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