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