A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Oliver, Owen, Emma, Aurora, and Jackson. In a statement by Daniel: "If Owen is a knave then Jackson is a knight". In Oliver's words: "Jackson is a knight if and only if Aurora is a knight". In a statement by Owen: "Emma is a knave". In a statement by Emma: "Daniel is a knave and Jackson is a knave". According to Aurora, "Daniel is a knave if and only if Jackson is a knave". Jackson noted, "Oliver is not a knight". So who is a knight and who is a knave?
Daniel is a knight, Oliver is a knight, Owen is a knight, Emma is a knave, Aurora is a knave, and Jackson is a knave.
(1) Daniel is a knight
(2) Oliver is a knight
(3) Owen is a knight
(4) Emma is a knave
(5) Aurora is a knave
(6) Jackson is a knave
Assume Daniel is a knight. No contradiction is found in their claim that If Owen is a knave then Jackson is a knight. Assume Owen is a knight. No contradiction is found in their claim that Emma is a knave. Emma cannot be a knight, because this would contradict the claim of Owen that Emma is a knave. Assume Emma is a knave. No contradiction is found in their false claim that Daniel is a knave and Jackson is a knave. Assume Jackson is a knight. No contradiction is found in their claim that Oliver is not a knight. Oliver cannot be a knight, because this would contradict the claim of Jackson that Oliver is not a knight. Assume Oliver is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Aurora is a knight. Aurora cannot be a knight, because this would contradict the false claim of Oliver that Jackson is a knight if and only if Aurora is a knight. Aurora cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave if and only if Jackson is a knave. We have exhausted all possibilities for Aurora and Oliver, so let us go back and reconsider Jackson. Assume Jackson is a knave. No contradiction is found in their false claim that Oliver is not a knight. Assume Oliver is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Aurora is a knight. Aurora cannot be a knight, because this would contradict the claim of Oliver that Jackson is a knight if and only if Aurora is a knight. Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Jackson is a knave.