The mathemagician and pied puzzler: a collection in tribute to Martin Gardner PDF
Preview The mathemagician and pied puzzler: a collection in tribute to Martin Gardner
Contents Foreword ElwynBerlekampandTomRodgers ix I Personal Magic 1 MartinGardner: A“Documentary” DanaRichards 3 Ambrose,Gardner,andDoyle RaymondSmullyan 13 ATruthLearnedEarly CarlPomerance 19 MartinGardner=Mint!Grand! Rare! JeremiahFarrell 21 ThreeLimericks: OnSpace,Time,andSpeed TimRowett 23 II Puzzlers 25 AMazewithRules RobertAbbott 27 BiblicalLadders DonaldE.Knuth 29 CardGameTrivia StewartLamle 35 CreativePuzzleThinking NobYoshigahara 37 v vi Contents NumberPlay,Calculators,andCardTricks: MathemagicalBlackHoles MichaelW.Ecker 41 PuzzlesfromAroundtheWorld RichardI.Hess 53 OBeirnesHexiamond RichardK.Guy 85 JapaneseTangram(TheSeiShonagonPieces) ShigeoTakagi 97 HowaTangramCatHappilyTurnsintothePinkPanther BernhardWiezorke 99 PollysFlagstones StewartCoffin 103 ThosePeripateticPentominoes KateJones 107 Self-DesigningTetraflexagons RobertE.Neale 117 TheOdysseyoftheFigureEightPuzzle StewartCoffin 127 MetagrobolizersofWire RickIrby 131 BeautifulbutWrong: TheFloatingHourglassPuzzle ScotMorris 135 CubePuzzles JeremiahFarrell 145 TheNineColorPuzzle SivyFahri 151 Twice: ASlidingBlockPuzzle EdwardHordern 163 PlanarBurrs M.OskarvanDeventer 165 Contents vii Block-PackingJambalaya BillCutler 169 ClassificationofMechanicalPuzzlesand PhysicalObjectsRelatedtoPuzzles JamesDalgetyandEdwardHordern 175 III Mathemagics 187 ACuriousParadox RaymondSmullyan 189 APowerfulProcedureforProvingPracticalPropositions SolomonW.Golomb 191 MisfiringTasks KenKnowlton 193 DrawingdeBruijnGraphs HerbertTaylor 197 ComputerAnalysisofSprouts DavidApplegate,GuyJacobson,andDanielSleator 199 StrangeNewLifeForms:Update BillGosper 203 HollowMazes M.OskarvanDeventer 213 SomeDiophantineRecreations DavidSingmaster 219 WhoWinsMisèreHex? JeffreyLagariasandDanielSleator 237 AnUpdateonOddNeighborsandOddNeighborhoods LeslieE.Shader 241 PointMirrorReflection M.OskarvanDeventer 245 HowRandomAre3x+1FunctionIterates? JeffreyC.Lagarias 253 Forward Martin Gardner has had no formal education in mathematics, but he has hadanenormousinfluenceonthesubject. Hiswritingsexhibitanextraor- dinaryabilitytoconveytheessenceofmanymathematicallysophisticated topicstoaverywideaudience. Inthewordsfirstutteredbymathematician JohnConway, Gardner hasbrought“moremathematics,tomoremillions, thananyoneelse." InJanuary1957,MartinGardnerbeganwritingamonthlycolumncalled “MathematicalGame”in ScientificAmerican. Hesoonbecametheinfluen- tialcenterofalargenetworkofresearchmathematicianswithwhomhecor- respondedfrequently. OnbrowsingthroughGardner’soldcolumns,oneis struck by the large number ofnow-prominent namesthatappear therein. Some of these people wrote Gardner to suggest topics for future articles; otherswrotetosuggestnoveltwistsonhispreviousarticles. Gardnerper- sonallyansweredalloftheircorrespondence. Gardner’s interestsextend well beyond the traditionalrealm of mathe- matics. His writings have featured mechanical puzzles as well as mathe- maticalones, LewisCarroll, and Sherlock Holmes. Hehas had alife-long interestinmagic,includingtricksbasedonmathematics,onsleightofhand, andoningeniousprops. Hehasplayedanimportantroleinexposingchar- latanswhohavetriedtousetheirskillsnotforentertainmentbuttoassert supernaturalclaims. Althoughhenominallyretiredasaregularcolumnist atScientificAmericanin1982,Gardner’sprolificoutputhascontinued. 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 tobring someofthesepeopletogether. The first“GatheringforGardner” (G4G1)washeld in January 1993. Elwyn Berlekamp helped publicize the ideatomathematicians.MarkSetteducatitooktheleadinreachingthema- gicians.TomRodgerscontactedthepuzzlecommunity.Thesitechosenwas Atlanta,partlybecauseitiswithindrivingdistanceofGardner’shome. The unprecedented gathering of the world’s foremost magicians, puz- zlists, and mathematiciansproduced a collection of papers assembled by ix x FORWARD ScottKim,distributedtotheconferenceparticipants,andpresentedtoGard- ner at the meeting. G4G1 was so successful that a second gathering was held in January 1995and a third in January 1998. As the gatheringshave expanded,somanypeoplehaveexpressedinterestinthepaperspresented atpriorgatheringsthatAKPeters,Ltd.,hasagreedtopublishthisarchival record. IncludedherearethepapersfromG4G1andafewthatdidn’tmake itintotheinitialcollection. Thesuccessofthesegatheringshasdependedonthegenerousdonations 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 effortofCarolyn ArtinandWillKlumpineditingandformattingthefinal versionofthemanuscript. Allofusfelthonoredbythisopportunitytojoin togetherin thistribute totheman in whosenamewegathered and tohis wife,Charlotte,whohasmadehisextraordinarycareerpossible. ElwynBerlekamp TomRodgers Berkeley,California Atlanta,Georgia Martin Gardner: A “Documentary” DanaRichards I’veneverconsciouslytriedtokeepmyselfoutofanythingIwrite, andI’vealwaystalkedclearlywhenpeople interviewme. Idon’t thinkmy life is too interesting. It’s livedmainly insidemy brain. [21] WhilethereisnobiographyofMartinGardner,therearevariousinterviews andarticlesaboutGardner. Insteadofatruebiography, wepresenthere a portraitinthestyleofadocumentary. Thatis,wegiveacollectionofquotes andexcerpts,withoutnarrativebutarrangedtotellastory. 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, wasaqueryto“TheOracle”inGernsback’smagazineScienceandInvention. The second was the “New Color Divination” in the magic periodical The Sphinx, a month later.Also below are two quotes showing a strong child- hoodinterestinpuzzles. Theearlyinterestinscience, magic,puzzles,and writingweretostaywithhim. *** “Ihaverecentlyreadanarticleonhandwritingandforgeriesinwhichitis statedthatinkeradicatorsdonotremoveink,butmerelybleachit,andthat inksobleached can beeasilybrought outby aprocessof‘fuming’known toall handwritingexperts. Can yougive meadescription ofthisprocess, whatchemicalsareused,andhowitisperformed?” [1] *** “Enclosedfindadollarbillforayear’ssubscriptiontoTheCryptogram. Iam deeply interestedinthe successoftheorganization, having beena fanfor sometime.”[2] *** Anablecartoonistwithanadeptmindforscience. [1932yearbookcaption.] *** [1934]“AsayoungsterofgradeschoolageIusedtocollecteverythingfrom butterfliesandhousekeystomatchboxesandpostagestamps—butwhen Igrewolder... Isoldmycollectionsandchucked thewholebusiness,and 3 4 D. RICHARDS begantolookforsomethingnewtocollect. ThusitwasseveralyearsagoI decidedtomakeacollectionofmechanicalpuzzles.... “ThefirstandonlypuzzlecollectorIevermetwasafictitiouscharacter. Hewasthe chief detective in a series ofshort storiesthatran many years agoinoneofthepopularmysterymagazines.... PersonallyIcan’tsaythat I have reaped from my collection the professional benefit which this man did,butatanyrateIhavefoundthehobbyequallyasfascinating.” [3] *** “MymotherwasadedicatedMethodistwhotreasuredherBibleand,asfar asI know, never misseda Sunday service unless she wasill. My father, I learned later, was a pantheist.... Throughout my first year in high school I considered myselfan atheist. I can recall my satisfactionin keeping my headuprightduringassemblieswhenwewereaskedtolowerourheadin prayer. Myconversiontofundamentalismwasdueinparttotheinfluence ofaSundayschoolteacherwhowasalsoacounseloratasummercampin MinnesotawhereIspentseveralsummers.Itwasn’tlonguntilIdiscovered DwightL.Moody... [and]Seventh-DayAdventistCarlyleB.Haynes.... For aboutayearIactuallyattendedanAdventistchurch.... Knowinglittlethen aboutgeology,Ibecameconvincedthatevolutionwasasatanicmyth.” [22] *** GardnerwasintriguedbygeometryinhighschoolandwantedtogotoCal- techtobecomeaphysicist. Atthattime,however,Caltechacceptedunder- graduatesonlyafterthey hadcompleted twoyearsofcollege, soGardner went tothe University of Chicago for whathe thought would be his first twoyears. Thatinstitutioninthe1930swasundertheinfluenceofRobertMaynard Hutchins,whohaddecreedthateveryoneshouldhaveabroadliberaledu- cationwithnospecializationatfirst. Gardner, thuspreventedfrompursu- ingmathandscience,tookcoursesinthephilosophyofscienceandthenin philosophy,whichwoundupdisplacinghisinterestinphysicsandCaltech. [19] *** “Myfundamentalismlasted,incredibly, throughthefirstthreeyearsatthe UniversityofChicago,thenasnowacitadelofsecularhumanism.... Iwas oneoftheorganizersoftheChicagoChristianFellowship.... Therewasno particulardayorevenyearduringwhichIdecidedtostopcallingmyselfa Christian.The erosionofmybeliefswasevenslowerthanmyconversion. Amajorinfluenceonmeatthetimewasacourseoncomparativereligions taught by Albert Eustace Haydon, a lapsed Baptist who became a well- knownhumanist.”[22]
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