A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Joseph, Isabella, Sophia, Emma, and James. "Emma is a knight or Isabella is a knight," Noah declared. In a statement by Joseph: "Isabella is a knight". Isabella stated, "James is a knave". "James is a knight" - Sophia. "Isabella is a knight," Emma declared. "Sophia is a knight if and only if Noah is a knave," James claimed. So who is a knight and who is a knave?
Noah is a knave, Joseph is a knave, Isabella is a knave, Sophia is a knight, Emma is a knave, and James is a knight.
(1) Noah is a knave
(2) Joseph is a knave
(3) Isabella is a knave
(4) Sophia is a knight
(5) Emma is a knave
(6) James is a knight
Assume Noah is a knight. No contradiction is found in their claim that Emma is a knight or Isabella is a knight. Assume Emma is a knight. No contradiction is found in their claim that Isabella is a knight. Assume Isabella is a knight. No contradiction is found in their claim that James is a knave. James cannot be a knight, because this would contradict the claim of Isabella that James is a knave. Assume James is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Noah is a knave. Sophia cannot be a knight, because this would contradict the claim of their own that James is a knight. Sophia cannot be a knave, because this would contradict the false claim of James that Sophia is a knight if and only if Noah is a knave. We have exhausted all possibilities for Sophia and James, so let us go back and reconsider Isabella. Isabella cannot be a knave, because this would contradict the claim of Emma that Isabella is a knight. We have exhausted all possibilities for Isabella, so let us go back and reconsider Emma. Assume Emma is a knave. No contradiction is found in their false claim that Isabella is a knight. Isabella cannot be a knight, because this would contradict the false claim of Emma that Isabella is a knight. Isabella cannot be a knave, because this would contradict the claim of Noah that Emma is a knight or Isabella is a knight. We have exhausted all possibilities for Isabella and Emma, so let us go back and reconsider Noah. Assume Noah is a knave. No contradiction is found in their false claim that Emma is a knight or Isabella is a knight. Emma cannot be a knight, because this would contradict the false claim of Noah that Emma is a knight or Isabella is a knight. Assume Emma is a knave. No contradiction is found in their false claim that Isabella is a knight. Isabella cannot be a knight, because this would contradict the false claim of Noah that Emma is a knight or Isabella is a knight. Assume Isabella is a knave. No contradiction is found in their false claim that James is a knave. Assume James is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Noah is a knave. Assume Sophia is a knight. No contradiction is found in their claim that James is a knight. Joseph cannot be a knight, because this would contradict the claim of their own that Isabella is a knight. Assume Joseph is a knave. No contradiction is found in their false claim that Isabella is a knight.