A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Elizabeth, Mia, Sophia, Grace, and Noah. In a statement by Henry: "Noah is a knight". Elizabeth noted, "Sophia is not a knight". "Henry is not a knight," Mia claimed. In Sophia's words: "Noah is a knave". Grace said, "Elizabeth is not a knight." Noah noted, "Mia is a knave if and only if Grace is a knight". So who is a knight and who is a knave?
Henry is a knave, Elizabeth is a knave, Mia is a knight, Sophia is a knight, Grace is a knight, and Noah is a knave.
(1) Henry is a knave
(2) Elizabeth is a knave
(3) Mia is a knight
(4) Sophia is a knight
(5) Grace is a knight
(6) Noah is a knave
Assume Henry is a knight. No contradiction is found in their claim that Noah is a knight. Assume Noah is a knight. No contradiction is found in their claim that Mia is a knave if and only if Grace is a knight. Mia cannot be a knight, because this would contradict the claim of their own that Henry is not a knight. Assume Mia is a knave. No contradiction is found in their false claim that Henry is not a knight. Assume Grace is a knight. No contradiction is found in their claim that Elizabeth is not a knight. Elizabeth cannot be a knight, because this would contradict the claim of Grace that Elizabeth is not a knight. Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is not a knight. Sophia cannot be a knight, because this would contradict the claim of their own that Noah is a knave. Sophia cannot be a knave, because this would contradict the false claim of Elizabeth that Sophia is not a knight. We have exhausted all possibilities for Sophia and Elizabeth, so let us go back and reconsider Grace. Grace cannot be a knave, because this would contradict the claim of Noah that Mia is a knave if and only if Grace is a knight. We have exhausted all possibilities for Grace and Mia, so let us go back and reconsider Noah. Noah cannot be a knave, because this would contradict the claim of Henry that Noah is a knight. We have exhausted all possibilities for Noah, so let us go back and reconsider Henry. Assume Henry is a knave. No contradiction is found in their false claim that Noah is a knight. Noah cannot be a knight, because this would contradict the false claim of Henry that Noah is a knight. Assume Noah is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Grace is a knight. Assume Mia is a knight. No contradiction is found in their claim that Henry is not a knight. Assume Grace is a knight. No contradiction is found in their claim that Elizabeth is not a knight. Elizabeth cannot be a knight, because this would contradict the claim of Grace that Elizabeth is not a knight. Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is not a knight. Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knave.