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, James, Noah, Samuel, Chloe, and Abigail. Penelope remarked, "Noah is not a knight". "Samuel is a knave or Samuel is a knight," James declared. Noah said, "Chloe is not a knight." Samuel remarked, "Noah is a knave if and only if Penelope is a knight". Chloe said, "Penelope is a knight or Penelope is a knave." "Noah is a knight if and only if James is a knave," Abigail declared. So who is a knight and who is a knave?
Penelope is a knight, James is a knight, Noah is a knave, Samuel is a knight, Chloe is a knight, and Abigail is a knight.
(1) Penelope is a knight
(2) James is a knight
(3) Noah is a knave
(4) Samuel is a knight
(5) Chloe is a knight
(6) Abigail is a knight
Assume Penelope is a knight. No contradiction is found in their claim that Noah is not a knight. Noah cannot be a knight, because this would contradict the claim of Penelope that Noah is not a knight. Assume Noah is a knave. No contradiction is found in their false claim that Chloe is not a knight. Assume Chloe is a knight. No contradiction is found in their claim that Penelope is a knight or Penelope is a knave. Assume James is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight. Assume Samuel is a knight. No contradiction is found in their claim that Noah is a knave if and only if Penelope is a knight. Assume Abigail is a knight. No contradiction is found in their claim that Noah is a knight if and only if James is a knave.