A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Evelyn, Sebastian, James, Oliver, and Sophia. Grace said, "Sebastian is not a knight." Evelyn remarked, "Oliver is not a knight". Sebastian expressed that Evelyn is not a knight. James stated, "Sophia is a knave if and only if Sophia is a knight". Oliver stated, "James is a knave or Sebastian is a knave". "James is a knave if and only if Sebastian is a knight," Sophia declared. So who is a knight and who is a knave?
Grace is a knave, Evelyn is a knave, Sebastian is a knight, James is a knave, Oliver is a knight, and Sophia is a knight.
(1) Grace is a knave
(2) Evelyn is a knave
(3) Sebastian is a knight
(4) James is a knave
(5) Oliver is a knight
(6) Sophia is a knight
Assume Grace is a knight. No contradiction is found in their claim that Sebastian is not a knight. Sebastian cannot be a knight, because this would contradict the claim of Grace that Sebastian is not a knight. Assume Sebastian is a knave. No contradiction is found in their false claim that Evelyn is not a knight. Assume Evelyn is a knight. No contradiction is found in their claim that Oliver is not a knight. Oliver cannot be a knight, because this would contradict the claim of Evelyn that Oliver is not a knight. Oliver cannot be a knave, because this would contradict the false claim of their own that James is a knave or Sebastian is a knave. We have exhausted all possibilities for Oliver, so let us go back and reconsider Evelyn. Evelyn cannot be a knave, because this would contradict the false claim of Sebastian that Evelyn is not a knight. We have exhausted all possibilities for Evelyn and Sebastian, so let us go back and reconsider Grace. Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is not a knight. Assume Sebastian is a knight. No contradiction is found in their claim that Evelyn is not a knight. Evelyn cannot be a knight, because this would contradict the claim of Sebastian that Evelyn is not a knight. Assume Evelyn is a knave. No contradiction is found in their false claim that Oliver is not a knight. Assume Oliver is a knight. No contradiction is found in their claim that James is a knave or Sebastian is a knave. James cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight. Assume James is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight. Assume Sophia is a knight. No contradiction is found in their claim that James is a knave if and only if Sebastian is a knight.