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Hide and destroy (Posted on 2006-02-15) Difficulty: 3 of 5
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?

See The Solution Submitted by Tristan    
Rating: 3.4000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Soviet Russia | Comment 2 of 13 |
In Soviet Russia, destroyers place YOU!
  Posted by Hugo on 2006-02-15 16:17:18
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