A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Henry, Jack, Grace, Daniel, and Elizabeth. Ava commented, "Grace is a knave or Ava is a knight". As Henry put it, "Elizabeth is a knight or Jack is a knave". Jack told you that Daniel is a knight. Grace said that Jack is a knight or Ava is a knave. As Daniel put it, "Ava is a knave and Elizabeth is a knight". Elizabeth stated, "If Elizabeth is a knight then Jack is a knight". So who is a knight and who is a knave?
Ava is a knave, Henry is a knight, Jack is a knight, Grace is a knight, Daniel is a knight, and Elizabeth is a knight.
(1) Ava is a knave
(2) Henry is a knight
(3) Jack is a knight
(4) Grace is a knight
(5) Daniel is a knight
(6) Elizabeth is a knight
Assume Ava is a knight. No contradiction is found in their claim that Grace is a knave or Ava is a knight. Assume Grace is a knight. No contradiction is found in their claim that Jack is a knight or Ava is a knave. Assume Jack is a knight. No contradiction is found in their claim that Daniel is a knight. Daniel cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Elizabeth is a knight. Daniel cannot be a knave, because this would contradict the claim of Jack that Daniel is a knight. We have exhausted all possibilities for Daniel, so let us go back and reconsider Jack. Jack cannot be a knave, because this would contradict the claim of Grace that Jack is a knight or Ava is a knave. We have exhausted all possibilities for Jack, so let us go back and reconsider Grace. Assume Grace is a knave. No contradiction is found in their false claim that Jack is a knight or Ava is a knave. Jack cannot be a knight, because this would contradict the false claim of Grace that Jack is a knight or Ava is a knave. Assume Jack is a knave. No contradiction is found in their false claim that Daniel is a knight. Daniel cannot be a knight, because this would contradict the false claim of Jack that Daniel is a knight. Assume Daniel is a knave. No contradiction is found in their false claim that Ava is a knave and Elizabeth is a knight. Elizabeth cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then Jack is a knight. Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knight then Jack is a knight. We have exhausted all possibilities for Elizabeth, Daniel, Jack, and Grace, so let us go back and reconsider Ava. Assume Ava is a knave. No contradiction is found in their false claim that Grace is a knave or Ava is a knight. Assume Grace is a knight. No contradiction is found in their claim that Jack is a knight or Ava is a knave. Assume Jack is a knight. No contradiction is found in their claim that Daniel is a knight. Assume Daniel is a knight. No contradiction is found in their claim that Ava is a knave and Elizabeth is a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Jack is a knight. Assume Henry is a knight. No contradiction is found in their claim that Elizabeth is a knight or Jack is a knave.