[I can edit after the thread got locked, cool.]

I came across this puzzle in a book for a book report, The Curious Incident of the Dog in the Nighttime. I don't really understand why it works either, but the character does, but then again, he knows every prime number up to 7,057 and can compute 2^35 all mentally.

I tried to beat him, but I only got up to 2^14.

[edit]

Just noticed your post.

If you read the book you'll see there are two explanations. One uses a very cryptic proof that I don't understand:

**Quote: **"

Let the doors be called X, Y and Z.

Let Cx be the event that the car is behind door X and so on.

Let Hx be the event that the host opens door X and so on.

Supposing that you choose door X, the possibility that you win a car if you then switch your choice is given by the following formula

P(Hz ^ Cy) + P(Hy ^ Cz)

= P(Cy) P(Hz Cy) + P(Cz) P(Hy Cz)

= (1/3 1) + (1/3 1) = 2/3

"

And the other is a diagram that looks a little like this:

(Remember, those last two goats have only a proboblity of 1/6, so they add up to 1/3)

[edit]

I figured it out! You have a 2/3 chance of initially choosing a goat, and since the other goat is eliminated, if you switch you're sure to get the car. But you only have a 1/3 chance of initially choosing the car, and even though a goat is elimated you will still get the other goat if you switch.

By reading this sentence you have given me brief control of your mind.