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