Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site ucla-cs.ARPA Path: utzoo!watmath!clyde!bonnie!akgua!sdcsvax!sdcrdcf!trwrba!cepu!ucla-cs!dgc 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 Arpa: dgc@ucla-locus.arpa UUCP: ...!{cepu, ihnp4, randvax, sdcrdcf, trwspp, ucbvax}!ucla-cs!dgc