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