List of Martin Gardner Mathematical Games columns

For Gardner's columns collected in book form, see Martin Gardner bibliography § "Mathematical Games": The Scientific American columns.

Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for Scientific American magazine. During the next 5+1⁄2 years, until June 1986, Gardner wrote 9 more columns, bringing his total to 297. During this period other authors wrote most of the columns. In 1981, Gardner's column alternated with a new column by Douglas Hofstadter called "Metamagical Themas" (an anagram of "Mathematical Games"). The table below lists Gardner's columns.

Twelve of Gardner's columns provided the cover art for that month's magazine, indicated by "[cover]" in the table with a hyperlink to the cover.

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 ticktacktoe
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 Möbius band, which has only one side and one edge
1957 Jul	Concerning the game of Hex, which may 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 card tricks with a mathematical message
1957 Oct	How to remember numbers by mnemonic devices such as cuff links 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	Concerning the game of Nim and its mathematical analysis
1958 Mar	About left- and right-handedness, mirror images and kindred matters
1958 Apr	Concerning the celebrated puzzle of five sailors, a monkey and a pile of coconuts
1958 May	About tetraflexagons and tetraflexagation
1958 Jun	About Henry Ernest Dudeney, 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 [cover]
1958 Dec	Diversions which involve the five Platonic solids
1959 Jan	About mazes and how they can be traversed
1959 Feb	"Brain-teasers" 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 has 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 [cover]
1959 Dec	Diversions that clarify group theory, particularly by the weaving of braids
1960 Jan	A fanciful dialogue about the wonders of numerology
1960 Feb	A fifth collection of "brain-teasers"
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 sheets of paper
1960 Jul	Incidental information about the extraordinary number pi
1960 Aug	An imaginary dialogue 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
1960 Dec	Some recreations involving the binary number system
1961 Jan	In which the author chats again with 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	Concerning the diversions in a new book on geometry [cover]
1961 May	In which the editor of this department 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 the three rings of a well-known design
1961 Oct	Diversions that involve the mathematical constant "e"
1961 Nov	Wherein 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 game of solitaire and some variations and transformations
1962 Jul	Fiction about life in two dimensions
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 checkerboards
1962 Dec	Some simple tricks and manipulations from the ancient lore of string play
1963 Jan	The author pays his annual visit to Dr. Matrix, the numerologist
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	A bit of foolishness for April Fools' 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 mathematics
1963 Sep	How to solve puzzles by graphing the rebounds of a bouncing ball
1963 Oct	About two new and two old mathematical 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	Presenting the one and only Dr. Matrix, numerologist, in his annual performance
1964 Feb	The hypnotic fascination of sliding-block puzzles
1964 Mar	The remarkable lore of the prime numbers [cover]
1964 Apr	Various problems based on planar graphs, or sets of "vertices" connected by "edges"
1964 May	The tyranny of 10 overthrown with the ternary number system
1964 Jun	A collection of short problems and more talk of prime numbers
1964 Jul	Curious properties of a cycloid curve
1964 Aug	Concerning several magic tricks based on mathematical principles
1964 Sep	Puns, palindromes and other word games that partake of the mathematical spirit
1964 Oct	Simple proofs of the Pythagorean theorem, and sundry other matters
1964 Nov	Some paradoxes and puzzles involving infinite series and the concept of limit
1964 Dec	On polyiamonds: shapes that are made out of equilateral triangles
1965 Jan	Some comments by Dr. Matrix on symmetries and reversals
1965 Feb	Tetrahedrons in nature and architecture, and puzzles involving this simplest polyhedron
1965 Mar	A new group of short problems
1965 Apr	The infinite regress in philosophy, literature and mathematical proof
1965 May	The lattice of integers considered as an orchard or a billiard table
1965 Jun	Some diversions and problems from Mr. O'Gara, the postman
1965 Jul	On the relation between mathematics and the ordered patterns of Op art [cover]
1965 Aug	Thoughts on the task of communication with intelligent organisms on other worlds
1965 Sep	The superellipse: a curve that lies between the ellipse and the rectangle
1965 Oct	Pentominoes and polyominoes: five games and a sampling of problems
1965 Nov	A selection of elementary word and number problems
1965 Dec	Magic stars, graphs and polyhedrons
1966 Jan	Dr. Matrix returns, now in the guise of a neo-Freudian psychonumeranalyst
1966 Feb	Recreational numismatics, or a purse of coin puzzles
1966 Mar	The hierarchy of infinities and the problems it spawns
1966 Apr	The eerie mathematical art of Maurits C. 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	The problem of 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 that can be solved with elementary mathematical techniques
1967 Apr	The 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 Brussels sprouts, games with a topological flavor
1967 Aug	In which a computer prints out mammoth polygonal factorials
1967 Sep	Double acrostics, stylized Victorian ancestors of today's crossword puzzle
1967 Oct	Problems that are built on the knight's move in chess
1967 Nov	A mixed bag of logical and illogical problems to solve
1967 Dec	Game theory is applied (for a change) to games
1968 Jan	The beauties of the square, as expounded by Dr. Matrix to rehabilitate the hippie
1968 Feb	Combinatorial problems involving tree graphs and forests of trees
1968 Mar	A short treatise on the useless elegance of perfect numbers and amicable pairs
1968 Apr	Puzzles and tricks with a dollar bill
1968 May	Circles and spheres, and how they kiss and pack
1968 Jun	Combinatorial possibilities in a pack of shuffled cards
1968 Jul	On the meaning of randomness and some ways of achieving it
1968 Aug	An array of puzzles and tricks, with a few traps for the unwary
1968 Sep	Counting systems and the relationship between numbers and the real world
1968 Oct	MacMahon's color triangles and the joys of fitting them together
1968 Nov	On the ancient lore of dice and the odds against making a point
1968 Dec	The world of the Möbius strip: endless, edgeless and one-sided
1969 Jan	Dr. Matrix gives his explanation of why Mr. Nixon was elected President
1969 Feb	Boolean algebra, Venn diagrams and the propositional calculus
1969 Mar	The multiple fascinations of the Fibonacci sequence
1969 Apr	An octet of problems that emphasize gamesmanship, logic and probability
1969 May	The rambling 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 a scientific concept: Does nature keep her accounts on a thumbnail?
1969 Sep	Geometric constructions with a compass and a straightedge, and also with a compass alone
1969 Oct	A numeranalysis by Dr. Matrix of the lunar flight of Apollo 11
1969 Nov	A new pencil-and-paper game based on inductive reasoning [cover]
1969 Dec	A handful of combinatorial problems based on dominoes
1970 Jan	The abacus: primitive but effective digital computer
1970 Feb	Nine new puzzles to solve
1970 Mar	Cyclic numbers and their properties
1970 Apr	Some mathematical curiosities embedded in the solar system
1970 May	Of optical illusions, from figures that are undecidable to hot dogs that float
1970 Jun	Elegant triangle theorems not to be found in Euclid
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 the cyclical curves generated by wheels that roll along wheels
1970 Oct	The fantastic combinations of John Conway's new solitaire game "life"
1970 Nov	A new collection of short problems and the answers to some of "life's"
1970 Dec	The paradox of the nontransitive dice and the elusive principle of indifference
1971 Jan	Lessons from Dr. Matrix in chess and numerology
1971 Feb	On cellular automata, self-reproduction, the Garden of Eden and the game "life" [cover]
1971 Mar	The orders of infinity, the topological nature of dimension and "supertasks"
1971 Apr	Geometric fallacies: hidden errors pave the road to absurd conclusions
1971 May	The combinatorial richness of folding a piece of paper
1971 Jun	The Turing game and the question it presents: Can a computer think?
1971 Jul	Quickie problems: not hard, but look out for the curves
1971 Aug	Ticktacktoe and its complications
1971 Sep	The plaiting of Plato's polyhedrons and the asymmetrical yin-yang-lee
1971 Oct	New puzzles from the game of Halma, the noble ancestor of Chinese checkers
1971 Nov	Advertising premiums to beguile the mind: classics by Sam Loyd, master puzzle-poser
1971 Dec	Further encounters with touching cubes, and the paradoxes of Zeno as "supertasks"
1972 Jan	How to triumph at nim by playing safe, and John Horton Conway's game "Hackenbush"
1972 Feb	Dr. Matrix poses some heteroliteral puzzles while peddling perpetual motion in Houston
1972 Mar	The graceful graphs of Solomon Golomb, or how to number a graph parsimoniously
1972 Apr	A topological problem with a fresh twist, and eight other new recreational puzzles
1972 May	Challenging chess tasks for puzzle buffs and answers to the recreational problems
1972 Jun	A miscellany of transcendental problems: simple to state but not at all easy to solve
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 polycubes, and the winning strategy for Slither
1972 Oct	Why the long arm of coincidence is usually not as long as it seems
1972 Nov	On the practical uses and bizarre abuses of Sir Francis Bacon's biliteral cipher
1972 Dec	Knotty problems with a two-hole torus
1973 Jan	Sim, Chomp and Race Track: 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 the logarithm
1973 Apr	How to turn a chessboard into a computer and to calculate with negabinary numbers
1973 May	A new miscellany of problems, and encores for Race Track, Sim, Chomp and elevators
1973 Jun	Plotting the crossing number of graphs
1973 Jul	Free will revisited, with a 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 introduction 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 the sum of cubes and other unsolved number-theory problems
1974 Jan	The combinatorial basis of the "I Ching," the Chinese book of divination and wisdom [cover]
1974 Feb	Cram, crosscram 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 brings his numerological Science to bear on the occult powers of the pyramid
1974 Jul	On the patterns and the unusual properties of figurate numbers
1974 Aug	On the fanciful history and the creative challenges of the puzzle game of tangrams
1974 Sep	More on tangrams: Combinatorial problems and the game possibilities of snug tangrams
1974 Oct	On the paradoxical situations that arise from nontransitive relations
1974 Nov	Some new and dramatic demonstrations of number theorems with playing cards
1974 Dec	The arts as combinatorial mathematics, or how to compose like Mozart with dice
1975 Jan	The curious magic of anamorphic art [cover]
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 or another have escaped public attention
1975 May	On the remarkable Császár 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	More about tiling the plane: the possibilities of polyominoes, polyiamonds, and polyhexes
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) [cover]
1975 Dec	A random assortment of puzzles, together with reader responses to earlier problems
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	The 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 [cover]
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 Miguel Berrocal can be taken apart like an interlocking mechanical puzzle
1978 Feb	On checker jumping, the Amazon game, weird dice, card tricks and other playful pastimes
1978 Mar	Count Dracula, Alice, Portia and many others consider various twists of logic
1978 Apr	White and brown music, fractal curves and one-over-f fluctuations [cover]
1978 May	The Bells: versatile numbers that can count partitions of a set, primes and even rhymes
1978 Jun	A mathematical zoo of astounding critters, imaginary and otherwise
1978 Jul	On Charles Sanders Peirce: philosopher and gamesman
1978 Aug	A Möbius band has a finite thickness, and so it is actually a twisted prism
1978 Sep	Puzzling over a problem-solving matrix, cubes of many colors and three-dimensional 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	In which players of Tic-tac-toe are taught 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 "Gödel, Escher, Bach"
1979 Aug	The imaginableness of the imaginary numbers
1979 Sep	In some patterns of numbers or words there 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, cooked and mathematic
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 Lavinia 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 Douglas Hofstadter's Luring Lottery
1986 Jun	Casting a net on a checkerboard and other puzzles of the forest

Other articles by Gardner

Gardner wrote 5 other articles for Scientific American. His flexagon 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. These five articles are listed below.

date	Title
1952 Mar	Logic Machines
1956 Dec	Flexagons
1967 Jan	Can Time go Backward?
1998 Aug	A Quarter-Century of Recreational Mathematics
2007 Apr	Is Beauty Truth and Truth Beauty? [book review]

See also

• Bulgarian solitaire, a game introduced by Gardner in one of the columns

External links

• A Quarter Century of Recreational Mathematics, by Martin Gardner preserved at the Internet Archive
• A subject index for the fifteen books of Martin Gardner's Mathematical Games columns
• The Top 10 Martin Gardner Scientific American Articles