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Mathematical Diamonds PDF

255 Pages·2003·2.07 MB·English
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MathematDiicaamlo 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

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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
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