A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Avery, Benjamin, Oliver, Isabella, and Aiden. Riley stated, "Benjamin is a knave". Avery told you that Aiden is a knight or Benjamin is a knave. Benjamin commented, "Aiden is a knight or Oliver is a knave". Oliver told you that Isabella is a knight if and only if Aiden is a knight. "Riley is not a knight," Isabella declared. Aiden said, "Oliver is a knave." So who is a knight and who is a knave?
Riley is a knight, Avery is a knight, Benjamin is a knave, Oliver is a knight, Isabella is a knave, and Aiden is a knave.
(1) Riley is a knight
(2) Avery is a knight
(3) Benjamin is a knave
(4) Oliver is a knight
(5) Isabella is a knave
(6) Aiden is a knave
Assume Riley is a knight. No contradiction is found in their claim that Benjamin is a knave. Benjamin cannot be a knight, because this would contradict the claim of Riley that Benjamin is a knave. Assume Benjamin is a knave. No contradiction is found in their false claim that Aiden is a knight or Oliver is a knave. Aiden cannot be a knight, because this would contradict the false claim of Benjamin that Aiden is a knight or Oliver is a knave. Assume Aiden is a knave. No contradiction is found in their false claim that Oliver is a knave. Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Aiden is a knight. Isabella cannot be a knight, because this would contradict the claim of Oliver that Isabella is a knight if and only if Aiden is a knight. Assume Isabella is a knave. No contradiction is found in their false claim that Riley is not a knight. Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knight or Benjamin is a knave.