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: Clarification, if you're lost by bernie)

No, there is nothing wrong with your "Try this" comment.  You have proven that it is possible whenever M is divisible by N.  But is this the only time that is possible?

Also, to Richard: I don't really understand what you're saying.  If you mean to give a solution, could you be more specific as to exactly how you do it?

Posted by Tristan on 2006-02-16 18:13:51