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