1. Hexaflexagons and other mathematical diversions

Introduction
Hexaflexagons
Magic with a Matrix
Nine Problems
Ticktacktoe
Probability Paradoxes
The Icosian Game and the Tower of Hanoi
Curious Topological Models
The Game Hex
Sam Loyd: America’s Greatest Puzzlist
Mathematical Card Tricks
Memorizing Numbers
Nine More Problems
Polyominoes
Fallacies
Nim and Tac Tix
Left or Right?
Afterword, 1988
References for Further Reading

2. The 2nd Scientific American book of mathematical puzzles & diversions

The Five Platonic Solids
Henry Ernest Dudeney: England’s Greatest Puzzlist
Digital Roots
Nine Problems
The Soma Cube
Recreational Topology
Phi: The Golden Ratio
The Monkey and the Coconuts
Recreational Logic
Magic Squares
James Hugh Riley Shows, Inc.
Nine More Problems
Eleusis : The Induction Game
Origami
Squaring the Square
Mechanical Puzzles
Probability and Ambiguity
The Mysterious Dr. Matrix

3. New mathematical diversions

The Binary System
Group Theory and Braids
Eight Problems
The Games and Puzzles of Lewis Carroll
Paper Cutting
Board Games
Packing Spheres
The Transcendental Number Pi
Victor Eigen : Mathemagician
The Four-Color Map Theorem
Mr. Apollinax Visits New York
Nine Problems
Polyominoes and Fault-Free Rectangles
Euler’s Spoilers: The Discovery of an Order-10
Graeco-Latin Square
The Ellipse
The 24 Color Squares and the 30 Color Cubes
H.S.M. Coxeter
Bridg-it and Other Games
Nine More Problems
The Calculus of Finite Differences

4. The unexpected hanging and other mathematical diversions

The Paradox of the Unexpected Hanging
Knots and Borromean Rings
The Transcendental Number e
Geometric Dissections
Scarne on Gambling
The Church of the Fourth Dimension
Eight Problems
A Matchbox Game-Learning Machine
Spirals
Rotations and Reflections
Peg Solitaire
Flatlands
Chicago Magic Convention
Tests of Divisibility
Nine Problems
The Eight Queens and Other Chessboard Diversions
A Loop of String
Curves of Constant Width
Rep-Tiles : Replicating Figures on the Plane
Thirty-Seven Catch Questions

5. The 6th book of mathematical diversions from Scientific American

The Helix
Klein Bottles and Other Surfaces
Combinatorial Theory
Bouncing Balls in Polygons and Polyhedrons
Four Unusual Board Games
The Rigid Square and Eight Other Problems
Sliding-Block Puzzles
Parity Checks
Patterns and Primes
Graph Theory
The Ternary System
The Trip around the Moon and Seven Other Problems
The Cycloid: Helen of Geometry
Mathematical Magic Tricks
Word Play
The Pythagorean Theorem
Limits of Infinite.Series
Polyiamonds
Tetrahedrons
Coleridge’s Apples and Eight Other Problems
The Lattice of Integers
Infinite Regress
O’Gara, the Mathematical Mailman
OpArt
Extraterrestrial Communication

6. Mathematical Carnival

Sprouts and Brussel Sprouts
Penny Puzzles
Aleph-null and Aleph-one
Hypercubes
Magic Stars and Polyhedrons
Calculating Prodigies
Tricks of Lightning Calculators
The Art of M. C. Escher
The Red-Faced Cube and Other Problems
CardShuffles
Mrs. Perkins' Quilt and Other Square-Packing Problems
The Numerology of Dr. Fliess
Random Numbers
The Rising Hourglass and Other Physics Puzzles
Pascal’s Triangle
Jam, Hot, and Other Games
Cooks and Quibble-Cooks
Piet Hein’s Superellipse
How to Trisect an Angle

7. Mathematical Magic Show

Nothing
More Ado About Nothing
Game Theory, Guess It, Foxholes
Factorial Oddities
The Cocktail Cherry and Other Problems
Double Acrostics
Playing Cards
Finger Arithmetic
Mobius Bands
Ridiculous Questions
Polyhexes and Polyaboloes
Perfect, Amicable, Sociable
Polyominoes and Rectification
Knights of the Square Table
The Dragon Curve and Other Problems
Colored Triangles and Cubes
Trees
Dice
Everything

8. Mathematical Circus

Optical Illusions
Matches
Spheres and Hyperspheres
Patterns of Induction
Elegant Triangles
Random Walks and Gambling
Random Walks on the Plane and in Space
Boolean Algebra
Can Machines Think?
Cyclic Numbers
Eccentric Chess and Other Problems
Dominoes
Fibonacci and Lucas Numbers
Simplicity
The Rotating Round Table and Other Problems
,Solar System Oddities
,Mascheroni Constructions
The Abacus
.Palindromes: Words and Numbers
Dollar Bills

9. The Magic Numbers of Dr.Matrix

Introduction
1. New York
2. Los Angeles
3. Sing Sing
4. Lincoln and Kennedy
5. Chicago
6. Miami Beach
7. Philadelphia
8. Pi
9. Wordsmith College
10. Squaresville
11. Left \'ersus Right
12. Fifth Avenue
13. The Moon
14. Honolulu
15. Houston
16. Clairvoyance Test
17. Pyramid Lake
18. The King James Bible
19. Calcutta
20. Stanford
21. Chautauqua
22. Istanbul
Answers and Commentary

10. Wheels, life, and other mathematical amusements

Wheels
Diophantine Analysis and Fermat’s Last Theorem
The Knotted Molecule and Other Problems
Alephs and Supertasks
Nontransitive Dice and Other Probability Paradoxes
Geometrical Fallacies
The Combinatorics of Paper Folding
A Set of Quickies
Ticktacktoe Games
Plaiting Polyhedrons
The Game of Halma
Advertising Premiums
Salmon on Austin’s Dog
Nim and Hackenbush
Golomb’s Graceful Graphs
Charles Addams' Skier and other Problems
Chess Tasks
Slither, 3X + 1, and Other Curious Questions
Mathematical Tricks With Cards
The Game of Life, Part l
The Game of Life, Part II
The Game of Life, Part Ill

11. Knotted doughnuts and other mathematical entertainments

CHAPTER ONE. Coincidence
CHAPTER TWO. The Binary Gray Code
CHAPTER THREE. Polycubes
CHAPTER FOUR. Bacon’s Cipher
CHAPTER FIVE. Doughnuts: Linked and Knotted
CHAPTER SIX. The Tour of the Arrows and Other Problems
CHAPTER SEVEN. Napier’s Bones
CHAPTER EIGHT. Napier’s Abacus
CHAPTER NINE. Sim, Chomp and Racetrack
CHAPTER TEN. Elevators
CHAPTER ELEVEN. Crossing Numbers
CHAPTER TWELVE. Point Sets on the Sphere
CHAPTER THIRTEEN. Newcomb’s Paradox
CHAPTER FOURTEEN. Reflections on Newcomb’s Paradox
CHAPTER FIFTEEN. Reverse the Fish and Other Problems
CHAPTER SIXTEEN. Look-See Proofs
CHAPTER SEVENTEEN. Worm Paths
CHAPTER EIGHTEEN. Waring’s Problems
CHAPTER NINETEEN. Cram, Bynum and Quadraphage
CHAPTER TWENTY. The I Ching
CHAPTER TWENTY-ONE. The Laffer Curve

12. Time travel and other mathematical bewilderments

CHAPTER ONE. Time Travel
CHAPTER TWO. Hexes and Stars
CHAPTER THREE. Tangrams, Part 1
CHAPTER FOUR. Tangrams, Part 2
CHAPTER FIVE. Nontransitive Paradoxes
CHAPTER SIX. Combinatorial Card Problems
CHAPTER SEVEN. Melody-Making Machines
CHAPTER EIGHT. Anamorphic Art
CHAPTER NINE. The Rubber Rope and Other Problems
CHAPTER TEN. Six Sensational Discoveries
CHAPTER ELEVEN. The Csaszar Polyhedron
CHAPTER TWELVE. Dodgem and Other Simple Games
CHAPTER THIRTEEN. Tiling with Convex Polygons
CHAPTER FOURTEEN. Tiling with Polyominoes, Polyiamonds, and Polyhexes
CHAPTER FIFTEEN. Curious Maps
CHAPTER SIXTEEN. The Sixth Symbol and Other Problems
CHAPTER SEVENTEEN. Magic Squares and Cubes
CHAPTER EIGHTEEN. Block Packing
CHAPTER NINETEEN. Induction and probability
CHAPTER TWENTY. Catalan Numbers
CHAPTER TWENTY-ONE. Fun with a Pocket Calculator
CHAPTER TWENTY-TWO. Tree-Plant Problems

13. Penrose Tiles to Trapdoor Ciphers

CHAPTER 1 Penrose Tiling
CHAPTER 2 Penrose Tiling II
CHAPTER 3 Mandelbrot’s Fractals
CHAPTER 4 Conway’s Surreal Numbers
CHAPTER 5 Back from the Klondike and Other Problems
CHAPTER 6 The Oulipo
CHAPTER 7 The Oulipo II
CHAPTER 8 Wythhoff’s Nim
CHAPTER 9 Pool-Ball Triangles und Other Problems
CHAPTER 10 Mathematical Induction and Colored Hats 137
CHAPTER 11 Negative Numbers
CHAPTER 12 Cutting Shapes into N Congruent Parts
CHAPTER 13 Trapdoor Ciphers
CHAPTER 14 Trapdoor Ciphers II
CHAPTER 15 Hyperbolas
CHAPTER 16 The New Eleusis
CHAPTER 17 Ramsey Theory
CHAPTER 18 From Burrs to Berrocal
CHAPTER 19 Sicherman Dice, the Kruskal Count and Other Curiosities
CHAPTER 20 Roymond Smullyan’s logic Puzzles
CHAPTER 21 The Return of Dr. Matrix

14. Fractal music, hypercards and more: mathematical recreations from Scientific: American

White, Brown, and Fractal Music
The Tinkly Temple Bells
Mathematical Zoo
Charles Sanders Peirce
Twisted Prismatic Rings
The Thirty Color Cubes
Egyptian Fractions
Minimal Sculpture
Minimal Sculpture II
Tangent Circles
The Rotating Table and Other Problems
Does Time Ever Stop? Can the Past Be Altered?
Generalized Ticktacktoe
Psychic Wonders and Probability
Mathematical Chess Problems
Douglas Hofstadter’s Godel, Escher, Bach
Imaginary Numbers
Pi and Poetry: Some Accidental Patterns
More on Poetry
Packing Squares
Chaitin’s Omega

15. The last recreations: hydras, eggs, and other mathematical mystifications

1 The Wonders of a Planiverse
2 Bulgarian Solitaire and Other Seemingly Endless Tasks
3 Fun with Eggs, Part I
4 Fun with Eggs, Part I1
5 The Topology of Knots
6 M-Pire Maps
7 Directed Graphs and Cannibals
8 Dinner Guests, Schoolgirls, and Handcuffed Prisoners
9 The Monster and Other Sporadic Groups
10 Taxicab Geometry
11 The Power of the Pigeonhole
12 Strong Laws of Small Primes
13 Checker Recreations, Part I
14 Checker Recreations, Part I1
15 Modulo Arithmetic and Hummer’s Wicked Witch
16 Lavinia Seeks a Room and Other Problems
17 The Symmetry Creations of Scott Kim
18 Parabolas
19 Non-Euclidean Geometry
20 Voting Mathematics
21 A Toroidal Paradox and Other Problems
22 Minimal Steiner Trees
23 Trivalent Graphs, Snarks, and Boojums

Gardner Books

1. Hexaflexagons and other mathematical diversions

2. The 2nd Scientific American book of mathematical puzzles & diversions

3. New mathematical diversions

4. The unexpected hanging and other mathematical diversions

5. The 6th book of mathematical diversions from Scientific American

6. Mathematical Carnival

7. Mathematical Magic Show

8. Mathematical Circus

9. The Magic Numbers of Dr.Matrix

10. Wheels, life, and other mathematical amusements

11. Knotted doughnuts and other mathematical entertainments

12. Time travel and other mathematical bewilderments

13. Penrose Tiles to Trapdoor Ciphers

14. Fractal music, hypercards and more: mathematical recreations from Scientific: American

15. The last recreations: hydras, eggs, and other mathematical mystifications