The Putnam Exam is a nationwide (USA and Canada) math exam held each December for undergraduates -- 12 questions, 6 hours, pretty challenging. Copies of previous exams (with solutions and comments) can be found in back issues of the American Mathematical Monthly; in addition there are several volumes of the collected exams (the bibliographic data follow below).

The exam is run by the Mathematical Association of America (MAA). There is a web page for the organization of the exam itself. The exam has been featured in TIME magazine.

Here is a typical page advertising the exam (at Kansas State) which might give you a sense of what it's like. Consult your nearest university or Internet search engine for similar pages at other schools. Some schools offer preparatory courses or practice, e.g. U. Waterloo, MIT, Duke, Stanford, Dalhousie, Duquesne, Gustavus Adolphus. (Thanks to Steve Yang for finding many of these.)

There are many sources on the internet for problems and solutions from prior years, and we have some available here as well. The exams are available in different formats (reflecting the fact that the Web is not well suited for the transmission of mathematics!). You may find the problems available in .TeX, .DVI, .PS, .PDF, .HTML, .GIF, .DOC, or flat text formats --- good luck!

In particular, John Scholes had a
very complete site,
giving statements of the problems from *all* years, and solutions
(or hints of solutions) to about half of them! However, the following line is
added to all the problem statements:

and this line is added to all solutions:To avoid possible copyright problems, I have changed the wording, but not the substance, of all the problems.

Moreover, the reader is advised that the presentation is in HTML and may not display suitably in all browsers. (It looks terrible in mine!) (Scholes left a few old problems undone; here are answers to 1941 A3; 1941 A6; 1942 B2; 1942 B3; 1942 B5; 1948 A6; 1948 B2; 1948 B4; 1948 B6(1); 1949 A1; 1949 B2. Also, here are the other ones -- 41B7, 42A5, 42A6, 49A2, 49A4, 49B6 -- on Scholes' list that I as well haven't gotten to yet.)The solutions given on this site are not always complete, they are designed to be sufficient for anyone who has thought hard about the problem.

Scholes' list stops with the 2003 Putnam exam as far as I can tell. His site has come down early in 2008 but pages are available in the wayback machine; for example, the captured versions of his page giving the problems for 1985 can be found with the URL

http://web.archive.org/web/*/http://www.kalva.demon.co.uk/putnam/putn85.htmlSimilarly the answer to problem B6 of that year is found at

http://web.archive.org/web/*/http://www.kalva.demon.co.uk/putnam/psoln/psol8512.html

Here are some other sites which offer information about several years' worth
of Putnam problems. For each site we indicate the years for which they
offer **P**roblems, **S**olutions, or **O**ther information in
some format (at the time of this writing).

Year | MP | UCSD | AMC | DJR | DJB | misc | |

1975 | P | ||||||

1976 | P | ||||||

1977 | P | ||||||

1978 | P | ||||||

1979 | P | ||||||

1980 | P | P | |||||

1981 | P | P | |||||

1982 | P | P | |||||

1983 | P | P | PS | ||||

1984 | P | P | |||||

1985 | P | P | P | P | PS* | ||

1986 | P | P | P | P | |||

1987 | P | P | P | P | PS | ||

1988 | P | P | P | P | PS | ||

1989 | P* | P | P | P,S* | P | PS | |

1990 | P | P | PS | PS | |||

1991 | P | P | S* | P | |||

1992 | P | P | PS | PS* | |||

1993 | P | P | S | P | S | ||

1994 | P | PO | S | PS | S | ||

1995 | P | PSO | S | PS | |||

1996 | P | PSO | S | PS | |||

1997 | P | PSO | S | PS | |||

1998 | P | PSO | S | PS | |||

1999 | P | PSO | S | PS | |||

2000 | P | PSO | P, P, P,S | PS | |||

2001 | P | PS | P S | PS | |||

2002 | P | PS | P S | PS | |||

2003 | P | PS | P S | PS | |||

2004 | P | PS | P S | PS | |||

2005 | P | PS | P S | PS | |||

2006 | P | PS | . . | ||||

2007 | P | PS | . . | ||||

2008 | P | PS | P S | ||||

2009 | P | PS | PS | S | |||

2010 | PS | PS | S | ||||

Year | MP | UCSD | AMC | DJR | DJB | misc |

I'm sorry, answers to the 2011 exam are not available at this time :-).

Notes:

- The asterisks indicate partial sets.
- Recall that problems and solutions are available in journals, and (through 1984) in book form too. The Internet is not the world's only information source...
- I have my own copies of most exams and solutions back to about 1975; contact me if it's critical, but the aforementioned books are a better resource. I do not have the 2006 and 2007 exams at my site. (I was on sabbatical!)
- The problems available from MathPro Press (MP) may be retrieved individually with their search engine; some have comments or hints there. These have generously been made available as GIF images of the problems from the exams 1975-1989, thanks to Mark Bowron, while the database was at the University of Missouri at Rolla. (The 1989 exam is incomplete.)
- The American Mathematics Competitions (AMC) page includes resources previously maintained independently by Kiran Kedlaya (kedlaya at math.berkeley.edu) It appears that the "miscellaneous" solutions for 1993/4 are his too.
- I try to compile solution sets from postings on the sci.math newsgroup. Much of the material was posted by me anyway, but I am taking the liberty of including (with attribution) comments posted by others. Here the reader gets to see bumblers in action as we collectively try to resolve the toughies; these are not the best solutions if you're looking for panache...
- Dan Bernstein posts pretty complete solutions, in recent years nicely TeXed, to the sci.math newsgroup most years (at least since 1995). Current location: Bernstein's web site Try a search to google.com like this. The solutions are linked on his home page.
- Problems and solutions for the 1987-1989 exams are part of the rec.puzzles archives. (The 1989 problems are labelled '1990.p' and '1990.s' for some reason.) The links above point to copies held here (taken from MIT); there's another site which has html-ized these and Bernstein's 1992 posts, as well as a 1967 Q and A.)
- I found the extra '92-'94 solutions while surfing the net one day.
- Problems and solutions for 1985 were kindly prepared by Gérard Petit who allowed me to post them here; select LaTeX (14K), DVI (25K), or PDF (295K !) format.
**Warning**: Some corrections have been sent to me as well; I haven't looked at the solutions carefully!

I am not at all clear about the copy rights for these questions and their solutions. If this issue is of concern to you, please contact me and I can explain what I know.

Here are the citations for the collected Putnam problems.

- TITLE: The William Lowell Putnam Mathematical Competition problems and solutions : 1938-1964 / A. M. Gleason, R. E. Greenwood, L. M. Kelly.
- PUBL.: Washington, D. C. : Mathematical Association of America,
- FORMAT: xi, 652 p. : ill. ; 25 cm.
- DATE: 1980
- OTHER NAME: Gleason, Andrew M.; Kelly, L. M. (Leroy Milton), 1914-; Greenwood, R. E.
- ISBN: 0883854287
- REISSUED: 2003, ISBN 0-8385-462-7

- TITLE: The William Lowell Putnam Mathematical Competition problems and solutions : 1965-1984 / edited by Gerald L. Alexanderson, Leonard F. Klosinski, Loren C. Larson.
- PUBL.: Washington, DC : Mathematical Association of America,
- FORMAT: xii, 147 p. : ill. ; 25 cm.
- DATE: 1985
- OTHER NAME: Klosinski, Leonard; Larson, Loren C., 1937-; Alexanderson, Gerald L.
- ISBN: 0883854414
- REISSUED: 2003, ISBN 0-8385-463-5

- TITLE: The William Lowell Putnam Mathematical Competition problems and solutions : 1985-2000 / edited by Kiran S. Kedlaya, Bjorn Poonen, Raki Vakil
- PUBL.: Washington, DC : Mathematical Association of America,
- FORMAT: 354 pp.
- DATE: 2002
- ISBN: 0-88385-807-X

For information about other mathematics competitions pitched to similarly select audiences see the American Mathematics Competitions page.

Similar in spirit is the Intermational Mathematical Olympiad; see e.g. this IMO site.

- Another pointer to an IMO site.
- I seem to have saved a copy of the 1994 IMO exam.
- A question from a 1995 IMO exam.
- Questions from the 2000 IMO exam
- THere is a lengthy discussion of the "Hardest IMO Problem Ever"

Here is a website which collects problems from mathematics magazines (e.g. Amer Math Monthly).

Other pages at my own web site you may find of interest:

- My home page is just a short introduction to the pages I maintain
- I keep a large set of pages which provide a thematic introduction to the subject areas of modern mathematics, complete with answers to thousands of more or less common questions.

This page is

http://www.math.niu.edu/~rusin/problems-math/index.htmlLast modified 2006/01/09 by Dave Rusin, rusin@math.niu.edu