Question

a man is on a game show. he is presented with two doors, one on the left, and one on the right. behind one is 2 million dollars, and behind the other is a donkey. choose the correct door to win the prize. there are also two men in front of the doors, and they know which door leads to the millions. one wears a black hat, the other wears a white hat. the host explains that one of the men is a liar, and will always lie, and the other man will always tell the truth - but you don't know which is which. you can only ask one of the men only one question. what is the question, and which man do you ask to ensure you win the money?

Answer 1

You ask either guy: Which door would the other guy say the money is behind.  Then pick the other door.  This is why: if you ask the truth teller, who will tell you the  door the liar will tell you, the wrong door.  If you ask the liar, he will tell you the wrong door, because he lies about what door the truth teller would say.  In  either case, they give you the wrong door, so you choose the other.

Answer 2

It doesn't matter which man you ask. The  answer you get will tell you
where the million $ is, although you still won't know whether the man
you asked was the liar or the truther.  (But who cares about that.  Right ?)

Pick either 'guard',and ask him:

" IF I were to ask you 'Is the money behind your door ?', would you say 'Yes' ? "