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