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 re: I hope this is right, but..... by Penny)

My previous answers were not entirely correct. This knavish puzzle has made me lie awake for many sleepless knights.

Let me try to revise these answers.

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

"I am not a knave and have never been a knave." 

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

"My answer to your next question will be a lie."

How can a knight prove himself in one statement (to a tourist who thinks the local knaves alternate truths and lies)  ?

"I am not a liar and have never been a liar, for if I were a liar then I would not be a knight."

How can a liar prove himself in one statement (to a tourist who thinks the local knaves alternate truths and lies) ?

"I am not a liar and I have never been a liar, since if I were a liar I would be nothing but a knave."  

What single statement (according to a tourist who thinks the local knaves alternate truths and lies) can be said by either a knight or liar but not a knave?

"I am not a liar and I have never been a liar."

   

Edited on December 10, 2004, 12:08 am

Posted by Penny on 2004-12-09 23:37:37