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, Emily, Luke, Lucas, Harper, and Ella. In Ava's words: "Luke is a knight if and only if Ella is a knave". Emily stated, "If Emily is a knight then Luke is a knave". Luke asserted: "Ella is a knight and Ella is a knave". "Harper is a knave and Luke is a knave," Lucas claimed. As Harper put it, "Lucas is a knave if and only if Ava is a knight". Ella was heard saying, "If Emily is a knight then Harper is a knight". So who is a knight and who is a knave?
Ava is a knight, Emily is a knight, Luke is a knave, Lucas is a knave, Harper is a knight, and Ella is a knight.
(1) Ava is a knight
(2) Emily is a knight
(3) Luke is a knave
(4) Lucas is a knave
(5) Harper is a knight
(6) Ella is a knight
Assume Ava is a knight. No contradiction is found in their claim that Luke is a knight if and only if Ella is a knave. Luke cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Ella is a knave. Assume Luke is a knave. No contradiction is found in their false claim that Ella is a knight and Ella is a knave. Assume Ella is a knight. No contradiction is found in their claim that If Emily is a knight then Harper is a knight. Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Luke is a knave. Assume Harper is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Ava is a knight. Lucas cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Luke is a knave. Assume Lucas is a knave. No contradiction is found in their false claim that Harper is a knave and Luke is a knave.