The car-goat-goat Problem

Where it came from

I'm not really sure how old this logic problem is, but the first time I heard it, it was was told to me by a friend who had read it in Parade Magazine in Marylin vos Savant's column. I hadn't heard of her before, and I haven't heard of her since, but for a while, she was the center of my life as I grappled with this problem.

The problem

I'm sure Marie set it much better than I'm about to, but here is the gist of the puzzle. You're on the Let's Make a Deal show with Monty Hall as your host...

Monty:

Here we have three boxes, and behind one of them is a fabulous new car, and behind the other two are goats. Now by "goat," I don't mean that there's an actual goat in there, I mean that there's a bum prize like a year's supply of Rice-a-Roni, the San Francisco treat or something like that.

Here's what we're going to do. You go ahead and point to one of the boxes.

Contestant:

Okay. I pick that one. (Points to a box)

Monty:

Now, since we know that at least one of the two boxes you didn't choose has to have a goat in it (because there are two goats), I'm going to go ahead and open up one of those two boxes and show you a goat. (One of the boxes rises smoothly into the ceiling and vanishes, revealing a year's supply of Rice-a-Roni, the San Franciso treat)

Now, I'll tell what we're gonna do. You can keep the box you've already chosen, or you can switch to the other box - the one I didn't expose. What do you want to do?

The Question

Is it to your advantage to take Monty's offer and switch to the other box?

The Answer(s)

vs.

There are two schools of thought on this, we'll call them the Wombat school, and the Katydid school. You should ponder long and hard about what you think the answer is, then you should read each of the schools of thought, and then you should know. If you don't then here's the real answer.

The car-goat-goat Problem / corby@intuit.com
July 1997 (updated April 6, 1998)