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:
To avoid possible copyright problems, I have changed the wording, but not the substance, of all the problems.and this line is added to all solutions:
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.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.)
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
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 Problems, Solutions, or Other information in some format (at the time of this writing).
|2000||P||PSO||P, P, P,S||PS|
I'm sorry, answers to the 2011 exam are not available at this time :-).
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.
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.
Here is a website which collects problems from mathematics magazines (e.g. Amer Math Monthly).
This page is
http://www.math.niu.edu/~rusin/problems-math/index.htmlLast modified 2006/01/09 by Dave Rusin, firstname.lastname@example.org