*Originally posted by beetlebomb*

**A man is on an island in which half the population always lie and the other half always tell the truth.
**

On his way to town he comes to a fork in the road and doesn't know which way to go.

How can this man word his question of which road to take so that whoever he asks, truth teller or liar will tell him the same right way to go?

This problem is more advanced than we might think at first.

The liar lies because he doesn't give the correct information to the man. If he knew that his proper lie would be interpreted in such a way that the correct information would be delivered, he wouldn't lie, would he? If anyone knew he always was lying, he is not interested to lie anymore. He would say something that sounded as a lie, that everyone would take as a lie, and furthermore act upon it in a way as if anyone would believe was a lie.

If I ask a man who is known to always lie, and he kows himself his reputation as a constant liar, the question "Do you speak the truth now?" Then the answer "Yes" wouldn't be trustworthy, and therefore to lie would be pointless.

But if he flipped a coin behind his back and answer accordingly the outcome of the coin, then the answer, a "Yes!" or a "No!" would be without any information, whatsoever.

If a lie means an answer that we can trust that it is a lie, it is not really a lie, is it? It gives reliable information.

But if the answer couldn't be trusted upon if it really is a lie or the truth, then we cannot trust it at all, can we?

So a real liar would give an answer that really is desinformation, to really make the one asking to act in a wrong way, then he would tell the truth if he knew himself that the answer would send the man who asks in the wrong direction.

So a good liar should always give an answer that makes the most harm. A chronic liar isn't a good liar if you can rely that he lies everytime.

So what kind of a liar would we have here? A good liar that we can never rely upon, or a chronic liar that we always can trust that he gives a false answer?

...assuming, of course, that we only asks question that can produce a 'yes' or a 'no'.

A liar that produces any kind of answer, we call a politician.