DOCSLIB.ORG

Homage to a Pied Puzzler

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

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.
Recommended publications
  • Snakes in the Plane

    Snakes in the Plane

    Snakes in the Plane by Paul Church A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Mathematics in Computer Science Waterloo, Ontario, Canada, 2008 c 2008 Paul Church I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract Recent developments in tiling theory, primarily in the study of anisohedral shapes, have been the product of exhaustive computer searches through various classes of poly- gons. I present a brief background of tiling theory and past work, with particular empha- sis on isohedral numbers, aperiodicity, Heesch numbers, criteria to characterize isohedral tilings, and various details that have arisen in past computer searches. I then develop and implement a new “boundary-based” technique, characterizing shapes as a sequence of characters representing unit length steps taken from a finite lan- guage of directions, to replace the “area-based” approaches of past work, which treated the Euclidean plane as a regular lattice of cells manipulated like a bitmap. The new technique allows me to reproduce and verify past results on polyforms (edge-to-edge as- semblies of unit squares, regular hexagons, or equilateral triangles) and then generalize to a new class of shapes dubbed polysnakes, which past approaches could not describe. My implementation enumerates polyforms using Redelmeier’s recursive generation algo- rithm, and enumerates polysnakes using a novel approach.
  • – Channing Pollock – Robert Harbin – Patrick Page

    – Channing Pollock – Robert Harbin – Patrick Page

    “To see Cardini is like watching a trick fi lm.” – Patrick Page “I had the greatest magical experience of my life when I watched him perform.” – Robert Harbin “If I had seen him work when I was at the start of my career, I would have scrapped the profession and learned a different trade.” – Channing Pollock 42 MAGIC • august 2007 M192 Cardini_v1_FIN.indd 2 7/12/07 11:41:33 AM “The world’s outstanding stage exponent of pure sleight-of-hand.” – Milbourne Christopher “The greatest single act that ever appeared in the world to my way of thinking.” – Dai Vernon ~By John Fisher~ Magicians today acknowledge that the examples set by the legendary Car- dini — in technique, in suavity, and in career achievement — shone the light for them. It is probable that Cardini has still not been surpassed as both an entertaining and an artistic exponent of pure sleight-of-hand within the limitations of a short vaudeville act. MAGIC • august 2007 43 M192 Cardini_v1_FIN.indd 3 7/12/07 11:41:37 AM There could be no greater contrast between nipulate the cards at all without gloves. So he the fi fth, thimbles and fi re. The digital dexter- the level of sophistication which Cardini’s act practiced with them on and laid the ground- ity was present throughout, but he still per- came to epitomize and his early background. work for the exquisite skill and sensitivity that sisted in being a talking magician upon whose He was born Richard Valentine Pitchford on would come to form his act in later years.
  • Eugene Burger (1939-2017)

    Eugene Burger (1939-2017)

    1 Eugene Burger (1939-2017) Photo: Michael Caplan A Celebration of Life and Legacy by Lawrence Hass, Ph.D. August 19, 2017 (This obituary was written at the request of Eugene Burger’s Estate. A shortened version of it appeared in Genii: The International Conjurors’ Magazine, October 2017, pages 79-86.) “Be an example to the world, ever true and unwavering. Then return to the infinite.” —Lao Tsu, Tao Te Ching, 28 How can I say goodbye to my dear friend Eugene Burger? How can we say goodbye to him? Eugene was beloved by nearly every magician in the world, and the outpouring of love, appreciation, and sadness since his death in Chicago on August 8, 2017, has been astonishing. The magic world grieves because we have lost a giant in our field, a genuine master: a supremely gifted performer, writer, philosopher, and teacher of magic. But we have lost something more: an extremely rare soul who inspired us to join him in elevating the art of magic. 2 There are not enough words for this remarkable man—will never be enough words. Eugene is, as he always said about his beloved art, inexhaustible. Yet the news of his death has brought, from every corner of the world, testimonies, eulogies, songs of praise, cries of lamentation, performances in his honor, expressions of love, photos, videos, and remembrances. All of it widens our perspective on the man; it has been beautiful and deeply moving. Even so, I have been asked by Eugene’s executors to write his obituary, a statement of his history, and I am deeply honored to do so.
  • Generating Single and Multiple Cooperative Heuristics for the One Dimensional Bin Packing Problem Using a Single Node Genetic Programming Island Model

    Generating Single and Multiple Cooperative Heuristics for the One Dimensional Bin Packing Problem Using a Single Node Genetic Programming Island Model

    Generating Single and Multiple Cooperative Heuristics for the One Dimensional Bin Packing Problem Using a Single Node Genetic Programming Island Model Kevin Sim Emma Hart Institute for Informatics and Digital Innovation Institute for Informatics and Digital Innovation Edinburgh Napier University Edinburgh Napier University Edinburgh, Scotland, UK Edinburgh, Scotland, UK [email protected] [email protected] ABSTRACT exhibit superior performance than similar human designed Novel deterministic heuristics are generated using Single Node heuristics and can be used to produce collections of heuris- Genetic Programming for application to the One Dimen- tics that collectively maximise the potential of selective HH. sional Bin Packing Problem. First a single deterministic The papers contribution is two fold. Single heuristics ca- heuristic was evolved that minimised the total number of pable of outperforming a range of well researched deter- bins used when applied to a set of 685 training instances. ministic heuristics are generated by combining features ex- Following this, a set of heuristics were evolved using a form tracted from those heuristics. Secondly an island model[19] of cooperative co-evolution that collectively minimise the is adapted to use multiple SNGP implementations to gener- number of bins used across the same set of problems. Re- ate diverse sets of heuristics which collectively outperform sults on an unseen test set comprising a further 685 prob- any of the single heuristics when used in isolation. Both ap- lem instances show that the single evolved heuristic out- proaches are trained and evaluated using equal divisions of a performs existing deterministic heuristics described in the large set of 1370 benchmark problem instances sourced from literature.
  • March 6 Special Interest Groups DVR ALERT from DAVE

    March 6 Special Interest Groups DVR ALERT from DAVE

    The SPIRIT | Official Newsletter of I.B.M. Ring 1 Meeting Update: March 6th M Arch 2 01 3 Special Interest Groups Volume 13, Issue 3 Inside this issue: The March 6 meeting program will feature “Special Interest Groups.” Three instructors will each simultaneously present 45 minute “hands on” teach-ins. Each instructor will only present 2 programs. You may select Meeting Update 1 any two of the three programs and when you have participated in your first program, you will then move on to your second program choice. DVR ALERT 1 Choices: Magic Past 2 Randy Kalin will present effective but simple card tricks with most being Ring Report 3-4 based on mathematical principles without difficult sleights. Schedule of Events 3 Mike Hindrichs, our close-up contest winner, will present his rope magic including routines and individual moves. Dues Info 4 Harry Monti will present the “Linking Rings.” He will demonstrate a Lecture Info 5 routine and then break it down and show the various elements. JDRF Info 6 These are “hands on” programs to be sure so bring your own cards, JDRF Photos 7 ropes and rings. Contest Winners 7 Harry Monti This Just In 8 NEW MEETING AGENDA 6:30 Magic 101 Quiet Please if you are not involved with Magic 101. 7:00 Refreshments/ Socialize and Jamming sessions 7:30 Special Interest Groups QUOTE: Following the meeting- Workshop and Fellowship till 10PM “Any sufficiently advanced technology is indistinguishable from magic.” DVR ALERT FROM DAVE Arthur C. Clarke, Profiles of the Future: An Inquiry into the Limits of the David Copperfield posted this on Facebook- Possible “Breaking news! Excited to announce that I will be hosting magic on the Today Show EVERY Monday in March! It starts this Monday on NBC.” 2 From The Magic Past \ By Don Rataj Here is an update that I have listed in Magicpedia, however I am missing several years.
  • A Combinatorial Analysis of Topological Dissections

    A Combinatorial Analysis of Topological Dissections

    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector ADVANCES IN MATHEMATICS 25, 267-285 (1977) A Combinatorial Analysis of Topological Dissections THOMAS ZASLAVSKY Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 From a topological space remove certain subspaces (cuts), leaving connected components (regions). We develop an enumerative theory for the regions in terms of the cuts, with the aid of a theorem on the Mijbius algebra of a subset of a distributive lattice. Armed with this theory we study dissections into cellular faces and dissections in the d-sphere. For example, we generalize known enumerations for arrangements of hyperplanes to convex sets and topological arrangements, enumerations for simple arrangements and the Dehn-Sommerville equations for simple polytopes to dissections with general intersection, and enumerations for arrangements of lines and curves and for plane convex sets to dissections by curves of the 2-sphere and planar domains. Contents. Introduction. 1. The fundamental relations for dissections and covers. 2. Algebraic combinatorics: Valuations and MGbius algebras. 3. Dissections into cells and properly cellular faces. 4. General position. 5. Counting low-dimensional faces. 6. Spheres and their subspaces. 7. Dissections by curves. INTRODUCTION A problem which arises from time to time in combinatorial geometry is to determine the number of pieces into which a certain geometric set is divided by given subsets. Think for instance of a plane cut by prescribed curves, as in a map of a land area crisscrossed by roads and hedgerows, or of a finite set of hyper- planes slicing up a convex domain in a Euclidean space.
  • The Dehn-Sydler Theorem Explained

    The Dehn-Sydler Theorem Explained

    The Dehn-Sydler Theorem Explained Rich Schwartz February 16, 2010 1 Introduction The Dehn-Sydler theorem says that two polyhedra in R3 are scissors con- gruent iff they have the same volume and Dehn invariant. Dehn [D] proved in 1901 that equality of the Dehn invariant is necessary for scissors congru- ence. 64 years passed, and then Sydler [S] proved that equality of the Dehn invariant (and volume) is sufficient. In [J], Jessen gives a simplified proof of Sydler’s Theorem. The proof in [J] relies on two results from homolog- ical algebra that are proved in [JKT]. Also, to get the cleanest statement of the result, one needs to combine the result in [J] (about stable scissors congruence) with Zylev’s Theorem, which is proved in [Z]. The purpose of these notes is to explain the proof of Sydler’s theorem that is spread out in [J], [JKT], and [Z]. The paper [J] is beautiful and efficient, and I can hardly improve on it. I follow [J] very closely, except that I simplify wherever I can. The only place where I really depart from [J] is my sketch of the very difficult geometric Lemma 10.1, which is known as Sydler’s Fundamental Lemma. To supplement these notes, I made an interactive java applet that renders Sydler’s Fundamental Lemma transparent. The applet departs even further from Jessen’s treatment. [JKT] leaves a lot to be desired. The notation in [JKT] does not match the notation in [J] and the theorems proved in [JKT] are much more general than what is needed for [J].
  • 13. Mathematics University of Central Oklahoma

    13. Mathematics University of Central Oklahoma

    Southwestern Oklahoma State University SWOSU Digital Commons Oklahoma Research Day Abstracts 2013 Oklahoma Research Day Jan 10th, 12:00 AM 13. Mathematics University of Central Oklahoma Follow this and additional works at: https://dc.swosu.edu/ordabstracts Part of the Animal Sciences Commons, Biology Commons, Chemistry Commons, Computer Sciences Commons, Environmental Sciences Commons, Mathematics Commons, and the Physics Commons University of Central Oklahoma, "13. Mathematics" (2013). Oklahoma Research Day Abstracts. 12. https://dc.swosu.edu/ordabstracts/2013oklahomaresearchday/mathematicsandscience/12 This Event is brought to you for free and open access by the Oklahoma Research Day at SWOSU Digital Commons. It has been accepted for inclusion in Oklahoma Research Day Abstracts by an authorized administrator of SWOSU Digital Commons. An ADA compliant document is available upon request. For more information, please contact [email protected]. Abstracts from the 2013 Oklahoma Research Day Held at the University of Central Oklahoma 05. Mathematics and Science 13. Mathematics 05.13.01 A simplified proof of the Kantorovich theorem for solving equations using scalar telescopic series Ioannis Argyros, Cameron University The Kantorovich theorem is an important tool in Mathematical Analysis for solving nonlinear equations in abstract spaces by approximating a locally unique solution using the popular Newton-Kantorovich method.Many proofs have been given for this theorem using techniques such as the contraction mapping principle,majorizing sequences, recurrent functions and other techniques.These methods are rather long,complicated and not very easy to understand in general by undergraduate students.In the present paper we present a proof using simple telescopic series studied first in a Calculus II class.
  • Open Problem Collection

    Open Problem Collection

    Open problem collection Peter Kagey May 14, 2021 This is a catalog of open problems that I began in late 2017 to keep tabs on different problems and ideas I had been thinking about. Each problem consists of an introduction, a figure which illustrates an example, a question, and a list related questions. Some problems also have references which refer to other problems, to the OEIS, or to other web references. 1 Rating Each problem is rated both in terms of how difficult and how interesting I think the problem is. 1.1 Difficulty The difficulty score follows the convention of ski trail difficulty ratings. Easiest The problem should be solvable with a modest amount of effort. Moderate Significant progress should be possible with moderate effort. Difficult Significant progress will be difficult or take substantial insight. Most difficult The problem may be intractable, but special cases may be solvable. 1.2 Interest The interest rating follows a four-point scale. Each roughly describes what quartile I think it belongs in with respect to my interest in it. Least interesting Problems have an interesting idea, but may feel contrived. More interesting Either a somewhat complicated or superficial question. Very interesting Problems that are particularly natural or simple or cute. Most interesting These are the problems that I care the most about. Open problem collection Peter Kagey Problem 1. Suppose you are given an n × m grid, and I then think of a rectangle with its corners on grid points. I then ask you to \black out" as many of the gridpoints as possible, in such a way that you can still guess my rectangle after I tell you all of the non-blacked out vertices that its corners lie on.
  • Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi

    Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi

    HEXAFLEXAGONS, PROBABILITY PARADOXES, AND THE TOWER OF HANOI For 25 of his 90 years, Martin Gard- ner wrote “Mathematical Games and Recreations,” a monthly column for Scientific American magazine. These columns have inspired hundreds of thousands of readers to delve more deeply into the large world of math- ematics. He has also made signifi- cant contributions to magic, philos- ophy, debunking pseudoscience, and children’s literature. He has produced more than 60 books, including many best sellers, most of which are still in print. His Annotated Alice has sold more than a million copies. He continues to write a regular column for the Skeptical Inquirer magazine. (The photograph is of the author at the time of the first edition.) THE NEW MARTIN GARDNER MATHEMATICAL LIBRARY Editorial Board Donald J. Albers, Menlo College Gerald L. Alexanderson, Santa Clara University John H. Conway, F.R. S., Princeton University Richard K. Guy, University of Calgary Harold R. Jacobs Donald E. Knuth, Stanford University Peter L. Renz From 1957 through 1986 Martin Gardner wrote the “Mathematical Games” columns for Scientific American that are the basis for these books. Scientific American editor Dennis Flanagan noted that this column contributed substantially to the success of the magazine. The exchanges between Martin Gardner and his readers gave life to these columns and books. These exchanges have continued and the impact of the columns and books has grown. These new editions give Martin Gardner the chance to bring readers up to date on newer twists on old puzzles and games, on new explanations and proofs, and on links to recent developments and discoveries.
  • Gemblo and Polyhex Blokus

    Gemblo and Polyhex Blokus

    with John Gough < [email protected]> Gemblo and Polyhex Blokus Blokus joined together whole-edge to whole-edge. Gemblo is one of the possible polyhex Blokus is an abstract strategy board game games that might be invented. Why for 2 to 4 players. It uses polyominoes obvious? Because both Blokus and Blokus WHicH are plane geometric lgures formed Trigon used families of shapes made from by joining one or more equal squares edge regular polygons that tessellate. How many to edge refer &igure . 0olyominoes HaVe are there? been described as being “a polyform whose cells are squaresv and they are classiled Gemblo according to how many cells they have. ie. number of cells. Wikipedia, 2017 March In 2005, Gemblo was created by Justin Oh 19). Polyominoes and other mathematically in Korea. It is an abstract strategy board patterned families of shapes were invented game with translucent, coloured pieces, by Solomon Golomb, and popularised by each of which is made up of one to lve hex- Martin Gardner. agons. The six colours are clear, red, yellow, green, blue, and purple. Despite the obvious similarities to Blokus, Oh has stated that when he was inventing Gemblo he did not know about Blokus. The name is based on the word ‘gem’, alluding to the gem-like colours used for the play- ing pieces and ‘blocking’—a central feature of playing. The size of the playing board depends on the number of people playing. Figure 1: Examples of polyominoes With players using a hexagonal shaped board that has sides of 8 unit-hexagons. Blokus—using squares—has a sister- game called Blokus Trigon that uses poly- Playing Gemblo iamonds, those families of shapes made s Gemblo can be played as a one- from unit-sided equilateral triangles joined person puzzle or solitaire, or by whole-edge to whole-edge.
  • Tangram Evolutif

    Tangram Evolutif

    Tangram Évolutif à Ronald Read, pionnier de l'univers du Tangram sans qui ce livre n'existerait pas 1 2 Tangram Évolutif La nature a une perfection à elle, surprenante, et qui résulte d'une addition de limites. La nature est parfaite parce qu'elle n'est pas infinie. Si on comprend les limites, on comprend comment le mécanisme fonctionne. Le tout est de comprendre les limites. Alessandro Baricco, Océan mer 3 4 Tangram Évolutif Le Tangram est un drôle de jeu. Son apparence est simple mais l'objet est insolite avec ses pièces géométriques qui se ressemblent et s'assemblent. Le manuel de jeu est un catalogue de formes variées – des silhouettes noires de bonshommes, des chats, des théières, etc. – que l'on doit reconstituer. De prime abord, il s'agit d'une sorte de puzzle destiné à un public assez jeune. Personnellement, je n'ai pas vraiment été attiré par cet aspect traditionnel du jeu mais j'en aimais le concept au point de vouloir m'en fabriquer en bois, en carton... Plus tard, un professeur de technologie de mon entourage qui voulait le faire fabriquer à ses élèves me posa une question au sujet de ce jeu et je commençais, pour lui répondre, à m'intéresser aux formes convexes qui étaient réalisables. Je m'étonnais qu'il n'en existait que treize, et me demandais si avec d'autres pièces on aurait pu en obtenir davantage. Je crayonnais des découpages de carrés et commençais des inventaires, puis je me dis que ce serait plus commode de chercher les formes convexes réalisables avec un jeu en programmant un ordinateur pour cela.