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From: gilje@stolaf.UUCP (Mark A. Gilje)
Newsgroups: net.puzzle
Subject: SOLUTION to intersection puzzle!
Message-ID: <1991@stolaf.UUCP>
Date: Fri, 12-Oct-84 14:18:37 EDT
Article-I.D.: stolaf.1991
Posted: Fri Oct 12 14:18:37 1984
Date-Received: Sat, 13-Oct-84 07:55:34 EDT
Organization: St. Olaf College, Northfield MN
Lines: 16

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