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From: dgc@ucla-cs.UUCP
Newsgroups: net.puzzle
Subject: Re: High School Math problems:Answers and a toughie!
Message-ID: <1590@ucla-cs.ARPA>
Date: Fri, 12-Oct-84 11:06:13 EDT
Article-I.D.: ucla-cs.1590
Posted: Fri Oct 12 11:06:13 1984
Date-Received: Sun, 14-Oct-84 07:11:46 EDT
References: <1975@stolaf.UUCP>
Organization: UCLA CS Dept.
Lines: 26


    >Find the greatest number of intersections in an n-gon if all
    >vertices are connected. Ex.  If you draw lines connecting all four
    >vertices of a quadrilateral, you get one intersection.

This problem appeared in the Fifteenth William Lowell Putnam
Mathematical Competition, held on March 5, 1955.  This is a university
level competition, sponsored by the Mathematical Association of America. 
Among former winners and "honorable mentioners" are some of the most
distinguished mathematicians and physicsists of today.

The answer to the problem is implicitly stated in the problem. 
Specifically, every four distinct vertices give rise to one intersection
and conversely, each intersection determines four distinct vertices.  So
the the answer is the number of ways one can choose four vertices from
the given n. That is, it is "n choose 4" which is

		n(n-1)(n-2)(n-3)
		----------------
		       24


David G. Cantor

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