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英数第三周周三1.Ihave6differentbooks,3withredcoversand3withbluecovers.InhowmanydifferentwayscanIarrangethesebooksonashelfsothatnotwobooksofthesamecolourarenexttoeachother?2.Assumethataballdroppedfromanyheightriseshalfthedistanceontherebound.Ifaballisdroppedfrom100m,whatdistancewilltheballhavecoveredbythetimeithitsthegroundthe4thtime?3.Howmany3letter”words”canbemadeusingtheconsonantsBCD,andthevowelsAandE?A“word”isdefindedtobeanysequenceof3letterscontainingtwoconsonantsandonevowelinanyorder(allowingletterstoberepeated).Forexample,ABCandCCEareboth“words”.4.Asetof1*1*1cubesisusedtoconstructahollow10*10*10cubewhoseshellistwolayersofcubesinthickness.Howmanycubesareneeded?5.Whatisthenextnumberinthesequence1,2,3,4,6,9,13,19,28,….?6.Theprimenumbersbetween10and20areaddedtogethertoformthenumberQ.WhatisthelargestprimedivisorofQ?7.Jimdrives60kmsouth,40kmwest,20kmnorth,and10kmeast.Whatisthedistancefromhisstartingpointtohisfinishingpoint?8.Inhowmanydifferentwayscansevennumbersbeclosenfromthenumbers1to9,inclusive,sothatthesevennumbershaveasumwhichisamultipleof3?9.Anantwalksinsidea150cmby18cmrectangle.Theant’spathfollowsstraightlineswhichalwaysmakeanglesof45°tothesidesoftherectangle.TheantstartsfromapointXononeoftheshortersides.Thefirsttimetheantreachestheoppositeside,itarrivesatthemidpoint.Whatisthedistance,incentimetres,fromXtothenearestcorneroftherectangle？10.Howmanyfive-digitintegers,divisibleby9,canbewrittenusingonlythedigits3and6?答案：1.722.275m3.544.7845.416.57.50km8.129.310.10