A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, William, Noah, Luke, Oliver, and Lily. Penelope said, "Lily is not a knave." William was heard saying, "Luke is a knight or Penelope is a knight". Noah noted, "William is a knave". Luke commented, "If William is a knight then Noah is a knave". Oliver said that Lily is a knight and William is a knight. According to Lily, "If Luke is a knight then William is a knight". So who is a knight and who is a knave?
Penelope is a knight, William is a knight, Noah is a knave, Luke is a knight, Oliver is a knight, and Lily is a knight.
(1) Penelope is a knight
(2) William is a knight
(3) Noah is a knave
(4) Luke is a knight
(5) Oliver is a knight
(6) Lily is a knight
Assume Penelope is a knight. No contradiction is found in their claim that Lily is not a knave. Assume Lily is a knight. No contradiction is found in their claim that If Luke is a knight then William is a knight. Assume Luke is a knight. No contradiction is found in their claim that If William is a knight then Noah is a knave. Assume William is a knight. No contradiction is found in their claim that Luke is a knight or Penelope is a knight. Noah cannot be a knight, because this would contradict the claim of their own that William is a knave. Assume Noah is a knave. No contradiction is found in their false claim that William is a knave. Assume Oliver is a knight. No contradiction is found in their claim that Lily is a knight and William is a knight.