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 by 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.
The MAA official Putnam home page
includes information about the competition, including exam administration details, as well as
information about three published compilations of Putnam exams (a fourth is under development):
- 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 (English) Wikipedia entry on the Putnam competition is quite lengthy and includes a lot of detail on historical results.
The Art of Problem Solving
discussion forums include numerous threads concerning recent Putnam competitions. Some discussion therein is reflected in the solutions posted here.
(The long-time moderator of the Putnam discussions, Kent Merryfield, died unexpectedly on November 27, 2018.)
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. One book specifically about the Putnam is Putnam and Beyond by Andreescu and Gelca.
This page is maintained by Kiran Kedlaya;
contact me with corrections and other comments about this material only.
I cannot provide individual scores (see your school's Putnam coordinator) or
assist with exam administration (see the MAA's Putnam home page for instructions).
Problems and solutions from the 2018 competition, held on Saturday, December 1, are now posted. Some updates may be posted until the end of