Duke University students have won North America's most prestigious event of its kind for undergraduates, the William Lowell Putnam Mathematical Competition, for the third time since 1993. A separate team was also a top placer, for Duke's fourth year in a row, in the illustrious Mathematical Contest In Modeling sponsored by the Consortium of Mathematics and its Applications. Duke's official three-member Putnam team, which included senior John Clyde and juniors Nathan Curtis and Kevin Lacker, out-competed teams from Caltech, Harvard, MIT and the University of Toronto in the grueling event, when 2,818 students from 434 colleges and universities in the United States and Canada vied to solve 12 very challenging problems. The problems in the competition administered by the Mathematical Association of America were so challenging that the median score was only 1 out of the 120 possible points; about half the students scored zero. Clyde, from New Plymouth, Idaho, Curtis, from Reston, Va., and Lacker, from Cincinnati, were each among the top 15 scorers and, under the Putnam's complicated rules, their team won first place overall. They will each receive $2,000 and Duke will receive $25,000. Students participated in Putnam competition on their individual campuses Dec. 2, 2000, but the results are not announced until March, about the time of the NCAA basketball tournament, which inevitably calls up comparisons between the two tests of collegiate skill and endurance. A total of 19 Duke students competed in the 2001 Putnam. But, by the rules, only three students can be designated as the school's official team. Another Duke senior, Carl Miller, of Bethesda, Md., was also among the top 15 scorers, although he was not a team member. He will receive $1,000. Duke freshman David Arthur, from Toronto, and senior Michael Colsher, from Waukesha, Wis., won honorable mention for scoring in the top 2 percent of competitors. Lacker, a mathematics and computer science double major and a Goldwater Scholar, led the Duke participants by scoring 85 points. He was followed closely by Clyde, a computer science major who also plays drums in Duke's basketball pep band, as well as by Curtis. "We're very happy with these young men here," said David Kraines, a Duke associate professor of mathematics who coaches the student math competitors. "We have been able to attract really great students to Duke's Department of Mathematics who excel even when they first come here by taking upper level courses or even graduate courses. The reputation of Duke in mathematics has increased many-fold in the last decade." Miller, the other Putnam top 15 scorer from Duke, also joined Duke junior Sam Malone, from Zebulon, and senior Daniel Neill, from Tampa, to place the university at the top ranks of the Mathematical Contest in Modeling, a different kind of event requiring students to design and justify a mathematical model of a real world problem over a long 96-hour weekend. Working from 12:01 a.m. on Friday, Feb. 9 to 11:59 p.m. on Monday, Feb. 12, the trio wrote a 47-page paper describing strategies to evacuate a half million people from hurricane-threatened coastal communities by road. The scenario was modeled on a flawed evacuation in South Carolina during Hurricane Floyd in 1999, when "authorities made one large announcement to everyone at the same time so that everyone all of a sudden tried to evacuate," Miller said. "That led to huge bottlenecks. A trip that usually takes a couple of hours took 18 hours." A total of 579 teams from around the globe competed in this year's modeling contest, supported by the National Security Agency, Mathematical Association of America, Society for Industrial and Applied Mathematics and the Institute for Operations Research and Management Science. Competing students get to choose between two problems, and the very best solutions -- about 2 percent of the total -- are judged as Outstanding. Those winning teams are presented with plaques, and their papers will be published in the journal Undergraduate Mathematics and its Applications.