Heaven & Hell
You are faced with a choice of two doors; one leading to heaven, the other to hell. A guard stands in front of each. You know that one guard always tells the truth and the other always lies but not which is which. (The guards know if they lie). What one question can you put to one guard to determine which is the door to heaven?
Answer:
You ask guard A whether guard B would say that his door leads to heaven. If the answer is "yes heaven", you want the door behind guard A; if the answer is "no hell", you want the door behind guard B.
Only one guard lies, so requesting information as if it were via both guards will cause one change from truth to lies. So when you ask the question, you will receive lies and you therefore know that the door you are informed to be for hell is in fact for heaven.
When asked where he wanted to end up after death, Oscar Wilde replied: 'Both. Heaven for the scenery, hell for the company.'