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Putnam Competition

The William Lowell Putnam Mathematical Competition is the preeminent mathematics competition for undergraduate college students in the United States and Canada. The Putnam Competition takes place annually on the first Saturday of December. The competition consists of two 3-hour sessions, one in the morning and one in the afternoon. During each session, participants work individually on 6 challenging mathematical problems.

The Putnam began in 1938 as a competition between mathematics departments at colleges and universities. Now the competition has grown to be the leading university-level mathematics examination in the world. Although participants work independently on the problems, there is a team aspect of the competition as well. Prizes are awarded to the participants with the highest scores and to the departments of mathematics of the five institutions the sum of whose top three scores is greatest.


The competition returned this year to its standard format after a year curtailed by the pandemic, featuring an individual competition and a team competition with awards and prizes. 

The competition took place on Saturday, December 4, proctored in-person on campuses across the US and Canada. Participants (undergraduate students) registered for the competition once a supervisor from their institution registered. By registering, participants were assigned a Putnam Identification Number (PIN), which they needed in order to participate in the competition on December 4. Any college or university in the United States or Canada that wishes to offer the competition to their students must name a regular faculty member to serve as the local supervisor of the competition.


82nd Putnam Competition Problems and Solutions

The 82nd William Lowell Putnam Competition Problems and Solutions are now available to download. Follow the links below to access the PDF files. Problems and solutions starting from the year 2017 can be found on the Putnam Competition Archive page.

    82nd Putnam Competition Problems A Session  

   82nd Putnam Competition Problems B Session 


82nd Putnam Competition Solutions A Session

  82nd Putnam Competition Solutions B Session

   2019 Putnam Competition Problems & Solutions


Click here to access the 2019 Announcement of Winners, which includes Putnam Fellows, next highest ranking individuals, honorable mentions, Elizabeth Lowell Putnam Prize winners, winning teams, and teams earning honorable mentions.

Click here to access the press release for the 2019 William Lowell Putnam Mathematical Competition.

Results for past William Lowell Putnam Mathematical Competitions can also be found here.


Preparing for the Putnam

The Putnam Competition covers a range of material in undergraduate mathematics, including elementary concepts from linear algebra, modern algebra, analysis, and number theory. Below are some books available for purchase that may help students prepare for this exam:



The competition is administered in two sessions (A and B). Each session lasts exactly three hours. Participants may start the A session on December 4 at the time indicated in the table in this document. After completing the A session, participants will have a 2-hour break. The B session must start at the time indicated in the same table.

For each of the 12 problems, participants will handwrite their work on plain 8.5-by-11 sheets of unlined paper. All work to justify a solution and all necessary steps of proof should be submitted. When working on one problem, participants should not refer to work on a different problem. Writing utensils, blank paper, and erasers are permitted, but other materials, such as books, calculators, computers, rulers, compass, lined paper, or graph paper, are not permitted.

Participants are prohibited from sharing or discussing the competition problem until 8:00 p.m. EST on December 4. There is to be no copying, posting, or distributing the exam until after this time.


FAQs for the 82nd Putnam

  1. Q. When is the 82nd Putnam Competition?

    A. The 82nd Putnam Competition will take place on Saturday, December 4, 2021.

  2. Q. Is the 82nd Putnam Competition official?

    A. Yes, the Putnam Competition will return this year to its standard format. We will again have an individual competition and a team competition, with awards, prizes, and honorable mentions.The competition will take place on Saturday, December 4, proctored in-person on campuses across the US and Canada.

  3. Q. When does supervisor registration open?

    ​A. Supervisor registration opens September 1, 2021.

  4. Q. How do students register?

    A. Participants need to pre-register for the competition. They may do so starting in early September 8, 2021, provided that the local supervisor from their institution has already registered. Please note that the supervisor approval may take up to 5 business days. A link will be provided on this page.

  5. Q. I have a bachelor’s degree. May I participate?

    A. No. The Putnam Competition is open only to actively enrolled undergraduate students who have not yet received a bachelor’s degree.

  6. Q. May I participate in the Putnam Competition without an association with an institution?

    A. No. If you are not regularly enrolled in an undergraduate institution in the US or Canada, then you are ineligible to participate. If you meet the eligibility requirements but your institution does not have a Putnam local supervisor, ask a faculty member (perhaps the math department chair) to become the Putnam local supervisor for your institution. If no faculty member is willing to play this role, then you will be unable to participate.

  7. Q. I am a degree candidate at one institution but temporarily at another. May I participate?

    A. Yes, and you could compete for either institution.

  8. Q. Must I have a high school diploma to participate?

    A. No. Students who are concurrently in high school but are taking classes at a US or Canadian college or university on a regular basis are deemed to be “regularly enrolled” undergraduates. Please note, a student may participate in the official Putnam Competition at most four times. Generally, we discourage high school students from exhausting their eligibility. If you are not regularly enrolled as an undergraduate at an institution of higher education, then you are ineligible.

  9. Q. Is there a limit to the number of times a student can participate in the competition?

    A. Yes. The limit is four, not counting the 81st (unofficial) Putnam competition that took place in February 2021.

  10. Q. I am a foreign student who is currently enrolled in a US or Canadian institution. May I participate?

    A. Yes.

  11. Q. I am regularly enrolled in a US or Canadian institution, but I am taking a year off. I intend to return to my institution next year. May I participate?

    A. Yes.

  12. Q. I will be away from my home institution on December 4. Can I still participate in the competition?

    A.  Possibly. Arrangements can sometimes be made to take the exam at another registered institution. Discuss this with your local supervisor.

  13. Q. I’ve registered. What do I need to bring with me to the exam room?

    A.  Bring pencils or pens (blue or black ink) and the PIN number that you were given at the registration platform. Nothing else is needed. Supervisors provide clean, white paper. Calculators, computers, references, and drawing tools are not allowed, and cell phones must be turned off and stowed away during the exam.

  14. Q. What is the registration deadline for supervisors and institutions?

    A. The deadline for supervisors to register their institutions is November 15

  15. Q. What is the registration deadline for student participants?

    A. Participants will need to register online before the start of the competition in their local time in order to obtain their Putnam identification number (PIN).

  16. Q. Will the problems for the exam appear at the Participant Portal?

    A. No. The exam this year will be in a proctored, on-campus setting, with supervisors providing the problems on paper.