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For the fourth consecutive year, a Lafayette team has taken first place in the Lehigh Valley Association of Independent Colleges Math Contest. Forty students forming 12 teams from Lafayette, Lehigh University, Muhlenberg College, Moravian College, and DeSales University competed Nov. 1 at Moravian.
The winning team, which earned a score of 69, included mechanical engineering major Varun Mehta ’06 (New Delhi, India), Marquis Scholar and electrical and computer engineering major John Kolba ’06 (Chelmsford, Mass.), and Marquis Scholar and mathematics major Kyle Palmer ’06 (Perkasie, Pa.).
The fifth-place team, which scored 59 points, was comprised of chemical engineering major Maria Azimova ’06(Tashkent, Uzbekistan), Trustee Scholarship recipient Jacob Carson ’06 (New Richmond, Ohio), and Ekaterina Jager ’05 (Tashkent, Uzbekistan), who is pursing a B.S. in electrical & computer engineering and B.A. in mathematics.
Two Lafayette teams tied for seventh place with 55 points. One included Maquis Scholar and mathematics major Ryan McCall ’07 (Seneca, Pa.), electrical and computer engineering major Farhan Ahmed ’05 (Utter Pradesh, India), and Marquis Scholar Rob McEwen ’05 (Morgantown, Pa.), who is pursuing B.S. degrees in computer science and mathematics. The other team was comprised of physics major Ibrahima Bah ’06(Bronx, N.Y), mathematics major Greg Francos ’05 (Haddonfield, N.J.), and Marquis Scholar and electrical and computer engineering major Josh Porter ’06 (Pittstown, N.J.).
The teams were advised by Gary Gordon, professor of mathematics, who will present books to the winning students Feb. 21 at the Pi Mu Epsilon Student Mathematics Conference hosted by Moravian. Fellow math faculty members Tom Yuster, Ethan Berkove, and Derek Smith assisted with developing and grading the problems. Gordon and Yuster founded the competition in 1989.
Eight of the students taking the LVAIC test were among the 12 Lafayette competitors who placed in the top 50 percent of participants in the 2002-03 William Powell Putnam Mathematical Competition, described by Time magazine as “the world’s toughest math test.” Overall, Lafayette finished 24th among the 476 participating institutions, best among Patriot League schools. It was paced by three seniors among the top ten percent of the 3,300 competitors.
Last school year, McEwen earned honorable mention in the fifth annual Interdisciplinary Contest in Modeling sponsored by the Consortium for Mathematics and its Applications, while Ahmed earned honorable mention at the consortium’s 19th annual Mathematical Contest in Modeling.
McEwen and Jager were among four Lafayette students who conducted mathematics research with peers at other top institutions from around the country this summer in the National Science Foundation’s Research Experience for Undergraduates (REU) at Lafayette. Mentored by Lafayette mathematics professors, just 12 students among more than 120 applicants were selected to participate in the program. Besides Lafayette, the REU students hailed from the Johns Hopkins, Princeton, Shaw, St. Joseph’s, California-Long Beach, North Carolina State, and Boston universities.
A sample LVAIC Math Contest problem: The numbers from 1 to 90 are placed in a box. Player A removes a number from the box, then B removes a number, then A, and so on, with the players alternately removing the numbers from the box. After all 90 numbers have been chosen, player A wins if the sum of all the numbers she has selected is even, while player B wins if the sum of the numbers player A selected is odd. Assuming both players follow an optimal strategy, who will win? What is the optimal strategy?
Answer: Player A can always win by first choosing an even number, then always matching whatever the other person selects (if person B chooses an odd, then A chooses an odd on the next turn, and so on).
Another problem: One hundred ping-pong balls, numbered 1-100, are placed in a box. You can remove two balls from the box and replace them with a new ball whose number is the sum of the numbers of the two balls you removed. This process is repeated many times; each time two balls are removed from the box and replaced by a ball with their sum. (During this process, it is possible for the box to have several balls with the same number.) After this process has been going on for a while, you notice there are only two balls left in the box. The number on one of these balls is 2003. What is the number on the other ball? Answer: 3407.
Gordon notes that the fifth problem in the examination was dedicated to the late James Crawford, former professor of mathematics at Lafayette, “who loved geometric problems that used similarity ideas.” This fall, the Eastern Pennsylvania and Delaware (EPADEL) section of the Mathematical Association of America renamed its Distinguished Teaching Award after Crawford.