Problem of the Week 1118

Monty Hall Takes a Vacation

Alice and Bob face three doors marked 1, 2, 3. Behind the doors are placed, randomly, a car, a key, and a goat. The couple wins the car if Bob finds the car and Alice finds the key.

First Bob (with Alice removed from the scene) will open a door; if the car is not behind it he can open a second door. If he fails to find the car, they lose. If he does find the car, then all doors are closed and Alice gets to open a door in the hope of finding the key and, if not, trying again with a second door.

Alice and Bob do not communicate except to make a plan beforehand. What is their best strategy?

Source: A. S. Landsberg (Physics, Claremont Colleges, California), Letters, Spring 2009 issue of The Mathematical Intelligencer.

© Copyright 2009 Stan Wagon. Reproduced with permission.