The Putnam Archive

The William Lowell Putnam Mathematics Competition is a North American math contest for college students, organized by the Mathematical Association of America (MAA). Each year on the first Saturday in December, several thousand US and Canadian students spend 6 hours (in two sittings) trying to solve 12 problems. Individual and team winners (and their schools, in the latter case) get some money and a few minutes of fame.

This unofficial site contains problem statements, solutions, and competition results for recent years.

• Problem statements given here are verbatim from the competition (except some diagrams are missing), and are copyrighted by the MAA. They appear here with permission, but further redistribution is subject to copyright restrictions which I am not authorized to waive; contact the MAA for assistance.

• Solutions given here have been compiled (in some combination) by Manjul Bhargava, Kiran Kedlaya, and Lenhard Ng based on numerous sources (see below). Copyright is held by the named authors, who request that you link to this page in lieu of reproducing these solutions elsewhere. Also, please do not refer to these as "official solutions", as this describes the solutions issued by the MAA which reflect the intent of the problem setters. Those appear in the official competition summary (see below).

  New problems and solutions will be posted here no sooner than the following Monday at 11:59pm Pacific; this embargo was set in consultation with competition director Daniel Ullman, in order to give exam supervisors time to scan and upload their exam papers. We suggest that others observe a similar delay before discussing the exam online.

• Competition results up to 2016 were transcribed by hand from the printed summary of results, which was sent by mail (I have added scans of the original documents where I have them). As of the 2017 competition, both the original summary of results issued by the MAA and an old-style HTML transcription are provided.

  New results will be posted here as soon as they are received; this generally takes place in mid-February. (Until 2016, results were mailed in late March or early April.)

Some additional resources concerning the Putnam competition include the following.

• The official MAA Putnam website. For additional information, email the competition director, Daniel Ullman (dullman [at] gwu [dot] edu).
• The (English) Wikipedia entry on the Putnam competition is quite lengthy and includes a lot of detail on historical results.
• The MAA has published four compilations of prior exams:
  • The William Lowell Putnam Mathematical Competition. Problems and Solutions: 1938-1964, by Gleason, Greenwood, and Kelly;
  • The William Lowell Putnam Mathematical Competition. Problems and Solutions: 1965-1984, edited by Alexanderson, Klosinski, and Larson;
  • The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary, by Kedlaya, Poonen, and Vakil;
  • The William Lowell Putnam Mathematical Competition 2001-2016: Problems, Solutions and Commentary, by Kedlaya, Kane, Kane, and O'Dorney.
• The Art of Problem Solving discussion forums include numerous threads concerning recent Putnam competitions. Some discussion therein is reflected in the solutions posted here.
• Joe Gallian maintains several pages of information about the Putnam, including a historical summary, a database of career trajectories of Putnam fellows, and a PDF summary of the database.
• For each competition, the MAA has published an official competition summary with problems, solutions, results, and statistics in the American Mathematical Monthly a few months after the exam date. The Monthly back catalog is available via JSTOR if you are affiliated with a subscribing institution. (Another MAA publication, Mathematics Magazine, has also published exam summaries in recent years.)
• There is a rich literature of books about math competitions and preparation for them, but books focusing on the Putnam are rare. A notable exception is Putnam and Beyond by Andreescu and Gelca.
• A Conversation about the Putnam Competition.

This page is maintained by Kiran Kedlaya; contact me with corrections and other comments about this material only (including additional scans of historical results summaries). I cannot assist with exam administration. If you are a student, see your school's Putnam coordinator (if you don't know who that is, ask the chair of the mathematics department); if you are a coordinator, contact the competition director (see above).

The 2024 competition was held Saturday, December 7; however, I am on an extended trip and so the next update will be somewhat delayed.

Footnote: the "2020" competition was postponed to February 20, 2021 due to the COVID-19 pandemic, then held in an unofficial mode with no prizes or official results.