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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: ( You must be logged in to post comments.)
  Subject Author Date
re: Solutionbernie2006-02-17 17:37:57
SolutionSolutionAvalonXQ2006-02-17 05:00:59
re(3): Clarification, if you're lostRichard2006-02-16 19:19:23
re(2): Clarification, if you're lostTristan2006-02-16 18:13:51
Not a valid solution?Richard2006-02-16 15:41:42
re: Clarification, if you're lostbernie2006-02-16 13:46:31
Hints/TipsClarification, if you're lostTristan2006-02-15 21:36:39
re: What constitutes an answer here?bernie2006-02-15 17:49:59
Some ThoughtsWhat constitutes an answer here?Richard2006-02-15 17:18:41
Try thisbernie2006-02-15 17:01:32
Some ThoughtsA solutionLeming2006-02-15 16:24:16
Soviet RussiaHugo2006-02-15 16:17:18
ThoughtsEric2006-02-15 15:29:16
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