Imagine that you open your math test to the first question, and see the following:

If you’re a little intimidated, “Don’t feel bad about it!” said Catalin Zara, an associate professor of mathematics at UMass Boston. This is the first question on the 2014 William Lowell Putnam Mathematical Competition, which is held every year on the first Saturday in December.

According to Zara, “Less than 2,000 students solved that problem this year – and some of their initial reactions would be the same as yours.” That is to say, total confusion. For successful Putnam competitors, the key is to get past the first reaction and start solving the problem.

The Putnam Competition is designed to get undergraduate students to think outside of the box. Zara is a local organizer of the competition, which is now in its 75th year.

The 12-question exam gives students some partial credit for correct work, but the questions are so challenging that some do not score a single point on any of their answers.

“The median score is usually around zero. This year it was two or three – so it was an easy exam this year,” Zara joked. “Easy” in this case included one question that did not elicit a single correct solution from the 4,230 undergraduate students who participated.

Four UMass Boston students beat those odds. UMass Boston had a strong showing in the competition, which included students from MIT, Harvard, and 575 other colleges and universities. Vincent Luczkow and Rory Martin-Hagemeyer were in the top 500, Sho Inaba was one point shy of the top 500. Xuezhu (Daisy) Luan also scored in the top third of all competitors. The rankings of Luczkow, Martin-Hagemeyer, and Inaba counted as the official UMass Boston team score. The team ranked 24th of 431 teams, a ranking that was only bested by the 2011 team, which came in 21st.

Luczkow, a senior from Holliston, said the exam is meant to be challenging. “This isn’t like a calculus exam, where you know the type of problem you’re solving. You’ve never seen this type of problem before, and you’ll probably never see it again.”

Martin-Hagemeyer, a sophomore from Hyde Park, agreed. “Some of the questions are intentionally contrived. One problem might take you through six or seven fields of mathematics as you work on a solution.”

Leading luminaries in mathematics, computer science, and business are among past years’ winners. But Zara believes there is a bigger goal than winning.

“It’s nice to do well, but even accepting the challenge, even participating is major,” he said. “You should try things outside of your comfort zone.”

Zara teaches a course, Mathematics 390, in which students focus on solving challenging problems like those on the Putnam. Zara’s unofficial motto for the class is, “What to do when you don’t know what to do.”

UMass Boston has had a history of strong team scores in the last five years, and Zara hopes to build on that success next year. To prepare for next year’s competition, Luczkow and Martin-Hagemeyer are holding practice sessions in the Integrated Sciences Complex.

“You know when one of us has reached a solution because someone will start shouting ‘I have an idea!’” said Martin-Hagemeyer. “It takes one little spark, and then the solution starts to fall into place.”

Mathematics Department Chair Eric Grinberg congratulated the team. “A glance at Putnam history shows that schools with a strong Putnam tradition do well year after year, and we are certainly building such a tradition.”

While the competition is fierce, Martin-Hagemeyer said he wouldn’t do it if he didn’t find the process of problem solving incredibly rewarding.

“Math is really fun. If I have an excuse to go spend a Saturday doing math instead of homework, I’m going to go take the Putnam.”

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