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