Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site utah-gr.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!sdcsvax!dcdwest!ittvax!decvax!linus!philabs!pwa-b!utah-gr!thomas 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