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