Math and Logic Puzzles: Truth-tellers and Liars

A well-known logic puzzle that I first encountered during elementary school in one of the puzzle books that my mom bought for us:

You are traveling on a road to a castle and come to a fork in the road where it splits into two paths. Standing at this fork in the road are two gatekeepers, one who always tells the truth, and one who always lies, but you don't know who is the truth-teller and who is the liar. You need to know which road leads to the castle. What question do you ask to find the road to the castle?

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If that's too easy, this one is not from elementary school:

The Truth-teller, the Liar, and the Ambiguous

The page includes the answer, and an interesting discussion. Which I haven't bothered to actually understand in detail yet.

If only real life were as clear as math.