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