Mathematical Puzzles

Peter Winkler has been collecting mathematical puzzles since childhood. He has had published two previous collections, and recently he compiled his largest curated collection to date. Mathematical Puzzles (A K Peters, 2021) also takes an alluring new approach to the genre: In the Roman-numbered front matter, 300+ puzzles are presented, roughly in order of increasing difficulty. Fuller discussions of the puzzles are then organized into 24 chapters according to the key insight that leads to their solutions. Each insight gets a brief mathematical treatment, and by the end of each chapter the reader is primed to appreciate an important and kindred mathematical result.

In our interview, Dr. Winkler walked me through a handful of puzzles from two chapters. The first, "The Law of Small Numbers", gives a tongue-in-cheek name to the strategy of gaining insight from a smaller version of a larger problem. The puzzles lead up to a discussion of perfect matchings, whose small-number analogues reveal an elegant geometric solution. The second, "Infinite Choice", begins with some variations on hat-guessing puzzles, which turn out to admit surprisingly powerful strategies even among infinitudes of players! The chapter closes with an accessible peek at graph coloring problems.

The book is delightfully designed with playful header fonts and illustrations by cartoonist Jess Johnson, through an equally delightful collaboration we took a moment to discuss. As Dr. Winkler aimed, i believe the book will appeal both to the puzzle enthusiast with a limited background in mathematics and to the mathematics enthusiast who, like myself, never really took to puzzles—as well, of course, to those dual enthusiasts whom the author epitomizes.

Suggested companion works:

• How to Solve It: A New Aspect of Mathematical Method by Georg Pólya
• Martin Gardner’s Mathematical Games: The Entire Collection of his Scientific
  American Columns

Peter Winkler is the William Morrill Professor of Mathematics and Computer Science at Dartmouth College and, for 2019–2020, the Distinguished Visiting Professor for the Public Dissemination of Mathematics at the National Museum of Mathematics. He is the author of 160 research papers, a dozen patents, two previous puzzle books, a book on cryptographic techniques in the game of bridge, and a portfolio of compositions for ragtime piano.