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1、..*r-Itsti;ItWHEELS,'LIFE,-..-iANDOTHERfhTr3MATHEMATICAL-=.".-.-.-AMUSEMENTS-2'iL---*I-,-.elk'1..*,'-$---;Q:a9-0,90,+-.r7954qp46-2*D-'*G610I,,MARTINGARDNER--WHEELS,LIFEANDOTHERMATHEMATICALAMUSEMENTSW.H.FreemanandCompanyNewYorkLil~rar!ofCor~gr-e,sCataloginginPublic,itio
2、nDataGardner,Xlartin,191.1-Wheels,life,andothrrmathenlaticalaniusemenrs.Inclutlesbibliograpliirs.~ndintlex.1.Rlathernaticalrecl-eations.I.Title.(LA9.5.(;3331983793.7'483-11.592ISBN0-7167-1588-0ISBN0-5167-1.589-1)(pbk.)Lifeconfigurationsconrtes!ofR.LV~lliarnGoaperofSit
3、)olic~.Jacketphotograp11bJenn~terL17alsliCop>rightC1983h!1V.H.FreemanandCornpan)Nopartofttiisbookma!bereprodrlcedh-an!mechanical,pl~otographic.orelectronicprocess,orit1theformofaphonog-I-apl~icrecortling,nurnlaitbestoredinaretrievals!stem,trari~rriitted.orothervisec
4、opirdforpublicor1)l.i-vateuse,vithoutwittenpermissio~lfromthepuhli5her.PRINTEDISTHEL'SITEI)S'I'AI'ESOFAAlt-KIC.aNinthprinting1996,VBForRonaldL.Grahamwhojugglesnunlbersandothermathematicalobjectsaselegantlyashejugglesballsandclubs,andtrvirlshimselfonthetrampolineCONTENT
5、SIntroductionviiWheels1DiophantineAnalysisandFermat'sLastTheorem10TheKnottedMoleculeandOtherProblems20AlephsandSupertasks31NontransitiveDiceandOtherProbabilityParadoxes40GeometricalFallacies51TheCombinatoricsofPaperFolding60ASetofQuickies74TicktacktoeGames94PlaitingPoly
6、hedrons106TheGameofHalma115AdvertisingPremiums124SalmononAustin'sDog134NimandHackenbush142Golomb'sGracefulGraphs152CharlesAddams'SkierandotherProblems166ChessTasks183Slither,3X+1,andOtherCuriousQuestions19419.MathematicalTricksWithCards20620.TheGameofLife,Partl21421.The
7、GameofLife,Part1122622.TheGameofLife,PartIll241NameIndex259INTRODUCTION"Thereremainsonemoregame.""LVhatisit?""Ennui,"Isaid."Theeasiestofall.Norules,noboards,noequipment.""LVhatisEnnui?"Amandaasked."Ennuiistheabqenceofgames."-DonaldBarthelme,GuzltjPltatultiUnfortunately,
8、asrecentstudiesof'educationinthiscountryhavemadeclear,oneofthechiefcharacteristicsofmathemat-.icalclasses,espe