A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Aria, Aiden, Grace, Ava, and Lily. "Lily is a knight if and only if Ava is a knight" - Lucas. In Aria's words: "Lily is a knave or Aiden is a knight". "Lucas is not a knight," Aiden claimed. Grace remarked, "Aiden is a knave or Grace is a knight". Ava commented, "Lily is a knight or Aria is a knave". Lily was heard saying, "Lucas is a knave if and only if Grace is a knight". So who is a knight and who is a knave?
Lucas is a knight, Aria is a knight, Aiden is a knave, Grace is a knight, Ava is a knave, and Lily is a knave.
(1) Lucas is a knight
(2) Aria is a knight
(3) Aiden is a knave
(4) Grace is a knight
(5) Ava is a knave
(6) Lily is a knave
Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ava is a knight. Assume Lily is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Grace is a knight. Grace cannot be a knight, because this would contradict the claim of Lily that Lucas is a knave if and only if Grace is a knight. Assume Grace is a knave. No contradiction is found in their false claim that Aiden is a knave or Grace is a knight. Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight. Aiden cannot be a knave, because this would contradict the false claim of Grace that Aiden is a knave or Grace is a knight. We have exhausted all possibilities for Aiden and Grace, so let us go back and reconsider Lily. Assume Lily is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Grace is a knight. Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knave or Grace is a knight. Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight. Assume Aiden is a knave. No contradiction is found in their false claim that Lucas is not a knight. Ava cannot be a knight, because this would contradict the claim of Lucas that Lily is a knight if and only if Ava is a knight. Assume Ava is a knave. No contradiction is found in their false claim that Lily is a knight or Aria is a knave. Assume Aria is a knight. No contradiction is found in their claim that Lily is a knave or Aiden is a knight.