A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Charlotte, Luke, Riley, Scarlett, and Emma. Evelyn said that If Scarlett is a knight then Emma is a knight. Charlotte remarked, "Luke is a knave and Riley is a knight". As Luke put it, "Luke is a knight or Evelyn is a knight". In a statement by Riley: "Scarlett is a knave if and only if Emma is a knight". Scarlett told you that Scarlett is a knight if and only if Charlotte is a knight. Emma noted, "Scarlett is a knight and Charlotte is a knave". So who is a knight and who is a knave?
Evelyn is a knave, Charlotte is a knight, Luke is a knave, Riley is a knight, Scarlett is a knight, and Emma is a knave.
(1) Evelyn is a knave
(2) Charlotte is a knight
(3) Luke is a knave
(4) Riley is a knight
(5) Scarlett is a knight
(6) Emma is a knave
Assume Evelyn is a knight. No contradiction is found in their claim that If Scarlett is a knight then Emma is a knight. Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Charlotte is a knight. Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knave and Riley is a knight. Luke cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave and Riley is a knight. Luke cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Evelyn is a knight. We have exhausted all possibilities for Luke, so let us go back and reconsider Charlotte. Charlotte cannot be a knave, because this would contradict the claim of Scarlett that Scarlett is a knight if and only if Charlotte is a knight. We have exhausted all possibilities for Charlotte, so let us go back and reconsider Scarlett. Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Charlotte is a knight. Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knave and Riley is a knight. Luke cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave and Riley is a knight. Luke cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Evelyn is a knight. We have exhausted all possibilities for Luke, so let us go back and reconsider Charlotte. Charlotte cannot be a knave, because this would contradict the false claim of Scarlett that Scarlett is a knight if and only if Charlotte is a knight. We have exhausted all possibilities for Charlotte and Scarlett, so let us go back and reconsider Evelyn. Assume Evelyn is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Emma is a knight. Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Charlotte is a knight. Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knave and Riley is a knight. Luke cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave and Riley is a knight. Assume Luke is a knave. No contradiction is found in their false claim that Luke is a knight or Evelyn is a knight. Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Emma is a knight. Emma cannot be a knight, because this would contradict the false claim of Evelyn that If Scarlett is a knight then Emma is a knight. Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knight and Charlotte is a knave.