A mouse has 3 rooms to go into.

If it goes into room 1, it will find the cheese after 3 minutes.

If it goes into room 2, it will look for cheese for 4 minutes, won't find it, and will go out.

If it goes into room 3, it will look for cheese for 5 minutes, won't find it, and will go out.

The mouse will not remember that it was in rooms 2 and 3 after it goes out of them, and it will continue going in and out until it finds the cheese. (It can go into the same room again and again.)

What is the average time for the mouse to find the cheese?

This problem (identical wording) was posted on mathforum.org in 1997 (by "Nadav Shalit").  The same solution (=12 min) was reached by various reasoning.  The main simplification is the obvious one of combining the logic for rooms 2 and 3 (2/3 probability, with T = 4.5 minutes for either).  The topography must be interesting, since it suggests zero time from leaving one room to entering the next (possibly the same) -- or else a very fast or very confused mouse.

 

Posted by ed bottemiller on 2008-09-11 17:03:16