A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Aurora, Lucas, Liam, Sofia, and Aiden. Harper was heard saying, "Aiden is a knave if and only if Lucas is a knave". Aurora expressed that If Sofia is a knave then Aurora is a knight. "Sofia is a knave," Lucas mentioned. "Lucas is a knave or Sofia is a knave," Liam claimed. Sofia told you that Harper is a knight. Aiden stated, "Sofia is not a knight". So who is a knight and who is a knave?
Harper is a knight, Aurora is a knight, Lucas is a knave, Liam is a knight, Sofia is a knight, and Aiden is a knave.
(1) Harper is a knight
(2) Aurora is a knight
(3) Lucas is a knave
(4) Liam is a knight
(5) Sofia is a knight
(6) Aiden is a knave
Assume Harper is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Lucas is a knave. Assume Aiden is a knight. No contradiction is found in their claim that Sofia is not a knight. Sofia cannot be a knight, because this would contradict the claim of Aiden that Sofia is not a knight. Sofia cannot be a knave, because this would contradict the false claim of their own that Harper is a knight. We have exhausted all possibilities for Sofia, so let us go back and reconsider Aiden. Assume Aiden is a knave. No contradiction is found in their false claim that Sofia is not a knight. Assume Sofia is a knight. No contradiction is found in their claim that Harper is a knight. Lucas cannot be a knight, because this would contradict the claim of Harper that Aiden is a knave if and only if Lucas is a knave. Assume Lucas is a knave. No contradiction is found in their false claim that Sofia is a knave. Assume Aurora is a knight. No contradiction is found in their claim that If Sofia is a knave then Aurora is a knight. Assume Liam is a knight. No contradiction is found in their claim that Lucas is a knave or Sofia is a knave.