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?

The fewest number of questions I found is two.

Independently arrived at, and basically the same as arrived at by Patrick, but with one main difference. I made an assumption the native may not know where "home" was, but would be more likely be familiar with which road leads to a gruesome demise. The two questions then being:

1. Are you a Knave?
2. Will the left fork take me to a gruesome demise?

If the answer to the first question is "No.", then the native is either a Knight or a lie-first Knave. The second answer will then be the truth. If the answer to the second question is "Yes", take the right fork.

If the answer to the first question is "Yes.", then the native is either a Liar or a truth-first Knave. The second answer will then be a lie. If the answer to the second question is "Yes", take the left fork.

Edited on May 23, 2006, 3:07 am

Posted by Dej Mar on 2006-05-23 00:57:41