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