Math Puzzles for the Public

When professor and "puzzle king" Peter Winkler set out to publish his third and most robust collection of math puzzles, he asked his publisher, CRC Press, to make the book free online after two and a half years. 

"This book belongs to math mavens all over the world," says Winkler, the William Morrill Professor of Mathematics and Computer Science. "It should be free to the world that created it." 

The revised edition of the critically acclaimed 2000 book, Mathematical Puzzles—heralded as "the best collection of mind-stretching teasers ever assembled" by celebrated computer scientist Donald Knuth—is now available free online on the mathematics department's website. The classic collection, which features puzzles from every continent, is designed for amateur mathematicians of any age, no calculus skills required. 

"I tried to put together the most entertaining, the most amusing, the most fun, the most paradoxical, and the most enjoyable puzzles I could find," says Winkler, who was named a fellow of the American Association for the Advancement of Science earlier this year.

In addition to including a handful of new puzzles, the revised edition incorporates several corrections and improvements—most of which Winkler says he received from readers. 

Winkler's passion for puzzles dates back to his own childhood, when he would jot favorite puzzles in a little blue book. "I always liked puzzles that are light, entertaining, and fun, and especially puzzles that reveal something interesting about mathematics," he says. "Math puzzles get you to try to think about how you would do something before you actually see how it's done."

In academic circles, Winkler quickly became known for his vast collection of math puzzles, which led to three published collections, beginning in 2003 with Mathematical Puzzles: A Connoisseur's Collection.

In 2019, Winkler was named the Distinguished Chair for the Public Dissemination of Mathematics at the National Museum of Mathematics in New York. During the one-year residency, he taught mini-courses in puzzle solving and hosted a series of puzzle-themed dinners for executives on probability and decision theory.

During the COVID-19 pandemic, Winkler collaborated with the museum on an online puzzle service that delivered a weekly puzzle to over 15,000 subscribers in 85 countries—some of whom sent Winkler puzzles for his growing collection.

Winkler also expresses gratitude to all of his Dartmouth colleagues, "who often have to put up with being peppered with puzzles that I test out on them," he says. 

Peers such as mathematics department chair Sergi Elizalde take pleasure in Winkler's dedication. "Any meal with Pete can turn into a fun discussion about mathematical puzzles and paradoxes," Elizalde says. 

Hints first, then solutions 

Winkler structured the book with his readers' enjoyment and learning in mind.

All the puzzles can be found in the first section, "so you can just read puzzles to your delight and work on the ones that you like," he says. 

But instead of putting answers alongside each puzzle, Winkler follows the first section with a collection of hints, which reveal which subsequent chapter discusses each respective puzzle. The chapters that follow are organized according to the technique utilized to solve the puzzles. Each chapter concludes with a theorem of mathematics that uses that technique in its proof. 

"So I've made it actually fairly difficult to go from the puzzle to the solution," Winkler says. "I want to encourage the readers as much as possible to try to solve the puzzle before they see the solution."

Winkler hopes that the free online edition will get more people excited about puzzles. 

"I hope to reach readers across the world who either can't afford to or wouldn't simply ordinarily buy a puzzle book, but they might just go to the website and say, 'Hmm, this is an interesting puzzle,' and then go back and say, 'Hmm, I'll try another one,'" he says.   

"People all over the world, of all backgrounds and all ages can enjoy puzzles, especially if they relax and don't worry too much about getting it right."