Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner's First Book of Mathematical Puzzles and Games

210 Pages·2008·2.643 MB·English

by  Gardner M.

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
morethanamillioncopies.Hecontinuestowritearegularcolumnfor
theSkepticalInquirermagazine.(Thephotographisoftheauthoratthe
timeofthefirstedition.)

THE NEW MARTIN GARDNER MATHEMATICAL LIBRARY
EditorialBoard
DonaldJ.Albers, MenloCollege
GeraldL.Alexanderson, SantaClaraUniversity
JohnH.Conway,F.R.S., PrincetonUniversity
RichardK.Guy, UniversityofCalgary
HaroldR.Jacobs
DonaldE.Knuth, StanfordUniversity
PeterL.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
columncontributedsubstantiallytothesuccessofthemagazine.The
exchanges between Martin Gardner and his readers gave life to these
columnsandbooks.Theseexchangeshavecontinuedandtheimpact
ofthecolumnsandbookshasgrown.TheseneweditionsgiveMartin
Gardnerthechancetobringreadersuptodateonnewertwistsonold
puzzles and games, on new explanations and proofs, and on links to
recent developments and discoveries. Illustrations have been added
andexistingonesimproved,andthebibliographieshavebeengreatly
expandedthroughout.
1. Hexaflexagons,ProbabilityParadoxes,andtheTowerofHanoi:
MartinGardner’sFirstBookofMathematicalPuzzlesandGames
2. Origami,Eleusis,andtheSomaCube:MartinGardner’s
MathematicalDiversions
3. SpherePacking,LewisCarroll,andReversi:MartinGardner’sNew
MathematicalDiversions
4. KnotsandBorromeanRings,Rep-Tiles,andEightQueens:Martin
Gardner’sUnexpectedHanging
5. KleinBottles,Op-Art,andSliding-BlockPuzzles:MoreofMartin
Gardner’sMathematicalGames
6. Sprouts,Hypercubes,andSuperellipses:MartinGardner’s
MathematicalCarnival
7. NothingandEverything,Polyominoes,andGameTheory:Martin
Gardner’sMathematicalMagicShow
8. RandomWalks,Hyperspheres,andPalindromes:MartinGardner’s
MathematicalCircus
9. Words,Numbers,andCombinatorics:MartinGardnerontheTrail
ofDr.Matrix
10. Wheels,Life,andKnottedMolecules:MartinGardner’s
MathematicalAmusements
11. KnottedDoughnuts,Napier’sBones,andGrayCodes:Martin
Gardner’sMathematicalEntertainments
12. Tangrams,Tilings,andTimeTravel:MartinGardner’s
MathematicalBewilderments
13. PenroseTiles,TrapdoorCiphers,andtheOulipo:MartinGardner’s
MathematicalTour
14. FractalMusic,Hypercards,andChaitin’sOmega:MartinGardner’s
MathematicalRecreations
15. TheLastRecreations:Hydras,Eggs,andOtherMathematical
Mystifications:MartinGardner’sLastMathematicalRecreations
Hexaflexagons,
Probability Paradoxes,
and the Tower of Hanoi
MARTIN GARDNER’S FIRST BOOK OF
MATHEMATICAL PUZZLES AND GAMES
Martin Gardner
®
TheMathematicalAssociationofAmerica
CAMBRIDGEUNIVERSITYPRESS
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,Sa˜oPaulo,Delhi
CambridgeUniversityPress
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521756150
(cid:1)c MathematicalAssociationofAmerica2008
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished2008
FirsteditionpublishedasTheSCIENTIFICAMERICANBookofMathematical
Puzzles&Diversions,SimonandSchuster,1959
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationData
Gardner,Martin,1914–
Hexaflexagons,probabilityparadoxes,andtheTowerofHanoi:Martin
Gardner’sfirstbookofmathematicalpuzzlesandgames/MartinGardner.
p. cm.– (ThenewMartinGardnermathematicallibrary)
Includesbibliographicalreferencesandindex.
ISBN978-0-521-75615-0(hardback)
1.Mathematicalrecreations. I.Title. II.Series.
QA95.G247 2008
793.74–dc22 2008012533
ISBN 978-0-521-75615-0hardback
ISBN 978-0-521-73525-4paperback
CambridgeUniversityPresshasnoresponsibilityfor
thepersistenceoraccuracyofURLsforexternalor
third-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuch
Websitesis,orwillremain,accurateorappropriate.
Contents
Acknowledgments pageviii
IntroductiontotheFirstEdition ix
PrefacetotheSecondEdition xiii
1 Hexaflexagons 1
2 MagicwithaMatrix 16
3 NineProblems 24
4 Ticktacktoe 37
5 ProbabilityParadoxes 48
6 TheIcosianGameandtheTowerofHanoi 63
7 CuriousTopologicalModels 73
8 TheGameofHex 82
9 SamLoyd:America’sGreatestPuzzlist 94
10 MathematicalCardTricks 109
11 MemorizingNumbers 115
12 NineMoreProblems 123
13 Polyominoes 137
14 Fallacies 157
15 NimandTacTix 166
16 LeftorRight? 177
Index 189
vii
Acknowledgments
martin gardner thanks Scientific American for allowing reuse of
material from his columns in that magazine, material Copyright
(cid:1)c 1956 (Chapter 1), and 1957 (Chapters 2–13), and 1958 (Chap-
ters 14–16) by Scientific American, Inc. He also thanks the artists
who contributed to the success of these columns and books for
allowing reuse of their work: James D. Egelson (via heirs Jan and
NicholasEgleson),IrvingGeis(viaheirSandyGeis),HaroldJacobs,
Amy Kasai, and Bunji Tagawa (via Donald Garber for the Tagawa
Estate).Artistsnamesarecitedwherethesewereknown.Allrights
otherthanuseinconnectionwiththesematerialsliewiththeorigi-
nalartists.
PhotographinFigure48iscourtesyoftheMuseumofFineArts,
Boston,2008.Usedbypermission.
viii