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