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