A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Grace, Olivia, Evelyn, Elizabeth, and Ava. "Ava is a knight and Evelyn is a knight," Luke claimed. Grace stated, "Olivia is a knave and Elizabeth is a knave". Olivia was heard saying, "Luke is a knave if and only if Grace is a knight". Evelyn told you that Elizabeth is not a knight. "Olivia is a knave if and only if Elizabeth is a knight," Elizabeth mentioned. "Evelyn is a knave if and only if Olivia is a knave," Ava declared. So who is a knight and who is a knave?
Luke is a knave, Grace is a knave, Olivia is a knave, Evelyn is a knave, Elizabeth is a knight, and Ava is a knight.
(1) Luke is a knave
(2) Grace is a knave
(3) Olivia is a knave
(4) Evelyn is a knave
(5) Elizabeth is a knight
(6) Ava is a knight
Assume Luke is a knight. No contradiction is found in their claim that Ava is a knight and Evelyn is a knight. Assume Ava is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Olivia is a knave. Assume Evelyn is a knight. No contradiction is found in their claim that Elizabeth is not a knight. Elizabeth cannot be a knight, because this would contradict the claim of Evelyn that Elizabeth is not a knight. Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Elizabeth is a knight. Olivia cannot be a knight, because this would contradict the false claim of Elizabeth that Olivia is a knave if and only if Elizabeth is a knight. Olivia cannot be a knave, because this would contradict the claim of Ava that Evelyn is a knave if and only if Olivia is a knave. We have exhausted all possibilities for Olivia and Elizabeth, so let us go back and reconsider Evelyn. Evelyn cannot be a knave, because this would contradict the claim of Luke that Ava is a knight and Evelyn is a knight. We have exhausted all possibilities for Evelyn, so let us go back and reconsider Ava. Ava cannot be a knave, because this would contradict the claim of Luke that Ava is a knight and Evelyn is a knight. We have exhausted all possibilities for Ava, so let us go back and reconsider Luke. Assume Luke is a knave. No contradiction is found in their false claim that Ava is a knight and Evelyn is a knight. Assume Ava is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Olivia is a knave. Evelyn cannot be a knight, because this would contradict the false claim of Luke that Ava is a knight and Evelyn is a knight. Assume Evelyn is a knave. No contradiction is found in their false claim that Elizabeth is not a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Elizabeth is a knight. Olivia cannot be a knight, because this would contradict the claim of Elizabeth that Olivia is a knave if and only if Elizabeth is a knight. Assume Olivia is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Grace is a knight. Grace cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Elizabeth is a knave. Assume Grace is a knave. No contradiction is found in their false claim that Olivia is a knave and Elizabeth is a knave.