Fork in the Road

Fork in the road puzzle image

Question:

You're on a journey to the picturesque Truthsville, where all the residents tell the truth all the time, but come to a fork in the road. One way leads to Liartown; a nasty place where everyone lies all the time, and the other to Truthsville, but the sign is broken and you don't know which way to go! Help is at hand, there's a resident from each town at the junction. The puzzle is this:

You may ask one question to either resident (not both), and the answer will tell you which way Truthsville is. What should the question be? Bear in mind that one will always lie, and the other always tell the truth, but you are unaware which is which.

Answer: (click to show)

You must ask either one "where would the other person say Truthsville is?" If you ask the liar, he'll say "The other guy is a liar, so he'd direct you to Liartown up there". The brilliant thing is that the truth teller would say the exact same thing! So both would say that the other would direct you to Liartown, and so you know to take the other path.

This plays on a simple rule of arithmetic: a positive times (and) a negative is always negative. So you get both residents to say what the other would say, and you get cross over a positive and negative answer, which together direct you the wrong way!