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 re(2): Clarification, if you're lost by Tristan)

My "solution" has a problem, I now see. Perhaps it can be saved, however, and maybe in such as way that the desired probability becomes your 2/25 value rather than the erroneous 1/13 I thought I had achieved. I'll have to ponder this some more.

Edited on February 16, 2006, 7:28 pm

Posted by Richard on 2006-02-16 19:19:23