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From: thomas@utah-gr.UUCP (Spencer W. Thomas)
Newsgroups: net.puzzle
Subject: Re: High School Math problems:Answers and a toughie!
Message-ID: <1214@utah-gr.UUCP>
Date: Fri, 19-Oct-84 13:22:07 EDT
Article-I.D.: utah-gr.1214
Posted: Fri Oct 19 13:22:07 1984
Date-Received: Mon, 22-Oct-84 07:05:29 EDT
References: <1975@stolaf.UUCP> <1590@ucla-cs.ARPA>
Reply-To: thomas@utah-gr.UUCP (Spencer W. Thomas)
Organization: Univ of Utah CS Dept
Lines: 27
Summary: 

In article <1590@ucla-cs.ARPA> dgc@ucla-cs.UUCP writes:
>
>    >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.
>
>
>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
>

I'm afraid it's more complicated than that.  For example, this formula
gives 15 for a hexagon, but a simple picture shows only 13.  This is
because of the three diagonals that intersect in a single point at the
center.

I don't have the answer, but it looks like it's back to the drawing
board.

=S