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