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