The Fork in the Road
A traveller comes to a fork in the road, and he isn't sure which path he should take. There are two men there: one who always lies and one who always tells the truth. The traveller doesn't know which is which, and he can only ask one question to one person to find his way. What is his question?
Hint: The question must force the liar to lie in a way that makes him tell the truth.
Solution: The traveller must ask, "If I were to ask you if I should take this path, would you say yes?" The truth-teller will tell the truth, while the liar will lie about lying, forcing him to tell the truth.