[net.puzzle] SOLUTION to intersection puzzle!

gilje@stolaf.UUCP (Mark A. Gilje) (10/12/84)

Here is the solution to the intersection puzzle.  Sorry to 
post it so soon, but I'm going off the net for a while.

For every four vertices in a polygon, there exists one and only one intersection
when they are all connected.  There are n choose 4 ways of choosing 4 vertices

out of n vertices.  Therefore, the maximum number of intersections in an

n-gon is ......... n choose 4 or n(n-1)(n-2)(n-3)/24 for non-probablility

experts.

Thanks to those who sent answers!

Mark Gilje
stolaf!gilje