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.

Region: USA
Type: Proof
Difficulty: 7 - 9
Difficulty Breakdown:

Problem A/B, 1/2: 7
Problem A/B, 3/4: 8
Problem A/B, 5/6: 9


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. 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. Each school's team score is determined by adding the ranks (not the scores) of its top three students, and the team with the lowest point total wins. For example, a school whose top students placed 1st, 2nd and 20th would place lower than a school whose top students 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 $\frac{1 + 2 + 3}{3}=2$.) Before 2019, schools were required to choose their team members in advance, which regularly lead to schools selecting the "wrong team." For example, only two of the six 2007 Putnam fellows were members of their school teams. 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. In recent years, this effect has been particularly noticeable at MIT: in both 2005 and 2006, MIT had three Putnam Fellows (out of six and five, respectively), but did not finish above third place either year.

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, $2,500
  • The next top ten individuals, $1,000
  • Next Ten Individuals , $250
  • Elizabeth Lowell Putnam Prize- The Elizabeth Lowell Putnam Prize is awarded periodically to a woman whose performance in the competition is 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


  • First Place team
    • Team members receive $1,000
    • School receives $25,000
  • Second Place Team
    • Team members receive $800
    • School receives $20,000
  • Third Place Team
    • Team members receive $600
    • School receives $15,000
  • Fourth Place Team
    • Team members receive $400
    • School receives $10,000
  • Fifth Place Team
    • Team members receive $200
    • School receives $5,000

Problem Books


See Also