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This was the last question, problem B6, on the 2013 William Lowell Putnam Mathematical Competition. None of the over 4000 students who wrote the exam succeeded in solving the problem.

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MIT took first place in the 2013 William Lowell Putnam Mathematical Competition this year, only the seventh time the Institute has claimed the top prize of $25,000 since the founding of the competition almost a century ago. This year’s team was composed of Benjamin P. Gunby ’15, Mitchell M. Lee ’16, and Zipei Nie ’15, all of whom placed in the top 25. The team members were designated before the competition from among a larger group of MIT students taking the test.

The Putnam is widely considered to be the most prestigious college-level math competition in the world, with a typical median score of zero out of a total possible 120 points. Students can earn a maximum of 10 points for each of the 12 questions on the test. Questions on this proof-based exam are meant “to test originality as well as technical competence,” covering topics from linear algebra to graph theory.

Of the top five scorers this year, four came from MIT — Lee, Nie, Bobby C. Shen ’17, and David H. Yang ’17. The fifth Putnam Fellow, Evan M. O’Dorney, came from Harvard. Each of these Fellows will receive $2,500 for their performance on the exam. Past Putnam Fellows include Richard P. Feynman ’39 and current MIT professor Bjorn Poonen, who was a Fellow for all four years of eligibility.

Almost half of the 81 students who earned honorable mention or above are from MIT. The school with the next highest number of students obtaining this award was Harvard, which claimed only 11.

Travis Hance ’14, who scored in the top 25, said he took the Putnam “out of fondness for competition math,” having competed extensively in high school math competitions.

“I took the Putnam in 2010 and 2011 as well,” said Hance. “I got honorable mention both those years, so this year was the best I have done. Maybe this year’s problems just played more to my strengths. It also helped that I didn’t trip up on any of the easier problems this year like I did in the past.”

Like Hance, fellow top-25 scorer Tianyou Zhou ’16 competed in math contests before coming to MIT.

“I think there is not much difference between this year’s [exam] and previous ones. Both are awesome,” said Hance.

This year, no one solved the last question, which described a game played with stones (see accompanying graphic). Each contestant had their own take on what they considered to be their favorite problem.

“I most enjoyed B4 [the tenth question], which felt to me like the most natural question on the whole exam – something one would encounter in the ‘mathematical wild,’ rather than just a problem contrived for the purposes of a contest,” explained Victor Y. Wang ’17, who also placed in the top 25. “I like how Professor Cohn from the freshman Putnam Seminar (18.A34) phrased it: B4 was the most ‘useful-looking’ problem on the test, for some weird definition of ‘useful.’”