Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.


  • A collection of the world’s best mathematical puzzles
  • Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof
  • Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not just exercises or contest problems.


chapter 1|16 pages

Out for the Count

chapter 2|12 pages

Achieving Parity

chapter 3|12 pages

Intermediate Math

chapter 4|14 pages


chapter 5|12 pages

Algebra Too

chapter 6|10 pages

Safety in Numbers

chapter 7|14 pages

The Law of Small Numbers

chapter 8|10 pages

Weighs and Means

chapter 9|8 pages

The Power of Negative Thinking

chapter 10|28 pages

In All Probability

chapter 11|14 pages

Working for the System

chapter 12|12 pages

The Pigeonhole Principle

chapter 13|18 pages

Information, Please

chapter 14|24 pages

Great Expectation

chapter 15|18 pages

Brilliant Induction

chapter 16|12 pages

Journey into Space

chapter 17|18 pages

Nimbers and the Hamming Code

chapter 18|20 pages

Unlimited Potentials

chapter 19|22 pages

Hammer and Tongs

chapter 20|8 pages

Let’s Get Physical

chapter 21|24 pages

Back from the Future

chapter 22|14 pages

Seeing Is Believing

chapter 23|12 pages

Infinite Choice

chapter 24|18 pages

Startling Transformation

chapter 25|22 pages

Notes and Sources