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 web 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 8pm Eastern (5pm Pacific); this embargo was set in consultation with competition director Daniel Ullman, in order to give exam supervisors time to mail 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. As of the 2017 competition, both the original summary of results, taken from the MAA historical Putnam results page, and old-style HTML transcriptions 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.

This page is maintained by Kiran Kedlaya; contact me with corrections and other comments about this material only. I cannot assist with exam administration. If you are a student, see your school's Putnam coordinator; if you are a coordinator, see the MAA's Putnam home page for instructions.

The MAA has announced that the 81st competition, originally scheduled for Saturday, December 5, 2020, will be postponed because of the COVID-19 pandemic. Further details will be reported here as I receive them.