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?

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.

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