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