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