Peter Winkler - Mathematical Puzzles

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

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

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

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 delight-ful 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 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 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.

Andy Liu, Leader of the Canadian team to the International Mathematical Olympiad in 2000 and 2003

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.

Vaek Chvtal, 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 unrivaled 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 Number land

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 bat costs $1 more than a ball; together they cost $1.10. How much does the bat cost?

It was the first day of class and Mrs. OConnor had two identical-looking pupils, Donald and Ronald Featheringstonehaugh (pronounced Fanshaw), sitting together in the first row.

You two are twins, I take it? she asked.

No, they replied in unison.

But a check of their records showed that they had the same parents and were born on the same day. How could this be?

A visitor points to a portrait on the wall and asks who it is. Brothers and sisters have I none, says the host, but that mans father is my fathers son. Who is pictured?

At what age is the average child half the height that he or she will be as an adult?

You need to pack for a midnight flight to Iceland but the power is out. In your closet are six pairs of shoes, six black socks, six gray socks, six pairs of brown gloves, and six pairs of tan gloves. Unfortunately, its too dark to match shoes or to see any colors.

How many of each of these items do you need to take to be sure of getting a matched pair of shoes, two socks of the same color, and matching gloves?

A phone call in the continental United States is made from a west coast state to an east coast state, and its the same time of day at both ends of the call. How is this possible?

How many people are two pairs of twins twice?

While you hold a US 25-cent piece firmly to the tabletop with your left thumb, you rotate a second quarter with your right forefinger all the way around the first quarter. Since quarters are ridged, they will interlock like gears and the second will rotate as it moves around the first.

How many times will it rotate?

Can West Virginia be inscribed in a square?

An anthropologist is surrounded by a circle of natives, each of whom either always tells the truth or always lies. She asks each native whether the native to his right is a truth teller or a liar, and from their answers, she is able to deduce the fraction of liars in the circle.

What fraction is it?

As a result of temporary magical powers (which might need to be able to change your gender), you have made it to the womens singles tennis finals at Wimbledon and are playing Serena Williams for all the marbles. However, your powers cannot last the whole match. What score do you want it to be when they disappear, to maximize your chances of notching an upset win?