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