perplexus.info :: Probability : Eight Points

Eight Points (Posted on 2016-08-24)

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?

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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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