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, Isabella, Avery, Olivia, William, and Noah. Aiden said, "Noah is a knave and Avery is a knave." As Isabella put it, "Aiden is a knave if and only if Noah is a knave". In Avery's words: "Noah is a knight". Olivia told you that Avery is a knight if and only if Noah is a knave. William asserted: "If Avery is a knave then Noah is a knave". In Noah's words: "William is a knight and Isabella is a knave". So who is a knight and who is a knave?
Aiden is a knave, Isabella is a knave, Avery is a knight, Olivia is a knave, William is a knight, and Noah is a knight.
(1) Aiden is a knave
(2) Isabella is a knave
(3) Avery is a knight
(4) Olivia is a knave
(5) William is a knight
(6) Noah is a knight
Assume Aiden is a knight. No contradiction is found in their claim that Noah is a knave and Avery is a knave. Noah cannot be a knight, because this would contradict the claim of Aiden that Noah is a knave and Avery is a knave. Assume Noah is a knave. No contradiction is found in their false claim that William is a knight and Isabella is a knave. Assume William is a knight. No contradiction is found in their claim that If Avery is a knave then Noah is a knave. Avery cannot be a knight, because this would contradict the claim of Aiden that Noah is a knave and Avery is a knave. Assume Avery is a knave. No contradiction is found in their false claim that Noah is a knight. Isabella cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Noah is a knave. Isabella cannot be a knave, because this would contradict the false claim of Noah that William is a knight and Isabella is a knave. We have exhausted all possibilities for Isabella and Avery, so let us go back and reconsider William. William cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Noah is a knave. We have exhausted all possibilities for William and Noah, so let us go back and reconsider Aiden. Assume Aiden is a knave. No contradiction is found in their false claim that Noah is a knave and Avery is a knave. Assume Noah is a knight. No contradiction is found in their claim that William is a knight and Isabella is a knave. Assume William is a knight. No contradiction is found in their claim that If Avery is a knave then Noah is a knave. Assume Avery is a knight. No contradiction is found in their claim that Noah is a knight. Isabella cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Noah is a knave. Assume Isabella is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Noah is a knave. Olivia cannot be a knight, because this would contradict the claim of their own that Avery is a knight if and only if Noah is a knave. Assume Olivia is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Noah is a knave.