Practice Problems for the Putnam Competition
To access problems and solutions from the most recent years of the Putnam Competition, see https://www.maa.org/math-competitions/putnam-competition-archive-0. Additionally, PDFs with the problems and solutions are posted below.
Problems and solutions from earlier years of the Putnam Competition can be accessed through the UNH library's subscription. You will have to log in to your UNH account to view them. You can find them on JSTOR here: https://www-jstor-org.unh.idm.oclc.org/action/doBasicSearch?Query=%28William+Lowell+Putnam+Mathematical+Competition%29+AND+jid%3A%28j100069%29.
You can find a list of easier Putnam Problems at https://sites.math.northwestern.edu/~mlerma/problem_solving/putnam/easy_putnam_problems.pdf. This document is also included below.
Art of Problem Solving has a forum dedicated to Putnam Competition problems here: https://artofproblemsolving.com/community/c7t441f7.