Every mathematician (beginner, amateur, and professional alike) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called “aha! solutions,” a phrase popularized by mathematics and science writer Martin Gardner in his books Aha! Gotcha and Aha! Insight. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics.

This book is a collection of problems whose aha! solutions I enjoy and hope you will enjoy too. The problems are at the level of the college mathematics student, but there should be something of interest for the high school student, the teacher of mathematics, the “math fan,” and anyone else who loves mathematical challenges.

As a student first learning mathematics, I was inspired by the works of Martin Gardner and mathematics expositor Ross Honsberger (I still am today). One of the best ways to capture the imagination of young people and get them interested in mathematics is by “hooking them” on irresistible problems. And such a hook is appropriate, since a great part of mathematical study and investigation consists of problem solving. Sometimes the problemsolving is at an advanced level, sometimes it is what we discover and create in our everyday mathematical lives.

For this collection, I have selected one hundred problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. Some of the problems I created, others are old but deserve to be better known.