2021年大聯(lián)盟(Math League)國際夏季四年級數(shù)學挑戰(zhàn)活動一

PAGEPAGE12021美國"大聯(lián)盟"(MathLeague)國際夏季數(shù)學挑戰(zhàn)活動2021MathLeagueInternationalSummerChallengeGrade4,IndividualQuestionsQuestion1:Thereisatableinfrontofyouwithonehundredquartersonit.Youhavebeenblindfoldedandarewearingathickpairofgloves.Youarenotabletoseewhetherthebecauseyouareblindfolded.Andyouarenotabletofeelwhetherthequartersareheadsortailsbecauseofthethickgloves.Yourfriendtellsyouthattwentyofthesequartersaretailsandremainingeightyareheads,butyoudonotknowwhicharewhich.Hetellsyouthatifyouareabletosplitthequartersintotwopileswherethenumberoftailsquartersisthesameineachpile,youwillwinallofthequarters.Youarefreetomovethequarters,flipthemover,andarrangethemintotwopilesofanynumber.Foryoutowinallofthequarters,howmanyquartersareineachofthetwopiles?(Pleaseenteryouranswersinascendingorder.)Note:heads:thefrontsideofacoin.tails:thebacksideofacoin.Figurebelow,headsandtailsofaquarter.Question2:Thepagesofabookareconsecutivelynumberedfrom1through384.Howmanydigit‘8’appearinthisnumbering?Question3:Annabellaisvisitinghergrandmawhoresides295milesawayfromher.Shestartedherdrivingtripataspeedof65mph(milesperhour)forthefirst3hours.Fortherestofthetrip,shedroveataspeedof50mph.Howmanyhoursdidshetaketodrivetohergrandma?Question4:Sarahisusingpopsiclestickstobuildsomegridsforhercityplanningproject.Sheneeds4popsiclestickstomakea1by1grid,and12stickstomakea2by2gridasshownbelow.Howmanysticksdoessheneedtomakea10by20grid?Question5:192Question6Thesidesofthelargerectangleare20mand16m,figurebelow,notdrawntoscale.Allsixshadedrectanglesareidentical.Whatisthetotalareaofalltheshadedregions,192Question6Question6:Alice,Bibi,andClaryarethreeintelligentgirls.Oneday,theirteacherdecidestoplayasimplegameandawardsomeprizetothefirstgirlwhosolvesit:head,andeachgirlcanseetheothergirls’hats,butnotherown.Theyareinstructedtoraisetheirhandsiftheyseeatleastoneblackhat.Andthefirstgirltotelltheteacherwhatcolorhatsheiswearingandhowoutwillgettheprize.AfterthehatsareplacedonAlice,Bibi,andAfterafewseconds,Alicesays:“Ihavefigureditout!”wearing?Threechoices:BlackWhiteNon-deterministicQuestion7:Youhaveabalancescaleandsixweights.Therearetworedweights,twoorangeweights,andtwoblueweights.Ineachpairofcoloredweights,oneweightisslightlyheavierthantheother,butisotherwiseidentical.Thethreeheavierweightsallweighthesame,andthethreelighterweightsallweighthesame.Whatisthefewestnumberoftimesyouneedtousethebalancescaleinordertopositivelyidentifytheheavierweightineachpair?Question8:Inaclassof5thgradestudents,15havepetcats,12havepetdogs,5havebothpetcatsandpetdogs,and8haveneitherpetcatsnorpetdogs.Howmanytotalstudentsareintheclass?Question9:Whatisthe5-digitmysterynumberthatfitsalltheconditionsbelow?Thesumofthefirsttwodigits(countingfromlefttoright,samebelow)isonesmallerthanthethirddigit.Thethirddigitisdoublethefourthdigit.Thefourthdigitisdoublethelastdigit.Thethirddigitistheproductofthefourthandfifthdigits.Theseconddigitisfivemorethanthefirstdigit.Thefirstdigitisone-eighthofthethirddigitandalsoone-fourthofthefourthdigit.Question10:Iftwosidesof