A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Olivia, Avery, Penelope, Owen, and Riley. William expressed that If Olivia is a knave then Owen is a knight. "Riley is a knight," Olivia claimed. "William is a knave and Riley is a knave," Avery mentioned. "Riley is not a knight," Penelope claimed. Owen stated, "Avery is a knight". According to Riley, "Owen is a knave or Olivia is a knave". So who is a knight and who is a knave?
William is a knight, Olivia is a knight, Avery is a knave, Penelope is a knave, Owen is a knave, and Riley is a knight.
(1) William is a knight
(2) Olivia is a knight
(3) Avery is a knave
(4) Penelope is a knave
(5) Owen is a knave
(6) Riley is a knight
Assume William is a knight. No contradiction is found in their claim that If Olivia is a knave then Owen is a knight. Assume Olivia is a knight. No contradiction is found in their claim that Riley is a knight. Assume Riley is a knight. No contradiction is found in their claim that Owen is a knave or Olivia is a knave. Owen cannot be a knight, because this would contradict the claim of Riley that Owen is a knave or Olivia is a knave. Assume Owen is a knave. No contradiction is found in their false claim that Avery is a knight. Avery cannot be a knight, because this would contradict the claim of their own that William is a knave and Riley is a knave. Assume Avery is a knave. No contradiction is found in their false claim that William is a knave and Riley is a knave. Penelope cannot be a knight, because this would contradict the claim of their own that Riley is not a knight. Assume Penelope is a knave. No contradiction is found in their false claim that Riley is not a knight.