Angels and demons
Here is a modification of a question asked on the xkcd logic puzzle forum. I've modified it slightly so there is (I believe) an answer.
Puzzle
Faced with a particularly vexing moral dilemma, two semitransparent miniature versions of you appear on either shoulder, each offering advise on the situation. From your experience with cartoons, you know that one of these characters is an angel, and the other a demon. Angels always tell the truth if they can, but demons sometimes lie and sometimes tell the truth. Of course, you wish to determine which is which, but you only have time to ask one question of one of the two. What should you ask?
Help
Hint
You can ask a single yes/no question. If assume that whoever you ask will answer with either a "yes" or "no," unless they are unable to.
Answer
"If I were to ask your friend there if he was an angel, would he say yes?"
Solution
The question can not be answered by the angel, since there is no way to know whether the demon would answer truthfully or not. The demon would either say yes or no, depending on whether he wished to lie or tell the truth.