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MIT team takes third in math contest

A three-student MIT team placed third in a national math competition, winning prizes for team members and the Department of Mathematics.

Ruth Britto-Pacumio, Sergey Ioffe and Thomas Weston, all seniors in mathematics, were among the 2,468 undergraduates from 405 US and Canadian schools who took part in the 56th annual William Lowell Putnam Mathematical Competition in December. Results of the competition were released in late March after the lengthy grading process for the essay-type problems. The team members were chosen in advance by Professors Hartley Rogers and Richard Stanley of mathematics, although 54 MIT students took the six-hour exam. (Team members take the exam as individuals, without collaboration).

The team from Harvard finished first this year, while Cornell finished second, Toronto was fourth and Princeton came in fifth. The top three finishers were the same as in the 1994 competition. In 1993, 1992 and 1991, MIT finished fourth, ninth and sixth respectively.

The average grade for MIT team members was 59.3 out of a possible 120 points for 12 problems. The highest score obtained in this year's competition was 86. The median grade for all those who took the exam was 8, while the median for the 54 who participated from MIT was 28. Six of the MIT students scored 50 points or more: juniors Alex Morcos of mathematics and Adam Meyerson of electrical engineering and computer science; Federico Ardila and David Jao, both sophomores in math; and freshmen Amit Khetan and Eric Kuo. Mr. Ardila had MIT's highest individual score.

Each MIT team member will receive $300, and the mathematics department will receive $3,000 to support and promote various activities within the department.

"Professor Stanley and I are very happy about the achievement of MIT's 1995 team," Professor Rogers said. "They did the uniformly solid and consistent job that's key to earning a place in the top five. Competitive standards among individuals and teams have become increasingly severe in recent years, and the examinations have been made correspondingly more difficult."

The fall-term undergraduate seminar 18S34 (Mathematical Problem Solving) serves as preparation for the Putnam Competition, though the contest is open to any interested undergraduate with or without the seminar, Professor Rogers noted.


(Among the top 204 contestants, one scored a perfect 10, one scored 8 and all others scored zero on this problem).

Suppose that each of n people wrote down the numbers 1, 2, 3 in random order in one column of a 3 x n matrix, with all orders equally likely and with the orders for different columns independent of each other. Let the row sums a, b, c of the resulting matrix be rearranged (if necessary) so that a < b < c. Show that for some n > 1995, it is at least four times as likely that both b = a + 1 and that c = a + 2 as that a = b = c.

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