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?

(In reply to Question by Dustin)

Conjunctions like "and" and "or" connect two phrases to make one statement.  You can also use an "if...then..." statement, if that works for you.  Recall that "If A, then B" is true if A is false.

In the second question, you are looking for a statement only a knave can say, but you cannot prove this statement by itself true or false.  For example, "I am a liar" does not work, because you know just from the statement, that the knave is lying.

The first question, like all the others, is actually possible in one statement.  Perhaps finding it will help with the second question...or not.

Edited on December 7, 2004, 11:34 pm

Edited on December 7, 2004, 11:43 pm

Posted by Tristan on 2004-12-07 23:32:08