Logic: Door to million dollars

Question

You approach two doors. There are two men. Each man stands in front of one door. Through one door you will win one million dollars. Through the other they will take one million dollars off you. One man always tells the truth. The other always lies. You have to ask one man only one yes/no question so that you go through the correct door. What is the question you will ask?

Answer 1

Ask the following question: "If I asked the other man whether he has a million dollars behind him, would he say yes?" If the man says yes, there is a million dollars through the door behind him. If he says no, the million dollars is behind the other man.

Consider the first case:

win money => tells truth

lose money => tells lie

If you ask the man who tells the truth, he will say yes. If you ask the man who lies, he will say no. Think about it and you will understand.

Now consider the second case:

win money => tells lie

lose money => tells truth

If you ask the man who tells the truth, he will say no. If you ask the man who lies, he will say yes.

Therefore, if you ask the question above, if the man says "yes", there's a million dollars behind him. If he says no, take the other door.

Answer 2

"If I asked the other man if his door leads to the million dollars, would he say 'yes'?". Work out the different scenarios and see what happens

Answer 3

Its pretty simple.Assume that the doors are named A,B respectively and the two men standing before the door as X,y respectively.For your reference consider that X always speaks truth and Y speaks lie and door A has 1million dollars and B will take 1million dollars from you.Go and ask X that what Y would tell him if he asks him where the million dollar prize was.Mr.X's answer will be that Y would tell the door B as the answer.considering this if X was a lier than A will hav the prize.Ask the same type of question to Y.(i.e..Go and ask Y that what X would tell him if he asks him where the million dollar prize was.Mr.Y's answer will be that X would tell the door B as the answer.considering this if Y was a lier then A will hav the prize.so therefore hence proved..........

 ......-hope that helped you 
        by A.Varun Akash