You're in a room with two guards, and each guard is guarding one of two exits. One guard always lies. One guard always tells the truth. You don't know which is which. One door leads to freedom. One door leads to the horrible man-eating tiger pit of doom from which there is no escape. You don't know which is which. And you don't know whether the truth-telling or the lying guard is guarding the "right" exit.

You know very little.

You're standing in the room. You're allowed to ask one question to one guard, and after that you have to choose your door. What question do you ask?

Highlight to see the answer: "Which door would the other guard tell me is the exit?" The truth-teller will point at the tiger door, because the other guard is a liar and wouldn't point at the exit. The liar will point to the tiger door, because the other guard is a truth-teller and would point at the exit. So either way this is a sure test to find the tiger door, and so you should take whichever door the guard doesn't point at.

In any event, it turns out this little brainteaser has some useful applications.