A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Mason, Samuel, Aiden, Benjamin, and Lucas. Oliver was heard saying, "Lucas is a knight if and only if Benjamin is a knave". Mason said that Aiden is not a knave. Samuel expressed that Mason is a knave if and only if Oliver is a knave. Aiden said, "Samuel is a knight if and only if Benjamin is a knave." Benjamin expressed that Oliver is a knight if and only if Aiden is a knave. According to Lucas, "Samuel is a knight". So who is a knight and who is a knave?
Oliver is a knight, Mason is a knight, Samuel is a knight, Aiden is a knight, Benjamin is a knave, and Lucas is a knight.
(1) Oliver is a knight
(2) Mason is a knight
(3) Samuel is a knight
(4) Aiden is a knight
(5) Benjamin is a knave
(6) Lucas is a knight
Assume Oliver is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Benjamin is a knave. Assume Lucas is a knight. No contradiction is found in their claim that Samuel is a knight. Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knave if and only if Oliver is a knave. Assume Mason is a knight. No contradiction is found in their claim that Aiden is not a knave. Assume Aiden is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Benjamin is a knave. Benjamin cannot be a knight, because this would contradict the claim of Oliver that Lucas is a knight if and only if Benjamin is a knave. Assume Benjamin is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Aiden is a knave.