A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Sofia, Joseph, Ethan, Evelyn, and Lily. "If Ethan is a knave then Joseph is a knight," James declared. Sofia asserted: "If Evelyn is a knight then Lily is a knight". Joseph was heard saying, "Joseph is a knight and Sofia is a knave". As Ethan put it, "If Sofia is a knight then Sofia is a knave". Evelyn stated, "Ethan is a knave or Lily is a knight". Lily stated, "Joseph is not a knight". So who is a knight and who is a knave?
James is a knave, Sofia is a knight, Joseph is a knave, Ethan is a knave, Evelyn is a knight, and Lily is a knight.
(1) James is a knave
(2) Sofia is a knight
(3) Joseph is a knave
(4) Ethan is a knave
(5) Evelyn is a knight
(6) Lily is a knight
Assume James is a knight. No contradiction is found in their claim that If Ethan is a knave then Joseph is a knight. Assume Ethan is a knight. No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave. Sofia cannot be a knight, because this would contradict the claim of Ethan that If Sofia is a knight then Sofia is a knave. Assume Sofia is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Lily is a knight. Assume Evelyn is a knight. No contradiction is found in their claim that Ethan is a knave or Lily is a knight. Lily cannot be a knight, because this would contradict the false claim of Sofia that If Evelyn is a knight then Lily is a knight. Lily cannot be a knave, because this would contradict the claim of Evelyn that Ethan is a knave or Lily is a knight. We have exhausted all possibilities for Lily, so let us go back and reconsider Evelyn. Evelyn cannot be a knave, because this would contradict the false claim of Sofia that If Evelyn is a knight then Lily is a knight. We have exhausted all possibilities for Evelyn and Sofia, so let us go back and reconsider Ethan. Assume Ethan is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave. Assume Sofia is a knight. No contradiction is found in their claim that If Evelyn is a knight then Lily is a knight. Assume Evelyn is a knight. No contradiction is found in their claim that Ethan is a knave or Lily is a knight. Assume Lily is a knight. No contradiction is found in their claim that Joseph is not a knight. Joseph cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Sofia is a knave. Joseph cannot be a knave, because this would contradict the claim of James that If Ethan is a knave then Joseph is a knight. We have exhausted all possibilities for Joseph, so let us go back and reconsider Lily. Lily cannot be a knave, because this would contradict the claim of Sofia that If Evelyn is a knight then Lily is a knight. We have exhausted all possibilities for Lily, so let us go back and reconsider Evelyn. Evelyn cannot be a knave, because this would contradict the false claim of their own that Ethan is a knave or Lily is a knight. We have exhausted all possibilities for Evelyn, so let us go back and reconsider Sofia. Sofia cannot be a knave, because this would contradict the false claim of Ethan that If Sofia is a knight then Sofia is a knave. We have exhausted all possibilities for Sofia and Ethan, so let us go back and reconsider James. Assume James is a knave. No contradiction is found in their false claim that If Ethan is a knave then Joseph is a knight. Ethan cannot be a knight, because this would contradict the false claim of James that If Ethan is a knave then Joseph is a knight. Assume Ethan is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave. Assume Sofia is a knight. No contradiction is found in their claim that If Evelyn is a knight then Lily is a knight. Assume Evelyn is a knight. No contradiction is found in their claim that Ethan is a knave or Lily is a knight. Assume Lily is a knight. No contradiction is found in their claim that Joseph is not a knight. Joseph cannot be a knight, because this would contradict the false claim of James that If Ethan is a knave then Joseph is a knight. Assume Joseph is a knave. No contradiction is found in their false claim that Joseph is a knight and Sofia is a knave.