| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, David, and Zoey. Penelope noted, \"David is a knight if and only if David is a knave\". David told you that Zoey is a knave if and only if Zoey is a knight. According to Zoey, \"If Penelope is a knave then David is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "David", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Penelope is a knave, David is a knave, and Zoey is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) David is a knave\n(3) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Penelope cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if David is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that David is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Zoey is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Penelope is a knave then David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('->', ('lying', 0), ('lying', 1)))", "index": 0} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Penelope, and Evelyn. \"Evelyn is a knight,\" Isabella declared. \"Isabella is a knave\" - Penelope. In a statement by Evelyn: \"Isabella is a knight or Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Penelope", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Isabella is a knight, Penelope is a knave, and Evelyn is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Penelope is a knave\n(3) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is a knight or Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('lying', 0), ('or', ('telling-truth', 0), ('telling-truth', 1)))", "index": 1} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jack, Sebastian, and James. According to Jack, \"James is a knight and Jack is a knight\". Sebastian commented, \"Jack is a knave and James is a knave\". James said, \"Sebastian is a knight if and only if Sebastian is a knave.\" So who is a knight and who is a knave?", "names": ["Jack", "Sebastian", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Jack is a knave, Sebastian is a knight, and James is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Sebastian is a knight\n(3) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that James is a knight and Jack is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Sebastian is a knave.", "James cannot be a knave, because this would contradict the claim of Jack that James is a knight and Jack is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight and Jack is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Sebastian is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jack is a knave and James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 0), ('lying', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))", "index": 2} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, David, and Jacob. According to Penelope, \"Jacob is a knight\". David said that Penelope is a knight or Penelope is a knave. Jacob said that David is a knight. So who is a knight and who is a knave?", "names": ["Penelope", "David", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Penelope is a knight, David is a knight, and Jacob is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) David is a knight\n(3) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Penelope is a knight or Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 1))", "index": 3} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Ethan, and Jackson. \"Jackson is a knave if and only if Jackson is a knight,\" Aurora mentioned. Ethan asserted: \"Aurora is a knight\". \"Ethan is a knave and Aurora is a knave\" - Jackson. So who is a knight and who is a knave?", "names": ["Aurora", "Ethan", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Aurora is a knave, Ethan is a knave, and Jackson is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Ethan is a knave\n(3) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Aurora cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Jackson is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Ethan is a knave and Aurora is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Aurora is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 0), ('and', ('lying', 1), ('lying', 0)))", "index": 4} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Riley, Jacob, and Avery. Riley asserted: \"If Avery is a knave then Jacob is a knave\". Jacob noted, \"Avery is a knave\". Avery told you that Avery is a knight or Riley is a knave. So who is a knight and who is a knave?", "names": ["Riley", "Jacob", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Riley is a knight, Jacob is a knave, and Avery is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Jacob is a knave\n(3) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that If Avery is a knave then Jacob is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight or Riley is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 1)), ('lying', 2), ('or', ('telling-truth', 2), ('lying', 0)))", "index": 5} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Amelia, and James. \"James is a knave\" - Olivia. Amelia expressed that Olivia is a knave. James stated, \"James is a knight if and only if Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Amelia", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Olivia is a knave, Amelia is a knight, and James is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Amelia is a knight\n(3) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Olivia that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight if and only if Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of James that James is a knight if and only if Amelia is a knight.", "We have exhausted all possibilities for Amelia and James, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that James is a knight if and only if Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('lying', 0), ('<=>', ('telling-truth', 2), ('telling-truth', 1)))", "index": 6} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Chloe, and Jacob. Owen said that Chloe is a knight and Jacob is a knight. Chloe remarked, \"Jacob is not a knight\". Jacob remarked, \"Chloe is a knave if and only if Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Chloe", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Owen is a knave, Chloe is a knave, and Jacob is a knight.", "solution_text_format": "(1) Owen is a knave\n(2) Chloe is a knave\n(3) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Chloe is a knight and Jacob is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of Chloe that Jacob is not a knight.", "Jacob cannot be a knave, because this would contradict the claim of Owen that Chloe is a knight and Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Owen that Chloe is a knight and Jacob is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Chloe is a knight and Jacob is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Owen that Chloe is a knight and Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('telling-truth', 2)), ('<=>', ('lying', 1), ('telling-truth', 2)))", "index": 7} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, Jackson, and Daniel. Mia told you that Daniel is a knight. Jackson was heard saying, \"Mia is a knight\". In a statement by Daniel: \"Jackson is a knight if and only if Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Jackson", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Mia is a knave, Jackson is a knave, and Daniel is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Jackson is a knave\n(3) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Jackson is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Mia that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Mia that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('telling-truth', 0), ('<=>', ('telling-truth', 1), ('lying', 1)))", "index": 8} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, James, and Sophia. Scarlett said, \"Sophia is not a knave.\" \"Scarlett is a knight if and only if James is a knight\" - James. According to Sophia, \"James is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "James", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Scarlett is a knight, James is a knight, and Sophia is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) James is a knight\n(3) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 1))", "index": 9} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Amelia, Lucas, and Aria. Amelia noted, \"Aria is a knave and Lucas is a knight\". Lucas told you that If Aria is a knave then Amelia is a knave. According to Aria, \"Aria is a knight and Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Lucas", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Amelia is a knave, Lucas is a knight, and Aria is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Lucas is a knight\n(3) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Aria is a knave and Lucas is a knight.", "Aria cannot be a knight, because this would contradict the claim of Amelia that Aria is a knave and Lucas is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight and Amelia is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that If Aria is a knave then Amelia is a knave.", "Lucas cannot be a knave, because this would contradict the claim of Amelia that Aria is a knave and Lucas is a knight.", "We have exhausted all possibilities for Lucas and Aria, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aria is a knave and Lucas is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight and Amelia is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Aria is a knave then Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 0)), ('and', ('telling-truth', 2), ('lying', 0)))", "index": 10} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Luke, Riley, and Elizabeth. \"Riley is a knight or Elizabeth is a knave,\" Luke mentioned. Riley said, \"Luke is a knight if and only if Elizabeth is a knave.\" \"Elizabeth is a knight,\" Elizabeth claimed. So who is a knight and who is a knave?", "names": ["Luke", "Riley", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Luke is a knight, Riley is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Riley is a knight\n(3) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Riley is a knight or Elizabeth is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Luke is a knight if and only if Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Riley that Luke is a knight if and only if Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('telling-truth', 2))", "index": 11} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Matthew, and Sebastian. \"Sebastian is not a knight,\" James mentioned. Matthew expressed that James is a knave if and only if Sebastian is a knight. Sebastian told you that James is a knight and Sebastian is a knight. So who is a knight and who is a knave?", "names": ["James", "Matthew", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "James is a knight, Matthew is a knight, and Sebastian is a knave.", "solution_text_format": "(1) James is a knight\n(2) Matthew is a knight\n(3) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of James that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight and Sebastian is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that James is a knave if and only if Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 2)))", "index": 12} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Jackson, and Matthew. As Charlotte put it, \"Jackson is a knight and Matthew is a knave\". In Jackson's words: \"Matthew is a knave\". \"Jackson is a knave if and only if Matthew is a knight\" - Matthew. So who is a knight and who is a knave?", "names": ["Charlotte", "Jackson", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Charlotte is a knave, Jackson is a knave, and Matthew is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Jackson is a knave\n(3) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knight and Matthew is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Charlotte that Jackson is a knight and Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Charlotte that Jackson is a knight and Matthew is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jackson is a knight and Matthew is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Jackson that Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of Charlotte that Jackson is a knight and Matthew is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('lying', 2), ('<=>', ('lying', 1), ('telling-truth', 2)))", "index": 13} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, Lily, and Mason. Scarlett noted, \"Mason is a knave\". \"Scarlett is not a knave,\" Lily claimed. In a statement by Mason: \"Scarlett is a knave and Lily is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Lily", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Scarlett is a knight, Lily is a knight, and Mason is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Lily is a knight\n(3) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Scarlett that Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Scarlett is a knave and Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Scarlett is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 1)))", "index": 14} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, Emma, and Lucas. Chloe expressed that Chloe is a knight or Lucas is a knave. \"Chloe is a knight and Lucas is a knight,\" Emma declared. \"Emma is a knight or Chloe is a knight,\" Lucas claimed. So who is a knight and who is a knave?", "names": ["Chloe", "Emma", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Chloe is a knight, Emma is a knight, and Lucas is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Emma is a knight\n(3) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight or Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emma is a knight or Chloe is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knight and Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('telling-truth', 0)))", "index": 15} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Jack, and Oliver. Avery said that Jack is a knight if and only if Oliver is a knave. Jack asserted: \"Avery is a knave or Oliver is a knave\". Oliver asserted: \"Jack is a knave if and only if Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Jack", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Avery is a knight, Jack is a knave, and Oliver is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Jack is a knave\n(3) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Jack is a knight if and only if Oliver is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Avery is a knave or Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Avery that Jack is a knight if and only if Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Jack is a knave if and only if Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Avery is a knave or Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Jack is a knave if and only if Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 2)), ('or', ('lying', 0), ('lying', 2)), ('<=>', ('lying', 1), ('telling-truth', 2)))", "index": 16} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, Aiden, and Amelia. Penelope expressed that Amelia is not a knave. As Aiden put it, \"Aiden is a knight\". \"Penelope is a knave and Aiden is a knight,\" Amelia declared. So who is a knight and who is a knave?", "names": ["Penelope", "Aiden", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Penelope is a knave, Aiden is a knave, and Amelia is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Aiden is a knave\n(3) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Aiden is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Penelope that Amelia is not a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Penelope that Amelia is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Penelope is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Amelia that Penelope is a knave and Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('telling-truth', 1), ('and', ('lying', 0), ('telling-truth', 1)))", "index": 17} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, David, and Liam. According to Scarlett, \"Liam is a knave if and only if Liam is a knight\". David stated, \"If Scarlett is a knave then Liam is a knave\". Liam stated, \"Scarlett is not a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "David", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Scarlett is a knave, David is a knight, and Liam is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) David is a knight\n(3) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Scarlett cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Liam is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Assume David is a knight. No contradiction is found in their claim that If Scarlett is a knave then Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('->', ('lying', 0), ('lying', 2)), ('not', ('lying', 0)))", "index": 18} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Chloe, and Lucas. \"Chloe is a knave if and only if Lucas is a knave\" - Charlotte. In a statement by Chloe: \"Charlotte is not a knight\". In Lucas's words: \"Charlotte is not a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Chloe", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Charlotte is a knight, Chloe is a knave, and Lucas is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Chloe is a knave\n(3) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Lucas is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Charlotte that Chloe is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Charlotte is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 2)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 0)))", "index": 19} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sofia, Matthew, and Benjamin. Sofia noted, \"If Benjamin is a knave then Matthew is a knight\". Matthew noted, \"Benjamin is a knave and Benjamin is a knight\". Benjamin remarked, \"Matthew is a knight and Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Matthew", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Sofia is a knave, Matthew is a knave, and Benjamin is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Matthew is a knave\n(3) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Benjamin is a knave then Matthew is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Matthew is a knight and Benjamin is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Benjamin is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Benjamin that Matthew is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Matthew is a knight and Benjamin is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Benjamin is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Sofia that If Benjamin is a knave then Matthew is a knight.", "We have exhausted all possibilities for Matthew and Benjamin, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Matthew is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Sofia that If Benjamin is a knave then Matthew is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Matthew is a knight and Benjamin is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Sofia that If Benjamin is a knave then Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Benjamin is a knave and Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 2)))", "index": 20} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sofia, Jack, and Olivia. Sofia said, \"Olivia is not a knave.\" \"Olivia is a knight and Olivia is a knave\" - Jack. Olivia told you that Olivia is a knight or Jack is a knave. So who is a knight and who is a knave?", "names": ["Sofia", "Jack", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Sofia is a knight, Jack is a knave, and Olivia is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Jack is a knave\n(3) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight or Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Olivia is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Olivia is a knight and Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 1)))", "index": 21} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Penelope, and Daniel. According to Lucas, \"Daniel is a knight if and only if Penelope is a knight\". Penelope was heard saying, \"Lucas is a knight\". Daniel said, \"Penelope is a knave.\" So who is a knight and who is a knave?", "names": ["Lucas", "Penelope", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Lucas is a knave, Penelope is a knave, and Daniel is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Penelope is a knave\n(3) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Penelope is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Daniel that Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the claim of Lucas that Daniel is a knight if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Lucas that Daniel is a knight if and only if Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight.", "We have exhausted all possibilities for Penelope and Daniel, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Penelope is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Lucas that Daniel is a knight if and only if Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('telling-truth', 0), ('lying', 1))", "index": 22} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Liam, and Ethan. In Emily's words: \"Liam is a knight and Ethan is a knave\". Liam said that If Liam is a knight then Emily is a knave. As Ethan put it, \"Emily is a knave or Liam is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Liam", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Emily is a knave, Liam is a knight, and Ethan is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Liam is a knight\n(3) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Liam is a knight and Ethan is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that If Liam is a knight then Emily is a knave.", "Liam cannot be a knave, because this would contradict the claim of Emily that Liam is a knight and Ethan is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Liam is a knight and Ethan is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Liam is a knight then Emily is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knave or Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('->', ('telling-truth', 1), ('lying', 0)), ('or', ('lying', 0), ('lying', 1)))", "index": 23} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aiden, Harper, and Emma. \"If Emma is a knave then Emma is a knight\" - Aiden. Harper was heard saying, \"Emma is a knight or Emma is a knave\". As Emma put it, \"Harper is a knight if and only if Harper is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Harper", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Aiden is a knave, Harper is a knight, and Emma is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Harper is a knight\n(3) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Emma is a knave then Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Harper is a knave.", "Emma cannot be a knave, because this would contradict the claim of Aiden that If Emma is a knave then Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Emma is a knave then Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Aiden that If Emma is a knave then Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Emma is a knight or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))", "index": 24} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Scarlett, and Ella. Emma remarked, \"Ella is a knight\". Scarlett said, \"Emma is a knave and Emma is a knight.\" Ella was heard saying, \"Emma is a knave and Ella is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Scarlett", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Emma is a knave, Scarlett is a knave, and Ella is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Scarlett is a knave\n(3) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Ella is a knight.", "Ella cannot be a knave, because this would contradict the claim of Emma that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Emma that Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Emma is a knave and Ella is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Emma is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emma is a knave and Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('and', ('lying', 0), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 2)))", "index": 25} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Ella, and Liam. Emily was heard saying, \"Ella is a knight\". Ella said, \"Emily is a knight if and only if Liam is a knight.\" \"Ella is a knight\" - Liam. So who is a knight and who is a knave?", "names": ["Emily", "Ella", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Emily is a knight, Ella is a knight, and Liam is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Ella is a knight\n(3) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Emily is a knight if and only if Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 1))", "index": 26} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, Lucas, and Samuel. Penelope commented, \"Lucas is a knave or Lucas is a knight\". Lucas asserted: \"Penelope is not a knight\". According to Samuel, \"Lucas is a knave if and only if Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Lucas", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Penelope is a knight, Lucas is a knave, and Samuel is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Lucas is a knave\n(3) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Lucas is a knave or Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Penelope is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Penelope is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 1), ('lying', 0)))", "index": 27} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Elizabeth, Zoey, and Victoria. Elizabeth said, \"Zoey is a knight or Victoria is a knight.\" \"Victoria is a knave and Zoey is a knight\" - Zoey. Victoria noted, \"Elizabeth is a knight and Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Zoey", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Elizabeth is a knave, Zoey is a knave, and Victoria is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Zoey is a knave\n(3) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Zoey is a knight or Victoria is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Victoria is a knave and Zoey is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Zoey that Victoria is a knave and Zoey is a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight and Zoey is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Victoria is a knave and Zoey is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Zoey is a knight.", "Victoria cannot be a knave, because this would contradict the claim of Elizabeth that Zoey is a knight or Victoria is a knight.", "We have exhausted all possibilities for Victoria and Zoey, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Zoey is a knight or Victoria is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Elizabeth that Zoey is a knight or Victoria is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Victoria is a knave and Zoey is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Elizabeth that Zoey is a knight or Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 1)))", "index": 28} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Matthew, and Henry. As Avery put it, \"If Henry is a knight then Henry is a knave\". Matthew expressed that If Henry is a knight then Avery is a knave. \"Matthew is a knight,\" Henry claimed. So who is a knight and who is a knave?", "names": ["Avery", "Matthew", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Avery is a knave, Matthew is a knight, and Henry is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Matthew is a knight\n(3) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Henry is a knight then Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Avery that If Henry is a knight then Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Henry that Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Henry is a knight then Avery is a knave.", "We have exhausted all possibilities for Matthew and Henry, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Henry is a knight then Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Henry is a knight then Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('->', ('telling-truth', 2), ('lying', 0)), ('telling-truth', 1))", "index": 29} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Penelope, Aurora, and David. \"Penelope is a knight if and only if David is a knave,\" Penelope mentioned. Aurora told you that Penelope is a knight and David is a knave. In a statement by David: \"Penelope is a knave or Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Aurora", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Penelope is a knight, Aurora is a knight, and David is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Aurora is a knight\n(3) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the claim of Penelope that Penelope is a knight if and only if David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Penelope is a knave or Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Penelope is a knight and David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 2)), ('or', ('lying', 0), ('lying', 1)))", "index": 30} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Henry, and Daniel. \"Daniel is a knave,\" Olivia declared. Henry asserted: \"Daniel is a knave or Olivia is a knave\". \"If Henry is a knave then Olivia is a knave,\" Daniel mentioned. So who is a knight and who is a knave?", "names": ["Olivia", "Henry", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Olivia is a knave, Henry is a knight, and Daniel is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Henry is a knight\n(3) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Olivia that Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Henry is a knave then Olivia is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Daniel that If Henry is a knave then Olivia is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Olivia is a knave.", "We have exhausted all possibilities for Henry and Daniel, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Henry is a knave then Olivia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Daniel is a knave or Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('lying', 2), ('lying', 0)), ('->', ('lying', 1), ('lying', 0)))", "index": 31} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, Aiden, and Chloe. Scarlett noted, \"Aiden is a knave\". Aiden remarked, \"If Scarlett is a knight then Chloe is a knight\". Chloe stated, \"Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Aiden", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Scarlett is a knave, Aiden is a knight, and Chloe is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Aiden is a knight\n(3) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Scarlett that Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Aiden that If Scarlett is a knight then Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Aiden is a knave.", "We have exhausted all possibilities for Chloe and Aiden, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Scarlett is a knight then Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 1))", "index": 32} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Jackson, and Abigail. Olivia said, \"If Jackson is a knave then Abigail is a knave.\" As Jackson put it, \"Abigail is a knave\". Abigail asserted: \"Olivia is a knight or Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Jackson", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Olivia is a knave, Jackson is a knave, and Abigail is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Jackson is a knave\n(3) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Jackson is a knave then Abigail is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Jackson that Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight or Jackson is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Olivia that If Jackson is a knave then Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of Jackson that Abigail is a knave.", "We have exhausted all possibilities for Abigail and Jackson, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Jackson is a knave then Abigail is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Olivia that If Jackson is a knave then Abigail is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Olivia is a knight or Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 2)), ('lying', 2), ('or', ('telling-truth', 0), ('lying', 1)))", "index": 33} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Amelia, Riley, and Aurora. Amelia asserted: \"Aurora is not a knave\". Riley was heard saying, \"Aurora is a knight or Amelia is a knave\". According to Aurora, \"Riley is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Riley", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Amelia is a knight, Riley is a knight, and Aurora is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Riley is a knight\n(3) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Aurora is a knight or Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 0)), ('telling-truth', 1))", "index": 34} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Benjamin, Alexander, and Daniel. According to Benjamin, \"Daniel is a knight or Benjamin is a knight\". In Alexander's words: \"Daniel is a knave and Daniel is a knight\". Daniel remarked, \"Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Alexander", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Benjamin is a knight, Alexander is a knave, and Daniel is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Alexander is a knave\n(3) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Daniel is a knight or Benjamin is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Daniel is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Daniel is a knave and Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 2), ('telling-truth', 2)), ('lying', 1))", "index": 35} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: David, William, and Noah. \"William is a knave\" - David. William stated, \"David is a knight and William is a knight\". \"David is a knave or William is a knight,\" Noah claimed. So who is a knight and who is a knave?", "names": ["David", "William", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "David is a knight, William is a knave, and Noah is a knave.", "solution_text_format": "(1) David is a knight\n(2) William is a knave\n(3) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of David that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that David is a knight and William is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that David is a knave or William is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that David is a knave or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 1)))", "index": 36} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Henry, Owen, and Luke. According to Henry, \"Henry is a knight if and only if Owen is a knight\". Owen told you that If Luke is a knight then Luke is a knave. Luke told you that Henry is a knight if and only if Luke is a knight. So who is a knight and who is a knave?", "names": ["Henry", "Owen", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Henry is a knight, Owen is a knight, and Luke is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Owen is a knight\n(3) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Luke is a knight then Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Owen that If Luke is a knight then Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 2)))", "index": 37} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jacob, Owen, and Harper. Jacob noted, \"Harper is a knight and Owen is a knight\". Owen stated, \"Jacob is not a knight\". Harper stated, \"Owen is a knave if and only if Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Owen", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Jacob is a knave, Owen is a knight, and Harper is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Owen is a knight\n(3) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Harper is a knight and Owen is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Owen is a knave if and only if Jacob is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Owen cannot be a knave, because this would contradict the claim of Jacob that Harper is a knight and Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Jacob that Harper is a knight and Owen is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Harper is a knight and Owen is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Owen is a knave if and only if Jacob is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Jacob that Harper is a knight and Owen is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Jacob is not a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Jacob is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 1), ('lying', 0)))", "index": 38} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, Joseph, and Mason. According to Grace, \"Joseph is a knave or Mason is a knight\". Joseph said that Grace is a knight or Joseph is a knight. Mason said that Joseph is a knight. So who is a knight and who is a knave?", "names": ["Grace", "Joseph", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Grace is a knight, Joseph is a knight, and Mason is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Joseph is a knight\n(3) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Joseph is a knave or Mason is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Grace is a knight or Joseph is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 1))", "index": 39} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Mia, and Emily. Ethan expressed that Emily is a knight and Mia is a knight. \"Emily is not a knave,\" Mia declared. According to Emily, \"Mia is a knave if and only if Emily is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Mia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Ethan is a knave, Mia is a knave, and Emily is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Mia is a knave\n(3) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knight and Mia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Mia is a knave if and only if Emily is a knight.", "Mia cannot be a knight, because this would contradict the claim of Emily that Mia is a knave if and only if Emily is a knight.", "Mia cannot be a knave, because this would contradict the claim of Ethan that Emily is a knight and Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Ethan that Emily is a knight and Mia is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emily is a knight and Mia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Mia is a knave if and only if Emily is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Ethan that Emily is a knight and Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Emily is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Emily is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Emily is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('lying', 2)), ('<=>', ('lying', 1), ('telling-truth', 2)))", "index": 40} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Evelyn, Luke, and Ava. In Evelyn's words: \"If Ava is a knight then Ava is a knave\". \"Ava is a knave if and only if Luke is a knight,\" Luke claimed. \"Luke is a knight if and only if Evelyn is a knight,\" Ava claimed. So who is a knight and who is a knave?", "names": ["Evelyn", "Luke", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Evelyn is a knight, Luke is a knave, and Ava is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Luke is a knave\n(3) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that If Ava is a knight then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Evelyn that If Ava is a knight then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Evelyn is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Ava that Luke is a knight if and only if Evelyn is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))", "index": 41} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Michael, Ava, and Elizabeth. Michael remarked, \"Ava is a knave\". \"Ava is a knight and Michael is a knight\" - Ava. Elizabeth remarked, \"Ava is a knave if and only if Michael is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Ava", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Michael is a knight, Ava is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Ava is a knave\n(3) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Michael that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Ava is a knight and Michael is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Ava is a knave if and only if Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 0)))", "index": 42} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Chloe, and Alexander. Charlotte noted, \"If Charlotte is a knight then Alexander is a knave\". Chloe commented, \"Charlotte is not a knight\". \"Chloe is a knight and Alexander is a knight,\" Alexander claimed. So who is a knight and who is a knave?", "names": ["Charlotte", "Chloe", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Charlotte is a knight, Chloe is a knave, and Alexander is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Chloe is a knave\n(3) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Charlotte that If Charlotte is a knight then Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Chloe is a knight and Alexander is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Charlotte is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 2)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 2)))", "index": 43} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sofia, Avery, and Jack. In Sofia's words: \"Jack is a knight or Avery is a knight\". According to Avery, \"If Avery is a knight then Jack is a knave\". \"Jack is a knight if and only if Avery is a knight,\" Jack claimed. So who is a knight and who is a knave?", "names": ["Sofia", "Avery", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Sofia is a knight, Avery is a knight, and Jack is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Avery is a knight\n(3) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Jack is a knight or Avery is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight if and only if Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Avery is a knight then Jack is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Avery is a knight then Jack is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Avery is a knight then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)))", "index": 44} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Chloe, and Scarlett. In a statement by Ethan: \"Scarlett is a knight if and only if Chloe is a knight\". In Chloe's words: \"Scarlett is a knight if and only if Scarlett is a knave\". Scarlett stated, \"Chloe is a knight and Ethan is a knave\". So who is a knight and who is a knave?", "names": ["Ethan", "Chloe", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Ethan is a knight, Chloe is a knave, and Scarlett is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Chloe is a knave\n(3) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Chloe is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Ethan is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is a knight and Ethan is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Ethan that Scarlett is a knight if and only if Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 0)))", "index": 45} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Grace, David, and Matthew. Grace commented, \"David is a knave and Matthew is a knight\". David asserted: \"Matthew is a knave or Grace is a knight\". As Matthew put it, \"Matthew is a knight if and only if David is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "David", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Grace is a knave, David is a knight, and Matthew is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) David is a knight\n(3) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that David is a knave and Matthew is a knight.", "David cannot be a knight, because this would contradict the claim of Grace that David is a knave and Matthew is a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or Grace is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that David is a knave and Matthew is a knight.", "Assume David is a knight. No contradiction is found in their claim that Matthew is a knave or Grace is a knight.", "Matthew cannot be a knight, because this would contradict the claim of David that Matthew is a knave or Grace is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('or', ('lying', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)))", "index": 46} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Noah, and Chloe. \"Matthew is a knight if and only if Chloe is a knave,\" Matthew mentioned. \"Noah is a knight if and only if Matthew is a knight,\" Noah declared. \"If Matthew is a knight then Noah is a knight,\" Chloe declared. So who is a knight and who is a knave?", "names": ["Matthew", "Noah", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Matthew is a knight, Noah is a knave, and Chloe is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Noah is a knave\n(3) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Matthew that Matthew is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Matthew is a knight then Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Chloe that If Matthew is a knight then Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)))", "index": 47} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Chloe, Alexander, and Abigail. Chloe asserted: \"If Abigail is a knight then Alexander is a knave\". Alexander said that Abigail is not a knight. \"Chloe is a knave,\" Abigail mentioned. So who is a knight and who is a knave?", "names": ["Chloe", "Alexander", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Chloe is a knight, Alexander is a knight, and Abigail is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Alexander is a knight\n(3) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that If Abigail is a knight then Alexander is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Abigail is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 2)), ('lying', 0))", "index": 48} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Aria, and Harper. Avery said that If Aria is a knight then Harper is a knave. Aria stated, \"Avery is a knave if and only if Aria is a knight\". Harper told you that Harper is a knight. So who is a knight and who is a knave?", "names": ["Avery", "Aria", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Avery is a knave, Aria is a knight, and Harper is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Aria is a knight\n(3) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Aria is a knight then Harper is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Avery is a knave if and only if Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Avery is a knave if and only if Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Aria is a knight then Harper is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Avery is a knave if and only if Aria is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('telling-truth', 2))", "index": 49} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mia, James, and Sophia. \"If Sophia is a knight then Sophia is a knave,\" Mia declared. \"Sophia is a knight if and only if James is a knight,\" James mentioned. Sophia told you that James is a knight if and only if Mia is a knave. So who is a knight and who is a knave?", "names": ["Mia", "James", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Mia is a knave, James is a knight, and Sophia is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) James is a knight\n(3) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Sophia is a knight then Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Mia that If Sophia is a knight then Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that James is a knight if and only if Mia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if James is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight if and only if James is a knight.", "We have exhausted all possibilities for James and Sophia, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that James is a knight if and only if Mia is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sophia is a knight if and only if James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 0)))", "index": 50} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Noah, and Charlotte. Aurora told you that Charlotte is a knave. \"Charlotte is a knight or Aurora is a knight,\" Noah declared. Charlotte said that Noah is a knave or Noah is a knight. So who is a knight and who is a knave?", "names": ["Aurora", "Noah", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Aurora is a knave, Noah is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Noah is a knight\n(3) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Aurora that Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Noah is a knave or Noah is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Charlotte is a knight or Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 1)))", "index": 51} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Owen, Sophia, and Elizabeth. Owen said that If Elizabeth is a knave then Sophia is a knight. \"If Elizabeth is a knave then Owen is a knave,\" Sophia declared. In a statement by Elizabeth: \"Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Sophia", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Owen is a knight, Sophia is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Sophia is a knight\n(3) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Sophia is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 0)), ('telling-truth', 1))", "index": 52} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Victoria, and William. Ella asserted: \"If Victoria is a knave then William is a knight\". Victoria noted, \"William is a knight if and only if Victoria is a knight\". William said that If William is a knight then Victoria is a knave. So who is a knight and who is a knave?", "names": ["Ella", "Victoria", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Ella is a knight, Victoria is a knave, and William is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Victoria is a knave\n(3) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that If Victoria is a knave then William is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that William is a knight if and only if Victoria is a knight.", "William cannot be a knight, because this would contradict the claim of their own that If William is a knight then Victoria is a knave.", "William cannot be a knave, because this would contradict the claim of Victoria that William is a knight if and only if Victoria is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that William is a knight if and only if Victoria is a knight.", "Assume William is a knight. No contradiction is found in their claim that If William is a knight then Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 1)))", "index": 53} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jackson, Henry, and Liam. Jackson was heard saying, \"Liam is a knight or Liam is a knave\". Henry commented, \"Liam is a knave and Jackson is a knave\". Liam was heard saying, \"Henry is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Henry", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Jackson is a knight, Henry is a knave, and Liam is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Henry is a knave\n(3) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Liam is a knight or Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Jackson is a knave.", "Henry cannot be a knave, because this would contradict the claim of Liam that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Jackson is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Liam is a knave and Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 2)), ('and', ('lying', 2), ('lying', 0)), ('telling-truth', 1))", "index": 54} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Michael, Mason, and Olivia. Michael told you that Michael is a knight. \"Olivia is a knave or Michael is a knave,\" Mason mentioned. Olivia expressed that If Mason is a knave then Michael is a knave. So who is a knight and who is a knave?", "names": ["Michael", "Mason", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Michael is a knave, Mason is a knight, and Olivia is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Mason is a knight\n(3) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Olivia is a knave or Michael is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Mason that Olivia is a knave or Michael is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Michael is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Olivia is a knave or Michael is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that If Mason is a knave then Michael is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of Mason that Olivia is a knave or Michael is a knave.", "We have exhausted all possibilities for Olivia and Mason, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Michael is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Olivia is a knave or Michael is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Mason is a knave then Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 0), ('or', ('lying', 2), ('lying', 0)), ('->', ('lying', 1), ('lying', 0)))", "index": 55} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, William, and Sebastian. \"William is not a knave,\" Avery mentioned. \"William is a knight if and only if Sebastian is a knight\" - William. Sebastian expressed that Sebastian is a knight if and only if Avery is a knight. So who is a knight and who is a knave?", "names": ["Avery", "William", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Avery is a knight, William is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) William is a knight\n(3) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that William is a knight if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))", "index": 56} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Amelia, Charlotte, and Oliver. \"Oliver is a knave and Charlotte is a knight,\" Amelia mentioned. \"Amelia is a knave or Oliver is a knave\" - Charlotte. Oliver was heard saying, \"Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Charlotte", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Amelia is a knight, Charlotte is a knight, and Oliver is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Charlotte is a knight\n(3) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Oliver is a knave and Charlotte is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Amelia that Oliver is a knave and Charlotte is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knave or Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 1)), ('or', ('lying', 0), ('lying', 2)), ('lying', 1))", "index": 57} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Chloe, and Sebastian. Olivia was heard saying, \"Olivia is a knight and Sebastian is a knight\". Chloe asserted: \"Sebastian is a knight\". Sebastian remarked, \"Olivia is a knight or Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Chloe", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Olivia is a knight, Chloe is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Chloe is a knight\n(3) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight and Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Olivia is a knight or Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 2), ('or', ('telling-truth', 0), ('lying', 1)))", "index": 58} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Oliver, and Evelyn. Isabella commented, \"If Isabella is a knight then Evelyn is a knight\". Oliver commented, \"Isabella is a knight or Isabella is a knave\". Evelyn stated, \"Oliver is a knight or Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Oliver", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Isabella is a knight, Oliver is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Oliver is a knight\n(3) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Isabella is a knight then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Oliver is a knight or Isabella is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight or Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 0)))", "index": 59} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jack, Isabella, and Emma. \"Isabella is a knave and Emma is a knight,\" Jack declared. According to Isabella, \"Isabella is a knight or Emma is a knight\". Emma noted, \"If Isabella is a knave then Jack is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Isabella", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Jack is a knave, Isabella is a knight, and Emma is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Isabella is a knight\n(3) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Isabella is a knave and Emma is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Jack that Isabella is a knave and Emma is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight or Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Isabella that Isabella is a knight or Emma is a knight.", "Emma cannot be a knave, because this would contradict the claim of Jack that Isabella is a knave and Emma is a knight.", "We have exhausted all possibilities for Emma and Isabella, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Isabella is a knave and Emma is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Isabella is a knave then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 1), ('lying', 0)))", "index": 60} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Chloe, and Charlotte. According to Ethan, \"Chloe is not a knight\". Chloe was heard saying, \"If Ethan is a knave then Charlotte is a knave\". According to Charlotte, \"Chloe is a knave or Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Chloe", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Ethan is a knave, Chloe is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Chloe is a knight\n(3) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Ethan that Chloe is not a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Charlotte is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Ethan is a knave then Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Chloe that If Ethan is a knave then Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Chloe is a knave or Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('lying', 0), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 0)))", "index": 61} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Scarlett, Avery, and James. In Scarlett's words: \"Avery is a knight if and only if Avery is a knave\". \"If James is a knight then James is a knave\" - Avery. James was heard saying, \"If Scarlett is a knight then James is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Avery", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Scarlett is a knave, Avery is a knave, and James is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Avery is a knave\n(3) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Scarlett cannot be a knight, because this would contradict the claim of their own that Avery is a knight if and only if Avery is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If James is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Avery that If James is a knight then James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If James is a knight then James is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Scarlett is a knight then James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 2)), ('->', ('telling-truth', 0), ('telling-truth', 2)))", "index": 62} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Noah, and Elizabeth. \"Noah is a knave if and only if Noah is a knight,\" Lucas declared. Noah remarked, \"Lucas is not a knave\". Elizabeth expressed that Lucas is not a knight. So who is a knight and who is a knave?", "names": ["Lucas", "Noah", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Lucas is a knave, Noah is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Noah is a knave\n(3) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Lucas cannot be a knight, because this would contradict the claim of their own that Noah is a knave if and only if Noah is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Lucas is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 0)), ('not', ('telling-truth', 0)))", "index": 63} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Evelyn, and Grace. Lucas expressed that If Lucas is a knight then Evelyn is a knave. Evelyn was heard saying, \"Grace is a knight\". Grace stated, \"Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Evelyn", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Lucas is a knight, Evelyn is a knave, and Grace is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Evelyn is a knave\n(3) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Lucas is a knight then Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Lucas that If Lucas is a knight then Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Evelyn that Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 2), ('lying', 0))", "index": 64} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Noah, Henry, and Abigail. \"Abigail is not a knight,\" Noah declared. Henry commented, \"Abigail is a knave and Abigail is a knight\". Abigail expressed that Noah is a knave and Henry is a knight. So who is a knight and who is a knave?", "names": ["Noah", "Henry", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Noah is a knight, Henry is a knave, and Abigail is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Henry is a knave\n(3) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Noah that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Noah is a knave and Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Abigail is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is a knave and Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 0), ('telling-truth', 1)))", "index": 65} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Luke, Jackson, and Elizabeth. Luke noted, \"Jackson is not a knight\". In Jackson's words: \"Elizabeth is a knave or Elizabeth is a knight\". Elizabeth told you that If Jackson is a knave then Luke is a knave. So who is a knight and who is a knave?", "names": ["Luke", "Jackson", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Luke is a knave, Jackson is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Jackson is a knight\n(3) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Luke that Jackson is not a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Elizabeth is a knave or Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Jackson is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 2)), ('->', ('lying', 1), ('lying', 0)))", "index": 66} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ava, Liam, and Charlotte. Ava stated, \"Charlotte is not a knight\". Liam said, \"Liam is a knight and Ava is a knave.\" Charlotte said that If Charlotte is a knight then Liam is a knight. So who is a knight and who is a knave?", "names": ["Ava", "Liam", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Ava is a knave, Liam is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Liam is a knight\n(3) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Ava that Charlotte is not a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knight then Liam is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight and Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 2), ('telling-truth', 1)))", "index": 67} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Jacob, Elizabeth, and David. According to Jacob, \"If Elizabeth is a knave then Elizabeth is a knight\". Elizabeth noted, \"David is a knight if and only if Jacob is a knave\". \"Elizabeth is a knight and Jacob is a knight\" - David. So who is a knight and who is a knave?", "names": ["Jacob", "Elizabeth", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Jacob is a knave, Elizabeth is a knave, and David is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Elizabeth is a knave\n(3) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that David is a knight if and only if Jacob is a knave.", "David cannot be a knight, because this would contradict the claim of Elizabeth that David is a knight if and only if Jacob is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight and Jacob is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Jacob that If Elizabeth is a knave then Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Jacob that If Elizabeth is a knave then Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that David is a knight if and only if Jacob is a knave.", "David cannot be a knight, because this would contradict the false claim of Elizabeth that David is a knight if and only if Jacob is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('and', ('telling-truth', 1), ('telling-truth', 0)))", "index": 68} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Victoria, Jack, and Logan. Victoria told you that Jack is not a knave. Jack said, \"Logan is a knave.\" According to Logan, \"Jack is a knight and Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Jack", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Victoria is a knight, Jack is a knight, and Logan is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Jack is a knight\n(3) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Jack that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Jack is a knight and Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('lying', 2), ('and', ('telling-truth', 1), ('lying', 0)))", "index": 69} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, David, and Victoria. \"David is a knight or Victoria is a knight,\" James mentioned. In a statement by David: \"James is not a knight\". Victoria said that James is a knight and David is a knave. So who is a knight and who is a knave?", "names": ["James", "David", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "James is a knight, David is a knave, and Victoria is a knight.", "solution_text_format": "(1) James is a knight\n(2) David is a knave\n(3) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that David is a knight or Victoria is a knight.", "David cannot be a knight, because this would contradict the claim of their own that James is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knight and David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 1)))", "index": 70} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Oliver, Jackson, and Penelope. According to Oliver, \"Penelope is a knight and Oliver is a knight\". Jackson told you that If Oliver is a knave then Penelope is a knight. \"Oliver is a knave,\" Penelope declared. So who is a knight and who is a knave?", "names": ["Oliver", "Jackson", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Oliver is a knave, Jackson is a knight, and Penelope is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Jackson is a knight\n(3) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Penelope is a knight and Oliver is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Penelope cannot be a knave, because this would contradict the claim of Oliver that Penelope is a knight and Oliver is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Penelope is a knight and Oliver is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Oliver is a knave then Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 2)), ('lying', 0))", "index": 71} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Luke, Ava, and Zoey. Luke expressed that Zoey is not a knave. In Ava's words: \"Zoey is a knight if and only if Zoey is a knave\". Zoey asserted: \"Ava is a knave or Luke is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Ava", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Luke is a knight, Ava is a knave, and Zoey is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Ava is a knave\n(3) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Ava is a knave or Luke is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Zoey is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 0)))", "index": 72} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Chloe, and Sofia. \"Sofia is a knave and Chloe is a knave,\" Isabella declared. Chloe expressed that Sofia is a knight if and only if Sofia is a knave. As Sofia put it, \"Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Chloe", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Isabella is a knight, Chloe is a knave, and Sofia is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Chloe is a knave\n(3) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knave and Chloe is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Isabella that Sofia is a knave and Chloe is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Isabella that Sofia is a knave and Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('telling-truth', 1))", "index": 73} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Matthew, Joseph, and Jackson. Matthew commented, \"If Jackson is a knight then Joseph is a knave\". \"If Jackson is a knight then Jackson is a knave,\" Joseph mentioned. Jackson was heard saying, \"If Matthew is a knave then Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Joseph", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Matthew is a knight, Joseph is a knave, and Jackson is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Joseph is a knave\n(3) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that If Jackson is a knight then Joseph is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Matthew is a knave then Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Matthew that If Jackson is a knight then Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Jackson is a knight then Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 1)))", "index": 74} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Jack, and Harper. According to Mason, \"Harper is not a knave\". In Jack's words: \"If Jack is a knight then Harper is a knight\". Harper said, \"Jack is a knight or Mason is a knave.\" So who is a knight and who is a knave?", "names": ["Mason", "Jack", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Mason is a knight, Jack is a knight, and Harper is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Jack is a knight\n(3) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Jack is a knight or Mason is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Jack is a knight then Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('lying', 0)))", "index": 75} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Elizabeth, and Noah. Isabella stated, \"Noah is not a knight\". \"Noah is a knight,\" Elizabeth mentioned. In a statement by Noah: \"Isabella is a knight and Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Elizabeth", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Isabella is a knight, Elizabeth is a knave, and Noah is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Elizabeth is a knave\n(3) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Isabella that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Isabella is a knight and Isabella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('telling-truth', 2), ('and', ('telling-truth', 0), ('lying', 0)))", "index": 76} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Charlotte, Zoey, and Chloe. Charlotte remarked, \"Chloe is not a knave\". \"Charlotte is a knave if and only if Zoey is a knight,\" Zoey claimed. In a statement by Chloe: \"Zoey is a knight or Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Zoey", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Charlotte is a knave, Zoey is a knave, and Chloe is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Zoey is a knave\n(3) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Zoey is a knight or Chloe is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave if and only if Zoey is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knave if and only if Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Charlotte that Chloe is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Charlotte that Chloe is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Zoey is a knight or Chloe is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Chloe that Zoey is a knight or Chloe is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 2)))", "index": 77} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, William, and Emma. In a statement by Mason: \"Mason is a knight if and only if William is a knave\". William remarked, \"If Emma is a knight then Mason is a knight\". As Emma put it, \"William is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "William", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Mason is a knave, William is a knave, and Emma is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) William is a knave\n(3) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Mason is a knight if and only if William is a knave.", "William cannot be a knight, because this would contradict the claim of Mason that Mason is a knight if and only if William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Mason is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Mason is a knight if and only if William is a knave.", "William cannot be a knight, because this would contradict the false claim of Mason that Mason is a knight if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Emma is a knight then Mason is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('lying', 1))", "index": 78} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Harper, and Jack. James expressed that James is a knight if and only if Jack is a knave. Harper stated, \"Jack is not a knight\". Jack commented, \"Harper is a knight and James is a knight\". So who is a knight and who is a knave?", "names": ["James", "Harper", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "James is a knave, Harper is a knight, and Jack is a knave.", "solution_text_format": "(1) James is a knave\n(2) Harper is a knight\n(3) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that James is a knight if and only if Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of James that James is a knight if and only if Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knight and James is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Jack that Harper is a knight and James is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that Jack is not a knight.", "We have exhausted all possibilities for Harper and Jack, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight if and only if Jack is a knave.", "Jack cannot be a knight, because this would contradict the false claim of James that James is a knight if and only if Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knight and James is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jack is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 2)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 0)))", "index": 79} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Benjamin, and Liam. In a statement by Olivia: \"Olivia is a knight and Benjamin is a knight\". Benjamin remarked, \"If Olivia is a knight then Olivia is a knave\". Liam remarked, \"Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Benjamin", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Olivia is a knave, Benjamin is a knight, and Liam is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Benjamin is a knight\n(3) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight and Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that If Olivia is a knight then Olivia is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Olivia that Olivia is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight and Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Olivia is a knight then Olivia is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 0)), ('lying', 1))", "index": 80} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Evelyn, Emma, and Owen. In a statement by Evelyn: \"Owen is a knave if and only if Emma is a knight\". Emma said, \"Owen is a knave if and only if Emma is a knight.\" Owen was heard saying, \"If Evelyn is a knave then Owen is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Emma", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Evelyn is a knave, Emma is a knave, and Owen is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Emma is a knave\n(3) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Owen is a knave if and only if Emma is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Evelyn is a knave then Owen is a knight.", "Emma cannot be a knight, because this would contradict the claim of Evelyn that Owen is a knave if and only if Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Owen is a knave if and only if Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knave then Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Emma is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Evelyn is a knave then Owen is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Owen is a knave if and only if Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of Evelyn that Owen is a knave if and only if Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Evelyn is a knave then Owen is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Evelyn that Owen is a knave if and only if Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 2)))", "index": 81} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Sofia, Samuel, and Jacob. Sofia said that Jacob is a knave and Samuel is a knave. As Samuel put it, \"Sofia is a knight and Jacob is a knave\". \"If Samuel is a knight then Jacob is a knight,\" Jacob declared. So who is a knight and who is a knave?", "names": ["Sofia", "Samuel", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Sofia is a knave, Samuel is a knave, and Jacob is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Samuel is a knave\n(3) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Jacob is a knave and Samuel is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Sofia that Jacob is a knave and Samuel is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Samuel is a knight then Jacob is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Sofia that Jacob is a knave and Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight and Jacob is a knave.", "We have exhausted all possibilities for Samuel and Jacob, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jacob is a knave and Samuel is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Samuel is a knight then Jacob is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Jacob is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knight and Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 1), ('telling-truth', 2)))", "index": 82} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ella, Oliver, and Logan. In a statement by Ella: \"Logan is a knight\". Oliver expressed that Logan is not a knave. Logan stated, \"Logan is a knight and Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Oliver", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Ella is a knave, Oliver is a knave, and Logan is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Oliver is a knave\n(3) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight and Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Logan that Logan is a knight and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Logan is not a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Ella that Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Ella that Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight and Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Logan is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('not', ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 1)))", "index": 83} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Isabella, Daniel, and Aurora. Isabella was heard saying, \"Daniel is a knave if and only if Isabella is a knight\". Daniel stated, \"Isabella is not a knave\". Aurora asserted: \"Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Daniel", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false], "solution_text": "Isabella is a knave, Daniel is a knave, and Aurora is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Daniel is a knave\n(3) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Isabella is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Isabella that Daniel is a knave if and only if Isabella is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Isabella is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Isabella that Daniel is a knave if and only if Isabella is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 0)), ('telling-truth', 0))", "index": 84} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emily, Ava, and Ethan. Emily asserted: \"Ethan is a knight or Ava is a knave\". Ava told you that Ethan is a knave or Ava is a knight. \"Ava is a knight\" - Ethan. So who is a knight and who is a knave?", "names": ["Emily", "Ava", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Emily is a knight, Ava is a knight, and Ethan is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Ava is a knight\n(3) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Ethan is a knight or Ava is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ethan is a knave or Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 1))", "index": 85} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aurora, Michael, and Benjamin. Aurora commented, \"Aurora is a knight and Benjamin is a knight\". \"Aurora is a knight if and only if Benjamin is a knight,\" Michael declared. Benjamin commented, \"Michael is not a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Michael", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Aurora is a knight, Michael is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Michael is a knight\n(3) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight and Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('lying', 1)))", "index": 86} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lily, Michael, and Owen. \"Owen is a knave or Lily is a knight,\" Lily declared. In Michael's words: \"Owen is a knave and Lily is a knave\". Owen said that Michael is a knight and Michael is a knave. So who is a knight and who is a knave?", "names": ["Lily", "Michael", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false], "solution_text": "Lily is a knight, Michael is a knave, and Owen is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Michael is a knave\n(3) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Owen is a knave or Lily is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Michael is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Michael is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Lily is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Owen is a knave and Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 0)), ('and', ('telling-truth', 1), ('lying', 1)))", "index": 87} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Elizabeth, Amelia, and Samuel. \"Samuel is a knight if and only if Elizabeth is a knight,\" Elizabeth claimed. \"Samuel is not a knight,\" Amelia claimed. Samuel told you that Elizabeth is a knave. So who is a knight and who is a knave?", "names": ["Elizabeth", "Amelia", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true], "solution_text": "Elizabeth is a knave, Amelia is a knave, and Samuel is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Amelia is a knave\n(3) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Elizabeth is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Elizabeth that Samuel is a knight if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Elizabeth is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Samuel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('telling-truth', 2)), ('lying', 0))", "index": 88} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Emma, Grace, and Abigail. \"Abigail is a knave or Grace is a knave,\" Emma claimed. According to Grace, \"Grace is a knight and Emma is a knight\". According to Abigail, \"Grace is a knave or Emma is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Grace", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Emma is a knight, Grace is a knave, and Abigail is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Grace is a knave\n(3) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Abigail is a knave or Grace is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Grace is a knave or Emma is a knight.", "Grace cannot be a knight, because this would contradict the claim of Emma that Abigail is a knave or Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 0)))", "index": 89} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: James, Jackson, and Olivia. James told you that If James is a knight then Olivia is a knave. In a statement by Jackson: \"If Olivia is a knight then James is a knight\". Olivia asserted: \"Jackson is a knave and Olivia is a knight\". So who is a knight and who is a knave?", "names": ["James", "Jackson", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "James is a knight, Jackson is a knight, and Olivia is a knave.", "solution_text_format": "(1) James is a knight\n(2) Jackson is a knight\n(3) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If James is a knight then Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of James that If James is a knight then Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jackson is a knave and Olivia is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Olivia is a knight then James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 2)))", "index": 90} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Avery, Victoria, and Oliver. According to Avery, \"If Avery is a knight then Victoria is a knight\". \"Avery is a knight\" - Victoria. Oliver remarked, \"Victoria is a knight or Avery is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Victoria", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Avery is a knight, Victoria is a knight, and Oliver is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Victoria is a knight\n(3) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Avery is a knight then Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Victoria is a knight or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 0), ('or', ('telling-truth', 1), ('lying', 0)))", "index": 91} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Mason, Jackson, and Emily. \"Emily is a knave if and only if Emily is a knight,\" Mason mentioned. Jackson commented, \"Mason is not a knight\". In a statement by Emily: \"Jackson is a knight if and only if Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Jackson", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false], "solution_text": "Mason is a knave, Jackson is a knight, and Emily is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Jackson is a knight\n(3) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Mason cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Emily is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Jackson is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Mason is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 1)))", "index": 92} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Olivia, Elizabeth, and Lucas. \"If Lucas is a knave then Elizabeth is a knight\" - Olivia. \"Elizabeth is a knight or Lucas is a knave\" - Elizabeth. In Lucas's words: \"Elizabeth is not a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Elizabeth", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Olivia is a knight, Elizabeth is a knight, and Lucas is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Elizabeth is a knight\n(3) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Lucas is a knave then Elizabeth is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight or Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 2)), ('not', ('lying', 1)))", "index": 93} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Riley, Aria, and Abigail. Riley said that Abigail is a knight. In Aria's words: \"Abigail is not a knight\". Abigail commented, \"Aria is a knave or Riley is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Aria", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true], "solution_text": "Riley is a knight, Aria is a knave, and Abigail is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Aria is a knave\n(3) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Aria is a knave or Riley is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Abigail is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('not', ('telling-truth', 2)), ('or', ('lying', 1), ('lying', 0)))", "index": 94} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Abigail, Ella, and Emma. According to Abigail, \"If Emma is a knight then Ella is a knave\". In Ella's words: \"Abigail is a knight\". Emma stated, \"Ella is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Ella", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "Abigail is a knight, Ella is a knight, and Emma is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Ella is a knight\n(3) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Emma is a knight then Ella is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Abigail that If Emma is a knight then Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('telling-truth', 0), ('lying', 1))", "index": 95} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Lucas, Logan, and Ava. Lucas said, \"Logan is a knave and Ava is a knight.\" Logan remarked, \"Ava is a knight if and only if Lucas is a knave\". Ava said, \"Lucas is not a knight.\" So who is a knight and who is a knave?", "names": ["Lucas", "Logan", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "Lucas is a knave, Logan is a knight, and Ava is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Logan is a knight\n(3) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Logan is a knave and Ava is a knight.", "Logan cannot be a knight, because this would contradict the claim of Lucas that Logan is a knave and Ava is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Lucas is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.", "Ava cannot be a knave, because this would contradict the claim of Lucas that Logan is a knave and Ava is a knight.", "We have exhausted all possibilities for Ava and Logan, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Logan is a knave and Ava is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Ava is a knight if and only if Lucas is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Lucas is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('not', ('telling-truth', 0)))", "index": 96} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Ethan, Grace, and Lucas. As Ethan put it, \"Grace is a knight if and only if Ethan is a knight\". \"Ethan is a knight or Lucas is a knight,\" Grace mentioned. Lucas was heard saying, \"Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Grace", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true], "solution_text": "Ethan is a knight, Grace is a knight, and Lucas is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Grace is a knight\n(3) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ethan is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Ethan is a knight or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 0))", "index": 97} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: William, Isabella, and David. \"David is not a knight,\" William mentioned. Isabella was heard saying, \"David is not a knight\". In a statement by David: \"David is a knight and William is a knight\". So who is a knight and who is a knave?", "names": ["William", "Isabella", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false], "solution_text": "William is a knight, Isabella is a knight, and David is a knave.", "solution_text_format": "(1) William is a knight\n(2) Isabella is a knight\n(3) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of William that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that David is a knight and William is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that David is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 0)))", "index": 98} | |
| {"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: David, Harper, and Abigail. David said that Harper is a knave and Abigail is a knight. Harper said, \"If David is a knight then Harper is a knight.\" Abigail said that If David is a knight then David is a knave. So who is a knight and who is a knave?", "names": ["David", "Harper", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true], "solution_text": "David is a knave, Harper is a knight, and Abigail is a knight.", "solution_text_format": "(1) David is a knave\n(2) Harper is a knight\n(3) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Harper is a knave and Abigail is a knight.", "Harper cannot be a knight, because this would contradict the claim of David that Harper is a knave and Abigail is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If David is a knight then Harper is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that If David is a knight then David is a knave.", "Abigail cannot be a knave, because this would contradict the claim of David that Harper is a knave and Abigail is a knight.", "We have exhausted all possibilities for Abigail and Harper, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Harper is a knave and Abigail is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If David is a knight then Harper is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If David is a knight then David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 0)))", "index": 99} | |