A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Jacob, Matthew, Sofia, David, and Chloe. "If Sofia is a knight then Chloe is a knave," Jackson claimed. In a statement by Jacob: "Chloe is a knave and Matthew is a knight". Matthew told you that Chloe is a knave or Jackson is a knave. Sofia commented, "Chloe is a knave and Jackson is a knight". David said, "Chloe is not a knight." According to Chloe, "If Matthew is a knight then Sofia is a knight". So who is a knight and who is a knave?
Jackson is a knight, Jacob is a knave, Matthew is a knave, Sofia is a knave, David is a knave, and Chloe is a knight.
(1) Jackson is a knight
(2) Jacob is a knave
(3) Matthew is a knave
(4) Sofia is a knave
(5) David is a knave
(6) Chloe is a knight
Assume Jackson is a knight. No contradiction is found in their claim that If Sofia is a knight then Chloe is a knave. Assume Sofia is a knight. No contradiction is found in their claim that Chloe is a knave and Jackson is a knight. Chloe cannot be a knight, because this would contradict the claim of Jackson that If Sofia is a knight then Chloe is a knave. Chloe cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Sofia is a knight. We have exhausted all possibilities for Chloe, so let us go back and reconsider Sofia. Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is a knave and Jackson is a knight. Assume Chloe is a knight. No contradiction is found in their claim that If Matthew is a knight then Sofia is a knight. Matthew cannot be a knight, because this would contradict the claim of their own that Chloe is a knave or Jackson is a knave. Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knave or Jackson is a knave. Jacob cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Matthew is a knight. Assume Jacob is a knave. No contradiction is found in their false claim that Chloe is a knave and Matthew is a knight. David cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight. Assume David is a knave. No contradiction is found in their false claim that Chloe is not a knight.