A record number of Scripps students competed in the 65th Annual Putnam Mathematics Competition, the premier mathematical competition for undergraduates on Saturday, December 3.
The 10 Scripps women included four seniors, three juniors, and two first-year students. A long-distance team member, junior Kat Shultis, participated while studying abroad in a mathematic program in Budapest. By comparison, Pomona, Claremont McKenna, and Pitzer College had 11, 7, and 3 participants, respectively, this year. Harvey Mudd, which typically has a large number of participants in the competition, continued the trend with approximately 60 competitors.
Students prepared for the competition through a series of 12 practice sessions, each led by a faculty member from CMC or Scripps. Session titles taught by Scripps faculty included “Number Theory,” “Pigeonhole Problems,” and “Algebra (Polynomials, Groups, and Rings).”
The annual competition, which is held at U.S. and Canadian colleges and universities, consists of 12 problems solved over a six-hour time period. The team prize has ranged from $5,000 to $25,000 in recent years, while each of the top five winners receive $2,500. Competition for these prizes is fierce—last year, the Putnam drew approximately 3,700 students from 515 institutions.
Scoring is based on a scale out of 120, but most of the competing students end up with zero. Each problem is graded on a basis of 0 to 10 points. All the necessary work justifying the answer must be clearly demonstrated to obtain full credit. As professor of mathematics Christopher Towse notes, “Getting a non-zero score is definitely considered an accomplishment.” The scores for this year’s competition will not be released until late March or early April.
Here is a sample problem from the Putnam website to wrap your head around. Let us know if you figure it out.
Players 1, 2, 3, …, n are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player 4, who passes two pennies to Player 5, and so on, players alternately passing one penny or two to the next player who still has some pennies. A player who runs out of pennies drops out of the game and leaves the table. Find an infinite set of numbers n for which some player ends up with all n pennies.
For more information about the Putnam Mathematical Competition visit http://math.scu.edu/putnam.