William Lowell Putnam Mathematical Competition

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The William Lowell Putnam Mathematical Competition is a highly challenging, proof-oriented mathematics competition for undergraduate students in North America.

Top scoring students on the Putnam exam are named Putnam Fellows.

The Competition

The Putnam Exam is a 6 hour undergraduate exam usually held the first Saturday in December. The test consists of two 3 hour sessions of six problems each with 2 hour lunch break between them. The problems are proof-oriented and written in roughly the same style as high school Olympiads are, although they include more advanced mathematics. Each problem is graded on a scale of 0 to 10, with nearly all scores falling in the ranges $[0, 3]$ and $[8, 10]$. The top five scorers (or more if there are ties) on the exam are named "Putnam Fellows."

Each school may have as many students as are interested sit for the exam. Before the contest, three students are selected as the official school Putnam team. Each team's score is determined by adding the ranks (not the scores) of the three students on the team, and the team with the lowest point total wins. For example, a school whose team members placed 1st, 2nd and 20th would place lower than a school whose team members placed 6th, 7th and 8th. (In the case of ties, every student is assigned the average of the range of ranks that would have been attained had there been no tie -- that is, if the top three students tie, they are all awarded a rank of $\frac{1 + 2 + 3}{3} = 2$.) The fact that the team members need to be chosen in advance regularly leads to schools selecting the "wrong team." For example, at least three of the six 2007 Putnam fellows were not members of their school team: AoPS member Arnav Tripathy of Harvard, Qingchun Ren of MIT, and Xuancheng Shao, also of MIT. In some cases this has led to a team placing lower than they would have had they chosen the three team members who went on to score the highest.

A person may take the Putnam Exam a maximum of four times. Typically, this means a student may sit each year he or she is an undergraduate, although high school seniors have occasionally taken the exam officially.

Placings and Prizes

The prizes are as follows:


  • Putnam fellows
    • <dollar/>2,500
  • The next top ten individuals
    • <dollar/>1,000
  • Next Ten Individuals
    • <dollar/>250


  • First Place team
    • Team members recieve $1,000
    • School recieves $25,000
  • Second Place Team
    • Team members recieve 800
    • School recieves $20,000
  • Third Place Team
    • Team members recieve $600
    • School recieves $15,000
  • Fourth Place Team
    • Team members recieves $400
    • School recieves $10,000
  • Fifth Place Team
    • Team members recieve $200
    • School recieves $5,000
  • Elizabeth Lowell Putnam Prize- The Elizabeth Lowell Putnam Prize will be awarded periodically to a woman whose performance in the competition has been deemed particularly meritorious. This prize would be in addition to any other prize she might otherwise win. Women contestants, to be eligible for this prize, must specify their gender.
    • $1,000

Problem Books


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