The Two Guards

The Two Guards (a 2000-year-old classic)

You stand at a fork in the road. Next to each of the two forks, there stands a guard. You know the following things: 1. One path leads to Paradise, the other to Death. From where you stand, you cannot distinguish between the two paths. Worse, once you start down a path, you cannot turn back. 2. One of the two guards always tells the truth. The other guard always lies. Unfortunately, it is impossible for you to distinguish between the two guards.

You have permission to ask one guard one question to ascertain which path leads to Paradise. Remember that you do not know which guard you're asking -- the truth-teller or the liar -- and that this single question determines whether you live or die. The question is: What one question asked of one guard guarantees that you are led onto the path to Paradise, regardless of which guard you happen to ask?

A classic puzzle brought to my childhood by Jim Henson's classic Labyrinth. It seems to be a variant of the Knights and Knaves puzzles popularized by Smullyan. Smullyan, never one to rest on previous laurels, developed far more difficult versions including the purported "Hardest Logic Puzzle Ever." (dubbed by Boolos)

The famous labyrinth scene can be found here, but I have prepared a formalized solution based on Boolean Algebra which might prove more intuitive....