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. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics. This book is a collection of problems with aha! solutions. 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. This collection includes 100 problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. The problems start out easy and generally get more difficult as you progress through the book. A few solutions require the use of a computer. An important feature of the book is the bonus discussion of related mathematics that follows the solution of each problem. This material is there to entertain and inform you or point you to new questions. If you don’t remember a mathematical definition or concept, there is a Toolkit in the back of the book that will help.

Martin Erickson has assembled a splendid collection of 100 aha! solutions—problems that seem difficult but yield readily to a sudden insight. They are arranged on a continuum starting with easy and growing steadily toward not so easy, each leading into a discussion of the math involved. Some old favorites are here, but most are little known. It is a great book about modern math, disguised as a set of cool puzzles.

Martin Gardner