A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Harper, James, Sofia, Scarlett, and William. According to Amelia, "Harper is not a knave". According to Harper, "James is not a knave". James said that Scarlett is not a knave. "William is a knight," Sofia claimed. Scarlett expressed that Sofia is not a knight. William was heard saying, "Harper is a knight or Amelia is a knave". So who is a knight and who is a knave?
Amelia is a knave, Harper is a knave, James is a knave, Sofia is a knight, Scarlett is a knave, and William is a knight.
(1) Amelia is a knave
(2) Harper is a knave
(3) James is a knave
(4) Sofia is a knight
(5) Scarlett is a knave
(6) William is a knight
Assume Amelia is a knight. No contradiction is found in their claim that Harper is not a knave. Assume Harper is a knight. No contradiction is found in their claim that James is not a knave. Assume James is a knight. No contradiction is found in their claim that Scarlett is not a knave. Assume Scarlett is a knight. No contradiction is found in their claim that Sofia is not a knight. Sofia cannot be a knight, because this would contradict the claim of Scarlett that Sofia is not a knight. Assume Sofia is a knave. No contradiction is found in their false claim that William is a knight. William cannot be a knight, because this would contradict the false claim of Sofia that William is a knight. William cannot be a knave, because this would contradict the false claim of their own that Harper is a knight or Amelia is a knave. We have exhausted all possibilities for William and Sofia, so let us go back and reconsider Scarlett. Scarlett cannot be a knave, because this would contradict the claim of James that Scarlett is not a knave. We have exhausted all possibilities for Scarlett, so let us go back and reconsider James. James cannot be a knave, because this would contradict the claim of Harper that James is not a knave. We have exhausted all possibilities for James, so let us go back and reconsider Harper. Harper cannot be a knave, because this would contradict the claim of Amelia that Harper is not a knave. We have exhausted all possibilities for Harper, so let us go back and reconsider Amelia. Assume Amelia is a knave. No contradiction is found in their false claim that Harper is not a knave. Harper cannot be a knight, because this would contradict the false claim of Amelia that Harper is not a knave. Assume Harper is a knave. No contradiction is found in their false claim that James is not a knave. James cannot be a knight, because this would contradict the false claim of Harper that James is not a knave. Assume James is a knave. No contradiction is found in their false claim that Scarlett is not a knave. Scarlett cannot be a knight, because this would contradict the false claim of James that Scarlett is not a knave. Assume Scarlett is a knave. No contradiction is found in their false claim that Sofia is not a knight. Assume Sofia is a knight. No contradiction is found in their claim that William is a knight. Assume William is a knight. No contradiction is found in their claim that Harper is a knight or Amelia is a knave.