Table Of ContentMathematDiicaamlo nds
© 200b3y
TheM athematiAcsasolc iatioofAn m eric(aI ncorporated)
Libraoryf C ongresCsa talCoagr dN umbe2r 002114177
ISBN0 -88853-332-9
Printiendt heU niteSdt atoefsA merica
Current (plraidsnittg iintg) :
109 78 6 5 4 3 2 1
TeDh olMhcaeitmaEpanxotisi ictailo ns
NUMBER TWE NTY-SIX
MathematDiicaamlo nds
RosHso nsberger
UniveorfWs aittye rloo
Publaindsd hiesdtt erbydi bu
TheM athematiAcsaslo ciaotfiA omne rica
THE
DOLCIANIM ATHEMATICAL EXPOSTIIONS
Publbiys hed
THEM ATHEMATICALA SSOCIATIOONF AMERICA
CommiotnPt uebaelt iisco n
Chair
GERALDL .A LEXANDERSON,
TheD OLCIANI MATHEMATICEAXLP OSITOINS serioefst heM athematical
AssociatoifAo mne ricwaa se stablitshhreodu agg he neroguisftt ot heA ssociafrtoimo n
MaryP .D olciaPnrio,f esosfoM ra themataitcH su nteCro lleogfet heC itUyn iversity
ofN ew YorkI.nm akintgh eg ifPtr,o fesDsoolrc iahneir,s ealnef x ceptiotnaallelnyt ed
ands uccessefuxlp osiotfom ra themathiacdst ,h ep urpoosfef urthertiheni gd eaolf
excelleinnmc aet hemateixcpaols ition.
TheA ssociatfioorin t,ps a rtw,as d elighttoea dc ceptth eg racioguess tuirnei ti
atintgh er evolvfiunngdf ort hisse riferso mo new hoh ass ervtehde A ssociawtiitohn
distincbtoitoahns ,a m embero ft heC ommittoeneP ublicatainodan ssa m embero f
thBeo arodf G overnorIstw. a sw itghe nuipnlee asturheat th Beo arcdh osteon amet he
seriienhs e rh onor.
Theb ookisn t hes eriaerses elecftoertd h eliurc iedx positsotryyla ned s timulat
ingm athematciocnatle Tnytp.i claylt,h ecyo ntaainna mplseu pployfe xercimsaensy,
witahc companysionlgu tiTohnesy.a rei ntendteobd e s ufficienetlleym entfaorrty h e
undergradaunadet vee tnh em athematiicnacllliyhn iegdh -scshtouodle tnout n derstand
ande njobyu,ta lstoo b ei nteresatnidsn ogm etimcehsa llentgoit nhgem ore advanced
mathematician.
1M.a themaGteimcsa,l
Ross Honsberger
2.M athemaGteimIcsI,a l
Ross Honsberger
3.Ma themaMtoircsaell s,
Ross Honsberger
4.Ma htemaPtliucmasl,
RossH onsber(geedr).
5.Gr eMaotm einMnta st hiemc(asBt ef165o0rH)eo,w arEdv es
6.Ma xiamndMa i niwmiat hCaoluctu lus,
Ivan Niven
7.G reMaotm einMnta sht etmia(cAsft1 6e5r0H )o,w arEdv es
8.Ma pC olnogPr,oyih ledarndat ,hF eo ur-PCrboolleoDamrv, iBd arn ette
9.Ma themaGteimIcsIa Il,
Ross Honsberger
10M.o rMeat hemaMtoircsaell s,
RossH onsberger
11O.la dnd N eUwn solPvrbeolde imPnsl eaG neomaendtN ryu mbTehre ory,
Victor
Kleea ndS taWna gon
12P.ro blfeoMmras t hieamcnsaiY,to nugan dO ld,
PauRl. H almos
1.3E xcusri snCia locnuAlnIu tnse:ary op tflh Ceo nntouiuasnd t hDesi crReobteert,
M. Young
1.4T hWeo hasCconuutymP robBloeomk ,
GeorgTe. G ilbeMratr,k K rusemeyaenrd,
LoreCn. L arson
1.5L ioHnu ngta indnO thMeatrh etmiaPcualr sAu Ciotlstl:ie oocMfna htetmiacs,
VerasndeS ,tr oibeyRs a lP.p Bho aJsr.e,,d i tbeydG eralLd.A lexanderasnodn
DalHe. M ugler
16L.i nAeglaerbP rar obBloeomk ,
PauRl. H amlos
17F.ro mE rdtOsKo i ePvro:b loeOfmyl sm piCaaldi bRoessr, Honsberger
18W.hi cWhayD itdhB eiy cclGeo .?, a.ndO thIetnrr inggMua tihemaMytsirtceiaels ,
Joseph DK.o nEha.u sDearn,V ellemaann,dS taWna gon
19I.Pn 6 yal'sF ootMsiteslpcnlseea:oP urosb laendmE ssy ssa,
RossH onsberger
20.D ioapnthuasnd D oipahnteEi qunatsiI,o.G .nB ashmako(vUap datbeydJ oseph
Silvennaann dt ranslbaytA ebde S henitzer)
LogaisAcg l ebra,
21. PauHla lmoasn dS teveGni vant
EulTehrMe:a setroU fs A ll,
22. WilliDaumn ham
ThBee nginignasnd E votliouoAfngl ebra,
23. I.G .B ashmakoavnadG .S .S mirnova
(Tranbsy.A beS henitzer)
MathemaCthiecsaftlrnA ourmto sdut nhWeo rld,
24. RossH onsberger
Coungot nFi ranmweorMkasht:e miacttsAod i t hDee snoi Rfgi gSitudrc tures,
25. Jack
E.G raver
MathemaDtiiancmsdao,l
26. RossH onsberger
MAA ServiCceen ter
P. BOo.x 9 1112
WashingtDoCn 2,0 090-1112
1-800-331-1MAAf ax3:0 1-206-9789
Preafce
Tmhiisscc oeolelflll eegacmecntemoebinsnorot tiuinaansl ris lynii sga hntts
fmraofmnmiayn t emh iTenmhmodaeoarjsi fti.tt it shcyt iaa omcnlpos r e
75
cofErmuoegcm eel ctoiormdmyegb,aei anonl maagnenmteutdbobr erryria, a l
thamenooodtfrs h yte, c adfnioc sloblcmeboufc ywsoo esrladitl oaenbgsle y
fershman.
Thineasort t etoi e nimgsioptitnnthvr ; eeuw chpfltereirewme i places
nariiedtsoo nnipalesrry efea gpo i tearfpnomr or aletlsioeownn.t ed
Tehsews riailnyte sstiata,es iry nunela rtm eseea, lnte ydhn eedm atical
tienrWhmtiameal enoeactf so. un itrcspheeo ree njify ntoc sireona mgte i on
otfhe xespsii,lehts a ot nphwaeacitdtoli t mleothb mxnheiaece ninnyetdt e
rioecflh enmeeswnsrit etaahrd yii nintmgso a ttp hleemaastuirces. Although
netctoerp syrssb o ategbhrfoolteyoitneos rnh mi oeegioly fnauoa rstube, l e
tgoti havle etim htf otIi'mulsr ygeuswoh rtituet,l ah lelm mlof ritenh de
enxgc.i ti
Tsheeaci rtneida oenbnpdreseie a mnnoanda rdyeyd n etr .
Af eexsw(ee wrssic ootainlshrsupoet)tru h iittrn bhokaoeulno gedkhd o ut
a fsimefitts cecoheef(anl swl lioilaioltgensnuhiante st vetghof) eneeuo nds sr
yfouuejrrnot yhmeern t.
Tbhcoeoo wnkaic ntlo phufiu di nbaeosdl snueii sbxnac,j dna eedtcx ta
geinnedreaxl.
Iw oluitlktadoehk p ieptts ooo r ettsDuhVsalnaenolin retk my aP nr of
ando ttfDhh oeEe1 d cBimioftetaaoomhnrrrbreid ieei aarcrnlse d w p atrimo n
gecnrottifmlht aeei.nT c uhiisemssc uim brcm boiphueopr ostcktofeha v eeidr
deadInid dceg aerttptaiol.htIoi y aeetns gamf p a ultileeonn ax dts eure
mwya tram htmEaoelPn saektaidsB nnr edeev fietorruhraline ynfi agrRi uledi
geantniedeac xlshipsienneet i mreycati atninlhugp rs uioct.bourh lngieihp c ta t
I
Godm uslto vmea thematicians
He'gsi vuesns om uctoh e njoy!
J
1
I
I
.�
,;,
Contents
Pr.e.fa ce vii
SecTRtheiemWo nainerP -krR.aoa bpcleker ty
1. 1
SecTRtheieLso .itn ol ne ss
2. 5
SecAtpaipSnolt.dnie csk s
3. 9
SecASt uiRrpoeoinsfsE u irlPndtago u sl
4. 13
SecMtiisGoclnee. la.lna.in.neg osu s
5. 19
SecAAtncpi apooTtlfnu'sTii r hoaenno rem
6. 35
SecFPtoriufoorPrbn uoPl tmae.n pm aesmr s
7. 43
SecTptoBiiaocPosonsrneb f dlQrue oammns t um
8. 49
SecTDtwiioso Itnni tneggueirssh ed
9. . . . . . .7 9 .
SecAPt riooofBpn ieCt nrohoteemyffi i caile nts
10. 83
SecNMtiiinsoePocn rbe .ll elmasneous
11. 87
SecAPt riiCoonobon ils. nes -miT ng
12. . 130
SecS-terimLeoiaPgntou tlliyacgreo ns
13. 190
SecSPtiorixbfo ltrCnehoa memns a dian Open
14.
MatChheamlalteincgse
. . . . . .1 71. .
SecTthPirrToeehneiteG ntoe yro emmest ry
15. 152
SecTGtwefrioEmoo usmnGc el.oi mdeetarny
16. 153
SecTTthhieouo rensS- eeM-.qH ueednlcuend
17. 134
SecTtwioo PMbnri losecmesl laneous
18. . . . . . 151
SecASt uiPrporronoRif pesP egiorunltlgyya g ro ns
19. 175
SecTthSirhSoeotineron trT iNheuesmo breyr
20. . . 136
SecTthGirePoeornemso e btlrey.m
21. . . ..... 196
SecTthPoirrbFoelrTneeoh mBmesa O llkyamnp iad
22. 1990 175
SecAJt ai"poFPanarn noe"bs lee m
23. . .. .. . . .1 8.1 . . .
SecStlaDii oocunig nhgn ut
24. . .. .. .. .. .. 1.78 . . . .
SecAt PfirtrohoonTuebm o rnl oaefTmmw oe ntnsht e
25. 1980 159
MatheimacDtailil monds
x
MoCrhea. l .l. e .n. g .e. s
203
SoTlToCuh hteai lolnesn ges .
209
In.d.i.c.e. s. . . . . . .
237
Description:Ross Honsberger has done it again. He has brought together another wonderful collection of elementary mathematical problems and their solutions abounding in striking surprises and brilliant ideas that reflect the beauty of mathematics. Many of these problems come from mathematical journals. Others c