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?

Over any finite amount of time, it is possible that a knave could masquerade as either a knight or a liar. In that sense the problem breaks down. However, there is a solution.

A knave can convince a tourist simply by repeating himself, since if knaves alternate truths and lies then the same statement twice cannot be both true and false. So, he can say "I am a knight. I am a knight."

The easiest and most direct way for a knave to say something that proves he is a knave is not to say something specific to knaves - no such thing exists. Rather, he can say "I am not a knight." A knight cannot say this because it is false; a liar cannot say this because it is true. Hence only a knave can make that statement.

To prove oneself a liar in one statement, you have to say something that is totally false in such a manner that even a knave cannot say it because it contradicts himself.

 

Edited on December 7, 2004, 9:01 pm

Posted by Eric on 2004-12-07 20:29:36