Ann and Art face three doors marked 1, 2, 3. Behind the doors are placed,
randomly, a car, a goat, and a key. The couple wins the car if Art finds
the car, then Ann finds the key.
First, Art (with Ann removed from the scene) opens a door; if car is not
behind it, he opens a second door. If he fails to find the car, they lose.
If he does find the car, then all doors are closed and Ann gets to open a
door; if key is not behind it, she is allowed to open a second door.
If she fails to find the key, they lose.
Ann and Art do not communicate except to make a plan beforehand.
Using the best strategy, what is the probability that they win the car?
Ok; I'll give you a hint: the probability (with best strategy) is 2/3.
Now this puzzle becomes: HOW do they do it?