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Eight Points (Posted on 2016-08-24) Difficulty: 3 of 5
Eight points are selected at random from the interior of a unit circle.

What is the probability that these eight points constitute the eight vertices of a convex octagon?

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Analytical solution | Comment 2 of 3 |
Who am I kidding?  A much simpler version of this extremely difficult problem popped up a few years ago in perplexus, entitled "Four Pins and a rubber band".  It was beyond our ability to do when n = 4. and it is exponentially more difficult now that n = 8.

Here is the link to the solution at Wolfram for n = 4.  The n = 8 situation is not covered.

  Posted by Steve Herman on 2016-08-24 21:23:32
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