1. Mathematical Puzzles and Diversions (1959)

, 1-15


       Magic with a Matrix

       Nine Problems

       Ticktacktoe, or Noughts and Crosses

       Probability Paradoxes

       The Icosian Game and the Tower of Hanoi

       Curious Topological Models

       The Game of Hex

       Sam Loyd: America's Greatest Puzzlist

       Mathematical Card Tricks

       Memorizing Numbers

       Nine More Problems



       Nim and Tac Tix

       Left or Right?

       References for Further Reading

2. More Mathematical Puzzles and Diversions (1962)

, 16-34

       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


       Squaring the Square

       Mechanical Puzzles

       Probability and Ambiguity

       References for Further Reading

3. New Mathematical Diversions from Scientific American (1966)

, . 35-46

, . 1-7


- , 2008


       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 Problem

       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 Numerology of Dr. Matrix (columns 1-7, 1967; expanded 1976 with columns 8-18 as The Incredible Dr. Matrix; expanded 1985 with columns 19-22 as The Magic Numbers of Dr. Matrix)

. .


       New York

       Los Angeles

       Sing Sing

       Lincoln and Kennedy


       Miami Beach



       Wordsmith College


       Left Versus Right

       Fifth Avenue

       The Moon



       Clairvoyance Test

       Pyramid Lake

       The King James Bible





       Answers and Commentary

5. The Unexpected Hanging (1969; UK Further Mathematical Diversions)

, . 8-25

       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


       Rotations and Reflections

       Peg Solitaire


       Chicago Magic Conventions

       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 (   26)


6. Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American (1971)

, . 26-37

, . 1-6

       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 Trick

       Word Play

       The Pythagorean Theorem

       Limits of Infinite Series - . 1

       Polyiamonds - . 2

       Tetrahedrons - . 3

       Coleridge's Apples and Eight Other Problems - . 4

       The Lattice of Integers - 5

       Infinite Regress

       O'Gara, the Mathematical Mailman - , . 6

       Op Art

       Extraterrestrial Communication

7 Mathematical Carnival (1977)

( )

- , 2009

       Sprouts and Brussels Sprouts - 23

       Penny Puzzles - 9

       Aleph-Null and Aleph-One - 10

       Hypercubes 16

       Magic Stars and Polyhedrons -

       Calculating Prodigies - . 20

       Tricks of Lightning Calculators - . 21

       The Art of M.C. Escher - 11

       The Red-Faced Cube and Other Problems -

       Card Shuffles -

       Mrs Perkins' Quilt and Other Square-Packing Problems - 15

       The Numerology of Dr. Fliess -

       Random Numbers -

       The Rising Hourglass and Other Physics Puzzles - 14

       Pascal's Triangle - 17

       Jam, Hot and Other Games -

       Cooks and Quibble-Cooks - . 12

       Piet Hein's Superellipse -

       How to Trisect an Angle - 13


8. Mathematical Magic Show (1977)

( )

1000 , - , 2009


       More Ado About Nothing

       Game Theory, Guess It, Foxholes - . 26

       Factorial Oddities

       The Cocktail Cherry and Other Problems - 25

       Double Acrostics

       Playing Cards

       Finger Arithmetic - 30

       Mobius Bands

       Ridiculous Questions - . 29

       Polyhexes and Polyaboloes - . 22

       Perfect, Amicable, Sociable - . 28

       Polyominoes and Rectification

       Knights of the Square Table - . 24

       The Dragon Curve and Other Problems - . 15

       Colored Triangles and Cubes

       Trees - . 27




9. Mathematical Circus (1979)

( )

- , 2008

       Optical Illusions


       Spheres and Hyperspheres

       Patterns of Induction

       Elegant Triangles

       Random Walks and Gambling

       Random Walks on the Plane and in Space

       Boolean Algebra - . 31

       Can Machines Think?

       Cyclic Numbers

       Eccentric Chess and Other Problems

       Dominoes - . 36

       Fibonacci and Lucas Numbers - 32


       The Rotating Round Table and Other Problems - . 34

       Solar System Oddities

       Mascheroni Constructions - . 35

       The Abacus

       Palindromes: Words and Numbers

       Dollar Bills


10. Wheels, Life and Other Mathematical Amusements (1983)



       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 I

       The Game of Life, Part II

       The Game of Life, Part III

11. Knotted Doughnuts and Other Mathematical Entertainments (1986)

ԣ .


       The Binary Gray Code


       Bacon's Cipher

       Doughnuts: Linked and Knotted

       The Tour of the Arrows and Other Problems

       Napier's Bones

       Napier's Abacus

       Sim, Chomp and Racetrack


       Crossing Numbers

       Point Sets on the Sphere

       Newcomb's Paradox

       Reflections on Newcomb's Paradox

       Reverse the Fish and Other Problems

       Look-See Proofs

       Worm Paths

       Waring's Problems

       Cram, Bynum and Quadraphage

       The I Ching

       The Laffer Curve

12. Time Travel and Other Mathematical Bewilderments (1988)

       Time Travel

       Hexes and Stars

       Tangrams, Part 1

       Tangrams, Part 2

       Nontransitive Paradoxes

       Combinatorial Card Problems

       Melody-Making Machines

       Anamorphic Art

       The Rubber Rope and Other Problems

       Six Sensational Discoveries

       The Csaszar Polyhedron

       Dodgem and Other Simple Games

       Tiling with Convex Polygons

       Tiling with Polyominoes, Polyiamonds, and Polyhexes

       Curious Maps

       The Sixth Symbol and Other Problems

       Magic Squares and Cubes

       Block Packing

       Induction and Probability

       Catalan Numbers

       Fun with a Pocket Calculator

       Tree-Plant Problems

13. Penrose Tiles to Trapdoor Ciphers (1989)

       Penrose Tiling

       Penrose Tiling II

       Mandelbrot's Fractals

       Conway's Surreal Numbers

       Back from the Klondike and Other Problems

       The Oulipo

       The Oulipo II

       Wythoff's Nim

       Pool-Ball Triangles and Other Problems

       Mathematical Induction and Colored Hats

       Negative Numbers

       Cutting Shapes into N Congruent Parts

       Trapdoor Ciphers

       Trapdoor Ciphers II


       The New Eleusis

       Ramsey Theory

       From Burrs to Berrocal

       Sicherman Dice, the Kruskal Count and Other Curiosities

       Raymond Smullyan's Logic Puzzles

       The Return of Dr. Matrix

14. Fractal Music, Hypercards and More (1992)


       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 Hofstader's Godel, Escher, Bach

       Imaginary Numbers

       Pi and Poetry: Some Accidental Patterns

       More on Poetry

       Packing Squares

       Chaitin's Omega

15. The Last Recreations (1997)


       The Wonders of a Planiverse

       Bulgarian Solitaire and Other Seemingly Endless Tasks

       Fun with Eggs, Part I

       Fun with Eggs, Part II

       The Topology of Knots

       M-Pire Maps

       Directed Graphs and Cannibals

       Dinner Guests, Schoolgirls, and Handcuffed Prisoners

       The Monster and Other Sporadic Groups

       Taxicab Geometry

       The Power of the Pigeonhole

       Strong Laws of Small Primes

       Checker Recreations, Part I

       Checker Recreations, Part II

       Modulo Arithmetic and Hummer's Wicked Witch

       Lavinia Seeks a Room and Other Problems

       The Symmetry Creations of Scott Kim


       Non-Euclidean Geometry

       Voting Mathematics

       A Toroidal Paradox and Other Problems

       Minimal Steiner Trees

       Trivalent Graphs, Snarks, and Boojums


[1] 15 , Scientific American, .