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Shiliang Cui ’09 (Shanghai, China), Jinjin Qian ’08 (Shanghai, China), and Ekaterina Jager ’06 (Tashkent, Uzbekistan) won the math department’s fall Team Barge competition, sharing the $750 prize for first place. “I thought the problems were more challenging than usual, and even still, four groups ended up clustered tightly near the top,” says organizer Ethan Berkove, assistant professor of mathematics.
Jager is a candidate for B.S. degrees in both mathematics and electrical & computer engineering and Cui is an economics and business major. The same trio took first place last semester in the 16th annual Lehigh Valley Association of Independent Colleges Math Contest. For the second straight year, the College fielded squads that took three of the top four places in the competition, and a Lafayette team has earned first place in the event for six consecutive years.
Claiming the second-place prize of $600 in Team Barge were Keming Liang ’08 (Zibo, China) and mathematics majors Xue Ji ’08 (Wuxi Jiangsu, China) and Jordan Tirrell ’08(West Grove, Pa.).
Two teams tied for third place and each shared $450. One group included Aydin Gerek ’07 (Istanbul, Turkey) and Haotian Wu ’07(Suzhou, China), who are pursuing B.S. degrees in physics and math; computer science major Smathi Charanasomboon ’07 (Bangkok, Thailand); Teruhisa Haruguchi ’07 (Saitamashi , Japan), who is seeking a B.S. degree in computer science and an A.B. degree with a math major; and Ko Ko Maung ’07 (Tharkayta Yangon, Myanmar), a mathematics-economics major. The other team was comprised of physics major and Marquis Scholar Jonathan Farrar ’07 (Alexandria, Va.), international economics and commerce major Huong Nguyen ’08 (Hanoi, Vietnam), and mathematics-economics major Lan Nguyen ’07 (Hanoi, Vietnam).
Held each semester, Team Barge has groups of three to five students attempting to solve a different weekly problem over eight weeks. Competitors are permitted to consult with books, computers, and other resources to solve the problems, but not faculty. Barge problems usually involve some ingenuity or insight and generally do not rely on much background information from previous courses. The topics range over all areas of mathematics: probability, geometry, number theory, combinatorics, algebra, calculus, etc.
A sample from this fall’s problems, which can be found on the Barge web page:
Since 2005 = 1002 + 1003, the number 2005 can be written as the sum of two consecutive positive integers. For five points, how many ways can 2005 be written as the sum of (more than two) consecutive positive integers? For another five points, how many ways can 2005 be written as the sum of (more than two) consecutive integers if the numbers can be both positive and negative? Answers: 6 ways.
-1001 + … + 1003
399 + … + 403
-398 + … + 403
196 + … + 205
-195 + … + 205
-2004 + … + 2005
There are two other solutions of one and two terms (2005 and 1002 + 1003).