# Martin Gardner's Puzzle Books

*Scientific American* Puzzles

### Mathematical and Logic Puzzles

### Word Play Puzzles

### Science Fiction Puzzles

### Science Puzzles

### Edited Puzzle Collections

### Other Puzzle Offshoots

### Optical Illusions

### Puzzlers on National Public Radio

Curiously, despite Martin's reputation as a puzzle master, he didn't see himself as a good puzzler solver or as a puzzle creator, but rather as a conduit for sharing puzzles conceived (or passed on) by others. In 2009, he told John Tierney*New York Times*, "The number of puzzles I've invented you can count on your fingers," which was probably an underestimate, but his observation is at least partially true. He generally credited the inventors and true sources of the wonders he wrote about, when known.

Martin published over 40 collections of puzzles in the 52-year period from 1959 to 2010. Many of the earlier volumes resurfaced decades later thanks to new publishers, often updated, and under new titles.

The great majority of the puzzles which Martin wrote about were logical, mathematical or scientific in some way, but he also loved visual and wordplay challenges.

Over 60 of his puzzles can be found online at the Puzzles.com
puzzles and brainteasers site.

## Martin Gardner's *Scientific American* Puzzle Collections

Martin is most famously associated with the puzzles posed in his 300-odd
*Scientific American*columns, and the fifteen resulting books which appeared between 1959 and 1997. Of course, those columns and books contained much material not in the puzzle vein.

The puzzles that did feature in the *Scientific American* columns range from
being merely thought-provoking to linking to deeper concepts. Here we list the
*Scientific American* spin-offs which focus on
items of particular interest to puzzle lovers.

*The Colossal Book
of Mathematics: Classic Puzzles, Paradoxes, and Problems* (W.W. Norton,
2001, 10 + 724 pages) was compiled by Martin himself. In the Preface, he writes,
"Robert Weil, my editor at W.W. Norton, suggested that I select 50 of what I
consider my 'best' [*Scientific American*] columns, mainly in the sense of
arousing the greatest reader response, to make this hefty, and in terms on my
career, definitive book you now hold."

The updated columns are organized into 12 chapters: Arithmetic and Algebra, Plane
Geometry, Solid Geometry and Higher Dimensions, Symmetry, Topology, Probability,
Infinity, Combinatorics, Games and Decision Theory, Physics, Logic and Philosophy,
and Miscellaneous. They include,
"The Monkey and the Coconuts,"
"Rep-Tiles,"
"Penrose Tiles,"
"Packing Spheres,"
"Hypercubes,"
"The Amazing Creations of Scott Kim,"
"The Art of M.C. Escher,"
"Knots,"
"Nontransitive Dice and Other Paradoxes,"
"Surreal Numbers,"
"Hexaflexagons,"
"The Soma Cube,"
"The Game of Life,"
"The New Eleusis,"
"Time Travel,"
"The Unexpected Hanging,"
"Newcomb's Paradox,"
"Gödel, Escher, Bach"
and
"Six Sensational Discoveries."

*The Colossal Book of Short Puzzles and Problems* (W.W. Norton, 2005,
8 + 496 pages) was compiled and edited by Dana Richards. Its 17 chapters, ranging
from Combinatorics to Physics, are divided into 4 parts: Combinatorial & Numerical,
Geometric, Algorithmic and Other Puzzles. There's an appendix called "Twelve More
Brain Teasers," which includes "Three Switches" (which made it onto NRP's *Car Talk*),
"Inscribed
Square" (a puzzle Martin gave to Marilyn vos Savant for her *Parade*
column in 1999), "Toothpick Giraffe" (featured in 2009 in Numberplay in the *New
York Times*), "Unattacked Queens," and "100 to CAT" (also featured in the
*NYT*).

## Mathematical and Logic Puzzles

In addition to the 20 main *Scientific American* books and spin-offs,
Martin published about 25 other books of puzzles, some aimed at children.

*The Arrow Book of Brain Teasers* (Scholastic Book Services, 1959, 64 pages,
charmingly illustrated by William Hogarth) was first out the gate, containing
over 60 items. The Arrow series of books published (and promoted in schools) by
Scholastic Book
Services was specifically aimed at grades 4, 5, & 6. Delightful word
puzzles, riddles, and visual illusions are mixed in with "spot the error"
headscratchers and teasers about science, knots and counting triangles and
squares. Mathematical results about the graph K_{3,3}, Eulerian
circuits, the permutation group on 3 objects, and the maximal number of pieces
a disc can be cut into with 4 straight cuts, as well as the pigeonhole principle,
are sneaked in unsuspected.

"The Colored Socks" (still doing the rounds today, e.g., see New York Times "Numberplay"), "Find the Missing Piece" (the optical illusion involving a slice of cheesecake or pie), and "Lewis Carroll's Squares" all appear, as does a variation on the classic about connecting three houses to three utilities. Page 26 shows two spacemen exploring the surface of the moon, a full decade before such a thing came to pass.

In the mid 1990s, this book was reworked as *Classic
Brainteasers* (Sterling, 1994, 96 pages, illustrated by Jeff Sinclair),
with many of the puzzles tweaked.

A few years later, the same publisher combined some of this material with
excerpts from other books by George J. Summers, Robert Steinwachs, and Edward
J. Harshman, for *Brain
Teasers* (2000, 96 pages).

*Science Puzzlers* (Viking, 1960) treated below also has excellent
mathematical puzzles.

*Mathematical Puzzles* (Crowell, 1961, 12 + 112 pages, illustrated by
Anthony Ravielli) came next. It's broken up in 9 parts contained 39 puzzles,
plus 28 "short and easy" items in a final part called Tricky Puzzles.

The earlier parts grouped problems by type, under the heading Arithmetic, Money, Speed, Plane Geometry, Solid Geometry, Game, Probability, Topology, or Miscillaneous Puzzles, and include brief essays on each topic. Unusually, by later standards, the solution to each problem is given immediately after it is posed.

In due course, this book resurfaced as *Entertaining Mathematical Puzzles*
(Dover, 1986).

In the Introduction, Martin reveals that many of the puzzles had appeared in his
column "On the Light Side" which ran in *Science World*. (He wrote 40 of
those between Feb 1957 and May 1959). The first problem is "The Colored Socks",
still doing the rounds today (see New York Times
"Numberplay").
Next up is "Weighty Problem," a variation of which can be
found at
www.puzzles.com. Other evergreen classics such as "The Bicycles and the Fly,"
"Corner to Corner" (see
"Rectangle Around"), "Outside or Inside" (see "In 'n" Out"),
and
"Six Numbers" appear, alongside Paul Curry's vanishing area squares, Mobius
band surprises, and truthtellers and liars.

*Perplexing Puzzles and Tantalizing Teasers* (Simon and Schuster, 1969, 96
pages, illustrated by Laszlo Kubinyi) contained 47 puzzles, and was included in
the *New York Times* list of Outstanding Books of the year on 9 Nov 1969.

*More Perplexing
Puzzles and Tantalizing Teasers* (Archway, 1977, 8 + 119 pages),
contained 46 more. These were later combined in a single volume as *Perplexing Puzzles and
Tantalizing Teasers* (Dover, 1988, 223 pages).

These books contain a lot of riddles, alongside mazes, optical illusions and other visual gags, and some mathematical material. The second volume ends with a then-rare "identify the pixilated portrait" question.

The last problem in the first book is the ever-popular "Shake Out the Cherry,"
learned from Fujimura (see below),
a version of which can be found at
www.puzzles.com.
The 1977 book includes
"The Two Spirals,"
"Find the Center," and another Fujimura classic, here dubbed "The Fish That
U-Turned" (see
"Turn the Fish.")

Along the way, there was
*Codes, Ciphers, and Secret Writing* (Simon and Schuster, 1972, and
Dover, 1984, 96 pages), and
*The Snark Puzzle Book* (Simon and Schuster, 1973, and Prometheus, 1990,
125 pages).

The first, appearing just a few years before cryptography was totally revolutionized by RSA methods—a story Martin himself broke to the general public— has child-friendly chapters on substitution and polyalphabetic ciphers, in addition to old-fashioned methods including invisible writing.

The second was subtitled, "Based on Lewis Carroll's Nonsense Poems The Hunting of
the Snark and Jabberwocky with the original illustrations by Henry Holiday and
Sir John Tenniel."

Two of Martin's more popular puzzle books were *Aha! Insight*
(Scientific American/W. H. Freeman, 1978, 8 + 179 pages, illustrated by
Jim Glen and Felix Cooper), and *aha! Gotcha:
Paradoxes to puzzle and delight* (W. H. Freeman, 1982, 10 + 164 pages,
illustrated by Jim Glen, Ray Salmon, and Scott Kim), later updated and combined
as
*Aha! Gotcha Aha! Insight* (MAA, 2006).

The origins of the material in these books is explained in
*Fernando Q. Gouvêa's review* at MAA.org,

"In the mid-1970s, Martin Gardner and Robert Tappay came up with the idea of producing filmstrips for use in high school classrooms, one about mathematical paradoxes and one about mathematical problems that can be solved easily provided one has just the right insight. The strips featured illustrations by Jim Glen; they were marketed as 'The Paradox Box' and 'The Aha! Box.'Of course, what Gardner and Tappay didn't realize (hardly anyone did, at the time) was the filmstrip was already dead, about to be replaced by fancier technologies such as video. So the two 'boxes' were transformed into books."

The 65 problems in

Aha! Insightare spread out over six chapters (Combinatorial, Geometry, Number, Logic, Procedural, and Word aha!). This is perhaps the most sophisticated of Martin's puzzle books. Many classic puzzles reappear wrapped up in inventive new storylines—followed immediately by solutions—before generalizations are suggested, and detailed analysis is presented.

Aha! Gotcha: Paradoxes to puzzle and delightis also divided into six chapters (Logic, Number, Geometry, Probability, Statistics, and Time). It contains 80 headscratchers ranging from all cretans are liars, truth tellers and liar scenarios, infinity, and vanishing leprechauns, to the gambler's fallacy, Pascal's wager, and Newcomb's paradox.

My Best Mathematical and Logic Puzzles(Dover, 1994, 8 + 82 pages), contains 66 items, and is one of Martin's best-known collections.In his Introduction, he writes:

"During the twenty-five years that I had the great privilege of writing the Mathematical Games column inScientific American, my practice was to devote a column, about every six months, to what I called short problems or puzzles.... [] the puzzle columns were reprinted in book collections.

Most of the problems in this book are selected from the first three collections. The last 12 puzzles are selected from two articles I contributed toGamesmagazine []."Classic puzzles featured include "The Returning Explorer" (aka the generalized "What Color Is the Bear?"), "The Mutilated Chessboard," "The Fork in the Roada" (liars and truth-tellers), "Cutting the Cube," "The Counterfeit Coins," "The Touching Cigarettes," "Hole in the Sphere," "The Twiddles Bolts," "The Colliding Missiles," "The Sliding Pennies," "Water and Wine," "A Fixed-Point Theorem" (aka "The Buddhust Monk"), "Out With the Onion" (aka "A Cherry and a Glass"), and "Crazy Cut."

The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays(Copernicus/Springer-Verlag, 1996, 10 + 158 pages) surveys the topics indicated by its title in the chapters Fiction and Verse, The Diaries, Letters, Books and Articles, Miscellaneous Amusements, Doublets, and Pamphlets on Games.

Mental Magic(Sterling, 1999, Dover, 2010, 95 pages, illustrated by Jeff Sinclair) is subtitled "Surefire Tricks to Amaze Your Friends." Its 89 predictive items are seemingly aimed at a young audience, and range from simple gags and forces with words, cards, dice and calculators, to classics by Bob Hummer, Paul Curry, George Sands, Max Maven, and Karl Fulves, as well as Jim Steinmeyer's "Nine Card Speller" from 1993. Much of the material is far from juvenile, such as the first trick: a word-based version of the Kruskal Count.Sterling included this entire book, repaginated, as pages 5–114 of

Mensa Brain Twisters, under their Main Street imprint (2004, 286 pages). Denoted "Official MENSA Puzzle Book," the level of its puzzles seems far short of MENSA standards. The rest of the book was drawn from earlier books by Helene Hovanec and Karen C. Richards.

## Word Play Puzzles

For Martin, a wordplay puzzle coule be just as much fun as a mathematical one. Here's an elementary visual one that Martin was very fond of.

Martin was a lifelong fan of wordplay, and contributed frequently to Can you change 100 below into CAT by moving two toothpicks?

Word Ways: The Journal of Recreational Linguistics, a quarterly magazine "established in 1968 at the behest of Martin Gardner."

His edited version of Dudeney's book

The World's Best Word Puzzles(The Daily News, 1925) appeared as300 Best Word Puzzlesby Henry Ernest Dudeney (Scribner's Sons, 1968, 12 + 172 pages), "edited and with an introduction by Martin Gardner." The sixteen chapters range from Enigmas or Riddles, Conundrums, Acrostics, and Charades, to Word Chains and Rings, Squares, Stars, Cross-Word Puzzles, and Miscellaneous Puzzles.

Mind-Boggling Word Puzzles(Sterling, 2001, Dover, 2010, 96 pages, illustrated by V. G. Myers), contained 103 items, ranging from riddles and visual effects with letters and words to palindromes, rebuses, crosswords, and anagrams.A few years later, the same publisher included 70 of them as the third part of the

Mensa Word Puzzlesunder their Main Street imprint (2004, 287 pages). Denoted "Official MENSA Puzzle Book," the level of its puzzles seems far short of MENSA standards. It was cobbled together from earlier books by Helene Hovanec, Mark Danna, and Martin.

A few months after Martin died, there appeared the jam-packed yet misnamed

Colossal Book of Wordplay(Puzzle Wright Press/Sterling, 2010, 160 pages), edited by Ken Jennings, who also added some material. (The front cover artwork makes it look as if "Wordplay" is two words, but the spine shows it as one.) It's broken up into six chapter: Palindromes, Anagrams, and Other Whimsies, Perplexing Puzzles and Curious Conundrums, Bizarre Poems, Brief Brain Busters, Entangled Word and Numbers, and Conjuring With Words. A taster from this had appeared inWord Waysin 2007 as "Linguistic Catches."

It includes a favorite puzzle of Martin's from his final decade, concerning an amusing coincidental circular letter/number tie-in with a mathematical punchline.

"Write out the alphabet starting with J, and wrapping around, namely:JKLMNOPQRSTUVWXYZABCDEFGHI

Erase all letters that have left-right symmetry (such as A)

and count the letters in each of the five groups that remain."

## Science Fiction Puzzles

Martin contributed 111 whimsical "puzzle tale" columns to his friend Isaac Asimov'sScience Fiction Magazinebetween 1977 and 1986. These featured puzzles woven, in his own words, "into a science fiction vignette or pastiche." Some of the puzzles, which ranged from mathematical and logical to science based, were familiar, but dressed up in entertaining new ways. TheInternet Speculative Fiction Databasehas a list of these.

Four books resulted, the Davis merely one being a sampling of the tales in the other three.

Science-Fiction Puzzle Tales(Potter, 1981, 148 pages) is more well known today in itsMathematical Puzzle Tales(MAA, 2000, 14 + 151 pages) incarnation, and it contains 36 puzzle tales.

Baffling Brainteasers(Davis, 1983, 64 pages) contains just 13 puzzle tales.

Puzzles From Other Worlds: Fantastical Brainteasers from Isaac Asimov's Science Fiction Magazine(Vintage, 1984, 12 + 189 pages) contains 37 puzzle tales.

Riddles of the Sphinx and Other Mathematical Puzzle Tales(MAA, 1987, 12 + 164 pages) contains the remaining 36 puzzle tales, here listed as riddles.Martin's words in the Foreword to last book apply to all of them:

Each chapter poses a problem answered in the First Answers section. The solution in turn raises another problem that is solved in the Second Answers section. This may suggest a third question, and in several instances there is a fourth.... Many of the problems lead into nontrivial regions of mathematics and science.

## Science Puzzles

Martin loved astronomy, physics and basic science, and he excelled at introducing physics principles (and related magic) to audiences of all ages with apppropriate puzzles and effects.

Science Puzzlers(Viking, 1960, 128 pages, illustrated by Anthony Ravielli) contains 100 entertainments organized into these chapters: Astronomy, Chemistry, Physiology, Psychology, General Mathematics, Topology, Probability, Geometry, Numbers, Light, Gravity, Static Eletricity, Mechanics, Air, Hydraulics, Heat, Sound, and Inertia. The presentation is nowhere near as daunting as those categories suggest, being informal and very much aimed at younger readers.It was republished two decades later under the title

Entertaining Science Experiments with Everyday Objects(Dover, 1981). Apart from omitting the final page (of "Selected References on Recreational Science") it was unchanged from the original.

Space Puzzles(Simon and Schuster, 1971, and Archway, 1972, 95 pages, illustrated by Ted Schroeder), later resurfaced asPuzzling Questions About the Solar System(Dover, 1997, 96 pages).

Many years later came

Science Magic: Martin Gardner's Tricks and Puzzles(Sterling, 1997, 98 pages, illustrated by Tom Jorgenson), which was issued in paperback asScience Tricks(Sterling, 1998).Finally, there is

Smart Science Tricks(Sterling, 2004, 144 pages, illustrated by Bob Steimle), which has been available with three different covers, and contains 95 items. About half of the material had appeared in Martin's long-running "Trick of the Week" feature forThe Physics Teachermagazine. The book is divided into seven chapters: I. Water, II. Motion, Inertia, Friction, III. Air, IV. Light and Mirrors, V. Optical and Sensory Illusions, VI. Mathematics, Sound, Physiology, and VII. Electricity, Magnetism, Gravity. The presentation is bright and breezy.

## Edited Puzzle Collections

Martin also edited several volumes of puzzles by revered masters, starting with old classic brainteasers Sam Loyd and Henry Dudeney.

The first two were

Mathematical Puzzles of Sam Loyd(Dover, 1959, 15 + 167 pages) andMathematical Puzzles of Sam Loyd, Volume Two(Dover, 1960, 208 pages), which were also issued asMathematical Puzzles of Sam Loyd, Volume OneandMathematical Puzzles of Sam LoydandMore Mathematical Puzzles of Sam Loyd, respectively.These draw on Loyd's posthumous

Cyclopedia(1914).The first contains 117 puzzles, including many that Martin either recycled or emulated in his own puzzle offerings, including the Hidden Star, the 14-15 Puzzle, the Joiner's Problem, the Passing Trains, and numerous dissection problems.

The second likewise contains 165 puzzles, including items about speed, arranging matches, the Monad (yin/yang symbol) bisection problem, and many more dissections.

Next came Dudeney's

536 Puzzles & Curious Problems(Charles Scribner's Sons, 1967, and Barnes & Noble, 1995, 14 + 428 pages), "Edited and with an introduction by Martin Gardner." It has chapters on Arithmetic and Algebraic Problems (256 puzzles), Geometric Problems (127), and Combinatorial and Topological Problems (87)—each of which is broken up into many parts—as well as separate chapters on Game Puzzles (8), Domino Puzzles (15), Match Puzzles (17), and Unclassified Puzzles (24). Many problems now considered classics can be found here. The Answers section take up almost 200 pages.Dudeney's

300 Best Word Puzzles(Scribners, 1968) soon followed, as already mentioned above.Finally, some Russian and Japanese puzzles were made available via versions edited by Martin.

Boris Kordemsky's 1956 book

Mathematical Know-howappeared in English asThe Moscow Puzzles: 359 Mathematical Recreations(Scribners, 1972, with a different cover for the paperback, and Dover, 1992, 299 pages), edited and with an introduction by Martin.Puzzles involving coins, matches, clocks, geometry, dissections, trains and chess abound, not to mention standards Martin loved and reused, such as the nine dots and four straight lines challenge, and the object that costs $1 plus half its price.

Kobon Fujimura's 1969 book appeared in English edited and with an introduction by Martin as

The Tokyo Puzzles(Scribners, 1978, 184 pages).In his introduction to this 98-puzzle book, Martin reveals that Fujimura treasured a letter Dudeney sent him in 1926.

The first problem is "A Cherry and a Glass," a version of which can be found at www.puzzles.com, and the fifth problem is "Tropical Fish" (see "Turn the Fish"). Both of these appear in several of Martin's other puzzle books. Problem 60 "Which Line Is Longer?" echoes Rectangle Around which Martin had included in his 1961 puzzle book above. Problem 75 is "Angle on a Cube" (see "Cube Angle").

## Other Puzzle Offshoots

There are two decks of 48 "knowledge cards"—

Mathematical GamesandMathematical Games Volume 2—"adapted from the column by Martin Gardner" (Pomegranate, 2006 and 2008). Each card has a puzzle or brainteaser on one side, and its solution on the back.Many of these had already shown up in assorted collections, such as

My Best Mathematical and Logic Puzzles(Dover, 1994).

Pomegranate also issued calendars for 2007 and 2008 featuring "mind-bending puzzles" drawn from some of Martin's edited puzzle collections.

## Optical Illusions

Even in his earliest puzzle collections, Martin had included optical illusions, those being a keen interest of his all his life. A few years before his death, he worked with illustrator Gilbert Ford on

Optical Illusion Play Pack(Sterling, 2008, 59 pages). In many ways, it resembled some of the material he published in "Humpty Dumpty" in the 1950s; readers had to cut out and fold paper or cardboard to form props with interesting properties.One of the 28 items included there is the motion parallax based "Rotating House" illusion, in which a stationary object gives the impression of moving as one walks around it. This has its roots in the work of Martin's friend Jerry Andrus, to whom this book is dedicated, and it reached new heights of effectiveness (and popularity) via the

Thinky the Dragonillusion a few years later. (This was highlighted as part of the Martin inspired Mathematics Awareness Month 2014, which includes an explanation of the corresponding mathematics.)

## Puzzlers on National Public Radio

NPR's long runningCar Talkradio show, whose last new broadcast was in Oct 2012, often opened with a "puzzler" for listeners. Sometimes these were borrowed from some of Martin's books; as noted above, he published a volume calledScience Puzzlersin 1959.Here's a classic example of one of these, which can be found in

My Best Mathematical and Logic Puzzles(Dover, 1994), among other places.

"Two missiles speed directly toward each other, one at 9,000 mph

and the other at 21,000 mph. They start 1,317 miles apart.

Without using pencil and paper, calculate how far apart they

are one minute before they collide."(It can of course be solved in one’s head—under no circumstances should a calculator be used!—once one realizes what the core of the problem is.)

Shortly after Martin's death in May 2010, the show bid him a fond farewell on air (5 Jun 2010), and also brought Martin's son Jim on board to highlight his favorite puzzle.

Car Talkcontinue to honor Martin with the track "The Truth About Martin Gardner" onCar Talk 25th Anniversary 2-CD Set.

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