Originally posted by Julian Davies
Point to one of them and ask the other "Would he call you a liar?" If the answer is no the one you are asking is the liar. If yes the one you are pointing at is the liar. Sorted with one question.
Correct answer - ask Mr Left the following: "If I asked Mr Right which way to go, what would he say?"
Let us assume North is the correct direction.
If Left is the liar, then Right would say North, but Left would change the answer to South.
If Left is the truth teller, Right would say South, and Left would correctly report the answer as South.
Either way, you get the wrong answer, and go the other way.