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, Benjamin, Harper, Ella, Sebastian, and Luke. "If Sebastian is a knave then Sebastian is a knight," William claimed. "Sebastian is a knave," Benjamin mentioned. Harper noted, "If Luke is a knight then Benjamin is a knight". "Luke is a knight if and only if William is a knight" - Ella. Sebastian expressed that Ella is not a knave. Luke said, "Harper is a knight and Luke is a knight." So who is a knight and who is a knave?
William is a knave, Benjamin is a knight, Harper is a knight, Ella is a knave, Sebastian is a knave, and Luke is a knight.
(1) William is a knave
(2) Benjamin is a knight
(3) Harper is a knight
(4) Ella is a knave
(5) Sebastian is a knave
(6) Luke is a knight
Assume William is a knight. No contradiction is found in their claim that If Sebastian is a knave then Sebastian is a knight. Assume Sebastian is a knight. No contradiction is found in their claim that Ella is not a knave. Assume Ella is a knight. No contradiction is found in their claim that Luke is a knight if and only if William is a knight. Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight and Luke is a knight. Assume Harper is a knight. No contradiction is found in their claim that If Luke is a knight then Benjamin is a knight. Benjamin cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave. Benjamin cannot be a knave, because this would contradict the claim of Harper that If Luke is a knight then Benjamin is a knight. We have exhausted all possibilities for Benjamin, so let us go back and reconsider Harper. Harper cannot be a knave, because this would contradict the claim of Luke that Harper is a knight and Luke is a knight. We have exhausted all possibilities for Harper, so let us go back and reconsider Luke. Luke cannot be a knave, because this would contradict the claim of Ella that Luke is a knight if and only if William is a knight. We have exhausted all possibilities for Luke, so let us go back and reconsider Ella. Ella cannot be a knave, because this would contradict the claim of Sebastian that Ella is not a knave. We have exhausted all possibilities for Ella, so let us go back and reconsider Sebastian. Sebastian cannot be a knave, because this would contradict the claim of William that If Sebastian is a knave then Sebastian is a knight. We have exhausted all possibilities for Sebastian, so let us go back and reconsider William. Assume William is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Sebastian is a knight. Sebastian cannot be a knight, because this would contradict the false claim of William that If Sebastian is a knave then Sebastian is a knight. Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is not a knave. Ella cannot be a knight, because this would contradict the false claim of Sebastian that Ella is not a knave. Assume Ella is a knave. No contradiction is found in their false claim that Luke is a knight if and only if William is a knight. Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight and Luke is a knight. Assume Harper is a knight. No contradiction is found in their claim that If Luke is a knight then Benjamin is a knight. Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knave.