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Barrycades and Septoku Papers in Honor of Martin Gardner and Tom Rodgers

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Barrycades and Septoku Papers in Honor of Martin Gardner and Tom Rodgers AMS / MAA SPECTRUM VOL 100 Barrycades and Septoku Papers in Honor of Martin Gardner and Tom Rodgers Thane Plambeck Tomas Rokicki Editors 10.1090/spec/100 Barrycades and Septoku Papers in Honor of Martin Gardner and Tom Rodgers Editors AMS/MAA SPECTRUM VOL 100 Barrycades and Septoku Papers in Honor of Martin Gardner and Tom Rodgers Thane Plambeck Tomas Rokicki Editors 2019 Editorial Committee James J. Tattersall, Editor Michael Barany Andrew Beveridge Virginia M. Buchanan Thomas L. Drucker Evan D. Fisher Donna L. Flint Richard K. Guy Dominic Klyve John Lorch Cayla Danielle McBee 2010 Mathematics Subject Classification. Primary 00A08, 00A09, 00B10, 97A20. For additional information and updates on this book, visit www.ams.org/bookpages/spec-100 Library of Congress Cataloging-in-Publication Data Names: Plambeck, Thane E., editor. | Rokicki, Tomas, editor. | Gathering 4 Gardner Foundation. Title: Barrycades and septoku : papers in honor of Martin Gardner and Tom Rodgers / Thane Plam- beck, Tomas Rokicki, editors. Description: Providence, Rhode Island : American Mathematical Society, [2020] | Series: Spectrum ; volume 100 | Copyrighted by Gathering 4 Gardner, Inc. | Includes bibliographical references. Identifiers: LCCN 2019041150 | ISBN 9781470448707 (paperback) | ISBN 9781470455187 (ebook) Subjects: LCSH: Mathematical recreations. | Puzzles. | Gardner, Martin, 1914–2010. | Rodgers, Tom, 1943–2012 | AMS: General – General and miscellaneous specific topics – Recreational mathe- matics [See also 97A20]. | General – General and miscellaneous specific topics – Popularization of mathematics. | General – Conference proceedings and collections of papers – Collections of articles of general interest. | Mathematics education – General, mathematics and education – Recreational mathematics, games [See also 00A08]. Classification: LCC QA95 .B3585 2020 | DDC 793.74–dc23 LC record available at https://lccn.loc.gov/2019041150 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for permission to reuse portions of AMS publication content are handled by the Copyright Clearance Center. For more information, please visit www.ams.org/publications/pubpermissions. Send requests for translation rights and licensed reprints to [email protected]. © 2020 by Gathering 4 Gardner, Inc. All rights reserved. Printed in the United States of America. ⃝1 The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at https://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 25 24 23 22 21 20 Contents Preface ix Remembrances xi Elwyn Berlekamp xi Nancy Blachman xii Rob Jones xiii Dick Esterle xv Part 1 Sequences, Tiling, and Packing 1 1 Eight Hateful Sequences 3 N. J. A. Sloane 2 Building Barrycades and Constructing Corrals 11 Richard K. Guy 3 Limited Placements of Polyominoes on Rectangles 19 Solomon W. Golomb 4 Polyominoes on a Multicolored Infinite Grid 29 Hans Hung-Hsun Yu Part 2 Fun and Games 37 5 A Chess Tribute to John Horton Conway 39 Carlos Pereira dos Santos 6 Some New Combinatorial Games 51 Aaron N. Siegel 7 Factor Subtractor 59 Barry Cipra v vi Contents 8 The Mathematics of Septoku 63 George I. Bell Part 3 History 77 9 Thirty Years of Computer Cubing: The Search for God’s Number 79 Tomas Rokicki 10 Nim-like Games: An Ancestry 99 Lisa Rougetet Part 4 Puzzles 113 11 Triangles of Absolute Differences 115 Brian Chen, YunHao Fu, Andy Liu, George Sicherman, Herbert Taylor, and Po-Sheng Wu 12 Generalization of a Puzzle Involving Set Partitions 125 Michael L. Fredman, Daniel A. Kleitman, and Peter Winkler 13 A Generalization of Retrolife 131 Yossi Elran 14 Coins of Three Different Weights 139 Tanya Khovanova and Konstantin Knop 15 Rubber Bandzzles: Three Mathematical Puzzle-Art Challenges 155 George Hart Part 5 Art, Sculpture, and Design 161 16 Comet! 163 George Hart 17 Developing Topsy Turvy and Number Planet 173 M. Oskar van Deventer and Igor Kriz Contents vii Part 6 Magic and Miscellany 181 18 Coin-Flipping Magic 183 Nadia Benbernou, Erik D. Demaine, Martin L. Demaine, and Benjamin Rossman 19 Three Puzzle Fonts 203 Erik D. Demaine, Martin L. Demaine, Belén Palop, and Jason Ku Preface This volume continues a series of books (Pegg et al., 2009; Wolfe and Rodgers, 2002; Gardner et al., 2008, 2009, 1999) containing papers contributed to the Gath- ering 4 Gardner (G4G) meetings that have been taking place in Atlanta, Geor- gia, every two years since the early 1990s. In 1991, Thomas Malin Rodgers, Jr., an Atlanta-based entrepreneur, philan- thropist, investor, and puzzle and book collector, conceived the idea of bringing together fans of Martin Gardner for a meeting. Contacting many people directly via phone calls, he received an enthusiastic response, and the first Gathering 4 Gardner (G4G1) took place in the spring of 1993. Martin Gardner attended this first Gathering, and attendees exchanged papers and gifts amongst themselves on many topics, principally including recreational mathematics, but also magic, mathematical art, and puzzle-related content. Papers contributed to the initial Gathering and subsequent ones (most re- cently G4G11, in the spring of 2014) have appeared in several previous volumes (see “Further Reading”, below), and this volume continues the series with contri- butions both from original G4G participants over 20 years ago as well as students as young as fifteen years old when they wrote their included papers. Rodgers indefatigably continued organizing these meetings, and advising the nonprofit G4G Foundation organized in 2006 to support them, almost untilthe very moment of his death in the spring of 2012. We’ve chosen to dedicate this volume to his memory. Thank you, Tom! Thane Plambeck and Tomas Rokicki Acknowledgments The editors are grateful for the encouragement of Stephen Kennedy and the MAA publications staff. ix x Preface Further Reading M. Gardner, E. R. Berlekamp, and T. Rodgers (1999). The mathemagician and pied puzzler: a collection in tribute to Martin Gardner. A. K. Peters, Natick, Mass. M. Gardner, E. D. Demaine, M. L. Demaine, and T. Rodgers (2008). A lifetime of puzzles: A collection of puzzles in honor of Martin Gardner’s 90th birthday. A. K. Peters, Ltd., Wellesley, Mass. M. Gardner, E. Pegg, A. H. Schoen, and T. Rodgers (2009). Mathematical Wizardry for a Gardner. A. K. Peters, Wellesley, Mass. E. Pegg, A. H. Schoen, and T. Rodgers (2009). Homage to a pied puzzler. A. K. Peters, Wellesley, Mass. D. Wolfe and T. Rodgers (2002). Puzzlers’ tribute: a feast for the mind. A. K. Peters, Natick, Mass. http://site.ebrary.com/id/10159715. Remembrances I I met Tom Rodgers in the late 1980s at a puzzle party in Livermore, CA. Soon thereafter, he recruited me to help him organize the first Gathering 4 Gardner. He concurrently invited Mark Setteducati to invite some magicians. I invited some of the mathematicians whom I knew to be fans of Martin Gardner, and we all came to G4G1 in Atlanta. My wife and our son came too. Tom showed us his collections of puzzles and books, and we met his family. Buck Rodgers was going to spend part of his summer at one of the language camps in northern Minnesota, which inspired David Berlekamp to go to another one there. From the beginning, Tom was always the driving force behind the Gather- ings. Under his leadership, they provided the forum for many wonderful con- tributions to recreational mathematics. Some of them are documented in the Tribute volumes, the first six of which Tom coedited. Others were distributed in the puzzle exchanges. G4G also provided a gathering point and erudite audience for some world-class magicians and mathematical artists, many of whom were personally recruited by Tom. He was also the Gatherings’ most generous finan- cial supporter. In later years, he hosted visits by all attendees at each Gathering to a big celebration at his Japanese-style house and grounds. These events became one of the major attractions of the Gatherings. Elwyn Berlekamp xi xii Remembrances II At my first Gathering 4 Gardner1—G4G9 at the Ritz hotel in Atlanta—I arrived during dinner, after registration was closed, and soon found myself being inter- rogated by Tom Rodgers to make sure I wasn’t crashing the conference, since I didn’t have a badge. For the rest of the Gathering, Tom checked in with me sev- eral times each day to make sure I was settling in comfortably and connecting with people I found interesting. The thought-provoking presentations, the magic shows, the art exhibit, and the attendees made G4G among the most intriguing conferences I’ve attended. After G4G9, Tom invited me to join the Gathering 4 Gardner Celebration of Mind2 host committee and encouraged me to invite women, minorities, and young people to G4G conferences. Practically daily, Tom sent me fascinating emails and he also sent me the book Complexities: Women in Mathematics. I put together a list of over 20 people with short bios of each one and, at Tom’s request, invited them all. In December of 2011, Tom asked me to join the G4G board of directors; while I was deeply honored at the invitation, I told Tom I wanted to attend a board meet- ing before deciding. At the board meeting at Tom’s house on Saturday, March 31, 2012, which coincided with the G4GX (the 10th G4G) conference, Tom was ob- viously in poor health, a fraction of his former self, sitting in a wheelchair.
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