Research in maths 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 maths. This book makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.

Author's Preface 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

Praise for the previous edition"Peter Winkler’s Mathematical Puzzles is his third, and most comprehensive, puzzle book. In addition to being an accomplished research mathematician, Winkler is a legend among mathematical puzzlers. The book requires nothing more than standard high school mathematics (occasionally supplemented with some basic ideas from probability theory and graph theory). The puzzles range in difficulty from those that are elementary to those that are likely to be challenging even to professional mathematicians."– Games World of Puzzles Magazine"This is the greatest collection of puzzles I’ve encountered, and is excellent reading for all ages of mathematically minded individuals from teenagers through experienced researchers. Whoever you are, do not expect to solve them all!Peter Winkler’s excellent taste in puzzles comes through in both his selection and his presentation. Many puzzles are framed in a mini-story with captivating language or characters; and there are a few non-mathematical teasers thrown in. [. . . ] Thank you, Peter, for assembling this magnificent potpourri!"– CMS Notes"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"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"Anyone, from novice to expert, with an interest in math or puzzles should have this book. The puzzles are artfully chosen and lucidly explained in a way that will boost the math IQ of readers at any level.As a reader with a lifelong interest in recreational math I was delighted with these superb puzzles with many surprises, elegant solutions and detailed information on their origins."– Dick Hess, author of Golf on the Moon and other puzzle books"Great problems teach us to delight in thinking, and this rich assortment will reward all who dare look at them with hours of enchantment and surprise."– Francis Su, author of Mathematics for Human Flourishing "A rare puzzle collection that ranges from funny riddles all the way into current mathematics research, sometimes within one and the same puzzle!"– Johan Wästlund, researcher at Chalmers University of Technology and the recipient of the Göran Gustafsson Prize by Royal Swedish Academy of Sciences"Peter Winkler has an extraordinary taste for mathematical puzzles. Each puzzle in his new book is a gem, which makes the book a real treasure chest."– Tanya Khovanova, Massachusetts Institute of Technology"On average, who has more sisters, men or women? When a coin is rolled once around another one of equal size, with no slipping, how many times does it rotate? How can you get a 50-50 decision by flipping a bent coin? If you enjoy challenges like these, you will be enthralled by this latest collection of delightful dazzlers from Peter Winkler. From old classics to new gems, wrestling with these brain ticklers will provide many weeks of fun and ‘Aha!’ moments. Warning: these are addictive, and you'll need to use a magic combination of skill, intuition and insight to solve them all!"– Colm Mulcahy, Professor of Mathematics at Spelman College and author of Mathematical Card Magic: Fifty-Two New Effects"Peter Winkler's Mathematical Puzzles is thought-provoking, and I fell in love with the puzzles. Their level ranges from questions for smart high-school students to rudiments of research problems for serious mathematicians. I was charmed by the bar trivia sprinkled here and there on top of respectable mathematics. This book is an ideal companion to pack in the vacation luggage for anyone interested in mathematics: it is bound to keep them entertained for hours."– Vašek Chvátal, Emeritus Professor at Concordia University"Peter Winkler is the puzzle master’s puzzle master: a serious mathematician not only with exquisite taste in what makes for a great puzzle but who also has an unrivalled elegance of delivery and clarity of explication. This book presents the crown jewels of mathematical puzzledom and will bring hours of joy - and pain! - to all curious and playful minds."– Alex Bellos, author of Alex's Adventures in Numberland"An absolute 'must' for personal, professional, college, and university library Advanced Mathematics collections and supplemental curriculum studies lists, Mathematical Puzzles is an extraordinarily elegant compendium of mathematically based puzzles and an unreservedly recommended acquisition selection."– Midwest Book Review