A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Jack, Alexander, Riley, Aria, and Emily. Emma told you that Jack is a knight and Aria is a knight. As Jack put it, "Emma is a knave if and only if Emily is a knight". In a statement by Alexander: "Emily is a knave if and only if Jack is a knave". Riley noted, "Aria is not a knight". In Aria's words: "Emily is a knave if and only if Alexander is a knave". "Jack is not a knight," Emily mentioned. So who is a knight and who is a knave?
Emma is a knight, Jack is a knight, Alexander is a knave, Riley is a knave, Aria is a knight, and Emily is a knave.
(1) Emma is a knight
(2) Jack is a knight
(3) Alexander is a knave
(4) Riley is a knave
(5) Aria is a knight
(6) Emily is a knave
Assume Emma is a knight. No contradiction is found in their claim that Jack is a knight and Aria is a knight. Assume Jack is a knight. No contradiction is found in their claim that Emma is a knave if and only if Emily is a knight. Emily cannot be a knight, because this would contradict the claim of Jack that Emma is a knave if and only if Emily is a knight. Assume Emily is a knave. No contradiction is found in their false claim that Jack is not a knight. Assume Aria is a knight. No contradiction is found in their claim that Emily is a knave if and only if Alexander is a knave. Alexander cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Jack is a knave. Assume Alexander is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Jack is a knave. Riley cannot be a knight, because this would contradict the claim of their own that Aria is not a knight. Assume Riley is a knave. No contradiction is found in their false claim that Aria is not a knight.