The Libraries, particularly the Science Library, collect many books of mathematical and statistical problems.
Springer publishes a series called Problem Books in Mathematics Find paper copies by searching "Series Title begins with" with the search terms Problem books in Mathematics in the Barton catalog Basic search.
Find problem books for competitions in the QA43 section of the Science Library (Hayden Library). Some are available online.
In the Barton catalog, go to the Basic Search, choose subject begins with and use these search terms mathematics - competitions