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G4G11 Exchange Book VOLUME 2 G4G11 Exchange Book VOLUME 2 ATLANTA, GEORGIA March 19 - 23, 2014 Published by: G4G11 Exchange Book VOLUME 2 The Gift Exchange is an integral part of the Gathering 4 Gardner biennial conferences. Gathering participants exchange gifts, papers, puzzles and other interesting artifacts. This book contains gift exchange papers from the conference held in Atlanta, Georgia from Wednesday, March 19th to Sunday, March 23rd, 2014. It combines all of the papers offered as exchange gifts in two volumes. Copyright © 2017 by Gathering 4 Gardner, Inc. All rights reserved. This book is a compilation of original material and contributers retain their rights. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database system, without the prior written permission of the publisher. 3 Table of Contents | VOLUME 2 LEGACY On the Autobiography of Martin Gardner | Jim Gardner and Vickie Kearn 8 Martin Gardner in the Twenty-First Century | Michael Henle and Brian Hopkins 31 The Martin Gardner Centennial Initiative | Colm Mulcahy 40 Martin Gardner, Yeoman/2c* | Dana Richards 43 PUZZLES Star Polygon Shortbread for the Puzzling Palate | Ellie Baker 50 The Pennyhedron Revisited | George Bell 52 11-Pointed Star | Derek Bosch 59 Touching Sticks | Sándor Bozóki, Tsung Lin Lee and Lajos Rónyai 62 Pot Pourri | Laurie Brokenshire 63 Maze of Martin | Tim Chartier 67 Some Puzzles – Invented, Designed and Discovered | James Dalgety 68 Trick-Opening Boxes from Sri Lanka | Frans de Vreugd 74 Linkage Puzzle Font | Erik and Martin Demaine 76 Retrolife Puzzles | Yossi Elran 80 John Horton Conway: A Puzzle Game | Jeremiah and Karen Farrell 83 Basic Strategies to Solve Disentanglement Puzzles | Markus Götz 88 Play with 2014 | Emrehan Halıcı 106 Constructing Acrostic Puzzles | Fred Henle 110 Elmo’s Excellent Excursion | Dick Hess 118 A Scanner, Darkly | Chris Hibbert 123 The Planar Tetrarhons Tetrahedron | Carl Hoff 124 4 Table of Contents (cont.) *At the author’s request, this paper is not included in the online version of this publication. 123456789 = 100 | Wei-Hwa Huang 125 Square in the Bag and Other Puzzles | Hirokazu Iwasawa 126 Quintetra Blocks | John and Jane Kostick 128 Self-Referential 9 Digits Repdigit Number | Rodolfo Kurchan 132 Solving Puzzles Backwards | Anany Levitin 134 Elevenses | Chris Maslanka 136 Two Parity Puzzles and Some Silk Scarves | Doug McKenna 138 Langford’s Problem, Remixed | John Miller 147 Manifold | Jerome Morin-Drouin 155 Sudoku Becomes Slidoku | Simon Nightingale 156 Dr. Matrix Talks to Owen O’Shea | Owen O’Shea 157 Binary Computing with Domino Logic Gates | Matt Parker and Katie Steckles 161 Alternate Magic Square | Tyler Rodgers 162 Solving Rubik’s Cube Positions | Tomas Rokicki 163 Tilings and Geometric Problems | Jaap Scherphuis 173 Three Puzzles | Alan Schoen 177 Pirate Math | Michael Serra 178 The Battersea Power Station Puzzle | David Singmaster 188 Polygons Folding into Three Different Boxes | Ryuhei Uehara 191 SCIENCE The Pseudosphere Uphill Roller | Kenneth Brecher 194 5 LEGACY Martin Gardner, Yeoman/2c | Dana Richards | Page 43 LEGACY | 7 LEGACY | 8 Who Wrote Martin Gardner’s Autobiography? Why did it take so long to publish it? Once Princeton University Press began to promote Undiluted Hocus Pocus: The Autobiography of Martin Gardner, some people began to ask, “Who wrote the book?” We initially thought they were confusing a biography with an autobiography but now that we have read a few reviews on amazon, we understand why they have asked the question. Some believe that Gardner’s friends put together bits and pieces of things that Martin Gardner wrote and that his son and editor possibly added pieces as well. So to clarify things, here is the back story about the publication of this book. I (Vickie) never met Martin Gardner. I never talked with him on the phone. But, we did write letters to one another for almost 25 years. No one writes letters anymore so when I receive one, I always get excited—especially when it is from Martin Gardner. His letters were always full of fun information and sometimes they concerned book projects we were working on. The letters were always written on a typewriter and corrected by hand in ink, often green. He wrote in small script and it sometimes took a while to sort out the handwriting but the letters were always a treasure trove and worth the effort to decipher. When Martin’s son, Jim Gardner, contacted me and asked if Princeton University Press would be interested in publishing Martin’s autobiography, I was thrilled. I could not think of a book I would more like to publish. As with many people, Martin Gardner had a huge amount to do with my becoming a math major so being able to do something for him was a fantastic opportunity. When Jim sent the manuscript I started laughing because it looked like an extremely long letter. It was written with the same typewriter and edited in the same way as his letters. When you look at the pages we have included, you will see what I mean. Jim and Vickie talked for a long time about Martin’s wishes for the manuscript and we decided that we would change as little as possible in the manuscript. We could not ask the author his opinion about any changes so we kept asking ourselves would Martin like any changes we planned before we made them. We worked to correct typos and filled in as many of his ??? notes as possible. He had sprinkled these throughout the manuscript. We tried our best to confirm dates and the order in which events took place. There are a few places in the manuscript where there is some repetition. Martin had many interests and we knew some people would go only to the chapters that interested them. So, we allowed the repeated material to stand. Some people ask why it took so long to publish the book after Martin’s death. He finished the manuscript a few months before he died and passed it to Jim to decide what to do with it. With any large estate, there are lots of decisions to make and time passes quickly. It simply got to a LEGACY | 9 point in time where the estate realized Martin’s desire to have it published needed to be implemented. People who knew Martin well have found some wonderful stories in the book that they never heard before. Other people wish there was more in the book about other things and wonder why he included what he did. We will never know the answer to that question but we do know the answer to “Who wrote Martin Gardner’s autobiography? “Martin Gardner did! Jim Gardner and Vickie Kearn Gathering for Gardner XI, March 2014 LEGACY | 10 LEGACY | 11 LEGACY | 12 LEGACY | 13 LEGACY | 14 LEGACY | 15 LEGACY | 16 LEGACY | 17 LEGACY | 18 LEGACY | 19 LEGACY | 20 LEGACY | 21 LEGACY | 22 LEGACY | 23 LEGACY | 24 LEGACY | 25 LEGACY | 26 LEGACY | 27 LEGACY | 28 LEGACY | 29 LEGACY |30 U.S. $24.95 “Martin is gone, but his depth and clarity will illuminate MARTIN GARDNER his uncompromising stance against pseudo- our world for a long time.” UNDILUTED science. For Gardner, our mathematically U N D—From theI foreword L by PersiU Diaconis T E D U N D I L U T E D structured universe is undiluted hocus- HOCUS-POCUS “A huge intellect, a prolifi c author, and a caring, responsible pocus—a marvelous enigma, in other words. THE AUTOBIOGRAPHY OF Undiluted Hocus-Pocus off ers a rare, inti- citizen of the world.” UNDILUTED mate look at Gardner’s life and work, and —From the afterword by James Randi the experiences that shaped both. MARTIN “Informative, original, unexpected, and always charmingly written ADAM ADAM FISH WWW.NICKELANDASSOCIATES.COM / with his uniquely subtle sense of fun, this fi nal autobiographical work of Martin Gardner, Undiluted Hocus-Pocus, sums up his own life and GARDNER H opinions,O Cin the way U that has S become P so familiar O and inspirationalC U to us S H OHOCUS-POCUS C U S P O C U S from his well-known writings on puzzles, mathematics, philosophy, Martin Gardner and the oddities of the world.” With a foreword by Persi Diaconis and —Roger Penrose, author of Cycles of Time: An Extraordinary THE AUTOBIOGRAPHY OF an afterword by James Randi New View of the Universe Martin Gardner wrote the Mathematical “Martin Gardner was the most learned man I have ever met. He wrote UNDILUTED HOCUS-POCUS Games column for Scientifi c American for articles and books for mathematicians, magicians, and puzzle lovers, twenty-fi ve years and published more than and he didn’t even get quantum mechanics wrong! Now you can read seventy books on topics as diverse as magic, T Hhow thisE amazing manA came to beU so amazing.” T O T H E A U T O philosophy, religion, pseudoscience, and —John Conway, John von Neumann Distinguished Professor Emeritus, Alice in Wonderland. His informal, recre- Princeton University ational approach to mathematics delighted MARTIN countless readers and inspired many to pur- “A curious read, reminiscent of Uriah Fuller’s attempts to persuade the sue careers in mathematics and the sciences. nonbelievers. I’m left wondering if Gardner’s questions have now been Gardner’s illuminating autobiography is a answered—which to some readers will always be an intriguing paradox!” disarmingly candid self-portrait of the man —Attributed to Armand T. Ringer evolutionary theorist Stephen Jay Gould called our “single brightest beacon” for “Undiluted Hocus-Pocus is a book that every fan of Gardner the defense of rationality and good science Martin Gardner (1914–2010) was an ac- B I O Gwill R want to own.”A P H Y B I O G R A P H Y against mysticism and anti-intellectualism.
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