A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Lily, Sophia, Luke, Noah, and Avery. In a statement by Daniel: "Luke is a knight or Noah is a knave". "Daniel is a knave or Sophia is a knave," Lily declared. Sophia said that Noah is a knight or Luke is a knight. Luke noted, "Avery is a knight and Noah is a knave". In Noah's words: "Luke is a knight". As Avery put it, "Daniel is a knave or Sophia is a knight". So who is a knight and who is a knave?
Daniel is a knight, Lily is a knight, Sophia is a knave, Luke is a knave, Noah is a knave, and Avery is a knave.
(1) Daniel is a knight
(2) Lily is a knight
(3) Sophia is a knave
(4) Luke is a knave
(5) Noah is a knave
(6) Avery is a knave
Assume Daniel is a knight. No contradiction is found in their claim that Luke is a knight or Noah is a knave. Assume Luke is a knight. No contradiction is found in their claim that Avery is a knight and Noah is a knave. Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knave or Sophia is a knight. Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knight or Luke is a knight. Noah cannot be a knight, because this would contradict the claim of Luke that Avery is a knight and Noah is a knave. Noah cannot be a knave, because this would contradict the false claim of their own that Luke is a knight. We have exhausted all possibilities for Noah, so let us go back and reconsider Sophia. Sophia cannot be a knave, because this would contradict the false claim of their own that Noah is a knight or Luke is a knight. We have exhausted all possibilities for Sophia, so let us go back and reconsider Avery. Avery cannot be a knave, because this would contradict the claim of Luke that Avery is a knight and Noah is a knave. We have exhausted all possibilities for Avery, so let us go back and reconsider Luke. Assume Luke is a knave. No contradiction is found in their false claim that Avery is a knight and Noah is a knave. Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knave or Sophia is a knight. Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knight or Luke is a knight. Noah cannot be a knight, because this would contradict the claim of Daniel that Luke is a knight or Noah is a knave. Noah cannot be a knave, because this would contradict the claim of Sophia that Noah is a knight or Luke is a knight. We have exhausted all possibilities for Noah, so let us go back and reconsider Sophia. Sophia cannot be a knave, because this would contradict the claim of Avery that Daniel is a knave or Sophia is a knight. We have exhausted all possibilities for Sophia, so let us go back and reconsider Avery. Assume Avery is a knave. No contradiction is found in their false claim that Daniel is a knave or Sophia is a knight. Sophia cannot be a knight, because this would contradict the false claim of Avery that Daniel is a knave or Sophia is a knight. Assume Sophia is a knave. No contradiction is found in their false claim that Noah is a knight or Luke is a knight. Noah cannot be a knight, because this would contradict the claim of Daniel that Luke is a knight or Noah is a knave. Assume Noah is a knave. No contradiction is found in their false claim that Luke is a knight. Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knave or Sophia is a knave.