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