You are lost once again in the land of Knights, Knaves, and Liars, and once again you find yourself at a fork in the road. You know that one path will lead you to a safe return home, while the other will lead you to your own gruesome demise. (You really need to find a better vacation spot next year!)

Standing at the fork is a native, who might be either a Knight (who always tells the truth), a Knave (who alternates between true and false statements), or a Liar (who always lies). You have no way of knowing which he is. Worse yet, you realize that if he is a knave, you don't know if he will tell you the truth first, and then lie, or lie first and then tell the truth, etc.

What is the fewest number of questions you have to ask to find out which is the safe road, and what are they?

One question.  I would ask, "If I were to ask you the right path to take, which way is NOT the way you would tell me to go?"

No matter whether he is a knight, liar, or knave, he is either going to tell the truth or a lie.  If he is going to tell the truth, the way he would NOT tell me to go is the wrong way.  And he is going to tell the truth, so he will indeed point in the wrong way.  If, however, he is going to tell me a lie, then the way he would NOT tell me to go is actually the RIGHT path.  But since he's going to lie, he will point to the WRONG path, just like if he were to tell the truth.

So no matter what he is, knight, liar, or knave, asking this question will retrieve the wrong path as the answer, and I will take the other path.

Posted by Caleb on 2006-05-23 02:59:55