A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, William, Sophia, Benjamin, Jack, and James. Aurora said, "Sophia is a knave if and only if Jack is a knave." In William's words: "James is a knight if and only if Benjamin is a knight". Sophia expressed that Benjamin is a knave. In a statement by Benjamin: "Benjamin is a knight and Aurora is a knight". As Jack put it, "If William is a knight then James is a knight". In James's words: "If Jack is a knight then Aurora is a knight". So who is a knight and who is a knave?
Aurora is a knight, William is a knave, Sophia is a knight, Benjamin is a knave, Jack is a knight, and James is a knight.
(1) Aurora is a knight
(2) William is a knave
(3) Sophia is a knight
(4) Benjamin is a knave
(5) Jack is a knight
(6) James is a knight
Assume Aurora is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Jack is a knave. Assume Sophia is a knight. No contradiction is found in their claim that Benjamin is a knave. Benjamin cannot be a knight, because this would contradict the claim of Sophia that Benjamin is a knave. Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight and Aurora is a knight. Assume Jack is a knight. No contradiction is found in their claim that If William is a knight then James is a knight. Assume William is a knight. No contradiction is found in their claim that James is a knight if and only if Benjamin is a knight. James cannot be a knight, because this would contradict the claim of William that James is a knight if and only if Benjamin is a knight. James cannot be a knave, because this would contradict the claim of Jack that If William is a knight then James is a knight. We have exhausted all possibilities for James, so let us go back and reconsider William. Assume William is a knave. No contradiction is found in their false claim that James is a knight if and only if Benjamin is a knight. Assume James is a knight. No contradiction is found in their claim that If Jack is a knight then Aurora is a knight.