List of Martin Gardner Mathematical Games columns

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For 24 years, starting in January 1957 and ending in December of 1980, Martin Gardner wrote 288 consecutive Mathematical Games columns in Scientific American. Over the next few years he alternated with other authors, producing 9 more columns under that title, for a total of 297.[1] These columns are listed in chronological order below.

date Title
1957 Jan A new kind of magic square with remarkable properties
1957 Feb An assortment of maddening puzzles
1957 Mar Some old and new versions of tick-tack-toe
1957 Apr Paradoxes dealing with birthdays, playing cards, coins, crows and red-haired typists
1957 May About the remarkable similarity between the Icosian Game and the Tower of Hanoi
1957 Jun Curious figures descended from the mobius band, which has only one side and one edge
1957 Jul Concerning the game of Hex, which can be played on the tiles of the bathroom floor
1957 Aug The life and work of Sam Loyd, a mighty inventor of puzzles
1957 Sep Concerning various tricks with a mathematical message
1957 Oct How to remember numbers by mnemonic devices such as cufflinks and red zebras
1957 Nov Nine titillating puzzles
1957 Dec More about complex dominoes
1958 Jan A collection of tantalizing fallacies of mathematics
1958 Feb The game of Nim and its mathematical analysis
1958 Mar About left- and right-handedness, mirror images and kindred matters
1958 Apr The celebrated puzzle of five sailors, a monkey, and a pile of coconuts
1958 May About tetraflexagons and tetraflexagation
1958 Jun About Henry Ernest Dudney, a brilliant creator of puzzles
1958 Jul Some diverting tricks which involve the concept of numerical congruence
1958 Aug A third collection of brain-teasers
1958 Sep A game in which standard pieces composed of cubes are assembled into larger forms
1958 Oct Four mathematical diversions involving concepts of topology
1958 Nov How rectangles, including squares, can be divided into squares of unequal size
1958 Dec Diversions which involve the five Platonic solids
1959 Jan May be traversed
1959 Feb Brainteasers that involve formal logic
1959 Mar Concerning the properties of various magic squares
1959 Apr The mathematical diversions of a fictitious carnival man
1959 May Another collection of brain teasers
1959 Jun An inductive card game
1959 Jul About Origami, the Japanese art of folding objects out of paper
1959 Aug About phi, an irrational number that had some remarkable geometrical expressions
1959 Sep Concerning mechanical puzzles, and how an enthusiast has collected 2,000 of them
1959 Oct Problems involving questions of probability and ambiguity
1959 Nov How three modern mathematicians disproved a celebrated conjecture of Leonhard Euler
1959 Dec Diversions that clarify group theory, particularly by the weaving of braids
1960 Jan A fanciful dialog about wonders of Numerology
1960 Feb A fifth collection of brainteasers
1960 Mar The games and puzzles of Lewis Carroll
1960 Apr About Mathematical games that are played on boards
1960 May Reflections on the packing of spheres
1960 Jun Recreations involving folding and cutting paper
1960 Jul Incidental information about the extraordinary number Pi
1960 Aug An imaginary dialog on mathemagic: tricks based on mathematical principles
1960 Sep The celebrated four-color map problem of topology
1960 Oct A new collection of brain-teasers
1960 Nov More about the shapes that can be made with complex dominoes (poly and pentominoes)
1960 Dec Some recreations involving the binary number system
1961 Jan Dr Matrix, numerologist extraordinary
1961 Feb Diversions that involve one of the classic conic sections: the ellipse
1961 Mar How to play dominoes in two and three dimensions
1961 Apr Diversions in a new book on geometry (Coxeter: Intro to Geometry)
1961 May MG meets the legendary Bertrand Apollinax
1961 Jun A new collection of brain-teasers
1961 Jul Some diverting mathematical board games
1961 Aug Some entertainments that involve the calculus of finite differences
1961 Sep Surfaces with edges linked in the same way as a well-known design (Borromean rings)
1961 Oct Diversions that involve the mathematical constant e
1961 Nov Where in geometrical figures are dissected to make other figures
1961 Dec On the theory of probability and the practice of gambling
1962 Jan An adventure in hyperspace at the church of the Fourth Dimension
1962 Feb A clutch of diverting problems
1962 Mar How to build a game-learning machine and teach it to play and win
1962 Apr About three types of spirals and how to construct them
1962 May Symmetry and asymmetry and the strange world of upside down art
1962 Jun The (board) game of solitaire and some variations and transformations
1962 Jul Fiction about life in two dimensions (Flatland)
1962 Aug A variety of diverting tricks collected at a fictitious convention of magicians
1962 Sep Tests that show whether a large number can be divided by a number from 2 to 12
1962 Oct A collection of puzzles involving numbers, logic, and probability
1962 Nov Some puzzles based on checker boards
1962 Dec Some tricks and manipulations from the ancient lore of string play
1963 Jan MG pays annual visit to Dr Matrix
1963 Feb Curves of constant width, one of which makes it possible to drill square holes
1963 Mar A new paradox, and variations on it, about a man condemned to be hanged
1963 Apr April Fool's Day
1963 May On rep-tiles polygons that can make larger and smaller copies of themselves
1963 Jun A discussion of helical structures from corkscrews to DNA molecules
1963 Jul Topological diversions, including a bottle with no inside or outside
1963 Aug Permutations and paradoxes in combinatorial math
1963 Sep How to solve puzzles by graphing the rebounds of a bouncing ball
1963 Oct About two new and two old board games
1963 Nov A mixed bag of problems
1963 Dec How to use the odd-even check for tricks and problem solving
1964 Jan Dr Matrix (numerologist) in his annual performance
1964 Feb The hypnotic fascination of sliding block puzzles
1964 Mar The remarkable lore of prime numbers
1964 Apr Various problems based on planar graphs, or sets of vertices connected by edges
1964 May The tyranny of 10 over thrown with the ternary number system
1964 Jun Short problems and more on prime numbers
1964 Jul The cycloid
1964 Aug Magic tricks based on mathematical principles
1964 Sep Puns, palindromes and other word games with math spirit
1964 Oct Pythagorean theorem
1964 Nov Infinite series and limits (geometric)
1964 Dec Polyiamonds
1965 Jan Dr Matrix on symmetries and reversals
1965 Feb Tetrahedrons
1965 Mar Short problems
1965 Apr Infinite regress in philosophy
1965 May The lattice of integers considered as an orchard or a billiard table
1965 Jun Diversions from Mr O'Gara/ the postman
1965 Jul Four bug problem
1965 Aug Communication with intelligent organisms on other worlds
1965 Sep Super ellipses
1965 Oct Pentominoes
1965 Nov Word and number problems
1965 Dec Magic stars, graphs and polyhedrons
1966 Jan Dr Matrix, neo-Freudian psychonumerologist
1966 Feb Recreational numismatics or a purse of coin purses
1966 Mar The hierarchy of infinities and the problems it spawns
1966 Apr The eerie mathematical art of Escher
1966 May How to cook a puzzle, or mathematical one-uppery
1966 Jun The persistence (and futility) of efforts to trisect the angle
1966 Jul Freud's friend Wilhelm Fliess and his theory of male and female life cycles
1966 Aug Puzzles that can be solved by reasoning based on elementary physical principles
1966 Sep Mrs Perkins quilt
1966 Oct Can the shuffling of cards (and other apparently random events) be reversed
1966 Nov Is it possible to visualize a four dimensional figure?
1966 Dec The multiple charms of Pascal's triangle
1967 Jan Dr Matrix delivers a talk on acrostics
1967 Feb Mathematical strategies for two person contests
1967 Mar An array of problems and dragon curve
1967 Apr Amazing feats of professional mental calculators and some tricks of the trade
1967 May Cube-root extraction and the calendar trick, or how to cheat in mathematics
1967 Jun The polyhex and the polyabolo/polygonal jigsaw puzzle pieces
1967 Jul Of sprouts and brussel sprouts, games with a topological flavor
1967 Aug In which a computer prints out mammoth polygonal factorials
1967 Sep Double acrostics, stylized Victorian ancestors or today's crossword puzzle
1967 Oct Problems that are built on the knight's tour in chess
1967 Nov A mixed bag of logical and illogical problems (including Langford's Problem!)
1967 Dec Game theory is applied (for a change) to games
1968 Jan Dr Matrix and the square
1968 Feb Combinatorial problems involving tree graphs and forests of trees
1968 Mar Perfect numbers, amicable pairs, Mersenne primes
1968 Apr Puzzles and tricks with a one dollar bill
1968 May Circles and spheres, and how they kiss and pack
1968 Jun Combinatorial possibilities on a pack of shuffled cards
1968 Jul On the meaning of randomness and some ways of achieving it
1968 Aug Array of puzzles and tricks
1968 Sep Counting systems and the relationship between numbers and the real world
1968 Oct Macmahon's color triangles
1968 Nov On the ancient lore of die and the odds against making a point
1968 Dec Mobius strip
1969 Jan Dr Matrix and Nixon
1969 Feb Boolean algebra, Venn diagrams and the propositional calculus
1969 Mar Fibonacci sequence
1969 Apr Octet of problems emphasizing gamesmanship, logic, and probability
1969 May Random walk and its gambling equivalent
1969 Jun Random walks by semidrunk bugs and others on the square and on the cube
1969 Jul Tricks, games, and puzzles that employ matches as counters and line segments
1969 Aug Simplicity as scientific concept — Does nature keep her accounts on a thumbnail?
1969 Sep Geometric construction with a compass and a straight edge
1969 Oct Numeranalysis of Apollo 11
1969 Nov Patterns
1969 Dec Combinatorial problems bases on dominoes
1970 Jan Abacus
1970 Feb Nine puzzles
1970 Mar Cyclic numbers and their properties
1970 Apr Mathematical curiosities embedded in the solar system
1970 May Optical illusions
1970 Jun Elegant triangle theorems
1970 Jul Diophantine analysis and the problem of Fermat's legendary last theorem
1970 Aug Backward run numbers, letters, words and sentences until boggles the mind
1970 Sep On cyclical curves generated by wheels that roll along wheels
1970 Oct Life
1970 Nov Short problems
1970 Dec Paradox of non-transitive dice and the elusive principle of indifference
1971 Jan Dr Matrix chess and numerology (Life)
1971 Feb Cellular automata
1971 Mar Orders of infinity, topological nature of dimension and supertask
1971 Apr Geometric fallacies-hidden errors pave the road to absurd conclusions
1971 May Combinatorial richness of folding a piece of paper
1971 Jun The Turning game and the question it presents: Can a computer think?
1971 Jul Quickie problems
1971 Aug Tick-tack-toe and its complications, and answers to the quickie problems
1971 Sep Plaiting of Plato's polyhedrons and the asymmetrical yin-yang-lee
1971 Oct Halma, the ancestor of Chinese checkers
1971 Nov Advertising premiums to beguile mind — classics by Sam Loyd, master puzzle poser
1971 Dec Touching cubes, paradoxes of Zeno as supertasks
1972 Jan How to triumph at nim by playing safe, and Conway's game hackenbush
1972 Feb Dr Matrix poses heteroliteral puzzles while peddling perpetual motion
1972 Mar Graceful graphs of Solomon Golomb, or how to number a graph parsimoniously
1972 Apr Topological problem with fresh twist, and eight other new recreational puzzles
1972 May Challenging chess tasks for puzzle buffs and answers to recreational problems
1972 Jun Transcendental problems
1972 Jul Amazing mathematical card tricks that do not require prestidigitation
1972 Aug The curious properties of the gray code and how it can be used to solve puzzles
1972 Sep Pleasurable problems with poly cubes and winning strategy for slither
1972 Oct Why the long arm of coincidence is usually not as long as it seems
1972 Nov Francis Bacon's bilateral cipher
1972 Dec Two-hole torus
1973 Jan Sam, chomp and race trace — new games for the intellect (and not for lady luck)
1973 Feb Up-and-down elevator games and Piet Hein's mechanical puzzles
1973 Mar The calculating rods of John Napier, the eccentric father of logarithms
1973 Apr How to turn a chessboard into a computer to calculate with negabinary numbers
1973 May Miscellany
1973 Jun Plotting the crossing number of graphs
1973 Jul Free will revisited, with mind bending prediction paradox by William Newcomb
1973 Aug An astounding self-test of clairvoyance by Dr Matrix
1973 Sep Problems on the surface of a sphere offer an entertaining intro to point sets
1973 Oct Look-see diagrams that offer visual proof of complex algebraic formulas
1973 Nov Fantastic patterns traced by programmed worms
1973 Dec On expressing integers as sum of cubes and other unsolved number theory problems
1974 Jan I Ching
1974 Feb Cram, cross cram and quadraphage — new games having elusive winning strategies
1974 Mar Reflections on Newcomb's problem-a prediction and free-will dilemma
1974 Apr Nine challenging problems, some rational and some not
1974 May On the contradictions of time travel
1974 Jun Dr Matrix and pyramids
1974 Jul On the patterns and unusual properties of figurate numbers
1974 Aug Tangrams
1974 Sep Tangrams — combinatorial problems and the game possibility of snug tangrams
1974 Oct Paradoxical situations that arise from non-transitive relationships
1974 Nov Dramatic demonstrations of number theorems with playing cards
1974 Dec The arts as combinatorial mathematics — How to compose like Mozart with dice
1975 Jan The curious magic of anamorphic art
1975 Feb How the absence of anything leads to thoughts of nothing
1975 Mar From rubber ropes to rolling cubes, a miscellany of refreshing problems
1975 Apr Six sensational discoveries that somehow have escaped public attention
1975 May On the remarkable Csaszar polyhedron and its applications in problem solving
1975 Jun Games of strategy for two players — star nim, meander, dodgem and rex
1975 Jul On tessellating the plane with convex polygon tiles
1975 Aug Polyominoes, polyiamonds and polyhexes more about tiling the plane
1975 Sep Dr Matrix finds numerological wonders in the King James Bible
1975 Oct Concerning an effort to demonstrate extrasensory perception by machine
1975 Nov On map projections (with special reference to some inspired ones)
1975 Dec A random assortment of puzzles
1976 Jan A breakthrough in magic squares and the first perfect magic cube
1976 Feb Some elegant brick-packing problems, and a new order-7 perfect magic cube
1976 Mar On the fabric of inductive logic, and some probability paradoxes
1976 Apr Snarks, boojums and other conjectures related to the four-color-map theorem
1976 May A few words about everything there was, is and ever will be
1976 Jun Catalan numbers — an integer sequence that materializes in unexpected places
1976 Jul Fun and serious business with the small electronic calculator
1976 Aug Symmetrical arrangement of the stars on the American flag and related matters
1976 Sep John Horton Conway's book covers an infinity of games
1976 Oct Combinatorial problems, some old, some new and all newly attacked by computer
1976 Nov In which DM (Dr Matrix) is revealed as the guru of pm (pentagonal meditation)
1976 Dec In which monster curves force redefinition of the word curve
1977 Jan Extraordinary nonperiodic tiling that enriches the theory of tiles
1977 Feb The flip strip sonnet, the lipogram and other mad modes of wordplay
1977 Mar Cornering a queen leads unexpectedly into corners of the theory of numbers
1977 Apr The pool table triangle, a limerick paradox and divers other challenges
1977 May The jump proof and its similarity to the toppling of a row of dominoes
1977 Jun The concept of negative numbers and the difficulty of grasping it
1977 Jul Cutting things into equal parts leads into significant areas of mathematics
1977 Aug A new kind of cipher that would take millions of years to break
1977 Sep On conic sections ruled surfaces and other manifestations of the hyperbola
1977 Oct On playing new eleusis, the game that simulates the search for truth
1977 Nov In which joining sets of points by lines leads into diverse (and diverting) paths
1977 Dec Dr Matrix goes to California to apply punk to rock study
1978 Jan The sculpture of Miquel Berrocal can be taken apart like an interlocking mechanical puzzle
1978 Feb Checker jumping, Sichermann dice, and Kruskal's card trick
1978 Mar Count dracula, alice, portia, others consider logic twists
1978 Apr White and brown music, fractal curves and 1/f fluctuations
1978 May The bells, numbers that can count partitions of a set, primes, rhymes
1978 Jun A mathematical zoo of astounding critters, imaginary and otherwise
1978 Jul On Charles Sanders Pierce, philosopher and gamesman
1978 Aug A mobius band has finite thickness, and so it is actually a twisted prism
1978 Sep Puzzling over a problem solving matrix, cubes of many colors, and 3d dominoes
1978 Oct Puzzles and number theory problems arising from the curious fractions of ancient Egypt
1978 Nov In which a mathematical aesthetic is applied to modern minimal art
1978 Dec Is it a superintelligent robot or does Dr Matrix ride again?
1979 Jan The diverse pleasures of circles that are tangent to one another
1979 Feb About rectangling rectangles, parodying Poe and many another pleasing problem
1979 Mar On altering the past, delaying the future and other ways of tampering with time
1979 Apr Aught to hunt bigger game
1979 May How to be a psychic, even if you are a horse or some other animal
1979 Jun Chess problems on a higher plane, including mirror images, rotations and the superqueen
1979 Jul Douglas R Hofstadter's Godel, Escher, Bach
1979 Aug The imaginableness of the imaginary numbers
1979 Sep May be less than meets the eye
1979 Oct Some packing problems that cannot be solved by sitting on the suitcase
1979 Nov The random number omega bids fair to hold the mysteries of the universe
1979 Dec A pride of problems, including one that is virtually impossible
1980 Jan Checkers, a game that can be more interesting than one might think
1980 Feb The coloring of unusual maps leads into uncharted territory
1980 Mar Graphs that can help cannibals, missionaries, wolves, goats and cabbages get there from here
1980 Apr Fun with eggs: uncooked and mathematical
1980 May What unifies dinner guests, strolling schoolgirls and handcuffed prisoners?
1980 Jun The capture of the monster: a mathematical group with a ridiculous number of elements
1980 Jul The pleasures of doing science and technology in the planiverse
1980 Aug On the fine art of putting players, pills and points into their proper pigeonholes
1980 Sep Dr Matrix, like Mr Holmes, comes to an untimely and mysterious end
1980 Oct From counting votes to making votes count: the mathematics of elections
1980 Nov Taxicab geometry offers a free ride to a non-Euclidean locale
1980 Dec Patterns in primes are a clue to the strong law of small numbers
1981 Feb Gauss's congruence theory was mod as early as 1801
1981 Apr How Lavina finds a room on University Avenue, and other geometric problems
1981 Jun The inspired geometrical symmetries of Scott Kim
1981 Aug The abstract parabola fits the concrete world
1981 Oct Euclid's parallel postulate and its modern offspring
1981 Dec The Laffer curve and other laughs in current economics
1983 Aug Tasks you cannot help finishing no matter how hard you try to block finishing them
1983 Sep The topology of knots, plus the results of Hofstadter's Luring Lottery
1986 Jun Casting a net on a checkerboard and other puzzles of the forest

Gardner wrote 4 other articles for Scientific American. His hexaflexagon article in December 1956 was in all but name the first article in the series of Mathematical Games columns and led directly to the series which began the following month.[2] These four articles are listed below.

date Title
1952 Mar Logic Machines
1956 Dec Hexaflexagons
1967 Jan Can time go backwards?
1998 Aug A Quarter Century of Recreational Mathematics

References[edit]