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Four Pins and a Rubber Band (Posted on 2005-02-10) Difficulty: 5 of 5
Four pins are randomly nailed to a square board (according to a uniform probability distribution), and a rubber band is stretched completely around them to form a convex shape. What is the probability that the rubber band is in the shape of a triangle?

  Submitted by David Shin    
Rating: 4.1000 (10 votes)
Solution: (Hide)
The answer is 11/36. This is actually a special case of Sylvester's Four Point Problem, whose solution is outlined in the following website:

http://mathworld.wolfram.com/SylvestersFour-PointProblem.html

When I submitted this problem, I did so without actually having computed an answer, though I figured it would not be overly complicated to compute. The above website indicates that the computation is an in fact an extremely difficult one; if I had known this previously, I would not have submitted the problem on perplexus. My apologies.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2008-03-03 11:02:36
Hints/TipsNumerical solutionBob Smith2005-06-15 21:07:38
Some Thoughtsre: i ve got itchris2005-02-26 06:28:05
re: about the solutionSteve Herman2005-02-20 21:05:12
Questionabout the solutionCharlie2005-02-20 16:35:28
Solutioni ve got itClara Levy2005-02-18 19:57:17
Some ThoughtsSuggestionAngela2005-02-15 11:43:23
SolutionSpoiler -- I concedeSteve Herman2005-02-12 14:00:03
formal solutionronen2005-02-12 11:31:06
re: thoughts--and a simulationSteve Herman2005-02-11 18:00:39
Hints/Tipsthoughts--and a simulationCharlie2005-02-10 18:07:01
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