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, Sofia, Matthew, Victoria, Ethan, and Isabella. Lily expressed that If Sofia is a knight then Sofia is a knave. "If Matthew is a knight then Ethan is a knight," Sofia claimed. In Matthew's words: "Lily is a knight". In Victoria's words: "Matthew is not a knight". "If Sofia is a knave then Victoria is a knave," Ethan declared. In Isabella's words: "If Ethan is a knight then Matthew is a knight". So who is a knight and who is a knave?
Lily is a knave, Sofia is a knight, Matthew is a knave, Victoria is a knight, Ethan is a knight, and Isabella is a knave.
(1) Lily is a knave
(2) Sofia is a knight
(3) Matthew is a knave
(4) Victoria is a knight
(5) Ethan is a knight
(6) Isabella is a knave
Assume Lily is a knight. No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave. Sofia cannot be a knight, because this would contradict the claim of Lily that If Sofia is a knight then Sofia is a knave. Assume Sofia is a knave. No contradiction is found in their false claim that If Matthew is a knight then Ethan is a knight. Assume Matthew is a knight. No contradiction is found in their claim that Lily is a knight. Ethan cannot be a knight, because this would contradict the false claim of Sofia that If Matthew is a knight then Ethan is a knight. Assume Ethan is a knave. No contradiction is found in their false claim that If Sofia is a knave then Victoria is a knave. Victoria cannot be a knight, because this would contradict the claim of their own that Matthew is not a knight. Victoria cannot be a knave, because this would contradict the false claim of Ethan that If Sofia is a knave then Victoria is a knave. We have exhausted all possibilities for Victoria and Ethan, so let us go back and reconsider Matthew. Matthew cannot be a knave, because this would contradict the false claim of Sofia that If Matthew is a knight then Ethan is a knight. We have exhausted all possibilities for Matthew and Sofia, so let us go back and reconsider Lily. Assume Lily is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave. Assume Sofia is a knight. No contradiction is found in their claim that If Matthew is a knight then Ethan is a knight. Matthew cannot be a knight, because this would contradict the claim of their own that Lily is a knight. Assume Matthew is a knave. No contradiction is found in their false claim that Lily is a knight. Assume Ethan is a knight. No contradiction is found in their claim that If Sofia is a knave then Victoria is a knave. Assume Victoria is a knight. No contradiction is found in their claim that Matthew is not a knight. Isabella cannot be a knight, because this would contradict the claim of their own that If Ethan is a knight then Matthew is a knight. Assume Isabella is a knave. No contradiction is found in their false claim that If Ethan is a knight then Matthew is a knight.