Brainteaser #7 – Game Show

Yellow and green doors

You’re a game show finalist. You’ve reached the final sequence and are faced with two doors, one on the left, one on the right. Behind one door lies £1,000,000 and behind the other lies a donkey (which you sadly don’t even get to keep).

A man and a woman stand in front of the doors and they know which prize is behind which door. Your host explains quite simply that one will always lie and one will always tell the truth about which door hides the prize, but you don’t know which is which.

You can ask one person one question and one question only and you obviously aren’t allowed to simply ask what door the prize is behind. You must then open a door. No mind-reading or Jedi mind tricks allowed!

What question do you ask to guarantee that you win?

You can ask either of them the following question: “If I asked the other person what door is hiding the money, what door would they say?” Regardless of the person you ask, you can choose the opposite door to what they answer to win the money.

But why does this guarantee you the money?

Person A – The Liar: “Person B would say it’s behind their door (Door B).” This means the prize is hidden behind door A.

Person B – The Truthful One: “Person A would say it’s behind my door (Door B).” This is the truth, as they know person A would try and lie, and thus the prize is hidden behind door A. In conclusion, you can safely choose the opposite door of either answer, Door A to win the money.

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