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