A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Owen, Matthew, Ava, Samuel, and Lily. Sebastian stated, "Ava is a knave". "Lily is a knight if and only if Matthew is a knave," Owen declared. As Matthew put it, "Lily is a knave". "If Owen is a knave then Lily is a knight" - Ava. Samuel said, "If Matthew is a knave then Ava is a knight." Lily noted, "Sebastian is a knight if and only if Owen is a knave". So who is a knight and who is a knave?
Sebastian is a knave, Owen is a knight, Matthew is a knave, Ava is a knight, Samuel is a knight, and Lily is a knight.
(1) Sebastian is a knave
(2) Owen is a knight
(3) Matthew is a knave
(4) Ava is a knight
(5) Samuel is a knight
(6) Lily is a knight
Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knave. Ava cannot be a knight, because this would contradict the claim of Sebastian that Ava is a knave. Assume Ava is a knave. No contradiction is found in their false claim that If Owen is a knave then Lily is a knight. Owen cannot be a knight, because this would contradict the false claim of Ava that If Owen is a knave then Lily is a knight. Assume Owen is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Matthew is a knave. Lily cannot be a knight, because this would contradict the false claim of Ava that If Owen is a knave then Lily is a knight. Lily cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight if and only if Owen is a knave. We have exhausted all possibilities for Lily, Owen, and Ava, so let us go back and reconsider Sebastian. Assume Sebastian is a knave. No contradiction is found in their false claim that Ava is a knave. Assume Ava is a knight. No contradiction is found in their claim that If Owen is a knave then Lily is a knight. Assume Owen is a knight. No contradiction is found in their claim that Lily is a knight if and only if Matthew is a knave. Assume Lily is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Owen is a knave. Matthew cannot be a knight, because this would contradict the claim of Owen that Lily is a knight if and only if Matthew is a knave. Assume Matthew is a knave. No contradiction is found in their false claim that Lily is a knave. Assume Samuel is a knight. No contradiction is found in their claim that If Matthew is a knave then Ava is a knight.