You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question. Except! One lies and one tells the truth, and you don't know which is which. So, What do you ask?
You ask each twin "What would your brother say?"
This works because.... Well let's say the correct path is on the left side. So say you asked the liar "What would your brother say?" Well, the liar would know his brother was honest and he would say the left side, but since the liar lies, he would say right. If you asked the honest twin the same question, he would say right, because he knows his brother will lie. Therefore, you would know that the correct path was the left.
A man is found murdered on a Sunday morning. His wife calls the police, who question the wife and the staff, and are given the following alibis: the wife says she was sleeping, the butler was cleaning the closet, the gardener was picking vegetables, the maid was getting the mail, and the cook was preparing breakfast.
Immediately, the police arrest the murdered. Who did it and how did the police know?