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The team of economics and business major Saad Rasool ’02 (Multan, Pakistan) and computer science majors Alex Balan ’03 (Bucharest, Romania) and Devin Wallace ’02 (Ridgefield, Conn.) took first place in this semester’s Team Barge Mathematics Competition.
In a separate competition sponsored by the mathematics department, 15 students competed in the Individual Barge Contest, open to first-year students and sophomores. A three-way tie for first place resulted among Ekaterina Jager ’05 of Tashkent, Uzbekistan; Myat Lin ’04, a biochemistry major from Yangon, Myanmar; and Volkan Oktem ’04, an electrical and computer engineering major from Islamabad, Pakistan. Honorable mentions went to Robert McEwen ’05 of Morgantown, Pa. and Joel Gross ’05 of Northampton, Pa.
In the Team Barge Mathematics Competition, eight groups of three to five students handed in the full set of solutions for the eight weeks in which a weekly problem was posed for the math department contest.
“This was an unusually strong field with a lot of nice solutions,” says Ethan Berkove, assistant professor of mathematics. “All of the top four teams were very close in final score.”
Second place went to Mike Lowe ’03, a math major from Easton, Pa.; Lazar Nikolic ’03, a double major in math and computer science from Roswell, Ga.; and Kris Miszler ’03, a math major from Hawley, Pa.
Two teams tied for third place: Gregg Berman ’02, an electrical engineering major from New Milford, Conn.; Dan Swarr ’03, a double major in physics and math from Clifton Park, N.Y.; and Guangxi Wang ’03, an electrical and computer engineering major from Shanghai, China; along with Steve DiMauro ’02, a math major from Haboro, Pa.; Josh Grubman ’03, an economics and business major from Boca Raton, Fla.; and Jon-Paul Marnien, a computer science major from Philadelphia, Pa.
The student teams split a $600 prize for first place, $450 for second, and $300 for third.
Competitors are permitted to consult with books, computers, and other resources to solve the problems, but not faculty. The 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.
The following is one of the team Barge problems for this semester: Pat and Danny are helping the City of Easton prepare for its [fictitious] first annual Mashed Potato Festival by peeling lots of potatoes. Pat and Danny start peeling potatoes at exactly the same time, and each peels one potato in exactly one minute. They both start with the same number of potatoes, but Danny throws one unpeeled potato onto Pat’s pile after every second one Danny peels. At a certain moment, Pat has twice as many potatoes to be peeled as Danny. Five minutes later this ratio has increased to 7:3. When will the ratio be 3:1? You can assume that Danny’s completion of the peeling of a potato and Danny’s tossing of a potato onto Pat’s pile occur simultaneously at the end of each second minute.
The answer: Pat and Danny each start with 100 potatoes. It takes 40 minutes to get to a 2:1 ratio, 45 minutes for a 7:3 ratio, and 50 minutes for a 3:1 ratio.
Chawne Kimber, assistant professor of mathematics, organized the Individual Barge Contest. Math professors Ethan Berkove, Jim Crawford, Qin Lu, and Tom Yuster assisted in writing problems for the exam. The winners receive $300 for first place, $200 for second place, and $100 for third.
A 1903 donation of $2,500 from Benjamin F. Barge funds the team Barge competition as well as the Benjamin F. Barge Mathematical Prize for a first-year student or sophomore.