The Red Book of Mathematical Problems (Dover Books on Mathematics)

In North America, the most prestigious competition in mathematics at the undergraduate level is the William Lowell Putnam Mathematical Competition. This volume is a handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the Putnam and other undergraduate mathematical competitions. Indeed, it will be of use to anyone engaged in the posing and solving of mathematical problems.
Many of the problems in this book were suggested by ideas originating in a variety of sources, including Crux Mathematicorum, Mathematics Magazine, and the American Mathematical Monthly, as well as various mathematical competitions. This result is a rich selection of carefully chosen problems that will challenge and stimulate mathematical problem-solvers at varying degrees of proficiency.