Another Digit, Another Dollar

Oxford University professor Nick Trefethen wasn’t kidding when he offered a dollar a digit for a series of 100 numbers. The difficulty was in deducing the right numbers from a series of 10 diabolically nasty numerical problems.

Trefethen’s “100-Dollar, 100-Digit Challenge” was sponsored by the Society for Industrial and Applied Mathematics (SIAM) and published in the January/February 2002 issue of SIAM News. A group of graduate students from Rice’s Department of Computational and Applied Mathematics (CAAM) took up the gauntlet, loaded their calculators with fresh batteries, and wound up with a first-place spot in the winner’s circle.

Every year, Trefethen, who is head of Oxford’s Numerical Analysis Group, assigns his new doctoral students in numerical analysis one problem per week for six weeks. The problems are stated in a sentence or two, and each has an answer that is a single real number. The students’ mission is to compute that number to as many digits of precision as they can. The problems from this class were used in the “100-Dollar, 100-Digit Challenge.”

“Each problem is ‘solved’ to Trefethen’s satisfaction with the submission of 10 correct decimal digits, so a complete solution to the suite consists of 100 digits,” says CAAM department chair Bill Symes. “These were truly difficult computations: Achieving 10-digit accuracy with any feasible expenditure of computational effort required in all cases clever and subtle approaches. The CAAM team deserves hearty congratulations for a very impressive piece of work.” The CAAM team actually submitted considerably more than 100 correct digits.

The competition drew 94 teams from 25 countries, and a total of 20 teams submitted correct answers. The Rice team consisted of graduate students Eric Dussaud, Chris Husband, Hoang Nguyen, and Dan Reynolds and postdoctoral research associate Chris Stolk, advised by Mark Embree, assistant professor, and Yin Zhang, associate professor, both in applied mathematics.

The original challenge and the problems are accessible online. The solutions and list of the first- and second-place winners are online. The solutions the Rice team submitted, as well as the team members’ approaches to solving the problems, are accessible online.

SIAM is an international organization with 9,000 members in academia, industry, and government laboratories. The society’s goal is to advance the research and application of mathematics and computational science to science, engineering, industry, and society.

—Ann Lugg