Martin Gardner
Mathematical Games Collections
David Langford

Source: David Langford's original Page

The great Columns reappearing in the The Colossal Book of Mathematics are marked with a star ★ in earlier listings below. – David Langford

Book Title List

Book Contents Lists

    Mathematical Puzzles and Diversions (1959)
  1. Hexaflexagons ★
  2. Magic with a Matrix
  3. Nine Problems
  4. Ticktacktoe, or Noughts and Crosses
  5. Probability Paradoxes
  6. The Icosian Game and the Tower of Hanoi
  7. Curious Topological Models
  8. The Game of Hex
  9. Sam Loyd: America's Greatest Puzzlist
  10. Mathematical Card Tricks
  11. Memorizing Numbers
  12. Nine More Problems
  13. Polyominoes
  14. Fallacies
  15. Nim and Tac Tix
  16. Left or Right?
  17. References for Further Reading
    More Mathematical Puzzles and Diversions (1962)
  1. The Five Platonic Solids
  2. Tetraflexagons
  3. Henry Ernest Dudeney: England's Greatest Puzzlist
  4. Digital Roots
  5. Nine Problems
  6. The Soma Cube ★
  7. Recreational Topology
  8. Phi: The Golden Ratio
  9. The Monkey and the Coconuts ★
  10. Mazes
  11. Recreational Logic
  12. Magic Squares
  13. James Hugh Riley Shows, Inc.
  14. Nine More Problems
  15. Eleusis: The Induction Game
  16. Origami
  17. Squaring the Square
  18. Mechanical Puzzles
  19. Probability and Ambiguity ★
  20. References for Further Reading
    New Mathematical Diversions from Scientific American (1966)
  1. The Binary System
  2. Group Theory and Braids
  3. Eight Problems
  4. The Games and Puzzles of Lewis Carroll
  5. Paper Cutting
  6. Board Games
  7. Packing Spheres ★
  8. The Transcendental Number Pi
  9. Victor Eigen: Mathemagician
  10. The Four-Color Map Problem
  11. Mr. Apollinax Visits New York
  12. Nine Problems
  13. Polyominoes and Fault-Free Rectangles
  14. Euler's Spoilers: The Discovery of an Order-10 Graeco-Latin Square
  15. The Ellipse
  16. The 24 Color Squares and the 30 Color Cubes
  17. H.S.M. Coxeter
  18. Bridg-it and Other Games
  19. Nine More Problems
  20. The Calculus of Finite Differences ★
    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), with 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 Versus 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
  23. Answers and Commentary
    The Unexpected Hanging (1969; UK Further Mathematical Diversions)
  1. The Paradox of the Unexpected Hanging ★
  2. Knots and Borromean Rings
  3. The Transcendental Number e
  4. Geometric Dissections
  5. Scarne on Gambling
  6. The Church of the Fourth Dimension ★
  7. Eight Problems
  8. A Matchbox Game-Learning Machine ★
  9. Spirals
  10. Rotations and Reflections ★
  11. Peg Solitaire
  12. Flatlands
  13. Chicago Magic Conventions
  14. Tests of Divisibility
  15. Nine Problems
  16. The Eight Queens and Other Chessboard Diversions
  17. A Loop of String
  18. Curves of Constant Width ★
  19. Rep-Tiles: Replicating Figures on the Plane ★
  20. Thirty-Seven Catch Questions
  21. Bibliography
    Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American (1971)
  1. The Helix ★
  2. Klein Bottles and Other Surfaces ★
  3. Combinatorial Theory
  4. Bouncing Balls in Polygons and Polyhedrons
  5. Four Unusual Board Games
  6. The Rigid Square and Eight Other Problems
  7. Sliding-Block Puzzles
  8. Parity Checks
  9. Patterns and Primes
  10. Graph Theory
  11. The Ternary System
  12. The Trip around the Moon and Seven Other Problems
  13. The Cycloid: Helen of Geometry
  14. Mathematical Magic Trick
  15. Word Play
  16. The Pythagorean Theorem
  17. Limits of Infinite Series
  18. Polyiamonds
  19. Tetrahedrons
  20. Coleridge's Apples and Eight Other Problems
  21. The Lattice of Integers
  22. Infinite Regress ★
  23. O'Gara, the Mathematical Mailman
  24. Op Art
  25. Extraterrestrial Communication
    Mathematical Carnival (1975)
  1. Sprouts and Brussels Sprouts ★
  2. Penny Puzzles
  3. Aleph-Null and Aleph-One ★
  4. Hypercubes ★
  5. Magic Stars and Polyhedrons
  6. Calculating Prodigies
  7. Tricks of Lightning Calculators
  8. The Art of M.C. Escher ★
  9. The Red-Faced Cube and Other Problems
  10. Card Shuffles
  11. Mrs Perkins' Quilt and Other Square-Packing Problems
  12. The Numerology of Dr. Fliess
  13. Random Numbers
  14. The Rising Hourglass and Other Physics Puzzles
  15. Pascal's Triangle
  16. Jam, Hot and Other Games
  17. Cooks and Quibble-Cooks
  18. Piet Hein's Superellipse ★
  19. How to Trisect an Angle
  20. Bibliography
    Mathematical Magic Show (1977)
  1. Nothing ★
  2. More Ado About Nothing
  3. Game Theory, Guess It, Foxholes
  4. Factorial Oddities
  5. The Cocktail Cherry and Other Problems
  6. Double Acrostics
  7. Playing Cards
  8. Finger Arithmetic
  9. Möbius Bands
  10. Ridiculous Questions
  11. Polyhexes and Polyaboloes
  12. Perfect, Amicable, Sociable
  13. Polyominoes and Rectification
  14. Knights of the Square Table
  15. The Dragon Curve and Other Problems
  16. Colored Triangles and Cubes
  17. Trees
  18. Dice
  19. Everything ★
  20. Bibliography
    Mathematical Circus (1979)
  1. Optical Illusions
  2. Matches
  3. Spheres and Hyperspheres ★
  4. Patterns of Induction
  5. Elegant Triangles
  6. Random Walks and Gambling
  7. Random Walks on the Plane and in Space
  8. Boolean Algebra
  9. Can Machines Think?
  10. Cyclic Numbers
  11. Eccentric Chess and Other Problems
  12. Dominoes
  13. Fibonacci and Lucas Numbers
  14. Simplicity ★
  15. The Rotating Round Table and Other Problems
  16. Solar System Oddities
  17. Mascheroni Constructions
  18. The Abacus
  19. Palindromes: Words and Numbers ★
  20. Dollar Bills
  21. Bibliography
    Wheels, Life and Other Mathematical Amusements (1983)
  1. Wheels
  2. Diophantine Analysis and Fermat's Last Theorem
  3. The Knotted Molecule and Other Problems
  4. Alephs and Supertasks ★
  5. Nontransitive Dice and Other Probability Paradoxes ★
  6. Geometrical Fallacies
  7. The Combinatorics of Paper Folding ★
  8. A Set of Quickies
  9. Ticktacktoe Games
  10. Plaiting Polyhedrons
  11. The Game of Halma
  12. Advertising Premiums
  13. Salmon on Austin's Dog
  14. Nim and Hackenbush
  15. Golomb's Graceful Graphs
  16. Charles Addams' Skier and Other Problems
  17. Chess Tasks
  18. Slither, 3X+1, and Other Curious Questions
  19. Mathematical Tricks with Cards
  20. The Game of Life, Part I ★
  21. The Game of Life, Part II
  22. The Game of Life, Part III
    Knotted Doughnuts and Other Mathematical Entertainments (1986)
  1. Coincidence
  2. The Binary Gray Code
  3. Polycubes
  4. Bacon's Cipher
  5. Doughnuts: Linked and Knotted ★
  6. The Tour of the Arrows and Other Problems
  7. Napier's Bones
  8. Napier's Abacus
  9. Sim, Chomp and Racetrack
  10. Elevators
  11. Crossing Numbers
  12. Point Sets on the Sphere
  13. Newcomb's Paradox ★
  14. Reflections on Newcomb's Paradox
  15. Reverse the Fish and Other Problems
  16. Look-See Proofs
  17. Worm Paths
  18. Waring's Problems
  19. Cram, Bynum and Quadraphage
  20. The I Ching
  21. The Laffer Curve
    Time Travel and Other Mathematical Bewilderments (1988)
  1. Time Travel ★
  2. Hexes and Stars
  3. Tangrams, Part 1
  4. Tangrams, Part 2
  5. Nontransitive Paradoxes ★
  6. Combinatorial Card Problems
  7. Melody-Making Machines ★
  8. Anamorphic Art
  9. The Rubber Rope and Other Problems
  10. Six Sensational Discoveries ★
  11. The Császár Polyhedron
  12. Dodgem and Other Simple Games
  13. Tiling with Convex Polygons
  14. Tiling with Polyominoes, Polyiamonds, and Polyhexes
  15. Curious Maps
  16. The Sixth Symbol and Other Problems
  17. Magic Squares and Cubes
  18. Block Packing
  19. Induction and Probability ★
  20. Catalan Numbers
  21. Fun with a Pocket Calculator
  22. Tree-Plant Problems
    Penrose Tiles to Trapdoor Ciphers (1989)
  1. Penrose Tiling ★
  2. Penrose Tiling II
  3. Mandelbrot's Fractals
  4. Conway's Surreal Numbers ★
  5. Back from the Klondike and Other Problems
  6. The Oulipo
  7. The Oulipo II
  8. Wythoff's Nim
  9. Pool-Ball Triangles and Other Problems
  10. Mathematical Induction and Colored Hats
  11. Negative Numbers
  12. Cutting Shapes into N Congruent Parts
  13. Trapdoor Ciphers
  14. Trapdoor Ciphers II
  15. Hyperbolas
  16. The New Eleusis ★
  17. Ramsey Theory ★
  18. From Burrs to Berrocal
  19. Sicherman Dice, the Kruskal Count and Other Curiosities
  20. Raymond Smullyan's Logic Puzzles
  21. The Return of Dr. Matrix
    Fractal Music, Hypercards and More (1992)
  1. White, Brown and Fractal Music ★
  2. The Tinkly Temple Bells
  3. Mathematical Zoo ★
  4. Charles Sanders Peirce
  5. Twisted Prismatic Rings
  6. The Thirty Color Cubes
  7. Egyptian Fractions
  8. Minimal Sculpture
  9. Minimal Sculpture II
  10. Tangent Circles
  11. The Rotating Table and Other Problems
  12. Does Time Ever Stop? Can the Past Be Altered? ★
  13. Generalized Ticktacktoe ★
  14. Psychic Wonders and Probability
  15. Mathematical Chess Problems
  16. Douglas Hofstader's Gödel, Escher, Bach ★
  17. Imaginary Numbers
  18. Pi and Poetry: Some Accidental Patterns
  19. More on Poetry
  20. Packing Squares
  21. Chaitin's Omega
    The Last Recreations (1997)
  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 II
  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 II
  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
    The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001)
  1. The Monkey and the Coconuts
  2. The Calculus of Finite Differences
  3. Palindromes: Words and Numbers
  4. Curves of Constant Width
  5. Rep-Tiles: Replicating Figures on the Plane
  6. Piet Hein's Superellipse
  7. Penrose Tiling
  8. The Wonders of a Planiverse
  9. The Helix
  10. Packing Spheres
  11. Spheres and Hyperspheres
  12. The Church of the Fourth Dimension
  13. Hypercubes
  14. Non-Euclidean Geometry
  15. Rotations and Reflections
  16. The Symmetry Creations of Scott Kim
  17. The Art of M.C. Escher
  18. Klein Bottles and Other Surfaces
  19. The Topology of Knots
  20. Doughnuts: Linked and Knotted
  21. Probability and Ambiguity
  22. Nontransitive Dice and Other Probability Paradoxes
  23. Nontransitive Paradoxes
  24. Infinite Regress
  25. Aleph-Null and Aleph-One
  26. Alephs and Supertasks
  27. White, Brown and Fractal Music
  28. Conway's Surreal Numbers
  29. Hexaflexagons
  30. The Soma Cube
  31. The Game of Life, Part I
  32. The Combinatorics of Paper Folding
  33. Ramsey Theory
  34. Bulgarian Solitaire and Other Seemingly Endless Tasks
  35. A Matchbox Game-Learning Machine
  36. Sprouts and Brussels Sprouts
  37. Generalized Ticktacktoe
  38. The New Eleusis
  39. Time Travel
  40. Does Time Ever Stop? Can the Past Be Altered?
  41. Induction and Probability
  42. Simplicity
  43. The Paradox of the Unexpected Hanging
  44. Newcomb's Paradox
  45. Nothing
  46. Everything
  47. Melody-Making Machines
  48. Mathematical Zoo
  49. Douglas Hofstader's Gödel, Escher, Bach
  50. Six Sensational Discoveries