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