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?

I do not conclude that the fewest number of questions can not be one, but I do not find that either Caleb’s or Robby’s solutions provide the answer.
Neither can I attest that my own reasoning here is valid.

Caleb’s question (re-phrased slightly to eliminate the abiguous word ‘right’).:

“If I were to ask you the ‘safe’ path to take, which way is NOT the way you would tell me to go?"

A question arises, do Knaves and Liars lie to themselves, or just provide an answer which is a lie?

In logic, the Truth table for the conditional statement is always TRUE except when the condition being true implies the statement to be false. Then the statement is FALSE.

The first fact is “I ask you the ‘safe’ path to take”. If I do ask, then the first fact is TRUE. If I do not ask, then the statement can not be judged, thereby by default it is given the value TRUE.
The second “fact”, re-phrased, is “which way IS NOT the ‘safe’ path”. The Knight and truth-telling Knave would provide a TRUE answer by indicating the WRONG path. As a lying Knave or Liar, to make a FALSE statement, i.e., tell a lie, they would implicate the fact to be “which way IS NOT NOT the ‘safe’ path”, and thus would indicate the RIGHT path. Thus, without knowing who was as Knight, Liar or the type of Knave, the ‘safe’ path is unknown.

Robby’s question:

“If the opposite of a knight is a liar and the opposite of a lie-first knave is a truth-first knave, what would your opposite have answered if I would have asked him/her which route does not lead home instead of this question ?"

This complex multi-conditional statement actually is written as a paradox. It is such because it can not provide a conclusion. A Knight would answer how a Liar would answer as a Knight would answer as a Liar would answer as a Knight would answer as a …… and, on and on.

Edited on May 24, 2006, 8:27 am

Posted by Dej Mar on 2006-05-24 08:26:24