Four Men in Hats

I stumbled upon a brain teaser today called the Four Men in Hats Puzzle (aka the Prisoners and Hats Puzzle). Here’s the puzzle:

Four Men in Hats

Shown above are four men buried up to their necks in the ground. They cannot move, so they can only look forward. Between A and B is a brick wall which cannot be seen through.

They all know that between them they are wearing four hats–two black and two white–but they do not know what color they are wearing. Each of them know where the other three men are buried.

In order to avoid being shot, one of them must call out to the executioner the color of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out.

After one minute, one of them calls out.

Question: Which one of them calls out? Why is he 100% certain of the color of his hat?

Keep reading if you want to know the answer.

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Car Goat Problem

Six or seven years ago, I took a philosophy class in which the professor introduced me to the “Car Goat Problem” (also known as the “Monty Hall problem“). The problem is this:

Imagine you are on a game show and there are three doors in front of you. Behind one of the doors is a car and behind the other two doors are goats. The game show hosts asks you to choose one of the doors (the one you believe has the car). Then, the host opens one of the other doors, which has a goat. The host then gives you an opportunity to change your mind. You win whatever is behind the door your choose. Should you switch doors or should you stay with your initial door? Or does it not matter?

So, what do you think? My solution is below.

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