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1、...Problem1Calla-digitnumbergeometricifithasdistinctdigitswhich,whenreadfromlefttoright,formageometricsequence.Findthedifferencebetweenthelargestandsmallestgeometricnumbers.Problem2ThereisacomplexnumberwithimaginarypartandapositiveintegersuchthatFind.Problem3Acointhatcomesupheadswithprobabilityandt
2、ailswithprobabilityindependentlyoneachflipisflippedeighttimes.Supposetheprobabilityofthreeheadsandfivetailsisequaltooftheprobabilityoffiveheadsandthreetails.Let,whereandarerelativelyprimepositiveintegers.Find.Problem4Inparallelogram,pointisonsothatandpointisonsothat.Letbethepointofintersectionofand
3、.Find.word可编辑...Problem5Trianglehasand.Pointsandarelocatedonandrespectivelysothat,andistheanglebisectorofangle.Letbethepointofintersectionofand,andletbethepointonlineforwhichisthemidpointof.If,find.Problem6Howmanypositiveintegerslessthanaretheresuchthattheequationhasasolutionfor?(Thenotationdenotes
4、thegreatestintegerthatislessthanorequalto.)Problem7Thesequencesatisfiesandfor.Letbetheleastintegergreaterthanforwhichisaninteger.Find.Problem8Let.Considerallpossiblepositivedifferencesofpairsofelementsof.Letbethesumofallofthesedifferences.Findtheremainderwhenisdividedby.Problem9word可编辑...Agameshowo
5、ffersacontestantthreeprizesA,BandC,eachofwhichisworthawholenumberofdollarsfrom$to$inclusive.ThecontestantwinstheprizesbycorrectlyguessingthepriceofeachprizeintheorderA,B,C.Asahint,thedigitsofthethreepricesaregiven.Onaparticularday,thedigitsgivenwere.Findthetotalnumberofpossibleguessesforallthreepri
6、zesconsistentwiththehint.Problem10TheAnnualInterplanetaryMathematicsExamination(AIME)iswrittenbyacommitteeoffiveMartians,fiveVenusians,andfiveEarthlings.Atmeetings,committeememberssitataroundtablewithchairsnumberedfromtoinclockwiseorder.CommitteerulesstatethataMartianmustoccupychairandanEarthlingmu
7、stoccupychair,Furthermore,noEarthlingcansitimmediatelytotheleftofaMartian,noMartiancansitimmediatelytotheleftofaVenusian,andnoVenusiancansitimmediatelytotheleftofanEarthling.Thenumberofpossibleseatingarrang
