The mathemagician and pied puzzler: a collection in tribute to Martin Gardner

252 Pages·1999·2.29 MB·english

by  Elwyn R. Berlekamp

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]