The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games

✍ Scribed by Jonas Peters, Nicolai Meinshausen

• Publisher: The MIT Press
• Year: 2021
• Tongue: English
• Leaves: 192
• Edition: 1
• Category: Library

✦ Synopsis

Games that show how mathematics can solve the apparently unsolvable.
This book presents a series of engaging games that seem unsolvable but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.

✦ Table of Contents

Cover
Contents
Preface and Acknowledgments
1 - Hat Colors and Hamming Codes
1.1 - The Game
1.2 - How Well Can a Strategy Work?
1.3 - Some Mathematics: Hamming Codes
1.4 - Solution
1.5 - Hamming Codes in Higher Dimensions
1.6 - Short History
1.7 - Practical Advice
2 - Twenty Boxes and Permutations
2.1 - The Game
2.2 - How Well Can a Strategy Work?
2.3 - Solution
2.4 - Some Mathematics: Permutations and Cycles
2.5 - Understanding the Solution
2.6 - Short History
2.7 - Practical Advice
3 - The Dovetail Trick and Rising Sequences
3.1 - The Trick
3.2 - Riffle Shuffling Cards
3.3 - Some Mathematics: Permutations
3.4 - Solution
3.5 - More Mathematics: Shuffling Distributions
3.6 - Measuring the Goodness of a Shuffle
3.7 - Short History
3.8 - Practical Advice
4 - Animal Stickers and Cyclic Groups
4.1 - The Game
4.2 - Solution for 3 Animals
4.3 - Some Mathematics: Cyclic Groups
4.4 - Variation: Colored Hats in a Line
4.5 - Short history
4.6 - Practical Advice
5 - Opera Singers and Information Theory
5.1 - The Game
5.2 - How Well Can a Strategy Work?
5.3 - Solution for 5 Singers
5.4 - Some Mathematics: Information Theory
5.5 - Variation: Ball Weighing
5.6 - Random Strategies
5.7 - Short History
5.8 - Practical Advice
6 - Animal Matching and Projective Geometry
6.1 - The Game
6.2 - Solution
6.3 - Fano Planes
6.4 - Some Mathematics: Projective Geometry
6.5 - Short History
6.6 - Practical Advice
7 - The Earth and an Eigenvalue
7.1 - The Game
7.2 - Solution
7.3 - Some Mathematics: Linear Algebra
7.4 - Short History
7.5 - Practical Advice
8 - The Fallen Picture and Algebraic Topology
8.1 - The Fallen Picture
8.2 - Solution for 2 Nails
8.3 - Dancing
8.4 - Some Mathematics: Algebraic Topology
8.5 - Solution, Continued
8.6 - Short History
8.7 - Practical Advice
Appendix A - What Do We Mean When We Write …?
Appendix B - What Is …
B.1 - … a Binary Number?
B.2 - … a Converging Sequence or Series?
B.3 - … An Exponential Function?
B.4 - … a Binomial Coefficient?
B.5 - … a probability?
B.6 - … an expectation?
B.7 - … a Matrix?
B.8 - … a Complex Number?
Appendix C - Chapter-Specific Details
C.1 - Chapter 1: Hat Colors and Hamming Codes
C.2 - Chapter 4: Animal Stickers and Cyclic Groups
C.3 - Chapter 5: Opera Singers and Information Theory
C.4 - Chapter 6: Animal Matching and Projective Geometry
C.5 - Chapter 8: The Fallen Picture and Algebraic Topology
References
Index