaa fbb eaaag bbb aaa bbc aaaa dbbc eaae bbb aaaabbd aaa cbb gaaab aag bbf daaae gaa bbb bbbaaa aaa ebb dbbf aag eaa bbd cbbd aaa aaa fbb bbb gaa aag bbc bbb aa gaa bbb dbbc aag aaa cbb fbbf aaa eaa bbf ebbb eaa aaa bbb bbb aae aag fbb bbbe aaa gaa cbb dbbc gaa aaa cbb cbbd aa eaa ebb bbb aag aaa bb bbb aaa aag bb dbbe gaagaa bbe fbbf aaaaa bbc ebbb aaaa bbf bbb aaaa bbf bbbe eaag bbb dbbc aa fbb cbbd ebb bbb bbe bbb bbf bbbe bbd fbbf dbb ebbb cbb bbb bb bbb bbc dbbc bbd cbbd dbb bbb fbb bbb ebb bbbe bbefbbf bbdbbb bbbbb fbbb ebbc df ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#72f594ff b,#fdc811ff c,#acfdc3ff d,#3cfb72ff e,#fbdf7bff f,#afd6afff g,#eff8eaff ``` ```image cddg adddc dddddc ddd gddddddc ddd cddddgdda cddda adddd gdda ddddd dddda dda dddddc ddddc dda gdddddd gddddg ddd addcdddg cdddd ddd ddd cddd adddd ddd ddd ddd dddda ddd cdda adda gddddc ddd dddg ddd cddddg ddd ddd ddd adddd ddd gddd ddd dddda ddd addc ddd ddddc ddd ddd addg gddddg ddd ddd cddc cdddd ddd cdda gdda adddd ddd dddg ddd dddda ddd ddd ddd gddddc ddd gddd ddd cddddg ddd addc ddd adddd ddd ddd addg dddda add ddd cddc ddddc addcdda gdda gddddg adddddg ddd cdddd addddd ddd adddd cddddd ddd dddda cddddc ddd gddddc cdddd addg cddddg cdddd cddc adddd cddda gdda dddda gdddg ddd ddddc gddd ddd gddddg gddd ddd cdddd ddg ddd adddd add dddda cddc ggggggggggddddc cddc ffffffffaddddffg dda fffffffaddddfffg ddd ffffffdddddffffg ddd fffffddddafffffg ddd ffffddddfffffffg ggggggggggdddgggggggg ffaddddffffffffg gffffffffffaddafffffff ffddddfffffffffg gffffffffffaddafffffff ffbddbfffffffffg gfffffffffffdddfffffff fffbbbbbfffffffg gfffffffffffdddfffffff ffffbbbbbffffffg gfffffffffffdddfffffff fffffebbbbeffffg gfffffffffffdddfffffff fffffffbbbbbfffg gfffffffffffdddfffffff ffffffffbbbbbffg gfffffffffffaddfffffff ffffffffffbbbbbg gfffffffffffaddaffffff fffffffffffbbbbbg gffffffffffffddaffffff ffffffffffffebbbbe gffffffffffffdddffffff ffffffffffffffbbbbb gffffffffffffdddffffff fffffffffffffffebbbbg gffffffffffffdddffffff fffffffffffffffggbbbbb gffffffffffffdddffffff fffffffffffffffg bbbbbggggggggeeeeeeeeeeeeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdddbbbfff fffffffffffffffg ebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddbbbfff bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddabbfff eeeeeeeeeeeeeeggggggg gfffffffffffffdddfffff gfffffffffffffdddfffff gfffffffffffffdddfffff gfffffffffffffdddfffff gfffffffffffffdddfffff gfffffffffffffaddaffff gffffffffffffffddaffff gffffffffffffffdddffff gffffffffffffffdddffff gffffffffffffffdddffff gffffffffffffffdddffff gffffffffffffffdddffff gffffffffffffffaddffff gffffffffffffffaddafff dda ddd ddd ddd ddd ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#75fa95ff b,#fec80fff c,#bbfdceff d,#3dfb72ff e,#fce07aff f,#fbd23aff g,#fef1c5ff ``` ```image addddddddc cdddddddda cdddddddda addddddddc addddddddc cddddddddd cdddddddda adddddddda addddddddc addddddddc cdddddddda cdddddddda addddddddc adddddddc gdddddde fbddddbbfg ebfdabbbbbe gfbbbbbbbbfg ebbbbbbbbbg gbbbbbbbbbe gfbbbbbbbbfg ebbbbbbbbbe gfbbbbbbbbfg ebbbbbbbbbg gbbbbbbbbbe fbbbbbbbbfg ebbbbbbbbbe gfbbbbbbbbf ebbbbbbbb gbbbbbbb fbbbbb ebbbb gfbb eb g ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Okay, let's proceed to the next area. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#6efb95ff b,#fec810ff c,#a4fdbdff d,#3bfb72ff e,#ffdb63ff f,#b3dc37ff g,#e1fadbff ``` ```image addddd adddddg cdddddc cdddddc gddddda ddddda dddddd addddd adddddg cdddddc cdddddc gddddda ddddda dddddd addddd adddddg cdddddg cdddddc gdddddc gddddda ddddda addddd adddddg cdddddg cdddddc gdddddc gddddda ddddda eeeeeeeeeeeeeeeeeeebbbbbbddddddbbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbddddddbbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbfdddddfbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbfdddddfbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbfdddddfbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbfdddddaeeeee gggggggggg ddddda dddddd addddd adddddg cdddddc cdddddc gddddda ddddda dddddd addddd adddddg cdddddg cdddddc gdddddc gddddda ddddda addddd adddddg cdddddg cdddddc gdddddc gddddda ddddda dddddd adddddg cdddddg cdddddc ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#71fc98ff b,#fec80fff c,#abfdc2ff d,#3cfb72ff e,#ffe798ff f,#f6d74fff g,#e8fbe2ff ``` ```image cdd adddc dddddc ddd gddddddc ddd cddddgdda cddda adddd gdda ddddd dddda dda dddddc ddddc dda gdddddd gddddg ddd addcdddg cdddd ddd ddd cddd adddd ddd ddd ddd dddda ddd cdda adda gddddc ddd dddg ddd cddddg ddd ddd ddd adddd ddd gddd ddd dddda ddd addc ddd ddddc ddd ddd addg gddddg ddd ddd cddc cdddd ddd cdda dda adddd ddd dddg ddd dddda ddd ddd ddd gddddc ddd ddd ddd cddddg ddd addc ddd adddd ddd ddd addg dddda add ddd cddc ddddc addcdda gdda gddddg adddddg ddd cdddd addddd ddd adddd cddddd ddd dddda cddddc ddd ddddc cdddd addg cddddg cdddd cddc adddd gddda gdda dddda gdddg ddd ddddc gddd ddd gddddg ddd ddd cdddd ddg ddd adddd add dddda cddc ddddc gddc cddddg dda adddd ddd dddda ddd ddddc ddd gddddg ddd cdddd addg dddd cddc bddbg dda gbbbbf ddd bbbbb ddd ebbbbe ddd bbbbb ddd fbbbbg addg gbbbbf cddc bbbbb gdda ebbbbe ddd bbbbb ddd fbbbbe ddd gbbbbf ddd g bbbbbg gggggeeeeeeeeeffffffffbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdddbbb ebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfddfbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfddaff efffffeeeeeeeeeegggg ddd ddd ddd ddd add cddc gdda ddd ddd ddd ddd ddd addg cddc dda ddd ddd ddd ddd ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for intersections. 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,#ecb0e4ff b,#9129eaff c,#b275eaff d,#b2d7b2ff e,#e66fc0ff f,#a3cea3ff g,#f2f1f3ff ``` ```image g b b b c gc aa e cg ag c a b e b e b ag b ga c e gc e aa e cg ga c e b e b e b ag b e c e gc e aa ag cg ga c e b e b a b ga b e c e gc e aa aa cg e gb efffffffffffffffffffffffffg gcbbcg efdddddddddddddddddddddddfg gcbbcg afdddddddddddddddddddddddfg gcbbcg gedddddddddddddddddddddddfg gcbbcg gedddddddddddddddddddddddfg gcbbcg gedddddddddddddddddddddddfg gcbbcg gedddddddddddddddddddddddfg gcbbcg gfeddddddddddddddddddddddfg gcbbcg gfeddddddddddddddddddddddfg gcbbcg gfeddddddddddddddddddddddfggcbbcg gfedddddddddddddddddddddcbbcg gfddddddddddddddddddcbbcdfg gfdeddddddddddddcbbcdddddfg gfddeedddddddbbcdddddddddfg gfddddeeeddddbdddddddddddfg gfdddddddeeebddddddddddddfg gfdddddddddceedddddddddddfg gfdddddddddbdddeeddddddddfg gfddddddddbdddddddeedddddfg gfdddddddcfdddddddddeeeddfg gfdddddddbdddddddddddddeeeg gfddddddbddddddddddddddddfeea gfdddddccddddddddddddddddfg geea gfdddddbdddddddddddddddddfg aeeg gfddddbddddddddddddddddddfg aeeg gfdddccddddddddddddddddddfg aea aeee gfdddbdddddddddddddddddddfg geea aeeg ge gfddbddddddddddddddddddddfg geeea e gfdfcddddddddddddddddddddfg e gfdbdddddddddddddddddddddfg eg gfbddddddddddddddddddddddfg eg a gfcfffffffffffffffffffffffg eg gb bgggggggggggggggggggggggg ea ba cg ea cc gc ea abb aa g ae ae ge ge ge e e e ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#f1a0d7ff b,#9229ebff c,#bf82f3ff d,#d9b6f8ff e,#ea68c1ff f,#a44eefff g,#f5d5f1ff ``` ```image eg ea ea ae aeg geg ea ee ae geg ea ee ae geg gea ea ae aeg gea ea g ae gdcfb aeg gdcfbbbfc geg gdcfbbbfcd ea gdcfbbbfcd ee gdcfbbbfcd aeeag dcfbbbfcd aeeeeag fbbfcd gaeeeea cbc gaeeeag gbf gaeeeag fbg gaeeeacbc geebbag fbeeeea dbc gaeeeag bf gaeeeag cbd gaeeeag dbc gaeeeag bb aeeeea cbd gaeeeag dbc gaeeeag fb gaeeea cbd gae gbf fbg cbd gbf fbg cbc gbf fbg dbc gbf fbg dbc bf cbd dbc bb cbd dbc fb cbd gbf ``` <!-- end of image --> Area A contains 1 intersection. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#ef91d1ff b,#9027ecff c,#bf82f3ff d,#ebbaebff e,#ea65c0ff f,#a854efff g,#f6e7f9ff ``` ```image g b b b f gc dd e cg dg f a b e b e b ag b gd f e gc e dd a cg gd f e b e b e b dg b a f e gc e dd dg cg ga f e b e b a b gd b e f e gc a dd dd cg a gf e gcbbcg e gcbbcg dg gcbbcg a gcbbcg e gcbbcg e gcbbcg a gcbbcg gd gcbbcg e gcbbcg e gcbbcg a gcbbcg dd gcbbcg e gcbbcg deeg fbc aea gf aeab feed gf geed b deeg cd dea b aea b gaed cd geed b deeg b deag dc aea aeae b gaed aeag ge b geeea e dc e b eg fg eg d df eg gb b ed bd fg ad ff gf aa dbb aa g da de ge ge ge e e e ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#9ac195ff b,#3d513eff c,#d3dbc5ff d,#b1d7b1ff e,#708271ff f,#eff3ecff g,#a4c166ff ``` ```image fdeebbbeab fcaebbbeacf ba caebbbbedf cbf fdeebbbeac ee fcaebbbeacf fbc bbedf ab e ba cc cbf e ee b fbc e ab df b b a a b b fd e b e cc e b e df b b a a b b fd e b aaaaaaaaaaabaaaaaaad ddddddddddaaddddddda ddddddddddbdddddddda ddddddddddbdddddddda ddddddddddedddddddda dddddddddeddddddddda dddddddddbddddddddda dddddddddbddddddddda dddddddddeddddddddda ddddddddedddddddddda dddgddddbdddddddddda ddddgdddbdddddddddda dddddgaaadddddddddda dddddddbgdddddddddda dddddddbdaggddddddda dddddddeddddggadddda ddddddaadddddddggdda ddddddbddddddddddgga ddddddbddddddddddddaggf ddddddedddddddddddda cgc dddddeddddddddddddda fggf dddddbddddddddddddda cgd dddddbddddddddddddda agf dddddeddddddddddddda fga ddddedddddddddddddda dgc ddddbdddddddddddddda fggf ddddbdddddddddddddda cgc fffcdfffffffffffffff fggf e cgd agf cgd dgc fgg cgc fggf cgd agf cgd dgc fgg dgc fggf cg ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#859284ff b,#394c39ff c,#dce2d3ff d,#c3d599ff e,#5e6e5eff f,#afb6afff g,#a4c063ff ``` ```image fb ee bf cbc ab ea bf fbc ae ea cbf fb ae ba cbc fb ee bf cbc ab ea gd bf cgd fbc dgc ae dgc ea dggd cbf cdggab cebgdc badggdc cbc cdggdc fb dgggc ee cdggdc bf dgggd cbc cdggdc ab cgggdc ea cdggd bf cd fbc ae ea cbf fb ae ba cbc fb ee bf fbc ab ea cbf fbc ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#96a097ff b,#3b4e3bff c,#cad3bfff d,#bcd18dff e,#667566ff f,#e8ece0ff g,#a3bf61ff ``` ```image fcaebbbeab caebbbeacf ba faebbbeacf cbf fcaebbbeac ee caebbbeacf bc beacf ab e ba cc cbf e ee b bc a ab cf b b a a b b fc e b e cc e b a cf b b a a b b fc e b e cf e b a af b b a a d b g e gcfc egf b cgd e dgf cf fgd e dgc b fgd a cgc a dgf b cgd b dgf a fgd a dgc b fgd e cgc fc ggf e cgd dgf fgd dgf fgd cgc ggf cgd dgf fgd dgf fgd cgc ggf cg ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#d22f81ff b,#e9c8efff c,#a4cea3ff d,#dd5d9eff e,#f2f4f2ff f,#cda0f1ff g,#b2d7b2ff ``` ```image bfb ffe bfb ffe eccccccccccccccccccccccce bfb ecgggggggggggggggggggggce ffe ecggggggggggggggggggggace bfb ecgggggggggggggggggggacce ffe ecggggggggggggggggggacgce bffbe ecgggggggggggggggggacggce ebfffbb ecggggggggggggggggacgggce ebffffbe ecgggggggggggggggacggggce bbfffbe ecggggggggggggggacgggggce ebffffbe ecgggggggggggggacggggggce bbfffbeecggggggggggggacgggggggce ebffffggggggggacggggggggce ecgggggfffffacgggggggggce ecgggggggggagfffffgggggce ecggggggggagggggggggfffce ecgggggggagggggggggggggce ecggggggaggggggggggggggce ecgggggagggggggggggggggce ecggggaggggggggggggggggce ecgggagggggggggggggggggce ecggaggggggggggggggggggce ecgagggggggggggggggggggce ecaggggggggggggggggggggce eagggggggggggggggggggggce acgggggggggggggggggggggce aeccccccccccccccccccccccce ae eeeeeeeeeeeeeeeeeeeeeee ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae a a a a a a a a a a d a bb a d a a a d a bb a d a a a d a bb a d a a a d a bb a d a a a d a bb a d a a a d a bb a da a ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#d53988ff b,#dcb5f4ff c,#f6d6e6ff d,#d84791ff e,#f8e7f4ff f,#ce9af4ff g,#e8d0f9ff ``` ```image e cab caac caac caac caac cadc cadc cadc cade cade cade cade cade cade cade cade cade fbbgge cade gbffffffbgge cade eggbbfffffbbgge cade eggbffffffbgbade eggbbfaaffbbgee cadggbbfffffbbgge cade eggbbfffffbbgee cade eegbbffffg cade ege cade cade cade cade cade cade cade cade cade cade cade cade cade cade cade cade cade cade ade de e ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Answer: A: 1; 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#d33083ff b,#dbb6f7ff c,#f2c4dbff d,#dd5d9eff e,#f8e9f4ff f,#ce9af5ff g,#ead3f9ff ``` ```image gfb bfe gfb bfe gfb bfe a gfb ae bfe ae gfbge ae gbfffbg ae egbffbge ae gbfffbg ae egbffbge ae gbfffbe ae egfffbg ae gbfffgae agbfffbg ae egbff ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae a a a a a a a a a a a a d a ec a d a a a d a cc a d a a a d a cc a d a a a d a cc a d a a a d a cc a d a a a d a cc a da a ``` <!-- 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 zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#492dbdff b,#7dd37cff c,#b2a6e3ff d,#96cb99ff e,#b1d8b1ff f,#7a72c3ff g,#e6ecedff ``` ```image ca caaaaa caaaaaaaaag cfaaaaaaaaaaaf gfaaaaaaaaaaafg gfaaaaaaaaaaafg caaaaaaaaaaafc caaaaaaaaaaaac caaaaaaaaaaaac gfaaaaaaaaaaafg gfaaaaaaaaaaafg gfaaaaaaaaaaafg caaaaaaaaaaaac caaaaaaaaaaaac caaaaaaaaaaaac gfaaaaaaaaaaafg gfaaaaaaaaaaafg gfaaaaaaaaaaafc caaaaaaaaaaaac caaaaaaaaaaaac aaaaaaaaaaac aaaaaaafg gaaafg caaa caaa faaf faaf aaac aaac aaag aaa aaa ggggggaaagggggggg eeeeeeaaaeeeeeeeed eeeeeeaaaeeeeeeeed eeeeedaaaeeeeeeeed eeeeefaaaeeeeeeeed eeeeefaaaeeeeeeeed bbbbeg eeeeefaafeeeeeeeed bbbbbbbbbbbbeg eeeeeaaafeeeeeeeed bbbbbbbbbbbbbbbbbbbbeeg eeeeeaaafeeeeeeeedbbbbdgedbbbbbbbbbbbbbbbbbbbbeeg eeeeeaaadeeeeeeeebbbbd gedbbbbbbbbbbbbbbbbbbbbdeg eeeeeaaaeeeeeeeebbbbd gedbbbbbbbbbbbbbbbbbbbbdeg eeeeeaaaeeeeeeebbbbb gedbbbbbbbbbbbbbbbbbbbbdeg eeeeeaaaeeeeeedbbbb gedbbbbbbbbbbbbbbbbbbbbdeg eeeeeaaaeeeeedbbbb gedbbbbbbbbbbbbbbbbbbbbdeg eeeeeaaaeeeedbbbbd gedbbbbbbbbbbbbbbbbg eeeeeaaaeeedbbbbed geebbbbbbbbb eeeedaaaeedbbbbeed geebb eeeefaaaedbbbbeeed eeeefaaaebbbbeeeed eeeefaafbbbbeeeeed eeeeaaafbbbeeeeeed eeeeaaafbbeeeeeeed eeeeaaabbeeeeeeeed eeeeaaabeeeeeeeeed eeebaaaeeeeeeeeeed eebbaaaeeeeeeeeeed eebbaaaeeeeeeeeeed eeebaaaeeeeeeeeeed eeedaaaeeeeeeeeeed eeefaaaeeeeeeeeeed eeefaaaeeeeeeeeeed eeefaaaeeeeeeeeeed eeeaaafeeeeeeeeeed eeeaaafeeeeeeeeeed eeeaaadeeeeeeeeeed eeeaaadeeeeeeeeeed eeeaaaeeeeeeeeeeed eeeaaaeeeeeeeeeeed eeeaaaeeeeeeeeeeed eeeaaaeeeeeeeeeeed eeeaaaeeeeeeeeeeed eedaaaeeeeeeeeeeed eefaaaeeeeeeeeeeed eefaaaeeeeeeeeeeed eefaafeeeeeeeeeeed eeaaafeeeeeeeeeeed eeaaafeeeeeeeeeeed ddaaadddddddddddde aaag aaa ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#492cbdff b,#7dd37dff c,#9384d6ff d,#bbb0e6ff e,#ace2acff f,#6b5cc2ff g,#dde0ebff ``` ```image faaaaac faaaaac aaaaaac aaaaaad gaaaaaad gaaaaaad gaaaaaag daaaaaag daaaaaa caaaaaa caaaaaf caaaaaf faaaaaf faaaaac faaaaac aaaaaac aaaaaad gaaaaaad gaaaaaag daaaaaag daaaaaag b daaaaaa eb caaaaaa ebb caaaaaf ebbb caaaaaf ebbbb faaaaaf ebbbbb faaaaac ebbbbbb aaaaaac ebbbbbbb aaaaaad ebbbbbbbb aaaaaad ebbbbbbbbg gaaaaaad ebbbbbbbbe gaaaaaag ebbbbbbbbe daaaaaag gbbbbbbbbe daaaaaa gbbbbbbbbe daaaaaa gbbbbbbbbe caaaaaa gbbbbbbbbe caaaaaf gbbbbbbbbe caaaaafgbbbbbbbbe faaaaafbbbbbbbbe faaaaafbbbbbbbe aaaaaafbbbbbbe aaaaaafbbbbbb aaaaaabbbbbb gaaaaaabbbbb gaaaaaabbbb daaaaaabbbg caaaaaabbg efaaaaaabg ebfaaaaaag ebbfaaaaaf ebbbfaaaaaf gbbbbfaaaaac ebbbaaaaaac ebbaaaaaac ebaaaaaad eaaaaaad gaaaaaag gaaaaaag daaaaaag daaaaaa caaaaaa caaaaaf caaaaaf faaaaaf faaaaac faaaaac aaaaaad aaaaaad gaaaaaad gaaaaaag daaaaaag daaaaaa daaaaaa caaaaaa caaaaaf caaaaaf faaaaac faaaaac aaaaaac aaaaaad aaaaaad gaaaaaad gaaaaaag daaaaaag daaaaaa daaaaaa caaaaaa caaaaaf faaaaaf faaaaac faaaaac aaaaaac aaaaaad gaaaaaad ``` <!-- end of image --> I can confirm that 1 intersection exists in area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#492cbdff b,#7dd37dff c,#9d8edbff d,#c5bce9ff e,#afe4aeff f,#735ecaff g,#e3eceaff ``` ```image ca caaaaa daaaaaaaaad dfaaaaaaaaaaac gfaaaaaaaaaaafg gcaaaaaaaaaaafd caaaaaaaaaaafd caaaaaaaaaaaad dfaaaaaaaaaaac dfaaaaaaaaaaacg gfaaaaaaaaaaafg gcaaaaaaaaaaafd caaaaaaaaaaafd daaaaaaaaaaaac dfaaaaaaaaaaac dfaaaaaaaaaaacg gfaaaaaaaaaaafg caaaaaaaaaaafd caaaaaaaaaaaad daaaaaaaaaaaac aaaaaaaaaaac aaaaaaacg gaaafg daaa caaa faaf faac aaac aaad aaag aaa aaa aaa aaa gaaa daaa daaa caaf bbbbeg faaf bbbbbbbbbbbbeg faac bbbbbbbbbbbbbbbbbbbbegg aaad bbbbegebbbbbbbbbbbbbbbbbbbbbeeg aaad bbbbb gebbbbbbbbbbbbbbbbbbbbbeeg aaag bbbbb gebbbbbbbbbbbbbbbbbbbbbeeg aaa ebbbb geebbbbbbbbbbbbbbbbbbbbeeg aaa ebbbb geebbbbbbbbbbbbbbbbbbbbeeg aaa ebbbb geebbbbbbbbbbbbbbbbbbbbeeg aaa ebbbb geebbbbbbbbbbbbbbbbg gaaa ebbbb geebbbbbbbbb daaa gbbbb geebb caaa gbbbb caafgbbbb faafbbbb aaafbbb aaabbb aaabbg aaabg baaag bbaaa bbaaa baaa gaaa daaa caaa faaf faac aaac aaad aaag aaa aaa aaa aaa aaa daaa daaa caaa faaf faac aaac aaad aaag aaa ``` <!-- 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 zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#a23c40ff b,#6b3e03ff c,#e3d0cbff d,#b1d7b1ff e,#ba9b8bff f,#a0745bff g,#99c795ff ``` ```image bbc cbba bbbb bbbb bbbbb bbbbbc fbb bbf bbb bbb fbbc bbb bbb ebb c ebbc cbb aaa bbb bbe eaae cbbe bba aaa bbb bbb caaa cbbe fbb aaac bbb c aaa bbf eaae bbb aaa bbb aaa fbb faac bbb aaa fbbc caaf bbb aaa ebbc aaa bbb eaac cbbe aaa bbb caaf cbbe aaa bbb aaa bbf eaae bbb aaa bbb caaa fbb faac ggggggggggggggggggggggggggbbbgggg aaa dddddddddddddddddddddddddfbbgdddd eaae dddddddddddddddddddddddddbbbddddd aaa ddddddddddddddddddddddddfbbgddddd aaa ddddddddddddddddddddddddbbbdddddd faac ddddddddddddddefdddddddebbfdddddd aaa ddddddddddddddaaaddddddbbbddddddd caaf dddddddddddddeaaaeddddgbbfddddddd aaa dddddddddddddaaaaaddddbbbdddddddd aaa dddddddddddddaaaaaadddbbfdddddddd eaae ddddddddddddgaaeeaaadbbbddddddddd aaa ddddddddddddfaaddaaafbbbddddddddd caaf ddddddddddddaaadddaabbbdddddddddd aaac ddddddddddddaaeddddabbbdddddddddd aaa dddddddddddfaadddddabbadddddddddd eaae dddddddddddaaadddddbbbafddddddddd aaa dddddddddddaafddddfbbaaaddddddddd aaa ddddddddddeaadddddbbbdaaadddddddd faac ddddddddddaaaddddebbfdeaaaddddddd aaa ddddddddddaafddddbbbdddaaafdddddd caae dddddddddeaagdddgbbfddddaaadddddd aaa dddddddddaaaddddbbbddddddaaaddddd aaa dddddddddaaaddddbbfddddddeaaadddd faac dddddddddaaedddbbbddddddddaaafddd aaa ddddddddfaaddddbbbdddddddddaaagdd caaf ddddddddaaadddbbbdddddddddddaaadd a aaa ddddddddaafdddbbbdddddddddddeaaad fbbd aaa dddddddeaadddfbbgddddddddddddaaaf bbbbb eaae dddddddaaadddbbbddddddddddddddaaac cbbbbf aaa dddddddaafddfbbgdddddddddddddddaaa faa fbbbbc caaa ddddddeaadddbbbddddddddddddddddeaaa aaa bbbbb aaacddddddaaaddebbfdddddddddddddddddaaae aaa ebbbbe aaaddddddaaaddbbbdddddddddddddddddddaaac aaa bbbbb eaafddddgaaedgbbfddddddddddddddddddd aaa aaf cbbbbf aaaddddfaaddbbbdddddddddddddddddddd caaa aae fbbbbc aaadddaaaddbbfdddddddddddddddddddd faae aae bbbbb faaeddaaedbbbddddddddddddddddddddd aaac aac ebbbbe aaadfaaddbbbddddddddddddddddddddd aaa aa bbbbb eaafaaadbbbdddddddddddddddddddddd caaa caa cbbbbf daaaaafdbbbdddddddddddddddddddddd faaeeaa fbbbbc ddaaaadfbbgdddddddddddddddddddddd aaafaa bbbbb ddfaaadbbbddddddddddddddddddddddd aaaaa ebbbbe gggaaffbbgggggggggggggggggggggggg caaaa bbbbb e bbb faaa cbbbbf dbbe aaf fbbbbbbbbbbbbbbbb c bbbbbbbbbbbbbbe dbbbbfffeedc ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#a33b40ff b,#6a3d01ff c,#d4b2adff d,#e9dad6ff e,#bf8d84ff f,#ac695fff g,#815a28ff ``` ```image dbbbbbe fbbbbb dbbbbbe fbbbbbd dbbbbbf ebbbbbd bbbbbf ebbbbbd gbbbbg cbbbbbc gbbbbg cffd cbbbbbc daaaad gbbbbg faaaaad dbbbbbe aaaaaaf fbbbbb caaaaaaac dbbbbbe eaaaaaaaad fbbbbbd aaaaaaaaaad dbbbbbf daaaaaaaaaaf ebbbbbd eaaaaffaaaaae bbbbbf faaaaedaaaaaad ebbbbbd daaaaad caaaaaad gbbbbg caaaaa eaaaaaf cbbbbbc faaaae faaaaaegbbbbg aaaaac daaaaaabbbbbc caaaaa caaaabbbbbg eaaaaf eaaabbbbbe aaaaac fabbbbbb daaaaad dabbbbbf eaaaaf gbbbbbad aaaaac dbbbbbbaf daaaaad ebbbbbaaae caaaaa bbbbbbaaaac faaaae ebbbbbaaaaaad daaaaad gbbbbgeaaaaaf caaaaa cbbbbbc faaaaae faaaae gbbbbg daaaaaac aaaaac cbbbbbc caaaaaad caaaaa gbbbbg eaaaaaf eaaaaf dbbbbbe faaaaae aaaaac fbbbbb daaaaaac daaaaad dbbbbbe caaaaaad eaaaaf fbbbbbd eaaaaaf faaaae dbbbbbf faaaaae daaaaad ebbbbbd daaaaaac caaaaa bbbbbf caaaaaad faaaae ebbbbbd eaaaaaf aaaaac gbbbbg faaaaae caaaaa cbbbbbc daaaaaac eaaaaf gbbbbg caaaaaad aaaaac cbbbbbc eaaaaaf daaaaad gbbbbg faaaaae eaaaaf dbbbbbe daaaaaac faaaae fbbbbb caaaaaad daaaaad dbbbbbe eaaaaaf caaaaa fbbbbbd faaaaa faaaae dbbbbbf daaaaa daaaaad ebbbbbd caaaa caaaaa bbbbbf eaaa faaaae ebbbbbd faa aaaaac gbbbbg daa caaaaa cbbbbbc ca eaaaaf gbbbbg e aaaaac cbbbbbc daaaaad gbbbbg c eaaaaf dbbbbbe a faaaae fbbbbb ae daaaaad dbbbbbe aad caaaaa fbbbbbd aaf faaaae dbbbbbf aaac aaaaac ebbbbbd aaaad caaaaa bbbbbf aaaae eaaaaf ebbbbbd aaaaad aaaaac gbbbbg aaaaaf daaaaad cbbbbbc eaaaaac eaaaaf gbbbbg aaaaaad faaaae cbbbbbc caaaaafdaaaaad gbbbbg faaaaafaaaaa dbbbbbe daaaaaaaaaae fbbbbb eaaaaaaaaac dbbbbbe faaaaaaaa fbbbbbd daaaaaaae dbbbbbf eaaaaaac ebbbbbd ``` <!-- end of image --> As I suspected, there's 1 intersection within area A. Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#a33b40ff b,#6a3d01ff c,#d3b4adff d,#e9dbd8ff e,#bf9086ff f,#ab6a5eff g,#815a28ff ``` ```image bbc dbbg bbbb bbbb gbbbb bbgbbc gbb bbf bbb bbb fbbd gbb bbb ebb dd ebbc dbbd aaa bbb bbe eaac cbbc bbg aaa bbb bbb daaf dbbe fbb faad bbb d aaa bbf caae gbb aaa bbg aaa gbb faad bbb aaa fbbd caaf bbb aaa ebbd aaa bbb eaac cbbc aaa bbb daaf dbbe aaad bbb aaa bbf eaae gbb aaa bbg daaa gbb faad bbb aaa fbbd caae bbb aaa ebbd aaa bbb faac cf cbbc aaa aaa bbb caaf caaae dbbe aaa aaaaad bbb aaa aafaaa bbf eaac daadcaaa gbb aaa faa faaebbg daaf aaa aabbb aaad aac abbb aaa eaa gbba eaae aaa bbbae aaa aae ebbaaad daaa caa bbb aaa faad aaa cbbc caaa aaa aaf bbb faae caae daad dbbe aaad aaa faa bbb aaa aaa aaa bbf caaa faac aac gbb faae aaa eaa bbg aaad daaf aaa gbb aaa g aaa aae bbb caaa ebbc aaa caa fbbd faae bbbbb eaac aaa bbb aaad cbbbbf aaa aae ebbd aaa faa gbbbbd daaf caad bbb caaa aaa bbbbg faad aaa cbbc faae aaa ebbbbc aaa aaf bbb aaad aaa gbbbb caae daad dbbe aaa aaf dbbbbf aaa faa bbb caaa aae fbbbbd aaa aaa bbf faae aac bbbbg faad aac gbb aaad aad ebbbbe aaa eaa bbg aaa daad gbbbb caafaaa gbb caaa daa dbbbbf aaaaae bbb faaecaa fbbbbd aaaa fbbd aaafaa bbbbg eaaa bbb aaaaa cbbbbe aafebbd caaaa gbbbb c bbb faaa dbbbbg cbbc aaf fbbbbbbbbbbbbbbbb d bbbbbbbbbbbbbbe cbbbggffeccd ``` <!-- end of image -->
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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,#c6da98ff b,#93ba3dff c,#dbe3cbff d,#f4ebf1ff e,#b1d7b1ff f,#a5c666ff g,#9bcb93ff ``` ```image dd dd dd dd dd dd dd dd dd dd b dd b dd f dd da dd ad dd f dd b dd b dd f dd da dd ad dd f dd b dd b dd f dd cc dd a dd b dd b dd b dd f dd cc dd a dd b dd b dd b dd a dd cc dd f dd b dd b dd b dd da dd ac dd f dd b dd b dd f dd da dd ad dd f dd b dd b dd ddddddddddddddfdddddddd dd dgeeeeeeeeeeeegfeeeeeeeeg dd deeeeeeeeeeeeefeeeeeeeeeg dddeeeeeeeeeeeeebeeeeeeeeeg ddeeeeeeeeeeeeebeeeeeeeeeg ba dceeeeeeeeeeeebeeeeeeeeeg ab dcceeeeeeeeeeefeeeeeeeeeg ba decceeeeeeeeeggeeeeeeeeeg cbd deecceeeeeeeefeeeeeeeeeeg ff deeecceeeeeeebeeeeeeeeeeg dbc deeeecdeeeeeebeeeeeeeeeeg ff deeeeecdeeeeebeeeeeeeeeeg dbc deeeeeecdeeeefeeeeeeeeeeg ab deeeeeeeedeeggeeeeeeeeeeg ba deeeeeeeeedefeeeeeeeeeeeg ab deeeeeeeeeedbeeeeeeeeeeeg ba deeeeeeeeeeebeeeeeeeeeeeg cbd deeeeeeeeeeebdeeeeeeeeeeg ff deeeeeeeeeeefedeeeeeeeeeg cbd deeeeeeeeeeggeedeeeeeeeeg ff deeeeeeeeeefeeeedeeeeeeeg dbc deeeeeeeeeebeeeeedeeeeeeg ab deeeeggggffbeeeeeedeeeeeg ba dcccaaafffbbbbbbbbbbfbffffgggeeeeeeeeeedeeeeg abbbfffaaaccdd deeeeeeeeeeeeeeeeeeedeeeg deeeeeeeeeeeeeeeeeeeedeeg deeeeeeeeeeeeeeeeeeeeedeg deeeeeeeeeeeeeeeeeeeeeeeg deeeeeeeeeeeeeeeeeeeeeeeg deeeeeeeeeeeeeeeeeeeeeeeg ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#c0d68dff b,#93ba3dff c,#e5edd0ff d,#f3def1ff e,#d2e1afff f,#aac866ff g,#f8f0f5ff ``` ```image gba cbe ebc abg fb bf gba cbe g ebc dg abg ddg ff gdd bf gdd gba gdd cbe gdd ebc gdd ab gdd ff gdd ba gdd gba gdd cbe gdd ebc gdd ab gdd ff gdd ba gdd cbe gdd ebc gdd abg gddg fb gddg ff ddgba dcbe ebc abdg fbddg bf ddg gba ddg cbe ddg ebc ddg abg ddg fb ddg bf ddg gba ddg cbe ddg gggcccceeeeaaafbc ddg ffbbbbbbbbbbbbbbbbbbbf ddg ffffaaaaeeeecccccgg gdd gdd gdd gdd gdd gdd gdg g ``` <!-- end of image --> As I suspected, there's 1 intersection within area A. Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#bad283ff b,#93ba3dff c,#dde9c3ff d,#f6e6f4ff e,#ccdea4ff f,#a7c660ff g,#eff4e2ff ``` ```image dd dd dd dd dd dd dd dd dd dd b dd b dd f dd ge dd eg dd f dd b dd b dd f dd ge dd eg dd f dd b dd b dd f dd ce dd a dd b dd b dd b dd a dd cc dd a dd b dd b dd b dd a dd cc dd a dd b dd b dd f dd ga dd eg dd f dd b dd b dd f dd ge dd eg dd f dd b dd b dd f dd ge dd ag dd b dd b be dd b eb dd a ba dd cc cbg dd a ff dd b gbg dd b ff dd b gbc d a ab d cc be d a eb db ba b cbg bd ff a d gbg ec d ff f d gbc b d ab ggcceeab d be ggcceeaaffbbbbbbbbbbffaaeeccgg d ebbbffaaeeccgg d d d ``` <!-- 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,#baf589ff b,#93ecd6ff c,#d5f9b8ff d,#e4faeaff e,#b2f2e2ff f,#b1d8b1ff g,#96ca95ff ``` ```image fggggggggggggggggggggggf gffbbffffffffffffffffffg gffafffffffffffffffffffg gffaabfffffffffffffffffg gffaabbffffffffffffffffg gffaabbbfffffffffffffffg gffaaabbbffffffffffffffg gfffaafbbffffffffffffffg dccaaaaa gfffaafbbbfffffffffffffg dcaaaaaaaaaaaa gfffaaffbbbfffffffffffaaaaaaaaaaaaaccd aa gfffaafffbbbffffaaaaaaaaaaaaacd aa gffffaaffaaaaaaaaaaaaaag aa gffffaaaaaaaaaaafffffffg aa gffffaaaaafbbbfffffffffg aa gfffffffffffbbbffffffffg aa gffffffffffffbbbfffffffg aa gfffffffffffffbbfffffffg aa gffffffffffffffbbffffffg aa gffffffffffffffbbbfffffg aa gfffffffffffffffbbbffffg aa gffffffffffffffffbbbfffg aad gfffffffffffffffffbbfffg aad gffffffffffffffffffbbffg aad gffffffffffffffffffbbbfg cac fgggggggggggggggggggbbbf cac bbe cac bbd cac dbb caad ebb daaaaaacd bbb dcaaaaaaaaacc bbe dcaaaaaaaaaacd bbd caaaaaaaaaacd dbb dcaaaaaaaaacc ebb dcaaaaaaaaaacd bbb caaaaaaaaaacd bbe dcaaaaaaaaa bbd dcaaac dbb ebb bbb bbe bbd dbb ebb bbb bbe bbd dbb ebb bbb bbe dbbd ebb bbb bbb bbbd bbbb dbbbd bbbe ebbb bbbe ebbb bbbd ebbb dbbbd bbbe dbbb bbbe ebbb bbbe ebbb dbbbd bbbb dbbbd bbbe dbbb bbbe ebbb bbbe ebbb dbbb 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,#baf588ff b,#93edd6ff c,#c1f6a5ff d,#ecfce0ff e,#b1f1e1ff f,#daf9c0ff g,#d9f8f0ff ``` ```image ee ebbe ebbbbg dcaacbg faaaabb daaaabbe aaaabbbe caaacbbbg faaaabbbbg daaaabbbbb aaaaebbbbe caaafebbbbe faaac bbbbbg daaaa gbbbbbg aaaad gbbbbb caaaf ebbbbe faaac ebbbbg daaaa bbbbbg ddfc aaaad gbbbbb ddffcaaaaaa caaaf gbbbbb dffcaaaaaaaaaaaaa faaac ebbbbcfccaaaaaaaaaaaaaaaaaaa daaaa ddffcaaaaaaaaaaaaaaaaaaaaaaaccf aaaacaaaaaaaaaaaaaaaaaaaaaaccffd caaaaaaaaaaaaaaaaaaaacffdd faaaaaaaaaaaaaacccd daaaaaaacffddebbbbe dffdd ebbbbg bbbbbg gbbbbb gbbbbe ebbbbe ebbbbg bbbbbg gbbbbb gbbbbe ebbbbe ebbbbg bbbbbg gbbbbb gbbbbe ebbbbe ebbbbg bbbbbg gbbbbb gbbbbe ebbbbe bbbbbg ``` <!-- end of image --> I can confirm that 1 intersection exists in area A. Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#baf589ff b,#92edd7ff c,#d1f8afff d,#e5fbd3ff e,#abf0dfff f,#edfbf2ff g,#ccf6ebff ``` ```image fbg daaf faab aabb aabbe cacbbg daafbbf fdcaaaaa aa gbb dcaaaaaaaaaaaa aa bbb fcaaaaaaaaaaaacdf aa cad bbe fdcaaaaaaaaaaaacd aa daa dcaaaaaaaaaaaacd aa aaaaaaaaaacdf aa aaaacdebb aa bbb aa bbe aa bbg aa fbbf aa ebb aa bbb aaf bbe aaf bbg aad fbbf cad ebb cad bbb cad bbe cac bbg cac gbbf daaf ebb daaaaaacd bbb dcaaaaaaaaacd bbe fcaaaaaaaaaacf bbg daaaaaaaaaacd gbb dcaaaaaaaaacd ebb fcaaaaaaaaaacf bbb dcaaaaaaaaacd bbe dcaaaaaaaaa fbbg fcaaac gbb ebb bbb bbe fbbf gbb ebb bbb bbe fbbf gbb ebb bbb bbe fbbf gbb ebb bbb bbbf bbbe gbbbf bbbe gbbb bbbg ebbb fbbbg ebbb fbbbf bbbe gbbbf bbbe gbbb bbbg ebbb fbbbg ebbb fbbbf bbbe gbbbf bbbe gbbb bbbg ebbb fbbb e ``` <!-- end of image -->
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Time to put on my detective hat and find those intersection points! My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#e70786ff b,#69bfd7ff c,#f6a5d3ff d,#b5dfebff e,#e359a6ff f,#b0d7b1ff g,#95c995ff ``` ```image bb bbb gfffffffffffffbbffff gfffffffffffffbbffff gfffffffffffffbbffff gffffffffffffbbbffff gffffffffffffbbfffff gffffffffffffbbfffff gfffffffffffbbbaffff gfffffffffffbbaaafff gfffffffffffbbaaffff gfffffffffffbaaeffff gffffffffffbaaafffff gffffffffffeaaffffff gffffffffffaaeffffff gfffffffffaaafffffff gffffffffaaaffffffff gffffffffaabffffffff gfffffffaaebffffffff gffffffaaabbffffffff gfffffeaabbfffffffff gfffffaaebbfffffffff gffffaaafbbfffffffff gfffeaafbbbfffffffff gfffaaffbbffffffffff gffaaaffbbffffffffff gfaaaffbbbffffffffff geaafffbbfffffffffff gaaefffbbfffffffffff aaaffffbbfffffffffff eaaffffbbbfffffffffff aaeffffbbffffffffffff aaafffffbbffffffffffff eaagfffffbbffffffffffff caa gffffbbbffffffffffff aae gffffbbfffffffffffff aaa gffffbbfffffffffffff caa gfffbbbfffffffffffff aac bbd aaa bb eaa dbb aac bbd aae bb ac aaa bb caaaae caa dbb eaaaaaaac aae bbd caaaaaaae aaa bb eaaaaaaac eaa bb caaaaaaaec aac bbb eaaaaaaae aaa bbd ceaaaaaaac aaa bb caaaaaaae caa dbb eaaaaaaac aae bbd caaaaaaae aaa bb eaaaaaaac caa bb caaaaaaaec aac dbb caaaaaaaa bbd ceaaa bb dbb bbd bb d bb dbbbbd dbb dbbbbbbbd bbd bbbbbbbd bb dbbbbbbbd bb dbbbbbbbd dbb dbbbbbbb bbd dbbbbbbbd bb bbbbbbbd dbb dbbbbbbbd bbd dbbbbbbbd bb dbbbbbbb bb dbbbbbbbd dbb bbbbbbbd bbd dbbbbbbbd bb dbbbbbbbd bb dbbbbbbb bbb dbbbbbbbb bbbbb dd ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#e70686ff b,#68bed7ff c,#f389c5ff d,#9acde1ff e,#dc45a3ff f,#facce6ff g,#c9e8f0ff ``` ```image bbbbg gbbbbg dbbbb bbbbd bbbbg gbbbb dbbbb bbbbd gbbbbg dbbbb dbbbd bbbbg gbbbbgf dbbbbcac bbbbdaaaef gbbbbaaaaac gbbbeaaaae dbbbaaaaaf bbbaaaaaf gbbeaaaae dbeaaaaa bbaaaaaf baaaaac geaaaae daaaaaf aaaaac eaaaae caaaaa faaaaad eaaaaeg caaaaebg faaaaabb aaaaaebd eaaaaebbg caaaaabbb faaaaabbbd eaaaaebbbd caaaaabbbbg faaaaadbbbb eaaaacbbbbd caaaae bbbbg faaaaafgbbbb aaaaac dbbbb eaaaae bbbbd caaaaa gbbbbg faaaaaf gbbbb eaaaac dbbbd caaaae bbbbg faaaaaf gbbbbg aaaaac dbbbb eaaaae bbbbd caaaaa bbbbg faaaaaf gbbbb eaaaac dbbbb caaaae bbbbd faaaaaf gbbbbg eaaaac dbbbb aaaae dbbbd aaaaf bbbbg aaac gbbbbg aae dbbbb aa bbbbd af gbbbbg c gbbbb dbbbd bbbbd gbbbbg dbbbb bbbbd bbbbg gbbbb ``` <!-- end of image --> Area A contains 1 intersection. Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#e80685ff b,#67bfd8ff c,#f491c9ff d,#99d4e4ff e,#ea4ba7ff f,#f9cbe5ff g,#ceeaf2ff ``` ```image gbb dbd bbg bb gbb bbd bb bb dbba bbaaa bbaaf gbaae baaa eaa aac aaa eaag faab aaeb aaabd caabbg aacbb aaagbb eaa bbd faaf bb aae bb aaa dbb caa bbg aae bb aaa gbb eaa dbd aac bbg aaa bb eaa gbb faaf bbd aae bb aaa bb caa dbb aac bbg aaa bb eaa gbb faaf bbd aae bb ef aaa bb caaaae caa dbb feaaaaaaac aae bbg caaaaaaaef aaa bb eaaaaaaac eaa gbb faaaaaaaef faac dbd caaaaaaac aaa bbg feaaaaaaaf eaa bb caaaaaaae faaf gbb feaaaaaaac aae bbd caaaaaaaef aaa bb eaaaaaaac caa bb feaaaaaaef aac dbb caaaaaaaa bbg feaaa bb gbb bbd bbg d bb gbbbbg dbb gbbbbbbbg bbd dbbbbbbd bb dbbbbbbbg bb gbbbbbbbd dbb dbbbbbbbg bbg gbbbbbbbg bb gdbbbbbbd gbb dbbbbbbbg bbd gbbbbbbbd bb dbbbbbbdg bb gbbbbbbbg dbb gdbbbbbbd bbg dbbbbbbbg bb gbbbbbbbd gbb dbbbbbbdg dbd gbbbbbbbbg gdbbbb dg ``` <!-- 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'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#6f8954ff b,#e1d3a0ff c,#466422ff d,#c9b560ff e,#b1d7b0ff f,#99c593ff g,#f0f2e8ff ``` ```image g c a ee a c a eg c c a fg gggggggggggggggg c eeeeeeeeeeeeeeeef c eeeeeeeeeeeeeeeef gf eeedeeeeeeeeeeeef fg eeedeeeeeeeeeeeef c eeefeeeeeeeeeeeef c eeeeeeeeeeeeeeeef gf eeeefeeeeeeeeeeef a eeeedeeeeeeeeeeef c eeeedeeeeeeeeeeef c eeeedeeeeeeeeeeef ge eeeedeeeeeeeeeeef a eeefdeeeeeeeeeeef c eeefdcfeeeeeeeeef a eeeedefcceeeeeeef ee eeeefeeeeacaeeeef a eeeeefeeeeeeacfef c eeeeedeeeeeeeefccg a eeeeedeeeeeeeeeeffca ee eeeeedeeeeeeeeeef acf a eeeeedeeeeeeeeeef gccg c eeeeedeeeeeeeeeef fca a eeeeedeeeeeeeeeef acf eg eeeeeedeeeeeeeeef gcce c eeeeeeffeeeeeeeef ecag c eeeeeeedeeeeeeeef fcf a ffffffffdfffffffe gac fg bg c c d c c d c gf bg c fg d c c d gb c c bg dg c gf d d c gc d gb c gc gb d c gc d d c gc bg bb c gc d d c gc d d c gc gd bg c gc d d c gc bb d c gc d bg c gc bg d c gc d gb c gc d d c gc gb d c gc d gb ecffffffffffffffc bg d fceeeeeeeeeeeeecg d d fceeeeeeeeeeeeceg d bb fceeeeeeeeeeeceeg gb d fceeeeeeeeeeceeeg d d fceeeeeeeeeceeeeg bdg bg faeeeeeeeeceeeeeg gddg d faeeeeeeeceeeeeeg bdb d faeeeeeeceeeeeeeg bdb bg faeeeeeceeeeeeeeggddg d faeeeeceeeeeeeeddb gb faeeeceeeeeeeddfg d faeeceeeeeddfeeeg d faeceeefddeeeeeeg gb faceeddeeeeeeeeeg d ffdddeeeeeeeeeeeg d gddeeeeeeeeeeeeeeg bb bdbefffffffffffffff db ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#7b8e5bff b,#d9c887ff c,#496626ff d,#cab35bff e,#ddd8b5ff f,#a1b08fff g,#efedddff ``` ```image db bb bd bd ed edg gdg gde de de db bb bd ed ed edg gdg gde egde ccddg gfdacae bdfcccfg bd eaccafg ed gfaccae edg gfcccfe gdg eacccfg gdg gfaccae gde gfcccae de eacc db f bb bd bd ed edg gdg gde de dd gde bdg db ede bdg gdb ``` <!-- end of image --> I observe 1 intersection inside area A. 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,#5f7940ff b,#dbcb8dff c,#43611eff d,#ccb45cff e,#eae2c2ff f,#798f5fff g,#b3bfa4ff ``` ```image af af af f af fc af fcg af fcg af fcg af fcg af fcg af fcg af fcg af fcg af fcg af fcg ff fcg ff fcg ff fcg fa fcg fa fcg fa fcg fa fcg fa fcg b fa fcg ebdd fa fcg ebddde fa fcg edddbe fa fcg ebddbe fa fcg bdddb fa fcg ebddbe fafcg ebddde fccg edddbe fcg ebddbe egbdddb ebddbe ddde ``` <!-- end of image --> I had hoped to find an intersection in area B, but there isn't one. Answer: A: 1; B: 0; 1 + 0 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#6c834fff b,#d2c68fff c,#456321ff d,#ccb45dff e,#ddd7b3ff f,#94a57fff g,#efeee0ff ``` ```image g c a ee a c a bg c c f fg c c f d f b c e c gg gf e f b c d c d gb d a ed c gdce a b ecag ee eg fcf a gg gace c e ecag a b fcf ee d acb a d eccg c d bca a d fcf bg d gace c ee bcag c d fcf f d gac fg eg c c d c c d c f bg c f d c c d gb c c bg b c gf d d c gc d ge c gc gb d c gc d d c gc eg ee c gc d d c gc d d c gc b eg c gc d d c c ee d c c d bg c c bg d c c d gb c c d d c c ge d c c d ge c c bg d c c d d a c d ee a c gb d a c d d a c edg eg a c gddg d a c bde d a c edb bg a c ddg d a c ede gb a c gddg d f c bde d f c edb ge fc gddg d gede d gdd ee bde db ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#a084aeff b,#47fc5aff c,#c9bad1ff d,#72f880ff e,#b1d9b2ff f,#a2cca3ff g,#ecf1edff ``` ```image ag ag ga bbbddegg ca bbbbbbbbbbbbbbbbddeeg ca ggeeddbbbbbbbbbbbbd aa geedbg aa bb ac bb ag ebe ga dbg ggggggggggggcaggggg bb gffffffffffffaafffff bd gfeeeeeeeeeeeaaeeeee ebe gfeeeeeeeeeeeaaeeeee db gfeeeeeeeeeeeaaeeeee bb gfeeeeeeeeeeeafeeeee gbd gfeeeeeeeeeeeaeeeeee ebe gfeeeeeeeeeefaeeeeee bb gfeeeeeeeeeefaeeeeee bb gfeeeeeeeeeeaaeeeeee gbd gfeeeeeeeeeeaaeeeeee dbg gfeeeeeeeeeeaaeeeeee bb gfeeeeeeeeeeafeeeeee bb gfeeeeeeeeeeafeeeeee gbddddddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdfeee dbbbbbbbbbbbbbbbbbbbddddddddddddddddbbbbbfeee gfeeeeeeeeeaaeeeeeee gfeeeeeeeeeaaeeeeeee gfeeeeeeeeeaaeeeeeee gfeeeeeeeeeaaeeeeeee gfeeeeeeeeeafeeeeeee gfeeeeeeeeeaeeeeeeee gfeeeeeeeefaeeeeeeee gfeeeeeeeeaaeeeeeeee gfeeeeeeeeaaeeeeeeee gfeeeeeeeeaaeeeeeeee gfeeeeeeeeaaeeeeeeee gfeeeeeeeeafeeeeeeee gfeeeeeeeeafeeeeeeee fffffffffafffffffff ca ca cg aa aaac aa gaaccac ac caa caa ag aac caa a gaag gaa ga aaa gaa ca aac aag aa caa aag aa aaa aac ac gaag aac ac caa cac ag aac caa ga caag caa ca aaa gaa ca gaac gaa aa caa aag aa aac aagac gaag aaag aaa aa aac caa aaa gaag caa aac gaag aaa gaac caa aaa gaag caa aac caag aaa gaac aa c ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#9e82adff b,#46fc59ff c,#cbbcd3ff d,#8bfd97ff e,#aefdb6ff f,#b49ec0ff g,#e3e4e7ff ``` ```image caac caac faag aaag aaa gaaa gaaf caaf caac faag faag aaa aaa gaaf gaaf caac caac faag aaag aaa gaaa gaaf caac caac faag faag eeeeeeeeeeedddddeeeeggaaa bbbbbbbbbbbbbbbbbbbbbbbbbbbddddg bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbg dddddddddddeeeeeddddbbbbbbbbbbbg caacggeeee faac faag aaag aaa gaaa gaaf caac caac faag faag aaa gaaa gaaf caaf caac faac faag aaag aaa gaaf gaaf caac caac faag aaag ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#9e82adff b,#47fc5aff c,#d2c4d9ff d,#74fd82ff e,#a8fdb1ff f,#b59fc0ff g,#e7eaeaff ``` ```image fg ag ga bbbdeegg ca bbbbbbbbbbbbbbbbddeeg fa ggeeddbbbbbbbbbbbbe aa geedbg af bb ac bb ag ebe a db ca bb fa bb aa ebe aa db af bb ac bd ag ebe ga bb ca bb fa gbd aa ebg af bb ac bb ag gbddddddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddg dbbbbbbbbbbbbbbbbbbbdddddddddeeeeeddbbbbbg fa aa aa af ac a ga ca fa aa af ac ag ga ca fa cg aa aaac af gaacfaf ac faa caf ag aaf caa a gaag gaa ga faa aa ca aac aa fa caa aag aa aaf aac af gaag fac ac faa faf ag aaf caa ga caag caa ca faa gaa fa gaac aa aa caa aag af aaf aagac gaag aaag faa fa aac caa aaf gaag faa aaf caag faa aac caa aaf gaag faa aac caa aaf gaac aa c ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#134664ff b,#08a990ff c,#6a9294ff d,#356777ff e,#4cbb9dff f,#b1d7b1ff g,#92c79bff ``` ```image ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgfffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdadffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaaaaffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaaadfffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaaaafffffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgaaaacffffffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdaaaaffffffffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaaaagfffffffffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaaadfffffffffffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaaaafffffffffffffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgaaaacffffffffffffffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdaaaaffffffffffffffffg fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaaaagfffffffffffffffffg ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaaadffffffffffggggeeeffg ffffffffffffffffffffffffffffffffffffffffffffffffggggeeeeeebbdaaaabbbbbbbbbbbbbbbbbbbffg ffffffffffffffffffffffffffffffffffffffffffebbbbbbbbbbbbbbbbaaaadbbbbbbbbbbbbbbbbbbbbffg ffffffffffffffffffffffffffffffffffffffgebbbbbbbbbbbbbbbbbaaaaabbeeeeeggggfffffffffffffg fffffffffffffffffffffffffffffffffffgbbbbbbbbgffffffffffdaaaagfffffffffffffffffffffffffg ffffffffffffffffffffffffffffffffebbbbbbbbgffffffffffcaaaaadfffffffffffffffffffffffffffg fffffffffffffffffffffffffffffebbbbbbbefffffffffffgaaaaaadfffffffffffffffffffffffffffffg fffffffffffffffffffffffffgebbbbbbbeffffffffffffdaaaaaagfffffffffffffffffffffffffffffffg ffffffffffffffffffffffgbbbbbbbbgffffffffffffcaaaaaacffffffffffffffffffffffffffffffffffg fffffffffffffffffffebbbbbbbbgfffffffffffffdaaaaadgffffffffffffffffffffffffffffffffffffg ffffffffffffffffebbbbbbbeffffffffffffffcaaaaaacfffffffffffffffffffffffffffffffffffffffg ffffffffffffgebbbbbbbeffffffffffffffgaaaaaadffffffffffffffffffffffffffffffffffffffffffg fffffffffgbbbbbbbbgfffffffffffffffdaaaaaagffffffffffffffffffffffffffffffffffffffffffffg ffffffebbbbbbbbgfffffffffffffffcaaaaaacfffffffffffffffffffffffffffffffffffffffffffffffg fffebbbbbbbefffffffffffffffffdaaaaadgfffffffffffffffffffffffffffffffffffffffffffffffffg ffbbbbbbefffffffffffffffffcaaaaaacffffffffffffffffffffffffffffffffffffffffffffffffffffg ffgbbgfffffffffffffffffgaaaaaadfffffffffffffffffffffffffffffffffffffffffffffffffffffffg fffffffffffffffffffffdaaaaaagfffffffffffffffffffffffffffffffffffffffffffffffffffffffffg ffffffffffffffffffcaaaaaacffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg ffffffffffffffffdaaaaadgffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg fffffffffffffcaaaaaacfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg ffffffffffgaaaaaadffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg ggggggggdaaaaaacggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggf gaaaac daa aaa aad aac aaf aa aa faa caa daa aaa aad aac aaf aa faa gaa caa daa aad aac aag aaf aa faa gaa caa aaa aad aac aaf aa aa faa caa daa aaa aad aac aaf aa aa faa caa caa ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#134764ff b,#08a990ff c,#7e9aaaff d,#476f86ff e,#4ec1afff f,#95cfcaff g,#cfe4e4ff ``` ```image f cag caaaa faaaaa caaaaag daaaaaf aaaaaag gdaaaaac daaaaaf caaaaag gdaaaaa aaaaadg aaaaaag gaaaaaa caaaaadg aaaaacg faaaaad caaaaad ggggffffe gaaaaacffffeeeeebbbbbbbbbbbbbb gfbbbbbbbbbbbbbbbbbbbbaaaaaabbbbbbbbbbbbbbbbbbbbbbbbb gebbbbbbbbbbbbbbbbbbbbaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbb febbbbbbbbbbbbbbbbbbbbbbaaaaaabbeeeeeffffgggg gbbbbbbbbbbbbbbeeeeefffffdaaaaac fbbbbbbbbbbe fdaaaaaac gfbbbbbbbbbef gcaaaaaaag ebbbbbbbbbbf gaaaaaaaad gebbbbbbbbbeg faaaaaaaac gebbbbbbbbbeg gaaaaaaaad fbbbbbbbbbbe caaaaaaaaf febbbbbbbbbfg cdaaaaaaacg ebbbbbbbbbbf gcaaaaaaaaf ebbbbbbbbbbg faaaaaaaacg gfbbbbbbbbbef gcaaaaaaadc gebbbbbbbbbef faaaaaaaac febbbbbbbbbfg daaaaaaaag febbbbbbbbbfg caaaaaaaad bbbbbbbbbbe daaaaaaaag ebbbbbbef caaaaaaaaf gbbef gcaaaaaaadf faaaaaaaacg gcaaaaaaadf gaaaaaaaad daaaaaaadg caaaaaaaad daaaaaaaag cdaaaaaaacg ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area A. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#134664ff b,#08a990ff c,#7c98a8ff d,#466e85ff e,#50c2b0ff f,#a4cdceff g,#d9e9e9ff ``` ```image g dad faaaa aaaad caaaag gaaaac daaaa faaaaf aaaad caaaag gaaaac daaaa faaaaf aaaad gggffffe gggfffeeeeebaaaaabbbbbbbbbbbbbbbbbbb ebbbbbbbbbbbbbbbbaaaaabbbbbbbbbbbbbbbbbbbb gebbbbbbbbbbbbbbbbbaaaaabeeeeffffggg fbbbbbbbbf gdaaaaf fbbbbbbbeg caaaaad ebbbbbbbe gaaaaaad gebbbbbbbf daaaaaaf fbbbbbbbbf faaaaaac fbbbbbbbeg gdaaaaadg ebbbbbbbe caaaaaaf gebbbbbbbf gaaaaaad fbbbbbbbbf daaaaaaf fbbbbbbbeg faaaaaac ebbbbbbbe gdaaaaadg ebbbbbf caaaaaaf gbbf gaaaaaad daaaaaaf faaaaaac gdaaaaadg caaaaaaf gaaaaaad daaaaaaf caaaac daag aaa aad aac aaf aag gaa faa caa daa aaa aad aac aaf aa gaa faa caa daa aaa aad aac aag aa faa caa daa aaa aad aac aaf aag gaa faa caa daa aaa aad aac aaf aag gaa faa caa caa ``` <!-- end of image -->
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Let's examine this image for potential line intersections. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#3f6b85ff b,#aec4c9ff c,#216968ff d,#6a9898ff e,#e7eeedff f,#b0d7b0ff g,#94c59aff ``` ```image be ccccccdbe ccccccccccccdbe dccccccccccccccccccdbe cccb bdcccccccccccccccccdb ccc bdcccccccccccccccccdb bccc bdcccccccccccccccccdb accd bdcccccccccccccccccdb ccce bdccccccccccccccccb eccc bdcccccccccc dcca ebdcccc cccb e ccc bccc dd cccg dccd ccc cccceccc dccccdcca cccccccce gcccccccc cccgccccc bccc ccccb cccd dccc bccc ccc cccd dce eccc cccd eccc ccca eccc ccca ccc accc ccce accc ccce dccc ggggggggggggggggggcccdgf fffffffffffffffffacccffg fffffffffffffffffcccgffg ffffffffffffffffdcccfffg ffffffffffffffffcccdfffg fffffffffffffffdcccffffg fffffffffffffffcccdffffg ffffffffffffffdcccfffffg ffffffffffffffcccdfffffg fffffffffffffgcccffffffg fffffffffffffcccdffffffg ffffffffffffgcccfffffffg ffffffffffffcccafffffffg ffdadffffffgcccffffffffg ffaaaaadfffcccaffffffffg ffaaaaaaaadcccfffffffffg fffdaaaaaaccccgffffffffg ffffffgaaacccaaaagfffffg fffffffffccccaaaaaaagffg fffffffffcccgaaaaaaaaaad ffffffffacccffffdaaaaaaaaab ffffffffcccgfffffffdaaaaaaaaad fffffffacccfffffffffffdaaaaaaaaade fffffffcccgffffffffffffg baaaaaaaaade ffffffacccfffffffffffffg baaaaaaaaaab ffffffcccgfffffffffffffg edaaaaaaaaab fffffdcccffffffffffffffg edaaaaaaaaab fffffcccdffffffffffffffg daaaaaaaaag ffffdcccfffffffffffffffg baaaaaaaaade ffffcccdfffffffffffffffg baaaaaaaaade fffdcccffffffffffffffffg baaaaaaaaaae fffcccdffffffffffffffffg eaaaaaaaaaab ffdcccfffffffffffffffffg edaaaaaaaaab ffcccdfffffffffffffffffg edaaaaaaaaab ggcccffffffffffffffffffg gaaaaaaaaad eeebdeeeeeeeeeeeeeeeeee baaaaaaaaade baaaaaaaaade baaaaaaaaaae edaaaaaaa edaaaaa eaaab daaa aaaa eaaab daa b ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#3f6b85ff b,#9db8beff c,#216968ff d,#5a8991ff e,#dfe8e9ff f,#7aa0a6ff g,#bdd0d3ff ``` ```image gccccccd dccccccg eccccccd dccccccg eccccccd fccccccg ecccccca fccccccg ecccccca fccccccb ecccccca bccccccb ccccccc bccccccb acccccc bccccccf acccccce bccccccf acccccce gccccccf dcccccce gccccccf dcccccce gccccccd dccccccg eccccccd ebe dccccccg baadbe eccccccd daaaaadbe fccccccg eaaaaaaaaadbg ecccccca baaaaaaaaaaaaafg fccccccg daaaaaaaaaaaaaaaafcccccca bdaaaaaaaaaaaaaaacccccccb ebdaaaaaaaaaaaacccccccbe egfaaaaaaaacccccccaaadbe gfaaaaacccccccaaaaaadbe gfaccccccccaaaaaaaaaafg cccccccaaaaaaaaaaaaaafg bcccccccaaaaaaaaaaaaaaaaafge accccccgbdaaaaaaaaaaaaaaaaaa bccccccf ebfaaaaaaaaaaaaaaa acccccce egfaaaaaaaaaaaa gccccccf gfaaaaaaaaa acccccce gfaaaaaa gccccccf ebdaa dcccccce eb gccccccd dcccccce gccccccd dccccccg eccccccd fccccccg eccccccd fccccccg ecccccca fccccccb ecccccca fccccccb cccccca bccccccb ccccccc bccccccb acccccce bccccccf acccccce gccccccf acccccce gccccccf dcccccce ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#3f6a85ff b,#a2bcc2ff c,#216968ff d,#618e96ff e,#e2eaecff f,#7ea3a9ff g,#bfd1d4ff ``` ```image ge ccccccdbe ccccccccccccdbe fccccccccccccccccccdb cccb gfcccccccccccccccccdb ccc gfcccccccccccccccccdg gccc gfcccccccccccccccccdg accf gdcccccccccccccccccfg ccce gdccccccccccccccccg eccc bdcccccccccc dcca bdcccc cccg e ccc bccc dd cccf dccf ccc cccceccc fccccdccd cccccccce bcccccccc cccfccccc bccc ccccb cccf fccc gccc ccc cccd fce gccc cccd eccc ccca eccc ccca ccc accc ccce accc ccce dccc cccg dccc cccg fccc cccb fccc cccb bccc cccf gccc cccd gccc cccd bab eccc aaaaaf ccca aaaaaaaadccc baaaaaacccce gaaacccaaadg ccccaaaaaaag cccgdaaaaaaaaab accc efaaaaaaaaab ccce faaaaaaaaaf dccc baaaaaaaaade cccg baaaaaaaaade dccc gaaaaaaaaaag cccg edaaaaaaaaag fccc edaaaaaaaaab cccb faaaaaaaaaf fccc baaaaaaaaaf cccb baaaaaaaaade bccc gaaaaaaaaadg cccf gdaaaaaaaaag bccc edaaaaaaaaab cccf efaaaaaaaaab eccc faaaaaaaaaf bd baaaaaaaaade baaaaaaaaade gaaaaaaaaaae edaaaaaaa edaaaaa eaaab daaa aaaa eaaab daa b ``` <!-- 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,#9dbe93ff b,#686337ff c,#dbc2bcff d,#c27572ff e,#b1d7b0ff f,#f0f2edff g,#838660ff ``` ```image c bb fbgb cba b abc b gbf b bb bf bb bc fbg be cba ba abc gg gbf ag bb ab bb cb fbg cb cba fb df abc eaaaaaabaaaaaaaaaaaa cdc gbf aeeeeeebeeeeeeeeeeee fdd bb aeeeeeebeeeeeeeeeeee ddf bb aeeeeeebeeeeeeeeeeee cdd fbg aeeeeeebaeeeeeeeeeee dd cba aeeeeeebaeeeeeebeeee ddc faaaaaaaaaaaaaaaaaaaaaaaf abc aeeeeeebaeeeeeadeeee fdd feeeeeeeeeeeeeeeeeeeeeeef gbf aeeeeeebgeeeeegdeeee ddf feeeeeeeeeeeeeeeeeeeeeeefbb aeeeeeeggeeeeebdeeee cdc feeeeeeeeeeeeeeeeeeeeeeebb aeeeeeegbeeeeebdeeee fdd feeeeeeeeeeeeeeeeeeeeeebg aeeeeeegbeeeeagdeeee ddffeeeeeeeeeeeeeeeeeeeeabgf aeeeeeeabeeeegddeeee cddeeeeeeeeeeeeeeeeeeegbaef aeeeeeeabeeeebdaeeee ddeeeeeeeeeeeeeeeeegbaeef aeeeeeeebeeeebdeeeee fddaeeeeeeeeeeeeeebbeeeef aeeeeeeebeeeabdeeeee feaddeeeeeeeeeeeebbeeeeef aeeeeeeebeeebgdeeeee feeeddeeeeeeeeeebbeeeeeef aeeeeeeebeeebadeeeee feeeedddeeeeeeabgeeeeeeef aeeeeeeebeeebadeeeee feeeeeeddeeeeabaeeeeeeeef aeeeeeeebeegbddeeeee feeeeeeeddaeebaeeeeeeeeef aeeeeeeebaebgddeeeee feeeeeeeeaddbbeeeeeeeeeef aeeeeeeebaebedaeeeee feeeeeeeeeeddeeeeeeeeeeef aeeeeeeebgebedeeeeee feeeeeeeeeebddaeeeeeeeeef aeeeeeeebggbedeeeeee feeeeeeeeebbeaddeeeeeeeef aeeeeeeeggbgedeeeeee feeeeeeeeabeeeeddeeeeeeef aeeeeeeegbbeadeeeeee feeeeeeeebaeeeeedddeeeeef aeeeeeeeabbeadeeeeee feeeeeeebbeeeeeeeeddeeeef aeeeeeeeabbeddeeeeee feeeeeegbeeeeeeeeeeddaeef aeeeeeeeebaedaeeeeee feeeeeebaeeeeeeeeeeeaddef aeeeeeeeebeedeeeeeee feeeeebgeeeeeeeeeeeeeeddf aeeeeeeeeaeedeeeeeee feeeegbeeeeeeeeeeeeeeeeddc aeeeeeeeeeeedeeeeeee feeeebaeeeeeeeeeeeeeeeeecdd aeeeeeeeeeeedeeeeeee feeebgeeeeeeeeeeeeeeeeeef ddf aeeeeeeeeeeadeeeeeee feegbeeeeeeeeeeeeeeeeeeef cdc aeeeeeeeeeeddeeeeeee feebeeeeeeeeeeeeeeeeeeeef fdd fffffffffffdcfffffff febgeeeeeeeeeeeeeeeeeeeef ddf dc fgbeeeeeeeeeeeeeeeeeeeeaf cdd df fbffffffffffffffffffffff dd d ba ddc d gb fdd fd cb ddf cd be cdc dd bb fdd dc cb ddf dc bc cdd d bb dd d eb ddc d bc cdd fd bg ddf cd ab cdc dd bf fdd dc bg ddf df ab cddd fbf dd bg c gb fbf ba gb fb ba gb cb be ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a4a187ff b,#696237ff c,#d4c0b7ff d,#c2706eff e,#cf8f8dff f,#ede3e0ff g,#847f5bff ``` ```image a gb fgbb fbbba cbbba ef abbbc ddf abbbc dddc gbbgf fdddef fgbbgf fedddc fbbba cddde cbbba fedddf cbbbc edddc abbbc cdddef gbbgf fedddf fgbbgf cdddc fbbba fdddef cbbba fedddc fbbbc cddde gbbc fddddf abbc edddc cbbg cdddefgbbf fedddbbc cdddd fgdddef abbedddc cbba cddde fbbbf fddddf gbbc edddc cbba cdddef fbbg fedddf gbbc cdddc cbba fdddef fbbg fedddc gbbf cddde abba fdddef fbbg edddc gbbf cdddef abba fedddf fbbg cddd gbbf fdd abbc fe cbbg gbbf abbc cbbg fbbbf abbc cbba fbbb gbbc cbba fbbg gbbc ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Time to investigate another area. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#a29e84ff b,#686236ff c,#cdbcb1ff d,#c16e6cff e,#cf908eff f,#e7ddd8ff g,#857b59ff ``` ```image bba gba gba gbg abg abb abb cbb cbbf cbbf cga fbbf abb fbbc gdd bbc fgdd bbc cdde bba adde gba bddc gba fbddc gbg cbddf abg agddf abb bgdd abb fbgdd cbb abdde cbbf gbdde cbbf bbddc fbbf cbbddf fbbc abbddf fbbc gbgddf bbc fbbedd bba cbbede gba abbede gba gbaddc gbg fbbcddc abg cbbfddf abg abgfddf abb bbacdd cbb fbbccdd cbbf cbbfede cbbf gbg ede fbbf bba ddc fbbc fbbc ddc fbbc abb fddf bbc gbg fddf bba bba cdd gba cbbf cdd gba abb ede gbg gbg ede abgfbbc ddc abgcbbf ddf abbabb fddf cbbbba fdd cbbbbc cdd cbbbbf ede fbbbg ede fbbba ddc fbbbc ddc bbb fddf bbg fddf gba cdd fc cdd ede ede ddc ddc fddf fddf cdd cdd ``` <!-- end of image --> No intersection in area B, but I'll keep looking. Answer: A: 1; B: 0; 1 + 0 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#9f9b80ff b,#686236ff c,#dbcbc3ff d,#c3716fff e,#cba79fff f,#f0e8e5ff g,#827b57ff ``` ```image c bb fbgb cbe b abc b gbf b bb bf bb bc fbg be cba ba abc ga gbf ag bb eb bb cb fbg cb cba fb df abc b ede gbf b fdd bb b ddf bb b cde fbg bf dd cba bc b edc ebc be fd fdd gbf ba ad ddf bb ga bd ede bb ag gd fdd fbg eb cgd ddf cba cb gde cde ebc cb bdc dd gbf fb bdf edc bb b cbd fdd bb b gad ddf bg b bcd ede fba b bcd fdd cbe bf ebed ddf be bc bade cdegb be bfdc dd bafb d bddc gaab d bg fdd agbe d eb ddf abb fd bc ede ebb cd bg fdd cbg ee eb ddf fbc dc bf cde b df bg dd e d ab edc d fbf fdd fd ba ddf cd ab ede ed fbf fdd de ba ddf dc gb cde df fb dd d be edc d gb fdd fd cb ddf cd be ede ed gb fdd de cb ddf dc bc cde d bg dd d eb edc d bc fdd fd bg ddf ed eb ede ee bf fdd dc bg ddf df ab cded fbf dd ba c ab fbf ba gb fb be gb cb be ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#8680b5ff b,#d5f763ff c,#4b329dff d,#eff5edff e,#b2d7b2ff f,#a6d0a7ff g,#ccec8dff ``` ```image gbg dbbbb gbbbg dbbbb bbbbd dbbbb bbbbd gbbbg dbbbbd gbbbg dbbbb bbbbd dbbbb bbbbd gbbbg dbbbbd gbbbg dbbbb bbbbg acc bbbb eccd dbbd ccc dbb cca dbb accd gbb ccc gbb ddccaddddddddddddddddddddddddddddddddddddddddddgbbddd dffaccffffffffffffffffffffffffffffffffffffffffffbbbfffd dfeeccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeefd dfeefccaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeefd dfeeeccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeefd dfeeeeccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeefd dfeeeefccaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeefd dfeeeeeccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeefd dfeeeeeeccceeeegeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbgeefd dfeeeeeeaccfeebbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeeeecccegbbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeeeeecccbbgbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeeeeeaccbbegbbgeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeeeeeeccceeebbbeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeeeeebbccaeeebbbeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeeeebbbaccfeeebbbeeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeeebbbeeccceeeebbgeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeeebbbeeefccaeeegbbeeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeeegbbgeeeeacceeeebbbeeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeegbbbeeeeeeccceeeebbbeeeeeeeeeeeeeeeeeeeeeeebbeeefd dfeeebbbeeeeeeefccaeeeebbbeeeeeeeeeeeeeeeeeeeeegbbeeefd dfeebbbeeeeeeeeeccceeeegbbgeeeeeeeeeeeeeeeeeeeegbbeeefd dfebbbeeeeeeeeeeeccceeeebbbeeeeeeeeeeeeeeeeeeeegbbeeefd dfbbbeeeeeeeeeeeefccfeeeebbbeeeeeeeeeeeeeeeeeeegbbeeefd dbbbeeeeeeeeeeeeeeccceeeeebbbeeeeeeeeeeeeeeeeeegbbeeefd gbbgeeeeeeeeeeeeeeeccceeeegbbgeeeeeeeeeeeeeeeeegbbeeefd gbbgeeeeeeeeeeeeeeeeaccfeeeebbbeeeeeeeeeeeeeeeeebbbeeefd dbbeeeeeeeeeeeeeeeeeeccceeeeebbbeeeeeeeeeeeeeeeebbbeeefd dfeeeeeeeeeeeeeeeeeeeccaeeeeebbbeeeeeeeeeeeeeeebbgeeefd dfeeeeeeeeeeeeeeeeeeeaccfeeeeebbgeeeeeeeeeeeeeebbgeeefd dfeeeeeeeeeeeeeeeeeeeeccceeeeegbbeeeeeeeeeeeeeebbgeeefd dfeeeeeeeeeeeeeeeeeeeefccaeeeeebbbeeeeeeeeeeeeebbgeeefd dfeeeeeeeeeeeeeeeeeeeeeacceeeeeebbbeeeeeeeeeeeebbgeeefd dfeeeeeeeeeeeeeeeeeeeeeeccceeeeeebbbeeeeeeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeefccaeeeeegbbgeeeeeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeccceeeeeebbbeeeeeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeebbbeeeeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeefccaeeeeeebbbeeeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeegbbgeeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeebbbeeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeaccfeeeeeebbbeeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeeebbbeeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeeebbgeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeaccfeeeeeegbbeeeebbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeeebbbeegbbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeccaeeeeeeebbbegbbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacceeeeeeeebbbgbbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeeegbbbbbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefccaeeeeeeebbbbbeeeefd dfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeccceeeeeeeebbbbeeeefd dffffffffffffffffffffffffffffffffffcccffffffffbbbfffffd dddddddddddddddddddddddddddddddddddcceddddddddbdddddd ccc cccccccccccccccccccccccccccccccccccccccccccc eccccccccccccccccccccccccccccccccccccccccccc acaaaaaaaaaaaaaaaaaaaeeeeeeeeddddddddddd ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#7360b1ff b,#d6f763ff c,#4a309dff d,#d4cee7ff e,#f1fccdff f,#a397cbff g,#e3f995ff ``` ```image dcccccd gbbbb fcccca gbbbb cccccf gbbbb dcccccd gbbbb acccca bbbbg cccccf bbbbg fcccccd bbbbg acccca bbbbg dcccccf bbbbg fccccc bbbbg acccca bbbbg dcccccd bbbbg fccccc ebbbbe acccca ebbbbe dcccccd ebbbbe fccccc gge ebbbbe cccccf ebbbbe ebbbbe dcccccd bbbbbb ebbbbe acccca gbbbbbbg ebbbbe cccccf gbbbbbbbbe ebbbbe dcccccdgbbbbbbbbbbe gbbbb accccabbbbbggbbbbb gbbbb dcccccfbbbg bbbbbg gbbbb fcccccbbb ebbbbbg gbbbb accccabe gbbbbbe gbbbb bcccccf gbbbbb gbbbb gbaccccc bbbbbg gbbbb gbbbacccca ebbbbbg gbbbb gbbbbbcccccd ebbbbbe bbbbg ebbbbbgfccccc gbbbbbe bbbbg ebbbbbg accccf bbbbbb bbbbg ebbbbbb dcccccd ebbbbbg bbbbg bbbbbbe fcccca ebbbbbe bbbbg gbbbbbe cccccf gbbbbbe bbbbg gbbbbbe dcccccd gbbbbb bbbbg gbbbbbg acccca bbbbbg bbbbg gbbbbbg cccccf ebbbbbg ebbbbe ebbbbbg fcccccd gbbbbbe ebbbbe ebbbbbb acccca gbbbbb ebbbbe ebbbbbb dcccccf bbbbbg ebbbbe bbbbbbe fccccc ebbbbbg ebbbbe gbbbbbe acccca ebbbbbe ebbbbe gbbbbbe dcccccd gbbbbbe ebbbbe gbbbbbg fccccc bbbbbb ebbbbe ebbbbbg accccf ebbbbbg gbbbb ebbbbbg dcccccd ebbbbbe gbbbb ebbbbbb fcccca gbbbbbe gbbbb bbbbbb cccccf gbbbbb gbbbb bbbbbbe dcccccd bbbbbg gbbbb bbbbbe acccca ebbbbbg gbbbb bbbbe cccccf gbbbbbe gbbbb bbbg fcccccd gbbbbb gbbbb bbg acccca bbbbbg bbbbg bg dcccccf ebbbbbg bbbbg b fccccc ebbbbbe bbbbg e acccca gbbbbbe bbbbg dcccccd bbbbbb bbbbg fccccc ebbbbbg bbbbg acccca ebbbbbe bbbbg dcccccd gbbbbbe bbbbg fccccc gbbbbb ebbbbe cccccf bbbbbg ebbbbe dcccccd ebbbbbg ebbbbe acccca gbbbbbe ebbbbe cccccf gbbbbb ebbbbe dcccccd bbbbbg ebbbbe acccca ebbbbbg ebbbbe dcccccf ebbbbbe ebbbbe fcccccd gbbbbbe gbbbb acccca bbbbbb gbbbb dcccccf ebbbbbg gbbbb fccccc ebbbbbe gbbbb acccca gbbbbbe gbbbb dcccccd gbbbbb gbbbb fccccc bbbbbg gbbbb accccf ebbbbbg gbbbb dcccccd gbbbbbe bbbbg fcccca gbbbbb bbbbg cccccf bbbbbg bbbbg dcccccd ebbbbbg bbbbg acccca ebbbbbe bbbbg cccccf gbbbbbe bbbbg fcccccd bbbbbb bbbbg acccca ebbbbbg bbbbg dcccccf ebbbbbe ebbbbe fccccc gbbbbbe ebbbbe acccca bbbbbb ebbbbe dcccccd bbbbbg ebbbbe fccccc ebbbbbg ebbbbe accccf gbbbbbe ebbbbe dcccccd gbbbbb ebbbbe fcccca bbbbbg ebbbbe cccccf ebbbbbggbbbb dcccccd gbbbbbbbbbb acccca gbbbbbbbbb cccccf bbbbbbbbb fcccccd ebbbbbbbb acccca ebbbbbbb dcccccf gbbbbbb fccccc bbbbbb ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#6e5ab0ff b,#d6f763ff c,#492f9dff d,#cec7e4ff e,#f1fccdff f,#9c8ec9ff g,#e3f995ff ``` ```image gbg bbbb gbbbg ebbbb bbbbe ebbbb bbbbe gbbbg bbbb gbbbg ebbbb bbbbe ebbbb bbbbe gbbbg bbbb gbbbg ebbbb bbbbe fca bbbb dccd ebbe ccc ebb cca ebb fcc ebb ccc gbb ccf gbb fcc gbb ccc gbb ccf bbg acc bbg ccc bbg dccd bbg acc bbe cca ge bbe dccd bbb bbe ccc gbbbb bbe ccabbgbbb bb fccbb ebbg bb ccc gbb bb bbccf bbb bb bbbfcc bbb bb bbb ccc ebbg bb gbbe ccf gbbe bb gbbg acc bbb bb ebbg ccc bbb ebb ebbb dccd bbg ebb bbb acc ebbe ebb bbb ccc bbb ebb bbb dccd bbb gbb bbb ccc bbb gbb gbbe cca ebbg gbb gbbg dccd gbb gbb ebg ccc bbb bbg cca bbb bbg fcc ebbg bbg ccc gbbe bbg ccf bbb bbe fcc bbb bbe ccc bbg bbe ccf ebbe bbe acc bbb bb ccc bbb bb dccd bbb bb acc ebbg bb cca gbb bb dccd bbb bb ccc bbb bb cca ebbg bb fcc gbbe ebb ccc bbb ebb ccf bbb ebb fcc bbgebb ccc gbbbbb ccf bbbbb acc bbbb ccc bbb dccd ebe acc cccaaaaccccccccccccccccccccccccccccccccccccc dccccccccccccccccccccccccccccccccccccccccccc faaaaaaaafffffffffffffdddddddddddddd ``` <!-- end of image -->
[ "" ]
I'm approaching this image with caution. Intersections might be tricky to spot. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#27e780ff b,#4706e5ff c,#796dd2ff d,#65e49eff e,#ebf5efff f,#9fcea1ff g,#b1d8b2ff ``` ```image effffffffffffffffffffffff efggggggggggggggggggggggf efgggggggggggggggggccgggf efgggggggggggggggggbbbfgf efgggggggggggggggggaaaggf efggggggggggggggggfaaaggf efggggggggggggggggcaaaggf efggggggggggggggggbaaaggf efggggggggggggggggbaaaggf efgggggggggggggggfcaadggf de efgggggggggggggggcaaadggf aaa efgggggggggggggggbaaafggf aaaa efgggggggggggggggbaaagggf eaaaa efgggggggggggggggbaaagggf eaaad efggggggggggggggcbaaagggf daaae efggggggggggggggbbaaagggf aaaa efggggggggggggggbcaadgggf aaaa efggggggggggggggbaaadgggf aaaa efgggggggggggggcbaaaggggf eaaad efgggggggggggggbbaaaggggf daaae efgggggggggggggbbaaaggggf aaaae efgggggggggggggbbaaaggggf aaaa efggggggggggggcbbaaaggggf aaaa efggggggggggggbbcaadggggf eaaad efggggggggggggbbaaadggggf daaag efggggggggggggbbaaagggggf aaaae efgggggggggggcbbaaagggggf aaaa efgggggggggggbbbaaagggggf aaaa efgggggggggggbbbaaagggggf eaaad efgggggggggggbbcaaagggggf gaaag efggggggggggcbbdaadgggggf daaae efggggggggggbbbaaafgggggf aaaa efggggggggggbbbaaaggggggf aaaa efggggggggggbbbaaaggggggf eaaad efgggggggggcbbbaaaggggggf gaaag efgggggggggbbbcaaaggggggf daaae efgggggggggbbbdaaaggggggf aaaa efgggggggggbbbdaadggggggf eaaa efggggggggcbbbaaafggggggf aaa efggggggggbbbcaaagggggggf aaa efggggggggbbbgaaagggggggf eeeeeeeeeeaaaeeeeeeeeeee efggggggggbbbgaaagggggggf ffffffffffaaafffffffffffe efgggggggcbbbfaaagggggggf fgggggggggaaaggggggggggfe efgggggggbbbcdaaagggggggf fgggggggggaaaggggggggggfe efgggggggbbbgdaadgggggggf fgggggggggaaaggggggggggfe efgggggggbbbgaaafgggggggf fgggggggggaaaggggggggggfe efggggggcbbbgaaaggggggggf fgggggggggaaaggggggggggfe efggggggbbbcgaaaggggggggf cbce fgggggggggaaafgggggggggfe efggggggbbbggaaaggggggggf bbbbbbbce fgggggggggaaafgggggggggfe efggggggbbbgfaaaggggggggf bbbbbbbbbbbbcggggggggaaadgggggggggfe efgggggcbbbgdaadggggggggf ecbbbbbbbbbbbbbbcgggdaadgggggggggfe efgggggbbbcgdaadggggggggf gcbbbbbbbbbbbbbdaadgggggggggfe efgggggbbbggaaafggggggggf cbbbbbbbbbcaaabcfggggggfe efgggggbbbggaaagggggggggf fggggcbbbbcaaabbbbbbcfgfe efggggcbbbggaaagggggggggf fggggggggfcaaabbbbbbbbbbbce efggggbbbcggaaagggggggggf fgggggggggfaaafcbbbbbbbbbbbbbcg efggggbbbggfaaagggggggggf fggggggggggaaagggggfcbbbbbbbbbbbbbce efggggbbbggdaadgggggggggf fggggggggggaaagggggggggfgcbbbbbbbbbbbbbc efgggcbbbggaaadgggggggggf fggggggggggaaagggggggggfe ecbbbbbbbbbbbbbce efgggbbbcggaaaggggggggggf fggggggggggaaagggggggggfe ecbbbbbbbbbbbbbcefgggbbbgggaaaggggggggggf fggggggggggaaagggggggggfe cbbbbbbbbbbbbbbcbbbgggaaaggggggggggf fggggggggggaaagggggggggfe ecbbbbbbbbbbbbbgggaaaggggggggggf fggggggggggaaagggggggggfe ecbbbbbbbcggfaaaggggggggggf fggggggggggaaagggggggggfe efgcbbbgggdaadggggggggggf fggggggggggaaadggggggggfe efggggggggaaadggggggggggf fggggggggggaaaaaadgggggfe efggggggggaaagggggggggggf ffffffffffffaaaaaaaadfffe efffffffffaaaffffffffffff edaaaaaaaag eeeeeeeeeaaaeeeeeeeeeeee eaaaaaaaaae aaa gaaaaaaaade gaaa gaaaaaaaad daad daaaaaaaad aaae daaaaaaaag aaa edaaaaaaaag aaa eaaaaaaaaae aaa gaaaaaaaade eaaa gaaaaaaaad gaad daaaaaaaad daad daaaaaaaag aaae edaaaaaaaaaaa eaaaaaaaaa gaaaaaa gaag ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#27e780ff b,#4705e6ff c,#c2adf6ff d,#71eeacff e,#865eedff f,#387ab2ff g,#b9f7d6ff ``` ```image daaaaag daaaaag daaaaad daaaaad daaaaad daaaaad gaaaaad gaaaaad gaaaaad gaaaaaa gaaaaaa gaaaaaa aaaaaa aaaaaa aaaaaa aaaaaag aaaaaag aaaaaag becc daaaaag bbbbbeecc daaaaag bbbbbbbbbbeec daaaaag bbbbbbbbbbbbbbbeec daaaaad bbbbbbbbbbbbbbbbbbbbfaaaaad bbbbbbbbbbbbbbbbbbbbfaaaaadc cebbbbbbbbbbbbbbbbbbfaaaaafbbbecc ccebbbbbbbbbbbbbfaaaaafbbbbbbbbecc ceebbbbbbbbfaaaaaabbbbbbbbbbbbeecc ceebbbfaaaaaabbbbbbbbbbbbbbbbbee ceaaaaaabbbbbbbbbbbbbbbbbbb gaaaaaabbbbbbbbbbbbbbbbbbb aaaaaa ccebbbbbbbbbbbbbbb aaaaaa ccebbbbbbbbbb aaaaaa ccebbbbb aaaaaa cee aaaaaag aaaaaag aaaaaag daaaaag daaaaag daaaaag daaaaad daaaaad daaaaad gaaaaad gaaaaad gaaaaad gaaaaaa gaaaaaa gaaaaaadg aaaaaaaaadg aaaaaaaaaaaadg ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Okay, on to the next area of interest. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#27e780ff b,#4706e5ff c,#bea8f5ff d,#71efabff e,#8359edff f,#3975b5ff g,#bbf7d7ff ``` ```image ecc bbbbec bbbbb eaaaff baaaaa faaaaa cfaaaad efaaaad baaaaag cbaaaaag ebaaaaa bfaaaaa bfaaaad ebaaaaag bbaaaaag bbaaaaa bbaaaaa bfaaaaa bfaaaad cbaaaaag ebaaaaag bbaaaaa bbaaaaa ebfaaaad bbfaaaad bbaaaaag cbbaaaaag ebbaaaaa bbbaaaaa cbbbaaaaa ebbbaaaaa ebbbaaaaa bbbbaaaaa ebbbfaaaaa ebbbfaaaad bbbbfaaaad bbbbfaaaad bbbbaaaaag bbbbaaaaa cbbbfaaaaa ebbbfaaaad ebbbfaaaad cbbbbaaaaag ebbbbaaaaag ebbbbaaaaa bbbbfaaaaa cbbbbfaaaad ebbbbaaaaag bbbbbaaaaag cbbbbbaaaaa ebbbbeaaaaa ebbbbfaaaaa cbbbbbdaaaad ebbbbedaaaag ebbbbeaaaaag bbbbbcaaaaa bbbbbgaaaaa bbbbbdaaaad bbbbbdaaaad cbbbbbdaaaag cbbbbbaaaaag ebbbbeaaaaa cbbbbb aaaaa cbbbbb aaaaa ebbbbe aaaaa bbbbbc aaaaa cbbbbb aaaaa ebbbbe gaaaaa bbbbbc gaaaad cbbbbb daaaad cbbbbb daaaad bbbbbc aaaaag cbbbbb aaaaa cbbbbb gaaaaa ebbbbe gaaaad bbbbbc daaaad bbbbb aaaaag bbbbb aaaaag bbbbb gaaaaa cbbbbb gaaaaa cbbbbb gaaaad bbbbbc daaaag cbbbbb aaaaag cbbbbb aaaaa ebbbbe gaaaaa bbbbbc gaaaaa cbbbbb daaaad ebbbbe daaaag bbbbbc aaaaag bbbbb aaaaa cbbbbb gaaaaa bbbbbc daaaad bbbbb daaaad cbbbbb daaaag ebbbbe aaaaag bbbbbc aaaaa bbbbb aaaaa bec bbbbb aaaaa bbbbeecbbbbb aaaaa bbbbbbbbbbbb aaaaa bbbbbbbbbbbb aaaaa bbbbbbbbbbbc gaaaaa cebbbbbbbbb gaaaad ccebbbbc daaaad cc daaaad aaaaag aaaaa gaaaaa ``` <!-- end of image --> My analysis shows that the lines in area B do not cross. Answer: A: 1; B: 0; 1 + 0 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#27e780ff b,#4706e5ff c,#b69df4ff d,#6beea8ff e,#865dedff f,#3689abff g,#b6f6d4ff ``` ```image ec bbb aaf aaa eaaa baaa baaa faad dg efaag aaa baaa aaaa baaa aaaa baaa gaaad ebaaa daaag bbaaa aaaa bfaad aaaa baaag aaaa ebaaa gaaad bbaaa daaag bbaaa aaaa bbaaa aaaa ebbaaa aaaa bbfaad gaaad bbaaag daaag bbaaa aaaa ebbaaa aaaa bbbaaa aaaa bbbaaa aaad bbfaaa gaaag ebbfaad daaa bbbaaag aaaa bbbaaa aaaa bbbaaa aaad cbbeaaa gaaag bbbcaaa daaa bbbgaad aaaa bbbdaad aaa cbbbaaag aaa bbbcaaa aaa bbb aaa aaa bbb aaa aaa cbbb aaa aaa bbbcgaad aaa bbb daag aaa bbb aaag aaa cbbb aaa aaa bbbc aaa ebe aaa bbb aaa bbbbbbbc aaag bbb gaaa bbbbbbbbbbbbc daag cbbb gaad cebbbbbbbbbbbbbec daag bbbc daag cebbbbbbbbbbbbbfaad bbb aaa cbbbbbbbbbfaafbec bbb aaa cbbbbfaafbbbbbbe cbbb aaa eaaabbbbbbbbbbbc bbbc aaa aaacebbbbbbbbbbbbbec bbb gaaa aaa cebbbbbbbbbbbbbe bbb daad aaa cebbbbbbbbbbbbbc cbbb daag aaa ebbbbbbbbbbbbbec bbbc aaa aaa cebbbbbbbbbbbbbe bbb aaa aaa cbbbbbbbbbbbbbecbbb aaa aaa ebbbbbbbbbbbbb aaa aaa cebbbbbbbc gaaa aaa cbbb daad aaad aaag aaaaaad aaa gaaaaaaaag aaa daaaaaaaag aaa gaaaaaaaaag aaa gaaaaaaaad gaaa gaaaaaaaad daad daaaaaaaad aaag daaaaaaaag aaa daaaaaaaag aaa gaaaaaaaaag aaa gaaaaaaaad aaa gaaaaaaaad gaaa daaaaaaaad daad daaaaaaaag aaag daaaaaaaaaaa gaaaaaaaaa gaaaaaa gaad ``` <!-- end of image -->
[ "" ]
Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#07b8fdff b,#f00ad9ff c,#63cce5ff d,#e452d9ff e,#b1d6b1ff f,#edebf3ff g,#96ca96ff ``` ```image df bbbf bbb fbbb aaa dbbd aaaa bbb aaaaa bbb aaaaaac fbbd aaaafaaa bbbf aaaaf aaa bbb aaaaf aaa bbb aaaaf caac dbbd aaaaf aaa bbb aaaaf aaa bbb aaaaf aaaf fbbb aaaac caac dbbf caaac aaa bbb caaac aaaggggggggggggggggggggbbbggggggg caaac faaaeeeeeeeeeeeeeeeeeeedbbdeeeeeee caaac fcaaceeeeeeeeeeeeeeeeeebbbeeeeeeee caaac feaaaeeeeeeeeeeeeeeeeeebbbeeeeeeee caaac feaaaeeeeeeeeeeeeeeeeeebbbeeeeeeee caaac feaaaeeeeeeeeeeeeeeeeedbbdeeaaaeee caaac fecaaceeeeeeeeeeeeeeeebbbeeeaaaeee caaac feeaaaeeeeeeeeeeeeeeeebbbeeeaaaeee caaac feeaaaeeeeeeeeeeeeeeeebbbeeeaaaeee caaac feeaaaeeeeeeeeeeeeeeedbbeeecaaceee caaaa feecaaceeeeeeeeeeeeeebbbeeeaaaeeee faaaa feeeaaaeeeeeeeeeeeeeebbbeeeaaaeeee faaaa feeeaaaeeeeeeeeeeeeedbbdeeeaaaeeee faaaa feeeaaaeeeeeeeeeeeeebbbeeeeaaaeeee faaaa feeecaaceeeeeeeeeeeebbbeeecaaceeee faaaa feeeeaaaeeeeeeeeeeeebbbeeeaaaeeeee faaaa feeeeaaaeeeeeeeeeeedbbdeeeaaaeeeee faaaa feeeeaaaeeeeeeeeeeebbbeeeeaaaeeeee faaaa feeeecaaceeeeeeeeeebbbeeeeaaaeeeee faaaa feeeeeaaaeeeeeeeeeebbdeeecaaceeeee eggggggggggggggg faaaa feeeeeaaaeeeeeeeeebbbeeeeaaaeeeeee geeeeeeeeeeeeeeefaaaa feeeeeaaaeeeeeeeeebbbeeeeaaaeeeeee geeeeeeeeeeeeeeeaaaa feeeeecaaceeeeeeeebbbeeeeaaaeeeeee geeeeeeeeeeeeeeaaaa feeeeeeaaaeeeeeeedbbdeeeeaaaeeeeee geeeeeeeeeeeeeaaaa feeeeeeaaaeeeeeeebbbeeeecaaceeeeee geeeeeeeeeeeeaaaa feeeeeeaaaeeeeeeebbbeeeeaaaeeeeeee geeeeeeeeeeeaaaaf feeeeeecaaceeeeeebbbeeeeaaaeeeeeee geeeeeeeeeeaaaaef feeeeeeeaaaeeeeedbbdeeeeaaaeeeeeee geeeeeeeeeaaaaeef feeeeeeeaaaeeeeebbbeeeeeaaaeeeeeee geeeeeeeeaaaaeeef feeeeeeeaaaeeeeebbbeeeecaaceeeeeee geeeeeeeaaaaeeeef feeeeeeecaaceeedbbdeeeeaaaeeeeeeee geeeeeeaaaaeeeeef feeeeeeeeaaaeeebbbeeeeeaaaeeeeeeee geeeeeaaaaeeeeeef feeeeeeeeaaaeeebbbeeeeeaaaeeeeeeee geeeeaaaaeeeeeeef feeeeeeeeaaaeeebbbeeeeeaaaeeeeeeee geeeaaaaeeeeeeeef feeeeeeeecaacedbbdeeeecaaceeeeeeee geeaaaaeeeeeeeeef feeeeeeeeeaaaebbbeeeeeaaaeeeeeeeee geaaaaeeeeeeeeeef feeeeeeeeeaaaebbbeeeeeaaaeeeeeeeee gaaaaeeeeeeeeeeef feeeeeeeeeaaaebbbeeeeeaaaeeeeeeeee gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbeeeeeeaaaeeeeeeeee gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeecaaceeeeeeeee gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeecaaceeeeeeeee geeeeeeeeeeeeeeefffffffffffffffffffffffffffffffffffffeeeeeeeeeecaaeeeeeeeaaaeeeeeeeeee geeeeeeeeeeeeeeef feeeeeeeeeecaaaeeeeeeaaaeeeeeeeeee geeeeeeeeeeeeeeef feeeeeeeeeeeaaaeeeeeeaaaeeeeeeeeee geeeeeeeeeeeeeeef feeeeeeeeeeeaaaeeeeecaaceeeeeeeeee eggggggggggggggg feeeeeeeeeeeaaaeeeeecaaceeeeeeeeee feeeeeeeeeeecaaaeeeeaaaeeeeeeeeeee feeeeeeeeeeeeaaaeeeeaaaeeeeeeeeeee feeeeeeeeeeeeaaaeeeeaaaeeeeeeeeeee feeeeeeeeeeeeaaaceeeaaaeeeeeeeeeee feeeeeeeeeeeecaaaeecaaceeeeeeeeeee feeeeeeeeeeeeeaaaeeaaaeeeeeeeeeeee feeeeeeeeeeeeeaaaeeaaaeeeeeeeeeeee feeeeeeeeeeeeeaaaceaaaeeeeeeeeeeee feeeeeeeeeeeeecaaaeaaaeeeeeeeeeeee feeeeeeeeeeeeeeaaacaaceeeeeeeeeeee feeeeeeeeeeeeeeaaaaaaeeeeeeeeeeeee feeeeeeeeeeeeeeaaaaaaeeeeeeeeeeeee fgeeeeeeeeeeeeecaaaaaeeeeeeeeeeeee fffffffffffffffaaaaafffffffffffff aaaac caaa faaa aaa caf ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#05b8fdff b,#f10adaff c,#52cdfeff d,#f450e4ff e,#9de2fdff f,#fcd5f8ff g,#ad3ce4ff ``` ```image c ca caa caaa caaaa caaaaa caaaaaa caaaaaaa caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac caaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaac eaaaaaaaa eaaaaaaaa eaaaaaaaa aaaaaaaa eggggggdddddddddddddddddddddd bbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbb ffffffffffffffffffffffffffff ``` <!-- end of image --> This isn't an intersection in area A, but I'm not discouraged. Time to investigate another area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#06b8fdff b,#f10bdaff c,#4acbfdff d,#ef56e5ff e,#8cdefeff f,#fabcf4ff g,#c9eefdff ``` ```image caaaaag dbbbbbd eaaaaae dbbbbbf gaaaaac bbbbbb aaaaaa fbbbbbd caaaaag dbbbbbf eaaaaae bbbbbbf gaaaaac fbbbbbb aaaaaa fbbbbbd caaaaae dbbbbbf eaaaaac bbbbbb gg gaaaaac fbbbbbd caacce caaaaae bbbbbbf gaaaaac eaaaaac bbbbbb eaaaaac gaaaaac fbbbbbd eaaaaae aaaaaa dbbbbbf caaaaag caaaaae bbbbbbf aaaaaa eaaaaac fbbbbbb gaaaaac gaaaaac dbbbbbd eaaaaac aaaaaag dbbbbbf eaaaaae caaaaae bbbbbb caaaaag eaaaaac fbbbbbd aaaaaa gaaaaaa dbbbbbd gaaaaac aaaaaa bbbbbbf eaaaaac caaaaa fbbbbbb eaaaaae eaaaaa fbbbbbd caaaaag gaaaaa dbbbbbf aaaaaa aaaaag bbbbbb gaaaaaa caaaae fbbbbbd gaaaaac eaaaac dbbbbbd eaaaaae gaaaaa dbbbbbf caaaaag aaaaag bbbbbb aaaaaa caaaae bbbbbd aaaaaa eaaaac bbbbbf gaaaaac gaaaaa bbbbbf eaaaaae caaaae fbbbbd aaaaaa eaaaac dbbbbf aaaaaa gaaaaa bbbbb gaaaaac aaaaag fbbbbd eaaaaae caaaae dbbbbd caaaaag eaaaac bbbbbf aaaaaag gaaaaa bbbbb aaaaaa aaaaag fbbbbd gaaaaac caaaae dbbbbf eaaaaae eaaaac bbbbbf caaaaae gaaaaa fbbbbb caaaaag aaaaag dbbbbd aaaaaa aaaaae dbbbbf gaaaaac aaaaac bbbbb eaaaaae aaaaaa fbbbbd caaaaae aaaaaag dbbbbd caaaaag caaaaae bbbbbf aaaaaa eaaaaac fbbbbb gaaaaac gaaaaaa fbbbbb eaaaaae aaaaaag dbbbbb caaaaae caaaaae bbbbbb caaaaag eaaaaac fbbbbbb aaaaaa aaaaaag dbbbbbf eaaaaac caaaaae bbbbbb eaaaaae eaaaaac fbbbbbd caaaaag gaaaaaa dbbbbbf aaaaaa aaaaaag bbbbbbf gaaaaac caaaaae fbbbbbb eaaaaac eaaaaac fbbbbbd eaaaaae gaaaaaa dbbbbbf caaaaag aaaaaag bbbbbb aaaaaa caaaaae fbbbbbd gaaaaac eaaaaac dbbbbbd eaaaaac gaaaaaa dbbbbbf eaaaaae aaaaaag bbbbbb caaaaag caaaaae fbbbbbd aaaaaa eaaaaac dbbbbbf gaaaaac gaaaaaa bbbbbbf gaaaaac caaaaafbbbbbb eaaaaae caaaaadbbbbbd caaaaag ddddddddddddddddddddddddbbbbbbf aaaaaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gaaaaaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbd gaaaaac bbbbbbbbbbbbbbbbbbbbbbbbbbbbbd eaaaaae bbbbbbbbbbbbbbbbbbbbbbbbbbbbf aaaaaa ffffffffffffffffffffcaaaaag aaaaaa eaaaaae gaaaaac eaaaaac eaaaaae aaaaaa caaaaag caaaaag aaaaaag eaaaaae aaaaaa gaaaaac gaaaaac aaaaaa eaaaaae caaaaag caaaaag eaaaaae aaaaaag gaaaaac aaaaaa aaaaaa gaaaaac caaaaag eaaaaae eaaaaae caaaaae gaaaaac caaaaag aaaaaa aaaaaa caaaaag aaaaac eaaaaae aaaaae gaaaaac aaaaae aaaaaa aaaaag caaaaag aaaaa eaaaaae gaaaac aaaaaa caaaae caaaaag caaaag eaaaaae aaaaa gaaaaac gaaaac aaaaaa eaaaac caaaaageaaaae eaaaaaecaaaag gaaaaacaaaaa aaaaaaaaaac caaaaaaaaac eaaaaaaaaae ``` <!-- end of image --> I observe 1 intersection inside area B. Answer: A: 0; B: 1; 0 + 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#06b8fdff b,#f00adaff c,#43c8fdff d,#f053e4ff e,#88ddfeff f,#fbcdf6ff g,#c6edfdff ``` ```image ff bbbf bbb fbbb aac dbbf aaaa bbb aaaaa bbb aaaaaae fbbd aaaagaaa bbbf aaaag aaa bbb aaaag aaa bbb aaaag eaae dbbd aaaag aaa bbb caaag aaa bbb caaag aaa fbbb caaae eaae dbbf caaae aaa bbb caaae aaa bbb caaae aaa fbbd caaae eaae bbbf caaae aaa bbb caaae aaa bbb g eaaac aaa dbbd aaa eaaac eaae bbb aaa eaaac aaa bbb aaa eaaac aaa fbbb gaac eaaac aaa dbbf eaae eaaac eaac bbb aaa eaaac aaa bbb aaa gaaac aaa fbbd aaa gaaac aaag bbbf gaac gaaaa eaac bbb eaae gaaaa aaa bbb aaa gaaaa aaa dbbd aaa gaaaa aaag bbb aaa gaaaa eaac bbb aaa gaaaa aaa fbbd eaae aaaa aaa dbbf caag aaaa aaag bbb aaa aaaa eaac bbb aaa aaaa aaa dbbd aaa aaaa aaa bbb eaae aaaa aaag bbb caag aaaa eaac fbbb aaa aaaa aaa dbbf aaa aaaa aaa bbb aaa aaaa aaag bbb eaae aaaa eaac fbbd caag aaaa aaa bbbf aaa aaaa aaa bbb aaa aaaa caag bbb aaa aaaa eaac dbbd eaac aaaa aaa bbb caag aaaa aaa bbb aaa aaaag caafbbb aaa ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbf aaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gaac bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb caag ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcaag aaa gaac aaa aaa aaa aaa gaac caag caag gaac aaa aaa aaa aaa aaa caag gaac gaac caae aaa aaa aaa aaa caag aaa gaacgaac aaaeaae aaaaaa caaaaa gaaaaa aaaac aaaae caaa gaaa aaa cae ``` <!-- end of image -->
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I'm analyzing this image to identify any points where lines intersect. 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,#c672e7ff b,#9929b9ff c,#e3b2f5ff d,#be39f4ff e,#b1d7b1ff f,#96c996ff g,#ad9cbbff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeedeef eeeeeeeeeeeeeeeeeeeeeeeeeeeedddaef eeeeeeeeeeeeeeeeeeeeeeeeeeaddddaef eeeeeeeeeeeeeeeeeeeeeeeeadddeeddef eeeeeeeeeeeeeeeeeeggbegdddeeeeddef eeeeeeeeeeggbbbbbbbbbdddgeeeeeddef eeggbbbbbbbbbbbbbggdddgeeeeeeeddef cabbbbbbbbbbbbbggeeeeeeddddbeeeeeeeeadef cabbbbbbbbbbbbbgeeeeeeeeeeeeedddaegbeeeeeeeeadef cabbbbbbbbbbbbac eeeeeeeeeeeeeadddeeeebbeeeeeeegdef cabbbbbbbbbbbbac eeeeeeeeeeeadddeeeeeebbeeeeeeegdef cabbbbbbbbbbbbac eeeeeeeeegdddeeeeeeeebbeeeeeeeedgf ccabbbbbbbbbbbbac eeeeeeegdddgeeeeeeeeegbgeeeeeeedaf bbbbbbaac eeeeeedddgeeeeeeeeeeeebbeeeeeeedaf c eeeedddaeeeeeeeeeeeeeebbeeeeeeeddf eedddaeeeeeeeeeeeeeeeebbeeeeeeeddf adddeeeeeeeeeeeeeeeeeegbgeeeeeeddf adddeeeeeeeeeeeeeeeeeeeeebbeeeeeeddf cdddeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeddf cdddc eeeeeeeeeeeeeeeeeeeeeeebbeeeeeeadf dddc eeeeeeeeeeeeeeeeeeeeeeegbgeeeeeadf dddc eeeeeeeeeeeeeeeeeeeeeeeebbeeeeegdf ddda eeeeeeeeeeeeeeeeeeeeeeeebbeeeeegdg adda eeeeeeeeeeeeeeeeeeeeeeeebbeeeeeedg addd eeeeeeeeeeeeeeeeeeeeeeeeebgeeeeegf cddd eeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeef cdddc eeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeef cdddc eeeeeeeeeeeeeeeeeeeeeeeeegbeeeeeef dddc eeeeeeeeeeeeeeeeeeeeeeeeeebgeeeeef ddda ffffffffffffffffffffffffffbbfffffe adda bb addd ab cddd bc cddd bb cddc bb ad ab dd ba dd bb dd bb da cb d dc ba cdc cdc bb ada cd bb ddd ad cb ddd dd ba ddd dd bb ddd dd bb cdcd da cb dd dc dc ba dd dc cd bb dd da cd bb dc dd ad cbc cd dd dd ba ad ad dd dd cd dd dd cd da da dc dc dc da cd cd dd ad dd dd dd dd dd dd da ad dd dc cd da cdc dc dc dc da cd dd ad dd dd dd dd ad dd cd da dcdc dadc ddd ddd ddd add cdd cda dc ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#cb61f6ff b,#9924b9ff c,#e1b1f2ff d,#be38f4ff e,#b562cdff f,#f1daf9ff g,#d28debff ``` ```image caa cddddc cadddddg faddddddda fadddddaadda fgddddddc gdda fgddddddg cddd gddddddgf cddd ffcgeeg cddddddgf fdddf ffcgeebbbbbbbbbgadddddaf fdddf fccgeebbbbbbbbbbbbbbbbddddddaf fdddc fccgeebbbbbbbbbbbbbbbbbbbbbbddddddac dddc fccgeebbbbbbbbbbbbbbbbbbbbbbeeggccaddddddc dddc geebbbbbbbbbbbbbbbbbbbbbbeeggcf fgddddddbc addg bbbbbbbbbbbbbbbbbeeggcf gdddddddbbe addg bbbbbbbbbeegccf cddddddgfebbb adda beegccf cadddddaf cbbbf gdda fadddddaf fbbbc gddd fadddddac ebbe cddd faddddddc ebbb cddd fgddddddc cbbbf fdddf gddddddg fbbbg fdddf cddddddgf ebbe dddc cadddddaf gbbb dddc cadddddaf cbbbf dddg fadddddac bbbg addg faddddddc ebbe adda fgddddddc gbbb gdda gddddddg cbbbf gdda cddddddgf bbbg cddd cddddddaf ebbe cddd cadddddaf gbbb cdddf fadddddac cbbbc fdddf addddddc bbbg fdddf dddddc ebbe dddc dddg gbbb dddc dgf fbbbc addg f bbbg addg ebbe adda gbbb gdda fbbbc gdda bbbg cddd ebbe cddd gbbbf fddd fbbbc fddd bbbe fddd ebbe ddd cbbbf ddd fbbbc ccf bbbe ebbb cbbbf fbbbc bbbe ebbb cbbbf fbbbc ebbe ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#ca5ef6ff b,#9823b9ff c,#e2b2f3ff d,#be38f4ff e,#b45fccff f,#f1dbf9ff g,#d288edff ``` ```image a addg addada gddd dd fge cdddf dd cgebbbbbbbbdddf dd cgebbbbbbbbbbbegcdddc dd cgebbbbbbbbbbbegf ddddb ad fcgebbbbbbbbbbbecf adda cbf gd fceebbbbbbbbbbbecf adda be cd fcebbbbbbbbbbbegcf gddd bb fdf fcebbbbbbbbbbbegc cdddf eb dc fgebbbbbbbbbbbegc cdddf cbf dg bbbbbbegc fdddc be dg f dddg bb da adda eb dd adda cbc dd gddd be dd cdddf bb ad cdddf eb ad fdddc fbc gd dddg be cd dddg bb fdf adda eb dc gddd fbc cf gdddf bb cdddf bb fdddc eb fdddc fbc dddg bb adda bb gddd gb gddd bg cdddf bb cddc bb gd gb dd bg dd bb dd bb da gb d dc bg fdc fdf bb gda cd bb ddd ad cbf ddd dd be ddd dd bb fddd dd bb cdcd dg cbf adfdc dc be dd dg fdf bb da da gd eb dc dd ad cbf cdf dd dd bg gd ad dd dd gd da dd cdf dg dg dc dc fdc dg cd gd dd gd ad dd ad dd dd dd da ad dd dc cd da fdf dg dc fdf da cd dd gd dd dd dd dd gd dd cd da fdcdc dadf ddd ddd ddd add gdd cdg dc f ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ab456ff b,#637486ff c,#6a9e22ff d,#b1d6b1ff e,#8a9ea0ff f,#9cc891ff g,#edf3edff ``` ```image g gbe bbb bbb dbbg bbe bbb ebbg gbbd bbb ebb gbbd bbb bbb dbbg bbe bbb ebbg gbbe bbb ebb gffffffffffffffffffffbbed gdddddddddddddddddddbbbdf gddddddddddddddddddbbbddf gdddddddddddddddddebbfddf gdddddddddddddddddbbbdddf gddddddddddddddddbbbddddf gdddddddddddddddebbdddddf gdddddddddddddddbbedddddf gddddddddddddddbbbddddddf gdddddddddddddebbdddddddf gdddddddddddddbbedddddddf gcccccccaafddg gddddddddddddbbbddddddddf dcccccccccccccccccccccccaaaffddddbbbdddddddddf dcc gddfaacccccccccccccccccccccccbbccccaafffdf dcc ggdfaaccccccccbbbccccccccccccccccccaafdd fcc gdddddddddbbbffaaaccccccccccccccccccc fcc gddddddddebbddddddddddddf ggdffacccc fcc gddddddddbbeddddddddddddf fcc gdddddddbbbdddddddddddddf fcc gddddddebbddddddddddddddf fcc gddddddbbeddddddddddddddf fcc gdddddbbbdddddddddddddddf fcc gddddbbbddddddddddddddddf fcc gdddfbbfddddddddddddddddf acc gdddbbbdddddddddddddddddf aca gddbbbddddddddddddddddddf aca gdebbdddddddddddddddddddf aca gfbbedddddddddddddddddddf aca bbbggggggggggggggggggggg aca ebb aca gbbd aca bbb aca bbb aca gbbg aca bbe aca bbb cca dbbg cca bbe ccf bbb ccf ebb gffffffffffffffffffffffccf gbbd gddddddddddddddddddddddccf bbb gddddddddddddddddddddddccf ebb gddddddddddddddddddddddccf gbbg gddddddddddddddddddddddccf bbe gddddddddddddddddddddddccf bbb gddddddddddddddddddddddccf dbbg gddddddddddddddddddddddccd bbe gddddddddddddddddddddddccd bbb gddddddddddddddddddddddccd ebb gfffddddddddddddddddddddccd gbbd dcccccccccccccccaaaffdddccd bbb fcccccccccccccccccccccccccd dbbb bedddddddfffaaaccccccccccbbbbbg ebbbedddddddddddddddddfbbbbbbe ebbbbedddddddddddddbbbbbbeg gdebbbbeddddddddebbbbbbdf gdddebbbbedddebbbbbbfdddf gfddddebbbbbbbbbbeddddddf gggggggdbbbbbegggggggggg de ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#89b151ff b,#637487ff c,#699e20ff d,#c8d7bcff e,#a0aab5ff f,#aeca87ff g,#e6ece2ff ``` ```image cc cc cc cc cc cc cc cc cc cc cc cc cc cc gcc gcc gcc gcc gcc gcc gcc fdddggg gcc ccccccccccaaaaffffdddggg gcc cccccccccccccccccccccccccccaaaaffffdddggg gcc ccccccccccccccccccccccccccccccccccccccccccccaacc cccccccccccccccccccccccccccccccccccccccccccccccc dggdddffffaaaacccccccccccccccccccccccccccccccccc bbd gggdddffffaaaaccccccccccccccccc bbbbd gggdddffffaabb bbbbbbd gebbbb bbbbbbbbd gebbbbbbb ebbbbbbbbbe gebbbbbbbbbb gebbbbbbbbbe debbbbbbbbbbbb gebbbbbbbbbeg debbbbbbbbbbbbeg gebbbbbbbbbeg gebbbbbbbbbbbbeg gebbbbbbbbbeg gebbbbbbbbbbbbeg gebbbbbbbbbeggebbbbbbbbbbbbed ``` <!-- end of image --> Unfortunately, there's no intersection inside area A. Hmm, interesting. Let's check out another area. I'm focusing my attention on this specific region, area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#93b861ff b,#627386ff c,#699e22ff d,#aeb6c0ff e,#83919fff f,#bbd39bff g,#dbe1dcff ``` ```image gbbbbbd ebbbbe dbbbbb gbbbbbg bbbbbd ebbbbe gbbbbbg gbbbbbd ebbbbe dbbbbbg gbbbbbd ebbbbe dbbbbb gbbbbbg bbbbbd ebbbbe gbbbbbg gbbbbbd ebbbbe dbbbbbg gbbbbbd ebbbbe dbbbbb gbbbbbg cccaaaaffffggg ebbbbd ccccccccccccccccccaaaaebbbbbg ccccccccccccccccccccccbbbbbccccccaaaaffffggg cccccccccccccccccccccbbbbbcccccccccccccccccccc faaaacccccccccccccccbbbbbbcccccccccccccccccccc gggffffaaaabbbbbccccccccccccccccccccc gbbbbbdggffffaaaaccccccccccc ebbbbe gggffff dbbbbb gbbbbbg ebbbbd dbbbbe gbbbbbg bbbbbd ebbbbe dbbbbbg gbbbbbd ebbbbe dbbbbb gbbbbbg ebbbbd dbbbbe gbbbbbg bbbbbd ebbbbe dbbbbbg gbbbbbd ebbbbe dbbbbb gbbbbbg ebbbbd ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 0; B: 1; 0 + 1 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#8bb453ff b,#637487ff c,#699e21ff d,#c2cfbfff e,#96a2aeff f,#afcb89ff g,#e1e7e1ff ``` ```image g gbe bbb bbb dbbg bbe bbb ebb bbe bbb ebb gbbd bbb bbb dbbg bbe bbb ebb bbe bbb ebb gbbd bbb bbb dbbg bbe bbb ebb bbe bbb ebb gbbd gcccccccaaffdg bbb fccccccccccccccccccccccaaffdg bbb fcc gdffaacccccccccccccccccccccccbbcccaafddg fcc gdffaacccccccbbbccccccccccccccccccaafdd fcc bbbgdffaacccccccccccccccccc fcc ebb gdffaccca fcc bbe fcc bbb fcc ebb fcc gbbd fcc bbb fcc bbb fcc dbbg acc bbe aca bbb aca dbbg aca bbe aca bbb aca ebb aca gbbd aca bbb aca bbb aca gbbg aca bbe aca bbb cca dbbg ccf bbe ccf bbb ccf ebb ccf gbbd ccf bbb ccf bbb ccf gbbg ccf bbb ccf bbb ccf dbbg ccf bbe ccf bbb ccf ebb gfdgg ccd gbbd dccccccccccccccaaffdgg ccd bbb fcccccccccccccccccccccccccd dbbb bd gddffaacccccccccbbbbbg ebbbd gbbbbbbe ebbbbd gbbbbbbe ebbbbe ebbbbbbg ebbbbe ebbbbbbg ebbbbbbbbbbd dbbbbbe de ``` <!-- end of image -->
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I'm optimistic that I'll find some intersections in this image. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#7551f3ff b,#edf6c4ff c,#ddd5fbff d,#b6a3f8ff e,#b1d7b1ff f,#f3f8edff g,#96c997ff ``` ```image c da da da da da da da da da da da da ca ca ca ca fggggggggggggggggggggggge ca feeeeeeeeeeeeeeeeeeeeeeeg cafeeeeeeeeeeeeeeeeeeeeeeeg caeeeeeeeeeeeeeeeeeeeeeeeg caeeeeeeeeeeeeeeeeeeeeeeg fbb fgaeeeeeeeeeeeeeeeeeeeeeg fbbbbf feeaeeeeeeeeeeeeeeeeeeeeg fbbbf feeeaeeeeeeeeeeeeeeeeeeeg fbbbbf feeeeaeeeeeeeeeeeeeeeeeeg fbbbbf feeeeeaeeeeeeeeeeeeeeeeeg fbbbf feeeeeeaeeeeeeeeeeeeeeeeg fbbbbf feeeeeeeaeeeeeeeeeeeeeeeg fbbbbf feeeeeeeeaeeeeeeeeeeeeebbbbf feeeeeeeeeaeeeeeeeebbbbeg feeeeeeeeeeaeebbbbbeeeeeg feeeeeeeeeebabeeeeeeeeeeg feeeeeeeebbeeaeeeeeeeeeeg feeeeeebbeeeeeaeeeeeeeeeg feeeebbeeeeeeeeaeeeeeeeeg feebbeeeeeeeeeeeaeeeeeeeg fbbeeeeeeeeeeeeeeaeeeeeeg fbbeeeeeeeeeeeeeeeeeaeeeeeg fbb feeeeeeeeeeeeeeeeeeaeeeeg fbb feeeeeeeeeeeeeeeeeeeaeeeg fbb feeeeeeeeeeeeeeeeeeeeaeeg fbb feeeeeeeeeeeeeeeeeeeeeaeg fbb feeeeeeeeeeeeeeeeeeeeeeag fbb feeeeeeeeeeeeeeeeeeeeeeeac bf fbb feeeeeeeeeeeeeeeeeeeeeeegac fbb feeeeeeeeeeeeeeeeeeeeeeeg ac fgeeeeeeeeeeeeeeeeeeeeeeg ac ffffffffffffffffffffffff ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac a ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#7451f3ff b,#eff8c7ff c,#ece8fcff d,#ac97f7ff e,#8667f3ff f,#f8fbe9ff g,#987ef4ff ``` ```image d ad aad caad caad caad caad cead cead cead cead cead cead cead cead ceag ceag ceag ceag ffb ceag ffbbbbb ceag ffbbbbbbbff ceag ffbbbbbbbbff ceag ffbbbbbbbff ceagbbbbbbbff fbbeagbbff fbbbbfeag fbbbbf cgag fbbbbf gag fbbbbf gagc fbbbbf gaec fbbbbf gaec fbbbbf gaec fbbbbf gaec fbbbbf gaec bbbbf gaec bbf gaec f gaec gaec gaec gaec daec daec daec daec daec dae da d ``` <!-- end of image --> Area A contains 1 intersection. Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#7551f3ff b,#eff7c5ff c,#d9cffbff d,#b4a1f8ff e,#e9e3fcff f,#f4fad9ff g,#fafceeff ``` ```image c da da da da da da da da da da da ca ca ca ca ca ca ca ca ca gfbb ea gbbbbg ea fbbbfg ea gfbbbg ea gbbbfg ea fbbbf ea gfbbbg ea fbbbfg ea gfbbbf ea gbbbfg ea fbbbf gbabg gbb a gbb a gbb ae gbb ae gbb ae gbb ae gbb ae gbb ae gbb ae gbb ae gbb ae gbb ae fg gbb ac gfbb ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ac ae ae ae ae ae ae ae ae ae ae ae ae ae ae a ``` <!-- 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,#b064f5ff b,#d8bcfbff c,#a070faff d,#f0edf6ff e,#b691ecff f,#96c996ff g,#b1d7b1ff ``` ```image fggggggggggggggggggggggggggggggf fggggggggggggggggggggggggggggggf fggggggggggggggggggggggggggagggf fgggggggggggggggggggggggggaaaggf fgggggggggggggggggggggggggacaggf fggggggggggggggggggggggggacccggf fgggggggggggggggggggggggaacccggf fgggggggggggggggggggggggacccgggf fggggggggggggggggggggggaccccgggf fgggggggggggggggggggggeacccggggf fgggggggggggggggggggggaccceggggf fggggggggggggggggggggaacccgggggf fgggggggggggggggggggeacccegggggf fgggggggggggggggggggaacccggggggf fggggggggggggggggggaaccceggggggf ccb fgggggggggggggggggeaacccgggggggf ccccccb fgggggggggggggggggaacccggggggggf ccccccccced fggggggggggggggggaaacccggggggggf cccc eccccccce fgggggggggggggggeaacccgggggggggf cccc decccccccb fgggggggggggggggaaccccgggggggggf bccd cccc dccccccccb fggggggggggggggaaacccggggggggggf cccccbdcccc bccccccccd fgggggggggggggeaaccceggggggggggf bccccccccc bccccccced fgggggggggggggaaacccgggggggggggf dcccccc eccccccce fggggggggggggaaacccegggggggggggf ecc decccccccb fgggggggggggeaaacccggggggggggggf dccccccccb fgggggggggggaaaccceggggggggggggf bccccccccbbbbbbdfggggggggggaaaecccgggggggggggggf bcccccccccccccccccccccccccccccggggggggggggggf eccccccccccccccccccccccccccggggggggggggggf dddbbbbbeeeeeeccccccccccgggggggggggggggf fgggggggeaaagggggggggggggggggggf fgggggggaaaggggggggggggggggggggf fggggggaaaaggggggggggggggggggggf fggggggaaagggggggggggggggggggggf fgggggaaaggggggggggggggggggggggf fggggaaaaggggggggggggggggggggggf fggggaaagggggggggggggggggggggggf fgggaaaggggggggggggggggggggggggf fggaaaaggggggggggggggggggggggggf fggaaagggggggggggggggggggggggggf fgaaaegggggggggggggggggggggggggf feaaaggggggggggggggggggggggggggf faaagggggggggggggggggggggggggggf aaaegggggggggggggggggggggggggggf eaaaggggggggggggggggggggggggggggf daaadddddddddddddddddddddddddddddd aaab eaaa daaa aaab eaaa aaa aaae baaa aaad aaae baaa aaad aaae baaa aaad aaae baaa aaad aaaa baaa aaad aaaa daaa aaab eaaa daaa aaab bed eaaa aaaaab daaa aaaaaaaaab aaab deaaaaaaaaaed eaaa baaaaaaaaaab daaa deaaaaaaaaaed aaab baaaaaaaaaab eaaa baaaaaaaaaabdaaa deaaaaaaaaaab baaaaaaa baa ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#af63f6ff b,#c69efaff c,#a070faff d,#e7d5fcff e,#b782f8ff f,#d6b5faff g,#f2eafdff ``` ```image bed daaaf eaaaaed bacaaaad daacccab eaccccced faaccccccd daaccccccb eaaccccccg faaccccccb gaaaccccccg eaaccccccf faaccccccc gaaaccccccf eaacccccce faaaccccccd gaaacccccce eaaaccccccd faaaccccccb gaaaaccccccg eaaaccccccb faaaaccccccg gaaaaccccccf baaaccccccc daaaaccccccf gaaaacccccce baaaaccccccd daaaacccccce gaaaaaccccccd baaaaccccccb daaaaaccccccg eaaaaccccccb baaaaaccccccg daaaaaccccccf eaaaaccccccc baaaaaccccccf daaaaacccccce eaaaaaccccccd faaaaacccccce daaaaaaccccccd eaaaaaccccccb faaaaaaccccccg gaaaaaaccccccb eaaaaacccccccg faaaaaaccccccf gaaaaaaecccccc eaaaaaaccccccf faaaaaaeccccce ddggggg gaaaaaaeccccccd cccccccccccccceeeeeeebccccccceccccce cccccccccccccccccccccccccccccccccccd ccccccccccccccccccccccccccccccccccb ccccccccccccccccccccccccccccccccccg cccccccccccccccccccccccccccccccccb ffbbbbbbbbeeeeeeccccccccccccccccb baaaaaadgggddg daaaaaaf gaaaaaae baaaaaad daaaaaaf gaaaaaae baaaaaad daaaaaab eaaaaae baaaaaad daaaaaab eaaaaae baaaaaad daaaaaab eaaaaaag faaaaaad daaaaaab eaaaaaag faaaaaad gaaaaaab eaaaaaag faaaaaaf gaaaaaae eaaaaaag faaaaaaf gaaaaaae eaaaaaag faaaaaaf aaaaaae ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#b063f6ff b,#c9a3faff c,#a070faff d,#e8d8fcff e,#ba82f8ff f,#d9bffbff g,#f4edfdff ``` ```image e eaad daca acccd eaccc dacccg acccc eaccc gaccce aaccc eacccb gaaccc aacccf ccf baaccc ccccccd gaacccd ccccccccceg aaaccc cccc bcccccccb baacccg cccc gecccccccb aacccc fccd cccc dccccccccf aaaccc cccccbgcccc fccccccccd baaccce fccccccccc bccccccceg aaaccc gcccccc bcccccccb aaacccb bcc gecccccccb faaaccc dccccccccf aaacccf fccccccccbffffdddggg aaaeccc bcccccccccccccccccccccccccccccd bcccccccccccccccccccccccccc gdddffffbbbbeeeecccccccc faaa aaad aaae daaa aaad eaae daaa aaad eaaa daaa aaaf eaaa gaaa aaaf eaaa gaaa aaab baaa gaaa aaab baaa aaag aaab baaa aaag aaab faaa aaag aaae faaa aaag aaae faaa aaad aaae daaa aaad eaae daaa aaad eaaa daaa aaaf deg eaaa eaaaaf gaaa aaaaaaaaed aaaf deaaaaaaaaabg eaaa faaaaaaaaaaf gaaa gbaaaaaaaaaed aaab deaaaaaaaaab baaa baaaaaaaaaafgaaa geaaaaaaaaaab faaaaaaa gbaa ``` <!-- 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,#d460fcff b,#6008ecff c,#e7b8fcff d,#8750e7ff e,#b1d7b1ff f,#96c996ff g,#b499dcff ``` ```image c bbbb bbg gbbg dbd bbd gbd dbb cbb gbbc cbb cbbg bbc dbd dbg dbbc fffffffffffffffffffffffe dbd cbbg eeeeeeeeeeeeeeeeeeeeeeef gbd bbd eageeeeeeeeeeeeeeeeeeeef cbb dbb eeageeeeeeeeeeeeeeeeeeef bb gbbc eeeageeeeeeeeeeeeeeeeeef bbc cbbd eeeeaeeeeeeeeeeeeeeeeeef dbg d eeeeeaeeeeeeeeeeeeeeeeedbd eeeeeeaeeeeeeeeeeeeeegbb eeeeeeeaeeeeeeeeeeegbbef eeeeeeegaeeeeeeeeebbeeef eeeeeeeegaeeeeeebbgeeeef eeeeeeeeegaeeedbdeeeeeef eeeeeeeeeegadbdeeeeeeeef eeeeeeeeeegbbeeeeeeeeeef eeeeeeeegbbaeeeeeeeeeeef eeeeeeebbeeageeeeeeeeeef eeeeebbgeeegaeeeeeeeeeef eeedbdeeeeeeaeeeeeeeeeef edbdeeeeeeeeaeeeeeeeeeef edeeeeeeeeeeaeeeeeeeeeef eeeeeeeeeeeeageeeeeeeeef eeeeeeeeeeeegaeeeeeeeeef eeeeeeeeeeeeeaeeeeeeeeef eeeeeeeeeeeeeaeeeeeeeeef eeeeeeeeeeeeeaeeeeeeeeef eeeeeeeeeeeeeageeeeeeeef eeeeeeeeeeeeegaeeeeeeeef ffffffffffffffaffffffffe a a ac ca a a a ac ca a a a ac ca a a a ac ca a a a ac ca a a a ac ca aac caaaac caaaaac caaaac caaaac caaaaac caaaac ccaaaac caaaacc caaaac ccaaaac caaaac caaaac caaa ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#d358fcff b,#5f06edff c,#daa3fbff d,#853df1ff e,#db79fcff f,#eccffdff g,#a674f4ff ``` ```image ec faac caac caaf caaf caaf eaaf eaaf eaaf eaa eae g aae cbb faae cdbbb faae fdbbbg faae fdbbbg faac fgbbbdf faac gbbbdf faac cbbbdc caac cdbbbc caaf fdbbbg caaf fdbbbgf caafgbbbdf edbbbdf cbbbdc cdbbbd fdbbbgaa fgbbbgf aaf gbbbdf eaf gbbbdc cac cbbbdc fae cdbbbg faa fdbbbg aaf fgbbbgf eaf gbbbdf cac cbbdc fae dc faa aaf eaf cac fae faa aaf eaf cac fae faa aaf eaf cac fae ``` <!-- end of image --> Incredible, there's actually 1 intersection in area A! Answer: A: 1; 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#d358fcff b,#6008edff c,#e5b7fcff d,#8a4af1ff e,#dd80fdff f,#f0dcfdff g,#b288f6ff ``` ```image f bbbbf bbg gbbg dbg fbbd gbd dbb cbb gbbc fbbf cbbg bbc dbd dbg gbbf dbd cbbg gbd fbbd ac cbb dbbf ac fbbf gbbc af bbc fbbg af dbg d af dbd fa gbd fa cbb fa fbbf ca bbc ca dbg eagbd gbb cbba fbbf ec bbc ce dbg a gbd a d a ec ce a a a ec ce a a a ec ce a a a ec ce a a a ec ce a a a ec ce a a a ec ce a a a af ce aaef feaaaac feaaaef caaaacf feaaaec ceaaaef caaaacf feaaaec ceaaaef caaaac feaaaec ceaaaef fcaaaac feaa ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! I've noticed 2 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#8c6006ff b,#ead5a9ff c,#a79455ff d,#f2f6eeff e,#a1ce9fff f,#b2d7b1ff g,#f2e5cdff ``` ```image d bb bbb b bb db bb gb bb bd bg b bg b dbd gb dbd bg gb bd gb b bb db bb gb bb bg bg b bg b dbd gb db bg gb bd gb b bb db bb gb bb bg bg b bg b dbd gb db bg gb bd gb b bb eeeeeebeeeeee bb ad fffffbbfffffe bb a fffffbffffffe bg ba fffffbffffffe bg ac fffffbffffffe dbd ag fffffbffffffe db a ffffbbffffffe gb ba ffffbfffffffe gb ac ffffbfffffffe bb ag ffffbfffffffe bb a fffbbfffffffe bb ba fffbbffffeeccccaaaaaaaaaaab bg ac fffaaaaaaaaaaacccbbgd baa bg ag ffffffffffffe aac dbd a ffffffffffffe gaad db ba ffffffffffffe cac gb ac eeeeeeeeeeeee daab gb ag ddddddddddddd baa bb a aac bb ea gaad bb ac cac bg ad aab bgdddddddddddddddddadddd baa ebfeeeeeeeeeeeeeeecaeeeed aac efbfffffffffffffffacfffed gaag efbbffffffffffffffaefffed cac effbbfffffffffffffaffffed aab efffbbfffffffffffcaffffed baa effffbbffffffffffacffffed aac efffffbbfffffffffaeffffed gaag effffffbbffffffffafffffed caa efffffffbfffffffcafffffed aacffffffffbffffffacfffffed baaffffffffbffffeaffffffed eaacffffffbbcaaaaffffffed efeaaefffcaaaceffffffffed efffcaaaaacfbbfffffffffed efffffcefffffbbffffffffed efffffffffffffbbfffffffed effffffffffffffbbffffffed efffffffffffffffbffffffed effffffffffffffffbfffffed efffffffffffffffffbffffed efffffffffffffffffbbfffed effffffffffffffffffbbffed efffffffffffffffffffbbfed effffffffffffffffffffbbed eeeeeeeeeeeeeeeeeeeeeebbd dddddddddddddddddddddddbg bd ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#8a5d02ff b,#ecd6aaff c,#b79a5eff d,#f7f0e2ff e,#cdba92ff f,#9f7b31ff g,#f0e2c6ff ``` ```image bbg dbbd dbb gbb bbg bbd dbbd gbb gbg bbg dbbd dbb gbb bbg bbd dbbd gbb gbb bbg dbbd dbb gbb bbg bbg ddgbbee gcccccfffaaaaaaaaaa eaaaaaaaaaaaaaaaaaa baaafffcccceeebggdd d ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area A. Alright, let's concentrate on the next area. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#8a5e02ff b,#ecd6abff c,#b89d64ff d,#f9f3e8ff e,#c8b386ff f,#a17e35ff g,#efe3caff ``` ```image bbbd gaab dbbbd eaad dbbbd faf dbbb aac gbbb gaab gbbg eaad gbbg faf bbbg aac bbbd gaab dbbbd eaad dbbbd faf dbbbd aac dbbb baab gbbb eaad gbbg faf gbbg daac bbbg baab bbbd eaad dbbbd faf b dbbbd daac afg dbbbd baab aaae dbbb dcaad caaafg gbbb gefaaaf gfaaacd gbbbbcaaaaaaab eaaaae gcfaaaaaafeg dfaaafg dbcfaaaaaaced baaaae gefaaaaaafcebd dcaaaaaaaaaafeg dbbbd gfaaaafcbd dbbbd eceg dbbbd dbbb gbbb gbbg gbbg bbbg bbbd dbbbd dbbbd dbbbd dbbb gbbg gbbg gbbg bbbg bbbd dbbbd dbbbd dbbbd dbbb gbb ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area B! Answer: A: 0; B: 1; 0 + 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#8a5e02ff b,#edd6aaff c,#b79b63ff d,#f7f0e4ff e,#cfbd98ff f,#9b7628ff g,#f1e3c7ff ``` ```image bb bgb b bb db bb gg bb bd bg b bd b dbd gb db bg gb bd gb b bb db bb gb bb bd bg b bd b dbd gb db bg gb bd gb b bb db bb gb bb bd bg b bd b dbd db db bg gb bd gb b bb db bb fd gb bb a bd bg ea b bd fc b dbd ag db db a bg gb ea bd gb fc b bb ag db bb a gb bb ea bg dbeecffaaaaaaaaaab bg fc aaaaaaaaaaffccebgd eaa bd ag d fac dbd a gaad db ea caf gb ac aab gb ad eaa bb a fac bb ea gaad bg ac caf bg ad aab bd a eaa dbd ea fac db ac gaad gb ad caf gb a aae bb ea eaa bb ac fac bg ad daad bg a caf bd ca aae dbd ac eaa db dad fac gbefaaa daag caaacd caaaaae bb cg bb bg bg bd dbd db gb bb bb bb bg bg bd ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#522122ff b,#f01bcaff c,#b2d7b2ff d,#826e65ff e,#e47fd1ff f,#f0f3efff g,#a3cca2ff ``` ```image fffffffffffffffffffff fggggggggggggggggggggg egcccccccccccccccccccg ebbbeccccccccccccccccg fgccebbbeccccccccccccg fgccccccebbbbecccccccg fgcccccccccccebbbecccg fgcccccccccccccccebbbef fgcccccccccccccccccccgbbbbe fgcccccccccccccccccccg febbbe fgcccccccccccccccccccg ebbbef fffffffffffffffffff fgcccccccccccccccccccg ebbbbe fggggggggggggggggggg fgcccccccccccccccccccg febbbe fgcccccccccccccccccc fgcccccccccccccccccccg ebbbef fgcccccccccccccccccc fgcccccccccccccccccccg eb fgcccccccccccccccccc fgcccccccccccccccccccg fb fgcccccccccccccccccc fgcccccccccccccccccccg eb fgcccccccccccccccccc fgcccccccccccccccccccg be fgcccccccccccccccccc fgcccccccccccccccccccg bf fgcccccccccccccccccc fgcccccccccccccccccccg b fgcccccccccccccccccc dgcccccccccccccccccccg fb fgcccccccccccccccccc gagccccccccccccccccccg eb fgcccccccccccccccccc fgaacccccccccccccccccg be fgcccccccccccccccccc fgcdagcccccccccccccccg bf fgcccccccccccccccccc fgccgadccccccccccccccg b fgcccccccccccccccccc fgccccdacccccccccccccg fb fgcccccccccccccccccc fgcccccgadcccccccccccg ee fgcccccccccccccccccc fgcccccccaaccccccccccg bf fgcccccccccccccccccc fgccccccccgadccccccccg b fgcccccccccccccccccc fgccccccccccaacccccccg fb fgcccccccccccccccccc fgcccccccccccdagcccccg eb fgcccccccccccccccccc fgcccccccccccccaaccccg be fgcccccccccccccccccc fgccccccccccccccdagccg bffgcccccccccccccccccc fgcccccccccccccccgadcg bfgcccccccccccccccccc fgcccccccccccccccccdag fbgcccccccccccccccccc fgccccccccccccccccccgag ebcccccccccccccccccc fgcccccccccccccccccccgaa fbeccccccccccccccccc fgcccccccccccccccccccg cac fgbccccccccccccccccc fgcccccccccccccccccccg aa fgcbcccccccccccccccc fgcccccccccccccccccccg gaf fgcebccccccccccccccc fgcccccccccccccccccccg ad fgccbbcccccccccccccc fgcccccccccccccccccccg da fgcccbeccccccccccccc fgcccccccccccccccccccg fa fgccccbccccccccccccc fgcccccccccccccccccccg fa fgcccccbcccccccccccc fgcccccccccccccccccccg faf fgcccccebccccccccccc fgcccccccccccccccccccg faf fgccccccbecccccacccc fgcccccccccccccccccccg faf fgcccccccbcccccacccc fgcccccccccccccccccccg faf fgccccccccbcccgacccc fgcccccccccccccccccccg faf fgcccccccccbccddcccc fgcccccccccccccccccccg af fgcccccccccebcaccccc fgcccccccccccccccccccg af fgccccccccccbeaccccc fgcccccccccccccccccccg ac fgcccccccccccbaccccc fgcccccccccccccccccccg ac fgcccccccccccdbccccc fgcccccccccccccccccccg ac fgcccccccccccaebcccc fgcccccccccccccccccccg ac fgcccccccccccacecccc fggggggggggggggggggggg ag fgcccccccccccacccccc fffffffffffffffffffff ag fgccccccccccgacccccc ag fgccccccccccddcccccc ad fgccccccccccaccccccc ad fgccccccccccaccccccc ad fgccccccccccaccccccc ad fgcccccccccddccccccc ad fgcccccccccagccccccc ad fgcccccccccacccccccc dd fgcccccccccacccccccc da fgccccccccgdcccccccc da fgccccccccdgcccccccc da fgccccccccaccccccccc da fgccccccccaccccccccc da fgcccccccgaccccccccc da fgcccccccddccccccccc ga fgcccccccacccccccccc ga fgcccccccacccccccccc gafgcccccccacccccccccc cagccccccddcccccccccc caccccccagcccccccccc fgacccccaccccccccccc fggaccccaccccccccccc fgcgaccgaccccccccccc fgccgacddccccccccccc fgcccgaacccccccccccc fgccccgacccccccccccc fgcccccccccccccccccc fgcccccccccccccccccc fgcccccccccccccccccc ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#501d1fff b,#f21accff c,#c5b5b6ff d,#9d8182ff e,#f778e0ff f,#f1d1e9ff g,#744b4dff ``` ```image ff bbbeef ebbbbbbeef febbbbbbbeff feebbbbbbeef feebbbbbbeef febbbbbbbef feebbbbbbeef feebbbbbbeef febbbbbbbef feebbbbbb feebb dc aad caagf fgaad daagf fgaac daagf cgaac daad caaac fgaad caagf fgaad daagf fgaac daagf cgaac daad caaac fgaad caagf fgaad daagf fgaac daagf cgaac daad caaac fgaad caa fg ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Hmm, interesting. Let's check out another area. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#511f21ff b,#f114caff c,#c4b2b3ff d,#8e6d6eff e,#f88ae4ff f,#f2dbebff g,#f449d6ff ``` ```image e b eg bg fbf ebf gb fbe bg gbg fbf ebf gb fbe bb gb ge fd bb dc eb af be ca bb da eg aa bg ad fbbac ebaf cbe dbb a eg ca f da aa cad dac aa ad ac a fd dc af ca da aa ad ac a cd dc fa ca da aa ad ac af a cd ac dc aa a cad ca aa da fad aa aad ad faa ac fada aad f ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area B. Answer: A: 0; B: 1; 0 + 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#501c1eff b,#f21accff c,#c2b0b1ff d,#9a7e7fff e,#f67ae0ff f,#efd1e7ff g,#72494aff ``` ```image f ebbbe ebbbef fbbbbf febbbe ebbbef fbbbbf febbbe ebbbef fbbbbf febbbe ebbbe fb b eb be bf b d fb caf eb ag be daf b ad b ga fb fad ee ga bf cac b ag b caf eb ag be daf bf ad b ga fb fad eb ga be cac b ag b caf fb ag ee da bf fa b fa b fa eb fa be a fa bf a af b a af fb dc af eb a af bea af ba ac cb ac geb ac a e ac a ac fg ad dc ad a ad a ad a ad cd gg gf gg a gg a gg cg gg gc gg a da a da a da dc da a ca a ca a ca cd ca gf ca a fa a fa fg fa dc faa fa ``` <!-- end of image -->
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Time to put on my detective hat and find those intersection points! The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#72933aff b,#99e0d2ff c,#c8ebe1ff d,#8cab65ff e,#b1d7b1ff f,#ecf6f1ff g,#99c894ff ``` ```image a aaa bc aaaac bbbf aaaac bbbbb fffffffaaaacffff bbbbbb fgeeeeeaaaageeeee cbbbbbbb feeeeeaaaageeeeee fbbbc bbb feeeeaaaageeeeeee fbbbb bbbc feeeaaaaeeeeeeeee bbbb bbb feeaaaaeeeeeeeeee bbbb bbbc feaaaaeeeeeeeeeee bbbb fbbb faaaaeeeeeebbbeee bbbbf bbbf aaaaeeeeeeebbbeee cbbbf cbbb aaaaeeeeeeeebbbeee fbbbc bbb aaaaeeeeeeeeebbbeee fbbbb cbbb aaaageeeeeeeebbbeeee bbbb eggggbbbggggggggggggggge aaaafeeeeeeeeebbbeeee bbbb geeeebbbbeeeeeeeeeeeeeeg aaaa feeeeeeeeebbbeeee bbbb geeeeebbbeeeeeeeeeeeeeeg aaaa feeeeeeeebbbeeeee bbbbf geeeeebbbbeeeeeeeeeeeeeg faaaa feeeeeeeebbbeeeee cbbbf geeeeeebbbeeeeeeeeeeeeeg faaaa feeeeeeeebbbeeeee fbbbc geeeeeebbbeeeeeeeeeeeeeg faaaa fgggggggebbbggggg bbbb geeeeeeebbbeeeeeeeeeeeeg faaaa bbbf bbbb geeeeeeebbbeeeeeeeeeeeeg faaaa bbb bbbb geeeeeeebbbbeeeeeeeeeeeg faaaa fbbb bbbb geeeeeeeebbbeeeeeeeeeeeg faaaa cbbc bbbbf geeeeeeeebbbeggdddaaaaaaaaaaaa bbb cbbbf fceegdaaaaaaaaaaaaaaaaaaaaaaaaaaaa bbb fbbbc aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa cbbb bbbb faaaaaaaaaaaaaaaaaaaaadddggeeeeeg bbbf bbbb daaaadggedgeeeeeeeeebbbeeeeeeeeeg bbb bbbb aaa geeeeeeeeeeebbbeeeeeeeeg fbbb bbbb caaa geeeeeeeeeeebbbeeeeeeeeg cbbc cbbbf aaae geeeeeeeeeeeebbbeeeeeeeg bbb cbbbc aaa geeeeeeeeeeeebbbeeeeeeeg bbb fbbbc gaad geeeeeeeeeeeebbbbeeeeeeg cbbb fbb aaaf geeeeeeeeeeeeebbbeeeeeeg bbbf faaa geeeeeeeeeeeeebbbbeeeeeg bbb aaae geeeeeeeeeeeeeebbbeeeeeg fbbb aaa geeeeeeeeeeeeeebbbbeeeeg cbbc eaaa egggggggggggggggbbbgggge bbb aaaf bbbf bbb faaa fbbb cbbb daag bbbf bbbf aaa cbbb bbb eaaa bbb fbbb aaae cbbb cbbc aaa bbb bbb gaad bbbc bbb aaaf bbb cbbb faaa bbbc bbbf aaae fbbb bbb aaa bbbf fbbb eaaa cbbb cbbc aaaf bbb bbb faaa cbbb bbb daag bbb cbbb aaa bbbc bbbf eaaa bbb bbb aaac bbbc fbbb aaa fbbb cbbc gaad bbbf bbb aaa fbbb bbb caaa bbbf cbbb aaae cbbb bbbf aaa bbb bbb gaad cbbb fbbb aaaf bbb cbbc faaa bbbc bbb daag bbb bbb aaa bbbc cbbb eaaa fbbb bbbf aaac bbbfbbb aaa cbbbbbb daad bbbbbc aaa cbbbb caaa bbbb aaae bbbb aaa bb gaad aaaf daa c ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#72933aff b,#98e0d2ff c,#e2f3ecff d,#88a65eff e,#cfdabcff f,#aabd88ff g,#baeae0ff ``` ```image cbbbbbbc gbbbbbg cbbbbbbc bbbbbbg cbbbbbbc bbbbbbg gbbbbbb bbbbbbg gbbbbbb cbbbbbbc gbbbbbb cbbbbbbc gbbbbbg cbbbbbbc bbbbbbg cbbbbbb bbbbbbg gbbbbbb bbbbbbc gbbbbbb cbbbbbbc cceeee gbbbbbbceeeeffffdddaaaaaaaaa cceeeeffffdddaaaaaaaaaaaaaaaaaaaaaaaaaa ffdddaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadddfff aaaaaaaaaaaaaaaaaaaaaaaaaddddfffeeeecc aaaaaaaadddffffeeeecccgbbbbbb eeecc cbbbbbbc gbbbbbb cbbbbbbc gbbbbbg cbbbbbbc bbbbbbg cbbbbbb bbbbbbg gbbbbbb bbbbbbc gbbbbbb cbbbbbbc gbbbbbg cbbbbbbc bbbbbbg cbbbbbbc bbbbbbg gbbbbbb bbbbbbg gbbbbbb ``` <!-- end of image --> As I suspected, there's 1 intersection within area A. Let's continue our search in the next region. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#729239ff b,#98e0d2ff c,#d6f2edff d,#86a256ff e,#b7c89bff f,#eef3ebff g,#b9e9e0ff ``` ```image eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf eaaaaaaadf cgc eaaaaaaadf gbbbgc aaaaaaadf bbbbbbf aaaaaadf cbbbbbb aaaaadf gbbbbbg aaaadf bbbbbbc aaadf fbbbbbb aadf cbbbbbg adf gbbbbbc df bbbbbbf f cbbbbbb gbbbbbg bbbbbbc fbbbbbb cbbbbbg gbbbbbc bbbbbbf cbbbbbb gbbbbbg bbbbbbc ``` <!-- end of image --> Area B is clear of intersections, but the search continues. Answer: A: 1; B: 0; 1 + 0 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#72933aff b,#98e0d2ff c,#d3eee4ff d,#99b172ff e,#c4d2adff f,#edf7f2ff g,#b1e7dcff ``` ```image a aaa bc aaaac bbbf aaaac bbbbb aaaac gbbbbb aaaac gbbbgbbg aaaac cbbbc bbb aaaaf fbbbg bbbg aaaaf bbbb bbb aaaaf bbbb bbbc aaaaf bbbb fbbb aaaaf gbgf gbbbf bbbf aaaaf bbb cbbbf cbbb aaaaf bbb fbbbc bbb aaaaf cbbg fbbbg gbbb aaaaf bbbf bbbb bbb aaaaf bbb bbbb gbbg aaaa fbbb bbbb bbb faaaa gbbc gbbbf bbbc faaaa bbb cbbbc fbbb faaaa bbb fbbbg bbbf faaaa cbbg fbbbg cbbb faaaa bbbf bbbb bbbf faaaa bbb bbbb cbbb faaaa fbbb bbbb bbb faaaa gbbc gbbbf gbbbceeddaaaaaaaaaaaa bbb cbbbc fceedddaaaaaaaaaaaaaaaaaaaaaaaaaaa bbb fbbbg aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa cbbg bbbg faaaaaaaaaaaaaaaaaaaaaddeecf bbbf bbbb daaaaddeeecf bbbc bbb bbbb aaa fbbb fbbb bbbb eaaa bbbf gbbc gbbbf aaae cbbb bbb cbbbc aaa bbb bbb fbbbg daad gbbb cbbg fbb aaaf bbb bbbf caaa gbbg bbb aaae bbb fbbb aaa bbbc gbbc eaaa fbbb bbb aaac bbbf bbb faaa cbbb cbbg daad bbbf bbbf aaa cbbb bbb eaaa bbb fbbb aaae gbbg gbbc aaa bbb bbb daad bbbg bbb aaaf bbb cbbg caaa bbbc bbbf aaae fbbb bbb aaa bbbf fbbb eaaa cbbb gbbc aaaf bbb bbb faaa gbbb bbb daad bbb cbbg aaa gbbg bbbf eaaa bbb bbb aaae bbbc fbbb aaa fbbb gbbc daad bbbf bbb aaa cbbb bbb caaa bbbf cbbg aaae cbbb bbbf aaa bbb bbb eaaa gbbg fbbb aaaf bbb gbbc faaa bbbg bbb daad bbb bbb aaa bbbc cbbg eaaa fbbb bbbf aaac bbbfbbb aaa cbbbbbb daad bbbbbc aaa gbbbb caaa bbbb aaae gbbg aaa bb eaaa aaaf daa c ``` <!-- 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,#a0280dff b,#1de98dff c,#dfb8afff d,#b0d8b2ff e,#b26e55ff f,#97c795ff g,#68e9aaff ``` ```image bbgd dbbbbbbbgd gbbbbbbbbbgd dbbbbbbbbbbd dgbbbbbbbbbg dgbbbbbbbbbg dgbbbbbbbbbg dgbbbbbbbd gbbg dbb bb bb bb bb bb bb bb bb bbd gbd cae gbg aac dbg caa bb eaa bb aaa bb aaa bb aae fdddddddddbbdddddddddddf aac fdddddddddbbdddddddddddd ceae caac fdddddddddbbdddddddddddd ceaaaaaaaa eaa fdddddddddbbdddddddddddd ceaaaaaaaaaaec aaa fdddddddddbbfddddddddddd ceaaaaaaaaaaec aaa fdddddddddbbgddddddddddd ceaaaaaaaaaaec aae fdddddddddgbgdddddddddfeaaaaaaaaaaec aac fdddddddddgbgddddeaaaaaaaaaaaec caac fdddddddddgbbaaaaaaaaaaec eaa fddddddddddbbaaaaeeddddd eaa fddddddddddbbedddddddddd aaa fddddddddddbbddddddddddd aae fddddddddddbbddddddddddd aae fdddddddddfbbddddddddddd caac fdddddddddebbddddddddddd caa fdddddddddabbddddddddddd eaa fdddddddddabbddddddddddd aaa fdddddddddabbfdddddddddd aaa fddddddddfabbgdddddddddd aae fddddddddeafbgdddddddddd caac fddddddddaafbbdddddddddd caa fddddddddaafbbdddddddddd eaa fddddddddaadbbdddddddddd aaafdddddddfaadbbdddddddddd aaadddddddeaedbbdddddddddd aaeddddddaaddbbdddddddddd caaddddddaaddbbdddddddddd aaddddddaaddbbdddddddddd aadddddeaaddbbdddddddddd aadddddaaeddbbdddddddddd aadddddaadddbbgddddddddd aadddddaadddgbgddddddddd aaddddfaadddgbgddddddddd aafdddeaedddgbbddddddddd eaedddaafddddbbfdddddddd eaedddaadddddbbbbbbgdddd eaadddaaddddddgbbbbbbbbg faaddfaaddddddddddgbbbbbbbbg daaffeaeffffffffffffffgbbbbbbbbgd aa aa gbbbbbbbbd aa aa gbbbbbbbbg aa aa dbbbbbbbbg aa caa dgbbbbbbbgd aaceac gbbbbbbbbd eacaa dbbbbbb eaeaa dgd caaaa aaae aaac aaa aaa aaa aae aac c ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a0270cff b,#1de88dff c,#cf9284ff d,#b3f7d8ff e,#aa5a41ff f,#e8cbc5ff g,#67edafff ``` ```image gbbbd gbbbg gbbbg dbbbg dbbbg dbbbb dbbbb bbbb bbbb bbbbd bbbbd gbbbd gbbbd gbbbg fc gbbbg ffceeaaa dbbbg fcceaaaaaaaaa dbbbg fcceaaaaaaaaaaaaaaa dbbbbeaaaaaaaaaaaaaaaaaaae dbbbbaaaaaaaaaaaaaaeecff bbbbaaaaaaaaaeccf bbbbaaaeccf bbbbac bbbbef bbbbe bbbbe bbbbg bbbbg febbbg febbbg cebbbg eebbbb aebbbb faabbbb caabbbb caabbbbd eaabbbbd aaabbbbd faaabbbbd caaabbbbg eaaagbbbg eaaagbbbg aaaadbbbg faaaadbbbg caaaedbbbb eaaacdbbbb aaaaf bbbb faaaa bbbb faaaa bbbbd f caaae bbbbd e eaaac gbbbd ae aaaaf gbbbd aac faaaa gbbbg aae caaae gbbbg aaa caaac dbbbg aaa eaaac dbbbg aaa aaaaf dbbbb aaaf faaaa dbbbb aaaf caaae bbbb aaac eaaac bbbb aaac eaaaf bbbbd aaac aaaaf bbbbd aaae faaaa gbbbd aaae caaae gbbbd aaaa eaaac gbbbd aaaa aaaaf gbbbg aaaa faaaa dbbbg aaaaf faaaa dbbbg eaaaf caaae dbbbg eaaac eaaac dbbbb eaaac aaaaf dbbbbdd caaac faaaa bbbbbbbggd caaae caaae bbbbbbbbbbbbgd caaae caaac dbbbbbbbbbbbbbbbgdd faaae eaaac dggbbbbbbbbbbbbbbbg faaaa aaaaf ddgbbbbbbbbbbbb aaaa faaaa ddgbbbbbbbb ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#a0270cff b,#1de98dff c,#cf9386ff d,#abf6d4ff e,#b85e4aff f,#e7c9c2ff g,#60eeaeff ``` ```image bbgd dbbbbbbbgd dbbbbbbbbbgd dbbbbbbbbbbd dgbbbbbbbbbd dgbbbbbbbbbg dgbbbbbbbbbgd dgbbbbbbbd dgbbg dbb bb bb bb bb bb bb bb bb bbd gbd fae gbg aac dbg faaf dbb eaa bb aaa bb aaa bb aae bb aac bb ceac faaf bb feaaaaaaaa caa bb fcaaaaaaaaaaec eaa bbd ceaaaaaaaaaacf aaa gbd feaaaaaaaaaaef aae gbd fcaaaaaaaaaaec aac dbg ceaaaaaaaaaacf faaf dbbaaaaaaaaaaef caa bbaaaaec eaa bbc aaa bb aae bb aac fbb faaf cbb caa abb eaa abb aaa abbd aae fabbd aac eagbg faaf aadbg caa aadbb eaa aa bb aaa faa bb aaa eac bb aac aa bb faa aa bb aa aa bb aa cae bb aa eaf bb aa aa gbd aa aa gbd aa faa dbg aaf cae dbg eac aaf bbd cae aa bbbbbgd faa aa gbbbbbbbbd aa faa dbbbbbbbbg aa eac dgbbbbbbbgd aa aaf gbbbbbbbbd aa aa dbbbbbbbbg aa aa dgbbbbbbbgd aa faa dgbbbbbbbgd aafeac gbbbbbbbbd eacaa dbbbbbb caeaa dgd faaaa faaae aaaf aaa aaa aaa aae aaf c ``` <!-- end of image -->
[ "" ]
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,#cc8fb0ff b,#ac6c78ff c,#e3c5d3ff d,#b1d7b1ff e,#f1f4f0ff f,#96c996ff g,#bab0a9ff ``` ```image eddddddddddddddddddddddddddddddddddddf eddddddddddddddddddddddddddddddddddddf eddddddddddddddddddddddddddddddddddddf edddddddddddddddddaaaddddddddddddddddf edddddddddddddddddaaagdddddddddddddddf edddddddddddddddddaaaadddddddddddddddf eddddddddddddddddaaaaaaddddddddddddddf eddddddddddddddddaaaaaaddddddddddddddf edddddddddddddddgaaagaaadddddddddddddf edddddddddddddddaaaddabbbbbbbbbbdddddf edddddddddddddddaaaddbbbbbbbbbbbgddddf eddddddddddddddgaagddbbbbbbbbbbbbddddf eddddddddddddddaaaddbbbaaaddddbbbbdddf eddddddddddddddaaaddbbbaaaaddddbbbgddf edddddddddddddgaagddbbbdaaaddddgbbbddf edddddddddddddaaaddbbbgdgaaaddddbbbbdf edddddddddddddaaaddbbbdddaaagddddbbbgf eddddddddddddgaagdgbbbddddaaaddddgbbbf eddddddddddddaaaddbbbdddddaaagddddbbbb eddddddddddddaaaddbbbddddddaaadddddbbbc edddddddddddgaagdgbbbddddddaaaaddddgbbb edddddddddddaaaddbbbddddddddaaadddddbbbb edddddddddddaaaddbbbddddddddgaaadddddbbbc eddddddddddaaagdgbbgdddddddddaaagddddfbbb eddddddddddaaaddbbbdddddddddddaaaddddfbbbb gg eddddddddddaaaddbbbdddddddddddaaagdddf bbbc abbb edddddddddaaaddbbbgddddddddddddaaadddf cbbb ebbbbbbc edddddddddaaaddbbbdddddddddddddaaaaddf bbbb eeeeeeeeeecbbbbbbaeeee eddddddddgaaadgbbbddddddddddddddaaaddf bbbc efdddddddbbbbbbbgdddddd eddddddddaaaddbbbgddddddddddddddgaaadf cbbb eddddddbbbbbbbgdddddddd eddddddddaaaddbbbddddddddddddddddaaagf bbbb edddgbbbbbbbddddddddddd edddddddgaaadgbbbdddddddddddddddddaaaf bbbc edgbbbbbbbaaaggdddddddd edddddddaaaddbbbddddddddddddddddddaaag cbbb abbbbbbbaaaaaaaaaaaaddd edddddddaaaddbbbdddddddddddddddddddaaa bbbb ebbbbbbbaaaaaaaaaaaaaaaddd eddddddgaagdgbbgdddddddddddddddddddaaaa bbbc cbbbbbbbddaagddddddggaaaaddd eddddddaaaddbbbdddddddddddddddddddddaaae cbbb gbbbbbbadddgaagddddddddddddddd eddddddaaaddbbbdddddddddddddddddddddgaaa bbbb abbbbbbc edddgaagddddddddddddddd edddddgaagdbbbgddddddddddddddddddddddaaac bbbbbbbbbbe edddgaagddddddddddddddd edddddaaaddbbbdddddddddddddddddddddddfaaa cbbbbbbb edddgaadddddddddddddddd edddddaaaddbbbdddddddddddddddddddddddfaaac bbbbg edddaaadddddddddddddddd eddddgaagdbbbgdddddddddddddddddddddddf aaa gc edddaaadddddddddddddddd eddddaaaddbbbddddddddddddddddddddddddf caaa edddaaadddddddddddddddd eddddaaadgbbbddddddddddddddddddddddddf aaae edddaaadddddddddddddddd edddaaagdbbbdddddddddddddddddddddddddf caaa edddaaadddddddddddddddd edddaaaddbbbdddddddddddddddddddddddddf aaac edddaaadddddddddddddddd edddaaadgbbbdddddddddddddddddddddddddf eaaa efffaaaffffffffffffffff eddaaagdbbbddddddddddddddddddddddddddf aaac aaa eddaaaddbbbddddddddddddddddddddddddddf aaa aaa eddaaadgbbgddddddddddddddddddddddddddf caaa aaa edaaaddbbbdddddddddddddddddddddddddddf aaae aaa edaaaddbbbdddddddddddddddddddddddddddf caaa aaa egaaadbbbgdddddddddddddddddddddddddddf aaac aaa eaaaddbbbddddddddddddddddddddddddddddf eaaa eaac eaaadgbbbddddddddddddddddddddddddddddf aaac eaac caagdbbbgddddddddddddddddddddddddddddf aaa caac aaaddbbbdddddddddddddddddddddddddddddf caaa caac aaadgbbbdddddddddddddddddddddddddddddf aaae caae caagdbbbddddddddddddddddddddddddddddddf caaa caae aaaffbbbffffffffffffffffffffffffffffffd aaac aaa caa gbba eaaa aaa bbb aaac aaa bbb aaa aaa abbc caaa aaa bbb aaae aaa ebbb caaa aaa bbbc aaac aaa bbb eaaa aaa cbbb aaac aaa bbbe aaa aaa bbb caaa aaa cbba aaae aac bbb caaa eaac bbb aaac eaac e eaaa caac aaac caae aaa caae caaacaa aaaaaa caaaaa aaaaa eaaaa aaaa aaa cac ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#cc8eb0ff b,#ac6a77ff c,#ebd7e0ff d,#d5a7bdff e,#f6eef2ff f,#b67c88ff g,#e1c2d0ff ``` ```image e daag aaaac eaaaaae gaaaaag eaaaaaaad gaaaaaaaac aaaaaaaaad caaaaaaaaaac gaaaaaaaaaaa aaaaacaaaaaa caaaad gaaaaae daaaac aafbbbffffffffffffae aaaaae cfbbbbbbbbbbbbbbbbbfe caaaad bbbbbbbbbbbbbbbbbbba eaaaaae abbbbbbbbbbbbbbbbbbbbfe caaaaa bbbbbbbbffffffffbbbbbba daaaaa gbbbbbaaaae abbbbbbc eaaaaaa abbbbbaaaad efbbbbbf gaaaaag ebbbbbbaaaaac gbbbbbb daaaaac gbbbbbaaaaaad abbbbbc eaaaaaa fbbbbbgaaaaaac efbbbbfe gaaaaag ebbbbbb gaaaaaae gbbbbba daaaaac dbbbbba eaaaaaag abbbbbg eaaaaaa fbbbbbc gaaaaaae efbbbbfe gaaaaag cbbbbbf aaaaaad gbbbbba aaaaad fbbbbbc daaaaad efbbbbf aaaaag bbbbbf eaaaaaa gbbbbb aaaaae bbbbbd gaaaaae bbbbb caaaad ebbbbbe eaaaaag fbbbb gaaaag gbbbbf gaaaaae cbbbb aaaaae abbbbg daaaad abbb caaaad ebbbbbe caaaaac efbb daaaac dbbbba daaaad cbb eaaaaae fbbbbg eaaaaag ab caaaad cbbbbb gaaaaae ef eaaaaa fbbbbc gaaaaae caaaad cbbbbf aaaaad daaaac abbbbd aaaaaac eaaaaa bbbbbe daaaaad gaaaag gbbbbf eaaaaaag daaaac abbbbg gaaaaaae eaaaaa ebbbbbe eaaaaaag gaaaaa gbbbbb gaaaaaa aaaaaa fbbbbb daaaaa eaaaaad ebbbbbb caaaaac aaaaaae fbbbbbc eaaaaag caaaaad cbbbbbf gaaaaae gaaaaag dbbbbbd eaaaaag aaaaaae fbbbbbc gaaaaae caaaaad cbbbbbf daaaad daaaaac abbbbbd caaaaac aaaaaae bbbbbbe daaaad caaaaad bbbbbf eaaaaa daaaaac bbbbbg aaaaa aaaaaa ebbbbbe aaaaa aaaaac fbbbbg daaa eaaaaa cbbbbb caaa gaaaag dbbbba daa daaaac fbbbbc eaa eaaaaa cbbbbf ga gaaaag dbbbbd ea daaaae bbbbbc g eaaaaa gbbbbf gaaaag abbbbd aaaaae ebbbbbe gaaaag fbbbbg aaaaae ebbbbbe caaaad dbbbbb gaaaag fbbbbb aaaaae cbbbbbf caaaaa dbbbbbd daaaaa fbbbbbc eaaaaaa cbbbbbf caaaaad abbbbbd daaaaac ebbbbbbe eaaaaaa gbbbbbf daaaaac ebbbbbbe eaaaaaa gbbbbba gaaaaag fbbbbbg daaaaac bbbbbb aaaaaa bbbbba aaaaag bbbbbc aaaaae cbbbbf eaaaad dbbbbd gaaaag bbbbbc aaaaae gbbbbf gaaaag ebbbbbe aaaaae gbbbba caaaad fbbbbg daaaac ebbbbbe aaaaae dbbbba caaaad fbbbbg daaaac cbbbbf eaaaaa dbbbbd caaaad fbbbbc daaaac cbbbbb aaaaa bbbbbb aaaaa gbbbbbf aaaaa abbbbbg aaaag ebbbbbbe aaaae gbbbbba ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Time for a closer look at another area. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#cc8eb0ff b,#ac6a77ff c,#ecd8e2ff d,#d6aabfff e,#f6ecf1ff f,#bc8392ff g,#e1c0d0ff ``` ```image gfbbbbbbbbbbbbfg edbbbbbbbbbbbbbac cabbbbbbbbbbbbbde cfbbbbbbbbbbbbfg gfbbbbbbbbbbbbfc edbbbbbbbbbbbbbac cabbbbbbbbbbbbbde gfbbbbbbbbbbbbfg egfbbbbbbbbbbbbbfaaaaddggcce edbbbbbbbbbbbbbfaaaaaaaaaaaaaaaaddggcce abbbbbbbbbbbbbfaaaaaaaaaaaaaaaaaaaaaaaad bbbbbbbbbbbbfaaaaaaaaaaaaaaaaaaaaaaaaaad bbbbbbbbbffaaaaaaaaaaaaaaaaaaaaaaaaaaaag bbbbbbbdcaaaaag eccggddaaaaaaaaaaaaaaaag bbbbfde eaaaaag eeccggddaaaaaac bbfg eaaaaag eeccge ac caaaaag caaaaac caaaaac gaaaaac gaaaaac gaaaaae gaaaaae daaaaae daaaaa daaaaa daaaaa aaaaaa aaaaad aaaaad aaaaad eaaaaad eaaaaag eaaaaag caaaaag ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area B. Answer: A: 1; B: 0; 1 + 0 = 1 There's only one, but is an intersection after all.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#cc8eb0ff b,#ac6a77ff c,#e9d3ddff d,#d6a9beff e,#f5ecf0ff f,#b77c89ff g,#e0beceff ``` ```image e daa aaag eaaaa aaaaad aaaaaa caadgaaa aaae fbbbbbbbbbf aaa bbbbbbbbbbbc caad bbbbfffffbbb aaa abbfaa fbbf aaa bbbdaad bbbc gaag ebbb aaae cbbb aaa fbbc gaaa fbbf aaa bbb aaac bbbc gaag cbbf eaaa cbbb aaa bbbe aaag fbbf aaa bbb aaa bbbc daac dbba daad cbbb aaa bbb aaae fbbf eaaa bbb caaa bbbg daac abbd aaac cbbb aaa bbb eaaa fbbf dd eaaa ebbb aaag bbbg fbbb aaae fbbg aaa cbbb ebbbbbbc aaa bbb daad fbbb gbbbbbbf caad cbbf aaae bbbg abbbbbbd aaae fbbc caaa cbbb fbbbbbbc aaa bbb aaac fbbb cbbbbbbfe caad gbbf eaaa bbbg gbbbbbbfaadgce aaa bbbe aaag cbbb abbbbbbfaaaaaaaaaaaa aaa bbb aaa fbbb efbbbbbbaaaaaaaaaaaaaaa caag dbba daad bbbg cbbbbbbfeeaag ecgdaaa aaa bbb aaae cbbb dbbbbbba caac aaa bbb caaa fbbb abbbbbbg caac gaag abbd aaac bbbbbbbbbbe gaae aaa bbb eaaa cbbbbbbf gaae aaa ebbb aaag fbbbd daa gaac fbbc aaa dg daa aaa bbb daaa aaa eaaa cbbf aaae aaa daac bbbe caaa aaa aaa bbb aaac aaa eaaa gbba eaaa aaa daae bbb aaag aaa aaa bbb aaa aaa eaad dbbd daaa aaa aaae bbb aaae aaa aaa ebbb caaa aad caad fbbg aaac aad aaae bbb eaaa eaag aaa cbbf aaag eaag caad fbbc aaa caac aaa bbb daaa caac aaa gbbf aaae gaae gaag bbbe caaa gaae aaa bbb aaac daa gaa dbba eaaa aaa bbb aaag aaa bbb aaa aaa abbd daaa aaa bbb aaae aaa ebbb caaa aaa fbbc aaac aaa bbb eaaa aaa cbbf aaad aaa bbbe aaa aaa bbb daaa aad gbba aaae aad bbb caaa eaag fbb aaac caag e eaaa caac aaad gaac aaa gaae gaaadaa aaaaaa caaaaa aaaaa eaaaa aaaa aaa cag ``` <!-- end of image -->
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This image seems promising for intersection detection. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#5a7870ff b,#3f605bff c,#b0d6b0ff d,#eef4eeff e,#a0b397ff f,#8a9a73ff g,#cfd6c9ff ``` ```image fd gfc ffe ffe fff dfff efff ffff ffff feff gfgff ff ef ff efd ff cfd dfc gfg efd dfg ff dfc ff fe fe ff gfg ff ff ff ff ff ff ff dfc ff efd ff ff ff ff ef fe cfd dbf gfg gfg bb ff gfg bb ff dfc bb ff fe bb dfc fe fbd efd ff cbg ff ff dbe ff ff ba ef fe ff bb abbbd gfg ff bb bbbfbba ff ff bb dbba dbbbg ff ff fb gbbe ebba ff ef cbg ebbg bbbg gfc ef dbe abbd ebbb efd cfd ba bbb bbbe ff gfg bb bba cbbb ff gfg bb dbbf abbe fe dfc bb cbbc gbbbd gfg fe ab fbbd abbf ff fe ebgabb dbbbd ff ff gbbbb fbba ff ff bba dbbbg dddddddddddddgfgddddddddddddffddddd ae ebba dcccccccccccccffcccccccccccccffccccc dbbbg dcccccccccccccffcccccccccccccffccccc ebbb dcccccccccccccffcccccccccccccffccccc bbbeccccccccccccefecccccccccccccffccccc cbbbcccccccccccffccccccccccccccffccccc abbfcccccccccffccccccccccccccefccccc debbbccccccccffccccccccccccccefccccc dccabbacccccefeccccccccccccccefecccc dcccebbbccccffccccccccccccccccfecccc dcccccabbaccffccccccccccccccccfecccc dcccccccbbbeffccccccccccccccccffcccc dccccccccabafeccccccccccccccccffcccc dccccccccccffbecccccccccccccccffcccc dccccccccccffbbbccccccccccccccffcccc dccccccccccffcbbbfccccccccccccffcccc dcccccceffffeccfbbbcccccccccccffcccc dccefffffffecccccbbbfcccccccccffcccc gefffffffeccccccccccebbbccccccccffcccc defffffffecccccccccccccccccabbaccccccffcccc gfffffffeg dccccccccccccccccccccebbbcccccefcccc gefffffffcd dccccccccccccccccccccccabbacccefcccc dcfffffffeg dccccccccccccccccccccccccbbbecefeccc gefffffffcd dcccccccccccccccccccccccccabbaefeccc dcfffffffeg dcccccccccccccccccccccccccccbbbfeccc gefffffffg dccccccccccccccccccccccccccccfbaaccc defffffffcd dccccccccccccccccccccccccccccccbcccc gfffffffeg dccccccccccccccccccccccccccccccccccc gefffffffcd dccccccccccccccccccccccccccccccccccc ffffeg dccccccccccccccccccccccccccccccccccc cd ddddddddddddddddddddddddddddddddddd ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#627c75ff b,#40615bff c,#b0bba7ff d,#e7eae5ff e,#95a48fff f,#8b9a71ff g,#ccd3c7ff ``` ```image cfffd gfffg efff gfffg dfffc dfffg gfffg dfffc cfffd dfffc efff fffc dfffc fffe c gfffg effe bad cfffd effe bbbc efff efff bbbbag dfffc cfff bbbbbbe gfffg cfffd debbbbbag cfffd cfffd gabbbbbe efff gfffd ebbbbbag dfffc gfffg gabbbbbed gfffg gfffg cbbbbbbc cfffd dfffg dabbbbbad efff dfffg cbbbbbbc dfffc dfffc dabbbbbad gfffg fffc cbbbbbbc cfffd fffc dfbbbbbadefff fffe gbbbbbbfffc effe debbbafffg efff gabafffe cfff effffbag cfff dfffabbbed cfffd gfffabbbbbg cfffd cfffgabbbbbad gfffd efff cbbbbbbc gfffg dgcfffc dabbbbbad gfffg dgcefffffffg cbbbbbbc dfffg dgcffffffffffffd dfbbbbbad dfffc dgceffffffffffffffcd gbbbbbbe dfffc dgcffffffffffffffecgd debbbbbag fffc ffffffffffffecgd gabbbbbe fffc ffffffffecgd ebbbbbag fffe fffecgd gabbbbbed effe gd ebbbbbbg efff dabbbbbad cfff cbbbbbbc cfff dabbbbbad cfffd cbbbbbbc gfffd dabbbbbad gfffd gbbbbbbe gfffg debbbbbagdfffg gabbbbbefffg ebbbbbfffc gabbbfffc ebbaaaad dabbbe cbbd dg ``` <!-- end of image --> Yes! I knew it! There's 1 intersection right here in area A! Answer: A: 1; 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#66807aff b,#40615cff c,#b2bdaaff d,#e6e9e4ff e,#99a78fff f,#8b9a71ff g,#ccd3c5ff ``` ```image f gfc efc ffe fff dfff cfff ffff ffff feff gfgff ef ef ff cf ff gfd dfc gfg cfd dfg ff dfc ff fe fe fe gfg ff ef ff ff ff ff ff dfc ff cfd ff ff ef ff ef fe cfd dbe gfg gfd bb ff gfg bb ff dfc bb ff fc bb dfc fe ab cfd ff cbg ff ff dbe ff ff bb ee fe ff bb abbbd gfg ff bb bbbabba ff ff bb bba dbbbg ff ff ab gbbe ebba ff ef cbg ebbg bbbg dfc cf dbe abbd cbbb cfd cfd ba bbb bbbc ff gfg bb bbb cbbb ff dfg bb dbba bbbe fe dfc bb cbbc gbbbd gfg fe ab abbd abba ff fe cbgbbb dbbbd ff ff dbbbb abba ff ff bba dbbbg gfg ff bc ebba ef ff bbbg ff ff cbbb ff ff bbbc gfg ef cbbb ef ef bbbe ff cf gbbb ff gfd abbf gfg gfg dbbbd ef dfg abba ff fc dbbbdff fe ebafg ff ffbg ff ffbbb ff ff bbbc ff gefffg cbbb ff dcfffffffc bbbe ff geffffffeg gbbb ff dcfffffffcd abbe ef gfffffffeg dbbbd cf defffffffcd abba cfd dcfffffffeg dbbbd gfd gefffffffg ebbadfg dcfffffffcd bbbfc geffffffeg ebaa dcfffffffcd bd gfffffffeg defffffffcd ffffeg g ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7da184ff b,#6daf20ff c,#d6e4ceff d,#9dc991ff e,#8cc054ff f,#eff6eeff g,#b1d7b1ff ``` ```image g b b cb dd bc b b b ge eg bf b b fb dd ec b b ag b aa ce cag ed aa bf cag b aa b caf fb faf ge faf eg fa b ca b ca b ca cb ga dd ga bc da b da b aa b ad ge ad eg ag bf ag b ac b ac fb ac ffffffffffffffffffffffff dd af fdggggggggggggggggggggggd ec faf fgggggggggggggggggggggggd b faf fgggggggggggggggggggggggd b fa fgggggggggggggggggggggggd b ca fgggggggggggggggggggggggd ce cafgggggggggggggggggggggggd ed gagggggggggggggggggggggggd bf gaggggggggggggggggggggggd b faagggggggggggggggggggggd b fgaaggggggggggggggggggggd fb fggaagggggggggggggggggggd ge fgggaaggggggggggggggggggd ec fggggaagggggggggggggggggd b fgggggaaggggggggggggggggd b fggggggadgggggggggggggggd b fgggggggadggggggggggggggd cb fggggggggadgggggggggggggd dd fgggggggggadggggggggggggd fcgdebbc fggggggggggaggggddeeebbbbbbbbbeedgc fgggdeeebbbbbbbbbbeeddggd fcgdebbbbbbbbbbeeddggggaggggggggggd fcgdeebbbbbbbbeedgcf fgggggggggggggagggggggggd deebbbbbbbbeedgcf fgggggggggggggdaggggggggd dgcf fggggggggggggggdagggggggd fgggggggggggggggdaggggggd fggggggggggggggggdagggggd fgggggggggggggggggaaggggd fggggggggggggggggggaagggd fgggggggggggggggggggaaggd fggggggggggggggggggggaagd fgggggggggggggggggggggaad fggggggggggggggggggggggaa fgggggggggggggggggggggggag fgggggggggggggggggggggggdag fgggggggggggggggggggggggd ac ffccccgggdda fgggggggggggggggggggggggd aaaaaaaaaaadddgggccc fgggggggggggggggggggggggd fgggggggggggggggggggggggd fgggggggggggggggggggggggd ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#7ca083ff b,#6daf20ff c,#e1ebdfff d,#a5ce77ff e,#86ba4eff f,#9cb7a2ff g,#c4d8baff ``` ```image g ag aac faac faac faac faac faac faa aaf caaf caaf caaf caaf caaf caag gaag gaag gaag gaag gaac faac faac faac cc faac ccgggdddeebbbbb ccgaeeddeebbbbbbbbbbbbbbbbbb ccgggdddeebbbbbbbbbbbbbbbbbbeedddgggcc eeebbbbbbbbbbbbbbbbbeeeeeeggcc bbbbbbbeedddgggcc caaf ggcc caaf caaf caaf caaf caaf gaag gaag gaag gaag gaac faac faac faac faac faac faac aaa caaf caaf caaf caa ca c ``` <!-- end of image --> My analysis confirms the presence of 1 intersection in area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#7da084ff b,#6daf20ff c,#dfead9ff d,#aad07dff e,#8bbf4eff f,#a2bba7ff g,#c4dab4ff ``` ```image g b b cb dd bc b b b ge eg b b b cb dd eg b b af b aa ge caf dd aa bc caf b aa b cac b ac ge a eg ca b ca b ca b ga cb ga dd fa bc fa b fa b aa b af ge af eg af b ag b ag b ac cb ac dd ac ec a b ca b ca b ca ge ga dd ga bc fa b fa b fa b aa ge af eg af b af b ag b ag cb ac dd ac cggdebbc ac cggdebbbbbbbbbeddgc cggdebbbbbbbbbeddgc ccgdeebbbbbbbbeedgc ca cgdeebbbbbbbbeedgc ca deebbbbbbbbeedgc ca dgcc ca ga fa fa fa aa af af af ag ag ac ccccggffffa aaaaaaaaaaaffffgggcc ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#4bf2feff b,#9f42c1ff c,#b1f9ffff d,#c092d4ff e,#eef3f1ff f,#78e8e1ff g,#b0d6b0ff ``` ```image eac aa fac aa caf aa eaa aae aa aac aa fac aa caf aa eaa aae aa aac aa cac aa caa aa eaa aae d aa ebbb aac bbbd aa dbbb cac ebbbd aa bbbb caa dbbbe aaeeeeeeeeeeeeeeeeeeeeeee ebbbd eaagggggggggggggggggggggge dbbb aagggggggggggggggggggggge dbbbe eaaggggggggggggggggggggge bbbd eaafgggggggggggggggggggge dbbb egaagggggggggggggggggggge ebbbe egfafggggggggggggggggggge bbbd eggaaggggggggggggggggggge dbbb eggfafgggggggggggggggggge ebbbe egggaagggggggggggggggggge bbbd egggfafggggggggggggggggge dbbb eggggaaggggggggggggggggge ebbbe eggggfafgggggggggggggggge bbbd egggggaagggggggggggggggge dbbb egggggfafggggggggggggggge ebbbd eggggggaagggggggggggggggebbbb eggggggfafgggggggggggggdbbbe egggggggaaggggggggggggbbbd egggggggfafgggggggggbbbbe eggggggggaagggggggdbbbgge eggggggggfafgggggbbbdggge egggggggggaagggbbbbggggge egggggggggfafdbbbggggggge eggggggggggbbbbdgggggggge eggggggggbbbbdgggggggggge egggggdbbbbgaagggggggggge egggbbbbbgggfafggggggggge egbbbbdggggggaaggggggggge dbbbbgggggggggfafgggggggge dbbbbggggggggggggaagggggggge ebbbbdegggggggggggggfafggggggge dbbbbe eggggggggggggggaaggggggge dbbbb eggggggggggggggfafgggggge ebbbbd egggggggggggggggaagggggge dbbbbe egggggggggggggggfafggggge dbbbb eggggggggggggggggaaggggge ebbbd eggggggggggggggggfafgggge be egggggggggggggggggaagggge cfe egggggggggggggggggfafggge caaaaaf eggggggggggggggggggaaggge caaaaaaac eggggggggggggggggggfafgge caaaaaaac egggggggggggggggggggaagge caaaaaaac egggggggggggggggggggfafge caaaaaaac eggggggggggggggggggggaage caaaaaaac eggggggggggggggggggggfafe caaaaaaac egggggggggggggggggggggaae caaaaaafc egggggggggggggggggggggfaaaaaaaafc eggggggggggggggggggggggaaaafe e ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#4bf1feff b,#9e3fc1ff c,#9bf7ffff d,#c494dcff e,#e3c9edff f,#eaf9fdff g,#ab65cdff ``` ```image aac aaaf aaac aaaaf caaac aaaaf caaaa aaaac faaaa caaac faaaa caaac faaaa caaac faaaa caaac faaaa caaac faaaa caaac faaaa caaac faaaa caaac faaaa caaac faaaaf caaac faaaaf caaac faaaaf caaac e faaaaf egb caaac dbbb faaaaf ebbbbb caaac egbbbbbg faaaaf dbbbbbbd caaac egbbbbbgf faaaaf fgbbbbbge caaac dbbbbbbd faaaaf egbbbbbge caaac fdbbbbbbe faaaaf dbbbbbbd caaacfdbbbbbbge faaagbbbbbbbe dgbbbbbbbdf fdbbbbbbbbdf edbbbbbbbbd egbbbbbbbgaaaf fdbbbbbbbbdecaaac edbbbbbbbgd faaaaf egbbbbbbbge caaac fdbbbbbbbbde faaaaf edbbbbbbbgdf caaac egbbbbbbbge faaaaf bbbbbbbde caaac bbbbbdf faaaaf bbge caaac de faaaaf caaac faaaaf caaac faaaaf caaac faaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaaf caaac aaaa caaa aaa caa ``` <!-- end of image --> Yes! I knew it! There's 1 intersection right here in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#4af2ffff b,#9e3fc1ff c,#b0f8ffff d,#cb9edfff e,#e8d2f0ff f,#81f5ffff g,#b268ceff ``` ```image ac aa fac aa caf aa aa aa aa aac aa fac aa caf aa aa aa aa fac aa faf aa caf aa aa aa d aa ebbg fac gbbg aa dbbb faf bbbe aa gbbg caf dbbb aa bbbd aa gbbg aa ebbbe aa bbbd fac gbbb aa ebbbe fac bbbd aa dbbb fac ebbbe aa bbbg fac dbbb aa ebbbe fac gbbg aa dbbb fac bbbd aa gbbg fac dbbb aa bbbd fac gbbg aa ebbbe fac bbbd aa gbbb cacdbbbe bbbbd ebbbbd dbbbbeaa gbbbg caf ebbbbd aa dbbbbe caf gbbbg aa ebbbbd caf dbbbbe aa gbbbg caf ebbbbd aa dbbbbe caf gbbbg aa ebbbd caf be aa cf caf cfaaaaf aa cfaaaaaac caf caaaaaaac aa caaaaaaac caf caaaaaaac aa caaaaaaac caf caaaaaafc aa caaaaaafc cafaaaaaafc aaaafc ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#7ecbe5ff b,#62a178ff c,#5abfe6ff d,#a7dcf1ff e,#94c796ff f,#b1d7b2ff g,#d6edf3ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ffffffffffffffffffffffffffffffffffffffe ffffffffffffffffffffffffffffffffffffffe fffcafffffffffffffffffffffffffffffffffe fffccfffffffffffffffffffffffffffffffffe fffccfffffffffffffffffffffffffffffffffe fffacfffffffffffffffffffffffffffffffffe ffffcaffffffffffffffffffffffffffffffffe ffffccffffffffffffffffffffffffffffffffe ffffccffffffffffffffffffffffffffffffffe ffffacffffffffffffffffffffffffffffffffe fffbbcafffffffffffffffffffffffffffffffe fffbbcceffffffffffffffffffffffffffffffe fffffccbbbefffffffffffffffffffffffffffe fffffacebbbbbbbeefffffffffffffffffffffe ffffffcaffebbbbbbbbbbbeeffffffffffffffe ffffffccffffffffeebbbbbbbbbbbeefffffffe ffffffccfffffffffffffffeebbbbbbbbbbbbee ffffffacffffffffffffffffffffffeebbbbbbbbbbbefg fffffffcafffffffffffffffffffffffffffffeebbbbbbbbbbbfg fffffffccfffffffffffffffffffffffffffffe gebbbbbbbbbbbefg fffffffccfffffffffffffffffffffffffffffe gfebbbbbbbbbbefg fffffffacffffffffffffffffffffccfffffffe gfebbbbbbbbbbefg ffffffffcafffffffffffffffffffcccffffffe gfebbbbbbbbbbbeg ffffffffccfffffffffffffffffffccccfffffe gfbbbbbbbf eeeeeeeecceeeeeeeeeeeeeeeeeeeccacceeeef gfg dcg cc gccg ca cc gccg cc cc ccd cc ca cca dcg ca cca ca ca acc cc cd acc cc cd dcc gcg cd gccg ca cd gccg cc gcg ccd ac gcg cca gcg gcg cca ca gcg acc cc dcg acc ac dc dcc gcg dc gccg ca dc gccg cc ac ccd ac ac cca gcd ac cca cc ac ccc cc cc acc ac cc dcc gcd cc gccg cc cc gccg cc cc ccd dc cc cca gcd cc cca cc cc ccc cc cc acc dc cc dcc cd cc gccg cc cc gccg cc ca ccd dc ca cca cd ca cca cc cd ccc cc cd acc dcg cd dcc cd cd gccg cc gcg gccg cc gcg ccd dcg gcg cca ca gcg c ccg dc cc dc dcd dc cc dc gcc ac acg ac cc ac dcaac cccc ccc acc cc ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#9dd8f0ff b,#61a077ff c,#5cbfe6ff d,#78af90ff e,#9cc3a9ff f,#c0d9c8ff g,#d8eceeff ``` ```image g accg ccca accc acccg gccca ccca accc acccg gccca ccca accc acccg gccca ccca accc fdfacccg ebbdccca bbbbcccc gebbbccccbeg fddcccdbbdf gcccdbbbbbeg ccccbbbbbbbdeffg acccgebbbbbbbbbbbddeffg gcccg fdbbbbbbbbbbbbbbbbdeefgg ccca gedbbbbbbbbbbbbbbbbbbbbdeeffg cccc ggfeedbbbbbbbbbbbbbbbbbbbbddeffg accc gffeddbbbbbbbbbbbbbbbbbbbbdeffg gcccg gffeedbbbbbbbbbbbbbbbbbbbbdeefgg ccca ggfeedbbbbbbbbbbbbbbbbbbbbdeeff cccc ggfeedbbbbbbbbbbbbbbbbbb accc gffeddbbbbbbbbbb gcccg gffeedbbb ccca gg cccc accc gcccg ccca accc g acccg cccg gcccg gccccg ccca gcccccg accc gcccccca acccg gccccccca ``` <!-- end of image --> Incredible, there's actually 1 intersection in area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#83ceecff b,#63a179ff c,#5bbfe7ff d,#abdef2ff e,#9dc3aaff f,#c9ded0ff g,#dbeff6ff ``` ```image gcd cc cc ac gcd cc cc ac bbcd gbbcce ccbbbf dcgbbbbbbeeg cd ebbbbbbbbbbbef cc febbbbbbbbbbbef cc febbbbbbbbbbbefg dc geebbbbbbbbbbeef cd gfebbbbbbbbbbbef cc febbbbbbbbbbbefg cc febbbbbbbbbbbefg dcg ac gfebbbbbbbbbbbef ca ccc gfebbbbbbbbbbbef cc cccc febbbbbbbe cc ccdcc feg dcg cc gccg ca cc gccg cc cc ccd cc ca cca dcg ca ccc ca ca ccc cc ca acc cc cd dcc dcg cd gccg ca cd gccg cc gcd ccd ac gcg cca gcg gcg ccc ca gcg ccc cc dcg acc ac dc dcc gcd dc gccg cc dc gccg cc ac ccd ac ac cca gcd ac ccc cc cc ccc cc cc acc ac cc dcc gcd cc gccg cc cc gccg cc cc ccd ac cc cca gcd cc cca cc cc ccc cc cc acc dc cc dcc cd cc gccg cc cc gccg cc ca ccd dc ca cca cd ca cca cc ca ccc cc cd acc dcg cd dcc ca cd dccg cc gcd gccg cc gcg ccd dcg gcg cca ca dcg c ccg dcg cc dc dcd dc cc dc gcc ac acg ac cc ac dcacc cccc ccc acc cc ``` <!-- 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,#2c7543ff b,#e5e20aff c,#93c397ff d,#e9eec6ff e,#b1d7b1ff f,#e1e65dff g,#579267ff ``` ```image bbb dbbbbbd bbbbbbbbf dag bbb dbbbbbf gaa fbbf dbbbbbb aaa bbb fbbbbbd eaac bbb fbbbbbf aaa fbbd dbbbbbf aaa bbb bbbbbbd eaac bbb fbbbbbd aaa fbbd fbbbbbf aaa dbbb dbbbbbb ccgaagccccccccccccbbbcce bbbbbbd eeeaaaeeeeeeeeeeebbbeeec fbbbbbd eeeeaaaeeeeeeeeefbbfeeec fbbbbbf eeeegaaceeeeeeeebbbeeeec dbbbbbb eeeeeaaaeeeeeeebbbeeeeec bbbbbbd eeeeecaageeeeefbbfeeeeec fbbbbbf eeeeeegaaceeeebbbeeeeeec dbbbbbf eeeeeeeaaaeeebbbeeeeeeec dbbbbbb eeeeeeecaagefbbfeeeeeeec bbbbbbd eeeeeeeeaaaebbbeeeeeeeec fbbbbbf eeeeeeeeeaabbbeeeeeeeeec dbbbbbf eeeeeeeeecbbbfeeeeeeeeec dbbbb eeeeeeeeeebbbeeeeeeeeeec fd eeeeeeeeebbbaaeeeeeeeeec eeeeeeeebbbgaaceeeeeeeec eeeeeeeebbbeaaaeeeeeeeec eeeeeeebbbeeeaaaeeeeeeec eeeeeebbbeeeegaaceeeeeec eeeeefbbfeeeeeaaaeeeeeec eeeeebbbeeeeeecaageeeeec eeeebbbeeeeeeeegaaceeeec eeefbbfeeeeeeeeeaaaeeeec eeebbbeeeeeeeeeecaageeec eebbbeeeeeeeeeeeeaaaeeec cfbbfcccccccccccccaaacce bbb eaac bbb aaa fbbd aaa bbb caae bbb aaa fbbd aag dbb gaad e aaa egaaaaa daag caaaaaaaaaa gaad egaaaaaaaaaac aad aaa dgaaaaaaaaaage aac eaag caaaaaaaaaage aag aaa egaaaaaaaaaacd gaa aaa dgaaaaaaaaaage caa eaac caaaaaaaaaage daa aaaaaaaaaaaaacd aad aaaaaaage aac eage aag gaa caa daa aad aac aag gaa caa daa aad aac aag gaa caa daa aad aac aag gaa caa daa aad aac aag gaa cag ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#2e7644ff b,#e5e209ff c,#b1ccb9ff d,#f2f189ff e,#eff3d9ff f,#e9e73eff g,#71a17bff ``` ```image eaaaaag fbbbbbe gaaaaac dbbbbbd aaaaaae ebbbbbf caaaaag fbbbbbe gaaaaac dbbbbbd eaaaaaa ebbbbbf caaaaag bbbbbbe gaaaaae fbbbbbd eaaaaag dbbbbbf caaaaac ebbbbbb gaaaaae fbbbbbe eaaaaag dbbbbbd caaaaac ebbbbbf gaaaaae fbbbbbe eaaaaag dbbbbbd gaaaaac ebbbbbf aaaaaae fbbbbbe caaaaag dbbbbbd gaaaaac ebbbbbf eaaaaaaefbbbbbe caaaaafbbbbbd gaaaabbbbbf eaaabbbbbbe cabbbbbbd gbbbbbf ebbbbbbg fbbbbbaac dbbbbbbaaae ebbbbbbaaaag fbbbbbgaaaaac dbbbbbd aaaaaae ebbbbbf caaaaag fbbbbbe gaaaaac dbbbbbd eaaaaaa ebbbbbf caaaaag fbbbbbe gaaaaae dbbbbbd eaaaaag ebbbbbf caaaaac bbbbbbe gaaaaae fbbbbbd eaaaaag dbbbbbf caaaaac ebbbbbb gaaaaae fbbbbbe eaaaaag dbbbbbd gaaaaac ebbbbbf aaaaaae fbbbbbe caaaaag dbbbbbd gaaaaac ebbbbbf aaaaaa fbbbbbe caaaaag ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#2c7543ff b,#e5e209ff c,#99bca3ff d,#f4f298ff e,#dfe9d7ff f,#ecea4aff g,#579169ff ``` ```image bbb dbbbbbd bbbbbbbbd eag bbb dbbbbbf gaae dbbd ebbbbbb aaa bbb fbbbbbd eaac bbb dbbbbbf aaa fbbd dbbbbbf aaa bbb bbbbbbe caac bbb fbbbbbd aaa fbbe dbbbbbf aaa ebbf dbbbbbf caac bbb bbbbbbe aaa bbbe fbbbbbd aag dbbf dbbbbbf gaae bbb ebbbbbb aaa bbb bbbbbbe eaag dbbf fbbbbbd gaae bbb dbbbbbf aaa bbb ebbbbbb eaac dbbd fbbbbbd aaa bbb fbbbbbd aabbb dbbbbbf cbbbd ebbbb bbb fd bbbaa fbbcaac ebbf aaa bbb aag bbbe gaae dbbf aaa bbb eaag bbb gaae dbbf aaa bbb eaag bbb aaa dbbd aaa bbb caac bbb aaa fbbd aaa bbb caac bbb aaa fbbe aag dbf gaae c aaa egaaaaa eaag ecaaaaaaaaaa gaae cgaaaaaaaaaaceaae aaa egaaaaaaaaaage aac eaag ecaaaaaaaaaagc aag aaa cgaaaaaaaaaace gaa aaa egaaaaaaaaaage caa caac caaaaaaaaaagc eaa aaaaaaaaaaaaace aae aaaaaaage aac cagc aag gaa caa eaa aae aac aag gaa caa eaa aae aac aag gaa caa eaa aae aac aag gaa caa eaa aae aac aag gaa cag ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#054b63ff b,#ebfb53ff c,#8fbd9dff d,#f7fea6ff e,#b1d7b2ff f,#4a7e8bff g,#e9fd05ff ``` ```image ggbbddd dgggggggggggggggggbbddd dg ddbbbgggggggggggggggggggggbbddd bg ddbbbgggggggggggggggggggb bg ddbbbggggg gg gg gg gg dg gg gg ggd gg gg bggg gg gg ggeggeeeeeeeeeeeeee gg gg bgceggeeeeeeeeeeeeee gg gg ggceeggeeeeeeeeeeeee gb gg gg ceeggeeeeeeeeafeee gb gg gg ceeeggeeeeeecaceee gb gg gg ceeebgbeeeeefaeeee gg dgb ceeeeggeeeeefaeeee gg gg ceeeeeggeeeeaaeeee gg dgb ceeeeeggeeeeaaeeee gg gg ceeeeeeggeeeaaeeee gg bgd ceeeeeeggeeeafeeee gg gg ceeeeeeeggeeafeeee gg bgd ceeeeeeebgbcaceeee gg gg ceeeeeeeeggfaeeeee gg gg ceeeeeeeeeggaeeeee gg gg ceeeeeeeeeggaeeeee gg gg ceeeeeeeeeeggeeeee gg gg ceeeeeeeeeeggeeeee gg gg ceeeeeeeeeeaggeeee gg dgb ceeeeeeeeecabgbeee gg gg ceeeeeeeeefaegeeee gg dgb ceeeeeeeeefaeeeeee gg gg ceeeeeeeeeaaeeeeee bg bgd ceeeeeeeeeaaeeeeee bg gg ceeeeeeeeeaaeeeeee bg bgd ceeeeeeeeeafeeeeee bg gg ceeeeeeeeeafeeeeee bg gg ceeeeeeeecaceeeeee bg gg ceeeeeeeefaeeeeeee bg gg ceeeeeeeeaaeeeeeee bg dgb ceeeeeeeeaaeeeeeee bg gg eccccccccaaccccccc bgdgb af bggg af bggd eae bgg ca bgd fa d aa aa aa af ac ea fa ae aa aa aa fa aa aa af aa ac af eae aa ca eaf fa aa aa eac aa aa aa cae af aa ac fa ea aa fa aa aa aa aa aa aa af af aa ac eaaaaaaafcee eae effaaaaaaaaaaaaaaffce ca ecfaaaaaaaaaaaaaaafce fa ecfaaaaaaaaaaaaaaafce aa ecffaaaaaaaaaaaaaaffce aa ecfaaaaaaaaaaaaaaafcaa ecfaaaaaaaaf e ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#044b62ff b,#effd57ff c,#7da2aaff d,#f7fdb4ff e,#bacdd3ff f,#477b7fff g,#e8fc05ff ``` ```image gggggb gbbgggd gddgggb b bgggd d gggg bgggb gggg dgggb eee bgggd aaac dgggb aaac bgggd eaaae gggg eaaae bgggb caaa gggg caaa dgggb faaf bgggd faaf dgggb aaac bgggd aaae gggg eaaae bgggb caaa gggg caaa dgggb faaf bgggd faaf dgggb aaac bgggd aaac gggg eaaae bgggb eaaae gggg caaa dgggbcaaa bgggfaaf dggggaaf bgggfac ggggae bgggfe ggggd cgggb fggggd ffgggb aaggggd aaagggg eaaabgggb eaaaegggb caaa dgd caaa faaf aaaf aaac eaaae eaaae caaa caaa faaf faaf aaac aaac eaaae eaaae caaa caaa faaf aaaf aaac eaaae ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#044b62ff b,#effd52ff c,#7ba0acff d,#f7fea9ff e,#bed0d6ff f,#3f7587ff g,#e9fd04ff ``` ```image ggbbddd dgggggggggggggggggbbddd dg ddbbbgggggggggggggggggggggbbddd bg ddbbbgggggggggggggggggggb bg ddbbbggggg gg gg gg gg dg gg gg ggd gg gg bggg gg gg ggdgb gg gg bgd gg gg gg gg gg gb gg gg bgd ac gb gg gg gg eae gb gg gg bgd ca gg dgb gg fa gg gg dgb aa gg dgb gg aa gg gg gg aa gg bgd bgd af gg gg gg ac gg bgd dgbeae gg gg ggca gg gg dgga gg gg gga gg gg gg gg gg ggd gg gg agg gg dgb eabgb gg gg ca g gg dgb fa bg gg aa bg bgd aa bg gg aa bg bgd af bg gg ac bg gg eae bg gg ca bg gg aa bg dgb aa bg gg aa bgdgb af bggg ac bggd eae bgg ca bgd fa d aa aa aa af ac eae ca ae aa aa aa fa aa aa af aa ac af eae aa ca eaf fa aa aa eac aa aa aa cae af aa ac fae eae aa ca fa aa af aa aa aa eaf af aa ac eaaaaaaafcee eae ecfaaaaaaaaaaaaaafcce ca eecfaaaaaaaaaaaaaaafce fa ecffaaaaaaaaaaaaaafcee aa eccfaaaaaaaaaaaaaafcce aa eecfaaaaaaaaaaaaaaffcaa ecffaaaaaaaf e ``` <!-- 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,#68a454ff b,#d8bbe8ff c,#eff2f0ff d,#95c893ff e,#2c8409ff f,#bb8bd6ff g,#b1d7b1ff ``` ```image f bf cfb ff ff bf fb ff ff bfc fb ff bf cfc fb ff bf cfc ff ff bf cfb ff ff bfc fb ff ff cfc fb ff bf cfc ff ff ccccccccccccccc bf ggggggggggggggd cfb ggggggggggggggd ff ggggggggggggggd ff ggggggggggggggd ccccccccccccccccccccccbf ggggggggggggggd dgggggggggggggggggggggffc ggggggggggggggd dggggggggggggggggggggffgc ggggggggggggggd dgggggggggggggggggggffggc ggggggggggggggd dgggggggggggggggggggfgggc gggdggggggggggd dggggggggggggggggggffgggc gggeeeedggggggd dgggggggggggggggggffggggc ggggdaeeeeedggd dggggggggggggggggffgggggc ggggggggdaeeeeeg dggggggggggggggggfggggggc gggggggggggggaeeeeeg dgggggggggggggggffggggggc ggggggggggggggd cdeeeeeg dggggggggggggggffgggggggc ggggggggggggggd cdeeeeed dgggggggggggggffggggggggc ggggggggggggggd deeeeeagggggggggggggfgggggggggc ggggggggggggggd deeeeeaggggggggffgggggggggc gggffgggggggggd dgaeeeeeagggffggggggggggc ggggfgggggggggd dgggggaeeeeafgggggggggggc ggggffggggggggd dgggggggggdfaeeeagggggggc dddddffdddddddg dgggggggggffggdeeeeeadggc ff dggggggggffgggggggdeeeeeac ff dggggggggfggggggggggggdeeeeeeeeaadgc cfb dgggggggffggggggggggggggc cgdaaeeeeeeeeeeeeeadggc bfc dggggggffgggggggggggggggc cgdaaeeeeeeeeec ff dgggggffggggggggggggggggc cg ff dgggggfgggggggggggggggggc ff dggggffgggggggggggggggggc fb dgggffggggggggggggggggggc cfc dggffgggggggggggggggggggc bf dggfggggggggggggggggggggc ff dgffggggggggggggggggggggc ff dffgggggggggggggggggggggc ff ffggggggggggggggggggggggc cfb cfdddddddddddddddddddddddc bfc ff ff ff ff bfc ff fb fb ff cfc ff bf cfc fffb ff ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f9832ff b,#d4b3e5ff c,#edeeedff d,#84b76fff e,#288204ff f,#bd8bd8ff g,#bbd7b0ff ``` ```image cg geeadg deeeeeeadg gdaeeeeeeeeadgc cgdaeeeeeeeeadgc cgdaeeeeeeeeadgc cgdaeeeeeeee cgdaeeee cgda cfb fffb cfffb cfffc bfffc bfff fffb ``` <!-- end of image --> There is no intersection present within area A. Let's continue our search in the next region. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#519835ff b,#d2b0e4ff c,#ebe1f0ff d,#84b471ff e,#298205ff f,#bc89d7ff g,#bbd6b0ff ``` ```image cff fff bffb cfff cfffc fffb bfff cfffc cfffc bffb bfff cfffc fffc bffb bfff cfffc fffb bffb cfff cfffc fffb bffb cfffc dg cfffc eeeadg fffb eeeeeeeadg bfff gdeeeeeeeeeadg cfffc cgdeeeeeeeeeadg fffc cgdaeeeeeeeeadg bffb cgdaeeeeeeedfffc cgdaeeafffaeadgc cgfffdeeeeeeadgc bffbgdaeeeeeeeeadgc bfff cgdaeeeeeeeeadgc cfffc cgdaeeeeeeeeadg fffb gdaeeeeeee bffb gdaeee cfff gd cfffc fffb bfff cfffc cfffc bffb bfff cfffc fffc bffb bfff cfffc fffb bffb cfff cfffc fffb bffb cfffc cfffc fffb bfff fffc ``` <!-- end of image --> 1 intersection present within area B. Answer: A: 0; B: 1; 0 + 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#539837ff b,#d3b3e5ff c,#ebe2efff d,#89b876ff e,#298205ff f,#bc89d7ff g,#bad6aeff ``` ```image f bf cfc ff ff bf fb ff ff cfc fb ff bf cfc fb ff bf cfc ff ff bf fb ff ff cf fb ff bf cfc fb ff bf cfc fb ff bf fc ff ff bf fb ff ff cfc g fb eeeag ff cdeeeeag bf cdeeeeag cfc cdeeeeag fb deeeeag ff deeeeeg bf deeeeed cfc deeeeed ff fb geeeeed ff cfc gaeeedfc bf gfaeeedc ff ff gaeeeedc ff ff gaeeeedc fb cf gaeeeeeeeaddgc cfb fb cgddaeeeeeeeeeeeeaadgg bfc ff cgddaeeeeeeeeec ff bf cg ff cfc ff fb fb ff cfc bf bf cfc ff fb ff ff fb bf cfb fc bfc ff ff ff ff bf ff fb fb ff cfc ff bf cfc fffb ff ``` <!-- end of image -->
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I'm optimistic that I'll find some intersections in this image. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#3edf54ff b,#b21f0bff c,#dfe6d3ff d,#b1d8b1ff e,#bf5644ff f,#8fd293ff g,#d59d90ff ``` ```image cd aaf afaa aa caa af caa fa aa aa aac cac aac aa aad ad aaf bg fa faa bb aa daa gbc ca caa be aa caa bb ad aa eb fa aac dffffffffffffffffffffffd cbg af aac fddddddddddddddddddddddf bb da aadfddddddddddddddddddddddf bb aa aaaddddddddddddddddddddddf gbc ac faadddddddddddddddddddddf be aa faaddddddddddddddddddddf bb af ffaadddddddddddddddddddf eb da fddaaddddddddddddddddddf cbg aa fdddaadddddddddddddddddf cebbb ac fddddaafdddddddddddddddf gbbbbec aa fdddddaafdddddddddddddebbbbg ac af fddddddaafdddddddddebbbbg ac da fdddddddaaaddddgbbbbbgdf a aa fddddddddfaagbbbbedddddf a cac fddddddddebbbbeddddddddf a aa fdddddebbbbgaadddddddddf ca ad fdgbbbbegddddaaddddddddf ca fa gbbbbedddddddddaadddddddf da aa ebbbbedddddddddddddaafdddddf da ca gbbbbg fdddddddddddddddaafddddf da aa bbc fddddddddddddddddaafdddf fa ad bc fdddddddddddddddddaaaddf fa fa gb fddddddddddddddddddfaadf fa aa bb fdddddddddddddddddddfaaf aa ca bg fddddddddddddddddddddfaa aa aa cb fddddddddddddddddddddddaa aa ad bb fddddddddddddddddddddddfaa aa fa be fddddddddddddddddddddddf aac aa af bc fddddddddddddddddddddddf aad aa d eb dffffffffffffffffffffffd aaf af bb faf af bg daa af gb caa af bb caa ad bg aa ad cb aa ac eb aac ac be aad ac bc aafa gb faa bb da bg cb cb gb gb gb eb eb bb bb bb be be be bg bg bg bbec bc gebbbbeg bc gebbbbeg b gebbbbeg cb cebbbbbg cb cebbbbbeb cebbb ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#3dde52ff b,#b2200bff c,#e0a79fff d,#e3eeddff e,#c36451ff f,#6ee77eff g,#a9efb1ff ``` ```image g af aaf aaafd gaaaad gaaaad gaaaag daaaag daaaag dfaaaf faaaf faaaf faaafd gaaaad gaaaad gaaaag ceb daaaag cebbbb daaaag dcebbbbbbb dfaaaf dcebbbbbbbbec faaaf cebbbbbbbbecd faaaf cebbbbbbbbecd gaaafdcebbbbbbbbecd gaebbbbbbbbbec cebbbbbbbbecd dcebbbbbbbbbeg dcebbbbbbbbecaaaag dcebbbbbbbbec daaaag cebbbbbbbbecd dfaaaf dcebbbbbbbbecd faaaf ebbbbbbbbec faaaf bbbbbbec gaaafd bbecd gaaaad cd gaaaad daaaag daaaag daaaag faaaf faaaf faaaf gaaaad gaaaad gaaaad daaaa daaa dfa f ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#3ddf52ff b,#b21f0bff c,#eac5c0ff d,#c4f5cbff e,#c45344ff f,#7ee98cff g,#d99389ff ``` ```image df aaf afaa aa daa af daa fa aa aa aa da aad aa aad af faf bg fa faf bb aa daa gbc da daa be aa aa bb ad aa eb fa aad cbg af aad bb da aad bb aa faf gbc ad faf be fa daa bb af daa eb da aa cbg aa aa cebbb ad aad gbbbbe aa aad gbbbbg ad af aaf ebbbbg ad fa faf cbbbbec a aa faagbbbbe a da gbbbbg a aa cebbbbgaa da af cbbbbec aa da fa gbbbbe aa da aa ebbbbg aad da da gbbbbc aad fa aa bbc aaf fa ad bc faf fa fa gb faa fa af bb daa fa da bg daa aa aa cb aa aa ad bb aa aa fa be aad aa af b aad aa d eb aaf af bb faf af bc faa af gb daa af bb daa ad bg aa ad cb aa ad eb aad ad be aad a bc fafa gb faa bb da bg cb cb cb gb gb eb eb bb bb bb be be be bg bg bc bbec bc gebbbbec b cebbbbec b cebbbbeg b cebbbbbg cb cebbbbbeb cebbb ``` <!-- 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,#bb7228ff b,#b2f7e9ff c,#e2c4a6ff d,#e9f7f0ff e,#c29860ff f,#99c895ff g,#b1d7b1ff ``` ```image caa aaa aac dbd daa dbbb bb eaa dbbbb dbb aac dbbbbb bbb aa dbbb bbd bbbd eaa dbbb bbb bbbb aae dbbb dbb bbbb aad dbbb bbd bbbb caa bbbb bbb bbbbd aaa bbbb dbb dbbbbb aac bbbb bb dbbdbb daa bbbb bbd bbb bb eaa bbbb bbb bbd bbd aac bbbb dbb bbd bbb aa bbbb bb bb dbb eaa bbbd bbd bb bb aae bbbd bbb dbb bbd aad bbbd dbb dbb bbb caa bbbd bb bbb bbb aaa bbbd bbd bbb bb aac bbbd bbb bbd bbd caa bbbd dbb bbd bbb eaa bbbd bb bb bbb aac bbbd bbb bb fffgbbfffffffffffffaaffg bbb bbb dbb dggggbbggggggggggggeaaggf d bbb dbb bbb dggggbbbgggggggggggaaeggf dbb bbb bbd bbb dggggbbbgggggggggggaagggf bbb bbb bbb bbd dgggggbbggggggggggeaagggf dbb bbb dbb bbd dgggggbbggggggggggaaagggf bbb dbbb bb bb dgggggbbggggggggggaafgggf bbd dbbb bbd bb dgggggbbbggggggggfaaggggfbbb dbbb bbb dbb dggggggbbggggggggaaaggggfbbb dbbb dbb dbb dggggggbbggggggggaaegggggbb fffgbbbffffff bb bbb dggggggbbggggggggaagggggbbb gggbbbgggggggd bbdbbb dggggggbbbggggggeaagggggbbd gggbbggggggggd bbbbbd dgggggggbbggggggaaeggggbbb gggggggggggggd dbbbb dgggggggbbggggggaagggggbbd gggggggggggggd bbbb dgggggggbbgggggeaagggggbb gggggggggggggd bbbb dgggggggbbbggggaaaggggbbb gggggggggggggd bbbb dgggggggbbbggggaafggggbbf gggafggggggggd dbbb dggggggggbbgggfaaggggbbbf ggaaaagggggggd bbb dggggggggbbgggaaaggggbbbf gggaaaaegggggd bbd dggggggggbbbggaaeggggbbgf ggggfaaaaggggd d dggggggggbbbggaaggggbbbgf ggggggeaaaeggd dgggggggggbbgeaaggggbbggf ggggggggaaaafd dgggggggggbbgaaegggbbbggf gggggggggeaaaa dgggggggggbbbaaggggbbbggf gggggggggggaaaac dgggggggggbbbaaggggbbgggf ggggggggggggeaaaa dggggggggggbbaagggbbbgggf gggggggggggggdaaaae dggggggggggbbafgggbbggggf gggggggggggggd daaaad dggggggggggbbfgggbbbggggf ggggggggggggfd eaaae dgggggggggggbbgggbbbggggf ddddddddddddd daaaac dggggggggggebbgggbbgggggf caaaa dggggggggggabbggbbbgggggf aaaac dgggggggggeabbggbbggggggf caaaa dgggggggggaabbbbbbggggggf eaaae dgggggggggaagbbbbbggggggf daaaad dggggggggeaagbbbbgggggggf eaaae dggggggggaaagbbbbgggggggf aaaac dggggggggaafgbbbggggggggf caaaa dgggggggfaaggbbbggggggggf aaaac dgggggggaaagggggggggggggf caaaad dgggggggaaegggggggggggggf eaaae dgggggggaaggggggggggggggf daaaad dggggggeaaggggggggggggggf eaaaa ffffffaaeffffffffffffffg aaaac aa caaaa caa aaaae aae daaaad aad eaaae caa daaaac aaa caaaa aac aaaac daa caaaaeaa eaaaae daaa cc ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#bb7228ff b,#b1f8eaff c,#dab38bff d,#e1fbf6ff e,#cb945cff f,#e6cdb3ff g,#f3e8dcff ``` ```image dbbbbbbd dbbbbbbd dbbbbbbd dbbbbbbd dbbbbbbd dbbbbd dbbd dd gc eaaf faaaaeg aaaaaaac geaaaaaaaeg faaaaaaaac caaaaaaaaf geaaaaaaaeg caaaaaaaaf geaaaaaaaeg faaaaaaaac geaaaaaaaeg faaaaaaaa caaaaaa geaaaa caaa gea f ``` <!-- end of image --> No luck this time. Area A doesn't have an intersection. Okay, let's direct our attention to the next zone. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#bb7127ff b,#b2f7e9ff c,#dcc1a0ff d,#d9fbf4ff e,#c48749ff f,#f0e0d0ff g,#cfa374ff ``` ```image dbbbbd aaaae bbbbb caaaag bbbbb gaaaaf dbbbbd aaaaa dbbbbd faaaag bbbbb gaaaac bbbbb eaaaa dbbbbd faaaae dbbbbd caaaac bbbbb eaaaaf bbbbb aaaae dbbbbd caaaag dbbbbd gaaaaf bbbbb aaaaa bbbbb faaaag dbbbb gaaaac dbbbbd eaaaa bbbbd faaaae bbbbb caaaac dbbbb eaaaaf dbbbbd aaaae bbbbd caaaag bbbbb gaaaaf bbbbb aaaaa d dbbbbd faaaag d dbbbbd gaaaac b bbbbb eaaaa db bbbbb faaaae bb dbbbbd caaaac dbb dbbbbd eaaaaf dbb bbbbb aaaae bbb bbbbb caaaag dbbb dbbbbd gaaaaf bbbb dbbbbd aaaaa dbbbb bbbbb faaaag dbbbb bbbbb gaaaac bbbbb dbbbbd eaaaa dbbbbd dbbbbd faaaae bbbbb bbbbb caaaac dbbbbb bbbbb eaaaaf dbbbbd dbbbb aaaae bbbbb dbbbbd caaaag dbbbbd bbbbd gaaaaf bbbbb bbbbb aaaaa dbbbbb dbbbb faaaag dbbbbd dbbbbdgaaaac bbbbb bbbbdeaaaa dbbbbd bbbbbaaaae bbbbb bbbbbeaaac dbbbbb dbbbbgaaaf bbbbbd dbbbbcaae bbbbb bbbbbaac dbbbbd bbbbbaaf bbbbb dbbbbga dbbbbb dbbbbcg bbbbbd bbbbbc bbbbb bbbbb dbbbbd fcbbbbd bbbbb cgbbbbd dbbbbb eebbbbb bbbbbd faabbbbb bbbbb caacbbbbd dbbbbd gaagbbbbd bbbbb aaaebbbbd dbbbbb faaaabbbbb bbbbbd gaaaabbbbbdbbbbb eaaaadbbbbbbbbbd faaaag bbbbbbbbb caaaac bbbbbbbbd eaaaaf dbbbbbbbd faaaae dbbbbbbb caaaac dbbbbbbd gaaaaf bbbbbb aaaae bbbbbd faaaag dbbbbd gaaaaf bbbd eaaaa dd faaaag caaaac eaaaaf faaaae caaaac gaaaaf aaaae ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area B. Answer: A: 0; B: 1; 0 + 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#bb7228ff b,#b1f7eaff c,#dbb791ff d,#d0faf2ff e,#ca935bff f,#ecd9c5ff g,#eef9f4ff ``` ```image caa aaa aaf gbg faa gbbb bd eaa gbbbb dbb aac gbbbbb dbb aa dbbb bbd bbbd caa dbbb dbb bbbb aae dbbb gbb bbbb aag dbbb bbg bbbb caa dbbb bbd bbbbd aaa dbbb dbb gbbbbb aaf dbbb bb dbbdbb faa bbbb bbg bbb bb eaa bbbd bbb bbd bbg aac bbbd dbb bbg bbb gaa bbbd bb bb dbb caa bbbd bbd bb bb aae bbbd bbb gbb bbg aag bbbd dbb dbb bbd caa bbbd bb dbb dbb aaa bbbg bbd bbd gbb aaf bbbg bbb bbd bbg faa bbbg gbb bbg bbd eaa bbbg bb bb dbb aac bbbg bbd bb gbb gaa bbbg dbb gbb bb eaa d bbb gbb dbb bbd aae dbb bbb bbg bbb bbb aag bbd bbb bbd bbd gbb caa gbb gbbb dbb bbg bb aaa bbb gbbb bb bb bbd aaf bbg gbbb bbg bb bbb faa dbb gbbb bbb gbb dbb eaa bbd gbbb dbb dbb bb aac gbb dbbb bb bbb bbd gaa bbb dbbb bbdbbd bbb eaa bbg dbb bbbbbd dbb aae dbb d gbbbbg bb aag bbd bbbb bbg caa gbb bbbb bbb aae bbb bbbb dbb aaf bbg af gbbb bb faa dbb aaaa bbb bbg aaa bbd aaaac bbd bbd aac gbb faaaag d dbb gaa bbb eaaae gbb eaa bbg gaaaaf bbgaae dbb caaaa bbdaag bbd aaaac dbbaa gbb faaaa gbbae bbb aaaac bbaf bbg faaaag bbc dbb eaaae bbb bbd gaaaaf ebb gbb caaaa gabb bbb aaaac eabbd bbg faaaag aabbbdbb eaaae aadbbbbd gaaaaf caa bbbb eaaae aae bbbb gaaaaf aaf bbb caaaa faa dbb aaaac aaa d faaaag aac eaaae gaa gaaaaf eaa caaaa aac aaaac aa caaaa caa aaaac aae faaaag aaf eaaae faa gaaaaf aaa caaaa aac aaaac gaa faaaaeaa eaaaac faaa cc ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#8c7cebff b,#298866ff c,#8fc49cff d,#bfb7f3ff e,#5ca389ff f,#b0d6b1ff g,#ecf1f2ff ``` ```image gaaa daaaad aaaaaaag gggggggggggggggggggggggg aaaaaaaad gcffffffffffffffffffffffc aaa daaaaag gfffffffffffffffffffffffc aaa aaaaaa gfffffffffffffffffffffffc aaa gaaaaad gffffffffffffffffffffffebbeg gaaa daaaaa gfffffffffffffffffffffebbbbbbf daad aaaaadgffffffffffffffffffffbbbbbbbbbbc daad daaaaafffffffffffffffffffbbbbb ebbbbbbbg aaag aaaaaaffffffffffffffffbbbbec fbbbbbbbf aaa gaaaaaffffffffffffffbbbbcfc gbbbbbbbe aaa daaaaaffffffffffcbbbbcffc cbbbbbbb aaa gfaaaaaafffffffcbbbbffffc fbbbbbbf aaa gfffaaaaafffffebbbbfffffc gebbbbb gaaa gffffaaaaaaffbbbbbffffffc gbbbbbc daad gffffffaaaaaebbbbfffffffc cbbbbbg daad gfffffffaaaaaabeffffffffc bbbbbe aaag gfffffffffaaaaaaffffffffc fbbbbbg aaa gfffffffcbbeaaaaafffffffc ebbbbb aaa gffffffcbbbbfaaaaaafffffc gbbbbbf aaa gfffffebbbbffffaaaaaffffc ebbbbb aaa gffffebbbbffffffaaaaaaffc gbbbbbc gaaa gfffbbbbbfffffffffaaaaaac cbbbbbg daad gffbbbbefffffffffffdaaaaag bbbbg daad gfcbbbeffffffffffffffaaaaaa fbe aaag gfbbbefffffffffffffffffaaaaad aaa gcbbbfffffffffffffffffffaaaaaa aaa gbbbefffffffffffffffffffcgaaaaad aaa fbbbffffffffffffffffffffc daaaaag aaa bbbeffffffffffffffffffffc aaaaaa gaaa gbbbfffffffffffffffffffffc gaaaaag daad bbbefffffffffffffffffffffc aaaaaa aaag gbbbffffffffffffffffffffffc gaaaaad aaa bbbcggggggggggggggggggggggg daaaaag aaa gbbb aaaaaa aaa bbbc gaaaaag aaa gbbb aaaaaa aaa bbbe gaaaaad gaaa gbbb daaaaag daad bbbe aaaaad aaag gbbb daaaaag aaa bbbe aaaaaa aaa gbbb gaaaaad aaa bbbe daaaaa aaa bbb aaaaad gaaa bbbe daaa daad bbb ad daad bbbe aaag bbb aaa ebbe aaa bbb aaa ebbe aaa bbb gaaa ebbb daad bbb daad ebbb aaag bbb aaa ebbb aaa bbbg ebbb bbbg ebbb bbbg ebbb bbbg ebbb bbbg cbbb bbbg cbbb bbbg cbbb bbbg cbbb bbbg cbbb bbbg cbbb bbbf ebb g ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#8b7cebff b,#298866ff c,#8bbdadff d,#c3ddd4ff e,#59a08bff f,#bbb1f3ff g,#e4e7f4ff ``` ```image c cb ebb gebbb gebbbb dbbbbbb ag dbbbbbbb aaf cbbbbbbbb aaaag cbbbbbbbbc aaaaafg ebbbbbbbbc aaaaaaaf gebbbbbbbbd aaaaaaaaag gebbbbbbbbd aaaaaaaaaaf dbbbbbbbbeg gaaaaaaaaaaag dbbbbbbbbeg faaaaaaaaaafg dbbbbbbbbe gaaaaaaaaaaaf cbbbbbbbbc faaaaaaaaaaag cbbbbbbbbc gfaaaaaaaaaaf ebbbbbbbbd gaaaaaaaaaaag gebbbbbbbbd faaaaaaaaaaf gbbbbbbbbbg gaaaaaaaaaaaebbbbbbbeg faaaaaaaaaaabbbbbe gfaaaaaaaaaaebbc gaaaaaaaaaaac gaaaaaaaaaaaf gebbaaaaaaaaaaaf gebbbbeaaaaaaaaaafg dbbbbbbbbaaaaaaaaaaaf dbbbbbbbbeggaaaaaaaaaaag cbbbbbbbbe faaaaaaaaaaf cbbbbbbbbc gaaaaaaaaaaag ebbbbbbbbc faaaaaaaaaafg gebbbbbbbbd gfaaaaaaaaaaf gebbbbbbbbd gaaaaaaaaaaag dbbbbbbbbeg faaaaaaaaaaf dbbbbbbbbeg gaaaaaaaaaa gbbbbbbbbe faaaaaaaa ebbbbbbbc gfaaaaaa dbbbbbbbc gaaaaa ebbbbbbd faaa dbbbbbbc gaa ebbbbbbg f dbbbbbbc ebbbbbbg dbbbbbbc ebbbbbbg bbbbbbc bbbbbbg bbbbbc bbbbbg bbbbc bbbbg bbbc bbbg bbc ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Answer: A: 1; 1 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#8b7becff b,#288866ff c,#8bbeacff d,#cbcdedff e,#559f87ff f,#aea3f1ff g,#e6eaf3ff ``` ```image aaa faaaad faaaaaa aaaaaaaaf aaa daaaaag aaa aaaaaa aaa gaaaaad cbbe aaa faaaaa ebbbbbbd daaf aaaaaf ebbbbbbbbbc faad daaaaag bbbbe ebbbbbbbg aaag aaaaaa bbbbc cbbbbbbbc aaa gaaaaad gbbbbd gbbbbbbbe aaa faaaaa gbbbbg cbbbbbbe aaa aaaaaf cbbbb dbbbbbbc aaa daaaaag cbbbb ebbbbb gaaa aaaaaa ebbbb bbbbbc daaf gaaaaaebbbe cbbbbbg faad faaaaabc bbbbbe aaag gaaaaaf dbbbbbd aaa gbbeaaaaag ebbbbe aaa dbbbbgaaaaaa gbbbbbc aaa cbbbb gaaaaad ebbbbb aaa ebbbb faaaaa bbbbbc gaaa bbbbe aaaaaf cbbbbbg daaf bbbbe daaaaag bbbbg faad dbbbc aaaaaf dbe aaag bbbc gaaaaad aaa dbbb faaaaa aaa bbbc aaaaaf aaa gbbb daaaaag aaa bbbc aaaaaf gaaf gbbb gaaaaad daaf bbbc faaaaa faad gbbb gaaaaaf aaa bbbc faaaaag aaa gbbb aaaaaf aaa bbbc daaaaag aaa gbbb faaaaa aaa bbbe gaaaaad daaf gbbb faaaaa faad bbbe aaaaaf faag gbbb daaaaag aaa bbbe aaaaaa aaa bbb gaaaaad aaa bbbe faaaaa aaa bbb aaaaaf gaaa bbbe daaa daaf bbb ad faad ebbe aaag bbb aaa ebbe aaa bbb aaa ebbe aaa bbb gaaa ebbe daaf bbb faad ebbb aaag bbb aaa ebbb aaa bbb ebbb bbbg ebbb bbbg ebbb bbbg cbbb bbbg cbbb bbbg cbbb bbbg cbbb bbbg cbbb bbbg cbbb bbbd cbbb bbbd ebb g ``` <!-- 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,#f30b15ff b,#b760c7ff c,#f2efefff d,#ee8586ff e,#ec434aff f,#e3b3d9ff g,#afd4aeff ``` ```image cf cbbb fbbbb bbbbbb bbbbbbb bbbbbbbb bbb fbbbb cc fbbb fbbbbc cfffbbbbbbbbb fbbb fbbbbc ccffbbbbbbbbbbbbbbbbbbbbb bbbf cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbc bbbc cbbbbbbbbbbbbbbbbbbbbbbbffc bbb cbbbbbbbbbbfffc bbb cc fbbb fbbb bbbf bbbc bbb bbb fbbb fbbb bbbf bbbc fbbb bbbb fbbb bbbb fbbb bbbf bbbb bbbf bbbb cbbbc bbbb cbbbc bbbb d fbbb eaad cggggggggggggggggbbbbgggc aaaaad cgggggggggggggggbbbbggggc eaaaaaae cgggggggggggggggbbbbggggc eaaaaaae cggggggggggggggbbbbaagggc daaaaaaaccggggggggggggggbbbeaaeggc daaaaaaagggggggggggggbbbbaaaaggc faaaaaaadggggggggggbbbdaaaaagc faaaaaaadgggggggbbbbeaaaaaec caaaaaaadgggggbbbgeaaaaaaf cgaaaaaaaeggbbbbgaaadaaaa cgggeaaaaaaebbbggaaadgaaae cgggggeaaaabbbbggaaaggeaaaf cgggggggeaebbbaagaaagggaaaa cgggggggggbbbbaaaaaaggggaaae cggggggggbbbbaaaaaaaggggdaaaf cgggggggbbbbgggaaaaaggggcaaaa cggggggbbbbggggggaaeggggc aaae cgggggbbbbggggggggggggggc daaaf cggggbbbbgggggggggggggggc aaaa cgggbbbbggggggggggggggggc aaaa cggbbbbgggggggggggggggggc daaaf cgbbbbggggggggggggggggggc aaaa cbbbbgggggggggggggggggggc aaaa bbbbggggggggggggggggggggc faaae bbbbgggggggggggggggggggggc eaaac bbbbfccccccccccccccccccccc aaaa bbbbf caaaa bbbbf daaad bbbbf aaaac bbbbf aaaa bbbbf caaae bbbbf eaaaf bbbbf aaaa bbbbb aaaa bbbbb faaad bbbbb eaaac bbbbb aaaa fbbbb caaaa dea fbb daaad cdaaaaaa c aaaa deaaaaaaaaaaf aaaa cdaaaaaaaaaaaaaef faaaedeaaaaaaaaaaaaadc eaaaaaaaaaaaaaef aaaaaaaaadc aaaef ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f30c16ff b,#b75fc6ff c,#f2d8e9ff d,#f5727cff e,#ed4257ff f,#faabafff g,#c989d5ff ``` ```image bbbbbbbc cbbbbbbg bbbbbbbc gbbbbbbg bbbbbbbc gbbbbbbbd cbbbbbbbaad gbbbbbbeaaaf cbbbbbbbaaaaac gbbbbbbeaaaaae c cbbbbbbbaaaaaaaf adc gbbbbbbeaaaaaaaac aaaec cbbbbbbbaaaaaaaaae aaaaaef bbbbbbbdaaaaaaaaaaf aaaaaaaef cbbbbbbgdaaaaaaaaaaac aaaaaaaaaef bbbbbbbceaaaaaaaaaaae aaaaaaaaaaaaf gbbbbbbg eaaaaaaaaaaaa aaaaaaaaaaaaaadc bbbbbbbc eaaaaaaaaaaaa daaaaaaaaaaaaaadc gbbbbbbg aaaaaadaaaaaa faaaaaaaaaaaaaadc cbbbbbbbc aaaaaadfaaaaa feaaaaaaaaaaaaaec gbbbbbbg aaaaaaf daaaa feaaaaaaaaaaaaaebbbbbbb caaaaaaf aaaa feaaaaaaaaaaabbbbbbbg caaaaaaf faaa ceaaaaaaaaebbbbbbb faaaaaac daa cdaaaaaabbbbbbbef faaaaaac aa cdaaaebbbbbbbaaad faaaaaac fa cdebbbbbbbeaaaaaeaaaaaa d cbbbbbbbbaaaaaaaaaaaaa cbbbbbbbbeaaaaaaaaaaaaa cbbbbbbbbdaaaaaaaaaaaaae cbbbbbbbbg feaaaaaaaaaaae cbbbbbbbbg ceaaaaaaaaad cbbbbbbbbg cdaaaaaaaf cbbbbbbbbg cdaaaae cbbbbbbbbg cfdf cbbbbbbbbg cbbbbbbbbg cbbbbbbbbg cbbbbbbbbg cbbbbbbbbg bbbbbbbbg bbbbbbbbb gbbbbbbbbc gbbbbbbbbc gbbbbbbbbc gbbbbbbbbc gbbbbbbbbc bbbbbbbbc bbbbbbbc bbbbbbc ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#f40b15ff b,#b75fc7ff c,#f0d5eaff d,#f7767dff e,#f3404cff f,#faadb0ff g,#d098dbff ``` ```image cc cbbb gbbbb bbbbbb bbbbbbb bbbgbbbb bbb gbbbb c cbbb gbbbb ccggbbbbbbbbb gbbg cbbbbc ccggbbbbbbbbbbbbbbbbbbbb bbbg cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbc bbbc cbbbbbbbbbbbbbbbbbbbbbbggcc bbb bbbbbbbbbbggcc bbb c cbbb gbbb bbbg bbbc bbb bbb cbbb gbbb bbbg bbbc cbbb bbbb gbbb bbbg gbbb bbbg gbbb bbbc bbbb bbbc bbbb cbbbc bbbb f cbbb eaad bbbb aaaaad gbbb eaaaaaae bbbb daaaaaae gbbbaa daaaaaaa bbbeaae faaaaaaac bbbbaaaac faaaaaaaf bbbdaaaaa caaaaaaaf bbbbeaaaaae caaaaaaad bbbceaaaaaac eaaaaaad bbbb aaadaaaa eaaaaaaebbb aaaf aaae eaaaabbbb aaac daaac daebbbaa aaa aaaa cbbbbaaaaaa aaae cbbbbaaaaaaa daaaf cbbbb caaaaa aaaa cbbbb caae aaae cbbbb daaaf cbbbb aaaa cbbbb aaaa bbbb faaaf bbbbc aaaa bbbbc aaaa bbbbc faaad bbbbc eaaac bbbbc aaaa bbbbc aaaa bbbbc daaad bbbbg aaaa bbbbg aaaa bbbbg caaae bbbbg eaaaf bbbbg aaaa bbbbg aaaa bbbbg faaad bbbbb eaaac bbbbb aaaa cbbbb caaaa fea cbb daaaf cdaaaaaa c aaaa feaaaaaaaaaaf aaaa cdaaaaaaaaaaaaaef caaaefeaaaaaaaaaaaaadc eaaaaaaaaaaaaaef aaaaaaaaadc aaaef ``` <!-- end of image -->
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This is the image I'm working with. The goal is to count the intersections. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#7a6fc3ff b,#b58955ff c,#d7cfd9ff d,#a7cca1ff e,#eff3f0ff f,#9d9cccff g,#b2d7b1ff ``` ```image gbbd cbbbbbbb cbbbbbbbbde edbbbbbbbbe gbbbbbbbbc eddddddddddddddddddddddde cbbbbbbbbc f edgggggggggggggggggggggde cbbbbbbbbde faa edgggggggggggggggggggggde edbbbbbbbde aaa edgggggggggggggggggggggde edbbbbbbbbc eaaa edgggggggggggggggggggggde cbbbbbbbbc eaaaedgggggggggggggggggggggde cbbbbbbbbg eaaadgggggggggggggggggggggde ebbbbbbbbde caaagggggggggggggggggggggde edbbbbbbbbc caaaggggggggggggggggggggdbbbbbbbbc caaagggggggggggggggggbbbbbbbg efaafgggggggggggggggbbbbde edfaafgggggggggggggbbbgde edgfaafgggggggggggbbbggde edggaaafgggggggggbbbgggde edgggaaadgggggggbbbggggde edggggaaadgggggbbbgggggde edgggggaaadgggbbbggggggde edggggggaaaggbbbgggggggde edgggggggaaabbbdgggggggde edggggggggabbbdggggggggde edggggggggbbbagggggggggde edgggggggbbbaaaggggggggde edggggggbbbdgaaagggggggde edgggggbbbdgggaaaggggggde edggggbbbdgggggaaagggggde edgggbbbdgggggggaaaggggde edggbbbdggggggggdaaagggde edgbbbdggggggggggdaaaggde edbbbdggggggggggggfaaagde ebbbdggggggggggggggfaaade bbbdggggggggggggggggfaafe bbbdggggggggggggggggggfaaf bbbdggggggggggggggggggggfaac bbbcdgggggggggggggggggggggaaac bbbcedgggggggggggggggggggggdaaac bbbc edgggggggggggggggggggggdeaaae bbbc edgggggggggggggggggggggde aaae bc edgggggggggggggggggggggde aaae edgggggggggggggggggggggde aaa eddddddddddddddddddddddde aaa eeeeeeeeeeeeeeeeeeeeeee aaa aaa aaa eaaa eaaa eaaa eaaa caaa caf caaf faa caaf faaf faaf faaa faaf faaac faac faaaa faac aafaae aaac aaffaa aaae aac aae aaae aac aaa aaae aac eaa aaa aac aaf aaa aae caa aaa aae aaf aaa aae caa aaa aa aac eaaa aa faa eaaa aa aae eaaa aa aaa eaaa aa aa eaaa aa aaf eaaa aa eaa aaaaa aaf aaaa caa aaa aac aa faa aac faa ae ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7a6fc2ff b,#b58854ff c,#c1bce3ff d,#c19c70ff e,#eae3e2ff f,#9990cfff g,#dcc8b2ff ``` ```image e ae aae aaae aaaf aaaaf e aaaaaf edbb caaaaaf gbbbb caaaaaf gbbbbb caaaaaf gbbbbbb caaaaaf gbbbbbdg caaaaac gbbbbbd faaaaac gbbbbbd faaaaac gbbbbbd faaaaac gbbbbbd faaaaac gbbbbbd faaaaac gbbbbbd faaaaae gbbbbbd faaaaae gbbbbbd eaaaaaae gbbbbbd eaaaaaae gbbbbbd eaaaaaae gbbbbbd eaaaaaae gbbbbbd eaaaaaf gbbbbbd eaaaaaf gbbbbbd caaaaafbbbbbde caaaabbbbbde caabbbbbde gbbbbbbe gbbbbbbaf gbbbbbbaaaf gbbbbbbaaaaac gbbbbbdefaaaaac ebbbbbde faaaaac ebbbbbde faaaaac ebbbbbde faaaaac ebbbbbde faaaaac ebbbbbbe faaaaae ebbbbbbe faaaaae ebbbbbbe eaaaaaae ebbbbbbe eaaaaaae ebbbbbbe eaaaaaae ebbbbbbe eaaaaaae ebbbbbbe eaaaaaf ebbbbbbe eaaaaaf ebbbbbbe caaaaaf ebbbbbbe caaaaaf ebbbbbbe caaaaaf ebbbbbbe caaaaaf bbbbbbe caaaaa bbbbbe caaaa bbbbe faaa bbbe faa bbe fa be f e ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#796ec3ff b,#b58954ff c,#c0bbe2ff d,#ccae8aff e,#eae6edff f,#9a92d1ff g,#e3d3c0ff ``` ```image gbbd gbbbbbbb edbbbbbbbde edbbbbbbbde dbbbbbbbbg gbbbbbbbbg f gdbbbbbbbd faa edbbbbbbbde aaa dbbbbbbbdg aaa gbbbbbbbbg eaaa gbbbbbbbbd eaaa edbbbbbbbde eaaa edbbbbbbbdg eaaf gbbbbbbbbg caaf bbbbbbbg caaf bbbbde caac bbb faac bbb faac bbb faae bbb aaae bbb aaae bbb aaae bbbe aaabbbe abbbe bbba bbbaaa bbbe aaa bbbe aaa bbbe aaa bbbe eaaa bbbe eaaa bbbe eaaf bbbe caaf bbbe caaf bbbe caaf bbbg faac bbbg faac bbbg faac bbbg faae bbbg aaae bbbg aaae bg aaae aaa aaa aaa aaa aaa aaa eaaa eaaa eaaa eaaf eaf caaf caa caaf faac caaf faaa faac faaac faac faaaa faac aafaae faae aacfaa aaae aac aa aaae aac aaa aaa aac eaa aaa aae aaf aaa aae eaa aaa aae aac aaa aae caa aaa aa aac aaa aa faa eaaa aa aae eaaa aa aaa eaaa aa aa aaa aa aaf aaa aa eaa aaaaa aaf aaaa caa aaa aac af caa aae faa ae ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#076db1ff b,#0f9e0bff c,#86b8d4ff d,#63bf61ff e,#d1e6e6ff f,#4894bfff g,#aed6aeff ``` ```image afce aaae aaae bbbbd aaa bbbbbbbbbg gggggggggggaaaggg dbbbbbbbbbbbbbg ggggggggggcaaaggg bbbbdbbbbbbbbbbbbde ggggggggggfaaaggg bbbbe edbbbbbbbbbbbbde ggggggggggfaaaggg dbbbd gdbbbbbbbbbbbbd ggggggggggaaaaggg bbbb gbbbbbbbbbbbbbd ggggggggggaaaaggg bbbbe gbbbbbbbbbbbbbgggggggggggaaafggg dbbbd dbbbbbbbbbbbbbdggggggaaafggg bbbb edbbbbbbbbbbbbbgggaaafggg bbbbe edbbbbbbbbbbbbbaacggg dbbbd dbbbbbbbbbbbbbdgg bbbb ggggdbbbbbbbbbdgg bbbbe ggggggggdbbbbbggg dbbbd gggggggggcaabbggg bbbb gggggggggfaaagggg bbbbe gggggggggfaaagggg dbbbd gggggggggaaaagggg bbbb gggggggggaaaagggg bbbbe gggggggggaaafgggg dbbbd gggggggggaaafgggg ebbbb gggggggggaaafgggg bbbb gggggggggaaacgggg dbbbd gggggggggaaaggggg ebbbb gggggggggaaaggggg bbbb eaaa dbbbd caaa ebbbb caaa bbbb faaa dbbbd aaaa ebbbb aaaa bbbb aaaf dbbbd aaac ebbbb aaac bbbb aaae dbbbd aaa ebbbb aaa bbbb eaaa dbbbd caaa ebbbb caaa bbbb faaa bbbbd aaaa ebbbb aaaa bbbb aaaf bbbbg aaac ebbbb aaac bbbb aaae bbbbg aaa gbbbb eaaa bbbb caaaaa bbbbg faaaaaaa gbbbb eaaaaaaaaf bbbb caaaaaaaac bbbbg faaaaaaaae gbbbb eaaaaaaaaf bbb caaaaaaaac gg faaaaaaaae eaaaaaaaaf caaaaaaaae aaaaaaaaf caaaaaaaac faaaaaaaae eaaaaaaaaf caaaaaaaac faaaaaaaae eaaaaaaaaf caaaaaaaac faaaaaaaae eaaaaaaaaf caaaaaaaac eac faaaaaaaa aaaae eaaaaaaaac faaaaaa faaaaaaaae eaaaaaac eaaaaaaaaf caaaaaae caaaaaaaac aaaaaaafaaaaaaaae eaaaaaaaaaaaf caaaaaaac faaae ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#066db0ff b,#0e9e0aff c,#7db3d6ff d,#2aa33bff e,#bedbdeff f,#3e8dc2ff g,#81cc7fff ``` ```image aaaaaaf eaaaaaaf eaaaaaaf eaaaaaac caaaaaac caaaaaac caaaaaae faaaaaae faaaaaae faaaaaa aaaaaaa aaaaaaa aaaaaaf e eaaaaaaf bdgg eaaaaaaf bbbbbdge eaaaaaac bbbbbbbbbdge caaaaaac bbbbbbbbbbbbbdge caaaaaac bbbbbbbbbbbbbbbbbdgecaaaaaae bbbbbbbbbbbbbbbbbbbbbdaaaaae bbbbbbbbbbbbbbbbbbbbbbbbbdae egdbbbbbbbbbbbbbbbbbbbbbbbbdg egdbbbbbbbbbbbbbbbbbbbbbg ggdbbbbbbbbbbbbbbbbbg eggbbbbbbbbbbbbbbe egdbbbbbbbbbd eaddbbbbbg eaaaaaddbg caaaaaac caaaaaac caaaaaae faaaaaae faaaaaae faaaaaa aaaaaaa aaaaaaa aaaaaaf eaaaaaaf eaaaaaaf eaaaaaac caaaaaac caaaaaac caaaaaae faaaaaae faaaaaae faaaaaa ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#076db1ff b,#0e9e0bff c,#89bad9ff d,#4fb84cff e,#cee6e2ff f,#4893c5ff g,#8fd18dff ``` ```image affe aaae aaae bbbbg aaa bbbbbbbbbg eaaa gbbbbbbbbbbbbdg caaa bbbbdbbbbbbbbbbbbde caaa bbbbe edbbbbbbbbbbbbde faaa gbbbd edbbbbbbbbbbbbg faaa bbbb gbbbbbbbbbbbbbg aaaa bbbbe gbbbbbbbbbbbbbg aaaf gbbbd gbbbbbbbbbbbbdg aaaf bbbb edbbbbbbbbbbbbde aaac bbbbe edbbbbbbbbbbbbbaae dbbbd edbbbbbbbbbbbbg bbbb gbbbbbbbbbg bbbbe gbbbbb dbbbd caabb bbbb caaa bbbbe faaa dbbbd faaa bbbb aaaa bbbbe aaaf dbbbd aaac ebbbb aaac bbbb aaae dbbbd aaa ebbbb aaa bbbb eaaa dbbbd caaa ebbbb caaa bbbb faaa dbbbd aaaa ebbbb aaaa bbbb aaaf dbbbg aaac ebbbb aaac bbbb aaae dbbbg aaa ebbbb aaa bbbb eaaa dbbbg caaa ebbbb caaa bbbb faaa dbbbg aaaa ebbbb aaaa bbbb aaaf dbbbg aaac ebbbb aaac bbbb aaae dbbbg aaa ebbbb eaaa bbbb caaaaa bbbbg faaaaaaa ebbbb eaaaaaaaaf bbbb caaaaaaaac bbbbg faaaaaaaae ebbbb eaaaaaaaaf bbb caaaaaaaac gg faaaaaaaae eaaaaaaaaf caaaaaaaae aaaaaaaaf caaaaaaaac faaaaaaaae eaaaaaaaaf caaaaaaaac faaaaaaaae eaaaaaaaaf caaaaaaaac faaaaaaaae eaaaaaaaaf caaaaaaaac eac faaaaaaaa aaaae eaaaaaaaac faaaaaa faaaaaaaae eaaaaaac aaaaaaaaf caaaaaae caaaaaaaac aaaaaaafaaaaaaaae eaaaaaaaaaaaf caaaaaaac faaae ``` <!-- 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 zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#c57187ff b,#673c79ff c,#c5a2b3ff d,#897296ff e,#e4d2dcff f,#b1d7b1ff g,#96c896ff ``` ```image ed bbbd cbbcdbc bbb bbe dbbe bb ebbd bb bbb bb cbbc ebb bbb ebd dbbe cbc ebbd dbe bbb bbe cbbc bb bbb bb be bb ebb cbd dbc dbe bb bb bb bb ebd cbd gffffffffffffffffffffffg dbc gffffffffffffffffffffffg bbe gffffffffffffffffffffffg bb gffffffffffffffffffffffg bb gffffffffffffffffffffffg bb gffffffffffffffffffffffg ebb gffffffffffffffffffffffg ebdgffffffffffffffffffffffg cbdffffffffffffffffffffffg dbgfffffffffffffffffffffg bbfffffffffffffffffffffg a gbbffffffffffffffffffffg caae gfbbfffffffffffffffffffg eaac gffbbffffffffffffffffffg aaa gffgbbfffffffffffffffffaaae gfffdbdfffffffffffffffaac gffffdbdffffffffffffaaag gfffffbbgfffffffffcaacfg gffffffbbffffffffaaafffg gfffffffbbfffffaaafffffg gffffffffbbffcaacffffffg gfffffffffbbaaaffffffffg gfffffffffaaaffffffffffg gfffffffcaaabdfffffffffg gffffffaaaffdbgffffffffg gffffaaafffffbbgfffffffg gffcaacfffffffbbfffffffg gfaaaffffffffffbbffffffg aaacffffffffffffbbfffffg eaaaffffffffffffffgbbffffg aaagffffffffffffffffgbdfffg caae gfffffffffffffffffdbfffg eaac gffffffffffffffffffbbffg aaa gffffffffffffffffffdbffg caae gfffffffffffffffffffbbfg eaaa gfffffffffffffffffffdbfg aaa gffffffffffffffffffffbdg caae gffffffffffffffffffffdbg aaa gfffffffffffffffffffffbd aaa gfffffffffffffffffffffbb eaac gffffffffffffffffffffffbc aaa gffffffffffffffffffffffbb caae gffffffffffffffffffffffgbe eaac gffffffffffffffffffffffgbb aaa gffffffffffffffffffffffgebe caae fggggggggggggggggggggggf bb eaac cb aaa bb caae cb eeecaac bd aaaaaaaaaaaaaaaa db aaaccceee bd db bc bb bc e ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#c66f87ff b,#663b79ff c,#d3b7c9ff d,#815c8fff e,#ebdde5ff f,#d290a2ff g,#a48bafff ``` ```image g bg bbc bbbc dbbbe ebbbde cbbbd cbbbd gbbbg gbbbg dbbbc dbbbe edbbbe ebbbde cbbbd ca cbbbg efaa gbbbg caaaa gbbbc caaaaac dbbbc efaaaafe dbbbe caaaaac ebbbbe eaaaaaf ebbbd efaaaafe cbbbd caaaaac cbbbg eaaaaaf gbbbg efaaaafe gbbbc caaaaac dbbbc efaaaafe edbbbfaaaaae ebdaaaaac eaaaaafe faaaaadd caaaaafbbbg efaaaafe gbbbg caaaaac dbbbc caaaaac dbbbe efaaaafe edbbbe caaaaac ebbbde eaaaaaf cbbbd efaaaafe cbbbg caaaaac gbbbg eaaaaaf gbbbc efaaaafe dbbbc aaaaac dbbbe aaafe ebbbbe afe ebbbd c cbbbd cbbbg gbbbe dbbg cbbb bbbg gbbb bbbc gbbd ebbbc gbbd ebbbc gbbd ebbbe dbbg cbbb dbb cbb db cb b g ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#c66f87ff b,#663c79ff c,#d1b6c8ff d,#846293ff e,#e9dae3ff f,#d595a6ff g,#a68db0ff ``` ```image eg bbbg gbbcdbc bbd bbe dbbe bb ebbg bb bbb bb gbbc ebb bbd cbd dbbe gbg ebbg dbc bbb bbe gbbc bb bbd bb be bb ebd cbd gbc dbe bb bb bb ebb ebd gbg dbc bbe bb bb bb ebb cbd gbg dbc bbe a bb faae bb eaaf bb aaa ebd faae cbd eaaf gbc aaa dbe caac bb eaaf bb aaa bb caac ebbaaa aaae caaabg aaa dbc faae bbe eaaf bb aaa bb faae bb eaaf ebb aaa cbd faae gbe eaaf bb aaa gb caac bd eaaf gb aaa bd caac db aaa bg faae db caac bc aaa bb faae ebc eaaf bb aaa ebe faae bb eaaf cb aaa bb faae gb eeccaaf bd aaaaaaaaaaaaaaaa gb aafffccee bd db bg bb bc c ``` <!-- end of image -->
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I'm optimistic that I'll find some intersections in this image. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#02cf96ff b,#c0919eff c,#89e8cdff d,#dad7d8ff e,#b1d6b1ff f,#90ca99ff g,#42d6a9ff ``` ```image acd aaad aaa aaa caaa gaag aaac aaad aaa aaa daaa caaa aaac aaad aaa aaa daaa caaa gaag aaac aaa aaa aaa caaa gaag aaac ddd aaa bbb aaa ffbbbffffaaafffffff aaa eebbbeeeaaaaaageeee caaa eebbbeeeaaaaaaaaage gaag eebbbeeeaaaaaaaaaaaac aaac eebbbeeeaaaeefaaaaaaaaac aaa eebbbbefaaaeeeeegaaaaaaaaad aaa eebbbbegaaaeeeeeeeegaaaaaaaag aaa eebbbbeaaageeeeeeee gaaaaaaaag caaa eebbbbeaaafeeeeeeee dgaaaaaaaac gaag eebbbbeaaaeeeeeeeee daaaaaaaaac aaac eeebbbeaaaeeeeeeeee caaaaaaaaac aaad eeebbbeaaaeeeeeeeee caaaaaaaaad aaa eeebbbfaaaeeeeeeeee gaaaaaaaag effffaaafffffffff eeebbbgaaaeeeeeeeee gaaaaaaaag feeefaaaeeeeeeeee eeebbbaaageeeeeeeee daaaaaaaaac feeegaaaeeeeeeeee eeebbbaaafeeeeeeeee caaaaaaaaac feeeaaageeebbbeee eeebbbaaaeeeeeeeeee caaaaaaaaad feeeaaafeeebbbeee eeebbbaaaeeeeeeeeee caaaaaaaagd feeeaaaeeeebbbeee eeebbbaaaeeeeeeeeee gaaaaaaaag feeeaaaeeeebbbeee eeebbfaaaeeeeeeeeee gaaaaaaaag feefaaaeeeebbbeee eeeebgaagbbbeeeeeee daaaaaaaaac feegaaaeeebbbbeee eeeeeaaafbbbbbeeeee caaaaaaaaafeaaageeebbbbeee eeeeeaaabbbbbbbbeee caaaaaaaaaaafeeebbbeeee eeeeeaaaeebbbbbbbbe caaaaaaaaeeeebbbeeee eeeeeaaaeeeeebbbbbbbd gaaaaaeeeebbbeeee eeeefaaaeeeeeeebbbbbbbd fefaageeeebbbeeee eeeegaaaeeeeeeeeebbbbbbbb feeeeeeeeebbbeeee eeeeaaageeeeeeeeeeebbbbbbbb feeeeeeeeebbbeeee eeeeaaafeeeeeeeeeee dbbbbbbb feeeeeeeebbbbeeee eeeeaaaeeeeeeeeeeee dbbbbbbbd feeeeeeeebbbbeeee eeeeaaaeeeeeeeeeeee dbbbbbbbd feeeeeeeebbbeeeee eeeeaaaeeeeeeeeeeee bbbbbbbb feeeeeeeebbbeeeee eeefaaaeeeeeeeeeeee bbbbbbbb feeeeeeeebbbeeeee fffgaaaffffffffffff dbbbbbbb effffffffbbbfffff aaac dbbbbbbbd bbb aaad dbbbbbbbd dbbb aaa bbbbbbbd dbbb aaa bbbbbbbb bbbd daaa dbbbbbbb bbbd caaa dbbbbbbbd bbb gaag dbbbbbbbd bbb aaac bbbbbbbd bbb aaa bbbbbbbb dbbb aaa dbbbbbbb dbbb dbbbbbbbd bbbb dbbbbbbbd bbbd bbbbbbbd bbbd bbbbbbbb bbb bbbbbbbb bbb dbbbbbbbd bbb dbbbbbbbbbb bbbbbbbb bbbbbd bbb ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#01cf96ff b,#bf909dff c,#b1efdeff d,#d9bbc4ff e,#75e3c4ff f,#eae9e9ff g,#3dd3a9ff ``` ```image fbbbbbb cggec fbbbbbbf caaaaaaec fbbbbbbf gaaaaaaaagef fbbbbbbf aaaaaaaaaaaagef fbbbbbbf faaaaaaaaaaaaaaagc fbbbbbbf caaaaaaaaaaaaaaaaaaec bbbbbbf eaaaaaaaaaaaaaaaaaaaa bbbbbbf eaaaaaaaaaaaaaaaaaaaa bbbbbbd gaaaaag ceaaaaaaaaaaa bbbbbbd aaaaaae cgaaaaaaaa bbbbbbd aaaaaae cgaaaaa bbbbbbd caaaaaac fegaa bbbbbbd caaaaaaf fe bbbbbbd eaaaaaa dbbbbbd gaaaaag dbbbbbd gaaaaag dbbbbbd aaaaaae dbbbbbd faaaaaac dbbbbbb caaaaaac dbbbbbb caaaaaa dbbbbbb eaaaaaa dbbbbbb gaaaaag dbbbbbb gaaaaae fbbbbbb aaaaaae fbbbbbb faaaaaac fbbbbbbfcaaaaaaf fbbbbbbfeaaaaaa fbbbbbbfeaaaaag fbbbbbbfgaaaaag fbbbbbbfaaaaaae bbbbbbfaaaaaac bbbbbbcaaaaaac bbbbbbeaaaaaaf bbbbbbeaaaaaa bbbbbbgaaaaag bbbbbbgaaaaae bbbbbbaaaaaae bbbbbbaaaaaac dbbbbbaaaaaac dbbbbgaaaaaabf fbbbbgaaaaaabbbd fdbbgaaaaagbbbbbdf fdaaaaaagbbbbbbbdf aaaaaagbbbbbbbbbdf caaaaaabbbbbbbbbbbbbf caaaaaabbbbbbbbbbbbbbbd eaaaaaa fdbbbbbbbbbbbbbbd eaaaaag fdbbbbbbbbbbbbbbd gaaaaag dbbbbbbbbbbbbb aaaaaae dbbbbbbbbbbb faaaaaac fdbbbbbbbb caaaaaac fdbbbbbb caaaaaaf fdbbbb eaaaaaa dbb gaaaaag d gaaaaae aaaaaae faaaaaac caaaaaaf eaaaaaa eaaaaag gaaaaag aaaaaae aaaaaae caaaaaac caaaaaaf eaaaaaa ``` <!-- end of image --> My investigation has led me to 1 intersection in area A! Time for a closer look at another area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#01cf96ff b,#c08f9dff c,#b0efddff d,#d8bac3ff e,#7be5c8ff f,#eae8e8ff g,#40dab0ff ``` ```image aaaaaae faaaaaac caaaaaac eaaaaaa eaaaaaa gaaaaag ff aaaaaae fbbbbbdf faaaaaac fbbbbbbf caaaaaac dbbbbbb eaaaaaa dbbbbbb eaaaaaa dbbbbbd gaaaaag bbbbbbd aaaaaae bbbbbbd aaaaaae bbbbbbf caaaaaac fbbbbbbf caaaaaaf fbbbbbbf eaaaaaa dbbbbbb ef gaaaaag dbbbbbb aagc aaaaaae dbbbbbd aaaaagcaaaaaae bbbbbbd aaaaaaaaaaaaac bbbbbbd aaaaaaaaaaaaaf fbbbbbbf aaaaaaaaaaaaa fbbbbbbf aaaaaaaaaaaag fbbbbbb cgaaaaaaaaaag dbbbbbb fegaaaaaaac dbbbbbb fegaaae dbbbbbd fcf bbbbbbd bbbbbbd fbbbbbbf fbbbbbbf dbbbbbb dbbbbbb dbbbbbd bbbbbbd bbbbbbd bbbbbbf fbbbbbbf fbbbbbbf dbbbbbb dbbbbbb ``` <!-- end of image --> Area B is clear of intersections, but the search continues. Answer: A: 1; B: 0; 1 + 0 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#01cf96ff b,#c0909dff c,#a9eedbff d,#d9bdc5ff e,#68dfbeff f,#e6eae9ff g,#2cd5a6ff ``` ```image gec aaaf aaa aaa caaa eaag aaae aaaf aaa aaa caaa eaaa gaae aaac aaa aaa faaa eaaa gaae aaac aaa aaa faaa caaa gaae aaac ddd aaa bbb aaa bbbf caagf faaa bbbf aaaaaagf caaa bbbf aaaaaaaaae gaag bbbf aaagaaaaaaaae aaac bbbd aaa caaaaaaaaac aaaf bbbd faaa caaaaaaaaac aaa bbbd eaaa eaaaaaaaagf aaa dbbd gaae gaaaaaaaae caaa dbbb aaac fgaaaaaaaae eaag dbbb aaa caaaaaaaaac aaae dbbb aaa caaaaaaaaac aaaf fbbb aaa eaaaaaaaagf aaa fbbbcaaa eaaaaaaaagf aaa fbbbeaag fgaaaaaaaae caaa fbbbaaae fgaaaaaaaae eaag bbbaaac caaaaaaaaac aaae bbbf bbbaaa caaaaaaaaac aaac bbb bbbaaa eaaaaaaaagf aaa bbb bbbaaa eaaaaaaaag aaa bbb bbeaaaf fgaaaaaaaae caaa fbbb bgaagbbd caaaaaaaaae eaaa dbbb aaaebbbbd caaaaaaaaac gaae dbbd aaabbbbbbbb eaaaaaaaaaaac bbbd aaa dbbbbbbbf eaaaaaaaa bbbf aaa dbbbbbbbf gaaaaa bbb caaa fbbbbbbbd fgae bbb eaaa bbbbbbbd bbb gaae bbbbbbbb fbbb aaac dbbbbbbbf dbbb aaa dbbbbbbbf bbbd aaa fbbbbbbbd bbbf aaa bbbbbbbd bbbf caaa bbbbbbbb bbb eaag dbbbbbbbf bbb aaae dbbbbbbbf fbbb aaaf fbbbbbbbd fbbb aaa bbbbbbbd dbbb aaa bbbbbbbb bbbd faaa dbbbbbbbf bbbf eaaa dbbbbbbbf bbb gaae fbbbbbbbd bbb aaac fbbbbbbbd bbb aaaf bbbbbbbb fbbb aaa dbbbbbbb dbbb dbbbbbbbf dbbd fbbbbbbbd bbbd fbbbbbbbd bbbf bbbbbbbb bbb dbbbbbbb bbb dbbbbbbbf bbb fbbbbbbbbbb fbbbbbbbb bbbbbd dbb ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#1a36e5ff b,#d4a911ff c,#687fe1ff d,#dbcd7aff e,#94c396ff f,#b1d7b0ff g,#b9c1f6ff ``` ```image dbbbd dbbbbbb bbbbbbbbb bbbbbbbbbbb dbbbbbbbd dbbb dbbbbbbb fbbb bbbbbbbbffffffebbbffff bbbbbbbbfffffffffbbbffff dbbbbbbbd efffffffffbbbffff dbbbbbbb efffffffffbbbffff bbbbbbbb efffffffffbbbffff bbbbbbbd efffffffffbbbffff dbbbbbbbd efffffffffbbbffff dbbbbbbb efffffffaaebbffff bbbbbbbb effffffaaaabbffff bbbbbbbd effffffaaaabbffff dbbbbbbbd efffffcaaaabbffff dbbbbbbb efffffaaaaaebffff bbbbbbbb efffffaaaaaabffff bbbbbbbd effffcaaaaaabffff dbbbbbbbd effffaaacaaabffff dbbbbbbb effffaaafaaabffff bbbbbbbb efffaaaafaaaeffff bbbbbbbd efffaaaffcaaaffff feeeeeeeeeeeeeee dbbbbbbbd effcaaafffaaadfff efffffffffffffff dbbbbbbb effaaacfffaaadfff efffffffffffffff bbbbbbbb effaaaffffaaaefff efffffffffffffff bbbbbbbd efcaaaffffaaacfff efffffffffffffdbbbbbbbd efaaacffffeaaafff efffffffffffdbbbbbbb eeaaafffffbaaafff efffffffffbbbbbbbb eaaaafffffbaaafff efffffffbbbbbbbb eaaaffffffdaaacff effffdbbbbbbbdff caaaffffffdbbbfff effdbbbbbbbfffff aaacffffffdbbbfff ebbbbbbbbfffffff aaafffffffdbbbfff ebbbbbbfffffffff caaafffffffdbbbfff eebbdfffffffffff aaaefffffffdbbbfff eaaaaaacefffffff gaaaffffffffdbbbfff eaaaaaaaaaaaacef aaacfffffffffbbbfff eaaaaaaaaaaaaaaaaaacg aaaffffffffffbbbfff effffecaaaaaaaaaaaaaaaaaa caaaffffffffffbbbfff effffffffffecaaaaaaaaaaaaa aaac bbb feeeeeeeeeeeeeee gcaaaaaaaa aaa bbb gaaac aaaa bbb caaag aaag bbb aaaa gaaa bbb aaaa aaac bbb gaaaa aaa bbb caaag caaa bbb aaaa aaag bbb aaaa aaa bbb aaaa aaaa bbd gaaac aaa aaaag gaaa aaaa aaac aaaa aaa gaaac caaa caaag aaag aaaa gaaa aaaa aaac aaaa aaa caaag caaa aaaa aaac aaaa aaa aaaa caaa gaaac aaag caaag gaaa aaaa aaac aaaa aaa gaaac caaa caaag aaag aaaa aaa aaaa aaaa aaaa aaag caaac gaaa aaaa aaac aaaaaaa aaaaaa gaaaag caaa aac ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#1a36e6ff b,#d5a90fff c,#7081eeff d,#efdfa7ff e,#948466ff f,#e1c359ff g,#bbc3f7ff ``` ```image df dbbb fbbbbb dfbbbbbbb dfbbbbbbbbb dbbbbbbbbbbbb fbbbbbbbbbbbbbb dfbbbbbbbbbbbbbbf dfbbbbbbbbbbbbbbd dbbbbbbbbbbbbbbfd fbbbbbbbbbbbbbbfd dfbbbbbbbbbbbbbbf dfbbbbbbbbbbbbbbd bbbbbbbbbbbbbfd fbbbbbbbbbbfd bbbbbbbbf eeebbbd aaaaaccgg aaaaaaaaaaaccgg gaaaaaaaaaaaaaaaaaccgg gaaaaaaaaaaaaaaaaaaaaaaaccgg caaaaaaaaaaaaaaaaaaaaaaaaaaaa caaaaaaaaaaaaaaaaaaaaaaaaaaaa ggccaaaaaaaaaaaaaaaaaaaaaa ggccaaaaaaaaaaaaaaaa ggccaaaaaaaaaa ggccaaaa gg ``` <!-- end of image --> I don't observe any intersections inside area A. Let's continue our search in the next region. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#1a36e5ff b,#d4a810ff c,#6073ecff d,#f2e6bfff e,#787181ff f,#e2c664ff g,#b1baf6ff ``` ```image bbbbbbbbbfd dbbbbbb bbbbbbbf dbbbbbb bbbbfd dbbbbbb bbfd dbbbbbbd fd dbbbbbbd bbbbbbd bbbbbbd bbbbbbd bbbbbbd bbbbbbd bbbbbbd bbbbbbd bbbbbbd bbbbbbf bbbbbbf gcaaebbbbbf aaaaaebbbbf gaaaaaabbbbf caaaaaabbbbf gaaaaaaaebbbf caaaaaaaebbbf aaaaaaaaebbbf gaaaaaaaaabbbf caaaaaaaaabbbf aaaaaaaaaaebbf gaaaaaaaaaaebbb aaaaaaaaaaaabbb gaaaaaaaaaaaabbb caaaaaaaaaaaabbb aaaaaacaaaaaaebb gaaaaaagcaaaaaebb caaaaaa caaaaaabb aaaaaac gaaaaaabb caaaaaag gaaaaaaeb aaaaaaa aaaaaaeb gaaaaaag caaaaaebd caaaaaa caaaaaabd aaaaaac gaaaaaabd gaaaaaag aaaaaaed caaaaaa aaaaaaed gaaaaaac caaaaaad caaaaaag gaaaaaad aaaaaac gaaaaaad gaaaaaag aaaaaae caaaaaa aaaaaac aaaaaac eaaaaaa gaaaaaag eaaaaaa caaaaaa faaaaaag gaaaaaac faaaaaag caaaaaag faaaaaac aaaaaac feaaaaaa gaaaaaag feaaaaaa caaaaaa fbaaaaaag aaaaaac fbaaaeeg gaaaaaag fbbbbbf aaaaaaa fbbbbbf aaaaaac fbbbbbb aaaaaa fbbbbbb aaaaac dbbbbbb aaaaag dbbbbbb aaaaa dbbbbbb aaaac dbbbbbb aaaag dbbbbbb aaaa dbbbbbb aaag dbbbbbb aaa dbbbbbb aac dbbbbbbd aag dbbbbbbd aa bbbbbbd ac bbbbbbd ag bbbbbbd ``` <!-- end of image --> I can confirm that 1 intersection exists in area B. Answer: A: 0; B: 1; 0 + 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#1b37e5ff b,#d5a90fff c,#7383eeff d,#f0e2b2ff e,#908066ff f,#e0c153ff g,#bec6f7ff ``` ```image dd dbbbd fbbbbbf bbbbbbbbb dbbbbbbbbbbb dbbbbbbbd dbbb fbbbbbbb dbbb bbbbbbbf dbbb dbbbbbbbf bbb dbbbbbbbd bbb fbbbbbbb bbb bbbbbbbf bbb dbbbbbbbf bbb dbbbbbbbd bbb fbbbbbbbd aaebb bbbbbbbf aaaabb dbbbbbbbf aaaabb dbbbbbbbd gaaaabb fbbbbbbbd aaaaaeb fbbbbbbf aaaaaab dbbbbbbbf caaaaaab dbbbbbbbd aaagaaab fbbbbbbbd gaaa aaab fbbbbbbb aaaa aaae dbbbbbbbf aaa caaad dbbbbbbbd gaaa aaad fbbbbbbbd aaac aaad fbbbbbbb aaa aaad dbbbbbbbf caaa aaac dbbbbbbbd aaag eaaa fbbbbbbbd gaaa faaa fbbbbbbb aaaa faaa bbbbbbbf aaa faaag dbbbbbbbd caaa febf fbbbbbbbd aaac dbbf fbbbbbbb aaa dbbb bbbbbf caaa dbbb eebd aaag dbbb aaaaaacg gaaa dbbb aaaaaaaaaaaacg aaac dbbb aaaaaaaaaaaaaaaaaacg aaa bbb gcaaaaaaaaaaaaaaaaaa caaa bbb gcaaaaaaaaaaaaa aaac bbb gcaaaaaaaa aaa bbb gaaac aaaa bbb caaag aaag bbb aaaa gaaa bbb aaaa aaac bbb gaaaa aaa bbb caaag caaa bbb aaaa aaag bbb aaaa gaaa bbb aaaa aaaa fff gaaac aaa aaaag gaaa aaaa aaac aaaa aaa gaaac caaa caaag aaag aaaa gaaa aaaa aaaa gaaaa aaa caaac caaa aaaa aaac aaaa aaa aaaa caaa gaaac aaag aaaag gaaa aaaa aaac aaaa aaa gaaac caaa caaag aaac aaaa aaa aaaa aaaa aaaa aaag caaac gaaa aaaa aaac aaaaaaa aaaaaa gaaaag caaa aac ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#8a6760ff b,#b2d6b2ff c,#36455bff d,#657380ff e,#96c897ff f,#a19997ff g,#d4cfd0ff ``` ```image fg ggg c ggbfffaaaaaaaaafffggg gd gggbffaaaaaaaaaafffggg beeeceeeeeeeeeeeeeeeeeeegggfffaaaaaaaaaaffbggg ebbbbcbbbbbbbaaaaaaaaaaabgg ebbbbdebbbbbbabbbbbbbbbe ebbbbbcbbbbbbabbbbbbbbbe ebbbbbfdbbbbbfbbbbbbbbbe ebbbbbbcbbbbfebbbbbbbbbe ebbbbbbecbbbabbbbbbbbbbe ebbbbbbbcbbbabbbbbbbbbbe ebbbbbbbbcbbabbbbbbbbbbe ebbbbbbbbdfbabbbbbbbbbbe ebbbbbbbbbcbabbbbbbbbbbe ebbbbbbbbbedfbbbbbbbbbbe ebbbbbbbbbbcebbbbbbbbbbe ebbbbbbbbbbacbbbbbbbbbbe ebbbbbbbbbbadebbbbbbbbbe ebbbbbbbbbbabcbbbbbbbbbe ebbbbbbbbbbabfdbbbbbbbbe ebbbbbbbbbbabbcbbbbbbbbe ebbbbbbbbbefbbbcbbbbbbbe cg ebbbbbbbbbfbbbbcebbbbbbe cc ebbbbbbbbbabbbbbcbbbbbbe gf c ebbbbbbbbbabbbbbddbbbbbe d c ebbbbbbbbbabbbbbbcbbbbbe c bd ebbbbbbbbbabbbbbbedbbbbe c dg ebbbbbbbbbabbbbbbbcbbbbe gf c beeeeeeeeffeeeeeeeeceeeb d c f fg c c a c c bd a gd gf dg a c d c a c c c f dg c c gg c gb bd f bf d db a c c c a d d c a d bb c a c c bd f fb c db gg c d c f gd bg c a c c c a c c bd a dg d db a c fg c f gf c c gg c c c f c d bd a dg fg db a c c c a ff c c f c d gb gd f bg c c f c c a fg gf a c d a gd c f c c gg c gf f dg d a c c a bf c a c gf a dd f dc gg d f a a a a f gg f a ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#86605aff b,#c3babbff c,#37465cff d,#646f80ff e,#e2dfe0ff f,#a2989bff g,#997a75ff ``` ```image ecd fcb eeeebbbbfffggggaa cc eaaaaaaaaaaaaaaggggff bcf baffbbbbeeee dce bae ecd fa fcb gg cc af bcf eaf dce eab ecd bae dcb fae ecd fa fcf gg dce af bcf eab dce eab ecd bae fcb fa cc fa bcf gg dceaf ecdab fcab ecce dcf gcce ggcd afdce eabecd bab fcb bae cc fa bcf gg dce ag ecd af fcb eab cc bae bcf bae dce fa ecd gg dcb af ecd af fcf eab dce bae bcf bae dce fa ecd gg fcb af cc ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#89635dff b,#b8b2b6ff c,#35455bff d,#636f81ff e,#ecebecff f,#9f8f91ff g,#d4cfd0ff ``` ```image e fg eggb c eggbbffaaaaaaaaaffbbge gd eggbfffaaaaaaaaaffbbgee c eegbbffaaaaaaaaafffbgge c aaaaaaaaffbbgge dg a c a bf eb c bg ed f de a c a fb a c f gdb cg fc adg a c a bf f c gb ec cg be de cce f c ef c a bb de ec a c c bd a ed c db f ce gf ce gg c d c be fg c ec a c c bd a gd gb db a c d ce a c c c f dg c ec gg c gb bd f bf d db a c c ce a ed d c a de bb ec a c c bd eb fb c db gg c d ce f gd bg c a c c ec a c c bd a dg d db f c bg ce eb bf c c bg c c ec f ec d bd a de fe db a c c ce a bb c c f c ef eb ed fe be ce c f c c a fg ef a c de a gd c f c c gb c gf be dg d a c c a bf c a c gb a edd f dc gg d fe a a a a f gg f a ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#84f1a6ff b,#8e6fa1ff c,#c9e6d6ff d,#96c996ff e,#a99db4ff f,#b1d7b1ff g,#edf6efff ``` ```image gdddddddddddddddddddddddddddddddddddddg cfffffffffffffffffffffffffffffffffffffg caaafffffffffffffffffffffffffffffffffffg aaaaaafffffffffffffffffffffffffffffffffg caaaaaaaffffffffffffffffffffffffffffffg gffaaaaaaaffffffffffffffffffffffffffffg gffffaaaaaaaffffffffffffffffffffffffffg gfffffffaaaaaaafffffffffffffffffffffffg gfffffffffaaaaaaafffffffffffffffffffffg gffffffffffffaaaaaaaffffffffffffffffffg gffffffffffffffaaaaaaaffffffffffffffffg gfbbbbbbeefffffffaaaaaaaafffffffffffffg gfbbbbbbbbbbbbeeffffaaaaaaafffffffffffg gfbbbbbbbbbbbbbbbbbbbeaaaaafffffffffffg gfbbbfffffebbbbbbbbbbbbbbbbeffffffffffg gfbbefffffffffffebbbbbbbbbbbbbbbbeffffg gfbbefffffffffffffffffebbbbbbbbbbbbbbbecg gfbbeffffffffffffffffffffaaaeebbbbbbbbbbbbbbecg gdbbeffffffffffffffffffffaaaffffffeebbbbbbbbbbbbbbbbbbbbbeeeeccgg gdbbfffffffffffffffffffffaaaffffffffffg cebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeee gdbbffffffffffffffffffffffaaffffffffffg ceeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gebbffffffffffffffffffffffaaafffffffffg ggccceeeebbbbbbbbbb gebbffffffffffffffffffffffaaafffffffffg gebbffffffffffffffffffffffaaafffffffffg gbbbffffffffffffffffffffffaaafffffffffg gbbbffffffffffffffffffffffaaafffffffffg gbbbfffffffffffffffffffffffaafffffffffg gbbbfffffffffffffffffffffffaaaffffffffg gbbbfffffffffffffffffffffffaaaffffffffg gbbbfffffffffffffffffffffffaaaffffffffg gbbbfffffffffffffffffffffffaaaffffffffg gbbbdddddddddddddddddddddddaaaddddddddg bbb gaac bbe aaa bbe faag bbe aaa bbc aaa bbc gaac gbbc aaa gbbg caag cbbg aaa cbb aaa ebb gaaf ebb aaa ebb caac bbb aaa bbb aaa bbb gaaa bbb aaa bbb caac bbb aaa bbb aaa bbe aaa bbe aaa bbe caac bbe aaa bbc faag gbbc aaa gbbg aaa cbbg gaac cbb aaa ebb faag ebb aaa ebb aaa ebb gaac ebb aaa caag cc aaa caaa aaa aaaaaag gaaf gaaaaaac aaa caaaaaac caac caaaaaag aaa aaaaaaf aaa gaaaaaac aaa caaaaaag aaa faaaaaag caac aaaaaaf aaa gaaaaaac aaag caaaaaag aaafaaaaaa aaaaaaaf caaaac aag ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#83f1a6ff b,#8e6ea1ff c,#c2b1ccff d,#d6fae1ff e,#a391b3ff f,#adf5c4ff g,#ded6e3ff ``` ```image d aaf aaaafd aaaaaaad aaaaaaaaafd aaaaaaaaaaafd daaaaaaaaaaaaafd dfaaaaaaaaaaaafd faaaaaaaaaaaaaf dfaaaaaaaaaaaafd dfaaaaaaaaaaaaad daaaaaaaaaaaaafd dfaaaaaaaaaaaafd faaaaaaaaaaaaaf dfaaaaaaaaaaaafd faaaaaaaaaaaaaf dfaaaaaaaaaaaafd dfaaaaaaaaaaaaad gg daaaaaaaaaaaaafd cbbbbeecgg dfaaaaaaaaaaaafd gbbbbbbbbbbbeecgg faaaaaaaaaaaaaf gbbbbbbbbbbbbbbbbbeecgg dfaaaaaaaaaaaafd cbbbbbbbbbbbbbbbbbbbbbbbeecgg dfaaaaaaaaaaaaf cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbecgg daaaaaaaaaaaf cbbbbbcebbbbbbbbbbbbbbbbbbbbbbbbbbbbbecggfaaaaaaaaa cbbbbe gccebbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeaaaaa ebbbbe gccebbbbbbbbbbbbbbbbbbbbbbbbbbbbbeecg ebbbbe gccebbbbbbbbbbbbbbbbbbbbbbbbbbbbbeccg ebbbbc gccebbbbbbbbbbbbbbbbbbbbbbbbbbbbbeccg ebbbbc gccebbbbbbbbbbbbbbbbbbbbbbbbbbbbbeccg ebbbbc gccebbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbc faeebbbbbbbbbbbbbbbbbbbbbb bbbbbc daaaaaggceebbbbbbbbbbbbbbb bbbbbg aaaaad ggceebbbbbbbbb bbbbbg aaaaaf ggceebbb bbbbbg faaaaf gg gbbbbbg faaaaa gbbbbbg daaaaa gbbbbb daaaaad gbbbbb aaaaad gbbbbb aaaaaf cbbbbb faaaaf cbbbbb faaaaa cbbbbe daaaaa cbbbbe daaaaad cbbbbe aaaaad ebbbbe aaaaaf ebbbbe faaaaf ebbbbc faaaaa ebbbbc daaaaa bbbbbc daaaaad bbbbbc aaaaad bbbbbg aaaaaf bbbbbg faaaaf bbbbbg faaaaa gbbbbbg daaaaa gbbbbbg daaaaad gbbbbbg aaaaad gbbbbb aaaaaf gbbbbb faaaaf ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#83f2a6ff b,#8e6ea1ff c,#cec1d6ff d,#c9f8d8ff e,#ac95baff f,#abf5c2ff g,#e8f2edff ``` ```image d daaf aaaaaag daaaaaaf gaaaaaaag faaaaaad gaaaaaaf faaaaaad daaaaaaf g aaaaaaag bbbbbbec daaaaaad bbbbbbbbbbbbec gaaaaaaf bbbebbbbbbbbbbbbbbecfaaaa bbe gcebbbbbbbbbbbbbbbcg bbe gcebbbbbbbbbbbbbbecg bbc gcebbbbbbbbbbbbbbecg bbc aaacebbbbbbbbbbbbbbecg gbbc aaa cebbbbbbbbbbbbbbbbbbbbbeeecccgg gbbg faa cebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeee cbbg gaag ceeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb cbb aaf ggccceeebbbbbbbbbb cbb aaa ebb aaa ebb aaa ebb faa bbb gaag bbb aaf bbb aaa bbb aaa bbb aaa bbb faa bbb gaad bbe aaa bbe faag bbe aaa bbc aaa bbc gaaf gbbg aaa gbbg faag cbb aaa cbb aaa cbb gaaf ebb aaa ebb daad bbb aaa bbb aaa bbb aaf bbb aaa bbb daad bbb aaa bbb faa bbe aaa bbe aaa bbe daad bbc aaa bbc faag gbbc aaa gbbg aaa cbbg gaaf cbb aaa cbb faag ebb aaa ebb aaa ebb gaaf ebb aaa faag dd aaa faaa aaa faaaaag gaaf gaaaaaaf aaa daaaaaad daad faaaaaag aaa aaaaaaf aaa gaaaaaad aaf daaaaaag aaa faaaaaa daad aaaaaaf aaa gaaaaaad faa daaaaaag aaafaaaaaa aaaaaaaf daaaad aag ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#a4689eff b,#97bd31ff c,#b1d7b0ff d,#e2dbd6ff e,#98ca95ff f,#abc864ff g,#bb98b7ff ``` ```image ag dad ga aa aa ag dd dad cbbd ga fbbbb aa fbb cbf aa bbb bbd ag bbf bb dad bbf cbb ga dbbc bbd aa dbbd bb aa fbb dbb ag fbb bbc dad bbb bb ga bbb dbb aa bbf fbc aa bbc bb ag dbbd dbb dad cbb fbf ga fbb bb aa bbb bb aa dd bbb fbf ag bf bbf bbd dad bb bbf bb ga fb dbbd cbf aa dbccbbd bbd aa bbbb bb ag bbb dbb dad df bbc aa bb aa dbb aa fbc ag bb dad dbb aa fbf aa bb aa bb ag fbf dad bbd aa bb aa cbf aa bbd ag bb gad efbbeeeeeeeeeeaaeeeeeeec ccbbecccccccccaaccccccce cccbbcccccccccaaccccccce cccebbccccccccagccccccce ccccbbfccccccgacccccccce cccccbbccccccaacccccccce cccccebbcccccaacccccccce ccccccbbfccccaacccccccce cccccccbbccccagcccccccce ccccccccbbccgaccccccccce ccccccccfbfcaaccccccccce cccccccccbbcaaccccccccce cccccccccgffaaccccccccce ddddggggaaaaaaaaaaaaaaaaaaaaaagccccccccce gaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaagggggccbbeccccccccce daaaaaaaaaaaggggdddd ccccccccccccbbccccccccce aaad ccccccccccccfbbcccccccce gaag cccccccccccccbbeccccccce daaa ccccccccccccccbbccccccce aaag ccccccccccccccebbcccccce gaaa cccccccccccccccbbfccccce aaad ccccccccccccccccbbccccce aaag ccccccccccccccccebbcccce daaa cccccccccccccccccbbfccce aaad ccccccccccccccccccbbccce gaag cccccccccccccccccccbbcce daaa eccccccccccccccccccfbfce aaag bbd gaaa bb aad fbf g bbd bb cbf f ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a4689eff b,#98bd32ff c,#d3e3a9ff d,#ddc8daff e,#efefe5ff f,#b1c869ff g,#c299beff ``` ```image ebbbbc gaaa cbbbbe aaag fbbbf eaaag ebbbbc daaad cbbbbe gaaae fbbbf gaaa ebbbbc aaag cbbbbe eaaag fbbbf daaad bbbbc gaaae ebbbbe gaaa cbbbf aaag fbbbc eaaag ebbbbe daaad cbbbb gaaae fbbbf gaaa ebbbbc aaag cbbbb eaaag fbbbf daaad ebbbbc gaaae cbbbbe gaaa fbbbf aaag ebbbbc eaaag cbbbbedaaad fbbbfgaaae eeeedddffffaaaa gggggggaaaaaaaaaaaaaaaaaaaag aaaaaaaaaaaaaaaaaaaaaaaaaaad aaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaggggggggddddddeedbbbbe cbbbf fbbbc ebbbbe cbbbb fbbbf ebbbbc cbbbbe fbbbf ebbbbc cbbbbe fbbbf ebbbbc cbbbbe fbbbf bbbbc ebbbbe cbbbf fbbbc ebbbbe cbbbb fbbbf ebbbbc cbbbbe fbbbf ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#a4689eff b,#97bd31ff c,#cfe0a0ff d,#d5b9d2ff e,#ebe9e0ff f,#aec960ff g,#bb8fb7ff ``` ```image ag ead ga aa aa ag ec dad cbbe ga fbbbb aa fbb cbf aa bbb bbe ag bbf bb dad bbf cbb ga ebbc bbc aa cbbe bb aa cbbe cbb ag fbb bbc dad bbb bb ga bbb ebb aa bbf fbc aa ebbc bb ag ebbe ebb dae cbbe fbf ga fbb bbe aa bbb bb aa ee bbb cbf ag bf bbf bbe dae bb ebbc bb ga fb ebbc cbf aa ebccbbe bbe aa bbbb bb ag bbb cbb dae ef bbc ga bb aa ebb aa fbc ag bb dae ebb aa fbf aa bb aa ebb ag fbf dae bbe aa bb aa cbf aa bbe ead bb dae cbb aa bbc aa bb aa ebb ead fbc dae bb aa ebb aa fbc aa bb ead ebb dae fbf aa bbeaa eeedffaa eeedddgggaaaaaaaaaaaaaaaaaaaaaad gaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaggggdddeebbe daaaaaaaaaaagggdddeee bb aaad cbb gaag bbc eaaae bb aaad cbb daaa bbc eaaae bb gaag ebb daaa fbc aaad bb gaag ebb eaaae fbf aaad bbe gaaa bb eaae fbf d bbe bb cbf f ``` <!-- end of image -->
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Here's an image. My task is to find intersections or areas where lines come close together. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#0e25a3ff b,#af4b48ff c,#ca9892ff d,#495ab4ff e,#d9cfdcff f,#aed5aeff g,#8897ccff ``` ```image aad aaaa eaaaaa gaaaaaa daaeaaaa aaa aaaa aaa aaaae aaa aaaae aaa aaaag aaa aaaag aad daaad eaad daaad gaag gaaag daae gad aaa e aaa aaa aaa aaa aaa eaad gaag daae aaa aaa aaa aaa aaa aaa eaad gaag daae daa ebb aaa bbb aaa cbbe aaa ebbb aaa bbb aaa bbb eaad cbbc gaag bbb gaae bbb daa bbbe fffffffffffaaaffffffffff ebbb fffffffffffaaaffffffffff bbb fffffffffffaaaffffffffff bbb fffffffffffaaaffffffffff cbbc fffffffffffaaaffffffffff bbb fffffffffffaadffffffffff bbb ffffffffffgaadffffffffff cbb bbbe ffffffffffdaagfffffffffccbbbbbb ebbb ffffffffffdaaffffffcbbbbbbbbbbb bbb ffffffffffaaaffcbbbbbbbbbbbbc bbb ffffffffffabbbbbbbbbbbbbe cbbc fffffffbbbbbbbbbbbbbffff bbb ffcbbbbbbbbbbbbcffffffff bbb cbbbbbbbbbbbbdafffffffffff bbbe cbbbbbbbbbbbbcffaadfffffffffff ebbb ecbbbbbbbbbbbbffffffgaadfffffffffff bbb ebbbbbbbbbbbbcefffffffffdaagfffffffffff bbb cbbbbbbbbbbbbc fffffffffdaaffffffffffff cbbc cbbbbbbbbbbbbe fffffffffaaaffffffffffff bbb ecbbbbbbbbbbbce fffffffffaaaffffffffffff bbb ebbbbbbbbbbbbc fffffffffaaaffffffffffff bbbe cbbbbbbbbbbbbc fffffffffaaaffffffffffff ebbbbbbbbbbbbbbbe fffffffffaaaffffffffffff bbbbbbbbbbce fffffffffaaaffffffffffff bbbbbbc eaad cc gaag daae aaa aaa aaa aaa aaa aaa eaad gaag eeeeedaae aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadddddddddddddddde ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0f26a2ff b,#ae4947ff c,#dbafadff d,#515eb7ff e,#dcd4e2ff f,#c67f7dff g,#929cd5ff ``` ```image aaaaaa aaaaaa eaaaaad eaaaaad gaaaaag gaaaaag gaaaaag daaaaae daaaaae aaaaaa aaaaaa eaaaaad eaaaaad gaaaaag gaaaaag gaaaaag daaaaae ecf daaaaae ccfbbbb aaaaaa ecfbbbbbbbbb aaaaaa ecfbbbbbbbbbbbbb eaaaaadcfbbbbbbbbbbbbbbbbb eaabbbbbbbbbbbbbbbbbbbbbbb ecfbbbbbbbbbbbbbbbbbbbbbbbfce ecfbbbbbbbbbbbbbbbbbbbbbbbfce ecfbbbbbbbbbbbbbbbbbbbbbbbfce cffbbbbbbbbbbbbbbbbbbbbbbffc ecfbbbbbbbbbbbbbbbbbbbbbbbfce bbbbbbbbbbbbbbbbbbbbbbbdaa bbbbbbbbbbbbbbbbbbfcaaaaaa bbbbbbbbbbbbbffc aaaaad bbbbbbbbbfce eaaaaad bbbbbfce eaaaaad bfce gaaaaag gaaaaag daaaaae daaaaae daaaaa aaaaaa aaaaad eaaaaad eaaaaad gaaaaag gaaaaag daaaaae daaaaae daaaaa aaaaaa ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Answer: A: 1; 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#0e25a3ff b,#ae4946ff c,#d49f9dff d,#4859b7ff e,#dacfdbff f,#c17270ff g,#8c97d2ff ``` ```image aad aaaa eaaaaa gaaaaaa daaeaaaa aaa aaaa aaa aaaae aaa aaaae aaa aaaag aaa aaaag aad daaad eaad daaad gaag gaaag daae gad aaa e aaa aaa aaa aaa aaa eaad gaag daae aaa aaa aaa aaa aaa aaa eaad gaag daae daa efb aaa bbb aaa fbbe aaa ebbb aaa bbb aaa bbb eaad cbbc gaag bbb gaae bbb daa fbbe aaa ebbf aaa bbb aaa bbb aaa cbbc aaa bbb eaad bbb gaag cbb fbbe gaag efbbbbbb ebbf daae efbbbbbbbbbb bbb aaa cbbbbbbbbbbbbc bbb abbbbbbbbbbbbfe cbbc efbbbbbbbbbbbfe bbb efbbbbbbbbbbbc bbb cbbbbbbbbbbbbda fbbe cbbbbbbbbbbbfe aad ebbf efbbbbbbbbbbbfe eaag bbb efbbbbbbbbbbbc gaag bbb cbbbbbbbbbbbbc daae cbbc cbbbbbbbbbbbfe aaa bbb efbbbbbbbbbbbfe aaa bbb efbbbbbbbbbbbc aaa bbbe cbbbbbbbbbbbbc aaa ebbbbbbbbbbbbbbfe aaa bbbbbbbbbbfe aad bbbbbbc eaad fc gaag daae aaa aaa aaa aaa aaa aaa eaad gaag eeeeedaae aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadddddddddddddddde ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#9a9db6ff b,#b9fbf0ff c,#ebf0efff d,#b1d8b2ff e,#71f4dbff f,#a1cda2ff g,#c3c3d4ff ``` ```image c a a gc gc cccggcccccccccccccccccccccccccc fffeafffffffffffffffffffffffffff dddeaddddddddddddddddddddddddddf dddeaddddddddddddddddddddddddddf dddeaddddddddddddddddddddddddddf dddeaddddddddddddddddddddddddddf dddeaddddddddddddddddddddddddddf dddeaddddddddddddddddddddddddddf dddeaddddddddddddddddddddddddddf ddddaddddddddddddddddddddddddddf ddddaddddddddddddddddddddddddddf ddddaddddddddddddddddddddddddddf bee ddddaddddddddddddddddddddddddddf beeb ddddaedddddddddddddddddddddddddf beeb ddddffeddddddddddddddddddddddddf beeb ddddffdeeddddddddddddddddddddddf beeb dddddadddedddddddddddddddddddddf beeb dddddaddddeddddddddddddddddddddf beeb dddddadddddeeddddddddddddddddddf beeb dddddaddddddeedddddddddddddddddf beeb dddddaddddddddeddddddddddddddddf beb dddddadddddddddeeddddddddddddddf beb dddddaddddddddddeedddddddddddddf beb dddddaddddddddddddeddddddddddddf beb dddddadddddddddddddeeddddddddddf beb dddddaddddddddddddddeedddddddddf ceb dddddaddddddddddddddddeddddddddf ceb dddddadddddddddddddddddeeddddddf cee dddddaddddddddddddddddddeedddddf cee dddddffddddddddddddddaddddeddddf cee ddddddaddddddddddddddadddddedddf cee ffffffaffffffffffffffaffffffeeeeeeb ccccccacccccccccccccaaccccccccc a aa a ag a gcgc a a gc a a cg a cg cg a a g a a a g a a gc gc a gc a a cg a a cg cg a g gc a a a a a a a a cg gc ccc a a gc ccccggggggaaaaaaaaaaaaaaaaaagggac a a caaaaaaaaaaaaaaaaggggggcccc a a a a a gc ga a a ac a a a gc cg a gc a ga gg a ac cg a a cg gg a a a gg a a ac a cg a a gc a a a a a cg a a a a g a ggc ga ca cg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#b4b6caff b,#8ff8e7ff c,#d1d2deff d,#969bb6ff e,#6df4dfff f,#e1f6f5ff g,#b6faefff ``` ```image cdc cdc edc eda eda eda bda bdd bdd bdd bdd bddf bddf gedf gedc gedc gedc gedc geda geda geda feda fedd fedd fedd gddg adeg cdbebf cdcgeef cdc geeg cdc fbebf fdc beef fda geeg da feeb da beef da geeg dd feeb ad beef ad geeg ad feeb adf beef cdf geeg cdf feeb cdc fbebf cdc geeg fdc feeg fdc fbebf fda geef da geeg da fbebf da beef dd geeg ad feeb ad beef ad geeg adf feeb cdf beef cdc geeg cdc a feeb cdc cdc beef fdc adc geeg fda ddc feeb ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#acaec4ff b,#9dfaeaff c,#e0e0e9ff d,#9798b5ff e,#6cf7e0ff f,#ccfcf4ff g,#c5c5d5ff ``` ```image d a g gc cc eg eg ea bd bd bd bd bd fd fd fd fee fd feef ae feef gcef feef cg eb feef cg fe feef a ef feeb a eb feeb d fe feeb d ef feb d eb feb d be feb d e feb d eb feb d be feb a fe feb g ef feb gc be feb cc g fe feb cg d ef feb g cd beeeeeb a dd d dd d aa d gcgc d d gc d d cg d cg cg d a a a d a a d d gc gc d gc d d cg d d cg a d a ac d a d d d d a d cg g cc d d gc ccccgggaaadddddddddddddddaaaggac d d cdddddddddddddddaaagggcccc d d a d d gc ca d d ac a d d g cg d gc a ca cc d ac cg d d g gc d a d ga d d dc d a d d gc d d d d d cg d a a d a a gac gd cd g ``` <!-- end of image -->
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This image looks interesting. I wonder if there are any intersections hidden in there? These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#a7476bff b,#57ee2dff c,#c18a9cff d,#b1d8b1ff e,#e0e3d3ff f,#77ed57ff g,#97cd93ff ``` ```image ac ff aa ebbb caa fbbbb aac ebbbebb aae fbbf fbe eaa ebbbe gbd caa fbbf dbg aac ebbbe ebf aa fbbf bb caa ebbbe bb aac fbbf bb aae ebbbe bb eaa fbbf bb caa ebbbe bb aac fbbf bb aa ebbbe fbe caa fbbf gbd aac ebbbe dbg aae fbbf ebf eaa ebbbe caa fbbb aacggggggggggggggggggggd ebbbe gaaddddddddddddddddddddg fbbb gcaadddddddddddddddddddg ebbbe gdaaaddddddddddddddddddg fbbb gddaagdddddddddddddddddg bbbd gdddaadddddddddddddddddgfbbb gdddaaaddddddddddddddddbbbd gddddaacdddddddddddddfbbb gdddddaaddddddddddddbbbf gdddddcaadddddddddfbbbdg gddddddaaadddddddbbbgddg gdddddddaagddddfbbbddddg gddddddddaadddbbbgdddddg gddddddddaaafbbbdddddddg gdddddddddabbbgddddddddg gddddddddfbbbddddddddddg gdddddddbbbgaadddddddddg gdddddfbbbddaaaddddddddg gddddbbbgddddaagdddddddg gddfbbbdddddddaadddddddg gdbbbfddddddddaaaddddddg fbbbdddddddddddaacdddddg bbbfdddddddddddddaadddddg gbbbdddddddddddddddcaaddddg ecc bbbdgddddddddddddddddaaadddg ecaaaaaaae gbbb gdddddddddddddddddaacddg ecaaaaaaaaaaccac bbbd gddddddddddddddddddaaddg ecaaaaaaaaaacc aa gbbb gddddddddddddddddddcaadg ecaaaaaaaaaace aa bbbd gdddddddddddddddddddaacg ecaaaaaaaaaace aa gbbb gddddddddddddddddddddaaaaaaaaaaaace cae bbbg dggggggggggggggggggggcaaaaace cac dbbb aa bg aa aa aa cae eac aa aa aa aae cac aa aa aa aa cae eac aa aa aa aae cac aa aa aa aa cae eac ce ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a7466bff b,#59ee2eff c,#d9b0c0ff d,#c0f8b0ff e,#eeede7ff f,#89f16bff g,#bc758eff ``` ```image aaaag caaaac gaaaae gaaaa eaaaag caaaac gaaaae eaaaag caaaac gaaaae gaaaa eaaaag caaaac gaaaae ef eaaaag dbb caaaac efbbb gaaaae dbbbbb gaaaae efbbbbbb eaaaag dbbbbbbfe caaaac efbbbbbbd gaaaae dbbbbbbfe eaaaag efbbbbbbd caaaac dbbbbbbfe gaaaae efbbbbbbd gaaaae dbbbbbbfe eaaaag efbbbbbbd caaaac dbbbbbbfe gaaaaefbbbbbbd eaaaabbbbbbfe cabbbbbbbd dbbbbbbfe efbbbbbbge dbbbbbbbaag efbbbbbbfaaaac dbbbbbbfe gaaaae efbbbbbbd eaaaag dbbbbbbfe caaaac fbbbbbbd caaaac dbbbbbbfe gaaaae fbbbbbbd eaaaag dbbbbbbfe caaaac fbbbbbbd gaaaae dbbbbbbfe eaaaag fbbbbbbd caaaac bbbbbbfe caaaac bbbbbd gaaaae bbbfe eaaaag bbd caaaac fe gaaaae eaaaag caaaac caaaac gaaaae eaaaag caaaac gaaaae eaaaag eaaaag caaaac gaaaa ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#a7466aff b,#58ef2dff c,#d4a6b8ff d,#adf598ff e,#e2e7d7ff f,#7cf25bff g,#bd7691ff ``` ```image ac fb aa ebbb caa fbbbb aag ebbbebb aae fbbf fbe eaa ebbbe dbd gaa fbbf dbd aac ebbbe ebf aa fbbf bb caa ebbbe bb aag fbbf bb aae ebbbe bb eaa fbbf bb gaa ebbbe bb aac fbbf bb aa ebbbe fbe caa fbbb dbd aag ebbbe dbd aae fbbb ebf eaa ebbbe gaa fbbb aac ebbbe aa fbbb caa ebbbe aag fbbb aae ebbbd eaa fbbb gaa bbbd aac fbbb aa bbbd caa fbbb aag bbbd aae fbbb eaa bbbd gaafbbb abbbd fbbb bbbdaa fbbb aag bbbd aae dbbb eaa bbbd gaa dbbb aac bbbd aa dbbb caa ecg bbbd aag ecaaaaaaac dbbb aae ecaaaaaaaaaagcag bbbd eaa egaaaaaaaaaagc aa dbbb gaa egaaaaaaaaaagc aa bbbd aac cgaaaaaaaaaagc aa dbbb aaaaaaaaaaaagc gae bbbd caaaaage cac dbbb aa bd aa aa aa gac eag aa aa aa gae cac aa aa aa aa gac eag aa aa aa gae cac aa aa aa aa gac eag ce ``` <!-- 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'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#5e774eff b,#d928b8ff c,#23440dff d,#b1d6b1ff e,#de7fccff f,#95bb91ff g,#ebd4e5ff ``` ```image eb gbbbe gbbbbbb bbbbg bb bbbbg bb ebbbe ebg ebbbe gbe gbbbe bb gbbbb bb bbbb bb bbbbg ebe bbbbg gbb gbbbe bb ebbb bb dfffffffffffffffffffffbbbg bbg fdddddddddddddddddddebbb ebe fddddddddddddddddddbbbed bb fddddddddddddddddebbbddd fdddddddddddddddbbbedddd fddddddddddddddbbbdddddd gd fdddddddddddddbbeddddddd fcccc fdddddddddddddbbdddddddd gaccccccc fddddddddddddbbedddddddd dccccccag cc fddddddddddddbbddddddddfaccccccf cc fdddddddddddebedddddfccccccag cc fdddddddddddbbdddaccccccf cc fdddddddddddbbaccccccfdd ac fdddddddddaccccccadddddd acg fdddddfaccccccfddddddddd acg fddfccccccabeddddddddddd acg accccccfddbbdddddddddddd acg dccccccafddddebbdddddddddddd acg fccccccaddddddddbbddddddddddddd acd gacccccag fddddddddbbddddddddddddd acd fccccccf fdddddddbbdddddddddddddd acd gaccccccd fdddddddbbdddddddddddddd acd fcccccca fddddddebedddddddddddddd acd accccccd fddddddbbddddddddddddddd fcd dccccccag fdddddebbddddddddddddddd fcf dcccccf fdddddbbdddddddddddddddd fcf cag fdddddbbdddddddddddddddd fcf fddddbbedddddddddddddddf fcf bb fcf ebe fcf bb fcf gbb dcf bbg dca bb dca ebe dca bb dca gbb dca bb gca bb gca bbg gca bb gca ebe gca bb ca gbb cc bbg cc bb cc ebe cc bb cc ebb cc bb cc gbb cc bbg cc bb cc ebe cc bb cc bg gbb cc ebbbe bb cc bbbbe bb cc bbbbb bbe cc ebbbb bb cc ebbbbg ebe cc gbbbbg bb cc gbbbbe gbb cc bbbbebbg cc dfaccf bbbbb ccacccccccccca ebe ccccccccafd gfg ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5d6d4cff b,#d827b7ff c,#23430cff d,#d2d8cdff e,#e367cdff f,#97a68dff g,#f1b3e6ff ``` ```image ebb gbbbb ebbbbb gbbbbbbe ebbbbbbg gbbbbbbe ebbbbbbg gbbbbbbe ebbbbbbg gbbbbbbe gbbbbbbg ebbbbe gbbbbg ebbbe bbbbg gbbbe bbbbg gbbbb ebbbg bbbb dfa ebbbe dfaccc bbbbg faccccccc gbbbe dfacccccccccc ebbbg faccccccccccccaf gbbbbfacccccccccccafd ebaccccccccccccafd dfacccccccccccafd dfacccccccccccafd dfaccccccccccccad dfaccccccccccccad faccccccccccccabbbg dfacccccccccccafdgbbbb accccccccccccafd ebbbe cccccccccafd bbbbg ccccccafd gbbbe cccfd bbbbg fd gbbbb ebbbe bbbb ebbbe bbbbg gbbbb ebbbg gbbbb ebbbe bbbbg gbbbe bbbbg gbbbb ebbbg bbbb ebbbe bbbbg gbbbe ebbbg ``` <!-- end of image --> As I suspected, there's 1 intersection within area A. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#597048ff b,#d928b9ff c,#23440cff d,#b7c2b0ff e,#e881d5ff f,#8b9c7fff g,#ecd2e6ff ``` ```image eb gbbbe gbbbbbb bbbbg bb bbbbg bb ebbbe ebg ebbbe gbb gbbbe bb gbbbb bb bbbb bb bbbbg ebe bbbbg gbb gbbbe bb ebbb bb gbbbg bbg ebbb ebe bbbg bb ebbb bbbg gbbb gd bbe dcccc bb gaccccccc bbg dccccccag cc bb fccccccd cc ebe dacccccag cc bb fccccccf cc gbbacccccad ac fccccccf acg gaccccccd acg dccccccabe acg fccccccd bb acg dacccccag ebb acg fccccccf bb acd gacccccag gbb acd fccccccf bbg acd gacccccad bb fcd dccccccf ebe fcd accccccd bb fcd dccccccag gbb fcd dcccccf bb fcd cag bb fcf bbe fcf bb fcf ebe dcf bb dcf gbb dcf bbg dcf bb dcf ebe dca bb dca gbb dca bb gca bb gca bbg gca bb gca ebe gca bb ca gbb cc bbg cc bb cc ebe cc bb cc ebb cc bb cc gbb cc bbg cc bb cc ebe cc bb cc bg gbb cc ebbbe bb cc bbbbe bb cc bbbbb bbe cc ebbbb bb cc ebbbbg ebe cc gbbbbg bb cc gbbbbe gbb cc bbbbebbg cc dfaccf bbbbb ccacccccccccca ebe ccccccccafd gdg ``` <!-- 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,#57c79cff b,#d20468ff c,#b0d7b1ff d,#db5e98ff e,#f0afcfff f,#86cfa5ff g,#ccede1ff ``` ```image gaf aa aa ee cccaaccccccccccccf ebbb cccaaccccccccccccf ebbbbbb cccaaccccccccccccf bbe ebbbb cccaaccccccccccccf bbd ebbbb cccaafcccccccccccf bbb dbbbb cccfafcccccccccccf bbb dbbbd cccfafcccccccccccf dbb dbbbd ccccaacccccccccccf ebb dbbbd ccccaacccccccccccf bbe bbbbd ccccaacccccccccccf bbd bbbb ccccaacccccccccccf bbb bbbe ccccaacccccccccccf dbb dbbd ccccaacccccccccccf ebb ebbb ccccaacccccccccccf bbe bbb ccccfafccccccccccf bbd bbb ccccfafccccccccccf bbb bbbe cccbbaadcccccccccf dbb dbbd ccdbbaabbbbbbdcccfebb ebbb cccccaadbbbbbbbbbbbbe bbb cccccaacccccddbbbbbd bbb cccccaaccccccccccf bbbe cccccaaccccccccccf dbbd cccccaaccccccccccf ebbb cccccfafcccccccccf bbb cccccfafcccccccccf bbb cccccfaacccccccccf bbbe ccccccaacccccccccf dbbd ccccccaacccccccccf ebbb ccccccaacccccccccf bbb ccccccaacccccccccf bbb ccccccaacccccccccf dbbe ccccccaacccccccccf ebbd ccccccaacccccccccf g ebbb ccccccfafccccccccf aag bbb ccccccfafccccccccf gaaag bbbe gaa fafaag dbb aa aa gaag e aa aa gaag aa gaf gaag aa fag gaag aa aa gaag aag aa gaag fag gaf gaac gac fag gaac gaf aa gaac aag aa gaac caa gaf gaac faa fag gaac faa aa gaaf aaa aa aaf aaa gaf aaf aaf fag aaf aaf aa aaf aac aa aaf gaag gaf aaf gaag fag aaf caa aa aaf faa aa aaf faa gaf aaa aaa aag aaa aaa aa aaa aaf aa aaa aaf gaf aaa aac aag aaa aag aa aaa gaag aa aaa gaacaf aaa faaag aaa faa aaa ff aaa aaa aaa aaa aaa aaa aaa aaa a ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#57c69cff b,#d10267ff c,#afe4d0ff d,#df5096ff e,#e99ec2ff f,#84d6b7ff g,#dcede7ff ``` ```image faaag faaag faaac caaac caaaf gaaaf gaaaf aaaa aaaa aaaag faaag faaac caaac caaac gaaaf gaaaf gaaaa aaaa aaaag faaag faaag caaac caaac caaaf gaaaf gaaaa aaaa aaaa faaag faaag faaac caaac caaaf ddeeaaaf bbbbaaaaeeg gbbbbaaaabbbbbddee ebbbbaaaabbbbbbbbbbbddeeg eeddaaaabbbbbbbbbbbbbbbbbddee faaaedbbbbbbbbbbbbbbbbbbb faaac geeddbbbbbbbbbbbb caaac geeddbbbbbb caaac eedd caaaf gaaaf gaaaa aaaa aaaa faaag faaag faaac caaac caaaf gaaaf gaaaf aaaa aaaa aaaag faaag faaac caaac caaaf gaaaf gaaaf gaaaa aaaa aaaag faaag faaac caaac caaac caaaf ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#56c79cff b,#d20368ff c,#a8e1ccff d,#e05699ff e,#f0aeceff f,#7ad2b0ff g,#d0efe3ff ``` ```image gaf aa aa ee aa ebbb aa ebbbbbb aa bbe ebbbb aa bbd ebbbb fag bbb dbbbb cac bbb dbbbd gaf dbb dbbbd aa ebb dbbbd aa bbe bbbbd aa bbd bbbb aa bbb bbbe aa dbb dbbd aa ebb ebbb fag bbe bbb cac bbd bbb cac bbb bbbe bbaae dbb dbbd ebbaabbbbbde ebb ebbb aadbbbbbbbbbbbbe bbb aa edbbbbbd bbb aa bbbe aa dbbd aa ebbb fag bbb cac bbb gaf dbbe aa dbbd aa ebbb aa bbb aa bbb aa dbbe aa ebbd fag g ebbb cac aag bbb gaf gaaag bbbe gaf fafaag dbb aa aa caag e aa aa caag aa gaf gaag aa fag gaag aa aa gaac fag aa gaac fag gaf gaac cac fag gaac gaf aa gaac aag aa gaac caa gaf gaac faa fag gaac faa aa gaaf aaa aa gaaf aaa gaf aaf aaf fag aaf aaf aa aaf aac aa aaf gaag gaf aaf gaag fag aaf caa aa aaf faa aa aaf faa gaf aaf aaa fag aaf aaa aa aaa aaf aa aaa aaf gaf aaa aac fag aaa gaag aa aaa gaag aa aaa caacaf aaa caaag aaa faa aaa ff aaa aaa aaa aaa aaa aaa aaa aaa a ``` <!-- end of image -->
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Time to put on my detective hat and find those intersection points! The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#5bb77aff b,#3e8cc4ff c,#b1d8b2ff d,#eef6efff e,#77afcfff f,#a0d0a6ff g,#bedcdeff ``` ```image dfffffffffffffffffffffffd dfcccccccccccccccccccccfd dfcccccccccccccccccccccfd dfccccccccccccccccccccafd dfcccccccccccccccccccfafd dfcccccccccccccccccccaafd dfccccccccccccccccccaacfd dfcccccccccccccccccfafcfd dfcccccccccccccccccaaccfd dfccccccccccccccccaacccfd dfccccccccccccccccafcccfd dfcccccccccccccccaaccccfd dfccccccccccccccfacccccfd dfccccccccccccccaacccccfd dfcccccccccccccaaccccccfd dfccccccccccccfafccccccfd dfccccccccccccaacccccccfd dfcccccccccccaaccccccccfd dfcccccccccccafccccccccfd gbbbbbbbeeffcccaacccccccccfd gebbbbegebbbbbbbbbbbbbbeefccccfd debbbbeg dfccccccccfabbbbbbbbbbbfd debbbbbg dfccccccccaaccccccccffefd gbbbbbg dfcccccccfafcccccccccccfd gbbbbbed dfcccccccaaccccccccccccfd gebbbbed dfccccccaacccccccccccccfd debbbbeg dfccccccaacccccccccccccfd debbbbbg dfcccccaaccccccccccccccfd gbbbbbg dfccccfafccccccccccccccfd gbbbbbe dfccccaacccccccccccccccfd gebbbbed dfcccaaccccccccccccccccfd debbbbeg dfccfafccccccccccccccccfd debbbbbg dfccaacccccccccccccccccfd gbbbbbg dfcaaccccccccccccccccccfd bbbe dfcaaccccccccccccccccccfd d dfaacccccccccccccccccccfd dfafcccccccccccccccccccfd daaccccccccccccccccccccfd aacccccccccccccccccccccfd dafcccccccccccccccccccccfd aafcccccccccccccccccccccfd fadfffffffffffffffffffffffd af ddddddddddddddddddddddd aa gad aa aa dag aa fa af aa gad aa aa dac aa fad af aa dgcccfffffaaaaaaaaaaaaaaaaaaaaaad aaaaaaaaaaaaaaaaaaafffffcccggggd da aa af ga aa ac ga ag aa aa ag dad ca aa aa ga ag aa ca ca aa af ag fa fa ac aa aa ad aaa aaf dad ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#58b678ff b,#3f8dc4ff c,#9ed4b0ff d,#e0efebff e,#83b5d9ff f,#75c292ff g,#bdded7ff ``` ```image d gac faac caaa daaag faaf gaaad daaac caaf gaaad faac caaa daaag faaf gaaad daaac caaf daaad faac caaad daaag faaf gaaad aaac caaf daaag faac caaad daaag faaf gaaad aaac eeggdd caaf bbbbbbbbbeeeeggdd daaag bbbbbbbbbbbbbbbbbbbbeeefaafd ggeeebbbbbbbbbbbbbbbbbbbbbbbbbbeeeggdd ddggeeeebbbbbbbbbbbbbbbbbbbbbbbbbeeeegd ddfabbebbbbbbbbbbbbbbbbbbbbd gaaad ddggeeeebbbbbbbbbd aaac ddggee caaf daaag faac gaaad daaag faaf gaaad faac caaf daaag faaf gaaad daaag caaf gaaad faac caaa daaag faaf gaaad daaac caaf gaaad faac caaa daaag faaf gaaad daaac caaf gaaad faac aaa aag af ad c ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#58b678ff b,#3e8cc4ff c,#addbbcff d,#d7eae7ff e,#70a9d3ff f,#80c798ff g,#a3c8e3ff ``` ```image a ca af aa dad aa fa ac aa ca af aa dad aa fa ac gbbbbbbbegdd aa debbbbeggebbbbbbbbbbbbeegd debbbbed dabebbbbbbbbbd gbbbbbg aa ddg gbbbbbg dad gbbbbbg aa debbbbed fa debbbbed ac gbbbbbg aa gbbbbbg cad gbbbbbg af debbbbed aa debbbbed dad ebbbbed aa gbbbbbg fa bbbg ac aa cad af fa dac aa fa af aa cad af fa dac aa ca af aa dad aa fa dac aa ca af aa dccccccfffffaaaaaaaaaaaaaaaaaaaad aaaaaaaaaaaaaaaaaffffffccccccddd da aa ac da aa ac ca ad aa aa ac dad ca aa aa ca ad af ca ca aa af ad fa ca ac af aa ad aaa aaf da ``` <!-- end of image -->
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I'm approaching this image with caution. Intersections might be tricky to spot. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#424ed8ff b,#21cea3ff c,#858de2ff d,#040cd5ff e,#afd6b0ff f,#76ddc1ff g,#c4ddedff ``` ```image cad dddg dddc ddda addd cddd gddd ddd dddc ddda dddd addd gddd ddd dddg dddc dddd addd cddd bf ddd bbbg dddg fbbbb dddc bbbbbf ddda bbbbbbb addd gbbbfbbbb cddd bbbb fbbbf gddd fbbbg bbbb dddg bbbb gbbbb eeeeeedddceeeeeeeeeeee bbbb bbbbg eeeeeedddaeeeeeeeeeeee bbbb bbbb eeeeeeddddeeeeeeeeeeee bbbb fbbbf eeeeeeadddeeeeeeeeeeee gbbbf bbbb eeeeeecdddeeeeeeeeeeee bbbb bbbb eeeeeeedddeeeeeeeeeeee fbbbg fbbbg eeeeeeedddceeeeeeeeeee bbbb bbbb eeeeeeedddaeeeeeeeeeee bbbb gbbbf eeefeeeddddeeeeeeeeeee bbbb bbbb eefbbeeadddeeeeeeeeeee bbbb bbbb eebbbbecdddeeeeeeeeeee gbbbf fbbbg eebbbbbfdddeeeeeeeeeee bbbb bbbb eeebbbbbdddeeeeeeeeeee fbbbg gbbbb eeeebbbbdddaeeeeeeeeee bbbb bbbb eeeeefbbdddaeeeeeeeeee bbbb bbbb eeeeeeebddddfeeeeeeeee gbbbf fbbbf eeeeeeeeadddbbeeeeeeee bbbb bbbf eeeeeeeeedddbbbeeeeeee fbbbf b eeeeeeeeedddbbbbeeeeee bbbb eeeeeeeeedddbbbbbfeeee fbbbg eeeeeeeeedddabbbbbbeee bbbb eeeeeeeeeddddefbbbbbee bbbb eeeeeeeeeadddeeebbbbbe gbbbf eeeeeeeeecdddeeeebbbbbf bbbb eeeeeeeeeedddeeeeebbbbbb fbbbg eeeeeeeeeedddceeeeefbbbbb bbbb eeeeeeeeeedddaeeeeeeebbbbbg bbbb eeeeeeeeeeddddeeeeeeeebbbbbf bbbb eeeeeeeeeeadddeeeeeeee bbbbbb bbbb eeeeeeeeeecdddeeeeeeee fbbbbb gbbbf eeeeeeeeeeedddeeeeeeee bbbbbg bbbb eeeeeeeeeeedddeeeeeeee bbbbbf fbbbg eeeeeeeeeeedddaeeeeeee fbbbbb bbbb ddda gbbbbb bbbb addd bbbbbg bbbb cddd bbbbbf bbbb gddd fbbbbb gbbbf ddd gbbbbb bbbb dddc bbbbbbbbg ddda bbbbbbb dddd fbbbb addd gbbf gddd ddd dddg dddc dddd addd ggcca cddd gcccaadddddddddddddd ddd ggccaaddddddddddddddddddddddddddddddg dddg ggccaadddddddddddddddddddddddddddddddddddddddddddddg dddcgccaaddddddddddddddddddddddddddddddddddddddddddddddddaaccg dddddddddddddddddddddddddddddddddddddddddaaccgg adddddddddddddddddddddddddaaccgg gdddddddddaacccg ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#223ed2ff b,#20cda3ff c,#999dedff d,#040cd5ff e,#5d63e3ff f,#6bdec2ff g,#c4e1ecff ``` ```image adddddd eddddddg eddddddc cdddddde gdddddde dddddda ddddddd addddddg eddddddc cddddddc cdddddde gdddddda ddddddd addddddg eddddddg cddddddc cdddddde gdddddde f dddddda fbf adddddd gbbbbg eddddddg gbbbbbbg eddddddc bbbbbbbbf cdddddde fbbbbbbbbbf gdddddde fbbbbbbbbbbgdddddda fbbbbbbbbbbddddddd gbbbbbbbbbaddddddg gbbbbbbbbaddddddc fbbbbbbaddddddc fbbbbbbdddddde gbbbbbdddddda gbbbbdddddddg fbbaddddddbg fbaddddddbbf gaddddddabbf cddddddabbbbg gddddddabbbbbg dddddddbbbbbbf addddddbbbbbbbf eddddddbbbbbbbbbg eddddddbbbbbbbbbbg cddddddebbbbbbbbbbf gddddddegbbbbbbbbbbf dddddda fbbbbbbbbbbg ddddddd fbbbbbbbbbbg addddddg gbbbbbbbbbbf eddddddc gbbbbbbbbbbf cddddddc fbbbbbbbbb cdddddde fbbbbbbbb gdddddda gbbbbbbb ddddddd gbbbbbb addddddg fbbbb eddddddg fbbb cddddddc gbb cdddddde gb gdddddde dddddda adddddd eddddddg eddddddc cdddddde gdddddde dddddda ddddddd addddddg ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#3d46ddff b,#20cea3ff c,#a8abf0ff d,#040cd5ff e,#7378e7ff f,#76e0c6ff g,#c7e6ecff ``` ```image cad dddg ddde ddda addd eddd gddd ddd dddc ddda dddd eddd cddd ddd dddc ddde dddd addd cddd bf ddd bbbg dddg fbbbb ddde bbbbbf ddda bbbbbbb addd gbbbfbbbb eddd bbbb fbbbf gddd fbbbg bbbb ddd bbbb gbbbb dddc bbbbg bbbbg ddda bbbb bbbb dddd bbbb fbbbf eddd gbbbf bbbb cddd bbbb bbbb ddd fbbbg fbbbg dddc bbbb bbbb ddde bbbb gbbbf f dddd bbbb bbbb fbb addd bbbb bbbb bbbb cddd gbbbf fbbbg bbbbbgddd bbbb bbbb bbbbbdddg fbbbg gbbbb fbbbddde bbbb bbbb gbbddda bbbb bbbb bddddg gbbbf fbbbf adddbf bbbb bbbf gdddbbb fbbbf b dddbbbb bbbb dddbbbbbg fbbbg dddabbbbbf bbbb dddd fbbbbb bbbb eddd gbbbbbg gbbbf cddd bbbbbf bbbb ddd bbbbbb fbbbg dddc fbbbbb bbbb ddde gbbbbbg bbbb dddd bbbbbf bbbb addd bbbbbb bbbb cddd fbbbbb gbbbf ddd bbbbbg bbbb dddg bbbbbf fbbbg ddde fbbbbb bbbb ddda gbbbbb bbbb addd bbbbbg bbbb eddd bbbbbf bbbb gddd fbbbbb gbbbf ddd gbbbbb bbbb dddc bbbbbbbbg ddda bbbbbbb dddd fbbbb eddd gbbf cddd ddd dddc ddde dddd addd gccea cddd gceeaadddddddddddddd ddd gcceeaddddddddddddddddddddddddddddddg dddg gcceaadddddddddddddddddddddddddddddddddddddddddddddc dddegceeadddddddddddddddddddddddddddddddddddddddddddddddaaeecg dddddddddddddddddddddddddddddddddddddddddaaeccg adddddddddddddddddddddddddaeeccg gdddddddddaaeecg ``` <!-- 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 need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#40fa3fff b,#3d8913ff c,#75f775ff d,#6ba64eff e,#d4f7d2ff f,#b1d8b0ff g,#95ca92ff ``` ```image ef faaa eaaaaa aaaaaaae aaaacaaaac aaaae eaaaac caaac aaaaa faaaa aaaaa eaaaa caaaae aaaa caaaac aaaa eaaaaafffffffffffffffffff aaaae aaaaaffffffffffffffffff caaac aaaaafffffffffffffffff faaaa aaaaagfffffffffffffff eaaaa gcaaaacffffffffffffff aaaa gfgaaaaafffffffffffff aaaa gfffaaaaaffffffffffff aaaae gffffaaaaafffffffffff caaac gfffffaaaaagfffffffff caaaa gffffffcaaaacffffffff eaaaa gfffffffgaaaaafgbbfff aaaa gfffffffffaaaaabbbfff aaaa gffffffffffaaaaabbbff aaaae gfffffffffgbaaaaagfff caaac gffffffffbbbbaaaaacff caaac gffffffbbbbbbdgaaagff eaaaa gffffdbbbbbbffffacfff aaaa gffgbbbbbbgffffffffff aaaa gfbbbbbbdffffffffffff aaaae bbbbbbdffffffffffffff aaaac gbbbbbbffffffffffffffff caaac ebbbbbbgfffffffffffffffff eaaaa bbbbbbdfffffffffffffffffff aaaa dbbbbbdgffffffffffffffffffff aaaa fbbbbbb gffffffffffffffffffff aaaae ebbbbbbf gffffffffffffffffffff aaaaf dbbbbbd fgggggggggggggggggggg caaac bbbbbb eaaaa bbbbbe aaaa ebbbbb aaaa gbbbbd aaaae bbbbbf aaaaf bbbbb caaac ebbbbb eaaaa gbbbbd aaaa dbbbbf aaaa bbbbbe aaaae ebbbbb aaaaf fbbbbd caaac dbbbbg faaaa bbbbbe eaaaa bbbbb aaaa fbbbbb aaaae dbbbbd aaaaf bbbbbf caaac bbbbb eaaaa ebbbbb aaaa gbbbbd aaae dbbbbf eaaa bbbbbe aaaa ebbbbb aaae fbbbbd eaaa dbbbbg caaa bbbbbe aaaf bbbbb aaa bbbbb caaa ebbbbd aaaf gbbbbg fgggaaaggggggggbbbbbf gffcaaafffffffbbbbb gffaaacffffffbbbbb gffaaafffffgbbbbb gfcaaaffffgbbbbd gfaaacfffdbbbbdf gfaaafffbbbbbgff gffcaffbbbbbffff gfffffbbbbbfffff gfffgbbbbbffffff gffdbbbbdfffffff gfdbbbbgffffffff ggbbbbgfffffffff gfdbbfffffffffff gffbffffffffffff gfffffffffffffff ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#41fb41ff b,#3c8912ff c,#8afc8aff d,#5c9c38ff e,#d6f2d2ff f,#85b56bff g,#b4d1a4ff ``` ```image caaaaaae aaaaaaa eaaaaaac ed caaaaaae ebb aaaaaaa gbbb eaaaaaac fbbbb caaaaaae fbbbbb aaaaaaa edbbbbbb eaaaaaac edbbbbbbb caaaaaae gbbbbbbbbb aaaaaaa gbbbbbbbbbf eaaaaaac fbbbbbbbbbg caaaaaae dbbbbbbbbbg aaaaaaa edbbbbbbbbde caaaaac ebbbbbbbbbde ecaae gbbbbbbbbbf e fbbbbbbbbbf fbbbbbbbbbg dbbbbbbbbbe edbbbbbbbbde gbbbbbbbbbd gbbbbbbbbbf fbbbbbbbbbg fbbbbbbbbbg edbbbbbbbbde gbbbbbbbbde fbbbbbbf fbbbbf dbbg edg ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Now, let's scrutinize the next spot. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#3ffa3fff b,#3c8912ff c,#a8eea3ff d,#58a137ff e,#d7f3d4ff f,#68fb68ff g,#8bbb73ff ``` ```image aaf aaafe aaaaae aaaaaac aaaaaaac aaaaaaaaf aaaaaaaaafe efaaaaaaaaae faaaaaaaaac caaaaaaaaac caaaaaaaaaf eaaaaaaaaafe efaaaaaaaaae faaaaaaaaac caaaaaaaaac caaaaaaaaaf eaaaaaaaaafe efaaaaaaaaae faaaaaaaaac caaaaaaaaac caaaaaaaaaf ede eaaaaaaaaafe egbbd efaaaaaaaaaegbbbbbc faaaaaaaaadbbbbbd caaaaaaaaadbbbbbg caaaaaaaaaabbbbd gaaaaaaaaaabbg cdbbaaaaaaaaaac edbbbbbaaaaaaaaaac egbbbbbbbbaaaaaaaaaac gbbbbbbbbbbbdaaaaaaaaf cdbbbbbbbbbbbgeeaaaaaaae edbbbbbbbbbbbde efaaaae gbbbbbbbbbbbbc faac cbbbbbbbbbbbbg cf edbbbbbbbbbbbde egbbbbbbbbbbbdc gbbbbbbbbbbbbg cdbbbbbbbbbbbge edbbbbbbbbbbbde bbbbbbbbbbbdc bbbbbbbbbbg bbbbbbbbge bbbbbbde bbbbbc bbbg bde c ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area B. Answer: A: 0; B: 1; 0 + 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#3ffa3fff b,#3c8913ff c,#92fc92ff d,#6ba54bff e,#d0f4cdff f,#60fb60ff g,#a5c992ff ``` ```image ee caaa eaaaaa aaaaaaae aaaacaaaac aaaae eaaaaf faaac aaaaa caaaf aaaaa eaaaa faaaae aaaa caaaac aaaa eaaaaf aaaae aaaaa faaac aaaaa caaaf faaaae eaaaa caaaac aaaa eaaaaf aaaa aaaaa aaaae aaaaa faaac faaaae caaaf caaaac eaaaa eaaaaf ebd aaaa aaaaabbb aaaa aaaaabbd aaaae gbaaaaae faaac bbbbaaaaac caaaf dbbbbbdeaaae eaaaa gbbbbbb ac aaaa ebbbbbbe aaaa bbbbbbg aaaae dbbbbbd faaac gbbbbbb caaaf ebbbbbbe eaaaa bbbbbbg aaaa dbbbbbd aaaa gbbbbbb aaaae ebbbbbbg faaac dbbbbbd caaaf bbbbbb eaaaa bbbbbe aaaa ebbbbb aaaa gbbbbd aaaae bbbbbe faaac bbbbb caaaf ebbbbb eaaaa gbbbbd aaaa dbbbbg aaaa bbbbbe aaaae bbbbb aaaac gbbbbd faaaf dbbbbg eaaaa bbbbbe eaaaa bbbbb aaaa ebbbbb aaaae dbbbbd aaaac bbbbbe faaaf bbbbb eaaaa ebbbbb aaaa gbbbbd aaae dbbbbg eaaa bbbbb faaa ebbbbb aaae gbbbbd eaaa dbbbbg faaa bbbbbe aaae bbbbb aaa bbbbb faaa ebbbbd aaac gbbbbg aaa dbbbbe caaa bbbbb aaac bbbbb aaa ebbbbb caaa ebbbbd aaac dbbbbg aaa dbbbbe ca bbbbb bbbbb ebbbbd gbbbbd dbbbbg gbbbbe dbb d ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#d5531dff b,#a1426cff c,#e7bab3ff d,#ca8a70ff e,#b1d7b0ff f,#f1f3edff g,#9bc596ff ``` ```image fbc fbbf dbb dbbd daabbffffffffffffffffffffff aabbbeeeeeeeeeeeeeeeeeeeeg faabbbeeeeeeeeeeeeeeeeeeeg fgaabbeeeeeeeeeeeeeeeeeeeg fedabbbeeeeeeeeeeeeeeeeeeg feeaabbbeeeeeeeeeeeeeeeeeg feeeaabbeeeeeeeeeeeeeeeeeg feeeeabbbeeeeeeeeeeeeeeeeg af feeeeeabbbeeeeeeeeeeeeeeeg daa feeeeedabbgeeeeeeeeeeeeeeg aaf feeeeeedabbeeeeeeeeeeeeeeg daa feeeeeeeabbbeeeeeeeeeeeeeg aaf feeeeeeeeabbgeeeeeeeeeeeeg caa feeeeeeeeeabbeeeeeeeeeeeeg aac feeeeeeeeegbbbeeeeeeeeeeeg caa feeeeeeeeeedbbgeeeeeeeeeeg aac feeeeeeeeeeeabbeeeeeeeeeeg faa feeeeeeeeeeeebbbeeeeeeeeeg aac feeeeeeeeeeeedbbgeeeeeeeeg faa feeeeeeeeeeeeeabbeeeeeeeeg aad feeeeeeeeeeeeeebbbeeeeeeeg faa feeeeeeeeeeeeeeabbdeeeeeeg aad feeeeeeeeeeeeeeeabbbbeeeeg aa feeeeeeeeeeeeeeedabbbbbeeg aad feeeeeeeeeeeeeeeeaadbbbbbg aa feeeeeeeeeeeeeeeeeaaeedbbbbc daa feeeeeeeeeeeeeeeeedaaeeegbbbbd aa feeeeeeeeeeeeeeeeeeaadeeegfbbbbbf fffffffffffffffffdaaffff feeeeeeeeeeeeeeeeeegaaeeeg bbbbbc fgeeeeeeeeeeeeeeeeaageeeg feeeeeeeeeeeeeeeeeeeaaaeeg dbbbbc feeeeeeeeeeeeeeeedaaeeeeg feeeeeeeeeeeeeeeeeeeeaaeeg cbbbbd feeeeeeeeeeeeeeeeaageeeeg feeeeeeeeeeeeeeeeeeeedaaeg fbbbbbf feeeeeeeeeeeeeeedaaeeeeeg feeeeeeeeeeeeeeeeeeeeeaadg bbbbbc feeeeeeeeeeeeeeeaageeeeeg feeeeeeeeeeeeeeeeeeeeegaag dbbbbc feeeeeeeeeeeeeegaaeeeeeeg feeeeeeeeeeeeeeeeeeeeeeaaa cbbbbd feeeeeeeeeeeeeeaadeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeaaf fbbbbbffeeeeeeeeeeeeegaaeeeeeeeg fgggggggggggggggggggggggdaa fbbbbbgeeeeeeeeeeeeaadeeeeeeeg aad dbbbbdeeeeeeeeeeaaeeeeeeeeg faa cbbbbdeeeeeeeaadeeeeeeeeg daa fegbbbbbeeeeeaaeeeeeeeeeg aac feeeebbbbbgeaadeeeeeeeeeg caa feeeeeedbbbbaaeeeeeeeeeeg aad feeeeeeeedbbbbdeeeeeeeeeg aa feeeeeeeeeeabbbbbeeeeeeeg daa feeeeeeeeedaaebbbbbgeeeeg aaf feeeeeeeeeaaeeeebbbbbgeeg daa feeeeeeeedaaeeeeeedbbbbdg aac feeeeeeeeaaeeeeeeeeegbbbbb caa feeeeeeedaaeeeeeeeeeeeebbbbbf aad feeeeeeeaageeeeeeeeeeeeegdbbbb faa feeeeeedaaeeeeeeeeeeeeeeg cbc aaa feeeeeeaageeeeeeeeeeeeeeg aa feeeeegaaeeeeeeeeeeeeeeeg daa feeeeeaadeeeeeeeeeeeeeeeg aaf feeeegaaeeeeeeeeeeeeeeeeg caa feeeeaadeeeeeeeeeeeeeeeeg aac feeeeaaeeeeeeeeeeeeeeeeeg caa fgggaadggggggggggggggggge aad aa faa aad aaa aa aaf daa daa aa aac daa caa aaf aac daa faa aaf aad caa aa aaf aaa caa aaf aac daa caa aacaac caaaa aaad faa cf ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#d5521dff b,#a0406bff c,#e6b8b2ff d,#e18661ff e,#bb4841ff f,#f3e0dfff g,#bc7997ff ``` ```image aaabbbbb aaaebbbbg aaaaebbbbc caaaabbbbbf daaaebbbbg daaaebbbbc faaaabbbbbf faaaebbbbg caaaebbbbc daaabbbbbf daaebbbbg faaaebbbbc faaabbbbbf caaabbbbg daaebbbbc daabbbbbf aaabbbbg faaebbbbc caabbbbbf caabbbbg daebbbbc dabbbbbf faabbbbg caebbbbg cabbbbbf dabbbbb debbbbg fabbbbbf fabbbbb cebbbbg debbbbf dbbbbb febbbbg cebbbbc dbbbbb febbbbg debbbbc abbbbbf cebbbbg debbbbc fabbbbbf cebbbbg debbbbgf fabbbbbbgf dabbbbbbbgc faebbbbbbbbbc caaebbbbbbbbbgf daaaebbbbbbbbbgf faaaadcgbbbbbbbbg daaaac fgbbbbbbb aaaaa fgbbbbb caaaad cbbb daaaaf cg faaaad caaaac aaaaa caaaad daaaaf faaaad caaaac daaaaf faaaad daaaac aaaaa caaaac daaaaf faaaad daaaa aaaa caaa daa ``` <!-- end of image --> This isn't an intersection in area A, but I'm not discouraged. Hmm, interesting. Let's check out another area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#df784eff b,#a1406bff c,#e1b5b7ff d,#e89f81ff e,#d6521bff f,#f3dfddff g,#bc7896ff ``` ```image feeeed deeee eeeed deeeef eeeed deeeef eeeea ceeeef aeeea ceeeef aeeea ceeeec aeeea feeeec aeeea feeeec deeee gf feeeed bbgc deeee bbbbbc feeeed bbbbbbbcf deeeef bbbbbbbbbgf eeeed cgbbbbbbbbgc deeeef fgbbbbbbbbbc eeeed fgbbbbbbbbbcf ceeeef cbbbbbbbbbgf eeeea cgbbbbbbbbgcceeeef fgbbbbbbbbbeeea fgbbbbbbbbbbc cbbbbbbbbbgf cbbbbbbbbbgf aebbbbbbbbbgc feeeegbbbbbbbbbc aeeee cbbbbbbbbbgf feeeec cgbbbbbbbbgf deeee fgbbbbbbbbgc feeeed fgbbbbbbbbbc deeee cbbbbbbbbbg feeeed cgbbbbbbb deeeef fgbbbbb eeeed fgbbb deeeef fcb eeeed ceeeef aeeea ceeeef aeeea ceeeec aeeea feeeec aeeea feeeec aeeee feeeed deeee feeeed deeee feeeed deeeef ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area B. Answer: A: 0; B: 1; 0 + 1 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#da6b3fff b,#a1406bff c,#e7b8b0ff d,#e59371ff e,#d5511bff f,#f3dfddff g,#bb7796ff ``` ```image fbg fbb gbb dbbg aeebb eebbb eebbg feebbf cebbb aebbg eebbf ebbb ef ebbg dee cebbf ee dabb dee ebbg eef ebbf cee ebb eef fbbb cee dbbf eec abb fee bbb eec dbbc fee ebb eed fbbb ee abbg aed ebbbg ee cebbbbbf aea eedgbbbbc ee ee gbbbbc dea dee cbbbbg ee eec fbbbbbf dee cee gbbbbf ee eea gbbbbc dee eef cbbbbg eef dee fbbbbb cee eed gbbbbf eef fee gbbbbc cee aea cbbbbg eec eef fbbbbb fee cee bbbbbf eec eed gbbbbc fee ee cbbbbg eed aee fbbbbb ee eec bbbbbf aed cee gbbbbee eea cbbbbg ee ebbbbg aee dea bbbbbf eef ee gbbbbc dee dee cbbbbg eec eef fbbbbg cee cee fbbbbbf eed eef gbbbb fee cee cbc aea eec ee fee dee eec eef fee cee eed eec fee fee eed eed ee ee aed aea ee ee aea dee ee eef dea cee ee eec dee fee eef eed cee ee eef aea cee eef eec dee fee eeceec ceeee eeed fee cf ``` <!-- end of image -->
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Time to put on my detective hat and find those intersection points! I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#7b3652ff b,#f8f8beff c,#b49aa1ff d,#b3d7b2ff e,#966677ff f,#f2f5ebff g,#a4cfa3ff ``` ```image dc aaa aaac bbbbb aaa bbbbbbbbbbf eaae fbbbbbbbbbbbbbbf aaa bbb fbbbbbbbbbbbbf caaa bbbb fbbbbbbbbbbbbf aaaf bbb fbbbbbbbbbbbbf caaa bbbf fbbbbbbbbbbbbf aaaf fbbb bbbbbbbbbbbbb daaa bbb fbbbbbbbbbbbbf aaad bbbb fbbbbbbbbbbbbf faaa bbb fbbbbbbbbbb aaac bbbf fbbbbb aaa fbbb fb eaae bbb aaa bbbb eaae bbb aaaf bbbf fcaaaffffffffffffffbbbf fggaaagggggggggggggbbbdgf fgdcaaadddddddddddbbbbdgf fgddaaacddddddddddbbbddgf fgddgaaadddddddddbbbbddgf fgdddaaacddddddddbbbdddgf fgddddaaadddddddbbbddddgf fgddddaaaedddddbbbbddddgf fgdddddaaadddddbbbdddddgf fgdddddeaaedddbbbbdddddgf fgddddddaaadddbbbddddddgf fgddddddeaaadbbbdddddddgf fgdddddddaaadbbbdddddddgf fgdddddddcaabbbddddddddgf fgddddddddabbbbddddddddgf fgddddddddgbbbdddddddddgf fgddddddddbbbecddddddddgf fgdddddddbbbbaaddddddddgf fgdddddddbbbaaaedddddddgf fgddddddbbbbdaaadddddddgf fgddddddbbbddeaaeddddddgf fgdddddbbbddddaaaddddddgf fgdddddbbbddddeaaadddddgf fgddddbbbddddddaaagddddgf fgdddbbbbddddddcaaaddddgf fgdddbbbddddddddaaagdddgf fgddbbbdddddddddcaaadddgf fgddbbbddddddddddaaacddgf fgdbbbdddddddddddgaaaddgf fgbbbbddddddddddddaaaedgf fgbbbggggggggggggggaaaggf bbbf eaae fbbb aaa bbb eaae bbbb aaa bbb caaa bbbf aaaf fbbb daaa bbb aaad bbbb faaa bbb aaac bbbf faaa fbbb eaac bbb aaa bbbb eaae cae bbb aaa eaaaa bf caaa faaaaaaaf aaaf daaaaaaef caaa caaaaaac aaaf eaaaaaad faaa faaaaaaaf aaac caaaaaae faaa eaaaaaac aaac faaaaaaaf aaa daaaaaae eaae caaaaaac aaa eaaaaaad caae faaaaaaaf aaaf caaaaaae caaaeaaaaaac aaaaaaaaf daaaae eac ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7b3552ff b,#f8f8beff c,#a47587ff d,#be9da8ff e,#8e536bff f,#dac7caff g,#f8f6e4ff ``` ```image daaaaaag gbbbbbbg eaaaaad bbbbbbb daaaaaag gbbbbbbg eaaaaac bbbbbbg faaaaaaf gbbbbbb eaaaaac gbbbbbbg faaaaaaf bbbbbbb caaaaae gbbbbbbg gaaaaaaf bbbbbbg caaaaae gbbbbbb gaaaaaad gbbbbbbg daaaaaag bbbbbbb gaaaaaad gbbbbbbg daaaaaag bbbbbbg eaaaaac gbbbbbb faaaaaaf bbbbbbg eaaaaac bbbbbbb faaaaaaf gbbbbbbg caaaaae bbbbbbg faaaaaaf gbbbbbb caaaaae bbbbbbg gaaaaaad bbbbbbb daaaaae gbbbbbbg gaaaaaad bbbbbbb daaaaaagbbbbbb eaaaaebbbbbbg faaaafbbbbbb eaacbbbbbbg faabbbbbbb cdbbbbbb fbbbbbbf bbbbbbbe gbbbbbbcad bbbbbbfaae gbbbbbbeaaad bbbbbbdaaaaag bbbbbbbeaaaaad gbbbbbbgdaaaaaag bbbbbbb eaaaaac gbbbbbb faaaaaaf bbbbbbg eaaaaac gbbbbbb faaaaaaf gbbbbbbg caaaaae bbbbbbb gaaaaaaf gbbbbbb caaaaae bbbbbbg gaaaaaad gbbbbbb daaaaaag gbbbbbbg gaaaaaad bbbbbbb daaaaaag gbbbbbbg eaaaaac bbbbbbg faaaaaag gbbbbbb eaaaaac gbbbbbbg faaaaaaf bbbbbbb caaaaae gbbbbbbg faaaaaaf bbbbbbg caaaaae gbbbbbb gaaaaaad gbbbbbbg daaaaae bbbbbbb gaaaaaad gbbbbbbg daaaaaag ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#7b3552ff b,#f8f8bfff c,#b08697ff d,#cbafbbff e,#945c72ff f,#e3d5daff g,#faf8e3ff ``` ```image dd aaa aaac bbbbg aaa bbbbbbbbbbg eaae gbbbbbbbbbbbbbbg aaa bbb gbbbbbbbbbbbbg caae bbbb gbbbbbbbbbbbbg aaag bbb gbbbbbbbbbbbbg daaa bbbg gbbbbbbbbbbbbg aaaf gbbb gbbbbbbbbbbbg faaa bbb gbbbbbbbbbbbbg aaad bbbb gbbbbbbbbbbbbg gaaa bbb gbbbbbbbbbb aaac bbbg gbbbbb aaa gbbb gb eaac bbb aaa gbbb caae bbb aaa bbbg caaa gbbb aaaf bbbg daaa gbbb aaaf bbb faaa bbbg aaad gbbb gaaa bbbg eaac gbbb aaa bbb eaae bbbg aaa bbb caaa bbbg aaagbbb daabbb abbbb fbbb bbbed gbbbaa bbbeaac bbbb aaa bbb eaae bbbg aaa gbbb caae bbb aaag bbbb daaa bbb aaaf bbbg faaa gbbb aaad bbb faaa bbbb aaac bbb aaa bbbg eaac gbbb aaa bbb caae bbbb aaa bbb caaa bbbg aaaf gbbb daaa bbb aaaf bbbb faaa bbb aaad bbbg gaaa gbbb eaac bbb aaa gbbb eaae dae bbb aaa caaaa bg caaa geaaaaaaf aaag faaaaaae daaa caaaaaac aaaf eaaaaaad faaa faaaaaaag aaad daaaaaae gaaa caaaaaad aaac gaaaaaaaf aaa daaaaaae eaae caaaaaac aaa eaaaaaad caae faaaaaaag aaag daaaaaac daaaeaaaaaad aaaaaaaaf faaaae eac ``` <!-- end of image -->
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I'm on the case! Let's uncover any intersections hidden in this image. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#5f03ecff b,#78c72fff c,#b297e8ff d,#b1d7b1ff e,#854ce5ff f,#edeff1ff g,#97cc8eff ``` ```image e aa ae caf aa a af ac ae aa ea ca fa a af ac ae aa ea ca fa a ac ac ae bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbf ea fbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbf ca bb ca db a bg af gb ac bg ae bb aa bd ea bb ca fbf fa bb a fbf af bb ac db ae bg aa gb ea bd fffcafffffffffffffffffffffffffffbbfff gdddgadddddddddddddddddddddddddddbgddgf gddddaddddddddddddddddddddddddddbbddddf gddddaddddddddddddddddddddddddddbdddddf gddddaeddddddddddddddddddddddddbbdddddf gddddaedddddddddddddddddddddddgbddddddf gddddaadddddddddddddddddddddddbbddddddf gddddeaddddddddddddddddddddddgbdddddddf gddddcaddddddddddddddddddddddbbdddddddf gdddddadddddddddddddddddddddbbddddddddf c gdddddadddddddddddddddddddddbgddddddddfcaaaae gdddddacdddddddddddddddddddbbddddddceaaaac faa gdddddaedddddddddddddddddddbgdddeaaaaef aa gdddddaeddddddddddddddddddbbeaaaaecdddf aaf gdddddeaddddddddddddddddcaaaaacdddddddf aac gdddddeadddddddddddddeaaaaedddddddddddf eae gdddddcadddddddddeaaaaedgbddddddddddddf caa gddddddadddddcaaaaacddddbbddddddddddddf faa gddddddadceaaaaedddddddgbdddddddddddddf aaf gddddddaaaaedddddddddddbgdddddddddddddf aaf gddddddcddddddddddddddbbddddddddddddddf eac gf gdddddddddddddddddddddbgddddddddddddddf cae bbbbbgddddddddddddddddddbbdddddddddddddddf faa fbbbbbbgddddddddddddddbgdddddddddddddddf faa gddgbbbbbbgdddddddddbbddddddddddddddddf aaf gdddddddbbbbbbgddddgbdddddddddddddddddf aac gdddddddddddgbbbbbgbbdddddddddddddddddf eae gdddddddddddddddgbbbddddddddddddddddddf cae af gdddddddddddddddddddddddddddddddddddddf faa a dggggggggggggggggggggggggggggggggggggg aa fa aaf ca eac ea eae ea caa ae faa ac aafac aaaf ea ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5f03ecff b,#73c525ff c,#b285f5ff d,#cdeab2ff e,#8947eeff f,#d7c2f9ff g,#9cd36aff ``` ```image caac gbbd faac dbbb faae bbbd aae dbbg aaa bbbd eaa gbbg eaaf bbb caaf gbbg caac dbbb faac gbbd aae dbbb aaa bbbd aaa dbbg eaa bbbd eaaf dbbg caac bbbd faac gbbg faae bbb aae gbbg aaa dbbb eaa gbbd eaaf dbbb f caaf bbbd fceaa caac dbbg fceaaaaaa faac bbbd feaaaaaaaaae faae gbbg fceaaaaaaaaecf aae bbbfceaaaaaaaaecf aaa ggeaaaaaaaaecf eaa fcaaaaaaaaaec eaaf fceaaaaaaaaecf caaf fceaaaaaaaaaef caac ceaaaaaaaaaegbbd faac fceaaaaaaaaecf dbbb faae fceaaaaaaaaecf bbbd aae fceaaaaaaaaecf dbbg aaa feaaaaaaaaaec bbbd eaa fceaaaaaaaaecf gbbg eaaeaaaaaaaaecf bbb caaaaaaaacf gbbg faaaaecf dbbb ccf gbbd dbbb bbbd dbbg bbgdd bbbd bbbbbbgdd dbbg gbbbbbbbbbgdd bbbd ddgbbbbbbbbbggd gbbg ddgbbbbbbbbbggd bbb dgbbbbbbbbbggd gbbg dgbbbbbbbbbbgd dbbb dgbbbbbbbbbbgd gbbd dggbbbbbbbbbgddbbb dggbbbbbbbbbbd ddgbbbbbg ddgg ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 The final count is: one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#5f02edff b,#78c72cff c,#ae80f5ff d,#d3ecbbff e,#833deeff f,#d8c2faff g,#a0d86cff ``` ```image e aa ac ca aa a af ac ae aa ea ca fa a af ac ae ea ca fa a a af ac ae gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ea dbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ca bb fa db a bg a gb af bg ac gb ae bd ea bb ca bd fa bb a db af bb ac db ae bg aa gb ea bd ca bb fa bd a bb af b ac bb ae db ea bg ca gb fa bg a gb f a bd caaaae af bb feaaaac faa ac bd caaaac aa ae bbcaaaaef aaf ea feaaaac eac ca feaaaae eae fa caaaaefdb faa a caaaaef bg faa a feaaaac gb aa aaaac bg aaf cf gb eac g bd cae bbbbgd bb faa dgbbbbgd bd aa dgbbbbgd bb aa gbbbbbd db aaf gbbbbbdbb eac gbbb cae af faa a aa a aaf fa eac ca cae ea faa ae aa ac aa af aaa ea ``` <!-- end of image -->
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Time to put on my detective hat and find those intersection points! These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#af268cff b,#deb7d8ff c,#823790ff d,#c28bb9ff e,#f0edefff f,#ae62a2ff g,#b0d6b0ff ``` ```image ab eab bae da fa aa aa aa ad ab eae ba fa aa aa aa af ad eab ba d da bccc fa cccdcc aa eccf dcc aa fcce dcc aa eccf bcc ad fccb bcc ab eccc bcc bae dccb bcc ggggggggggggfaggggggg ccc bcc eggggggggggggfaggggggg dccd ecc eggggggggggggaaggggggg ccc ecc eggggggggggggaaggggggg bccd ecceggggggggggggaaggggggg ccce eccggggggggggggafggggggg bccf eccgggggggggggafggggggg fcce eccggggggggggadggggggg eccf egccggggggggdagggggggg fccb eggccgggggggfagggggggg eccc egggccggggggaagggggggg dccb eggggccgggggaagggggggg ccc egggggccggggaagggggggg dccb eggggggccdggaagggggggg ccc egggggggccdgafgggggggg bccd eggggggggccdadgggggggg ccce egggggggggccaggggggggg bccf eggggggggggccfgggggggg ccce eggggggggggfccfggggggg eccf eggggggggggaaccfgggggg fcce eggggggggggaagccfggggg eccf eggggggggggaaggccfgggg fccb eggggggggggafgggccfggg eccc eggggggggggadggggcgggg dccb eggggggggggagggggggggg ccc egggggggggdagggggggggg eccd egggggggggfagggggggggg c egggggggggaagggggggggg egggggggggaagggggggggg egggggggggaagggggggggg egggggggggafgggggggggg egggggggggafgggggggggg egggggggggadgggggggggg eggggggggdaggggggggggg eggggggggfaggggggggggg eeeeeeeefaeeeeeeeeeee aa aa aa af ab eae ba aafdbe da aaaaaaaaaaafdbe aa bdfaaaaaaaaaaaaafdb aa ebdfaaaaaaaaaaaafdbe aa ebdfaaaaaaaaaaaafdbe af ebdfaaaaaaaaaaaaadbb ad bbdaaaaaaaaaaaaafdbe eab ebdfaaaaaaaaaaaafddae ebdfaaaaaaa e ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#ae268cff b,#dcb1d5ff c,#833791ff d,#c88bc0ff e,#ecd9eaff f,#c057a6ff g,#9f66aaff ``` ```image daaa daaf faaf faad aaab aaab eaaae baaa baaa g daaf cg faaf ccg faad cccg aaad gcccge aaab gcccge eaaae gcccge eaaae gcccge baaa gcccce daaa gcccce daaf gcccce faaf gcccce faad gcccce aaab gcccce aaab dcccce eaaae dcccce baaa dccccb baaa dccccb daaf dccccb faaf dccccb faad dccccb aaad dccccbaaab bccccaaae bccccaae bcccca bccccd fccccd faccccd faaccccd aaadccccd eaaabeccccd eaaae eccccd baaa eccccg baaa eccccg daaf eccccg faaf eccccg faad ecccb aaad ecd aaab eaaae baaae baaa daaf daaf faad faad aaab eaaab eaaae baaa daaa daaf faaf faad aaab aaab eaaae baaae baaa daaf ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#af268cff b,#dbb2d5ff c,#833791ff d,#ca88bfff e,#ecdaeaff f,#c055a5ff g,#a067abff ``` ```image ab ab ba da fa aa aa aa ad ab eae ba fa aa aa aa af ad eab ba d da bccc fa cccdcc aa eccg dcc aa gcce bcc af eccg bcc ad gcce bcc ab ccc bcc eae dccb bcc da ccc ecc fa dccd ecc aa ccc ecc aa bccd ecc aa ccc ecc af eccg ecc ad gcce cce eae eccg cce ba gcce cce da eccc cce fa gccb cce aa ccc cce aa dccb ccb af ccc ccb ad bccd ccbab ccc ccae bccg ccd ccce fccd eccg aaccd gcce aa ccd eccg aa ccg gccb af ccg ccc ad c dccb eae ccc ba eccd da c fa aa aa af ad ab bae da fa aa aa aa af ab eae ba aafdbe da aaaaaaaaaaafdbe aa edfaaaaaaaaaaaaafde aa ebdfaaaaaaaaaaaafdbe aa ebdfaaaaaaaaaaaafdbe af bdfaaaaaaaaaaaafdbe ad ebdfaaaaaaaaaaaafdb ab ebdfaaaaaaaaaaaafdda ebdfaaaaaaa e ``` <!-- end of image -->
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I'm curious to see if this image contains any intersection points. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f4b134ff b,#92ebc8ff c,#fadda7ff d,#e9c46bff e,#eaf6ecff f,#b1d8b1ff g,#a6cfa1ff ``` ```image eeccccdddaaaaaaaaaaaddddc eeccccdddaaaaaaaaaaadddccccee ec eeccccdddaaaaaaaaaaadddccccee c dadddcccce c c d d d d d d a a a a a a a a a a a a a a a a a a a e a ebbbe a ebbbe a ebbbe a ebbbe d ebbbe ggggggggggggggaggggg ebbb egfffffffffffffdfffff ebbe egfffffffffffffdfffff bbbe egfffffffffffffdfffff bbbe egfffffffffffffdfffff ebbbe egfffffffffffffdfffff ebbbe egfffffbbffffffdfffff ebbbe egfffffbbffffffdfffff ebbbe egffffbffbfffffdfffff ebbbe egffffbffbfffffdgffff ebbbe egfffbfffffffffdgffff ebbbegfffbffffbffffdgffff ebbbbfffffbffffggffff egffbffffffbfffggffff egfffffffffbfffgdffff egfffffffffbfffgdffff egffffffffffbffgdffff egffffffffffbfffdffff egfffffffffffbffdffff egfffffffffffbffdffff egfffffffffffbffdffff egffffffffffffbfdffff egffffffffffffbfdffff egffffffffffffffdffff egfffffffffffffbdffff egfffffffffffffbaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egffffffffffffffaffff egggggggggggggggagggg eeeeeeeeeeeeeeeaeeee ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#f4b134ff b,#b3f2daff c,#fadca4ff d,#f6c870ff e,#dbf8edff f,#8cebc7ff g,#fcedd1ff ``` ```image dd dd da da da da da da da da fe da bff ca fffe ca efefb ca ff bf ca efe efe ca ff fb ca efe bf cag bf efb cag efb bf cag bf efe cag efb fb cag bf bf cag fbee fb efb gag bffffbebfe ff gag eebfffb efe gag ee fb gag bf gag efe gac ff gac bfe gac fb gac bf gac efe gac fb ac bfe ac efb ac bf ac efe ac fb ad bf ad efb ad ff ad efe ad fb ad bf ad efead ffad bfad fad bad ead da dae dab da da da da da da da ca ca ca ca ca cag cag cag cag cag cag cag gag gag gag gag gac gac gac gac gac gac ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#f5b133ff b,#acf0d7ff c,#fad89aff d,#f8c66aff e,#d8f8ecff f,#8aebc7ff g,#fceacaff ``` ```image gggccdddaaaaaaaaaaaddddc ggcccdddaaaaaaaaaaadddccggg c gggcccdddaaaaaaaaaaadddccggg c ddddcccggg c c d d d d d d a a a a a a a a a a a a a a a a a a a e a ebfbe a effbe a effbe a effb d effb d effb d bffb d bffb d bffe d bffe e c ebffe ff c ebffe bb c ebfbe f b c ebfbe f f cg effbe b ee cg effbe f f gg effbbe b gg e b gg f gg ee gc f gc f c b c f c b c f d f d eed fd bd a a a a a a a a a a a a a a a a a a ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#db0f0cff b,#8d78c7ff c,#ecc6cdff d,#b1d7b1ff e,#d37064ff f,#a9abc7ff g,#97c995ff ``` ```image cc aaac aaa caaa aaac aaa caaa eaac aaa aaa eaae aaa aaa eaae aaa aaa eaae aaa aaa caae aaac aaa caaa aaac aaa caaa eaac aaa aaa eaae aaa aaa eaae aaa aaa eaae aaa aaa caae aaac aaa ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggd caaa ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg aaac ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg aaa ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg caaa ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg eaac bbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg aaa bbb ddddddddddddddddddddfbbfddddddddddddddddddddddddddddddddddddg aaa bbb ddddddddddddddddddfbbbbbbdddddddddddddddddddddddddddddddddddg eaae cbbf ddddddddddddddddfbbbbbbbbbfdddddddddddddddddddddddddddddddddg aaa fbbc ddddddddddddddbbbbbbbdfbbbbbddddddddddddddddddddddddddddddddg aaa bbb ddddddddddddbbbbbbbdddddbbbbbfddddddddddddddddddddddddddddddgeaae bbb dddddddddfbbbbbbbddddddddfbbbbbdddddddddddddddddddddddddddddgaaa bbb dddddddfbbbbbbfddddddddddddbbbbbfdddddddddddddddddddddddddddgaaa fbbc dddddfbbbbbbfdddddddddddddddfbbbbbddddddddddddddddddddddddddeaae bbb dddbbbbbbbfdddddddddddddddddddbbbbbfddddddddddddddddddddddddaaa bbb dbbbbbbbdddddddddddddddddddddddfbbbbbdddddddddddddddddddddddaaa bbb cbbbbbbbdddddddddddddddddddddddddddbbbbbfddddddddddddddddddddeaae fbbc bbbbbfddddddddddddddddddddddddddddddfbbbbbdddddddddddddddddddaaac bbb fbbfddddddddddddddddddddddddddddddddddbbbbbfdddddddddddddddddaaa bbb aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaebbbbbeeeeeeeeeeeeeegeaaa bbb aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbeaaaaaaaaaaaaaaaac fbbf aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbaaaaaaaaaaaaaaa bbb ddddddddddddddddddddddddddddddddddddddggggbbbbbbeeeeeeeeeeeeg bbb dddddddddddddddddddddddddddddddddddddddddddfbbbbbdddddddddddg bbb dddddddddddddddddddddddddddddddddddddddddddddbbbbbfdddddddddg cbbf ddddddddddddddddddddddddddddddddddddddddddddddfbbbbbddddddddg bbb ddddddddddddddddddddddddddddddddddddddddddddddddbbbbbfddddddg bbb ddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbdddddg bbb dddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbfdddg cbbf dddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbddg fbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbfg bbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbb bbb dddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbf bbf dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbb fbbc ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbf bbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg bbbbb bbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg fbbbbf bbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg bbbbbbbc ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg fbbbbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg bbbb ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddg fbf ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggd ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#db0d0aff b,#8e78c8ff c,#f1a6a5ff d,#e6d8e8ff e,#e6787bff f,#b9abdcff g,#e03f3fff ``` ```image ddd fbbbbd dbbbbbbbf fbbbbbbbbbbbd fbbbbbbbbbbbbbbf dfbbbbbbbbbbbbbbbbbb dbbbbbbbbbbbfd dbbbbbbbbbd fbbbbbbbbbbbbf dfbbbbbbbbf fbbbbbbbbbbbbf dbbbbbbbbbd dfbbbbbbbbbbbbd dfbbbbbbbbf dfbbbbbbbbbbbfd dbbbbbbbbbd bbbbbbbbbbbbfd bbbbbbbbbf fbbbbbbbbbbbbd dbbbbbbbbbbd fbbbbbbbbbbbbf fbbbbbbbbb dfbbbbbbbbbbbbd dbbbbbbbbbd dfbbbbbbbbbbbfd fbbbbbbbbf dfbbbbbbbbbbbfd dbbbbbbbbbd d fbbbbbbbbbbbbf dbbbbbbbbbd g dfbbbbbbbbbbbbf fbbbbbbbbf a bbbbbbbbbbbbd bbbbbbbbbbd ca bbbbbbbbbfd fbbbbbbbbb ga bbbbbbbfd dbbbbbbbbbd aa bbbbbb fbbbbbbbbf caa bbbbf dbbbbbbbbbd eaa bbeeeeeeeeecccccccccccccccccddddddddddddd fbbbbbbbbf aaa gaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaagggggggggggggebbbbbbbbbeeeeeeeeeeeecccccccccccccccccaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaebbbbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaebbbbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaagbbbbbbbbbgaaaaaaaaaaaaaaaaaaaaaaaaaa ccccccccccccccccceeeeeeeeeeeeeeeeggggggggggggggggggaaaaaaaaaaaaaaaaaaaaaaaaaaebbbbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaa dddddddddddfbbbbbbbbbfcccccccceeeeeeeeeeeeeee fbbbbbbbbfd dbbbbbbbbbf fbbbbbbbbfd bbbbbbbbbbf fbbbbbbbbbd dbbbbbbbbbf fbbbbbbbbbd fbbbbbbbbbd dbbbbbbbbbf fbbbbbbbbbd bbbbbbbbbbf fbbbbbbbbbd dbbbbbbbbbf fbbbbbbbbbd dbbbbbbbbbf fbbbbbbbbb dbbbbbbbb fbbbbbb fbbbb dfbb fb d ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#dc0d0aff b,#8d77c8ff c,#f1a3a2ff d,#e3d4e7ff e,#e8706fff f,#b2a2d8ff g,#dd3536ff ``` ```image cc aaad aaa daag gaac aaa daaa gaac aaa aaa eaac aaa aaa eaae aaa aaa caae aaa aaa caag aaad aaa daag gaac aaa daaa gaac aaa aaa eaac aaa aaa eaae aaa aaa caae aaa aaa caag aaad aaa caag gaac aaa daaa gaac bbb aaa bbb dbbd aaa bbb dbbbbbb eaac dbbf fbbbbbbbbbd aaa fbbd fbbbbbbddbbbbb aaa bbb bbbbbbb bbbbbd eaae bbb dbbbbbbf dbbbbb aaa dbbf dbbbbbbf bbbbbd aaa fbbd fbbbbbbd dbbbbb caae bbb fbbbbbbd bbbbbd aaa bbb bbbbbbb dbbbbb aaa bbb dbbbbbbf bbbbbd caag fbbd bbbbbf dbbbbb aaad bbb fbbd bbbbbd aaa bbb agaaaaaaaaaaaaaaaaaaaaaaaaaaaaaggggggggebbbbbeeeeecccccccccccaag bbb aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbgaaaaaaaaaaaaaaaac fbbf aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaagbbbbbaaaaaaaaaaaaaaa bbb ddddddbbbbbfccccceeeeeeed bbb dbbbbb bbb bbbbbd dbbf dbbbbb bbb bbbbbf bbb dbbbbb bbb bbbbbf dbbf dbbbbb fbbd fbbbbf bbb dbbbbb bbb fbbbbf dbbf dbbbbb fbbd fbbbbf bbb dbbbbb bbb fbbbbf bbb bbbbbbbd fbbbbb bbbb fbf ``` <!-- end of image -->
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I'm examining this image closely. My goal: find any and all intersections. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#1001d9ff b,#6a5fd7ff c,#9991e2ff d,#3b20c7ff e,#ccc8f3ff f,#b1d7b1ff g,#97c39fff ``` ```image cee dddddddddddbcce dddddddddddddddddddddddbbcee cbddddddddddddddddddddddddddddddddddbcce eecbbdddddddddddddddddddddddddddddddddbbcee eccbdddddddddddddddddddddddddddddddd eecbbddddddddddddddddddde eccbdddddddd ddd ddde cddd ddd ddde cddd ddd ddde cddd ddd dddc eddd ddd dddc eddd ddd dddc eddd ddd dddc eddd ddd ee bddc eaaa eddd aaaaad ddd daaaaaaab bddc eaaa daaaaac ddd aaab aaaaaae ddd daaa eaaaaaa bddb eaaae caaaaad ddd aaad baaaaab ddd baaa daaaaa bddb aaae aaaab ddd aaad caad ddd baaa aaa bddb aaac aaa gfffffgdddfffffffffffff aaaa aaa gffffffdddgffffffffffff caaa aaa gffffffbdddffffffffffff aaac aaa gfffffffdddffffffffffff aaaa aaa gfffffffdddgfffffffffff eaaa aaa gfffffffbdddfffffffffff aaab aaa gffffffffdddfffffffffff daaa daae gffffffffdddgffffffffff eaaa baac gffffffffbdddffffffffff aaab baab gfffffffffdddffffffffff daaa caab gfffffffffdddgfffffffff eaaae eaad gfffffffffbdddfffffffff aaad aaa gffffffffffdddfffgbdfff baaa aaa gfffffffffgdddaaaaaafff aaae aaa gffgbdaaaaaadddaaaaafff aaad aaa cbaaaaaaaaaaaaadddaaadbfff baaa aaa eaaaaaaaaaaaaaaaddddcfffffff aaac aaa daaaaaaaaadbgfffffcdddfffffff aaaa aaa eaaaaacegffffffffffffdddfffffff caaa aaa baaaad gffffffffffffdddcffffff aaac daaeaaaaae gffffffffffffcdddffffff aaaa daaaaaad gfffffffffffffdddffffff eaaa baaaaae gfffffffffffffdddcfffff aaab caaad gfffffffffffffgdddfffff daaa aae gffffffffffffffdddfffff eaaa gffffffffffffffdddbffff aaab gffffffffffffffgdddffff daaa gfffffffffffffffdddffff eaaae gfffffffffffffffdddbfff aaad gfffffffffffffffgdddfff baaa ddd aaae bdde aaaa baaa aaac aaaa caaa aaac baa ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#1001d9ff b,#5744d5ff c,#9c90e6ff d,#3a1ec6ff e,#bfb8efff f,#7b6de0ff g,#ddd9f5ff ``` ```image eddddddg ddddddc fdddddb eddddddg ddddddc fdddddb eddddddg bdddddc fdddddb gddddddg bdddddc cdddddb gddddddg bdddddc cdddddb gddddddg bdddddc cdddddb gddddddg bdddddc cdddddb gdddddde bdddddf cdddddd gdddddde bdddddf gecfbe cddddddecfbdaaaaaac gcddddddaaaaaaaaaaaf gecfbdaaadddddddaaaaaaaaaab gecfbdaaaaaaaaaaaddddddaaaaaaaaaad ecfbdaaaaaaaaaaaaaaaaaaddddddaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaadddddddaaaaadbfce aaaaaaaaaaaaaaaaaaaaaaaaddddddfceg aaaaaaaaaaaaaaaaaaaaadbfdddddde aaaaaaaaaaaaaadbfceg fdddddf aaaaaaadbfceg edddddd dbfceg dddddde fdddddf edddddd dddddde fdddddf eddddddg ddddddc fdddddb eddddddg ddddddc fdddddb eddddddg ddddddc fdddddb eddddddg bdddddc fdddddb gddddddg bdddddc cdddddb gddddddg bdddddc cdddddb gddddddg ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#1001daff b,#5746d9ff c,#a197e9ff d,#3a1ec7ff e,#c3bcf0ff f,#7f70e0ff g,#e0ddf8ff ``` ```image ceg dddddddddddbfceg dddddddddddddddddddddddbfceg ffbddddddddddddddddddddddddddddddddbbfceg gecfbdddddddddddddddddddddddddddddddddbfceg gecffbddddddddddddddddddddddddddddddb gecfbdddddddddddddddddddg gecfbbddddddb ddd ddde cddd ddd ddde cddd ddd ddde cddd ddd dddc eddd ddd dddc eddd ddd dddc eddd ddd bddc gddd ddd gg bddf eaaag gddd aaaaad ddd daaaaaaab bddf eaaagbaaaaac gddd aaab aaaaaag ddd baaa gaaaaaa bddf gaaag caaaaab gddd aaad baaaaaf ddd baaa daaaaa fddf aaae gaaaab ddd aaad caad dddg faaa aaa fddb aaac aaa ddd aaaa aaa dddg caaa aaa fddb aaaf aaa ddd aaaa aaa dddg eaaa aaa fddb aaaf aaag ddd daaa daae dddg eaaag baac cddb aaab faaf ddd baaa caab ddde gaaag eaad cddd aaad gaaa ddd gcb baaa aaa gdddaaaaaa aaae aaa gcbaaaaaadddaaaaa aaad aaa cbaaaaaaaaaaaaadddaaabc faaa aaa gaaaaaaaaaaaaaaabddde aaac aaa baaaaaaaaabcg eddd aaaa aaa gaaaaacg ddd caaa aaa baaaad dddc aaaf daaeaaaaae eddd aaaa baaaaaad ddd eaaa faaaaae dddc aaaf caaad eddd daaa aae ddd eaaag bddc aaab eddd baaa ddd gaaag bddc aaad gddd baaa ddd aaae bdde aaaa g faaa aaac aaaa caaa aaaf faa ``` <!-- 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,#0ae4aaff b,#d25b7cff c,#66eac5ff d,#d69da8ff e,#ecf3eeff f,#b0d7b1ff g,#94c997ff ``` ```image eggggggggggggggggggggggge efffffffffffffffffffffffe ca efffffffffffffffffffffffe caaac efffffffffffffffffffffffe eaacaaa efffffffffffffffffffffffe aaf eaaaf efffffffffffffffffffffffe aac caaa efffffffffffffffffffffffe aaa eaaae efffffffffffffffffffdfffe caa aaaa effffffffffffffffffdbbffe caa eaaae effffffffffffffffffbbfffe eaae aaac effffffffffffffffffbbfffe aaf faaae efffffffffffffffffbbdfffe aac aaac efffffffffffffffffbbffffe aaa caaa effffffffffffffffbbdffffe caa aaac effffffffffffffffbbfffffe faa caaa efffffffffffffffdbbfffffe eaae aaac efffffffffffffffbbffffffe aac caaa effffffffffffffdbbffffffe aac eaaafffffffffffffffbbfffffffe aaa caaafffffffffffffbbfffffffe caa eaaagffffffffffbbdfffffffe faa eaaaafffffffffbbffffffffe eaae efgaaafffffffbbdffffffffe aac efffaaaafffffbbfffffffffe aac effffcaaafffdbbfffffffffe aaa effffffaaacfbbffffffffffe caa efffffffcaaabbffffffffffe eaa efffffffffaaacffffffffffe eaae effffffffffgaaafffffffffe aac efffffffffbbdaaacfffffffe aaa efffffffffbbffcaaaffffffe aaa effffffffbbdffffaaacffffe caa effffffffbbffffffaaaafffe eaae efffffffdbbffffffffaaaffe eaae efffffffbbffffffffffafffe aac effffffdbbffffffffffffffe aaa effffffbbfffffffffffffffe aaa effffffbbfffffffffffffffe caa efffffbbdfffffffffffffffe eaae efffffbbffffffffffffffffe aae effffbbdffffffffffffffffe aac effdbbbfffffffffffffffffe aaa efbbbbffffffffffffffffffe caa dbbbffffffffffffffffffffe caa ebbbdfffffffffffffffffffffe ae bbbbfffffffffffffffffffffffe dbbbeefffffffffffffffffffffffe bbbd efffffffffffffffffffffffe dbbbe efffffffffffffffffffffffe ebbbd efffffffffffffffffffffffe bbbb efffffffffffffffffffffffe dbbbe efffffffffffffffffffffffe bbbd efffffffffffffffffffffffe dbbbe efffffffffffffffffffffffe ebbbd efffffffffffffffffffffffe bbbb eggggggggggggggggggggggge ebbbe bbbb dbbbe ebbbd dbbb ebbbd bbbb dbbbe ebbbd dbbb ebbbd bbbb dbbbe bbbd dbbb ebbbd bbbb dbbbe bbbd dbbbe ebbbd bbbb ebbbe bbbb dbbbe dbbd b ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#09e3aaff b,#d2597cff c,#a0f4deff d,#ecbbc9ff e,#edededff f,#51e6bfff g,#df8aa2ff ``` ```image dd bbbge dbbbb gbbbg ebbbbe gbbbg ebbbbe dbbbg bbbbd dbbbb bbbbd dbbbb gbbbg ebbbbe gbbbg ebbbbe dbbbg bbbbd dbbbb bbbbd dbbbb gbbbg c ebbbbe af gbbbg aaac ebbbbe aaaaf dbbbg aaaaaae bbbbd caaaaaac dbbbb efaaaaafe bbbbd caaaaaac dbbbb caaaaaafe gbbbg faaaaaac ebbbbe caaaaaafe gbbbg faaaaaac ebbbbe caaaaaafe dbbbg efaaaaaac bbbbd caaaaaaf dbbbb efaaaaaacgbbbd caaaaaafbbbe efaaaaaabg caaaaaaf eaaaaaafe ebfaaaaaac dbbbaaaaaafe bbbbdfaaaaaac dbbbb caaaaaafe gbbbd faaaaaac dbbbbe caaaaaafe gbbbg efaaaaaac ebbbbe caaaaaaf gbbbg efaaaaaac ebbbbd caaaaaaf dbbbg efaaaaae bbbbd caaac dbbbb eff gbbbd e dbbbbe gbbbg ebbbbe gbbbg ebbbbd dbbbg bbbbd dbbbb gbbbd dbbbbe dbbbbg egbbbbbe dbbbbbbg egbbbbbbd gbbbbbbge dbbbbbbbd gbbbbbbg bbbbbge bbbbd bbge bd ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#08e4aaff b,#d3597cff c,#88f1d5ff d,#eec1cdff e,#c5f8ebff f,#47e8beff g,#e08ba3ff ``` ```image fa caaac eaafaaa aae aaae aaf faaa aaa eaaae d faa faaf dbb caa eaaae bb eaae aaaf bb aac eaaa bbd aaf aaaf bb aaa caaa gbg faa aaac bb caa caaa gbg eaae aaac bb aac faaa dbb aaf aaae bb aaa faaa bb faa eaaae bbd eaa faaf bb aae eaaae gbg aac aaaf bb aaf eaaa dbg aaa aaaf bb faa caaabb eaa aaac aae faaa aac bbdaaac aaf bb faaa faa gbg aaae caa bb faaa eaa dbg eaaa aae bb f aac dbb aaf bb faa bb caa bbd eaa bb aae bbg aaf dbbb aaa bbbg faa gbbb caa dbbbd a bbbb dbbbd bbbg gbbb bbbd bbbb dbbbd bbbg gbbb bbbg gbbb dbbbd bbbg gbbb bbbg gbbb dbbbd bbbb dbbb bbbg gbbb dbbbd bbbb dbbbd bbbg gbbb bbbd bbbb dbbbd bbbg gbbb bbbg gbbb dbbbd bbbg gbbb dbbg b ``` <!-- 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,#7b783eff b,#2c1b2fff c,#a4bd98ff d,#b2d6b1ff e,#5d545eff f,#949573ff g,#e1e0d8ff ``` ```image fa aa aac gaaa daaa faaad fa aadaa aaa aa aa aaac aa aag cafaag aa caf aagcaa gaa aa aa aaa daf aa aa aaf fad fac dddddddddddfaadddcaacc aag gaa dddddddddddaacddddcaac aa aa dddddddddddaaddddddaaa aa aad dddedddddddaadddddddaaf aa gaa ddebbdddddcaaddddddddaag gaa aa dddbbbddddfafddddddddfaa daf aag d ddddbbfdddaadddddddddcfaa fad caf gaaf ddddcbbcddaadddddddddc aaf aag aa gaaaag dddddebbdcaadddddddddc aad aa aa aaaag ddddddbbbfafdddddddddc gaa aa fac aaaad dddddddbbaaddddddddddc faa aa aa aaaac dddddddcbaaddddddddddc aaa aa aaaaac ddddddddfaaddddddddddc aac daf aaaf ddddddddfaebdddddddddc gaa fad c ddddddddaabbeddddddddc caa aag ddddddddaadbbfdddddddc aaa aa ddddddddaadfbbdddddddc aac aa dddddddcaaddebbddddddc gaag aa dddddddaacdddbbbdddddc caa aa dddddddaadddddbbfddddc aaa daf dddddddaadddddcbbcdddc aaf cac ddddddcaaddddddebbdddc aag aag ddddddfafdddddddbbbddc daa aa ddddddaadddddddddbbedc faa aa ddddddaadddddddddcbbcc aaf aa ccccccaaccccccccccebbd aag aa fac bbb gaa gaf aa bbe faa cac aa bbd aaf aag aa cbb aad aa caf ebb gaa aa aag bbe faa aa aa bbc aaa aa aa gbb aad gaf daf ebb gaa cac aag bbb caa fag aa bbf aaa aa aa gbbg aac aa gaa fbb gaag aa g bbb caa aa bbe aaa gaf bbg aac cac cbb aag fag ebb daa aa bbe faa aa bbc aafaa dbb aaaa ebb daaf bbb fac bbf g gbbg fbb bbb bbe gbbg cbb ebb bbe bbd dbb ebb bbe bbc gbbg fbb gdcffeebbbbbbbbbbe bbbeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbbeeffcdg fcdgg ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#7a773dff b,#2c1c2fff c,#a9a591ff d,#c6c3b7ff e,#5a4d58ff f,#8e896fff g,#e4e2deff ``` ```image gaaaa caaaad daaaf faaaag caaac gaaaaa faaad daaaaf aaaag caaaa daaaf faaa g caaac gaaa ee faaad daa gebbf aaaag ca ebbbbc gaaaa f gbbbbbg daaac g dbbbbe faaad cbbbbe aaaag ebbbbc gaaaa ebbbbd daaaf gbbbbbg caaad cbbbbe aaaag fbbbbf gaaaa ebbbbd daaaf gbbbbbgcaaac dbbbbefaaad fbbbbaaaa ebbbaaaf gbbeaaac dbaaaad caaaae gaaaabc caaaebbd faaaebbbg aaaabbbbe gaaaafbbbbc daaaf ebbbbd caaad gbbbbbg aaaag dbbbbe gaaaa fbbbbf daaaf ebbbbd caaac gbbbbbg faaad dbbbbe gaaaa cbbbbf daaaf ebbbbc caaac gebbbbg faaad gbbbbeg aaaag cbbbbe gaaaa fbbbbc caaac ebbbbd faaad gbbbbbg aaaag dbbbbe gaaaa fbbbbf daaaf ebbbbd caaad gbbbbbg ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#7a773eff b,#2c1b2fff c,#b0ac97ff d,#cdcbbdff e,#5e515fff f,#938f6dff g,#e8e7e2ff ``` ```image fa aa aac gaaa daaa faaad fa aadaa aaa aa aa aaac aa aag cafaag aa caf aagcaa gaa aa aa faa daf aa aa aaf fad fac daf aag aag gaa fad daa aa aa aa faa aa aad e aa aaf aa daa ebb daa aad gaa aa bbe fad daa daf aag d bbc aa faa cad caf daaf gbbg aa aaf aag aa gaaaag fbb gaa aad aa aa gaaaad bbbcac gaa aa fac aaaad bbaag faa aa gaa faaac gbaa aaa gaa aaaaac caa aac daf aaaf caeb gaag cad c aabbe caa aag aa bbd aaa aa aa dbb aac aa daf ebb gaag aa fad bbe caa aa aa bbc aaa daf aa dbbg aac cac daa ebb aag aag fad bbb daa aa aa bbf faa aa aa gbbg aaf aa gaa fbb aad aa cac bbb daa daf aa bbe faa cac aa bbd aaf aag aa cbb aad aa cac ebb gaa aa aag bbe faa aa aa bbc aaf aa aa dbbg aad daf daf ebb gaag cac aad bbb caa fag aa bbf aaa aa aa gbbg aac aa daf fbb gaag aa g bbb caa aa bbe aaa daf gbbd aac cac cbb gaag fad ebb daa aa bbe faa aa bbc aafaa dbb aaaa ebb daaf bbb fac bbc g gbbg fbb bbb bbf gbbd cbb ebb bbe bbd dbb ebb bbe bbc gbbg fbb gdccfeebbbbbbbbbbe bbbeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbbeefccdg fcddg ``` <!-- end of image -->
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This image looks interesting. I wonder if there are any intersections hidden in there? The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#962d80ff b,#1ad211ff c,#b1d8b1ff d,#d6aecdff e,#53d54cff f,#92d090ff g,#ad659eff ``` ```image bec cbbbbbc cbbbbbbf ebbbbbf ebbbbbe fbbbbbec cbbbbbbc cebbbbbf ebbbbbe fbbbbbe fbbbbbbc cbbbbbbf cebbbbbf ebbbbbe fbbbbbec cbbbbbbc cbbbbbbf ebbbbbf ebbbf bb bbc aa bb gad bb aa cbb aa bb dag fbe aa bb aa ebf aa bb gad bbc aa bb aa bbc dag cbb aa cffbbfffffffffffaafffffff aaad fccfbbccccccccccaaccccccc aaaaag fcccbbcccccccccgagccccccc aa gaaaad fcccebeccccccccaacccbcccc aa daaaag fccccbbccccccccaaccebeccc aa gaaaad fccccebeccccccgagccbbcccc ag daaaag fcccccbbccccccaaccbbecccc dag gaaaad fcccccbbfcccccaaccbbccccc dad daaaag fccccccbbcccccaacbbfccccc gad gaaaad fccccccbbfcccgagfbbcccccc ga daaaag fccccccfbbcccaacbbfcccccc aa gaaaad fcccccccbbcccaaebbccccccc aa daaaag fcccccccebbcfagbbcccccccc aa gaaaad fccccccccbbcaaebecccccccc aa daaaag fccccccccebeaabbccccccccc aa gaaaad fcccccccccbbaabeccccccccc aa daaaag fcccccccccbaaebcccccccccc aa gaaaad fccccccccccaabfcccccccccc aa daaaag fccccccccccaabccccccccccc ag gaaaad fcccccccccfaacccccccccccc dag daaaag fcccccccccaaccccccccccccc dad gaaaad fcccccccccaaccccccccccccc dad daaaag fcccccccccaaccccccccccccc gad gaaaaccccccccgagccccccccccccc ga daaccccccccaacccccccccccccc aa gaccccccccaacccccccccccccc aa dagcccccccaacccccccccccccc aa aaccccccaaccccccccccccccc aa aaccccccaaccccccccccccccc aa aaccccccaaccccccccccccccc aa aa dag aa gad aa aa dag aa ag aa dag aa gad aa aa aa aa gad dag dag aa aa aa aa aa aagad aaaa gaaa daag aa aa ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#962f80ff b,#1ad111ff c,#89e784ff d,#debed7ff e,#4cd245ff f,#cbf4c9ff g,#b978abff ``` ```image fbbbb gaaag ebbbc gaaad cbbbb aaaa bbbbf daaag cbbbe gaaad bbbbf aaaa f cbbbe daaaa cbc fbbbbf gaaag fbbbbf ebbbc gaaad ebbbe fbbbb aaaa fbbbbf ebbbc daaag ebbbe fbbbb gaaad fbbbbf ebbbc aaaa bbbbc cbbbe daaaa cbbbb bbbbf gaaag bbbbc cbbbe gaaad cbbbe bbbbf aaaa fbbbbf cbbbe daaag ebbbe fbbbbf gaaad fbbbbf ebbbc aaaad ebbbe fbbbb daaaa cbbbbf ebbbc daaag bbbbc cbbbb gaaadcbbbb bbbbf aaaafbbbbc cbbbe daaagcbbbe bbbbf gaaagbbbbf cbbbe aaaaebbbe fbbbbfdaaaabbbbf ebbbcdaaaabbbc fbbbbgaaaebbbf ebbbaaaabbbc fbbeaaaabbb ebaaaaebbc cbaaaabbe eaaaabbf gaaaabe gaaaebf aaaabc daaaae gaaag aaaad aaaa daaag gaaad aaaa d daaag ad gaaag ag aaaad aa aaaa aa daaag aad gaaad aad aaaa aag daaag aag gaaag aaa aaaad aaa aaaa aaad daaag aaad gaaad aaag aaaa ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#962d80ff b,#1bd212ff c,#a7eda3ff d,#d3a7caff e,#60db59ff f,#e6e9e4ff g,#ae5e9eff ``` ```image bef cbbbbbc cbbbbbbc febbbbbe ebbbbbef cbbbbbbc cbbbbbbc fbbbbbbc febbbbbe ebbbbbef cbbbbbbc cbbbbbbc febbbbbe febbbbbef ebbbbbef cbbbbbbc cbbbbbbc febbbbbe ebbbc bb bbc faa fbb gad bbf aa cbb aa bb dag cbe aaf bb aa ebe faa bb gad bbc aa bb aa bbf dag fbb aaf bb aa aaad cbb faa aaaaag bb gad aa gaaaad ebe aa bf aa daaaag bb aa ebe aa gaaaad ebc dag bb fag daaaag bb aaf bbe dag gaaaad bbc aa fbb dad daaaag fbb aa bbc gad gaaaad bbf gadcbb gaf daaaag cbb aa bbf aa gaaaad bb aacbb aa daaaag cbe dagbb aa gaaaad bb aaebe aa daaaag ebeaabb aa gaaaad bbaabc aa daaaag baaeb aa gaaaad aabc aa daaaag aab fag gaaaad daaf fag daaaag gaf dad gaaaad aa dad daaaag aa gaf gaaaa dad ga daa aa aa gaf aa aa dad fag aa fag gaf aa aa aa aa aa aa aa aa dad aa gaf aa aa dag aa fgg aa fag aa gad aa aa aa aa gad dad dag aa aa aa aafag aagad aaaa daaa faag aa aa ff ``` <!-- end of image -->
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I'm on the case! Let's uncover any intersections hidden in this image. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#7767e6ff b,#f88842ff c,#bcb3f6ff d,#f4b78cff e,#aed5afff f,#f2eee9ff g,#371ae9ff ``` ```image d dbbb bbbbbbf dbbbbbbd dbbbbbbd fbbbbbbbf cc bbbbbbbf cggg dbbbbbbd cgggggf dbbbbbbd cggggggc fbbbbbbbf fffffffffffffffffffffff aggggggf dbbbbbbd feeeeeeeeeeeeeeeeeeeeeeef aggggggf dbbbbbbd feeeeeeeeeeeeeeeeeeeeeeef agggggg fbbbbbbb feeeeeeeeeeeeeeeeeeeeeeef gggggga fbbbbbbbf feeeeeeeeeeeeeeeeeeeeeeef gggggga dbbbbbbd feeeeeeeeeeeeeeeeeeeeeeeffgggggga dbbbbbbdfeeeeeeeeeeeeeeeeeeeeeeegggggga fbbbbbbbeeeeeeeeeeeeeeeeeeeeggggggc bbbbbbbdeeeeeeeeeeeeeeaggggggc dbbbbbbdeeeeeeeeeeaggggggc fdbbbbbbbeeeeeeaggggggeef feeebbbbbbbeeaggggggeeeef feeeeebbbbbaggggggeeeeeef feeeeeeedgggggggeeeeeeeef feeeeeeggggggabbbbeeeeeef feeeeggggggaebbbbbbbeeeef feeggggggaeeeeedbbbbbbdef cggggggaeeeeeeeeedbbbbbbd cggggggaeeeeeeeeeeeeeebbbbbbbf cggggggeeeeeeeeeeeeeeeeeeebbbbbbbf aggggggeeeeeeeeeeeeeeeeeeeeeeedbbbbbbd aggggggffeeeeeeeeeeeeeeeeeeeeeeef fbbbbbbb agggggg feeeeeeeeeeeeeeeeeeeeeeef fbbbbbbbf agggggg feeeeeeeeeeeeeeeeeeeeeeef dbbbbbbd gggggga feeeeeeeeeeeeeeeeeeeeeeef dbbbbbf fgggggga feeeeeeeeeeeeeeeeeeeeeeef fbbbd fgggggga eeeeeeeeeeeeeeeeeeeeeee bbb cggggggc bbb cggggggc bbb cggggggc bbb gggggf dbb agggf dbbf ggg fbbd ggg bbb cgga bbb aggc bbb ggg bbb ggg bbb cgga dbbf ggg fbbd ggg bbb fggg bbb aggc bbb ggg bbb ggg bbb cgga dbbf aggf fbbd ggg bbb ggg bbb cgga bbb ggg bbb ggg bbb fggg dbbf aggc fbbd ggg bbb ggg bbb cgga bbb aggf bbb ggg bbb ggg dbbf cgga fbbd ggg bbd ggg bbb fggg bbb aggc bbb ggg bbb ggg dbbf cgga fbbd gggf bbd ggg bbb cg bbb bbb bbb ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#6143e1ff b,#f88741ff c,#d7d1faff d,#ec9872ff e,#9788f2ff f,#fbccafff g,#3619eaff ``` ```image c df cag bbbf caggg bbbbbd caggggg bbbbbbbdf eaggggggg bbbbbbbbbbf eaggggggggg bbbbbbbbbbbbf egggggggggggg fbbbbbbbbbbbbbdf eggggggggggggac fdbbbbbbbbbbbbdf ceggggggggggggec dbbbbbbbbbbbbbf ceggggggggggggec fbbbbbbbbbbbbbd cegggggggggggge fdbbbbbbbbbbbbdagggggggggggge fdbbbbbbbbdagggggggggggae fbbbbdagggggggggggae fdagggggggggggae eagggggggggggadbbdf eggggggggggggadbbbbbbbf eggggggggggggadbbbbbbbbbbbf ceggggggggggggec fdbbbbbbbbbbbbdf ceggggggggggggec fdbbbbbbbbbbbbdf cegggggggggggge dbbbbbbbbbbbbbf cagggggggggggge fbbbbbbbbbbbbbd cagggggggggggae fdbbbbbbbbbbb gggggggggggae fdbbbbbbbbb gggggggggac fbbbbbbb gggggggac fbbbbb gggggac fdbb gggac fd gec c ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#5c41e7ff b,#f98841ff c,#c9c1f8ff d,#fab58aff e,#907ff2ff f,#fcdecaff g,#3619eaff ``` ```image d dbbb bbbbbbf dbbbbbbd dbbbbbbd fbbbbbbb cc bbbbbbbf cggg dbbbbbbd cgggggc fbbbbbbd eggggggc bbbbbbbf eggggggc dbbbbbbf egggggg dbbbbbbd aggggga fbbbbbbb aggggga bbbbbbbf gggggga dbbbbbbd gggggge fbbbbbbd cgggggge fbbbbbbb cgggggge bbbbbbbf cggggggc dbbbbbbd eggggggc fbbbbbbb eggggggc bbbbbbbf egggggg dbbbbaggggga daggggga agggggabbbb gggggge bbbbbbbf cgggggge dbbbbbbd cgggggge fbbbbbbd cggggggc fbbbbbbb eggggggc dbbbbbbf eggggggc dbbbbbbd egggggg fbbbbbbb aggggga bbbbbbbf aggggga dbbbbbbf aggggga dbbbbbf gggggge fbbbd cgggggge bbb cgggggge bbb cggggggc bbb cggggggc bbb gggggc dbb eggg dbbf ggg fbbd ggg bbb cgga bbb aggc bbb ggg bbb ggg dbb cgge dbbf ggg fbbd ggg bbb ggg bbb eggc bbb ggg bbb ggg bbb cgga dbbf aggc fbbd ggg bbb ggg bbb egge bbb ggg bbb ggg bbb gga dbbf eggc fbbd ggg bbb ggg bbb cgga bbb aggc bbb ggg bbb ggg dbbf egge fbbd ggg bbd ggg bbb gga bbb eggc bbb ggg bbb ggg dbbf cgge fbbd agg bbd ggg bbb ca bbb bbb bbb ``` <!-- end of image -->
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This image looks interesting. I wonder if there are any intersections hidden in there? These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#bd0ba4ff b,#cb6001ff c,#d9b28cff d,#efc8ddff e,#cc5bbcff f,#d0853fff g,#afd6afff ``` ```image ggggggggggggggggggggggg ggggggggggggggggggggggg ggggggggggggggggggggggg gggggggggggggggggcbfggg gggggggggggggggggbbbggg ggggggggggggggggfbbgggg ggggggggggggggggbbcgggg eaa gggggggggggggggbbbggggg daa ggggggggggggggfbbgggggg aae eed ggggggggggggggbbcgggggg daa aaaaaaaaed gggggggggggggbbbggggggg aad aaaaaaaaaaaaaaegggggggggfbbgggggggg eaa aaa deaaaaaaaaaaaaegggbbfgggggggg aa aad ceaaaaaaaaaaafggggggggg aaa aaa ggggggceaaaaaaggggggggg aa aa ggggggggggbbaaggggggggg aae aaa gggggggggbbbaaegggggggg daa aa ggggggggcbbgeaagggggggg aad aaa ggggggggbbfggaagggggggg eaa aa gggggggbbbgggaagggggggg aad aaa gggggggbbcgggaaeggggggg aaa aa ggggggbbbggggeaaggggggg aa aaa gggggfbbggggggaaggggggg aae aa gggggbbcggggggaacgggggg daa aaa ggggbbbgggggggaaagggggg aae aa gggfbbggggggggcaagggggg eaa aaa gggbbfgggggggggaagggggg aad aa ggbbbggggggggggaaeggggg eaa aaa gfbbgggggggggggeaaggggg aa aa bbc daa aae aaa bbb aa daa aa cbb aae aae aaa bbf eaa eaa daa bbb aa aad aaa dbbd aa eaa daa bbf aae aa aaa fbb eaa aaa daa dbbd d daa aaa bbb aae daa fbb daa aaa bbc aad daa bbb eaa aae cbb aa daa bbc aaa aae bbb daa daa cbb aae aae bbc daa daa bbb aad aae cbb eaa daa bbf aad aae bbb aaa daa dbbd aa aae bbf aae daa fbb f daa aae dbbd fbb aad daa bbb bbb eaa aae fbb bbb aad daa bbc bbbd aaa aae bbb bbbd aadaa cbb bbbd aaaae bbc bbbc daaa bbb bbbc aae cbb fbbc de bbf fbbf bbb fbbf cbb fbbf bbf cbbf fbb cbbb dbbd cbbb bbf dbbb fbb dbbb dbbd dbbb bbb bbb fbb bbb bbc bbb bbb bbb cbb bbbd bbc bbbd bbb bbbd cbb bbbcbbf bbbbb fbb cc ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#bd0aa3ff b,#cb5f01ff c,#e5b083ff d,#e191d5ff e,#ce4abaff f,#d47b38ff g,#f3d8d7ff ``` ```image g cbc gbbbfg fbbbbc cbbbbf gbbbbbg fbbbbc cbbbbf gbbbbbg fbbbbf cbbbbb bbbbbc fbbbbf gbbbbbg fbbbbc cbbbbf gbbbbbg g fbbbbc aaaeddg cbbbbf aaaaaaaaaeddg gbbbbbg aaaaaaaaaaaaaaaeddg fbbbbc aaaaaaaaaaaaaaaaaaaaaeefbbbf ddeeaaaaaaaaaaaaaaaaaaaaaafg gddeeaaaaaaaaaaaaaaaaag gddeeaaaaaaaaaaad gddaaaaaaae fbbbaaaaa cbbbbfaaaad bbbbbcaaaad cbbbbf eaaae gbbbbbg daaaa fbbbbc gaaaad cbbbbf aaaae gbbbbbg eaaaa fbbbbc daaaag cbbbbf gaaaad gbbbbbg aaaae fbbbbc eaaaa cbbbbf daaaag gbbbbbg gaaaad fbbbbc aaaae cbbbbb eaaaa gbbbbbg daaaag fbbbbf aaaad gbbbbbg eaaae bbbbbc daaaa cbbbbf daaaad gbbbbbg aaaae fbbbbc eaaaa cbbbbf daaaag gbbbbbg gaaaad fbbbbc aaaae cbbbbf eaaaa ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#bd0ba5ff b,#cb6001ff c,#e7b78eff d,#e7a9deff e,#d158c1ff f,#d6833eff g,#f5dee1ff ``` ```image g gbf bbf fbb gbbc eaa bbb gaa fbb aae eed bbc daa aaaaaaaaed bbb aad aaaaaaaaaaaaaaeg cbb eaa aaa deaaaaaaaaaaaaeg bbc aag aag deaaaaaaaaaaaf aaa aaa deaaaaaa gaa aag bbaa aae aaa bbbaae daa aag gbbgeaa aad aaa bbf aa eaa aag fbb aag aag aaa gbbg aae aaa aa bbf daa aa aaa fbb aa aae aa gbbc aad daa aaa bbb aae aad aa fbb daa eaa aaa bbc aa aag gaa bbb aad eaa aaa cbb eaa aa gaa bbc gaa aae aaa bbb aa gaa gaa cbb aae aae aaa bbf eaa daa gaa bbb aa aad aaa gbbg aag eaa gaa bbf aae aa aaa fbb daa aaa gaa gbbg d gaa aaa bbb aae gaa fbb daa aaa gbbc aad gaa bbb eaa aae cbb aa gaa bbc aaa aae bbb gaa gaa cbb aae aae bbc daa daa bbb aad aae cbbg eaa daa bbf aag aae bbb aaa daa gbbg gaa aae bbf aae daa fbb f daa aae gbbg fbb aad daa bbb bbb eaa aae fbb bbbg aag daa bbc bbbg aaa aae bbb bbbg aadaa cbb bbbg aaaae bbc bbbc daaa bbb bbbc aae cbb fbbc ge bbf fbbf bbb fbbf cbbg fbbf bbf cbbf fbb cbbb gbbg cbbb bbf gbbb fbb gbbb gbbg gbbb bbb gbbb fbb bbb bbc bbb bbb bbbg cbb bbbg bbc bbbg bbb bbbc cbb bbbcbbf bbbbb fbbg cc ``` <!-- end of image -->
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Based on a first glance, I suspect there could be intersection regions here. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#4ecd9cff b,#87290dff c,#b1d7b1ff d,#9dc295ff e,#ab6955ff f,#dce5dcff g,#82d8b3ff ``` ```image cccccccccccccccd cccccccccccccccd cccccccccccccccd cccccccccccccccd fcgaaaaa cccccccccccccccd fcgaaaaaaaaaaaaaaa ccccccccggaaaaaaaaaaaaaaaaaaaaggfaaf ffgaaaaaaaaaaaaaaaaaaaaagcf aag fcggaaaaaaaaaaaaaaaaaaaaaaaggcd aaa ffcggaaaaaaaaaaaaaaaaaaaaaaaaaaggcccccccccccd gaa gaaaaaaaaaaaaaaaaaaaaaaaagcff cccccccccccccccd faa caaaaaaaaaaggcff cccccccccccccccd aa ff cccccccccccccccd aa cccccccccccccccd aaf cccccccccccccccd aag cccccccbbdcccccd gaa dccccdbbbbdccccd caa fbbbbbbf faa fbbb bbbf aa dbbb bbbf aaf ebbb bbbf aac ebbb bbbf aag ebbb bbbf gaa bbbe bbbf caa bbbe bbbf faa bbbe bbbf aa bbbd bbbf aaf bbbc bbbf aac bbbf bbbf aag fbbbf bbbf gaa fbbb bbbf faa cbbb bbbf aa dbbb bbbf aa ebbb bbbf aaf ebbb bbbf aag ebbb bbbddddddddaaadddddddddd bbbe bbbdccccccgaacccccccccc bbbe bbbdcccccgaacccccccccc bbbe bbbdcccccaacccccccccc bbbd cbbbdccccaacccccccccc bbbf ccbbbdcccaagccccccccc fbbbf cccbbbdccaagccccccccc fbbbf ccccbbbdcaaaccccccccc fbbb cccccbbbdgaaccccccccc cbbb ccccccbbbdaaccccccccc ebbb cccccccbbbaaccccccccc ebbb ccccccccbbbaccccccccc ebbb cccccccccbbbdcccccccc bbbe ccccccccccbbbdccccccc bbbe ccccccccccabbbdcccccc bbbe ccccccccccgabbbdccccc bbbd cccccccccccaabbbdcccc bbbc cccccccccccaacbbbdccc bbbf cccccccccccaaccbbbccc bbbf cccccccccccaagccbdccc b cccccccccccaaaccccccc cccccccccccgaaccccccc cccccccccccgaaccccccc ccccccccccccaaccccccc ccccccccccccaaccccccc ccccccccccccaagcccccc ddddddddddddaaadddddd aaa gaa faa aa aa aaf aag gaa caa faa aa aa aac aag gaa caa faa aa aaf aac aag gaa fag ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4dcd9cff b,#892c11ff c,#a3e5cbff d,#c6998bff e,#a7634fff f,#d8f0e5ff g,#79d8b4ff ``` ```image fffccg fffccgggaaaaaaaa ffcccggaaaaaaaaaaaaaaaaaa cggaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaggcccff aaaaaaaaaaaaaggcccff aaagggccfff f deef ebbbbf ebbbbbbf ``` <!-- end of image --> Unfortunately, there's no intersection inside area A. Next up, a closer look at another region. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#4ecc9bff b,#882a0fff c,#c2edddff d,#b98373ff e,#796d4cff f,#e8d8d3ff g,#88dcbbff ``` ```image f aaaag bf aaaaa bbf gaaaa bbbf gaaaac bbbbf caaaac bbbbbf caaaac bbbbbbf aaaag dbbbbbbf aaaag dbbbbbbf aaaaa dbbbbbbf gaaaa dbbbbbbf gaaaac dbbbbbbf caaaac dbbbbbbf caaaag dbbbbbbf aaaag dbbbbbbf aaaag dbbbbbbf gaaaa dbbbbbbf gaaaa dbbbbbbf gaaaac dbbbbbbfcaaaac dbbbbbbfaaaag dbbbbbbaaaag dbbbbbbaaaa dbbbbbbaaa dbbbbbbaa dbbbbbbac dbbbbbbg dbbbbbbf dbbbbbbf ebbbbbbf gebbbbbbf gaebbbbbbf caaebbbbbbf caaaebbbbbbf aaaaebbbbbbf aaaagdbbbbbbf aaaaa dbbbbbbf gaaaa dbbbbbbf gaaaac dbbbbbe caaaac dbbbbf caaaag dbbf aaaag df aaaag gaaaa gaaaa gaaaac caaaac caaaag aaaag aaaaa gaaaa gaaaa caaaac caaaac ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#4dcc9cff b,#87280cff c,#aae5ceff d,#c69a8dff e,#a15741ff f,#e3e3dcff g,#7ad9b5ff ``` ```image ccgaaaaa fcgaaaaaaaaaaaaaaa fcggaaaaaaaaaaaaaaaaaaagccaaf fccgaaaaaaaaaaaaaaaaaaaggcf aac fccgaaaaaaaaaaaaaaaaaaaaaagcf aaa fccggaaaaaaaaaaaaaaaaaaaaaaaaagcc caa caaaaaaaaaaaaaaaaaaaaaaaggccf faa caaaaaaaaaaggccf aa ff aa aac aag bbf gaa fbbbbf caa fbbbbbbf faa fbbb bbbf aa dbbb bbbf aaf dbbb bbbf aac ebbb bbbf aag ebbb bbbf gaa ebbe bbbf caa bbbe bbbf faa bbbd bbbf aa bbbd bbbf aaf bbbd bbbf aac bbbf bbbf aag fbbbf bbbf gaa fbbb bbbf caa dbbb bbbf aa dbbb bbbf aa dbbb bbbf aaf ebbb bbbf aac ebbe bbbf aaa bbbe bbbf caa bbbe bbbf faa bbbd bbbf aa bbbd bbbf aa bbbf bbbf aac fbbbf bbbf aag fbbbf bbbf gaa fbbb bbbfcaa dbbb bbbcaa dbbb bbbaa ebbb bbba ebbb bbbc ebbe bbbf bbbe gbbbf bbbd cabbbf bbbd faabbbf bbbd aa bbbf bbbf aaf bbb bbbf aac bf b aag gaa caa aa aa aaf aac aaa caa faa aa aa aac aag gaa caa faa aa aa aac aag gaa caa faa aa aaf aac aag gaa cag ``` <!-- 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've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#8f4faeff b,#f99f42ff c,#ead4d9ff d,#efbc7bff e,#b1d6b0ff f,#ad89c1ff g,#96ca96ff ``` ```image fc faac caaaaf aa aaf aa aaf fac faf caf faa aa faa aa faa aac caa faf caa caa caa aa aa aa aa fac aac caf aac aa aac aa aaf aac a faf caa aa aa fac caf aa aa aa faf caa aa aa egggggggggggggggggggggaac geeeeeeeeeeeeeeeeeeeefaa geeeeeeeeeeeeeeeeeeeeaae geeeeeeeeeeeeeeeeeeeaaee geeeeeeeeeeeeeeeeeeaaeee geeeeeeeeeeeeeeeeefafeee geeeeeeeeeeeeeeeeeaaeeee geeeeeeeeeeeeeeeeaaeeeee geeeeeeeeeeeeeeeaaeeeeee geeeeeeeeeeeeeeaaeeeeeee bbbdc geeeeeeeeeeeeefafeeeeeee dbbbbbbbbdc geeeeeeeeeeeeeaaeeeeeeee cdbbbbbbbbddeeeeeeeeeeaaeeeeeeeee cdbbbbbbbbddeeeaaeeeeeeeeee geeedbbbbbbbbbdeeeeeeeee geeeeeeeeedbbbbbbbbddeee geeeeeeeeeaaeeeedbbbbbbbbdc geeeeeeeeaaeeeeeeeeeeedbbbbbbbbdc geeeeeeeaaeeeeeeeeeeeeee cdbbbbbbbbdc geeeeeefafeeeeeeeeeeeeee cdbbbbbbbbdc geeeeeeaaeeeeeeeeeeeeeee cdbbbbbd geeeeeaaeeeeeeeeeeeeeeee bbc geeeeaaeeeeeeeeeeeeeeeee bbc geeeaafeeeeeeeeeeeeeeeee bb geefaaeeeeeeeeeeeeeeeeee bb geeaaeeeeeeeeeeeeeeeeeee bb geaaeeeeeeeeeeeeeeeeeeee cbb gaaeeeeeeeeeeeeeeeeeeeee cbb fafeeeeeeeeeeeeeeeeeeeee dbd caaeeeeeeeeeeeeeeeeeeeeeg dbd aa bbc aa bbc fac bb caf bb b aa bb dbc aa bb bb aac cbb bb faf dbbbbc caa dbbd aa db aa fac caf aa aa aac faf caa c ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#8f4eaeff b,#f99f42ff c,#c8a9d7ff d,#fabd7fff e,#e6d8edff f,#a876bfff g,#fcddbeff ``` ```image fa faa caaa eaaaf eaaaae faaac caaac caaaf eaaaae faaae faaac caaaf eaaaf eaaaae faaac caaac caaaf eaaaa faaae faaac caaaf eaaaf eaaaae faaae bbddgg caaac bbbbbbbbddgg caaaf bbbbbbbbbbbbbbddgg eaaaa ggddbbbbbbbbbbbbbbbbddgfaaae ggddbbbbbbbbbbbbbbbbddgg ggddbbbbbbbbbbbbbbbbddgg ggdbbbbbbbbbbbbbbbbbddgg eaaaaggddbbbbbbbbbbbbbbbbdd faaae ggddbbbbbbbbbbbb faaac ggddbbbbbb caaaf ggdd eaaaa aaaae faaac caaaf eaaaf eaaaae faaae faaac caaaf eaaaa aaaae faaac caaaf eaaaf eaaaae faaae faaac caaaf eaaaf aaaae faaac caaac aaaf ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#8f4fafff b,#f99f42ff c,#ccafdaff d,#fabc7dff e,#eaddeeff f,#ad7ec4ff g,#fcdebeff ``` ```image fe caac eaaaac aa aaf aa aaf fac faf caf faa aa faa aa caa aae caa fac eaa eaa eaa aa eaa aa aae fac aae caf aae aa aac aa aac aae a fac eaa aa aa fae caf eaa aa aae fac eaa aa aa fae caf eaa aa aae fac eaa aa aa aae bbbdg caf dbbbbbbbbdg eaa gdbbbbbbbbdg aa gdbbbbbbbbdg aae gdbbbbbbbbdg gdbbbbbbbbdg aa gdbbbbbbbbdg aa gdbbbbbbbbdg aae gdbbbbbbbbdg caf gdbbbbbbbbdg eaa gdbbbbbd aa bbg aa bbg fac bb caf bb aa bb aa ebb aae gbb caf dbd eaa dbd aa bbg aa bbg fac bb caf bb b aa bb dbg aa bb bb aae gbb bb fac gbbbbe eaa dbbd aa db aa fac caf aa aa aae fac eaa e ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#6a914fff b,#6e0898ff c,#9266aaff d,#b1d7b1ff e,#99c498ff f,#84a871ff g,#edf3edff ``` ```image edddddddddddddddg edddddddddddddddg edddddddddddddddg edbbceddddddddddg ecbbbbbbbcddddddg eddcaabbbbbbbcddg edddaaaecbbbbbbbbcg edddaaadddddcbbbbbbbbbd edddaaaddddddddddcbbbbbbbbcg edddaaaeddddddddg gcbbbbbbbbcg edddaaaaddddddddg cbbbbbbbc edddaaaaddddddddg dcbbb edddaaaaddddddddg bbb eddeaaaaedddddddg bbc eddeaafafdddddddg dbbg eddfafeaadddddddg bbb eddfafdaaddddddeg bbc gggaadgaadgggggg gbbg aag faf bbb aa gaa bbcgggggggggggggggggggggggggggggggggggggggggggggg aa aa gbbedddddddddddddddddddddddddddddddddddddddddddde aa aag cbbdddddddddddddddddddddddddddddddddddddddddddde aa faf gbbbddddddddddddddddddddddddddddddddddddddddddde aa gaa gebbedddddddddddddddddddddddddddddddddddddddddde gaa aa gdcbbdddddddddddddddddddddddddddddddddddddddddde daa aag gddbbbdddddddddddddfddddddddddddddddddddddddddde eaf faf gdddbbcdddddddddddaaadddddddddddddddddddddddddde fae daa gdddcbbddddddddddfaaaeddddddddddddddddddddddddde aad aa gddddbbbdddddddddaaaaaddddddddddddddddddddddddde aag aag gdddddbbcdddddddaaadaaddddddddddddddddddddddddde aag faf gdddddcbbddddddfaaddfaadddddddddddddddddddddddde aa gaaf gddddddbbbddddeaaedddaadddddddddddddddddddddddde aa daaf gdddddddbbcdddaafddddfaaddddddddddddddddddddddde aa daaf gdddddddebbddaaaddddddaaddddddddddddddddddddddde aa daaf gddddddddbbbfaadddddddaaadddddddddddddddddddddde gaa gaaf gdddddddddbbaaeddddddddaadddddddddddddddddddddde daa gaaf gdddddddddeaaadddddddddaaaddddddddddddddddddddde g gaaa gdddddddddfaabddddddddddaaddddddddddddddddddddde gaaa gddddddddeaabbbdddddddddaafdddddddddddddddddddde gaaa gddddddddaafdbbedddddddddaadddddddddddddddddddde gaaa gdddddddaaaddcbbdddddddddaafddddddddddddddddddde gaaa gddddddfaaddddbbbddddddddeaaddddddddddddddddddde gaaa gddddddaaedddddbbcddddddddaafdddddddddddddddddde gaaa gdddddaaaddddddcbbddddddddeaadddddddddddddddddde gaaa gddddfaaddddddddbbbddddddddaafddddddddddddddddde aaa gdddeaaedddddddddbbcdddddddeaaddddddddddddddddde aaa gdddaafddddddddddcbbddddddddaafdddddddddddddddde aaa gddaaaddddddddddddbbbdddddddeaadddddddddddddddde aaa gdfaaddddddddddddddbbcdddddddaaeddddddddddddddde aaa geaaeddddddddddddddebbdddddddeaaddddddddddddddde aaa gaaaddddddddddddddddbbbdddddddaaedddddddddddddde aaa faaddddddddddddddddddbbcddddddfaadddddddddddddde aaa gaaeddddddddddddddddddebbeddddddaaeddddddddddddde aaa aafddddddddddddddddddddbbbddddddfaaddddddddddddde aaaaaddddddddddddddddddddddbbbddddddaaedddddddddddde aaagdddddddddddddddddddddddbbedddddfaadddddddddddde fggdddddddddddddddddddddddcbbddddddaaeddddddddddde gddddddddddddddddddddddddbbbdddddfaaddddddddddde gdddddddddddddddddddddddddbbcdddddaaddddddddddde gdddddddddddddddddddddddddcbbdddddfaadddddddddde gddddddddddddddddddddddddddbbbdddddaadddddddddde gdddddddddddddddddddddddddddbbcddddaaaddddddddde gdddddddddddddddddddddddddddcbbdddddaaddddddddde gddddddddddddddddddddddddddddbbbddddaaadddddddde gdddddddddddddddddddddddddddddbbcddddaadddddddde gdddddddddddddddddddddddddddddebbddddaafddddddde gddddddddddddddddddddddddddddddbbbddddaaddddddde gdddddddddddddddddddddddddddddddbbcdddaafdddddde gdddddddddddddddddddddddddddddddebbeddeaadddddde gddddddddddddddddddddddddddddddddbbbdddaafddddde gdddddddddddddddddddddddddddddddddbbbddeaaddddde gddddddddddddddddddddddddddddddddddbbeddaafdddde gddddddddddddddddddddddddddddddddddcbbddeaadddde gdddddddddddddddddddddddddddddddddddbbbddaafddde gddddddddddddddddddddddddddddddddddddbbcdeaaddde gddddddddddddddddddddddddddddddddddddcbbddaaedde gdddddddddddddddddddddddddddddddddddddbbbdeaadde gddddddddddddddddddddddddddddddddddddddbbcdeddde gddddddddddddddddddddddddddddddddddddddcbbddddde gdddddddddddddddddddddddddddddddddddddddbbbdddde gddddddddddddddddddddddddddddddddddddddddbbcddde gddddddddddddddddddddddddddddddddddddddddcbbddde gdddddddddddddddddddddddddddddddddddddddddbbbdde gddddddddddddddddddddddddddddddddddddddddddbddde gdddddddddddddddddddddddddddddddddddddddddddddde gdddddddddddddddddddddddddddddddddddddddddddddde ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#6a9050ff b,#6e0898ff c,#c9a3d9ff d,#aac09bff e,#a15fbdff f,#87a672ff g,#d9dad7ff ``` ```image eecg bbbbbecg cbbbbbbbbbeec ebbbbbbbbbbbbbbecg cebbbbbaaabbbbbbbbbecg ceaaaabbbbbbbbbbbbbeec aaaaabbbbbbbbbbbbbbbbbe aaaaf gcebbbbbbbbbbbbbb aaaaa ceebbbbbbbbb gaaaaag gcebbbbb gaaaaad gceb gaaaaaf daaaaaa daaaaaag daaaaaad faaaaaaf faaaaaaa faaaaaaag aaaaaaaad aaaaaaaaf gaaaadaaaa gaaaagaaaag gaaaa aaaad daaaa daaaf daaaf daaaa daaaf gaaaag faaad aaaad faaad faaaf ``` <!-- end of image --> Area A does not contain any intersection points. Next up, a closer look at another region. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#6b9150ff b,#6e0798ff c,#c79fd7ff d,#bdceb1ff e,#9a52b7ff f,#91ae7eff g,#e4e0e5ff ``` ```image bb bbc bbbe ebbbe gbbbbg cbbbb bbbbe cbbbbg ebbbe bbbbc gbbbbg dff ebbbc aaaaa gbbbb aaaaa bbbb daaaaag ebbbc gaaaaaaf gbbbbg faaaaaaag ebbbe daaaag faaag gbbbbg aaaad gaaaf cbbbb aaaa faaag bbbbe daaaf gaaad cbbbb aaaad aaaa ebbbe faaaf faaa bbbbc daaaag daaad gbbbbg gaaaag faaa ebbbe faaaa daaad gbbbbaaaag daaad bbbaaaad aaaa ebaaaaf daaad gbaaaa aaaf faaaabc aaaaf aaaabbbg daaaa gaaaabbbb aaaa aaaadbbbbe daaag faaaf bbbbb gaaaf gaaaag ebbbe gaaaf faaad bbbbc faaag daaaa cbbbbg gaaaf aaaaa ebbbe faaag faaaf gbbbb aaaag daaaa bbbb aaaaf gaaaag ebbbc faaaa faaad gbbbbg gaaaa daaaf cbbbe faaa aaaa gbbbbg faaa faaaf cbbbb daaad daaaa bbbbe faaa gaaaag bbbbb daaad daaaf ebbbe daaad gaaaag bbbbc aaaa aaaaa cbbbbg aaaa aaaaf ebbbe aaaa daaaa bbbbc daaad faaad bbbb daaad aaaf ebbbc aaaf aaag gbbbbg daaag aad cbbbe gaaaf aa gbbbbg gaaaf ag cbbbb aaaag d bbbbe aaaaf bbbbb faaaa ebbbe faaag bbbbc gaaaf cbbbbg faaag ebbbe gaaad bbbbc faaa bbbbe faaa ebbbb daaad gbbbbg aaaa cbbbe aaaa gbbbbg daaad cbbbe aaaa ebbbe daaad gbbbb aaaa bbbb daaad gbbbbc daaad cbbbbg aaaf ebbbe aaaag bbbbc aaaaf bbbbe gaaaa ebbbb faaag gbbbbg gaaaf cbbbe faaag ebbbc gaaaf cbbbe gaaaf ebbbe faaag gbbbb gaaad bbbb aaaa gbbbbc faaa cbbbb daaad ebbbe faaa bbbbc daaad gbbbbg aaaa bbbbb aaaa gbbbbg daaad cbbbe aad ebbbc d cbbbe ebbbc gbbbb bbbb ebbbe cbbbb ebbbe bbbbc cbbbg c ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area B! Answer: A: 0; B: 1; 0 + 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#6a9150ff b,#6e0798ff c,#c093d2ff d,#bbccafff e,#954ab4ff f,#8dab79ff g,#e0dfdfff ``` ```image bbeg cbbbbbbec caabbbbbbbc aafgebbbbbbbbeg aaa cbbbbbbbbec aaa cebbbbbbbbc aaad gebbbbbbbbeg aaaf cbbbbbbbc aaaa cebbb aaaa bbb gaaaag bbc daafaf cbb fafgaa bbb fad aa bbe aad aag gbbg aag faf ebb aa gaa bbe aa aa gbbg aa aag ebb aa faf bbb aa gaa bbc gaa aa ebb daa aag bbb f daf faf bbc aaa faf gaa cbb daaag aad aa bbb aaaaa aag aag bbc aaa aag aa faf cbb faa faa aa gaaf bbb gaag aa aa daaf bbe aaf faa aa daaf gbbg aaa aa aa gaaf ebbdaa aaa gaa gaaf bbaad aa daa gaaa gaaa aaf g gaaa faab aa gaaa gaabbb aaf gaaa aaf bbg gaa gaaa aaa ebb aaf gaaa daa bbb gaa aaa aad bbc aaf aaa aaa cbb gaa aaa faa bbb aad aaa gaag bbc gaa aaa aaf cbb aad aaa aaa bbb daa aaa daa bbe aad aaa aad gbbg daa aaa aaa bbb aad aaa faa bbe daa aaa gaag gbbg aag aaa aaf ebb daa aaaaa bbe aag aaa gbbg faa fg ebb aag bbb faa bbc aa cbb faa bbb aa bbc faa cbb aa bbb aaf bbe aa cbb aaf bbb aa bbe aaf gbbg gaa ebb aaf bbe gaa gbbg aad ebb gaa bbb aad bbc daa cbb aad bbb daa bbc d cbb bbb bbe cbb bbb b ``` <!-- 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,#d799b5ff b,#4e5aa8ff c,#f0eceeff d,#8794bdff e,#b1d6b0ff f,#dcbfd3ff g,#96c997ff ``` ```image cc aaa aaa aaa aaf caac faa aaa aaa aaa caaf faac aaa aaa aaa aaf caac faa aaa fbbdc aaa cbbbbbbbbbdc aaa dbbbbbbbbbbbbbbbdf caaf fbbbbbbbd cdbbbbbbbbbbbf faa bbbbbbbc dbbbbbbbbbbbdc aaa dbbbf fbbbbbbbbbbbdc aaa d fdbbbbbbbbbbdf aaa cdbbbbbbbbbbbf aaf cdbbbbbbbbbbbdc caac fbbbbbbbbbbbdc faa fdbbbbbbbbbbdf aaa cdbbbbbbbbbbbf aaa cdbbbbbbbbbbbd aaa fbbbbbbbbb caaf fdbbbbf faa f bbb aaa faaaf dbbd aaa aaaaaaaf egggbbbggggggaaagggggggg caaaaaaaaf geeedbbdeeeeeaaaeeeeeeeec caaaaaaaafc geeeebbbeeeeeaaeeeeeeeeec caaaaaaaaac geeeedbbbeeeaaaeeeeeeeeec cfaaaaaaaac geeeeebbbeeeaaaeeeeeeeeec faaaaaaaac geeeeedbbbeeaaaeeeeeeeeec faaaaaaaac geeeeeebbbeeaaaeeeeeeeeec faaaaaaaac geeeeeedbbbeaaeeeeeeeeeec faaaaaaaac geeeeeeebbbaaaeeeeeeeeeec faaaaaaa geeeeeeegbbbaaeeeeeeeeeec faaaaf geeeeeeeebbbaaeeeeeeeeeec aaa geeeeeeeeebbbaeeeeeeeeeec aaa geeeeeeeeebbbdeeeeeeeeeec faac geeeeeeeeeebbbeeeeeeeeeec caaf geeeeeeeeeabbbdeeeeeeeeec aaa geeeeeeeeeaabbbeeeeeeeeec aaa geeeeeeeeeaabbbdeeeeeeeec faac geeeeeeeeeaaabbbeeeeeeeec aaf geeeeeeeeeaaedbbdeeeeeeec aaa geeeeeeeeaaaeebbbeeeeeeec aaa geeeeeeeeaaaeedbbbeeeeeec faac geeeeeeeeaaaeeebbbeeeeeec aaa geeeeeeeeaaaeeedbbbeeeeec aaa geeeeeeeeaaaeeeebbbeeeeec aaa geeeeeeeeaaeeeeedbbbeeeec caac geeeeeeeaaaeeeeeebbbgeegc aaa cccccccaaaccccccfbbbccc aaa aaa bbbc aaa aaf cbbb caaf caac bbbf aaa faa b aaa aaa faa aaa caaf aaa aaa caaf aaa faac faa aaa caaf aaa aaa aaa aaa cfaaaaf faac cfaaaaaaaaaac aaf cfaaaaaaaaaaaaaaaf aaa cfaaaaaaaaaaaaaaafc aaaaaaaaaaaaaaafc faaaaaaaaff aaafc ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#d798b5ff b,#4d59a8ff c,#e9dfeaff d,#9293c4ff e,#696fb2ff f,#e4bacdff g,#b8bbdaff ``` ```image cbbbbbbc faaaaac dbbbbbd faaaaa cbbbbbbc aaaaaf dbbbbbd aaaaaf cbbbbbbc caaaaac dbbbbbd caaaaac cbbbbbbc faaaaa dbbbbbe faaaaa bbbbbbg aaaaaf gbbbbbe aaaaaf ebbbbbg caaaaac gbbbbbe faaaaa ebbbbbg faaaaa gbbbbbe aaaaaf ebbbbbg aaaaaf gbbbbbb caaaaac ebbbbbdcaaaaac cbbbbbbfaaaaa dbbbbbdaaaaa cbbbbbbaaaaf dbbbbbeaaaf cbbbbbbaaac dbbbbbeaa cbbbbbbaa dbbbbbef bbbbbbg dbbbbbe fbbbbbbg fdbbbbbe fabbbbbbg aadbbbbbe caaaebbbbbg caaadbbbbbb faaaaebbbbbd faaaaabbbbbbc aaaaafdbbbbbd aaaaafcbbbbbbc caaaaac dbbbbbd caaaaac cbbbbbbc faaaaa dbbbbbd faaaaa cbbbbbbc aaaaaf dbbbbbe caaaaaf bbbbbbg caaaaac gbbbbbe faaaaa ebbbbbg faaaaa gbbbbbe aaaaaf ebbbbbg aaaaaf gbbbbbe caaaaac ebbbbbg caaaaac gbbbbbb faaaaa ebbbbbd faaaaa cbbbbbbc ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#d898b5ff b,#4d59a8ff c,#eee0eaff d,#939bcaff e,#6b74b6ff f,#e3b8ccff g,#bdc2deff ``` ```image cc aaa aaa aaa aaf caac faa aaa aaa aaa caac faa aaa aaa aaa aaf caac faa aaa gbbdc aaa cebbbbbbbbdc aaf dbbbbbbbbbbbbbbbeg caac gbbbbbbbd cdbbbbbbbbbbbg faa bbbbbbec dbbbbbbbbbbbdc aaa dbbbg gebbbbbbbbbbdc aaa d gebbbbbbbbbbeg aaa cdbbbbbbbbbbeg aaf dbbbbbbbbbbbd caac gebbbbbbbbbbdc faa gebbbbbbbbbbeg aaa cdbbbbbbbbbbeg aaa cdbbbbbbbbbbbd aaf gbbbbbbbbb caac gebbbbg faa f bbb aaa faaaf ebbd aaa aaaaaaaf bbb aaa caaaaaaaaf dbbd aaf caaaaaaaaf bbb caac cfaaaaaaafc dbbe faa faaaaaaaac bbb aaa faaaaaaaac gbbe aaa faaaaaaaac bbb aaf faaaaaaaac gbbbcaac faaaaaaaac bbbfaa faaaaaaa cbbbaa faaaaf bbbaa aaa cbbba aaa bbba faa fbbb aaf fbbbg aaa aabbb aaa aaebbd faac aafbbb aaf caacdbbd aaa faa bbb aaa aaa dbbe caac aaa bbb aaf aaa gbbe aaa aaf bbb aaa caac gbbb caac faa bbbc aaa aaa cbbb aaa aaa bbbc aaa aaf cbbb caac caac bbbg aaa faa e aaa aaa faa aaa caaf aaa aaa aaf aaa caac faa aaa caaf aaa aaa aaa aaa cfaaaaf faa cfaaaaaaaaaac aaf cfaaaaaaaaaaaaaaaf aaa cfaaaaaaaaaaaaaaafc aaaaaaaaaaaaaaafc faaaaaaaafc aafc ``` <!-- end of image -->
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I have a feeling there might be some intersections in this image. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#e14755ff b,#f3bac8ff c,#dc617dff d,#dd206eff e,#f2f3efff f,#b1d7b0ff g,#d19297ff ``` ```image ee aa aca cc aa ae ac ba ag ab eab ea bae ag ga a c ca ae ba ab ea ac a ga ae ba ag ea cc a ga ab eac gab cae aa bac gab aae eaa bag cab aa eaa bag eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee cae fffffffffffffffffffffffffffffffffffffe aa fffffffffffffffffffffffffffffffffffffe eac ffffdffffffffffffffffffffffffffffffffe gab ffffddfffffffffffffffffffffffffffffffe cae ffffddgffffffffffffffffffffffffffffffe aa ffffdfdffffffffffffffffffffffffffffffe bac ffffdfcdfffffffffffffffffffffffffffffegab ffffdffddffffffffffffffffffffffffffffaae fffgdfffdgffffffffffffffffffffffffffaa fffgdfffgdffffffffffffffffffffffffgace fffgdffffddffffffffffffffffffffffcagfe fffgdfffffdcffffffffffffffffffffaafffe fffcdffffffddgfffffffffffffffffaaffffe fffccfffffffgdddgffffffffffffgagfffffe fffccffffffffffcddcfffffffffcafffffffe fffdcfffffffffffffdddgfffffaaffffffffe fffdcfffffffffffffffgdddffacfffffffffe fffdgffffffffffffffffffcddcffffffffffe fffdgffffffffffffffffffaagdddgfffffffe fffdgfffffffffffffffffaaffffcddcfffffe fffdgfffffffffffffffgacffffffffdddgffe fffdfffffffffffffffcagfffffffffffgdddb fffcffffffffffffffaaffffffffffffffffcddc fffffffffffffffffaaffffffffffffffffffebdddb fffffffffffffffgacfffffffffffffffffffe gddde ffffffffffffffcagffffffffffffffffffffe ecddg fffffffffffffaaffffffffffffffffffffffe bdddb ffffffffffffaafffffffffffffffffffffffe gddc ffffffffffgagffffffffffffffffffffffffe edddb fffffffffcaffffffffffffffffffffffffffe bddde ffffffffaafffffffffffffffffffffffffffe cddc fffffffacffffffffffffffffffffffffffffe bdddb fffffgagfffffffffffffffffffffffffffffe gddce ffffaafffffffffffffffffffffffffffffffe ecddg fffaaffffffffffffffffffffffffffffffffe bdddb fffgfffffffffffffffffffffffffffffffffe gddc eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee edddb bddde cddc bdde ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#e24856ff b,#f0a2b8ff c,#ea7a99ff d,#de1e6dff e,#fae2e8ff f,#f5c3d3ff g,#e55482ff ``` ```image e cdc gddb gddde ddddg dddddb ddbgddf ddbeddde ddb bddc eddb cddb eddf gdde eddf fddg fddf bddc b fddf gddf ca fdde eddde egaa fdde fddg faaac bdde cddb baaab bdd gdde ecaaaf bdd eddg eaaage bdd bddc baaac cdd cddcf caaab cdd eddddgbe egaaae cdg ecdddddgb faaace cdg bgdddddcf baaab gdg ebdddddgbe caaaf gdg fcdddddcf egaage gdc ebgdddddce faaac gdc ecdddddgb baaab gdc fgdddddcf caaaf ddc ebgddddgbe egaage ddc fcdddddgaaac ddb bgdddddgf ddb egddddddgbe ddb eaaagbcdddddcf eddb baaac ebgdddddce eddf caaab ecdddddgb eddf egaaae fgdddddcf fddf faaace ebgddddgbe fddf baaab fcdddddgf fdde caaaf bgddddd fdde egaage ecddd fgge faaac fc baaab caaaf egaage faaac baaab ecaaaf eaaage baaac caaab egaaae faaace baaab caaaf egaage faaac baaab caaaf egaage faaac baaab ecaaaf eaaage baaac baaab eaae ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#e24655ff b,#f09eb4ff c,#ea7695ff d,#de1e6dff e,#fae3e9ff f,#f5c3d0ff g,#e5567bff ``` ```image ee aa aca gg aa ae ag ba ab af eaf ea fa ac ca a g ca ae ba ab ea ac a ca ae fa ab a gg a ba af eag bab gae aa fac caf aa aa fac caf aa eag bab gae aa eag d bab dd gae ddb aa dede fac ed cd caf ed dg aa fd df aa fd fd fac bd gd caf bd dc aa cd eddb eag cg bdddf bab gg cddc gae gc edddb aa dc bddgeeag db gddg db gafdddf df aa cddg df fac egddb de caf bddde ge aa cddc aa edddb fac bddge caf gddc aa fdddf eag cddg bab egddb gae bddde aa cddc eag fdddf bab bddge gae egddc aa fdddf f cddg edddb bddde cddc fdde ``` <!-- end of image -->
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Alright, let's get to work and investigate this image for intersections. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#d36461ff b,#bdead1ff c,#cf2d2fff d,#df9f9bff e,#e4e9e1ff f,#b2d7b1ff g,#98c795ff ``` ```image ce c ac ca ce dc cc cd e ec gggbfgccgggggggggf ac fffbbfcccffffffffg ca fffbbfcdccfffffffg ce fffbbfcdfccdfffffg dc fffbbfcgffacaffffg cc fffbbfcffffdccfffg cd ffffbfcffffffccffg ec ffffbfcfffffffccgg ac ffffbfcffffffffcca ca ffffbgcfffffffffaca ce ffffbdcffffffffffgcc dc ffffbdcffffffffffg cce cc ffffbdcffffffffffg ccd cd ffffbacffffffffffg aca ec ffffbacffffffffffg dcc ac ffffbacffffffffffg ecc ca fffffacffffffffffg cce ce fffffccffffffffffg ccd dc fffffccffffffffffg aca cc fffffccffffffffffg dca eedcd fffffcaffffffffffg dce eedddaacccccccccccccc fffffcaffffffffffg cc edddaacccccccccccccccccccaaddee fffffcaffffffffffg cccccccccccccccaaddde fffffcaffffffffffg eddee fffffcdffffffffffg fffffcdffffffffffg fffffcfffffffffffg fffffcfffffffffffg fffffcfbfffffffffg fffffcfbfffffffffg fffffcfbbffffffffg fffffcffbbfffffffg ffffgcfffbfffffffg ffffdcfffbbffffffg e ffffdcffffbffffffg bbbbbbbbbee ffffacffffbbfffffg bbe eebbbbbbbbbbbee ffffacfffffbbffffg bbe eebbbbbbbbbbbee ffffacffffffbffffg ebe eebbbbbbbbbbbee ggggacggggggbbgggf ebe eebbbbbbbbbbbee ac be ebe eebbbbb cc bb ebe cc be ebe ca eb ebe ca bb ebe ca b ebb cd bb ebb cd be ebb cd eb bb cd bb bb ce bebb ce bbb c e c c ec ec dc dc dc ac ac ac cc cc cc ca ca ca cd cd cd ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#d55455ff b,#bee9d2ff c,#cf2d2fff d,#e1a19fff e,#eec7c6ff f,#d97b7aff g,#e6f2e9ff ``` ```image gbbg dfg gbbg eccae gbbg dcccce gbbg dcccccd gbbb dccccccf bbb fccdfcccag bbb fcce dcccce bbb fcce eccccd bbb fcce eacccf bbbg acce gacccag gbbg acce fcccae gbbg accg dcccce gbbg accg eccccd gbbg ccc gacccf gbbb ccc fcccag bbb ccc dcccce bbb ccc eccccd bbbgcca eaccc bbbgcca gacc bbbecca fc gbbecca d gbbeccf gbbdccf gbbdccf gbbdccf bbdccd bbfccd bbfccd bbfccd bbfcce gbacce gbacce gbacce gbaccg gbaccg bccc bccc bccc bccc bcca bcca ecca ecca ecca eccf eccf dccf dccf dccf dccfg fccdg fccdg fccdg fccdg accdb accbb accbbg accbbbg cccbbbb ccc bbbg ccc gbbb ccc bbbg gcca gbbbg gcca gbbb ecca bbbg ecca gbbb eccf bbbg eccf gbbbg eccf gbbb dccf bbbg dccd gbbb dccd bbbg dccd gbbb fccd bbbb fcce bbbg fcce gbbb fcce bbbg ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#d65556ff b,#beead2ff c,#cf2d2fff d,#e7a9a8ff e,#f5d7d8ff f,#dc7e7dff g,#dbf3e6ff ``` ```image ae c fc ca ce dc cc cf g ec bg ca fc bg ccc ca bb cdcce ce bb cd ccd dc gb ce aca cc gb ce dcc cd gb c ecc ec b c cce ac bec acf ca bec fca ce bdc ecc dc bdc cce cc bfc ccd cd bfc acf ec bfc dcc ac gac ecc ca gac cce ce cc ccd dc cc fca cc ca dcf eedcd ca fce eeddfaacccccccccccccc ca cc eddffaccccccccccccccccccaaffdee cf cccccccccccccccaffdde cf eddee cf cd cd cb cbb c bg c bb ec bb ec gb dc bb g dc bg bbbbbbbbbgg dc bb bbg ggbbbbbbbbbbbgg fc bb gbg ggbbbbbbbbbbbgg fc gb gbg ggbbbbbbbbbbbgg ac bb gbg ggbbbbbbbbbbbgg ac bg gbg ggbbbbb cc bb gbg cc bg gbg ca gb gbg ca bb gbg cf bg gbg cf bb gbb cd bg gbb cd gb gbb cd bb bb ce bgbb ce bbb c g c c ec ec dc dc fc fc fc ac ac cc ca ca ca cf cf cd cd ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ae28cff b,#c0dd7cff c,#d7f0c0ff d,#b1d8b1ff e,#a0d09fff f,#bada4cff g,#eef7ecff ``` ```image c ff fb fc g fc a gfg a cf a bf ga ff ga fb ca fc dd fg ac gfg ac cf ag bf a ff a fb a fc a gfg ga gf ca cf de bf ed ff ac fb ag fc a gfg a cf a cf a bf ga ff ca fb ca fc dd gfg ac cf ag bf ag bf a ff a fb a fc a gfg ga cf ca bf dd bf ggggggggggggggggggggggggggggggggggadggggggg ff eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeee fb edddddddddddddddddddddddddddddddddaddddddde fc edddddddddddddddddddddddddddddddddaddddddde gfgedddddddddddddddddddddddddddddddddadddfddde cfedddddddddddddddddddddddddddddddddadbffddde bfddddddddddddddddddddddddddddddddaaffedddde ffdddddddddddddddddddddddddddddeaaffdddddde effdddddddddddddddddddddddddddaaffeddddddde edfbddddddddddddddddddddddddaaeffddddddddde eddfbdddddddddddddddddddddeaaffbdddddddddde edddfddddddddddddddddddddaaeffdddddddddddde ac edddbfdddddddddddddddddaaebfbddddddddddddde ga eddddbfddddddddddddddeaadffddddddddddddddde ea edddddffddddddddddddaadbfbdddddddddddddddde ag eddddddffdddddddddaaedffdddddddddddddddddde ga edddddddfbddddddeaadbfbddddddddddddddddddde ae eddddddddfbddddaaddffddddddddddddddddddddde ag edddddddddfddaaedbfbdddddddddddddddddddddde ca edddddddddbaaaddffdddddddddddddddddddddddde ad edddddddddaafdbffddddddddddddddddddddddddde ag edddddddaaedfffddddddddddddddddddddddddddde ca edddddaaaddddbdddddddddddddddddddddddddddde ad edddeaaddddddddddddddddddddddddddddddddddde a eddaaedddddddddddddddddddddddddddddddddddde da eaaadddddddddddddddddddddddddddddddddddddde ac gaadddddddddddddddddddddddddddddddddddddddde ga aaaddddddddddddddddddddddddddddddddddddddddde da dad eddddddddddddddddddddddddddddddddddddddddde ac gaa eddddddddddddddddddddddddddddddddddddddddde ga aag eddddddddddddddddddddddddddddddddddddddddde ea dad eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ag gaa ggggggggggggggggggggggggggggggggggggggggggg ga gdaag aa gaaadg ag caaad ca daaac aaeg ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ae38bff b,#c7e16eff c,#d8f2c9ff d,#acebadff e,#d8ea9bff f,#bada4aff g,#eff8e4ff ``` ```image aac aac gaag gaag caa caa caa g dad cfe dad gbfffg b dad cfffbg fe aac efffe ffe caaacfffbg bffc gdaaaafffe bffg daaaabffbg gfffg caaaadfffe gffb gdaaadbfffc cffb daaadefffe effe caaaacbfffc effe gdaaadefffbg bffc daaadcbfffc bffg caaaacefffbg gfffg gdaaadgbfffc gffb daaadgcfffbg cffb caaaacgbfffe effe gdaaad cfffbg effe daaadg efffe bffc caaaac cfffbg gbffg gdaaad efffe gfffg daaadg cbffbg gffb caaaac efffe cffb gdaaad gbffbg effe daaadg efffe effe caaaac gbfffc bffc gdaaad efffe gbffg daaadg gbfffc gfffg caaaac efffbg cffbgdaaad gbfffc cfaaaadg cfffbg caaaac gbfffc gdaaaafe cfffbg daaadgbffcbfffe caaaac gbffffbg gdaaac gfffe gdaaadg geg caaaac gdaaac gdaaadg caaaac gaaaac gdaaadg caaaac aaaac aadg ac ``` <!-- end of image --> Incredible, there's actually 1 intersection in area A! Answer: A: 1; 1 = 1 I've found a single intersection point in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#8ae38cff b,#c8e16eff c,#daf3cdff d,#afebb0ff e,#d9ea9cff f,#bada4aff g,#ecf8e5ff ``` ```image e ff fb fe g fc a gfg a ef a bf ga ff ca fb ca fe dd fg ad gf ac ef ag bf a ff a fb a fe a fg ga gf ca ef dd bf dd ff ac fb ag fe a gfg a cf a ef a bf ga ff ca fb da fe dd gfg ac cf ag ef a bf a fb a fb a fc a gfg ga cf ca ef dd bf ad fb ac fe ag fc a gfg a f cf a cfb ef aaffg bf daafb fb gaabfc fe aadff fc dadbfc gfg gaagff ac cf aacbfe ga ef dad ff aa bf gaa efe ag fb aac ff ga fe dad efe aa fc gaa ff ag gfg aac efb ca caad ffg ad gaaf cfb ag aac bffg ca dad e ad gaa a aac da dad ad gaa a aac da dad ac caa ga aag da dad ac caa ga gdaag aa caaadg ag caaad ca daaac aadg ``` <!-- end of image -->
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This is the image I'm working with. The goal is to count the intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#278bd2ff b,#67f616ff c,#afd7aeff d,#a5cfecff e,#90ef66ff f,#5da9d2ff g,#ebf5eeff ``` ```image ggggggggggggggg ccccccccccccccecg cccccccccccccebbg cccccccccccccbbbg ccccccccccccbbbcg cccccccccccbbbccg ccccccccccebbeccg ccccccccccbbbcccg bbeeeccg cccccccccbbbccccg cbbbbbbbbbbbbbbbbbbeeccgg ccccccccbbbcccccg cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeccg cccccccebbecccccg ebb gcceebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeccgg cccccccbbbccccccg ebb ggceeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeebbbcccccccg ebb ggcceebbbbbbbbbbbbbbbbbbbbbbbccccccccg bbb ggceebbbbbbbeccccccacg bbe cccccccccccccaaag bbe ccccccccccccaaafg bbe cccccccccccaaafcg bbc cccccccccfaaacccg bbc ccccccccfaaaccccg bbg ggggggfaaaggggg bbg aaaa bb aaaf bb gaaad bb daaag gbb daaag gbb faaa cbb aaaa cbb aaaf ebb gaaad ebb gaaad ebb daaag bbb faaa bbb aaaa bbe aaaf bbe aaaf bbe gaaad ccccbbeccccccccc daaag ccccbbecccccccccg faaa ccccbbccccccccccg faaa ccccbbccccccccccg aaaa ccccbbccccccccccg aaaf ccccbbccccccccccg gaaad ccccbbccccccccccg daaag ccccbbccccccccccg daaa ccfaabccccccccccg faaa ccfaabccccccccccg aaaa ccfaabccccccccccg aaaf cccaabccccccccccg gaaad cccaabccccccccccg gaaad cccaabccccccccccg daaag cccaabccccccccccg faaa cccaaeccccccccccg aaaa cccaaeccccccccccg aaaf cccaafccccccccccg aaaf cccaafccccccccccg gaaad cccaaaccccccccccg daaag cccaaaccccccccccg faaa cccfaaccccccccccg aaaa ccceaaccccccccccg aaaf ccceaaccccccccccg aaaf cccbaaccccccccccg gaaad cccbaaccccccccccg daaag ccebaaccccccccccg faaa ccebaaccccccccccg faaa ccebaaccccccccccg aaaa ccebaafcccccccccg aaaf ccccaafcccccccccg gaaad ccccaafcccccccccg daaag ggggaaaggggggggg daaag faa faaa faa aaaa daa aaaf daa gaaad gaa gaaad aa daaag aa faaa aag aaaa aadaaaf aaaaaf aaaad aaag gf ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#278cd1ff b,#66f517ff c,#b7f79aff d,#7dbcdcff e,#8ef658ff f,#4abf7dff g,#d4efe1ff ``` ```image cbbbbc cbbbbc cbbbbc cbbbbg ebbbbg ebbbbg ebbbbg ebbbb ebbbb bbbbb bbbbb bbbbe bbbbe bbbbe gbbbbe gbbbbe gbbbbc daaaabbc daaaabbc daaaafbc daaaafbc gaaaafbg gaaaafbg gaaaafbg gaaaafbg aaaaab aaaaab aaaaab aaaaab daaaae daaaae daaaae daaaaf daaaaf daaaaf caaaad caaaad caaaad caaaaa caaaaa eaaaaa eaaaaa efaaaa efaaaag efaaaag bfaaaag bfaaaad bfaaaad bfaaaad bbaaaad gbbaaaad gbbaaaad gbbaaaaa cbbaaaaa cbbaaaaa cbbfaaaa cbbfaaaag cbbfaaaag ebbfaaaag ceefaaaad gaaaad gaaaad gaaaad gaaaad ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared 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,#288cd3ff b,#66f715ff c,#b5fa8eff d,#c5e0f3ff e,#8df850ff f,#74b4e2ff g,#d9fcc5ff ``` ```image c ebe cbbb gbbbb ebbbb ebbbbb cbbbbbe gbbbbbe bbbbbbg ebbbbbg cbbbbbc gbbbbbe bbbbbbg ebbbbbg cbbbbbc gbbbbbe bbbbbb ebbbbbg cbbbbbc gbbbbbe bbbbbb ebbbbbg bbbbeeeeccccebbbbbc bbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbg eeebbbbbbbbbbbbc daf gggccccg daaa daaaa faaaaa faaaaaa faaaaaaf daaaaaaad daaaaaaad daaaaaaad faaaaaaf faaaaaaf ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area B. Answer: A: 1; B: 0; 1 + 0 = 1 There's only one, but is an intersection after all.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#278bd2ff b,#66f615ff c,#bdfa9aff d,#9dcaeaff e,#8af359ff f,#5ea9dcff g,#dcf1eaff ``` ```image c cbb bbb bbb bbbg cbbe bbb bbeecccg bbb cbbbbbbbbbbbbbbbbbbeeccgg bbbg cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeecccg cbbc cbb gccceebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeccg gbbb ebb ggcceebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeccbbb ebb gcceeebbbbbbbbbbbbbbbbbbbbbb bbb ggcceebbbbbbc a bbe aaa bbe aaaf bbe gaaad bbc daaag bbc faaa bbc faaa bbg aaaa bb aaaf bb gaaad bb gaaag gbb daaa gbb faaa cbb aaaa cbb aaaf cbb aaad ebb gaaag ebb daaag bbb faaa bbe aaaa bbe aaaf bbe aaaf bbc gaaad bbc daaag bbc faaa bbg faaa bb aaaa bb aaaf bb gaaad gbb daaag gbb daaa daab faaa daab aaaa daab aaaf gaab aaad aab gaaag aab daaag aae faaa aae aaaa aae aaaf aaf aaaf aaf gaaad aaa daaag aaa faaa aaa aaaa eaa aaaa eaa aaaf gbaa gaaad gbaa daaag cbaa faaa cbaag faaa cbaag aaaa ceaad aaaf aad gaaad aaf gaaag aaa daaa faa faaa faa aaaa daa aaaf daa aaad gaa gaaag aa daaag aa faaa aag aaaa aagaaaf aaaaaf aaaad aaag gf ``` <!-- end of image -->
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This image might have some surprises. Let's look for intersections carefully. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#a5482fff b,#361b47ff c,#b2d7b2ff d,#ad8a7aff e,#efefeaff f,#a0ca9eff g,#655b70ff ``` ```image dge bbbd bbb gbbb bbbf ebbb gbbb ddd bbbc aaa ebbb aaae gbbg aaae bbbe aaae cbbb aaae bbbg aaae bbbe aaae cbbb aaae bbbg aaae bbb aaae dbbb aaac bbbd aaac bbb aaac dbbb aaac bbbf aaac bbb aaac gbbb aaac bbbc aaad ebbb aaad gbbb daad bbbe daad ebbb daad bbbg daad bbbe daad cbbb daad bbbg daad bbb daad fbbb daad bbbd daad bbb daad dbbb daad bbbd daad bbb daaa gbbb caaa bbbc caaa ebbb caaa gbbb caaa bbbc caaa ebbb caaa gbbg caaa bbbe caaa cbbb eaaa eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbgeeeee eaaa fffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffe eaaa fcccccccccccccccccccccccccccccccccccccccccccccccccccccdbbbcccccfe eaaa fcccccccccccccccccccccccccccccccccccccccccccccccccccccbbbgcccccfe eaaa fcccccccccccccccccccccccccccccccccccccccccccccccccccccbbbccccccfe eaaa fccccccccccccccccccccccccccccccccccccccccccccccccccccgbbbccccccfe eaaa fccccccccccccccccccccccccccccccccccccccccccccccccccccbbbgccccccfe eaaa fccccccccccccccccccccccccccccccccccccccccccccccccccccbbbcccccccfe eaaa fcccccccccccccccccccccccccccccccccccccccccccccccccccgbbbcccccccfe aaa fcccccccccccccccccccccccccccccccccccccccccccccccccccbbbdcccccccfe aaa fcccccccccccccccccccccccccccccccccccccccccccccccccccbbbccccccccfe aaa fccccccccccccccccccccccccccccccccccccccccccccccccccgbbbccccccccfe aaa fccccccccccccccccccccccccccccccccccccccccccccccccccbbbdfddafcccfe aaa fccccccccccccccccccccccccccccccccccccccccccccccfddaaaaaaaaaafccfe aaa fccccccccccccccccccccccccccccccccccccccfddaaaaaaaaaaaaaaaaaaafcfe aaa fccccccccccccccccccccccccccccccfddaaaaaaaaaaaaaaaaaaaaaaadaaaaffe aaa fccccccccccccccccccccccfddaaaaaaaaaaaaaaaaaaaaaaaabbbccccccaaaafe aaa fccccccccccccccfddaaaaaaaaaaaaaaaaaaaaaaaddfcccccbbbgcccccccaaaae aaa fccccccfddaaaaaaaaaaaaaaaaaaaaaaaddfcccccccccccccbbbfccccccccaaaae aaa eddaaaaaaaaaaaaaaaaaaaaaaaddfccccccccccccccccccccdbbbccccccccccaaaae aaaaaaaaaaaaaaaaaaaaaaaddfccccccccccccccccccccccccfgbbbbbgcccccccccccaaaae aaaaaaaaaaaaaaaddfcccccccccccccccccccccccccccdgbbbbbbbbbbccccccccccccfaaaae aaaaaaaddfcccccccccccccccccccccccccccccfgbbbbbbbbbbbbbbbgccccccccccccfeaaaae e fcccccccccccccccccccccccccccfgbbbbbbbbbbbbbbbbgfcccccccccccccccfeeaaaae fccccccccccccccccccccccdgbbbbbbbbbbbbbbbgdcccccccccccccccccccccfe eaaaae fccccccccccccccccfgbbbbbbbbbbbbbbbbgfccccccccccccccccccccccccccfe eaaaae fcccccccccccdgbbbbbbbbbbbbbbbgdfcccccccccccccccccccccccccccccccfe eaaaae fcccccfgbbbbbbbbbbbbbbbbgdcccccccccccccccccccccccccccccccccccccfe eaaaae ffgbbbbbbbbbbbbbbbbgfccccccccccccccccccccccccccccccccccccccccccfe eaaaa cgbbbbbbbbbbbbbbbgdccccccccccccccccccccccccccccccccccccccccccccccccfe eaaad bbbbbbbbbbbbbbbgdffffffffffffffffffffffffffffffffffffffffffffffffffffff ead bbbbbbbbbgde e bbbbgc e ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a5482fff b,#361b47ff c,#c1a4a5ff d,#867590ff e,#e0d0d1ff f,#ba7461ff g,#5d4466ff ``` ```image cbbbbbc dbbbbb bbbbbd cbbbbbc bbbbbd cbbbbbe gbbbbb ebbbbbd dbbbbbe gbbbbb ebbbbbb gbbbbbg ebbbbbbc dbbbbbbe bbbbbbg bbbbbbc bbbbbb bbbbbd cbbbbbc bbbbbd cbbbbbe eecffffe gbggaaaaaaaaaaaae eccffaaaaaaaaaaaaaaaaaae eeccffaaaaaaaaaaaaaaaaaaaaaaaaaa eeccffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaae eeccffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaae eeccfaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaafccee faaaaaaae eecffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffagbbbc faaaaaaa eecffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffcce dbbbbbe faaaaaa eccffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffcce bbbbbg faaaaa eccffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffcee ebbbbbc faaaa eeccffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffcee dbbbbb aaaa eeccffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaafccee bbbbbb faaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffccee edgbbbbbb fa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaffccee ecdgbbbbbbbbbd f aaaaaaaaaaaaaaaaaaaaaaffccee ecgbbbbbbbbbbbbbbc aaaaaaaaaaaaaaaffcce ecdgbbbbbbbbbbbbbbbbbbb aaaaaaaaffcce ecdgbbbbbbbbbbbbbbbbbbbbbbd affcee eddgbbbbbbbbbbbbbbbbbbbbbbbbbbd ecdgbbbbbbbbbbbbbbbbbbbbbbbbbbbgdce ecgbbbbbbbbbbbbbbbbbbbbbbbbbbbgdde ecdgbbbbbbbbbbbbbbbbbbbbbbbbbbggdce ecdgbbbbbbbbbbbbbbbbbbbbbbbbbbbgde ecdgbbbbbbbbbbbbbbbbbbbbbbbbbbbgdce ecgbbbbbbbbbbbbbbbbbbbbbbbbbbbgddc ecddgbbbbbbbbbbbbbbbbbbbbbbbbbbbdce ecdgbbbbbbbbbbbbbbbbbbbbbbbbbbbgdce cdgbbbbbbbbbbbbbbbbbbbbbbbbbbbgdee ecgbbbbbbbbbbbbbbbbbbbbbbbbbbbgddc gbbbbbbbbbbbbbbbbbbbbbbbbbbbdce bbbbbbbbbbbbbbbbbbbbbbbgdce bbbbbbbbbbbbbbbbbbgdce ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 The image features one single intersection point.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#a5482fff b,#361b47ff c,#cbaeadff d,#8e7e97ff e,#e9dcdbff f,#bf7e6dff g,#634e70ff ``` ```image dg bbbd bbb dbbb bbbc bbb gbbb ccc bbbc aaa ebbb aaa gbbg aaa bbbe aaae ebbb aaae bbbg aaae bbb aaae cbbb aaae bbbd aaae bbb aaae dbbb aaae bbbd aaac bbb aaac dbbb aaac bbbc aaac bbb aaac gbbb aaac bbbc aaac ebbb faac gbbb faac bbbe faac ebbb faaf bbbg faaf bbbe faaf cbbb faaf bbbg faaf bbb faaf cbbb faaf bbbd faaf bbb faaf dbbb caaf bbbd caaf bbb caaf dbbb caaa bbbc caaa ebbb caaa gbbb caaa bbbe caaa ebbb caaa gbbg caaa bbbe eaaa cbbb eaaa bbbg eaaa bbb eaaa cbbb eaaa bbbd eaaa bbb eaaa dbbb eaaa bbbd aaa bbb aaa dbbb aaa bbbc aaa bbb aaa gbbb aaa bbbcecffe aaa ecfaaaaaaaaaae aaa ecfaaaaaaaaaaaaaaaaaaae aaa ecfaaaaaaaaaaaaaaaaaaaaaaafaaaae aaa ecfaaaaaaaaaaaaaaaaaaaaaaafbbb aaaae aaa ecfaaaaaaaaaaaaaaaaaaaaaaafce bbbg aaaae aaa ecfaaaaaaaaaaaaaaaaaaaaaaafce bbbe aaaae aaa ecfaaaaaaaaaaaaaaaaaaaaaaafce cbbb aaaae aaaaaaaaaaaaaaaaaaaaaaafce edbbbbbd aaaae aaaaaaaaaaaaaaafce cgbbbbbbbbbb aaaae aaaaaaafce edgbbbbbbbbbbbbbbd aaaae e cdbbbbbbbbbbbbbbbgde eaaaae cgbbbbbbbbbbbbbbbgc eaaaa edbbbbbbbbbbbbbbbbde eaaaa cgbbbbbbbbbbbbbbbgc eaaaa edgbbbbbbbbbbbbbbbdc eaaaa edbbbbbbbbbbbbbbbbde eaaaa cgbbbbbbbbbbbbbbbgc eaaaf bbbbbbbbbbbbbbbde eac bbbbbbbbbgde e bbbbgc e ``` <!-- 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 need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#faee33ff b,#89dfe5ff c,#e9eb72ff d,#c3eff2ff e,#fdf9bdff f,#b1d7b1ff g,#97ca94ff ``` ```image d db bb bb bdb b b db b b b a db b ca bd b ea b b ae bb b aa b b ca db b a b b ac db b aa bd b ea b b ae bb b ac b b ca db b ea b b ae db b aa bd b ca b b a bb b ac b b aa db b ea bd b ae db b ac bd b ca b b ea bb bd ae b bd aa db bd ea bd bd ae db bd ac bd bd ca b bd ea bb bd ac b bd a db bd ea bd bd ac b bd a bd bd ea b bd ac bb bd a b bd ea db bd ac bd bd a b bbggggggggggggggggggggggggaggggg bd bbfffffffffffffffffffffffacfffff b bbfffffffffffffffffffffffaffffff bb dbffffffffffffffffffffffcaffffff b dbffffffffffffffffffffffacffffff db dbffffffffffffffffffffffafffffff bd dbfffffffffffffffffffffcafffffff b dbfffffffffffffffffffffacfffffff bd dbfffffffffffffffffffffaffffffff b dbffffffffffffffffffffcaffffffff db dbffffffffffffffffffffacffffffff b dbffffffffffffffffffffafffffffff db dbfffffffffffffffffffcafffffffff bd dbfffffffffffffffffffacfffffffff dbfffffffffffffffffffaffffffffff dbffffffffffffffffffcaffffffffff bbbbbbbbfffffffffffacffffffffff gfffffbbbbbbbbbbfffafffffffffff gffffffffffffbbbbbfabbbffffffff gfffffffffffffffffacfbbbbbbbbbbd gfffffffffffffffffaffffffffffbbbbbbbbbdd gffffffffffffffffcaffffffffffff ddbbbbbbbdd gffffffffffffffffacffffffffffff ddbbbbbbb gfffffffffffcaaaaafffffffffffff d gfffccaaaaaaaccffffffffffffffff eecaaaaaaaccfffffffffffffffffffffff ecaaaaaaacegffffffffffffffffffffffffffffff ecaaaaaaace gffffffffffffffffffffffffffffff eecaaaaaaace gffffffffffffffffffffffffffffff aaaacee gffffffffffffffffffffffffffffff gffffffffffffffffffffffffffffff gffffffffffffffffffffffffffffff gffffffffffffffffffffffffffffff ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#faef31ff b,#86dfe7ff c,#fbf47eff d,#a7e7eaff e,#fdf9c1ff f,#d2f2f5ff g,#faf04aff ``` ```image bd eaae bd caa bd aac bd eaae bd cag bd aac bd eaae bd cag bd aac bd eaae bd cag bd aac bd eaae bd cag bd aac bb eaae bb cag bb aac bb eaae bb cag bb aac bb eaae bb cag bb aac bb eaae bb cag bb aac bb eaae bb cag bb aac bbf eaae bbbbbbddfff cag bbbbbbbbbbbbbdddff aac fffddbbbbbbbbbbbbbbddfff eaae fffddbbbbbbbbbbbbbbddfff cag fffdddbbbbbbbbbbbbbddaac fffddbbbbbbbdaadbbbddfff fffdcagbbbbbbbbbbbbddfff aac ffdddbbbbbbbbbbbbbddd eaae fffddbbbbbbbbb cag fffddb aac eaae cag aac eeecgaae eeccggaaaaaaag eeeccgaaaaaaaaaaaaggce eeccggaaaaaaaaaaaagcceee eeccgaaaaaaaaaaaaggccee aaaaaaaaaaagcccee aaaagccee ee ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#fbef32ff b,#87dfe7ff c,#fcf58bff d,#abe8edff e,#fdf9c3ff f,#d2f2f5ff g,#fbf262ff ``` ```image f fb bb bb bdb b b db b b b a fb b ga bf b ea b b ae bd b ag b b ca db b a bf b ac fb b aa bf b ea b b ae bd b ag b b ga db b ea bf b ae fb b aa bf b ca b b a bd b ac b b ga db b ea bf b ae fb b ag bd bf ga b bf ea bb bf ac b bf aa db bf ca bf bf ae fb bf ag bd bf ga b bf ea db bf ag b bf a fb bf ea bf bf ac fb bf a bd bd ea b bd ac db bd a b bd ea fb bd ac bf dd a fb dd ea bd dd ac b dd a db dd ea b dd ac fb dd a bf dd ea b db ac bd db a b db ea db db ac b fb a fb fb ea bf fb ac fb a fb ea bbbbbbddf ac fdbbbbbbbdff a ffdbbbdabbdf acfddbbbbbbbdf a fdbbbbbbbdff ea ffdbbbbbbbdf ac fddbbbbbb ecgaaaa f ecaaaaaaagce ecgaaaaaaace ecgaaaaaagce ecaaaaaaage ecgaaaaaagce aaaagce ``` <!-- end of image -->
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Let's examine this image for potential line intersections. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#ec2e1bff b,#043cabff c,#f69f97ff d,#5f85c2ff e,#e95f4eff f,#add4afff g,#e8d7ddff ``` ```image c eaa aaae aaaa aaaac gaaaaa caaaaa eaaaaae aaaaaaa aaagaaac aaa eaaa aaa aaa aaa aaae gaaa caaa caaa aaac eaae eaaa aaac aaa aaag aaae aaa caaa aaa aaac aaa eaaa ggccccec caaa aaa eeeaaaaaaaaaaaaaaaaaaaaaaag caaa aaae aaaaaaaaaaaaaaaaaaaaaaaaaae eaae caaa aaaaaaaaaaaaaaaaaaaaaaaaaaa aaac aaac eeccccgg aaa aaag eaaa aaa aaa aaa aaag aaa aaae aaac gaaa caaa eaae caaa aaae caaa eaae caaag aaa aaac aaaa aaa aaag aaae aaag aaa caaag aaac aaa aaaa caaa aaa aaae gaaagaaa caaag aaacaaa faaaafffffffffffffffffff aaaeaae ffaaaeffffffffffffffffff g aaaaaac ffeaaaffffffffffffffffff dbb eaaaaag fffaaaafffffffffffffffff dbbbbg caaaaa ffffaaaeffffffffffffffff dbbbbbbf gaaaaa ffffeaaaffffffffffffffffdbbbbbbd aaaaa fffffaaaafffffffffffffdbbbbbbd aaaaa ffffffaaaefffffffffffbbbbbbd bb aaaaa ffffffeaaafffffffffbbbbbbd fbbbd eaaae fffffffaaaaffffffbbbbbbb dbbbbbg caaac ffffffffaaaefffbbbbbbbff dbbbbbbd aaag ffffffffeaaafbbbbbbbffff dbbbbbbbbg aaa fffffffffaaaabbbbbffffff dbbdgbbbbbb aaa fffffffffdaaaabbdfffffff dbbd dbbbbbg fffffffdbbeaaadfffffffff bbbd bbbbbb ffffffbbbbbaaaafffffffff bbbd dbbbbbf fffffbbbbbdfaaaeffffffff bbbd bbbbbb ffffdbbbbfffeaaaffffffff bbbd dbbbbbf ffffbbbdfffffaaaafffffff bbbf bbbbbb ffffbbbfffffffaaaeffffff bbbf fbbbbbd fffdbbbfffffffeaaaffffff bbbf bbbbbb fffbbbdffffffffaaaafffff bbbg gbbbbbd fffbbbffffffffffaaaeffff bbbg bbbbbb ffbbbbffffffffffeaaaffff bbbg gbbbbbd ffbbbdfffffffffffaaaafff bbbg dbbbbbg ffbbbfffffffffffffaaaeff bbb gbbbbbd fbbbbfffffffffffffeaaaff dbbbbbg fbbbfffffffffffffffaaaaf bbbbbb dbbbffffffffffffffffaaae dbbbbbg bbbd eaaa bbbbbb bbb aaaa dbbbbbf dbbb gaaae bbbbbb bbbd eaaa fbbbbbd bbb aaaa bbbbbb dbbb gaaae fbbbbbd bbbf eaaa bbbbbbfbbb aaaa gbbbbbbbb gaaac dbbbbbg eaaa gbbbb aaaa dbg gaaac eaaa aaaa gaaac eaa c ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#ec2f1cff b,#023babff c,#f8b7b0ff d,#3c5fb4ff e,#f06d61ff f,#809bd2ff g,#c1cfeaff ``` ```image eaaaaaaac aaaaaaae caaaaaaac eaaaaaaac aaaaaaae caaaaaaac eaaaaaaac aaaaaaae caaaaaaac eaaaaaaac aaaaaaae caaaaaaac eaaaaaaac aaaaaaae caaaaaaac gd eaaaaaaa gdbb aaaaaaae gdbbbb caaaaaaac gdbbbbbb eaaaaaaa fbbbbbbbb aaaaaaae fbbbbbbbbbb caaaaaaac fbbbbbbbbbbbb eaaaaaaa fbbbbbbbbbbbbbf aaaaaaae fdbbbbbbbbbbbbf caaaaaaac gdbbbbbbbbbbbbf eaaaaaaa gdbbbbbbbbbbbbf aaaaaaaabbbbbbbbbbbbdg caaaaaaadbbbbbbbbbdg eaaaaaaabbbbbbbdg faaaaaaaabbbbdg fbbdaaaaaaadbdf fbbbbbaaaaaaaaf fdbbbbbbbaaaaaaae gdbbbbbbbbbdaaaaaaac gbbbbbbbbbbbbeaaaaaaa dbbbbbbbbbbdg aaaaaaae bbbbbbbbbdg caaaaaaac fbbbbbbbdg eaaaaaaa dbbbbbbg aaaaaaae gbbbbbbd caaaaaaac fbbbbbbg eaaaaaaa dbbbbbb aaaaaaae gbbbbbbf caaaaaaac fbbbbbbg eaaaaaaa bbbbbbd aaaaaaae gbbbbbbf caaaaaaac dbbbbbbg eaaaaaaa bbbbbbd aaaaaaae fbbbbbbf caaaaaaac dbbbbbb eaaaaaaa gbbbbbbd aaaaaaae fbbbbbbg caaaaaaac dbbbbbb eaaaaaaa gbbbbbbf aaaaaaae fbbbbbbg caaaaaaac bbbbbbd eaaaaaaa gbbbbbbf aaaaaaae dbbbbbbg caaaaaaac ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#ec2e1bff b,#033cabff c,#f6a69eff d,#5178c4ff e,#f1685aff f,#9fb3deff g,#eedee2ff ``` ```image c aaa aaae aaaa aaaac gaaaaa caaaaa eaaaaae aaaaaaa aaacaaac aaa eaaa aaa aaa aaa aaae gaaa caaa caaa aaac eaae eaaa aaac aaa aaag aaae aaa caaa aaa aaac aaa eaaa gggccceec caaa aaa eeeaaaaaaaaaaaaaaaaaaaaaaag eaaa aaae aaaaaaaaaaaaaaaaaaaaaaaaaae eaae caaa aaaaaaaaaaaaaaaaaaaaaaaaaaa aaac aaac eeecccggg gaaa aaag eaaa aaa aaa aaa aaag aaa aaae aaac gaaa caaa eaae caaa aaaa caaa eaae caaag aaa aaac aaaa aaa aaac aaae aaag aaa caaag aaae aaa aaaa eaaa aaa aaae gaaagaaa caaag aaacaaa aaaa aaaeaae aaae g aaaaaac caaag dbb aaaaaag aaaa dbbbbf caaaaa aaae dbbbbbbf gaaaaa eaaag fbbbbbbf aaaaa aaaa fbbbbbbd aaaaa aaae gbbbbbbd bb aaaaa eaaag gbbbbbbd fbbbd eaaae aaaa bbbbbbb dbbbbbg caaac aaae bbbbbbb dbbbbbbd aaag eaaagdbbbbbbg dbbbbbbbbg aaa aaaabbbbbg dbbdgbbbbbd aaa daaaabbf dbbd dbbbbbf fbbaaaaf dbbd bbbbbb gbbbbbaaaa bbbd dbbbbbf bbbbbdgaaae bbbf bbbbbb fbbbd eaaag bbbf fbbbbbf bbbd aaaa bbbf bbbbbb bbb gaaae bbbf fbbbbbf dbbb eaaag bbbf bbbbbb bbbf aaaa bbbf fbbbbbd gbbb gaaae bbbg bbbbbbg dbbb eaaag bbbg gbbbbbd bbbf aaaa bbbg dbbbbbg fbbb gaaae bbb gbbbbbd bbbb eaaag dbbbbbg bbbg aaaa bbbbbb fbbb gaaae dbbbbbf bbbd eaaa bbbbbb bbb aaaa fbbbbbf dbbb gaaae bbbbbb bbbf eaaa fbbbbbf gbbb aaaa bbbbbb dbbb gaaae fbbbbbd bbbf eaaa bbbbbbfbbb aaaa gbbbbbbbb gaaae dbbbbbg eaaa gbbbb aaaa dbg gaaae eaaa aaaa gaaac eaa c ``` <!-- end of image -->
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This image seems promising for intersection detection. There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#f1387aff b,#8ea7ebff c,#f0c3dcff d,#b1d7b1ff e,#476debff f,#e9779cff g,#95c997ff ``` ```image ca af a c a a fc a cf c a f a a cc f f c a a f a c c a f a a cc f f c a ac f fafc f cfaf a caac f faac dggggggggggggggggg cc cfafc gddddddddddddddddd dggggggggggggggagggggggd caaf gddddddddddddddddd gddddddddddddddadddddddg caac gddddddddddddddddd gddddddddddddddfdddddddg fafc gddddddddddddddddd gdddddddddddddfddddddddg cfafddddddddddddddddd gdddddddddddddaddddddddg gfaafddddddddddddd gdddddddddddddfddddddddg gddddfaafddddddddd ebddddddddddddfdddddddddg gddddddddfafdddddd gedddddddddddadddddddddg gddddddddddddadddd gdbedddddddddadddddddddg gddddddddddddddddd gdddebdddddddfdddddddddg gddddddddddddddddd gdddddegddddfddddddddddg gddddddddddddddddd gddddddbedddaddddddddddg gddddddddddddddddd gddddddddeedfddddddddddg gddddddddddddddddd gddddddddddebddddddddddg gddddddddddddbdddd gddddddddddagedddddddddg gddddddddddddedddd gddddddddddaddbedddddddg gdddddddddddggdddd gddddddddddfddddebdddddg e gdddddddddadddddddeddddg b gdddddddddaddddddddbeddg b gdddddddddfddddddddddeeg e gddddddddfdddddddddddddeb cc gddddddddadddddddddddddgce e gddddddddadddddddddddddg be b gddddddddddddddddddddddg eb b gdddddddaddddddddddddddg e e gdddddddaddddddddddddddg be b gdddddddfddddddddddddddg eb e f ec e a be b f be e cc eb b a ce e a be e c eb b f ec e a be b f eb e c eb e a ce b a be e c eb b f e b a be e f eb cc c ece a bb a cc f a f f a f cc a ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f33c7dff b,#748defff c,#fabfd4ff d,#d5ddfaff e,#4469edff f,#f67eaaff g,#a6b8f6ff ``` ```image af cac ca ff ac cac fa af cac fa af ac g ca eed fa dbebd af geeg cac geeg fa dbebd af deeb ac geeg ca beed fa dbebd af geeg cac geeg fa dbebd af deebac geeg fbebd afdbebd cac geeg fa beed af dbebd cac geeg fa geeg ff dbebd ac deeb ca geeg fa beed af dbebd cac gee fa g af ac ca fa af cac fa af ac ca fa ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Time for a closer look at another area. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#f33579ff b,#9fb2f5ff c,#fab1cbff d,#f784adff e,#4369edff f,#f55c92ff g,#f8ddeaff ``` ```image adcg dfaafdc gcdaaafcg gcfaaadcg cdfaafdc gcdaaafdg gcfaaafcg gdfaaadg cdfc bg geb be eb ``` <!-- end of image --> Area B doesn't meet the criteria for an intersection. Answer: A: 1; B: 0; 1 + 0 = 1 There's only one, but is an intersection after all.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#f3377aff b,#859df3ff c,#f99fbfff d,#c5d0f9ff e,#466cedff f,#f56c9dff g,#fbcfdfff ``` ```image ga af a c a a cg a gf c a f a a gg f f c a a f a c cg a f a a gg f f c a ac c fafg c gfaf a caac f caag gg gfafg a gaac a caac c fafg f gfaf a caac f caag eb cg gfafg ded a ga be a eb c ed f de a bb f ed d ade e a be dd gg eb e f ed b a de b c eb e c ed dd a de e f be b gg eb b f ded e a be dd c eb e c ed e a de b f bb e gg ed d a de e a be e c eb d f ed e a de b f bb e c ed e a de dd a be e gc eb b f ded b a be e f eb dd c ede a db a gg f a c c a f gg a ``` <!-- end of image -->
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I'm optimistic that I'll find some intersections in this image. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#8046f0ff b,#a2ea57ff c,#cdb6f9ff d,#b2d8b0ff e,#9e81e5ff f,#edf1eeff g,#98cb93ff ``` ```image fdb fdbbbbbbb dbbbbbbbbbbbbbf fdbbbbbbbbbbbbbbbbbbf fdbbbbbbbbbbbbbbbbbbdf fdbbbbbbbbbbbbbbbbbbdf dbbbbbbbbbbbbbbbbdf dbbbbbbbbbbbbd fbbbbbbbdf bbbb bbbbf bbbbd bbbbd dbbbb fbbbb fbbbb bbbbf bbbbf bbbbd dbbbb dbbbb fbbbb aaa bbbb eaaa bbbbf ffffffaaaaffffffffffff bbbbd gdddddaaaaaedddddddddddbbbbb gddddaaaaaaeddddddddddgbbbb gdddeaaaaaaaddddddddddbbbb gdddaaaaeaaadddddddddbbbb gddaaaaddaaaddddddddbbbbf gdeaaaeddaaadddddddbbbbg gdaaaadddaaaddddddbbbbbg gaaaaddddaaadddddbbbbbdg aaaadddddaaaedddgbbbbddg eaaaedddddaaaedddbbbbdddg faaaaddddddeaaaddbbbbddddg aaaadddddddeaaadbbbbdddddg fae aaaadddddddddaaabbbbgdddddg aaaa caaaedddddddddaagbbbbddddddg eaaaaaa aaaagdddddddddagbbbbdddddddg faaaaaaf aaaa gdddddddddebbbbddddddddg aaaaaac eaaac gdddddddddbbbbdddddddddg eaaaaaa faaaa gddddddddbbbbedddddddddg caaaaaaf aaaa gdddddddbbbbeadddddddddg aaaaaac aaaaf gddddddbbbbgaadddddddddg eaaaaae caaac gdddddbbbbbaaadddddddddg caaaaaa caa gddddgbbbbdaaadddddddddg faaaaaac gddddbbbbddaaadddddddddg aaaaaae gdddbbbbdddaaadddddddddg caaaaaa gddbbbbddddaaadddddddddg faaaaaaf gdbbbbgddddaaaeddddddddg aaaaaae gbbbbbdddddaaaeddddddddg eaaaaaa gbbbbddddddeaaaddddddddg caaaaaaf fbbbbdddddddeaaaddddddddg aaaaaac bbbbdddddddddaaaddddddddg eaaaaae bbbbddddddddddaaaddddddddg aaaaaa bbbbgddddddddddaaaddddddddg aaaaac bbbbbdddddddddddaaaddddddddg aaaae dbbbbgdddddddddddaaaedddddddg faaaac fbbbb fffffffffffaaaefffffff faaaac bbbb eaaa faaaac bbbbf caaa faaaac bbbbf faaa faaaac fbbbd aaa caaaac fbb aaa caaaaf aaaf caaaaf aaac caaaaf aaae caaaaf eaaa caaaaf caaa caaaaf faaa eaaaa aaa eaaaa aaa eaaaa aaaf eaaaa aaac eaaaa aaae eaaaa eaaaeaaaa caaaaaaa caaaaaa aaaaa aaaa aaa ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#8045f0ff b,#a2ea56ff c,#bda0f6ff d,#bced89ff e,#9b73ecff f,#dcccf9ff g,#def7c4ff ``` ```image eaaaaaaaaaf caaaaaaaaaac faaaaaaaaaaac d aaaaaaaaaaaae gb eaaaaaaaaaaaae gbb caaaaaaaaaaaaaa gbbb faaaaaaaaeaaaaaa bbbb eaaaaaaafcaaaaaaf dbbbb caaaaaaac faaaaaaf dbbbbb faaaaaaae faaaaaac dbbbbbb aaaaaaaa aaaaaac gbbbbbbb eaaaaaaaf aaaaaae gbbbbbbbb caaaaaaac eaaaaae gbbbbbbbbg faaaaaaae eaaaaaa bbbbbbbbd aaaaaaaaf caaaaaa dbbbbbbbd eaaaaaaac caaaaaa dbbbbbbbb caaaaaaae faaaaaaf gbbbbbbbb faaaaaaaa faaaaaaf gbbbbbbbbg eaaaaaaaf aaaaaac gbbbbbbbbg aaaaaaac aaaaaac bbbbbbbbd aaaaaae eaaaaae dbbbbbbbd aaaaaa eaaaaae dbbbbbbbd aaaaaf caaaaaa dbbbbbbbb aaaac caaaaaa gbbbbbbbbg aaae faaaaaafgbbbbbbbbg aaaf faaaaaafbbbbbbbbg aac aaaaaabbbbbbbbd ae aaaaabbbbbbbbd a aaaadbbbbbbbb f eaaebbbbbbbb eaebbbbbbbbg cebbbbbbbbg cbbbbbbbbd dbbbbbbbd dbbbbbbbb dbbbbbbbbc gbbbbbbbbee gbbbbbbbbeae bbbbbbbbeaaa bbbbbbbbdaaaa dbbbbbbbbaaaaaf dbbbbbbbbaaaaaaf gbbbbbbbbfaaaaaac gbbbbbbbbg aaaaaac gbbbbbbbbg aaaaaae bbbbbbbbd eaaaaae dbbbbbbbd eaaaaaa dbbbbbbbb caaaaaa gbbbbbbbb caaaaaaf gbbbbbbbbg faaaaaaf gbbbbbbbbg faaaaaac bbbbbbbbd aaaaaac dbbbbbbbd aaaaaae dbbbbbbbd eaaaaae dbbbbbbbb eaaaaaa gbbbbbbbbg caaaaaa gbbbbbbbbg caaaaaa bbbbbbbbg faaaaaaf bbbbbbbd faaaaaaf bbbbbbd aaaaaac bbbbbb aaaaaac bbbbb eaaaaae bbbbg eaaaaae bbbg caaaaaa bbd caaaaaa bd faaaaaaf d faaaaaaf ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Answer: A: 1; 1 = 1 I have found one intersection!
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#8045f0ff b,#a2ea56ff c,#c5abf7ff d,#c6f297ff e,#a179f0ff f,#e5dafbff g,#e6f9d3ff ``` ```image gdb gdbbbbbbb gdbbbbbbbbbbbbg gdbbbbbbbbbbbbbbbbbdg gdbbbbbbbbbbbbbbbbbbdg dbbbbbbbbbbbbbbbbbbdg dbbbbbbbbbbbbbbbbdg dbbbbbbbbbbbdg gbbbbbbbdg bbbb bbbbg bbbbg bbbbd dbbbb gbbbb bbbb bbbb bbbbg bbbbd dbbbb gbbbb gbbbb aaa bbbb eaaa bbbbg faaaaf bbbbd aaaaac dbbbd aaaaaae dbbbb caaaaaaa gbbbb aaaacaaa bbbb aaaa faaa bbbb eaaac aaa bbbbg faaae aaa bbbbd aaaa aaaf dbbbb aaaa aaac gbbbb caaac aaae bbbb faaaa eaaa bbbb aaaa caaa bbbbg fae aaaaf faaabbbbd aaaa caaae aabbbbd caaaaaa aaaa aebbbb faaaaaaf aaaa abbbb aaaaaac eaaac bbbb eaaaaae faaaa bbbbc faaaaaaf aaaa bbbbee aaaaaac aaaa bbbbbaa eaaaaae caaac dbbbbaaa caaaaaa faa gbbbb aaa faaaaaaf bbbb aaa eaaaaae bbbb aaa caaaaaa bbbbg aaaf faaaaaaf bbbbd aaac aaaaaac dbbbb eaae eaaaaaa gbbbb eaaa faaaaaaf gbbbb caaa aaaaaac bbbb faaa eaaaaae bbbbg aaa aaaaaa bbbbg aaa aaaaac bbbbd aaaf aaaae dbbbb aaac aaaac gbbbb aaae faaaac bbbb eaaa faaaac bbbb caaa faaaac bbbbg faaa faaaaf gbbbd aaa faaaaf gbb aaa faaaaf aaaf caaaaf aaac caaaaf aaae caaaaf eaaa caaaa caaa caaaa faaa eaaaa aaa eaaaa aaa eaaaa aaaf eaaaa aaac eaaaa aaae eaaaa eaaaeaaaa caaaaaaa faaaaaa aaaaa aaaa aaa ``` <!-- end of image -->
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I'm on the case! Let's uncover any intersections hidden in this image. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#5a0efbff b,#53a57bff c,#a083eeff d,#d4c3fcff e,#b0d7b1ff f,#7c49f2ff g,#93c798ff ``` ```image d aa caa a ac ac ca fa a da a ad ac af ca ca a a a ac ac fa ca da a ad a aa ac ca ca ad a af a fa ac da da ad a aa a da fc ad da bb af a bgbb egggggggggggggggggggfage ad ebe gbe geeeeeeeeeeeeeeeeeeeaeeg ff gb dbg geeeeeeeeeeeeeeeeeeaceeg da bb bb geeeeeeeeeeeeeeeeeaaeeeg a bb gbgeeeeeeeeeeeeeeeecaeeeeg ad a bb ebbeeeeeeeeeeeeeeeaeeeeeg ff a bg gbbeeeeeeeeeeeeeafeeeeeg da ad gebbeeeeeeeeeeefaeeeeeeg a ad geegbgeeeeeeeeeaeeeeeeeg ad ad geeeebbeeeeeeeaceeeeeeeg ff dac geeeeebbeeeeeaaeeeeeeeeg da cac geeeeeegbgeecaeeeeeeeeeg a cac geeeeeeeebbeaeeeeeeeeeeg ad faf geeeeeeeeebbfeeeeeeeeeeg ff aaf geeeeeeeeeffbgeeeeeeeeeg da afa geeeeeeeeeaeebbeeeeeeeeg a aca geeeeeeeeaceeebbeeeeeeeg ad ada geeeeeeefaeeeeebbgeeeeeg ff ada geeeeeecaeeeeeeegbbeeeeg da ada geeeeeeageeeeeeeeebbeeeg a a a geeeeeafeeeeeeeeeeebbgeg ad da a geeeefaeeeeeeeeeeeeegbbg cf da a geeeeaeeeeeeeeeeeeeeeebb a cf a geeeaceeeeeeeeeeeeeeeeebb a ff a geefaeeeeeeeeeeeeeeeeeegebe ad ac a gecaeeeeeeeeeeeeeeeeeeeg bb ca ad a geageeeeeeeeeeeeeeeeeeeg bb a ad a gafeeeeeeeeeeeeeeeeeeeeg ebe a a a ca bb ac a a a bb ca a ad ac gbe a a ad fa bg a da ad d da bb ac da ac ad ad gbd ca ca ac ac af dbg a ff fc cf ca bb a fc ff da a gb gggggafggacggffgggg a ac ebg eeeeecaeeaeeefaeeee a fa bb eeeeeeaeeaeeecaeeee a da bb eeeeeeaeeaeeecaeeee ad ad ebe eeeeeeaceaeeecaeeee fc af bbeeeeeecaeaeeeeaeeee ca ca bbeeeeeeaeaeeeeaeeee da a gbgeeeeacaeeeeaeeee a ac eebbeeeaaaeeeeaeeee a fa eeebbeecafeeeeaeeee ada eeeegbgeafeeeeaeeee aad eeeeegbbaceeeeaeeee cf eeeeeeebbeeeeeaeeee eeeeeeeebbgeeeaeeee eeeeeeeeegbbeeceeee eeeeeeeeeeebbeeeeee eeeeeeeeeeeebbgeeee eeeeeeeeeeeeegbeeee geeeeeeeeeeeeeeeeee ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#5c11fbff b,#51a27bff c,#bea0fdff d,#e2e3f2ff e,#b3d7c4ff f,#8c58fcff g,#7fba9eff ``` ```image aaad faac caaf daaf faad caac daaf aaad faac bd caaf bbe daaf bbbg faad dgbbgd caac ebbbe daaf ebbbg aaad dgbbgd faac gbbbe caaf ebbbe daaa dbbbgd faad gbbbd caac ebbbe daaf dbbbg aaad gbbbd faac ebbbe caaf dbbbg daaa dgbbbd faad ebbbgaac ebbbbf dbbbbd fabbbbe caafebbbg daaa dgbbgd faad gbbbe caac ebbbe daaf dbbbgd aaad gbbbd faac ebbbe caaf dbbbg daaa gbbbd faad ebbbe caac dbbbg daaf dgbbbd faad ebbbe faac ebbbg caaf dgbb daaa gb faad e caac daaf faad faac caaf daaa faad caac ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Next up, a closer look at another region. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#590efbff b,#50a379ff c,#b290fcff d,#dcd6f7ff e,#b3d7c4ff f,#864efcff g,#7ab79bff ``` ```image daad aac faf aac aac faf faf daad caf caa daad caf daad daa caa aac caa caa faf caa caa caa caf caa daad faf caa aac faf daad faf fac daad d caa aac daad be daad aac daad bbg aacdaad daad gbbbd fafdaad aad ebbbe caacaad aac ebbbg daafaa aac gbbgd aaaaa aac ebbbe faaaf aac ebbbg caaaf fac dgbbgd daaaf fac gbbbe aaac faf ebbbe faac faf dgbbgcaac faf gbbbaad faf ebbbg faf dbbbg caf gbbbd caa ebbbe caa dbbbg dcd gbbbd ebbbe ebbbg gbbgd ebbbe ebbbd dge ``` <!-- end of image --> My analysis shows that the lines in area B do not cross. Answer: A: 1; B: 0; 1 + 0 = 1 It was tricky, but I finally found one single intersection in the image.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#5a0efcff b,#52a47bff c,#a57cfdff d,#dee0f0ff e,#c7aefdff f,#7e43fbff g,#92c5abff ``` ```image e aa caa adae ac ca fa a da a ae ac af ca ca a ad a ac ac fa ca da a ae a af ac ea ea ad a af a fa ac da ea ae a aa ad ea fc ad ea bb af a dbgbb ca ad dbg gbd da fc gbd dbg ae ea bb bb fa a bb gbd ea ad a bb dbg ad ff ad bg bb af ea ad bbd ca a ae dbg da ad ae bb ac ff dac bb fa da eac gbg ea a cac dbb ad ae faf bbf ff aaf cbbd da aff da dbb a aca ac bb ae aea fa gbd ff aea ea dbg da ada ad bb a a a af gbd ae da a ca dbg cf ea a da bb da cf a ac bbd a ff a fa gbg ae ac a ea bb cf ae a ae bb a ad a af gbg a a a ca dbb ae a a a bb ca a ad ac gbd a a ae fa dbb a da ae d ea bb ac ea ae ad ae gbd ca ca ac ac af dbg a ff fc cf ca bb a fc ff ea ad gbd ac ae cf a ac dbg ca ad cf a fa bb a a ca a da bbd a a ea ae ae gbg ac a ea fc af bb ea a da ca ca bb ada da da ad gbg aea a a ac dbb aaa a a fa bb eaf a aea gbd ac a aae dbgae a cf bb a gbd a dbg e bb gbd dbd ``` <!-- end of image -->
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This image seems promising for intersection detection. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#3e902aff b,#8576e3ff c,#b0d7b1ff d,#b3aaebff e,#63a552ff f,#e7ecedff g,#95c692ff ``` ```image f ag afa ge fa a gg af af ge a fdbbd a ge fbbbdf b af af fbbbdf b ge a bbbdf df a ca fd af ac b ce a b a fa df af eg b ce a b a fa caa b af eg feaag dd ce af gaaec b a a feaag b af gegaaef b ce eg dd a b ac b ce fffffffbffffffffffffaff fgcccccccbccccccccccagccg fccccccccbcccccccccgacccg fccccccccbcccccccccaccccg fccccccccbccccccccagccccg fcccccccccbccccccgacccccg fcccccccccbccccccaccccccg fcccccccccbcccccagccccccg fcccccccccddcccgacccccccg fccccccccccbcccaccccccccg fccccccccccbccagccccccccg fccccccccccbcgacccccccccg fccccccccccddaccccccccccg fcccccccccccagccccccccccg fccccccccccgacccccccccccg fccccccccccabcccccccccccg fcccccccccagcbccccccccccg fccccccccgaccbccccccccccg fccccccccacccbccccccccccg fcccccccagcccbccccccccccg fccccccgacccccbcccccccccg fccccccaccccccbcccccccccg fcccccagccccccbcccccccccg fccccgacccccccbcccccccccg fccccacccccccccbccccccccg fcccagcccccccccbccccccccg fccgaccccccccccbccccccccg ggagggggggggggbggggggggc ec b fa b a b ec fd fa b a b ec df fa fd a b eg b fa df a fb eg b fa b a dd eg b fa b a b eg dd fa bf a fdbbbbbdf fdbbbbbdd fdbbbbbddf fddbbbbddf fddbbbbbdf fddbbbbbdf fdbbb ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#41922dff b,#8372e3ff c,#c4ddbdff d,#a498ebff e,#81b575ff f,#eceef3ff g,#c7bff3ff ``` ```image gbg caa fbd faac bb eae dbf caaf gbg faac fbd eae bb caaf dbf faac gbg eae fbd caaf bbf faac dbg eae gbd caaf fbb faac dbf eae gbg caaf fbd faac bb eae dbf caaf gbg faac fbd eae bb caaf dbffaac gbgeae fbbaaf baac eae caad faabd eaedbf caafgbg faac gbd eae bb caaf dbf faac gbg eae fbd caaf bb aac dbf eae gbg caaf fbd aac bb eae dbg caaf gbg aac fbd eae bbf caaf dbg aac gbd eae fbb caaf dbf aac gbg eae fbd caaf bb ``` <!-- end of image --> I can confirm that 1 intersection exists in area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.
1
<!-- image --> ```palette Key,Color ,#fefefeff a,#3e902aff b,#8574e5ff c,#aacda1ff d,#afa4eeff e,#63a553ff f,#d5e7d1ff g,#d9d3f6ff ``` ```image ac afa ce a a ee af af ce a gdbbd a ce gbbbdg b af af gbbbd b ce a bbbd dg a ca gd af ac b ce a b a fa dg af ec b ce a b a fa caa b af ee feaac dg ce a caaef b a a feaac b af cecaaef b ce ec gd a b af b ce dg a gd af b ce b a dg af b ca b a b af dg fa b a b af b fa gda af fa ab ecgd fa b a b ec dg fa gd a b ec b fa dg a b ec b fa b a dd ec b fa b a b ec gd fa b a b ec dg fa gd a b ec b fa dg a b ec b fa b a dg ec b fa b a b ec gd fa bg a gdbbbbbdg gdbbbbbdg gdbbbbbdg gddbbbbddg ggdbbbbbdg gdbbbbbdg gdbbb ``` <!-- end of image -->
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I'm ready to tackle this image and find those intersections! It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#6b9144ff b,#95a3a5ff c,#cdd5caff d,#3d6c07ff e,#96c490ff f,#ecf1ecff g,#b1d6b1ff ``` ```image cbf bbbbf bbbbbb bb fbbbb cbc cbbbb bb cbbbg bb cbbbc bb gbbbc fbg bbbbc bbf bbbbf bb bbbbf bb fbbbbf fbb fbbbb cbc fbbbb bb cbbbb bb cbbb bb bbc cbc bb fae bbf gbb cda bb bbf ede bb cbb edg fbg bbc adc gbf bb adf bb gbb dd bb bbf dd bb fbb dd cbc bbc dd bb bb dd bb cbb dd bb bbf dd cbg fbb dd bbc dd bb cda cbb gda bbf ede fbb edg bbg adc bbc adf fbbf dd f cbb dd dd cbb dd dd gbb dd edd bbb geeeeeeeeeeeeeeeeeeeeedd ddd bbbegggggggggggggggggggggddf ddd bbbgggggggggggggggggggggddf ddd bbbggggggggggggggggggggddf gddd bbggggggggggggggggggggddf addd ebbggggggggggggggggggedaf dddd egbbgggggggggggggggggedaf dddd egbbbggggggggggggggggadaf cdadd eggbbbgggggggggggggggadef adcdd egggbbbggggggggggggggadef dd dd eggggbbbgggggggggggggddef dd dd egggggbbbggggggggggggddgf cda dd eggggggbbbgggggggggggddgf adg dd egggggggbbgggggggggggddgf dd dd eggggggggbbggggggggggddgf dd dd egggggggggbbeeeeeaaaaddgf fdd dd eeddddddddabbddddddddddgf ede dd gaddddddddddddbbbaaaaaeeeggf dd dd gaddddddaegggggggggbbbgggggggggf dd dd gaddddddac eggggggggggggbbbggggggggf dd dd gaddddddac egggggggggggggbbbgggggggf ede dd gaddddddac eggggggggggggggbbbggggggf ddf dd gaddddddac egggggggggggggggbbggggggf dd ddf caddddddac eggggggggggggggggbbgggggf dd adf caddddddac egggggggggggggggggbbggggf gda adf caddddddac eggggggggggggggggggbbgggf ddf adf caddddddac eggggggggggggggggggbbbggf dd adfcaddddddac egggggggggggggggggggbbbgf dd addddddac eggggggggggggggggggggbbbf gda eddac egggggggggggggggggggggbbb adc eggggggggggggggggggggggbbg dd egggggggggggggggggggggggbf dd egggggggggggggggggggggggf cda geeeeeeeeeeeeeeeeeeeeeee adg dd dd fdd eg ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5f8534ff b,#95a3a5ff c,#bcc7bcff d,#3d6c06ff e,#a2b888ff f,#dfe4dfff g,#7f9d61ff ``` ```image edd edd gdd gdd gdd c add bc add bbc ddd bbbc ddd bbbbf ddd bbbbbf fddd fbbbbbf fddd fbbbbb cddd fbbbbb cddd fbbbbc eddd cbbbbc eddd cbbbbc eddd cbbbbc gddd cbbbbf gddd bbbbbf addd bbbbbf addd fbbbbbf addd fbbbbb dddd fbbbbb dddd cbbbbc fddda cbbbbc fddda cbbbbc fdddg cbbbbf cdddg bbbbbf cdddg bbbbbf eddde fbbbbbf eddde fbbbbbffffccccceeeeeeggadddc fceggggaaaaaadabbbbbddddddddddddddddddddc fcgadddddddddddddddabbbbgdddddddddddddddddddf addddddddddddddddddddgbbbbgdddddddddddddddddg dddddddddddddddddddddagbbbbgggggeeeeeecccccf ddddddgecccfffff cbbbbf ddgef bbbbbf f bbbbbf fbbbbbf fbbbbb fbbbbb fbbbbc cbbbbc cbbbbc cbbbbf bbbbbf bbbbbf fbbbbbf fbbbbb fbbbbb fbbbbc cbbbbc cbbbbc cbbbbc bbbbbf bbbbb fbbbb fbbb fbb fb c ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.
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<!-- image --> ```palette Key,Color ,#fefefeff a,#688c3eff b,#95a2a4ff c,#cbd5c7ff d,#3d6c06ff e,#94ad77ff f,#e6e9e6ff g,#b2bfb0ff ``` ```image fbf bbbbf bbbbbb bb fbbbb cbc cbbbg bb cbbbg bb cbbbc bb gbbbc fbg gbbbc gbf bbbbf bb bbbbf bb bbbb fbb fbbbb cbc fbbbb bb cbbbg bb cbbb bb bbc cbc bb fae bbf gbg cde bb bb gde bb fbb edg fbg bbc adc gbf bb adf bb gbb dd bb bbf dd bb fbb dd cbc bbc dd bb bb dd bb gbb dd bb bbf dd fbg fbb dd bbc dd bb fda cbb cde bbf gde fbb edg bbg adc bbf adf fbbf dd fbb dd dd cbb dd dd gbb dd edd bbb dd ddd bbb dd ddd bbg dd ddd bbc dd gddd bbc fda addd fbbf cda dddd fbb gde dddd cbb ede cdadd gbb edg adcdd bbb adc dd dd bbb ad dd dd bbg dd cda dd bbg dd adg dd bbc dd dd dd fbbf dd dd dd fbbffccggeeedd fdd dd gadddddddabbdddddddddd ede dd gaddddddddddddebbaeeeggcc dd dd gaddddddac gbb dd dd gaddddddac bbb dd dd caddddddac bbg ede dd caddddddac bbg ddf dd caddddddac bbc dd ad caddddddac bbf dd adf caddddddac fbbf gde adf caddddddac cbb adf adf caddddddac gbb dd adfcaddddddac gbb dd addddddac bbb cda eddac bbb adc bbg dd bf dd cda adg dd dd fdd gg ``` <!-- end of image -->
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The hunt for intersections begins! Let's analyze this image closely. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#b8b43cff b,#60bf44ff c,#b1d7b0ff d,#b0a208ff e,#96cc8eff f,#e4e9c3ff g,#cfca75ff ``` ```image ffffcccceeeeef fbbbbbbbbbbbbbbbbf bbb bbc ebb bbe cbb bbb f fbbf da ebb fdf bbe dd cbb dd bbb fdg fbbf ad ebb dd bbe da cbb gdf bbb dd fbbf dd ebb fdg bbc ad cbb dd bbe ecedacccccccccccccccccce fbbf cccadcccccccccccccccccceebb ccccddcccccccccccccccccbbc cccccddccccccccccccccebb cccccgdgccccccccccccbbbe f ccccccddccccccccccebbece fdddg cccccccddccccccccbbbccce fddddgdd cccccccedaccccccbbecccce fddddg dd ccccccccadccccebbcccccce fddddg ad cccccccccddccbbbccccccce fddddg gd ccccccccccdabbecccccccce fddddg fd ccccccccccbbbcccccccccce fddddg d cccccccccbbddcccccccccce fddddg df cccccccebbccddccccccccce fddddg dg ccccccbbbcccedgcccccccce fddddg da ccccebbccccccadcccccccce fddddg dd cccbbbccccccccddccccccce fddddg ad ccbbeccccccccccdacccccce fddddg gd bbbccccccccccccadccccccefddddg gd bbbccccccccccccccddccceddddg fd cbbeccccccccccccccccdddddda d bbb cccccccccccccccccgddacce df fbbc ccccccccccccccccccccccce dg ebb eeeeeeeeeeeeeeeeeeeeeeec da be dd ad gd fd fd d df dg da dd ad gd fd d df df dg da dd ad gd fd d df dg dg da dd ad gd fd d df ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#bbb131ff b,#5fbe42ff c,#cae0a9ff d,#b0a106ff e,#8acf75ff f,#e8efd5ff g,#d0c86eff ``` ```image cdddf adda fdddg cdddc gdddf adda fdddg gdddf fb adda cbb fdddg febbb cdddc cbbbbe gdddf ebbbbc adda fbbbbef fdddc cbbbbe gdddf febbbbc adda cbbbbef fdddg ebbbbc cdddf fbbbbef adda ebbbbe fdddg febbbbc cdddc cbbbbe gdddf ebbbbc addabbbbef fdbbbbbe fbbbbbf cbbbbba febbbbaddg cbbbbefcdddc ebbbbc gdddf febbbbf adda cbbbbe fdddc febbbbc gdddf cbbbbef adda ebbbbc fdddg fbbbbbf cdddf cbbbbe adda febbbbc fdddg cbbbbef cdddc ebbbbc gdddf bbbbbf adda bbbe fdddg fga bbc gdddf fgaddd ef addagadddddd fdddddddddgf cdddddgf gagf ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 The image features one single intersection point.
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<!-- image --> ```palette Key,Color ,#fefefeff a,#b7ac24ff b,#5fbe42ff c,#cae0a9ff d,#b0a105ff e,#90d27cff f,#e7ebcbff g,#cfc66aff ``` ```image ffffcccceeeeef cbbbbbbbbbbbbbbbbf bbb fbbc ebb bbe cbb bbb f fbbc da ebb cdf bbe ad cbb dd bbe fdg fbbf gd ebb dd bbe da cbb gdf bbe dd fbbf da ebb fdc bbc ad cbb dd bbe dg fbbf gdf ebb dd bbc da cbb cdc bbe f ad fbbf fdddg dd ebb fadddgda fdg bbc fadddg ad gd ebb fadddg gd dd bbe fadddg cd dabbf fadddg fd bbb fadddg d bbad fadddg df ebb da fadddg dg bbe fdc fadddg dg cbbf ad fadddg da bbb dd fadddg ad fbbc dg fadddg gd ebb gdf fadddg cd bbe dd fadddg fd cbbf daadddg d bbb cddg df fbbc dg ebb da be dd ad gd cd fd d dc dg da dd ad gd cd fd df dc dg da dd ad gd fd d df dc dg da dd gd gd fd d df ``` <!-- end of image -->
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