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