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英数第一周周六90s1.Thenumbersfrom1to8areplacedattheverticesofacubeinsuchamannerthatthesumofthefournumbersoneachfaceisthesame.Whatisthiscommonsum?120s2.Twotourguidesareleadingsixtourists.Theguidesdecidetosplitup.Eachtouristmustchooseoneoftheguides,butwiththestipulationthateachguidemusttakeatleastonetourist.Howmanydifferentgroupingsofguidesandtouristsarepossible?180s90s4.Atrianglewithsidelengthsintheratio3:4:5isinscribedinacircleofradius3.Whatistheareaofthetriangle?120s5.Integersa,b,c,andd,notnecessarilydistinct,arechosenindependentlyandatrandomfrom0to2007,inclusive.Whatistheprobabilitythatad-bciseven?60s6.Supposethatmandnarepositiveintegerssuchthat75m=n3.Whatistheminimumpossiblevalueofm+n?140s7.Let∠ABC=24°and∠ABD=20°.WhatisthesmallestpossibledegreemeasureforangleCBD?140s8.Lastyear100adultcats,halfofwhomwerefemale,werebroughtintotheSmallvilleAnimalShelter.Halfoftheadultfemalecatswereaccompaniedbyalitterofkittens.Theaveragenumberofkittensperlitterwas4.Whatwasthetotalnumberofcatsandkittensreceivedbytheshelterlastyear?90s9.Howmanyorderedpairs(m,n)ofpositiveintegers,withmn,havethepropertythattheirsquaredifferby96?90s10.Roy’scateats1/3ofacanofcatfoodeverymorningand1/4ofacanofcatfoodeveryevening.BeforefeedinghiscatonMondaymorning,Royopenedaboxcontaining6cansofcatfood.Onwhatdayoftheweekdidthecatfinisheatingallthecatfoodinthebox?答案①18②62③¾④8.64（直角三角形外心在斜边中点）⑤½⑥26⑦4⑧200⑨4⑩NextTuesdaymorning