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, James, Daniel, Henry, Owen, and Chloe. "Chloe is a knave or Jack is a knight," Jack claimed. "Owen is a knave and Jack is a knave," James claimed. Daniel noted, "Henry is a knave". "Owen is a knight if and only if Jack is a knight" - Henry. Owen told you that If Jack is a knight then Jack is a knave. Chloe asserted: "Owen is a knave or James is a knight". So who is a knight and who is a knave?
Jack is a knight, James is a knave, Daniel is a knight, Henry is a knave, Owen is a knave, and Chloe is a knight.
(1) Jack is a knight
(2) James is a knave
(3) Daniel is a knight
(4) Henry is a knave
(5) Owen is a knave
(6) Chloe is a knight
Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knave or Jack is a knight. Assume Chloe is a knight. No contradiction is found in their claim that Owen is a knave or James is a knight. Owen cannot be a knight, because this would contradict the claim of their own that If Jack is a knight then Jack is a knave. Assume Owen is a knave. No contradiction is found in their false claim that If Jack is a knight then Jack is a knave. James cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Jack is a knave. Assume James is a knave. No contradiction is found in their false claim that Owen is a knave and Jack is a knave. Assume Daniel is a knight. No contradiction is found in their claim that Henry is a knave. Henry cannot be a knight, because this would contradict the claim of Daniel that Henry is a knave. Assume Henry is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Jack is a knight.