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