A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Mason, Jacob, Abigail, Owen, and Matthew. Zoey remarked, "If Owen is a knight then Jacob is a knight". Mason commented, "Jacob is a knight or Owen is a knave". Jacob told you that Zoey is a knight and Abigail is a knave. Abigail expressed that Jacob is not a knave. "Zoey is a knave," Owen claimed. According to Matthew, "Mason is a knave". So who is a knight and who is a knave?
Zoey is a knave, Mason is a knave, Jacob is a knave, Abigail is a knave, Owen is a knight, and Matthew is a knight.
(1) Zoey is a knave
(2) Mason is a knave
(3) Jacob is a knave
(4) Abigail is a knave
(5) Owen is a knight
(6) Matthew is a knight
Assume Zoey is a knight. No contradiction is found in their claim that If Owen is a knight then Jacob is a knight. Owen cannot be a knight, because this would contradict the claim of their own that Zoey is a knave. Assume Owen is a knave. No contradiction is found in their false claim that Zoey is a knave. Assume Jacob is a knight. No contradiction is found in their claim that Zoey is a knight and Abigail is a knave. Abigail cannot be a knight, because this would contradict the claim of Jacob that Zoey is a knight and Abigail is a knave. Abigail cannot be a knave, because this would contradict the false claim of their own that Jacob is not a knave. We have exhausted all possibilities for Abigail, so let us go back and reconsider Jacob. Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knight and Abigail is a knave. Abigail cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave. Abigail cannot be a knave, because this would contradict the false claim of Jacob that Zoey is a knight and Abigail is a knave. We have exhausted all possibilities for Abigail, Jacob, and Owen, so let us go back and reconsider Zoey. Assume Zoey is a knave. No contradiction is found in their false claim that If Owen is a knight then Jacob is a knight. Assume Owen is a knight. No contradiction is found in their claim that Zoey is a knave. Jacob cannot be a knight, because this would contradict the false claim of Zoey that If Owen is a knight then Jacob is a knight. Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knight and Abigail is a knave. Abigail cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave. Assume Abigail is a knave. No contradiction is found in their false claim that Jacob is not a knave. Mason cannot be a knight, because this would contradict the claim of their own that Jacob is a knight or Owen is a knave. Assume Mason is a knave. No contradiction is found in their false claim that Jacob is a knight or Owen is a knave. Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knave.