When I visited the Knights and Liars Archipelago, one island I visited was called Liontruth. The tourism had a great influence on the island, so much that the knaves on the island spoke differently from most knaves. They didn't have to follow an alternating pattern, but could tell truths (like knights always do) and lie (like liars always do) in whatever pattern they wanted. The three types of inhabitants are indistinguishable by eye.

If a tourist thinks the local knaves alternate truths and lies how can a knave convince the tourist that he is not a knave?

How can a knave from this island prove himself in one statement without revealing whether he is lying or not?

How can a knight prove himself in one statement?

How can a liar prove himself in one statement?

What single statement can be said by either a knight or liar but not a knave?

A knight can prove himself by stating the following: "If I am not a knight, then I am not a knave." For a knight, the premise is false, so the consequence is irrelevant. For a liar, both the premise and the consequence are true, which is impossible. If a knave is lying, then the premise is true, a contradiction. If a knave is telling the truth, then the consequence is false, also a contradiction.

Posted by Eric on 2004-12-07 21:37:41