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«Contents Ü Foreword Elwyn Berlekamp and Tom Rodgers ½ I Personal Magic ¿ Martin Gardner: A “Documentary” Dana Richards ½¿ Ambrose, Gardner, ...»

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Elwyn Berlekamp and Tom Rodgers


I Personal Magic


Martin Gardner: A “Documentary”

Dana Richards


Ambrose, Gardner, and Doyle

Raymond Smullyan


A Truth Learned Early

Carl Pomerance


Martin Gardner = Mint! Grand! Rare!

Jeremiah Farrell


Three Limericks: On Space, Time, and Speed

Tim Rowett


II Puzzlers


A Maze with Rules

Robert Abbott


Biblical Ladders

Donald E. Knuth


Card Game Trivia

Stewart Lamle


Creative Puzzle Thinking Nob Yoshigahara v vi Contents

Number Play, Calculators, and Card Tricks:

½ Mathemagical Black Holes Michael W. Ecker ¿ Puzzles from Around the World Richard I. Hess OBeirnes Hexiamond Richard K. Guy Japanese Tangram (The Sei Shonagon Pieces) Shigeo Takagi How a Tangram Cat Happily Turns into the Pink Panther Bernhard Wiezorke ½¼¿ Pollys Flagstones Stewart Coffin ½¼ Those Peripatetic Pentominoes Kate Jones ½½ Self-Designing Tetraflexagons Robert E. Neale ½¾ The Odyssey of the Figure Eight Puzzle Stewart Coffin ½¿½ Metagrobolizers of Wire Rick Irby ½¿ Beautiful but Wrong: The Floating Hourglass Puzzle Scot Morris ½ Cube Puzzles Jeremiah Farrell ½½ The Nine Color Puzzle Sivy Fahri ½¿ Twice: A Sliding Block

–  –  –

Martin Gardner has had no formal education in mathematics, but he has had an enormous influence on the subject. His writings exhibit an extraordinary ability to convey the essence of many mathematically sophisticated topics to a very wide audience. In the words first uttered by mathematician John Conway, Gardner has brought “more mathematics, to more millions, than anyone else."

In January 1957, Martin Gardner began writing a monthly column called “Mathematical Game” in Scientific American. He soon became the influential center of a large network of research mathematicians with whom he corresponded frequently. On browsing through Gardner’s old columns, one is struck by the large number of now-prominent names that appear therein.

Some of these people wrote Gardner to suggest topics for future articles;

others wrote to suggest novel twists on his previous articles. Gardner personally answered all of their correspondence.

Gardner’s interests extend well beyond the traditional realm of mathematics. His writings have featured mechanical puzzles as well as mathematical ones, Lewis Carroll, and Sherlock Holmes. He has had a life-long interest in magic, including tricks based on mathematics, on sleight of hand, and on ingenious props. He has played an important role in exposing charlatans who have tried to use their skills not for entertainment but to assert supernatural claims. Although he nominally retired as a regular columnist at Scientific American in 1982, Gardner’s prolific output has continued.

Martin Gardner’s influence has been so broad that a large percentage of his fans have only infrequent contacts with each other. Tom Rodgers conceived the idea of hosting a weekend gathering in honor of Gardner to bring some of these people together. The first “Gathering for Gardner” (G4G1) was held in January 1993. Elwyn Berlekamp helped publicize the idea to mathematicians. Mark Setteducati took the lead in reaching the magicians. Tom Rodgers contacted the puzzle community. The site chosen was Atlanta, partly because it is within driving distance of Gardner’s home.

The unprecedented gathering of the world’s foremost magicians, puzzlists, and mathematicians produced a collection of papers assembled by ix x FORWARD Scott Kim, distributed to the conference participants, and presented to Gardner at the meeting. G4G1 was so successful that a second gathering was held in January 1995 and a third in January 1998. As the gatherings have expanded, so many people have expressed interest in the papers presented at prior gatherings that A K Peters, Ltd., has agreed to publish this archival record. Included here are the papers from G4G1 and a few that didn’t make it into the initial collection.

The success of these gatherings has depended on the generous donations of time and talents of many people. Tyler Barrett has played a key role in scheduling the talks. We would also like to acknowledge the tireless effort of Carolyn Artin and Will Klump in editing and formatting the final version of the manuscript. All of us felt honored by this opportunity to join together in this tribute to the man in whose name we gathered and to his wife, Charlotte, who has made his extraordinary career possible.

–  –  –

I’ve never consciously tried to keep myself out of anything I write, and I’ve always talked clearly when people interview me. I don’t think my life is too interesting. It’s lived mainly inside my brain.

[21] While there is no biography of Martin Gardner, there are various interviews and articles about Gardner. Instead of a true biography, we present here a portrait in the style of a documentary. That is, we give a collection of quotes and excerpts, without narrative but arranged to tell a story.

The first two times Gardner appeared in print were in 1930, while a sixteen-year-old student at Tulsa Central High. The first, quoted below, was a query to “The Oracle” in Gernsback’s magazine Science and Invention.

The second was the “New Color Divination” in the magic periodical The Sphinx, a month later.Also below are two quotes showing a strong childhood interest in puzzles. The early interest in science, magic, puzzles, and writing were to stay with him.

*** “I have recently read an article on handwriting and forgeries in which it is stated that ink eradicators do not remove ink, but merely bleach it, and that ink so bleached can be easily brought out by a process of ‘fuming’ known to all handwriting experts. Can you give me a description of this process, what chemicals are used, and how it is performed?” [1] *** “Enclosed find a dollar bill for a year’s subscription to The Cryptogram. I am deeply interested in the success of the organization, having been a fan for some time.” [2] *** An able cartoonist with an adept mind for science. [1932 yearbook caption.] *** [1934] “As a youngster of grade school age I used to collect everything from butterflies and house keys to match boxes and postage stamps — but when I grew older... I sold my collections and chucked the whole business, and 4 D. RICHARDS began to look for something new to collect. Thus it was several years ago I decided to make a collection of mechanical puzzles....

“The first and only puzzle collector I ever met was a fictitious character.

He was the chief detective in a series of short stories that ran many years ago in one of the popular mystery magazines.... Personally I can’t say that I have reaped from my collection the professional benefit which this man did, but at any rate I have found the hobby equally as fascinating.” [3] *** “My mother was a dedicated Methodist who treasured her Bible and, as far as I know, never missed a Sunday service unless she was ill. My father, I learned later, was a pantheist.... Throughout my first year in high school I considered myself an atheist. I can recall my satisfaction in keeping my head upright during assemblies when we were asked to lower our head in prayer. My conversion to fundamentalism was due in part to the influence of a Sunday school teacher who was also a counselor at a summer camp in Minnesota where I spent several summers. It wasn’t long until I discovered Dwight L. Moody... [and] Seventh-Day Adventist Carlyle B. Haynes.... For about a year I actually attended an Adventist church.... Knowing little then about geology, I became convinced that evolution was a satanic myth.” [22] *** Gardner was intrigued by geometry in high school and wanted to go to Caltech to become a physicist. At that time, however, Caltech accepted undergraduates only after they had completed two years of college, so Gardner went to the University of Chicago for what he thought would be his first two years.

That institution in the 1930s was under the influence of Robert Maynard Hutchins, who had decreed that everyone should have a broad liberal education with no specialization at first. Gardner, thus prevented from pursuing math and science, took courses in the philosophy of science and then in philosophy, which wound up displacing his interest in physics and Caltech.

[19] *** “My fundamentalism lasted, incredibly, through the first three years at the University of Chicago, then as now a citadel of secular humanism.... I was one of the organizers of the Chicago Christian Fellowship.... There was no particular day or even year during which I decided to stop calling myself a Christian. The erosion of my beliefs was even slower than my conversion.

A major influence on me at the time was a course on comparative religions taught by Albert Eustace Haydon, a lapsed Baptist who became a wellknown humanist.” [22] MARTIN GARDNER: A “DOCUMENTARY” 5 “After I had graduated and spent another year at graduate work, I decided I didn’t want to teach. I wanted to write.” [24] *** Gardner returned to his home state after college to work as assistant oil editor for the Tulsa Tribune.“Real dull stuff,” Gardner said of his reporting stint.He tired of visiting oil companies every day, and took a job... in Chicago. [17] *** He returned to the Windy City first as a case worker for the Chicago Relief Agency and later as a public-relations writer for the University of Chicago.

[9] *** [1940] A slim, middling man with a thin face saturnined by jutting, jetted eyebrows and spading chin, his simian stride and posture is contrasted by the gentilityand fluent deftness of his hands. Those hands can at any time be his passport to fame and fortune, for competent magicians consider him one of the finest intimate illusionists in this country today. But to fame Gardner is as indifferent as he is to fortune, and he has spent the last halfdozen years of his life eliminating both from his consideration.

In a civilization of property rights and personal belongings, Martin Gardner is a Robinson Crusoe by choice, divesting himself of all material things to which he might be forced to give some consideration. The son of a wellto-do Tulsa, Oklahoma, family that is the essence of upper middle-class substantiality, Gardner broke from established routine to launch himself upon his self-chosen method of traveling light through life.

Possessor a few years ago of a large, diversified, and somewhat rarefied library, Martin disposed of it all, after having first cut out from the important books the salient passages he felt worth saving or remembering. These clippings he mounted, together with the summarized total of his knowledge, upon a series of thousands of filing cards. Those cards, filling some twenty-five shoe boxes, are now his most precious, and almost only possession. The card entries run from prostitutes to Plautus — which is not too far — and from Plato to police museums.

Chicagoans who are not too stultified to have recently enjoyed a Christmas-time day on Marshall Field and Company’s toy floor may remember Gardner as the “Mysto-Magic” set demonstrator for the past two years. He is doing his stint again this season. The rest of the year finds him periodically down to his last five dollars, facing eviction from the Homestead Hotel, and triumphantly turning up, Desperate Desmond fashion, with fifty or a hundred dollars at the eleventh hour — the result of having sold an idea 6 D. RICHARDS for a magic trick or a sales-promotion angle to any one of a half-dozen companies who look to him for specialties.During the past few months a determined outpouring of ideas for booklets on paper-cutting and other tricks, “pitchmen’s” novelties, straight magic and card tricks, and occasional dabblings in writings here and there have made him even more well known as an “idea” man for small novelty houses and children’s book publishers....

To Gardner’s family his way of life has at last become understandable, but it has taken world chaos to make his father say that his oldest son is perhaps the sanest of his family....

His personal philosophy has been described as a loose Platonism, but he doesn’t like being branded, and he thinks Plato, too, might object with sound reason. If he were to rest his thoughts upon one quotation it would be Lord Dunsany’s: “Man is a small thing, and the night is large and full of wonder.” [5] *** Martin Gardner ’36 is a professional [sic] magician. He tours the world pulling rabbits out of hats. When Professor Jay Christ (Business Law) was exhibiting his series of puzzles at the Club late last Fall Gardner chanced to be in town and saw one of the exhibits.He called up Mr. Christ and asked if he might come out to Christ’s home. He arrived with a large suitcase full of puzzles! Puzzles had been a hobby with him, but where to park them while he was peregrinating over the globe was a problem.Would Mr. Christ, who had the largest collection he had ever heard of, accept Mr. Gardner’s four or five hundred? [4] *** He was appointed yeoman of the destroyer escort in the North Atlantic “when they found out I could type.” “I amused myself on nightwatch by thinking up crazy plots,” said the soft-spoken Gardner. Those mental plots evolved into imaginative short stories that he sold to Esquire magazine. Those sales marked a turning point in Gardner’s career. [18] *** His career as a professional writer started in 1946 shortly after he returned from four years on a destroyer escort in World War II.Still flush with musteringout pay, Gardner was hanging around his alma mater, the University of Chicago, writing and taking an occasional GI Bill philosophy course. His breakcame when he sold a humorous short story called “The Horse on the Escalator” to Esquire magazine, then based in Chicago. The editor invited the starving writer for lunch at a good restaurant.

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