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 What constitutes an answer here? by Richard)

This problem has some semantic issues I think.  In the generalized M and N question, the problem gets better stated.  How do you randomly place a destroyer onto a grid so that the probability a square is covered is the same for all squares.

The issue with the way the 5 by 5 problem is laid out is that after the destroyer is placed, the probablitiy that a square chosen at random "hits" is always 2/25, no matter how the destroyer is placed.  The condition of the probability is that the destroyer is in place.  It's a given.

Posted by bernie on 2006-02-15 17:49:59