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CAS and SOA Sponsor International Math Competition

by John P. Robertson, Liaison Representative to the Mathematical Association of America

Hundreds of the world's most talented high-school mathematics students will converge on Washington, DC, in July 2001 to participate in the 42nd Annual International Mathematical Olympiad (IMO). Each of about 90 countries will send up to six contestants for a two-day competition. Three problems are set each day, with 4 1/2 hours allotted for the contestants to attempt solutions. CAS members can appreciate the fact that it then takes several days to grade the papers. The U.S. team has generally done very well, placing in the top 5 in 21 of the 24 years for which the U.S. has participated. Last year's team was third out of 76 countries. At the 1994 IMO every member of the U.S. team got a perfect score on every question, a feat that is unique in the history of this competition.

The sponsoring nonprofit corporation, IMO 2001 USA, Inc., has goals beyond that of staging a contest:

For the participants, IMO 2001 USA will provide a unique opportunity to build friendships with students from other countries, to exchange mathematical ideas, and to learn about other cultures.

Hosting the visiting teams and underwriting the associated events costs money. The CAS and SOA provide support by being members of IMO 2001 USA, Inc., and participating on its board of directors.

In order to raise the $3.7 million needed to run the contest and provide funding to meet the related goals, additional sponsorship is being sought. Corporate donors that might be willing to contribute $100,000 or more are being approached. Ideas for likely candidates are welcomed.

To get the IMO 2001 USA, Inc. started, the U.S. Department of Education awarded a grant of $100,000 for five years to provide the initial organizational base and initiate the research aspect of the program. Notification has recently been received from the National Security Agency that a $250,000 proposal and one to the National Science Foundation for $400,000 have been approved. Wolfram Research, Inc., maker of the Mathematica software, has become the first major corporate sponsor of IMO 2001 USA, Inc. with a total sponsorship of $270,000.

The U.S. team is selected through the sequence of three contests run by the American Mathematics Competitions. This organization is sponsored by 13 mathematical science organizations, including the CAS and the SOA. The first competition attracts over 350,000 students from every state in the nation. The second and third competitions are by invitation only, based mainly on results in the previous rounds. The third contest is 1999 United States of America Mathematical Olympiad (USAMO), and involves about 180 students. The six students with the best performance in the USAMO become the U.S. IMO team, and the next two become alternates.

The questions can be quite challenging, even to those who think they are mathematically inclined. Here are a few from past IMOs:

    1. In a competition there are a contestants and b judges, where b 3 3 is an odd integer. Each judge rates each contestant as either "pass" or "fail". Suppose k is a number such that for any two judges their ratings coincide for at most k contestants. Prove k/a3 (b-1)/2b.
    2. Determine all integers greater than 1 such that (2n + 1)/n2 is an integer.
    3. For any positive integer n, let d(n) denote the number of positive divisors of n (including 1 and n). Determine all positive integers k such that d(n2) = k d(n) for some n.

More problems for all of the contests can be found at the American Mathematics Contests web page http://www.unl.edu/amc/problems.html. A complete set of the IMO problems, and solutions, are at http://www.kalva.demon.co.uk, along with problems from some other contests.

The winners of the 1999 USAMO held on April 27, 1999, are Reid W. Barton Arlington, MA; Gabriel D. Carroll, Oakland, CA; Lawrence O. Detlor, New York, NY; Stephen E. Haas, Sunnyvale, CA; Po-Shen Loh, Madison, WI; Alexander B. Schwartz, Bryn Mawr, PA; Paul A. Valiant, Belmont, MA; and Melanie E. Wood, Indianapolis, IN. Alexander Schwartz was the overall winner, and is the son of an FSA. Melanie Wood was on the team last year, when she was the first woman to so represent the U.S. Po-Shen Loh was in eighth grade when he took the USAMO. The winners were honored at ceremonies in Washington D.C. that included a presentation of gifts from sponsors, including the Casualty Actuarial Society. Ceremonies were held at the headquarters of the Mathematical Association of America, the National Institute of the Sciences, and the State Department.

Please send your suggestions for corporate sponsors and questions about the program to either Melvin D. George, President of IMO 2001 USA, at (573) 882-1250, Walter E. Mientka, Executive Director at (888) 449-2001, or myself at (973) 898-9393.