A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Benjamin, Abigail, Harper, Owen, and Sophia. Ethan was heard saying, "Harper is a knight". Benjamin asserted: "Sophia is not a knave". Abigail noted, "Ethan is a knight or Sophia is a knight". Harper told you that Harper is a knight if and only if Benjamin is a knave. As Owen put it, "If Benjamin is a knave then Harper is a knave". Sophia remarked, "Benjamin is a knight if and only if Abigail is a knight". So who is a knight and who is a knave?
Ethan is a knight, Benjamin is a knave, Abigail is a knight, Harper is a knight, Owen is a knave, and Sophia is a knave.
(1) Ethan is a knight
(2) Benjamin is a knave
(3) Abigail is a knight
(4) Harper is a knight
(5) Owen is a knave
(6) Sophia is a knave
Assume Ethan is a knight. No contradiction is found in their claim that Harper is a knight. Assume Harper is a knight. No contradiction is found in their claim that Harper is a knight if and only if Benjamin is a knave. Benjamin cannot be a knight, because this would contradict the claim of Harper that Harper is a knight if and only if Benjamin is a knave. Assume Benjamin is a knave. No contradiction is found in their false claim that Sophia is not a knave. Sophia cannot be a knight, because this would contradict the false claim of Benjamin that Sophia is not a knave. Assume Sophia is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Abigail is a knight. Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knight or Sophia is a knight. Owen cannot be a knight, because this would contradict the claim of their own that If Benjamin is a knave then Harper is a knave. Assume Owen is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Harper is a knave.