A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Jack, Sophia, Noah, Charlotte, and Harper. "Noah is a knave if and only if Harper is a knave," Emily claimed. Jack stated, "Emily is not a knave". "Emily is a knave and Jack is a knave," Sophia declared. Noah told you that If Charlotte is a knave then Harper is a knave. Charlotte was heard saying, "Jack is a knave". According to Harper, "Noah is a knight and Sophia is a knave". So who is a knight and who is a knave?
Emily is a knave, Jack is a knave, Sophia is a knight, Noah is a knight, Charlotte is a knight, and Harper is a knave.
(1) Emily is a knave
(2) Jack is a knave
(3) Sophia is a knight
(4) Noah is a knight
(5) Charlotte is a knight
(6) Harper is a knave
Assume Emily is a knight. No contradiction is found in their claim that Noah is a knave if and only if Harper is a knave. Assume Noah is a knight. No contradiction is found in their claim that If Charlotte is a knave then Harper is a knave. Assume Charlotte is a knight. No contradiction is found in their claim that Jack is a knave. Jack cannot be a knight, because this would contradict the claim of Charlotte that Jack is a knave. Jack cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave. We have exhausted all possibilities for Jack, so let us go back and reconsider Charlotte. Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knave. Assume Jack is a knight. No contradiction is found in their claim that Emily is not a knave. Harper cannot be a knight, because this would contradict the claim of Noah that If Charlotte is a knave then Harper is a knave. Harper cannot be a knave, because this would contradict the claim of Emily that Noah is a knave if and only if Harper is a knave. We have exhausted all possibilities for Harper, so let us go back and reconsider Jack. Jack cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave. We have exhausted all possibilities for Jack and Charlotte, so let us go back and reconsider Noah. Assume Noah is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Harper is a knave. Charlotte cannot be a knight, because this would contradict the false claim of Noah that If Charlotte is a knave then Harper is a knave. Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knave. Assume Jack is a knight. No contradiction is found in their claim that Emily is not a knave. Harper cannot be a knight, because this would contradict the claim of Emily that Noah is a knave if and only if Harper is a knave. Harper cannot be a knave, because this would contradict the false claim of Noah that If Charlotte is a knave then Harper is a knave. We have exhausted all possibilities for Harper, so let us go back and reconsider Jack. Jack cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave. We have exhausted all possibilities for Jack, Charlotte, and Noah, so let us go back and reconsider Emily. Assume Emily is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Harper is a knave. Assume Noah is a knight. No contradiction is found in their claim that If Charlotte is a knave then Harper is a knave. Assume Charlotte is a knight. No contradiction is found in their claim that Jack is a knave. Jack cannot be a knight, because this would contradict the claim of their own that Emily is not a knave. Assume Jack is a knave. No contradiction is found in their false claim that Emily is not a knave. Harper cannot be a knight, because this would contradict the false claim of Emily that Noah is a knave if and only if Harper is a knave. Assume Harper is a knave. No contradiction is found in their false claim that Noah is a knight and Sophia is a knave. Assume Sophia is a knight. No contradiction is found in their claim that Emily is a knave and Jack is a knave.