*Yet hundreds of schools compete each year, and this time the Blue Devils* *made it into the top three*

Every year, thousands of college students from across the U.S. and Canada give up a full Saturday before finals begin to take a notoriously difficult, 6-hour math test — and not for a grade, but for fun.

In “the Putnam,” as it’s known, contestants spend two 3-hour sessions trying to solve 12 proof-based math problems worth 10 points apiece.

More than 150,000 people have taken the exam in the contest’s 85-year history, but only five times has someone earned a perfect score. Total scores of 1 or 0 are not uncommon.

Despite the odds, the Blue Devils had a strong showing this year.

A total of 3,857 students from 471 schools competed in the December contest. In results announced Feb. 16, a Duke team consisting of Erick Jiang ’26, James “Fletch” Rydell ’26 and Kaixin “Kai” Wang ’27 ranked third in North America behind MIT and Harvard, winning a $15,000 prize for Duke and each taking home $600 for themselves.

According to mathematics professor Lenny Ng, it’s Duke’s best performance in almost 20 years.

“This is the first time a Duke team has placed this high since 2005,” said Ng, who was a three-time Putnam Fellow himself, finishing in the top five each year he was an undergraduate at Harvard.

There’s no official syllabus for prepping for the Putnam. To get ready, the students practice working through problems and discussing their solutions in a weekly problem-solving seminar held each fall.

Students serve as the instructors, focusing on a different topic each week ranging from calculus to number theory.

“They get a sense of what the problems are like, so it’s not quite as intimidating as it might be if they went into the contest cold,” said math department chair Robert Bryant.

“Not only do they learn how to do the problems, but they also get to know each other,” said professor emeritus David Kraines, who has coached Duke Putnam participants for more than 30 years.

Kraines said 8-10 students take his problem-solving seminar for credit each fall. “We always get another 10 or so who come for the pizza,” Kraines said.

The biggest difference between a Putnam problem and a homework problem, said engineering student Rydell, is that usually with a homework problem you’ve already been shown what to do; you just have to apply it.

Whereas most of the time in math competitions like the Putnam, “there’s no clear path forward when you first see the problem,” Rydell said. “They’re more about finding some insight or way of looking at the problem in a different perspective.”

Putnam problems are meant to be solvable using only paper and pencil — no computing power required. The contestants work through each problem by hand, trying different paths towards a solution and spelling out their reasoning step-by-step.

This year, one problem involved determining how many configurations of coins are possible given a grid with coins sitting in some of the squares, if those coins are only allowed to move in certain ways.

Another question required knowing something about the geometry of a 20-sided shape known as a icosahedron.

“That was the one I struggled with the most,” said Wang, whose individual score nevertheless tied him for sixth place overall out of 3,857 contestants.

The most common question he gets asked about the Putnam, Rydell said, is not so much what’s on the test, but why people take it in the first place.

This year’s test was so challenging that a score of 78 out of 120 or better — just 65% — was enough to earn a spot in the top 10.

Most of the people who took it scored less than 10%, which means many problems went unsolved.

“For days after I took the Putnam, I would think about the problems and wonder: could I have done it better this way? You can become obsessed,” said Bryant, who took the Putnam in the 1970s as a college student at NC State.

Sophomores Jiang and Rydell, who both ranked in the top 5%, see it as an opportunity to “meet people who also enjoy problem solving,” Jiang said.

“I’m not a math major so I probably wouldn’t do much of this kind of problem solving otherwise,” Rydell said.

For Rydell it’s also the aha moment: “Just the reward of when you solve a problem, the feeling of making that breakthrough,” Rydell said.

Professor Kraines’ weekly problem-solving seminar, MATH 283S, takes place on Tuesday evenings at 6:15 p.m. during the fall semester. Registration for Fall 2024 begins April 3.