A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Oliver, Chloe, Mason, Liam, and Lily. Aiden asserted: "Liam is not a knight". Oliver stated, "Aiden is not a knave". Chloe said that Mason is not a knight. "Aiden is a knight and Chloe is a knight," Mason mentioned. According to Liam, "Aiden is a knave and Lily is a knave". Lily said that Mason is a knave and Mason is a knight. So who is a knight and who is a knave?
Aiden is a knave, Oliver is a knave, Chloe is a knight, Mason is a knave, Liam is a knight, and Lily is a knave.
(1) Aiden is a knave
(2) Oliver is a knave
(3) Chloe is a knight
(4) Mason is a knave
(5) Liam is a knight
(6) Lily is a knave
Assume Aiden is a knight. No contradiction is found in their claim that Liam is not a knight. Liam cannot be a knight, because this would contradict the claim of Aiden that Liam is not a knight. Assume Liam is a knave. No contradiction is found in their false claim that Aiden is a knave and Lily is a knave. Lily cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Mason is a knight. Assume Lily is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight. Assume Mason is a knight. No contradiction is found in their claim that Aiden is a knight and Chloe is a knight. Chloe cannot be a knight, because this would contradict the claim of their own that Mason is not a knight. Chloe cannot be a knave, because this would contradict the claim of Mason that Aiden is a knight and Chloe is a knight. We have exhausted all possibilities for Chloe, so let us go back and reconsider Mason. Assume Mason is a knave. No contradiction is found in their false claim that Aiden is a knight and Chloe is a knight. Chloe cannot be a knight, because this would contradict the false claim of Mason that Aiden is a knight and Chloe is a knight. Chloe cannot be a knave, because this would contradict the false claim of their own that Mason is not a knight. We have exhausted all possibilities for Chloe, Mason, Lily, and Liam, so let us go back and reconsider Aiden. Assume Aiden is a knave. No contradiction is found in their false claim that Liam is not a knight. Assume Liam is a knight. No contradiction is found in their claim that Aiden is a knave and Lily is a knave. Lily cannot be a knight, because this would contradict the claim of Liam that Aiden is a knave and Lily is a knave. Assume Lily is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight. Mason cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Chloe is a knight. Assume Mason is a knave. No contradiction is found in their false claim that Aiden is a knight and Chloe is a knight. Assume Chloe is a knight. No contradiction is found in their claim that Mason is not a knight. Oliver cannot be a knight, because this would contradict the claim of their own that Aiden is not a knave. Assume Oliver is a knave. No contradiction is found in their false claim that Aiden is not a knave.