Question - if a certain mathematical exam gives contestants six hours to answer 12 problems, how many minutes should each contestant spend per problem if they distribute their time evenly?
If your answer was 30 minutes per problem, you might be ready to participate in the William Lowell Putnam Competition, North America's premier mathematical challenge.
"It's definitely the big enchilada," said Mathematics Prof. Stephen Theriault, who coached this year's group of University participants to one of their strongest finishes ever.
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Last December, University students Chris Marcellin, Sawyer Tabony, Brandon Ku and Robby Yan participated in the six hour exam. Their results, which the Mathematical Association of America recently announced, were quite impressive.
Yan and Tabony captured 121th and 288th respectively, two of the University's best individual performances in recent memory. And they both are only first years.
"The typical good score around here is 20 out of 120, which puts you only in about 700th place," said Mathematics Prof. Robert Stong, former coach of the University Putnam team.
Fortunately for the University, Yan already has his eyes set on next year's competition.
"I definitely plan to take the Putnam again, in the hope that I can place even higher. I only have to answer three more questions to become a Putnam Fellow," he said.
Started in 1938 to foster mathematical competition between colleges in the United States and Canada, the Putnam competition has become to undergraduate mathematics what the Super Bowl is to football.
Each year nearly 3,000 high school and college students trade in six hours and plenty of pencil lead for a shot at mathematical glory.
The exam breaks down into 12 questions that cover topics typically appearing in undergraduate mathematics courses.
Each of the top five scorers are designated Putnam Fellows and receive $2,500 in cash.
The Putnam also recognizes team efforts, awarding $25,000 to the school that produces the best team. Cash prizes aside, most would agree this isn't your standard calculus exam.
"It tests a totally different set of skills. Some of the problems could theoretically be done by a high-schooler, but it would take a great deal of effort," said 1998 Putnam Fellow Nathan Curtis, a senior at Duke University.
In fact, the exam is so challenging that nearly half the students fail to score a single point. Those that do score usually get only a handful of points out of a possible 120.
Some competitors such as Curtis actually like the steep odds.
"The fact that it is hard is to my advantage because it brings out my competitive side," Curtis said. "I like to go through a few problems each week, which is usually enough to keep me in shape."
And in case you're wondering, cramming for the Putnam doesn't work.
"The kids who do very well work year after year on old problems," Stong said.
Yan agrees long-term preparation was key to his success.
"It requires a commitment over a long period of time to develop the problem solving skills needed to answer the problems," said Yan, who also participated in math competitions while in high school.
But even a steady diet of old exams does not ensure Putnam success. The solution to each problem involves a subtle trick that only a flash of mathematical inspiration can reveal.
"The Putnam basically asks, 'Can you be clever?' It is more a test of creative problem solving than it is a test of ability in any one area of mathematics," Curtis said.
Of course, mathematical ingenuity doesn't hurt your chances. Some of this century's finest mathematicians and physicists first displayed their problem-solving prowess on the Putnam exam.
John Nash, the central character portrayed in the Oscar-winning film "A Beautiful Mind," placed very highly on the exam, and went on to make important contributions to mathematics and economics.
Still, some doubt that success on the Putnam guarantees success in mathematics.
"It is the skill of problem solving, rather than mathematical ability, that is being measured. Problem solving is not necessarily being good at math," Stong said.
Regardless of whether Putnam directly measures math ability, Yan says the competition is good for the field.
"These competitions foster appreciation of and interest in mathematics. I'd like to see more participation next year," he added.
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