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 question to ask is:

"Will you say yes or no if i asked you the question 'are you a knight?'"

Asking the 1st native the same question twice, and assuming you picked (by chance) the knave to ask this first, he will answer 'yes' and 'no' in either order.

Ask the 2nd native the same question once, and if he were a knight, he would say 'yes', because he would say 'yes' to the question 'are you a knight?' Then proceed to ask this same person to point you to the correct path home.

Instead, if this 2nd native was a liar, he would say 'no' because he wants to lie about the fact that he would say 'yes' to the question 'are you a knight?' And so you ask the 3rd native to show you the way home.

thus, a total of 4 questions.

If the 1st native you asked was not the knave, then you would get either the knight answering 'yes' and 'yes', or the liar answering 'no' and 'no'.

If the knight was figured out first, then just ask the knight to tell you which path to take, and you would have asked 3 questions (the sweetest & easiest!!!).

If the liar was figured out first, then ask the 2nd native the question twice. A knight will say 'yes' and 'yes' and so you can ask him the path to home. A knave wil give 'yes' and 'no' answers in either order and so you have the last person, the knight, to ask the question bout the right path home. Both these required you to ask 5 questions in total to know the correct path home.

Posted by liz on 2006-06-09 09:27:09