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?

(In reply to 3 to 5 questions, depending on who you figure out first by liz)

SORRY!!!! i read the question too quickly i thought there were 3 people in the story!!!

the ammended solution is... you hav to ask 3-4 questions, depending on who the native is.

1st question:

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

Asking the native the same question twice, and assuming he was a knave, he will answer 'yes' and 'no' in either order.

Then ask, "Are you a knave?" To this he can say, again, 'yes' or 'no' in either order. If he says 'no' he is lying and not telling the truth, so you know he will tell you the true answer to your next question: (pointing to one of the paths) "Does this path lead to home?"
Instead, if he says 'yes' to "Are you a knave?", then he is telling the truth, and so he will lie about the next question. So you ask "Does this path lead to home?" and take the opposite path that he says is the path to home.

Thus, any of the above possibilities require you to ask 4 questions in total to get the correct path home.



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

If the native was a liar, then ask him which path was the path to home, and he will lie about it. So you just take the other path. This also requires you to ask 3 questions.

Posted by liz on 2006-06-09 09:48:16