You must randomly place a destroyer (a 1x2 sized ship) on a 5x5 grid such that if I searched in any single square, my probability of finding the destroyer there is exactly 2/25. Is such a probability distribution possible? You cannot simply choose randomly one of the 40 possible positions of a destroyer because corners would have a 1/20 chance to contain the destroyer, while the center would have 1/10 chance.

Generalize to a 1xN sized ship in a MxM grid. When is it possible to place the ship with an even probability distribution in each square?

(In reply to Clarification, if you're lost by Tristan)

Anything wrong with the "Try this" solution?  It works when M is a multiple of N, so maybe the 5x5 with the 1x2 can't be done?

Posted by bernie on 2006-02-16 13:46:31