A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Michael, Joseph, Grace, Harper, and Benjamin. Jack remarked, "Harper is a knight if and only if Harper is a knave". "Harper is a knight if and only if Harper is a knave," Michael mentioned. "If Benjamin is a knight then Jack is a knave," Joseph claimed. Grace said, "If Joseph is a knight then Michael is a knave." Harper expressed that Michael is not a knave. Benjamin stated, "Jack is not a knave". So who is a knight and who is a knave?
Jack is a knave, Michael is a knave, Joseph is a knight, Grace is a knight, Harper is a knave, and Benjamin is a knave.
(1) Jack is a knave
(2) Michael is a knave
(3) Joseph is a knight
(4) Grace is a knight
(5) Harper is a knave
(6) Benjamin is a knave
Jack 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. Assume Jack 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 Michael is not a knave. Michael 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. Michael cannot be a knave, because this would contradict the claim of Harper that Michael is not a knave. We have exhausted all possibilities for Michael, so let us go back and reconsider Harper. Assume Harper is a knave. No contradiction is found in their false claim that Michael is not a knave. Michael 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. Assume Michael 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 Joseph is a knight. No contradiction is found in their claim that If Benjamin is a knight then Jack is a knave. Benjamin cannot be a knight, because this would contradict the claim of their own that Jack is not a knave. Assume Benjamin is a knave. No contradiction is found in their false claim that Jack is not a knave. Assume Grace is a knight. No contradiction is found in their claim that If Joseph is a knight then Michael is a knave.