A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Abigail, Aurora, Emily, Luke, and Aria. Evelyn commented, "Abigail is a knight if and only if Luke is a knave". Abigail told you that Evelyn is a knight and Emily is a knight. Aurora commented, "Luke is a knave". Emily remarked, "Aria is a knight if and only if Aria is a knave". Luke said, "If Aria is a knight then Evelyn is a knight." Aria noted, "Aurora is a knight if and only if Emily is a knight". So who is a knight and who is a knave?
Evelyn is a knight, Abigail is a knave, Aurora is a knave, Emily is a knave, Luke is a knight, and Aria is a knight.
(1) Evelyn is a knight
(2) Abigail is a knave
(3) Aurora is a knave
(4) Emily is a knave
(5) Luke is a knight
(6) Aria is a knight
Assume Evelyn is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Luke is a knave. Assume Abigail is a knight. No contradiction is found in their claim that Evelyn is a knight and Emily is a knight. Emily cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Aria is a knave. Emily cannot be a knave, because this would contradict the claim of Abigail that Evelyn is a knight and Emily is a knight. We have exhausted all possibilities for Emily, so let us go back and reconsider Abigail. Assume Abigail is a knave. No contradiction is found in their false claim that Evelyn is a knight and Emily is a knight. Emily cannot be a knight, because this would contradict the false claim of Abigail that Evelyn is a knight and Emily is a knight. Assume Emily is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Aria is a knave. Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Emily is a knight. Aurora cannot be a knight, because this would contradict the claim of Aria that Aurora is a knight if and only if Emily is a knight. Assume Aurora is a knave. No contradiction is found in their false claim that Luke is a knave. Assume Luke is a knight. No contradiction is found in their claim that If Aria is a knight then Evelyn is a knight.