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