A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Amelia, Isabella, Oliver, Henry, and Aiden. "Isabella is a knight and Oliver is a knight," Liam claimed. Amelia said that Aiden is a knave if and only if Oliver is a knave. Isabella was heard saying, "Aiden is a knight if and only if Liam is a knight". "Isabella is a knave" - Oliver. Henry said, "Oliver is a knight and Isabella is a knight." Aiden said, "Aiden is a knight if and only if Isabella is a knight." So who is a knight and who is a knave?
Liam is a knave, Amelia is a knight, Isabella is a knight, Oliver is a knave, Henry is a knave, and Aiden is a knave.
(1) Liam is a knave
(2) Amelia is a knight
(3) Isabella is a knight
(4) Oliver is a knave
(5) Henry is a knave
(6) Aiden is a knave
Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knight and Oliver is a knight. Assume Isabella is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Liam is a knight. Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Isabella is a knight. Oliver cannot be a knight, because this would contradict the claim of their own that Isabella is a knave. Oliver cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight and Oliver is a knight. We have exhausted all possibilities for Oliver, so let us go back and reconsider Aiden. Aiden cannot be a knave, because this would contradict the claim of Isabella that Aiden is a knight if and only if Liam is a knight. We have exhausted all possibilities for Aiden, so let us go back and reconsider Isabella. Isabella cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight and Oliver is a knight. We have exhausted all possibilities for Isabella, so let us go back and reconsider Liam. Assume Liam is a knave. No contradiction is found in their false claim that Isabella is a knight and Oliver is a knight. Assume Isabella is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Liam is a knight. Aiden cannot be a knight, because this would contradict the claim of Isabella that Aiden is a knight if and only if Liam is a knight. Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Isabella is a knight. Oliver cannot be a knight, because this would contradict the false claim of Liam that Isabella is a knight and Oliver is a knight. Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knave. Assume Amelia is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Oliver is a knave. Henry cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Isabella is a knight. Assume Henry is a knave. No contradiction is found in their false claim that Oliver is a knight and Isabella is a knight.