Easy Putnam Problems,
the "easiest" problems from each competition for the last few years
(easy = solved by more contestants).
Putnam Training Problems - 2023
(last updated: 06/28/23),
ever-growing document with some problems discussed during current or
past training sessions.
AoPS Putnam Forum, discussions and solution of problems that have appeared in the Putnam Competition. Typically answers are posted and discussed here shortly after each examination.
Paul Zeitz: The Art and Craft of Problem Solving, John
Wiley & Sons, Inc., 1999. (Mathematical problem solving for
college-level novices.)
Arthur Engel: Problem-Solving Strategies, Springer, 1998.
(A unique collection of competition problems from over twenty major national
and international mathematical competitions for high school students.)