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 increase one's armory of techniques for doing mathematics. Mathematical Puzzles will, for the first time, make the 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.
Table of Contents
The Puzzles. The Hints. 1. Out for the Count. 2. Achieving Parity. 3. Intermediate Math. 4. Graphography. 5. Algebra Too. 6. Safety in Numbers. 7. The Law of Small Numbers. 8. Weighs and Means. 9. The Power of Negative Thinking. 10. In All Probability. 11. Working for the System. 12. The Pigeonhole Principle. 13. Information, Please. 14. Great Expectation. 15. Brilliant Induction. 16. Journey Into Space. 17. Nimbers and the Hamming Code. 18. Unlimited Potentials. 19. Hammer and Tongs. 20. Let's Get Physical. 21. Back from the Future. 22. Seeing is Believing. 23. Infinite Choice. 24. Startling Transformation. Notes & Sources
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.
"This book may well be the best collection of mind-stretching teasers ever assembled. You can't help but be inspired, when Peter winks at you."
– Donald E. Knuth, Emeritus Professor at Stanford University and winner of Turing Award
"A fantastic collection of mathematical puzzles! The clever, elegant, and surprising solutions should bring a sense of wonder and pleasure to all mathematicians."
– Richard Stanley, Emeritus Professor of Applied Mathematics, Massachusetts Institute of Technology
"Peter Winkler is a wizard! He transforms the latest results in mathematics and computer science into enticing puzzles. The solutions are Eureka moments for all."
– Joel H. Spencer, Professor of Mathematics and Computer Science, Courant Institute of Mathematical Sciences
"This is the third and by far the most substantial of Peter Winkler's books on mathematical puzzles, drawing from everyday life and from a wide spectrum of mathematical topics. Mathematics' answer to Ripley's Believe It or Not, Peter brings out the romantic side of mathematics rather than its utilitarian side. It is sincerely hoped that his trilogy will contain more than three volumes."
– Andy Liu, Emeritus Professor at University of Alberta
"This is an incredible collection of puzzles. While many books claim to be `for all levels', here it is really true: the range of problems is truly remarkable. There are simple ones for teens and pre-teens, right up toones for grown-ups. I do not know any book with such a spread.
A particular feature of the book is that its easiest problems, aimed say at youngsters, are so attractive. Thus for example each of `Phone Call' and `Winning at Wimbledon' are surprising and clever. And then there are problems like `Watermelons', where the calculation is easy but the result itself is very unexpected indeed. Such interest is rare among easy problems, and this feature by itself would make this a must-buy.
At the other end of the scale, there are problems like 'Alternating Powers' that lead on to some very deep mathematics.
All of the book is written in Peter Winkler's trademark fun and chatty style."
– Imre Leader, Professor of Mathematics at Cambridge University and 12-time winner of the Othello National championship
"Peter Winkler’s collection of attractive puzzles will appeal to readers at all levels. Many famous puzzles are discussed, but there are also new and attractive problems that readers will surely not be familiar with. I thoroughly enjoyed the book and highly recommend to those with an interest in the best that modern puzzling has to offer."
– Stan Wagon, Macalester College, author of Which Way Did the Bicycle Go? and Bicycle or Unicycle?
"This is a beautiful collection of mathematical puzzles, followed by hints and solutions. No advanced mathematics is necessary, and yet many of the puzzles are truly challenging, even for a professional mathematician. Peter Winkler has led a Year of Puzzles at the National Museum of Mathematics in New York. His superb exposition ensures that while reading the book and trying to solve the puzzles you will have hours of fun, intrigue, joy and enlightenment."
– Noga Alon, Princeton University