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