A Friendly Mathematics Competition: 35 Years of Teamwork in Indiana

196 Pages·1.111 MB·English

by  Rick Gillman

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A Friendly Mathematics
Competition
35 Years of Teamwork in Indiana
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(cid:13)c 2003by
TheMathematicalAssociationofAmerica(Incorporated)
LibraryofCongressCatalogCardNumber2002107971
PrintISBN978-0-88385-808-0
ElectronicISBN978-1-61444-400-8
PrintedintheUnitedStatesofAmerica
CurrentPrinting(lastdigit):
10987654321
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A Friendly Mathematics
Competition
35 Years of Teamwork in Indiana
Edited by
Rick Gillman
Valparaiso University
PublishedandDistributedby
TheMathematicalAssociationofAmerica
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MAAPROBLEMBOOKSSERIES
Problem Books is a series of the Mathematical Association of America
consistingofcollectionsofproblemsandsolutionsfromannualmathemat-
icalcompetitions;compilationsofproblems(includingunsolvedproblems)
specifictoparticularbranchesofmathematics;booksontheartandpractice
ofproblemsolving,etc.
CommitteeonPublications
GeraldAlexanderson,Chair
RogerNelsenEditor
IrlBivens ClaytonDodge
RichardGibbs GeorgeGilbert
ArtGrainger GeraldHeuer
ElginJohnston KiranKedlaya
LorenLarson MargaretRobinson
A Friendly Mathematics Competition: 35 Years of Teamwork in Indiana,
editedbyRickGillman
TheInquisitiveProblemSolver,PaulVaderlind,RichardK.Guy,andLoren
C.Larson
MathematicalOlympiads1998–1999:ProblemsandSolutionsFromAround
theWorld,editedbyTituAndreescuandZumingFeng
MathematicalOlympiads1999–2000:ProblemsandSolutionsFromAround
theWorld,editedbyTituAndreescuandZumingFeng
TheWilliamLowellPutnamMathematicalCompetition1985–2000:Prob-
lems,Solutions,andCommentary,KiranS.Kedlaya,BjornPoonen,Ravi
Vakil
USA andInternationalMathematicalOlympiads2000,editedbyTituAn-
dreescuandZumingFeng
USA andInternationalMathematicalOlympiads2001,editedbyTituAn-
dreescuandZumingFeng
MAAServiceCenter
P.O.Box91112
Washington,DC20090-1112
1-800-331-1622 fax:[phone]
www.maa.org
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Preface
A college level mathematics competition has been held in Indiana for
more than35years as ofthewritingof thisbook.Orginallyknownas the
Indiana Small College Mathematics Competition, its official title became
theIndianaCollegeMathematicsCompetition.However,manypeoplerefer
toitby itspopularnickname “The FriendlyExam” earned because of the
collegialnatureofthecompetitionandthemodestlevelofcompetitiveness
betweentheparticipantsandtheinstitutionsinvolved.Itisreallymoreabout
gettingtogethertodomathematicsandtochallengeoneselfthanitisabout
winningacompetition.
Thisbookshares theeffortsofthe many studentsandfacultywhohave
participatedintheIndiana CollegeMathematics Competitionover itsfirst
35years.
Iwouldliketospecificallyidentifytheindividualfacultymembers who
havecomposedtheexams.Unfortunately,thisistheonepieceofthehistory
that has been lost over the years. Their attentive work at identifying or
creating goodquestionshas been a majorreason whythecompetitionhas
beenasuccessforsolong.
Overtheyears,examauthorshaveborrowedmanyclassicproblemsfrom
othersources.Thesehavebeenincludedtoprovideacompleterecordofthe
exam,buthavenotgenerallybeenattributedtoanoriginalsource.
I’dliketotakethisopportunitytothankallofthepeoplewhohavemade
this book possible by helping in one way or another. Among all of these
people, the following individuals provided noteworthy help: James Lee,
Ken Luther, Steve Shonefeld, Pat Sullivan,Eric Tkaczyk, and the Purdue
UniversityMathClub.
I wouldalso like to thank Pete Edson for having the idea for the com-
petition,and extend a very special thankyou to Paul Mielke on behalf of
v
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vi Preface
myselfandmycolleaguesinIndiana.WithoutPaul’seffortstodevelopthe
contest,tosupportitovertheyears, andtoleadthesectioninbuildingthe
endowment,IndianaandtheMAAwouldnothavethiswonderfulexample
of a “friendly” competition that does so much to build the mathematical
communityinIndiana.
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Contents
Preface v
TheIndianaCollegeMathematicsCompetition:AShortHistory 1
AnUpdateoftheHistoryoftheICMC 5
Exams 7
Exam#1–1966 . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Exam#2–1967 . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Exam#3–1968 . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Exam#4–1969 . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Exam#5–1970 . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Exam#6–1971 . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Exam#7–1972 . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Exam#8–1973 . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Exam#9–1974 . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Exam#10–1975 . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Exam#11–1976 . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Exam#12–1977 . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Exam#13–1978 . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Exam#14–1979 . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Exam#15–1980 . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Exam#16–1981 . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Exam#17–1982 . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Exam#18–1983 . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Exam#19–1984 . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Exam#20–1985 . . . . . . . . . . . . . . . . . . . . . . . . . . 28
vii
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viii Contents
Exam#21–1986 . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Exam#22–1987 . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Exam#23–1988 . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Exam#24–1989 . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Exam#25–1990 . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Exam#26–1991 . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Exam#27–1992 . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Exam#28–1993 . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Exam#29–1994 . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Exam#30–1995 . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Exam#31–1996 . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Exam#32–1997 . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Exam#33–1998 . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Exam#34–1999 . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Exam#35–2000 . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Solutions 51
Exam#1–1966 . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Exam#2–1967 . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Exam#3–1968 . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Exam#4–1969 . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Exam#5–1970 . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Exam#6–1971 . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Exam#7–1972 . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Exam#8–1973 . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Exam#9–1974 . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Exam#10–1975 . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Exam#11–1976 . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Exam#12–1977 . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Exam#13–1978 . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Exam#14–1979 . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Exam#15–1980 . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Exam#16–1981 . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Exam#17–1982 . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Exam#18–1983 . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Exam#19–1984 . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Exam#20–1985 . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Exam#21–1986 . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Exam#22–1987 . . . . . . . . . . . . . . . . . . . . . . . . . . 122
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Contents ix
Exam#23–1988 . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Exam#24–1989 . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Exam#25–1990 . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Exam#26–1991 . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Exam#27–1992 . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Exam#28–1993 . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Exam#29–1994 . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Exam#30–1995 . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Exam#31–1996 . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Exam#32–1997 . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Exam#33–1998 . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Exam#34–1999 . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Exam#35–2000 . . . . . . . . . . . . . . . . . . . . . . . . . . 176
IndexbyProblemType 181
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