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Homage to a Pied Puzzler i i i i Homage to a Pied Puzzler i i i i i i i i i i i i i i i i Homage to a Pied Puzzler Edited by Ed Pegg Jr. Alan H. Schoen Tom Rodgers A K Peters, Ltd. Wellesley, Massachusetts i i i i CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150225 International Standard Book Number-13: 978-1-4398-6500-2 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reason- able efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organiza- tion that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com i i i i Contents Preface ix In Memoriam xi Jay Marshall: A Legacy of Magic and Laughter xiii Robert Cotner Conversations with Jay xxi David Meyer IHistoryandHoaxes 1 Sam Loyd’s Most Successful Hoax 3 Jerry Slocum II Numbers and Shapes 23 The Seven-Colored Torus 25 sarah-marie belcastro and Carolyn Yackel A Property of Complete Symbols 33 Peter Hilton, Jean Pedersen, and Byron Walden v i i i i i i i i vi Homage to a Pied Puzzler Seven-Fold Symmetry in Mathematica(l) Graphics and Physical Models 53 S´andor Kabai Seven Knots and Knots in the Seven-Color Map 75 Louis H. Kauffman Seven from the Sea 85 Michael S. Longuet-Higgins Seven Staggering Sequences 93 N. J. A. Sloane Seven Water Lilies 111 P´eter G´abor Szab´oandZs´ofia Ruttkay III Puzzles and Games 117 Developing the Transmission Puzzle 119 M. Oskar van Deventer Triple-7 Hamiltonian Chess 125 David S. Dillon, Jeremiah Farrell, and Tom Rodgers Retrolife 129 Yossi Elran The Logologicomathemagical 7 × 7 Puzzle 137 Jeremiah Farrell and Robert Friedhoffer Seven Roads to Roam: A Magical Journey 141 Jeremiah Farrell and Judith H. Morrel Fractal Tilings Based on Dissections 145 Robert W. Fathauer Creating the NAVIGATI Puzzle 159 Adrian Fisher Crazy Elephant Dance 165 Markus G¨otz i i i i i i i i Contents vii The Two Ovals-to-Table Story 175 Serhiy Grabarchuk Folding Regular Heptagons 181 Thomas C. Hull Combinatorial Philosophy 193 Kate Jones Variations of the 14-15 Puzzle 201 Rodolfo Kurchan Pentomino Battleships 207 Mogens Esrom Larsen Horses in the Stream and Other Short Stories 215 Earnest Hammingway A Potpourri of Polygonal and Polyhedral Puzzles 231 Alan H. Schoen The Hexa-Dodeca-Flexagon 257 Ann Schwartz and Jeff Rutzky Golomb, Gardner, Benjamin and Jones: Midwives to a Puzzle 269 Norton Starr Walk, Slide, and Jump 277 James W. Stephens Polyomino Number Theory Developments 281 Robert Wainwright i i i i i i i i i i i i i i i i Preface Every two years or so, mathematicians, puzzlers, and magicians assemble in Atlanta to pay tribute to Martin Gardner, whose life- long devotion to recreational mathematics and to magic is honored throughout the world. The seventh of these ”Gatherings for Gard- ner,” G4G7, was held March 16-19, 2006. Most of the articles in this volume are drawn from oral presentations delivered at G4G7. Overflow articles will appear in a companion volume, Mathematical Wizardry for a Gardner. Mathematicians everywhere recognize that even though Martin Gardner is not himself a professional mathematician, he has been astoundingly effective in popularizing not just recreational mathe- matics, magic, and puzzles, but also so-called serious mathemat- ics. A number of professional mathematicians have acknowledged that their passion for their subject was first kindled by one of Mar- tin’s columns or essays concerning either a hoary old chestnut or a brand-new problem. His columns in Scientific American, which first appeared in 1956, earned him readers worldwide, and he con- tinues writing to this day. His published writings are available in both book form and on CD. Martin’s unique influence has been the result of a refined taste in subject matter combined with a famously clear and witty writ- ing style. His well-known addictions to magic and to word puzzles have inspired countless others to attempt to emulate him in these arts, but he is still the undisputed master. Perhaps his most bril- liant invention is Dr. Irving Joshua Matrix, a proxy he used to ix i i i i i i i i x Homage to a Pied Puzzler spoof virtually every known variety of charlatan, including-but not limited to-Biblical cryptographers and numerologists. Those among us who were fortunate to attend G4G6 will never forget that Jay Marshall, the legendary iconoclast who was loved and admired by all who revere magic and magicians, graced us with his presence. Even though Jay was not at all well, he cheer- fully performed one of his classic routines. We were deeply moved. Not many weeks later, Jay shuffled off this mortal coil. The first two articles in this book are dedicated to his memory. It was Tom Rodgers who in 1993 first thought of assembling admirers of Martin Gardner for a few days of celebration. He has hosted all of these gatherings since then, thanks to the fine work by the co-organizers Elwyn Berlekamp in the math community and Mark Setteducati in the magic world, as well as the generous help of Karen Farrell, Jeremiah Farrell, Scott Hudson, Thane Plambeck, Emily DeWitt Rodgers, Stephen Turner, and the many G4G partic- ipants who volunteered at moments of need. The editors are especially indebted to Charlotte Henderson, as- sociate editor for our publisher, A K Peters, Ltd., for her patient ministrations in the task of assembling and editing authors’ contributions. Wehopethatreadersderiveasmuchpleasurefromthisvolume as we have had in assembling it. Ed Pegg Jr. Champaign-Urbana, Illinois Alan H. Schoen Carbondale, Illinois Tom Rodgers Atlanta, Georgia i i i i i i i i In Memoriam i i i i i i i i i i i i i i i i Jay Marshall: A Legacy of Magic and Laughter Robert Cotner “Lefty” is silent—and he’ll never talk again. You see, his progenitor and master has died. Born from the creative spirit of Jay Marshall in the South Pacific during World War II—out of a khaki Army glove—Jay and Lefty have traveled the world, entertaining people in London, New York, Las Vegas, Chicago, and all points between. All that ended on May 10, 2005, when Jay Marshall died at Swedish Covenant Hospital in Chicago. The Chicago Tribune (May 13, 2005, Sec. 2, p. 13), in an il- lustrated obituary, remembered Jay as “Ventriloquist, magic-shop owner” and celebrated his professional career on stage and on tele- vision, particularly on the “Ed Sullivan” show, where he and Lefty “gained fame as the opening act for performers ranging from Mil- ton Berle to Liberace.” Jay appeared on the Sullivan show 14 times and opened, as well, for Frank Sinatra at the Desert Inn in Las Vegas. The standard routine between Jay and Lefty included Jay’s ques- tion, “Shall we sing?” xiii i i i i i i i i xiv Homage to a Pied Puzzler Figure 1. Jay in 1980 at the Hild branch of the Chicago Public Library, after a Punch and Judy show. Caxtonian Peggy Sullivan discovered this photo in the Special Collections and Preservation division of the library. Lefty would respond, “What do you want to sing?” Jay would reply, “If I Had My Way.” And Lefty would counter, “If I had my way, I wouldn’t sing!” Lefty was, indeed, as the Tribune reported, a “wiseacre rabbit.” The article quotes Marc DeSouza, a member of the Society of American Magicians, “Jay is one of the most influential magicians of our age.” Jay came to Chicago in the mid-1950s to marry Frances Ire- land, who was also a magician. Frances was the owner of a magic shop that had been in business since the 1930s. She had mar- ried the founder in 1931. The founder died in the early 1950s, and sometime after his death, Frances and Jay were married.
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