Three first-years won a prestigious mathematics contest after spending 96 hours—including one stretch of 50 sleepless hours—solving a problem involving an elephant, a motorcyclist and cardboard boxes.

The Harvard team, composed of Sheel C. Ganatra ’06, Nikita Rozenblyum ’06 and Ivan Z. Corwin ’06 received the top honors on Tuesday—an “outstanding” ranking—along with 15 other undergraduate teams for the international Mathematical Contest in Modeling.

More than 600 three-person teams worldwide participated in the annual contest, which the non-profit Consortium for Mathematics and Its Applications ran early last month.

The participants remained in their dorms and were allowed to use any inanimate source to help answer one of two problems during a four-day period.

“The competition involves a lot of intensive research, a lot of intensive work, and a lot of teamwork,” Ganatra said.

The Harvard team became stunt coordinators when they chose Problem A—a challenge to create the best arrangement of cardboard boxes to cushion the fall of a stunt person on a motorcycle jumping over an elephant.

The Harvard team attributed their success to the amount of time they spent perfecting the 45-page explanatory paper they submitted.

Corwin said that the team “kept fighting until the end,” editing and re-writing its paper in the competition’s last 10 hours.

“A lot of [our success] had to do with revising our paper at the end of the contest,” said Ganatra. “It was a good decision to have a clear, coherent paper.”

The Harvard team’s computer-tested model involved 60-centimeter cubed boxes arranged in a pyramid to cushion the fall of a stunt motorcyclist.

The mathematicians’ model also called for abrasive—a high-friction substance—to be added to the boxes to increase the pyramid’s effectiveness in cushioning the blow.

He said the team studied actual tests from the cardboard industry, scouring the internet and libraries for facts about the elasticity of cardboard and the process of boxes buckling under weight.

As a result, the first-years learned a lot more about cardboard than they ever wanted to know, Ganatra said.

“It was cool because it was applying math, and we’re all pretty good at math, but it’s something else to apply it to the real world and get nice results,” Corwin said.

Corwin said that the contest is usually dominated by schools with well-established engineering programs.

“It’s very unusual for Harvard to participate and to win,” Corwin said.

The team’s advisor, Petschek Professor of Mathematics Clifford Taubes, said his role in the first-years’ success involved only signing contest paperwork.

“This is all the kids’ doing,” Taub said. “Their success is their own.”