A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Jack, Amelia, Elizabeth, Oliver, and Sophia. "Elizabeth is a knight" - Lily. Jack remarked, "Lily is a knight". "Sophia is a knave if and only if Sophia is a knight," Amelia mentioned. Elizabeth told you that If Oliver is a knave then Jack is a knave. Oliver said, "If Jack is a knave then Elizabeth is a knave." Sophia stated, "Amelia is a knight or Elizabeth is a knight". So who is a knight and who is a knave?
Lily is a knight, Jack is a knight, Amelia is a knave, Elizabeth is a knight, Oliver is a knight, and Sophia is a knight.
(1) Lily is a knight
(2) Jack is a knight
(3) Amelia is a knave
(4) Elizabeth is a knight
(5) Oliver is a knight
(6) Sophia is a knight
Assume Lily is a knight. No contradiction is found in their claim that Elizabeth is a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that If Oliver is a knave then Jack is a knave. Assume Oliver is a knight. No contradiction is found in their claim that If Jack is a knave then Elizabeth is a knave. Assume Jack is a knight. No contradiction is found in their claim that Lily is a knight. Amelia cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight. Assume Amelia is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight. Assume Sophia is a knight. No contradiction is found in their claim that Amelia is a knight or Elizabeth is a knight.