# Solve This: Math Activities for Students and Clubs

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*James Tanton*

MAA Press: An Imprint of the American Mathematical Society

Recipient of the Mathematical Association of America's
Beckenbach Book Prize in 2004!

Solve This irresistibly tempts the reader to
embark on a journey of investigation and discovery. All the activities
are immediate, catchy and fun, but upon investigation, begin to unfold
into surprising layers of depth and new perspectives. The necessary
mathematics in increasing levels of sophistication is fully explained
along the way, but readers may amend the journey in any way to match
their mathematical abilities.

Elementary, middle and high school students, college students and
mathematics majors, faculty from all divisions and professional
mathematicians, as well as self-described math phobics have all
enjoyed these activities and have all attained a sense of satisfaction
and accomplishment from them. Mathematics educators will find this an
invaluable resource of fresh and innovative approaches to topics in
mathematics.

#### Reviews & Endorsements

If you want a book with a bounty of activities that you could use in your mathematics classroom or as part of a mathematics club, try this one. We, as mathematicians, are always looking for ways to stimulate interest in mathematics in others. In particular, if one were to visit a high school mathematics classroom and want to show the students that mathematics can actually be FUN, look to this book for some wonderful ideas.

-- Herbert E. Kasube, MAA Reviews

# Table of Contents

## Solve This: Math Activities for Students and Clubs

Table of Contents pages: 1 2

- cover cover11
- copyright page ii3
- title page iii4
- Introduction v6
- Contents ix10
- PART I ACTIVITIES AND PROBLEM STATEMENTS 116
- 1 Distribution Dilemmas 318
- 2 Weird Shapes 520
- 3 Counting the Odds … and Evens 722
- 4 Dicing, Slicing, and Avoiding the Bad Bits 924
- 5 "Impossible" Paper Tricks 1126
- 6 Tiling Challenges 1328
- 7 Things That Won't Fall Down 1530
- 8 Möbius Madness: Tortuous Twists on a Classic Theme 1732
- 9 The Infamous Bicycle Problem 2136
- 10 Making Surfaces in 3- and 4-Dimensional Space 2338
- 11 Paradoxes in Probability Theory 2540
- 12 Don't Turn Around Just Once 2742
- 13 It's All in a Square 2944
- 14 Bagel Math 3146
- 15 Capturing Chaos 3348
- 16 Who has the Advantage? 3550
- 17 Laundry Math 3954
- 18 Get Knotted 4156
- 19 Tiling and Walking 4560
- 20 Automata Antics 4964
- 21 Bubble Trouble 5166
- 22 Halves and Doubles 5368
- 23 Playing with Playing Cards 5772
- 24 Map Mechanics 6176
- 25 Weird Lotteries 6580
- 26 Flipped Out 6782
- 27 Parts That Do Not Add Up to Their Whole 6984
- 28 Making the Sacrifice 7186
- 29 Problems in Parity 7388
- 30 Chessboard Maneuvers 7792

- PART II HINTS, SOME SOLUTIONS, AND FURTHER THOUGHTS 8196
- 1 Distribution Dilemmas 8398
- 2 Weird Shapes 8398
- 3 Counting the Odds … and Evens 8499
- 4 Dicing, Slicing, and Avoiding the Bad Bits 8499
- 5 "Impossible" Paper Tricks 85100
- 6 Tiling Challenges 86101
- 7 Things That Won't Fall Down 87102
- 8 Möbius Madness: Tortuous Twists on a Classic Theme 88103
- 9 The Infamous Bicycle Problem 88103
- 10 Making Surfaces in 3- and 4-Dimensional Space 88103
- 11 Paradoxes in Probability Theory 90105
- 12 Don't Turn Around Just Once 90105
- 13 It's All in a Square 91106
- 14 Bagel Math 91106
- 15 Capturing Chaos 93108
- 16 Who has the Advantage? 93108
- 17 Laundry Math 94109
- 18 Get Knotted 95110
- 19 Tiling and Walking 96111
- 20 Automata Antics 96111
- 21 Bubble Trouble 97112
- 22 Halves and Doubles 98113
- 23 Playing with Playing Cards 98113
- 24 Map Mechanics 99114
- 26 Flipped Out 101116
- 27 Parts That Do Not Add Up to Their Whole 101116
- 28 Making the Sacrifice 103118
- 29 Problems in Parity 103118
- 30 Chessboard Maneuvers 104119

- PART III SOLUTIONS AND DISCUSSIONS 107122
- 1 Distribution Dilemmas 109124
- A Note on Unit Fractions 109124
- 2 Weird Shapes 111126
- A Note on Fractal Dimensions 112127
- 3 Counting the Odds … and Evens 116131
- 4 Dicing, Slicing, and Avoiding the Bad Bits 117132
- A Note on Minimality Formulae for Slicing and Dicing 117132
- 5 "Impossible" Paper Tricks 120135
- 6 Tiling Challenges 124139
- 7 Things That Won't Fall Down 125140
- A Note on Polygonal Wheels 126141
- 8 Möbius Madness: Tortuous Twists on a Classic Theme 130145
- 9 The Infamous Bicycle Problem 131146
- A Note on Bicycle Tracks 132147
- 10 Making Surfaces in 3- and 4-Dimensional Space 134149
- A Note on the Fourth Dimension 135150
- A Note on Constructing Surfaces 138153
- 11 Paradoxes in Probability Theory 140155
- A Note on Probability and Measure Theory 142157
- 12 Don't Turn Around Just Once 143158
- 13 It•s All in a Square 146161
- A Note on Modified Square Maneuvers 147162
- 14 Bagel Math 148163
- A Note on Euler•s Equation 150165
- 15 Capturing Chaos 151166
- A Note on Population Models 153168
- 16 Who has the Advantage? 154169
- A Note on Computing Probabilities in a Three-Way Duel 155170
- A Note on Social Choice Theory 157172
- 17 Laundry Math 160175
- 18 Get Knotted 162177
- 19 Tiling and Walking 164179
- 20 Automata Antics 167182
- A Note on Ant Motions 168183

Table of Contents pages: 1 2