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