袋鼠B级别2013-2023真题合集

KangarooMathCompetition2014{Ecolier3points#1.Whichdrawingisthecentralpartofthepicturewiththestar?Gambarajahyangmanakahmenunjukkanbahagiantengahgambarbintangtersebut?以下哪个图案是星星图片中间的部分？(A)(B)(C)(D)(E)#2.Whichhousesaremadeusingexactlythesamepiecesoftriangularorrectangularshape?Rumah-rumahyangmanakahdibinamenggunakanbahagiansegitigadansegiempatyangsama?以下哪几间屋子是由完全相同的三角形和长方形组成的？(A)1,4(B)3,4(C)1,4,5(D)3,4,5(E)1,2,4,5#3.WhenKokotheKoaladoesnotsleep,heeats50gramsofleavesperhour.Yesterday,heslept20hours.Howmanygramsofleavesdidheeatyesterday?ApabilaKokosiKoalatidaktidur,diamemakan50gramdaunsetiapjam.Semalam,diatelahtidurselama20jam.Berapagramdaunyangdimakanolehnyasemalam?当Koko这只树熊不睡觉时，它每小时能吃50克的叶子。昨天它睡了20小时。请问它昨天共吃了多少克的叶子？(A)0(B)50(C)100(D)200(E)4001,KangarooMathCompetition2014{Ecolier#4.Mariasubtractsandgetsasresultsthenumbersfrom0to5.Sheconnectsthedots,startingatthedotwiththeresult0andendingatthedotwiththeresult5.Whichguredoessheget?Mariamembuatoperasitolakdanmendapathasildaripada0hingga5.Diamenyam-bungkantitik-titiktersebutbermuladarititikbernilai0danberakhirdengantitikbernilai5.Gambarajahmanakahyangdilukisolehnya?Maria使用减法并获得从0至5的答案。她从答案0的点开始一直连接到答案5的点。请问她会得到什么图形？(A)(B)(C)(D)(E)2,KangarooMathCompetition2014{Ecolier#5.AdambuiltfewersandcastlesthanMartinbutmorethanSusan.LucybuiltmoresandcastlesthanAdamandmorethanMartin.DanabuiltmoresandcastlesthanMartinbutfewerthanLucy.Whoofthembuiltthemostsandcastles?AdammembinakurangistanapasirberbandingMartintetapilebihberbandingSusan.LucymembinalebihistanapasirberbandingAdamdanlebihberbandingMartin.DanamembinalebihistanapasirberbandingMartintetapikurangberbandingLucy.Siapakahdiantaramerekayangmembinapalingbanyakistanapasir?Adam建的沙堡比Martin少但比Susan多。Lucy建的沙堡比Adam和Martin多。Dana建的沙堡比Martin多但却比Lucy少。请问谁建的沙堡最多？(A)Martin(B)Adam(C)Susan(D)Dana(E)Lucy#6.Monicawritesnumbersinthediagramsothateachnumberistheproductofthetwonumbersbelowit.Whichnumbershouldshewriteinthegreycell?Monicamenulisnombor-nombordidalamgambarajahberikutsupayasetiapnomboradalahhasildarabduanombordibawahnya.Nomborapakahyangperluditulisdidalampetakkelabutersebut?Monica在图表中填写数字，使得每个数字是下方两个数字的积。请问灰格中她应填写什么数字？642211(A)0(B)1(C)2(D)4(E)83,KangarooMathCompetition2014{Ecolier#7.Annhasfourpiecesasshown.Withthesepiecesshecancompletelycovertheshape.Whereshouldsheputthepiecebelow?Annmempunyaiempatbentuksepertiditunjukkan.Denganmenggunakanbentuk-bentuktersebut,diadapatmenutupkeseluruhangambarajah.Dimanakahdiaperlumeletakkanbentukdibawah?Ann拥有四块如图的纸片，用这些纸片她可以完整的覆盖整个图形。请问她该把这张纸片放在以下的哪里？(A)(B)(C)(D)(E)4,KangarooMathCompetition2014{Ecolier#8.Mr.Brownhaspainted owersonthestorewindow(seepicture).Howdoesthese owerslooklikefromtheothersideofthewindow?Mr.Browntelahmengecatgambarbungaberikutditingkapsebuahkedai(lihatgambara-jah).Bagaimanakahrupabungatersebutdariarahseberangtingkapitu?Brown先生在橱窗上画了一些花朵（如图）。请问这些花朵从橱窗的另一边看是怎样的？(A)(B)(C)(D)(E)#9.Somecandieswereinabowl.Sallytookhalfofthecandies.ThenTomtookhalfofthecandiesleftinthebowl.AfterthatClaratookhalfoftheremainingcandies.Intheendtherewere6candiesinthebowl.Howmanycandieswereinthebowlatthebeginning?Suatumangkukmengandungibeberapagula-gula.Sallymengambilseparuhdaripadagula-gulatersebut.Kemudian,Tommengambilseparuhdaripadagula-gulayangtinggal.Selepasitu,Claramengambilseparuhdaripadagula-gulayangtinggal.Akhirnyaterdapat6gula-guladidalammangkukitu.Berapakahbilangangula-gulapadaasalnya?在一个碗中有一些糖果。Sally拿走了一半的糖果，然后Tom从剩下的糖果中又拿了一半。之后Clara又从剩下的糖果中再拿一半。如果最后碗中剩下6粒糖果，请问一开始时碗中有多少粒糖果？(A)12(B)18(C)20(D)24(E)485,KangarooMathCompetition2014{Ecolier#10.Whichtilemustbeaddedtothepicturesothatthetotallightgreyareaisasbigasthetotaldarkgreyarea?Petakmanakahyangperluditambahkepadagambartersebutsupayaluaskawasankelabucairsamadenganluaskawasankelabugelap?以下哪个瓷砖必需加入图片中以便浅灰色和深灰色的总面积相等？?(A)(B)(C)(D)(E)4points#11.Paulashootsarrowsatthefollowingtarget.Whenshemisses,sheobtainszeropoints.Paulashootstwoarrowsandaddsthenumberofpoints.Whichofthefollowingsumscannotbeherscore?Paulasedangmemanahmenggunakansasaranberikut.Jikadiaterlepassasaran,diamen-dapat0markah.Paulamenembakduaanakpanahdanmengirajumlahmarkahyangdiperoleh.Yangmanakahdiantaraberikuttidakbolehmenjadijumlahmarkahnya?Paula向图中的靶子射箭。如果她射不中靶子，她将获得零分。Paula射了两箭并把分数加了起来。以下哪个不可能是她的分数？305070(A)60(B)70(C)80(D)90(E)1006,KangarooMathCompetition2014{Ecolier#12.RabbitBoryalikescabbagesandcarrotsverymuch.Inadayheeatseither9carrots,or2cabbages,or1cabbageand4carrots.DuringoneweekBoryahaseaten30carrots.Howmanycabbageshasheeatenduringthisweek?BoryasiArnabsukamemakankobisdanlobak.Setiaphari,diaakanmemakansamaada9lobak,atau2kobis,atau1kobisdan4lobak.Sepanjangsatuminggu,Boryatelahmemakan30lobak.Berapakahbilangankobisyangdimakannyasepanjangmingguitu?兔子Borya非常喜欢吃包菜和萝卜。每天它只吃9根萝卜，或2个包菜，或1个包菜和4根萝卜。一个星期内Borya吃了30根萝卜。请问这个星期里它共吃了多少个包菜？(A)6(B)7(C)8(D)9(E)10#13.Thesolidinthepicturewasmadebystickingeightequalcubestogether.Howdoesthissolidlookfromabove?Bongkahyangditunjukkandalamgambarajahberikutdiperolehdenganmencantumkan8kiubyangserupa.Apakahrupabongkahinidariatas?图中的立体是由八个相同大小的立方体粘成的。请问这立体从上方看是怎么样的？(A)(B)(C)(D)(E)7,KangarooMathCompetition2014{Ecolier#14.Howmanydotsarethereinthispicture?Berapakahbilangantitikdalamgambarajahberikut?图中共有多少点？(A)180(B)181(C)182(D)183(E)265#15.OnKangarooplaneteachkangyearhas20kangmonthsandeachkangmonthhas6kangweeks.Howmanykangweeksarethereinonequarterofakangyear?DiplanetKangaroo,setiap\tahunkang"mengandungi20\bulankang"dansetiap\bu-lankang"mengandungi6\minggukang".Berapakahbilangan\minggukang"didalamsatuperempat\tahunkang"?在袋鼠星球上，每一个袋鼠年有20个袋鼠月，而每个袋鼠月有6个袋鼠星期。请问四分之一的袋鼠年中有多少个袋鼠星期？(A)9(B)30(C)60(D)90(E)1208,KangarooMathCompetition2014{Ecolier#16.Evearrangedcardsinalineasitisshowninthegurebelow.AteachmoveEveisallowedtointerchangeanytwocards.WhatisthesmallestnumberofmovesEveneedstogetthewordKANGAROO?Evemenyusunbeberapakaddalamsatubarissepertidalamgambarajahberikut.Padasetiaplangkah,Evedibenarkanuntuksalingmenukarmana-manaduakad.BerapakahbilanganlangkahminimumyangEveperlukanuntukmenghasilkanperkataanKANGAROO?Eve把卡片排成一行（如图）。Eve每移动一次卡都只可互换任何两张卡的位子。若Eve要把卡排成KANGAROO这个字，最少需移多少次？(A)2(B)3(C)4(D)5(E)6#17.Asequenceoftrianglesofdiamondsismade.Therstthreestagesareshown.Ineachstagealineofdiamondsisadded.Inthebottomlinetheouterdiamondsarewhite.Allotherdiamondsinthetriangleareblack.Howmanyblackdiamondshasthegureinstage6?Suatujujukansegitigadibinamenggunakanbentuk\diamond".Tigalangkahpertamadi-tunjukkan.Padasetiaplangkahsatubaris\diamond"ditambahkan.Padabarisanyangter-akhir,\diamond"yangterletakdihujungdiwarnakanputih.Kesemua\diamond"yanglaindiwarnakanhitam.Berapakahbilangan\diamond"hitampadalangkahke-6?有一序列由菱形排成的三角形。前三个阶段已显示（如图）。每个阶段将加入一行菱形。底行最外面的菱形是白色的，而其它则是黑色的。请问在第六阶段时共有多少个黑色的菱形？123(A)19(B)21(C)26(D)28(E)349,KangarooMathCompetition2014{Ecolier#18.Writeeachofthenumbers0,1,2,3,4,5,6inthesquarestomaketheadditioncorrect.Whichdigitwillbeinthegreysquare?Tuliskansetiapnombor0,1,2,3,4,5,6dalampetak-petakberikutsupayapenambahanberikutsah.Digitapakahyangterletakdalampetakkelabu?把每个数字0，1，2，3，4，5，6放进格中使加法正确。哪个数字会在灰格中？+(A)2(B)3(C)4(D)5(E)6#19.Whatisthelargestnumberofsmallsquareswhichcanbeshadedsothatnosquaremadeoffourshadedsmallsquaresappearsonthegure?Berapakahbilanganpetakkecilyangbolehdiwarnakansupayatiadapetakyangdiben-tukdariempatpetakkecilberwarnadalamgambarajahtersebut?请问最多可涂黑多少个图中的小方格并使得由四个小灰格组成的正方形没有出现在图中？(A)18(B)19(C)20(D)21(E)2210,KangarooMathCompetition2014{Ecolier#20.Nickhaswritteneachofthenumbersfrom1to9inthecellsofthe33table.Onlyfourofthesenumberscanbeseeninthegure.Nickhasnoticedthatforthenumber5thesumofthenumbersintheneighbouringcellsequals13(neighbouringcellsarecellssharingsides).Henoticedthesameappliesforthenumber6.WhichnumberhasNickwrittenintheshadedcell?Nicktelahmenulissetiapnombordaripada1hingga9didalampetak-petakpadajadualber-saiz33.Hanyaempatnombortersebutyangdapatdilihatdalamgambarajah.Nickmendapatibahawauntukpetakbernombor5,hasiltambahnombor-nombordalamsemuapetakyangberse-belahandengannyabersamaandengan13(petak-petakyangbersebelahanadalahpetak-petakyangberkongsisisiyangsama).Nickmendapatibahawaperkarayangsamajugaberlakuuntukpetakbernombor6.NomborapakahyangditulisolehNickdidalampetakyangdigelapkan?Nick在一个33的表里填写1至9的数字，图中可见其中四个数字。Nick发现数字5的相邻格子的数字的和是13（相邻格子即是共享同一个边的格子）。他发现同样的事情也发生在数字6身上。请问Nick应该在灰格中填写什么数字？(A)5(B)6(C)7(D)8(E)9ENDOFPAPER答案：DADAEECEEBDBCBBBCDDD11,KangarooMathCompetition2015–Ecolier1,KangarooMathCompetition2015–Ecolier#4.Lucyhadsome‘kangas’currencyinthewallet(seethepicture).Shewenttoashopwheresheboughtaballandpaid7kangas.Howmanykangasdidshehavewhenshelefttheshop?Lucyadabeberapamatawang‘kanga’didalamdompetnya(rujukgambar).Diapergikekedaidanmembelisebijibolalalumembayarnyadengan7kanga.Berapakahnilaikangayangtinggaldalamdompetnyaapabiladiameninggalkankedaiitu?Lucy有一些袋鼠币在钱包里（如图）。她去了一间店买了一粒球后付了7袋鼠币。请问当她离开店时共剩下多少袋鼠币？(A)(B)(C)(D)(E)2,KangarooMathCompetition2015–Ecolier#5.Awholenumberhastwodigits.Theproductofthedigitsofthisnumberis15.Thesumofthedigitsofthisnumberis:Suatunomborbulatmempunyaiduadigit.Hasildarabduadigitnyaialah15.Hasiltambahduadigitnyaialah:有一个两位数的整数，它的积为15，请问它的和是？(A)2(B)4(C)6(D)7(E)8#6.Inthefigure,weseeanislandwithahighlyindentedcoastlineandseveralfrogs.Howmanyofthesefrogsaresittingontheisland?Gambarajahmenunjukkansebuahpulaudenganpesisiranpantaiyangsangatberlekukdanbeberapaekorkatak.Berapakahbilangankatakyangberadadiataspulauini?图中可见一座拥有曲折海岸线的小岛与数只青蛙。请问共有几只青蛙是在岛上的？(A)5(B)6(C)7(D)8(E)9#7.MyumbrellahasKANGAROOwrittenontop.Itisshowninthepicture.Whichofthefollowingpicturesalsoshowsmyumbrella?PayungsayatertulisKANGAROOdiatasnyasepertidalamgambar.Yangmanakahdiantaragambarberikutjugamenunjukkanpayungsaya?作者的雨伞上印有KANGAROO的字母（如图）。请问以下图中哪一支雨伞是作者的？GARNOAKONGKARAGNAGNKRGA(A)(B)(C)(D)(E)3,KangarooMathCompetition2015–Ecolier#8.BasilwantstocuttheshapedepictedinFigure1intoidenticaltrianglesasinFigure2.Howmanytriangleswillheget?BasilinginmemotongbentukpadaFigure1kepadasegitiga-segitigayangserupasepertipadaFigure2.BerapakahbilangansegitigayangBasilakanperoleh?Basil想把Figure1描绘的形状剪成如Figure2相同的三角形。请问他最多能剪出多少个？(A)8(B)12(C)14(D)15(E)16#9.Luishas7applesand2bananas.Hegives2applestoYuriwho,inreturngivesbananastoLuis.ThenLuishasasmanyapplesasbananas.HowmanybananasdidYurigivetoLuis?Luismempunyai7bijiepaldan2bijipisang.Diamemberi2bijiepalkepadaYuri,laluYurimemberibeberapabijipisangkepadaLuis.Luissekarangmempunyaibilanganepaldanpisangyangsamabanyak.BerapakahbilanganpisangyangdiberikanolehYurikepadaLuis?Luis拥有7个苹果和两条香蕉。他把两个苹果给了Yuri。作为回报，Yuri给了Luis香蕉。现在Luis拥有相同数量的香蕉和苹果。请问Yuri之前共给了Luis多少条香蕉呢？(A)2(B)3(C)4(D)5(E)7#10.Jackbuiltacubeusing27smallcubeswhicharecoloredeitherblackorwhite(seefigure).Notwoofthesmallcubeswhicharecoloredinthesamecolorhaveacommonface.HowmanywhitecubesdidJackuse?Jackmembinasebuahkiubmenggunakan27kiubkecilyangberwarnasamaadahitamatauputih(rujukgambarajah).Duakiubyangsamawarnatidakmempunyaipermukaanyangbersentuh.BerapakahbilangankiubputihyangdigunakanolehJack?Jack用了27个黑和白的小立方体建了一个立方体（如图）。没有任何两个颜色相同的小立方体相邻地被放在任何一面。请问Jack共用了多少个小的白立方体？(A)10(B)12(C)13(D)14(E)154,KangarooMathCompetition2015–Ecolier5,KangarooMathCompetition2015–Ecolier6,KangarooMathCompetition2015–Ecolier7,KangarooMathCompetition2015–Ecolier#17.Peterhastenballs,numberedfrom0to9.Hedistributedtheseballsamongthreefriends:Johngot3balls,George4andAnn3.Thenheaskedeachofhisfriendstomultiplythenumbersontheballstheygotandtheresultswere:0forJohn,72forGeorgeand90forAnn.WhatisthesumofthenumbersontheballsthatJohnreceived?Petermemilikisepuluhbijibola,bernombor0hingga9.Diamengagihkansemuabolatersebutkepadatigaorangrakannya:Johnmendapat3bijibola,Georgemendapat4danAnnmendapat3.Diakemudianmemintarakan-rakannyauntukmendarabkannombor-nomboryangterterapadabolayangmerekaterima.Hasilnyaialah:Johnmendapat0,Georgemendapat72,danAnnmendapat90.Apakahhasiltambahnombor-nomborpadabolayangditerimaolehJohn?Peter拥有是个球，标注着0至9。他把球全分给了他三个朋友，John得到3个，George得到了4个，Ann得到了3个。之后他要求他每个朋友找出球上号码的积。结果John得到0，George得到72，Ann得到90。请问John手上的球的号码的和是？(A)11(B)12(C)13(D)14(E)15#18.Threeropesarelaiddownonthefloorasshown.Youcanmakeonebig,completeloopwiththreeotherpiecesofrope.Whichoftheropesshownwillgiveyouonebigloop?Tigautastalidiletakkandiataslantaisepertidalamgambar.Andabolehmenghasilkansatugelungtaliyangbesardanlengkapdenganmencantumkantali-talitersebutbersamatigautastaliyanglain.Yangmanakahdiantaratali-taliberikutmemberikanandasatugelungtaliyangbesar?三根绳子被平放在地上（如图）。如果你可以用另外三条绳子接成一个完整的环路，请问哪些绳子能让你完成一个大环路？(A)(B)(C)(D)(E)8,KangarooMathCompetition2015–Ecolier答案：EAEBEBADBCBDCACDECDC9,KangarooMathCompetition2016{Ecolier3points#1.Amy,Bert,Carl,DorisandErnsteachrolledtwodiceandaddedthenumberofdots.Whorolledthelargesttotal?Amy,Bert,Carl,DorisdanErnstmelambungkanduabuahdadudanmerekodkanjumlahyangditerima.Siapakahyangmempunyaijumlahtertinggi?Amy,Bert,Carl,Doris和Ernst各掷了两颗骰子并把两个骰子的点数相加起来.请问谁的点数之和最大?AmyBertCarlDorisErnst(A)Amy(B)Bert(C)Carl(D)Doris(E)Ernst#2.SmallKangais7weeksand2daysold.Inhowmanydayswillhebe8weeksold?SmallKangaberumur7minggudan2hari.Berapaharilagikahdiaakanberumur8minggu?小Kanga现在7个星期又2天大.在多少天以后Kanga将会是8个星期大?(A)1(B)2(C)3(D)4(E)5#3.17+320–16+?(A)24(B)28(C)36(D)56(E)801,KangarooMathCompetition2016{Ecolier#4.WhatdoesPiposeewhenhelooksathimselfinthemirror?ApakahyangdilihatolehPipoapabiladiamelihatdirinyapadacermin?Pipo照镜子时将看见什么?(A)(B)(C)(D)(E)#5.Geogoeswithhisfathertoacircus.Theirseatsarenumbered71and72.Whichwayshouldtheygo?Geodanayahnyapergikepertunjukansarkas.Tempatdudukmerekabernombor71dan72.Kearahmanakahmerekaperlupergi?Geo和他的爸爸去观赏一个马戏团.他们的座位编号为71和72.他们应该向哪个方向走去?(A)(B)(C)(D)(E)2,KangarooMathCompetition2016{Ecolier#6.Annasharessomeapplesbetweenherselfand5friends(atotalof6people).Everyonegetshalfofanapple.Howmanyapplesdoessheshare?Annaberkongsibeberapabijiepalantaradirinyadan5orangrakannya(sejumlah6orangkesemuanya).Setiaporangmenerimasetengahbijiepal.BerapakahbilanganepalyangdikongsiolehAnna?Anna与她的5位朋友(共6人)一起分享苹果.每人各获得半粒苹果.请问她共分享了多少粒苹果?(A)21(B)3(C)4(D)5(E)62#7.Arectangleispartlyhiddenbehindacurtain.Whatshapeisthehiddenpart?Suatusegiempattepatterlindungsebahagiannyadisebaliklangsir.Apakahbentukbahagianyangterlindung?一个长方形的一部分藏在一个窗帘后面.被隐藏的部分是什么形状?(A)Triangle/Segitiga/三角形(B)Square/Segiempatsama/正方形(C)Hexagon/Heksagon/六边形(D)Circle/Bulatan/圆形(E)Rectangle/Segiempattepat/长方形#8.Thesumofthedigitsoftheyear2016isequalto2+0+1+6=9.Whatisthenearestyear,after2016,wherethesumofthedigitsoftheyearisequalto9again?Hasiltambahdigit-digitbagitahun2016ialah2+0+1+6=9.Apakahtahunyangterdekat,selepas2016,apabilahasiltambahdigitnyajugabersamaan9?年份2016的数字之和为2+0+1+6=9.请问2016年之后下一个有数字之和同样为9的是哪一年?(A)2007(B)2025(C)2034(D)2108(E)21343,KangarooMathCompetition2016{Ecolier#9.Themousewantstoescapefromthemaze.Howmanydierentpathscanthemousetakewithoutpassingthroughthesamegatemorethanonce?Seekortikusinginmelarikandiridarisuatuperangkap.Berapakahbilanganlaluanyangbolehdiambilnyatanpamelaluipagaryangsamalebihdaripadasekali?图片中这只老鼠想逃出迷宫.该老鼠在不经过同样的门超过一次的情况下有几条路线能使它成功逃脱?(A)2(B)4(C)5(D)6(E)7#10.Zoehastwocards.Shewroteanumberonbothsidesofeachcard.Thesumofthetwonumbersontherstcardisequaltothesumofthenumbersonthesecondcard.Thesumofthefournumbersis32.Whatcouldbethetwonumbersonthesidesthatwecannotsee?Zoemempunyaiduakad.Diamenulissatunomborpadakedua-duapermukaanbagisetiapkadtersebut.Hasiltambahduanomborpadakadpertamaadalahsamadenganhasiltambahduanomborpadakadkedua.Hasiltambahempatnombortersebutialah32.Apakahduanomborpadapermukaan-permukaankadyangtidakditunjukkan?Zoe有两张卡.她在每一张卡的两面都各写了一个数目.已知第一张卡的两个数目之和与第二张卡的两个数目之和相等.这两张卡的四个数目之和为32.请问在我们所无法看见的面上的是下列哪两个数字?(A)7&0(B)8&1(C)11&4(D)9&2(E)6&34,KangarooMathCompetition2016{Ecolier4points#11.Fivechildrenhadapapersquare,apapertriangleandapapercircle.Everychildplacedtheirownpapersinapile,asshowninthepictures.Then,theteacherremovedallthepapercircles.Howmanypileshavethetriangleabovethesquare?Limaorangpelajardiberikansatupetakkertas,satusegitigakertas,dansatubulatankertas.Setiappelajarmenyusunbentuk-bentuktersebutsepertiyangditunjukkan.Kemudian,gurumerekamembuangsemuabulatankertas.Berapakahbilangansusunanyangmempunyaisegitigadiataspetak?五位孩子有一个纸正方形，一个纸三角形和一个纸圆形.如图所示，每位孩子都把自己的纸形状堆起来.接着,老师把所有的纸圆形移走.请问有几堆纸形状的三角形位于正方形之上?(A)0(B)1(C)2(D)3(E)4#12.Whichthreeofthevejigsawpiecesshowncanbejoinedtogethertoformasquare?Yangmanakahtigabentukdaripadalimabentukberikutyangdapatdicantumkanmenjadisatusegiempatsama?下列五片拼图中有哪三片可以结合起来拼成一个正方形?(A)1,3,5(B)1,2,5(C)1,4,5(D)3,4,5(E)2,3,55,KangarooMathCompetition2016{Ecolier#13.Loeshasstartedtowritesomenumbersinthetable.Shedecidesthateachrowandcolumnwillcontainthenumbers1,2and3exactlyonce.Whatisthesumofthenumbersthatshewillwriteinthetwoshadedsquares?Loestelahmenulisbeberapanombordidalamjadualberikut.Diainginmeletakkannombor1,2dan3tepatsatukalipadasetiaplajurdanbaris.Apakahhasiltambahnombor-nomboryangakanditulisdalamduapetakberlorek?Loes已经开始在桌子上写下一些数目,使得数字1,2,3都各出现在每一行,每一列正好一次.请问那两个写在涂黑格子里的数目之和为多少?(A)2(B)3(C)4(D)5(E)6#14.Havingturnedacardoverarounditsrightside,weseewhatisdrawninthegure.Whatshallweseeifweturnthiscardoverarounditsupperside?Apabilakitamembalikkansuatukadpadasisikanannya,apayangditunjukkanadalahsepertidalamgambarajahberikut.Apakahyangdilihatjikakadtersebutdibalikkanpadasisiatasnya?如果我们依据卡片的右边翻转该卡,则我们看见图中所画的一面.如果我们依据卡片的上边翻转该卡,请问我们看见下列哪一面?(A)(B)(C)(D)(E)6,KangarooMathCompetition2016{Ecolier#15.Tim,TomandJimaretriplets(threebrothersbornonthesameday).TheirbrotherPaulisexactly3yearsolder.Whichofthefollowingnumberscanbethesumoftheagesofthefourbrothers?Tim,TomdanJimadalahkembartiga(tigaadik-beradikyanglahirpadahariyangsama).AbangmerekaPauladalahtepat3tahunlebihtuadaripadamereka.Yangmanakahdiantaraberikutmungkinmerupakanhasiltambahumurempatorangadik-beradiktersebut?Tim,Tom和Jim是三胞胎(三位同一天出生的兄弟).他们的哥哥Paul比他们大正好3岁.下列哪个可能成为四兄弟的岁数之和?(A)25(B)27(C)29(D)30(E)60#16.Magictreesgrowinamagicgarden.Eachtreecontainseither6pearsand3apples,or8pearsand4apples.Thereare25applesinthegarden.Howmanypearsarethereinthegarden?Suatutamanajaibmempunyaibeberapapohonajaib.Setiappohonmempunyaisamaada6buahpirdan3buahepal,atau8buahpirdan4buahepal.Terdapat25buahepalditamantersebut.Berapakahbilanganbuahpiryangterdapatditamantersebut?魔幻树长在魔幻果园里.每棵树有6颗梨和3颗苹果,或8颗梨和4颗苹果.果园里共有25颗苹果.那么果园里共有多少颗梨?(A)35(B)40(C)45(D)50(E)567,KangarooMathCompetition2016{Ecolier#17.Mycatshave18morelegsthannoses.HowmanycatsdoIhave?Kucing-kucingpeliharaansayamempunyai18bilangankakilebihdaripadabilanganhidung.Berapaekorkahkucingyangsayapelihara?我有若干只猫.它们腿的总数量比鼻子的总数量多18只.请问我有多少只猫?(A)4(B)5(C)6(D)8(E)9#18.Racheladdssevennumbersandgets2016.Oneofthenumbersintheadditionis201.Shereplacesthenumber201with102.Whatanswerdoessheget?Rachelmenambahkantujuhnombordanmemperoleh2016.Salahsatunomboryangdi-tambahialah201.Diamenggantikannombor201dengan102.Apakahjawapanbaruyangdidapatinya?Rachel把七个数目加起来,得2016.七个数目当中,其中一个数目为201.她用102来取代201后再次把数目加起来.现在她会得到什么答案?(A)1815(B)1914(C)1917(D)2115(E)2118#19.Maltehasbuiltabarof27bricks.Hebreaksthebarintotwobarssuchthatoneofthemistwicethelengthoftheother.Thenhetakesoneofthenewbarsandbreaksitthesameway.Hecontinuesinthisway.Whichofthefollowingbarswillhenotbeabletoget?Maltemempunyaisatubongkahyangterdiridaripada27unit.Diamenceraikanbongkahtersebutkepadaduabongkahsupayabongkahpertamaadalahduakalilebihpanjangdaripadabongkahkedua.Kemudian,diamengambilsalahsatubongkahyangbarudanmenceraikannyadengancarayangsama.Diameneruskanberbuatdemikian.BongkahyangmanakahantaraMaltehasbuildabarof27legobricks.Maltehasbuildabarof27legobricks.Maltehasbuildabarof27legobricks.yangberikutyangtidakmungkindiperoleh?Malte用27块一模一样的砖块建造了一个砖条.他把该砖条切成两条,使得其中一条的Maltehasbuildabarof27legobricks.Maltehasbuildabarof27legobricks.长度为另一条的两倍.然后,他再把其中一条砖条依同样的方法再切成两条.他持续以相同的272727Maltehasbuildabarof27legobricks.方法切割砖条.请问他不可能取得下列哪项砖条?Hebreaksthebarintotwobarssuchthatoneofthemistwicethelengthoftheother.ThenHebreaksthebarintotwobarssuchthatoneofthemistwicethelengthoftheother.ThenHebreaksthebarintotwobarssuchthatoneofthemistwicethelengthoftheother.Then2727hetakesoneofthenewbarsandbreaksitthesameway.Hecontinuesthisway.hetakesoneofthenewbarsandbreaksitthesameway.Hecontinuesthisway.hetakesoneofthenewbarsandbreaksitthesameway.Hecontinuesthisway.Hebreaksthebarintotwobarssuchthatoneofthemistwicethelengthoftheother.ThenHebreaksthebarintotwobarssuchthatoneofthemistwicethelengthoftheother.ThenWhichofthefollowingbarsisnotpossibletogetthisway?Whichofthefollowingbarsisnotpossibletogetthisway?27Whichofthefollowingbarsisnotpossibletogetthisway?hetakesoneofthenewbarsandbreaksitthesameway.Hecontinuesthisway.hetakesoneofthenewbarsandbreaksitthesameway.Hecontinuesthisway.Hebreaksthebarintotwobarssuchthatoneofthemistwicethelengthoftheother.ThenWhichofthefollowingbarsisnotpossibletogetthisway?Whichofthefollowingbarsisnotpossibletogetthisway?hetakesoneofthenewbarsandbreaksitthesameway.Hecontinuesthisway.(AA))2B)A)42C)(BB))A)642B)C)D)468(CC))D)6E)810D)E)810Whichofthefollowingbarsisnotpossibletogetthisway?A)2A)2B)4B)4C)6C)6(DD))8D)8E)(10EE))10A)2B)4C)6D)8E)108111111,KangarooMathCompetition2016{Ecolier#20.Fivesparrowssitonabranch,asshowninthegure.Eachsparrowchirpsthesamenumberoftimesasthenumberofsparrowsitsees.Forexample,Davidchirpsthreetimes.Then,onesparrowturnstolookintheoppositedirection.Again,eachofthesparrowschirpsthesamenumberoftimesasthenumberofsparrowsitsees.Thistime,thetotalnumberofchirpsismorethanthersttime.Whichofthesparrowshasturnedtolookintheoppositedirection?Limaekorburungsedanghinggappadasuatudahan,sepertidalamgambarajahberikut.Setiapburungberkicausamabanyakkalidenganbilanganburungyangdilihatnya.Contohnya,Davidberkicausebanyaktigakali.Kemudian,seekorburungmenolehpandangannyakearahyangberlawanan.Sekalilagi,setiapburungberkicausamabanyakkalidenganbilanganburungyangdilihatnya.Padakaliini,bilangankicauanadalahlebihbanyakdaripadakalipertama.Burungyangmanakahyangtelahmenolehpandangannyakearahyangberlawanan?如图,五只麻雀坐在树枝上.每只麻雀的呼叫次数相等于它所看见麻雀的数量.举例:David呼叫三次.接着,一只麻雀转头看向另一边.与之前一样,每只麻雀的呼叫次数相等于它所看见麻雀的数量.现在,呼叫的总数量比第一次多.请问哪只麻雀转头看向另一边?(A)Angel(B)Bertha(C)Charlie(D)David(E)EglioENDOFPAPER答案：EEAADBABBCDACDBDCCEB9,KangarooMathCompetition2017{Ecolier3points#1.Whichpiececanbeplacedbetweentheabovetwopiecessotheequationsarecorrect?Bahagianyangmanakahbolehdiletakkandiantarakedua-duabahagiandiatassupayapersamaannyabenar?请问哪一块拼图能被放在以下两块拼图之间，以获得正确的等式？8–3=2=55–1=34–2(A)(B)=51+2=45–3(C)(D)=51+1(E)1,KangarooMathCompetition2017{Ecolier#2.Johnlooksthroughthewindow.Heseeshalfofthekangaroosinthepark,asinthepicture.Howmanykangaroosarethereinthepark?Johnmelihatkeluartingkap.Dianampakseparuhdaripadasekumpulankanggaruditaman,sepertiditunjukkanpadagambarberikut.Berapakahbilangankanggaruyangadaditamantersebut?John往窗外看。他看见公园里一半的袋鼠，如图所示。请问公园里有多少只袋鼠？(A)12(B)14(C)16(D)18(E)20#3.Apictureoffootprintswasturnedupsidedown.Whichfootprintsaremissing?Suatugambaryangmengandungibeberapakesantapakkakitelahditerbalikkan.Kesantapakkakiyangmanakahtelahhilang?一张含有多双脚印的图片被上下颠倒。请问哪一双脚印不见了？(A)(B)(C)(D)(E)211111,KangarooMathCompetition2017{Ecolier#4.Whatnumberishiddenbehindthepanda?Nomborapakahyangtersembunyidisebalikpandatersebut?请问熊猫后面藏着什么数字？+8+810+6=–6=–10==A(A)16(B)18(C)20(D)24(E)28#5.Thefollowingisanadditiontable,withsomenumbershidden.Whatnumberisintheboxwiththequestionmark?Berikutmerupakanjadualbagioperasitambah,denganbeberapanomboryangtersembunyi.Apakahnomboryangterletakpadakotakyangbertandasoal?以下是一个不完整的加法表。请问含有问号的格子里是什么数字？+1172617138?11(A)10(B)12(C)13(D)15(E)163,KangarooMathCompetition2017{Ecolier#6.Inthegurebelowweseeanecklacewithsixbeads.Whichoneisthesamenecklace?Gambardibawahmenunjukkansaturantaidenganenambijimanik.Rantaiyangmanakahsamadenganrantaipadagambartersebut?如图所示，我们看见一条含有六颗珠子的项链。请问下列哪项是同一条项链？(A)(B)(C)(D)(E)4,KangarooMathCompetition2017{Ecolier#7.ThepictureshowsthefrontofAnn'shouse.Thebackofherhousehasthreewindowsandnodoor.WhatdoesAnnseewhenshelooksatthebackofherhouse?GambarberikutmenunjukkanbahagianhadapanrumahAnn.Bahagianbelakangrumahnyaadatigatingkapdantiadapintu.ApakahyangdilihatolehAnnapabiladiamelihatbahagianbelakangrumahnya?下图展示Ann的家的前方。她的家后方有三个窗口，并且没有门。请问Ann看她的家的后方时会看见什么？(A)(B)(C)(D)(E)5,KangarooMathCompetition2017{Ecolier#8.Whichoneistrue?Yangmanakahbenar?请问下列哪项是正确的？(A)(B)(C)(D)(E)#9.Balloonsaresoldinpacketsof5,10and25.Mariusbuysexactly70balloons.Whatisthesmallestnumberofpacketshecouldbuy?Belon-belontelahdibungkuskedalampaketyangmengandungi5belon,10belondan25belonuntukjualan.Mariusmembelitepat70belon.Berapakahbilanganpaketpalingsedikityangbolehdibelinya?气球以每包5粒、10粒和25粒的形式出售。Marius买了恰好70粒气球。请问他最少买了多少包？(A)3(B)4(C)5(D)6(E)76,KangarooMathCompetition2017{Ecolier#10.Bobfoldedapieceofpaper.Hecutoneholeinthepaper.Thenheunfoldedthepieceofpaper.Theresultisasshowninthepicture.HowdidBobfoldhispieceofpaper?Bobmelipatsekepingkertas.Diamenebuksatulubangpadakertastersebut.Kemudiandiamembukalipatanitusemula.Hasilnyaditunjukkanpadagambarberikut.BagaimanakahBobmelipatkertastersebut?Bob把一张纸折起来。他在纸上剪了一个洞。接着，他把那一张纸打开来，结果如图所示。请问Bob起初如何折那一张纸？(A)(B)(C)(D)(E)7,KangarooMathCompetition2017{Ecolier4points#11.Thereisatournamentatthepool.First,13childrensignedup.Andthen,another19childrensignedup.Sixteamswithanequalnumberofmembersareneededforthetournament.Atleasthowmanymorechildrenneedtosignup,sothatthetournamentcanstart?Satupertandingandiadakandikolamrenang.Padaawalnya,13muridtelahmendaftar.Kemudian,19muridlagitelahmendaftar.Pertandinganakandimulakansekiranyaterdapatenampasukandenganbilanganmuridyangsama.Berapakahbilanganmuridpalingsedikityangperluditambahkansupayapertandinganitubolehdimulakan?泳池有一个比赛。起初，13位小孩报名参加。之后，另外19位小孩报名参加。比赛需要六组，每组必须含有等量成员。请问至少还需要多少位小孩报名，比赛才能开始？(A)1(B)2(C)3(D)4(E)5#12.Numbersareplacedinthe44squareshowninthepicturebelow.Marywantstonda22squarewherethesumofthenumbersisthelargest.Whatisthatsum?Beberapanombordiisikandidalamkotak44sepertipadagambarberikut.Marymahumencarikotak22yangmempunyaihasiltambahnomboryangpalingbesar.Apakahhasiltambahtersebut?如图所示，数字被填入一个44平方。Mary想要找一个22平方，使得那22平方内数字之和是最大的。请问那一个和是多少？(A)11(B)12(C)13(D)14(E)158,KangarooMathCompetition2017{Ecolier#13.Davidwantstocook5disheswithonly2stoves.Thetimesneededtocookthe5dishesare40minutes,15minutes,35minutes,10minutesand45minutes.Hemayonlyremoveadishfromastovewhenitiscooked.Whatistheshortesttimeinwhichhecancookallofthedishes?Davidmahumemasak5laukdenganmenggunakan2dapurgassahaja.Masayangdiper-lukanuntukmemasaksetiaplaukialah40minit,15minit,35minit,10minitdan45minit.Diahanyabolehmemindahkanlaukdariatasdapurgasapabilalauktersebuttelahmasaksepenuh-nya.Berapakahmasaterpendekyangdiperlukanuntukmemasakkesemualauktersebut?David想要烹饪5道菜肴，但他只有2个火炉。烹饪菜肴所需的时间分别为40分钟、15分钟、35分钟、10分钟以及45分钟。他只能在一道菜肴烹饪完后，才把它从火炉上拿下。请问他至少需要多少时间来烹饪所有菜肴？(A)60min(B)70min(C)75min(D)80min(E)85min#14.Whichnumbershouldbewritteninthecirclecontainingthequestionmark?Nomboryangmanakahsepatutnyaditulispadabulatanyangmempunyaitandasoal?请问哪一个数字应该被填在含有问号的圆圈里？-15x4+4+6?x0(A)10(B)11(C)12(D)13(E)149,KangarooMathCompetition2017{Ecolier#15.Thepictureshowsagroupofbuildingblocksandtheplanofthatgroup.Someinkhasdrippedontotheplan.Whatisthesumofthenumbersundertheinkblots?Gambardibawahmenunjukkanbinaanbatubatadanpelanbinaantersebut.Beberapatitisandakwattelahtertumpahdiataspelantersebut.Apakahhasiltambahnombor-nomboryangtersembunyidibawahtitisandakwattersebut?下图展示一组积木以及它的平面图。一些墨汁被滴在平面图上了。请问墨迹下面的数字之和是什么？3411131(A)3(B)4(C)5(D)6(E)710,KangarooMathCompetition2017{Ecolier#16.Howlongisthetrain?Berapakahpanjangkeretaapitersebut?请问这列火车有多长?(A)55m(B)115m(C)170m(D)220m(E)230m11,KangarooMathCompetition2017{Ecolier#17.Georgestartshisfootballtrainingat5.00pm.Thejourneyfromhishousetothebusstoptakes5minutes.Thebusjourneytakes15minutes.Ittakeshim5minutestogofromthisbusstoptothetrainingeld.Atwhattimedoeshehavetoleavehishousetoarriveatthetrainingeldexactlyontime?Georgememulakanlatihanbolasepakpadapukul5.00pm.Perjalanandarirumahnyakeperhentianbasmengambilmasa5minit.Perjalananbaspulamengambilmasa15minit.Beliauperluberjalankaki5minitlagiuntuksampaikepadanglatihandariperhentianbas.Padapukulberapakahdiaperlukeluardarirumahnyasupayadiatibadipadanglatihantepatpadamasanya?George在5.00pm开始足球训练。从他的家到巴士站的行程为5分钟。巴士行程为15分钟。下巴士之后，他得步行5分钟以到达训练场地。请问他必须在什么时间从家里出发，以准时到达训练场地？(A)(B)(C)(D)(E)#18.Asmallzoohasagirae,anelephant,alionandaturtle.Susanwantstoplanatourwhereshesees2dierentanimals.Shedoesnotwanttostartwiththelion.Howmanydierenttourscansheplan?Terdapatseekorzirafah,seekorgajah,seekorsingadanseekorpenyudidalamsebuahzoo.Susaninginmerancangsatulawatanuntukmelihat2haiwanyangberbeza.Diatidakmahubermuladenganmelihatsingaterlebihdahulu.Berapakahbilanganlawatanyangbolehdirancangnya?一个小型动物园拥有一只长颈鹿、一头大象、一头狮子以及一只龟。Susan想要安排一个行程，以让她游览2种不一样的动物。她不想从狮子开始。请问她能安排多少个不一样的行程？(A)3(B)7(C)8(D)9(E)1212,KangarooMathCompetition2017{Ecolier#19.Fourbrothershaveeaten11cookiesintotal.Eachofthemhaseatenatleastonecookie.Notwoofthemhaveeatenthesamenumberofcookies.Threeofthemhaveeaten9cookiesintotalandoneofthemhaseatenexactly3cookies.Howmanycookieshavebeeneatenbytheboywhohaseatenthelargestnumberofcookies?Empatorangadik-beradiktelahmemakansejumlah11biskut.Setiaporangtelahmemakansekurang-kurangnyasatubiskut.Tiadaduaorangyangtelahmemakanbilanganbiskutyangsama.Tigaorangdaripadamerekatelahmemakansejumlah9biskutdansalahseorangdaripadamerekatelahmemakan3biskut.Berapakahbilanganbiskutyangtelahdimakanolehorangyangtelahmemakanpalingbanyakbiskut?四位兄弟一共吃了11块曲奇饼。每一位吃了至少一块曲奇饼，而且没有两位吃了等量的曲奇饼。其中三位一共吃了9块曲奇饼，而其中一位吃了3块曲奇饼。请问吃最多曲奇饼的男孩吃了多少块曲奇饼？(A)3(B)4(C)5(D)6(E)7#20.Tenbagseachcontainadierentnumberofcandiesfrom1to10.Thereare5boys.Eachboytooktwobagsofcandies.Alexgot5candies,Bobgot7candies,Charlesgot9candies,andDennisgot15candies.HowmanycandiesdidEricget?Terdapatsepuluhbegdansetiapbegmengandungibilangangula-gulayangberbezadaripada1hingga10.Terdapat5budaklelaki.Setiapdaripadamerekamendapatduabeggula-gula.Alexmendapat5gula-gula,Bobmendapat7gula-gula,Charlesmendapat9gula-gula,danDennismendapat15gula-gula.Berapakahgula-gulayangEricdapat?十个袋子里各包含不一样数量的糖果，从1粒到10粒。有5位男孩，而每一位拿了两个袋子。Alex拿到了5粒糖果、Bob拿到了7粒糖果、Charles拿到了9粒糖果以及Dennis拿到了15粒糖果。请问Eric拿到多少粒糖果？(A)9(B)11(C)13(D)17(E)19ENDOFPAPER答案：EACAEAEEBCDDCDCBADCE13,KangarooMathCompetition2018{Ecolier3points#1.Leoniehas10rubberstamps.Eachstamphasoneofthedigits:0,1,2,3,4,5,6,7,8and9.ShestampsthedateoftheKangaroocontestbelow.Howmanystampsdoessheuse?Leoniemempunyai10cop.Setiapcopmempunyaisalahsatudigitberikut:0,1,2,3,4,5,6,7,8dan9.DiamengecoptarikhbagipertandinganKangaroosepertiberikut.Berapakahbilangancopyangdigunakan?Leonie有10个橡皮图章。每个图章拥有0，1，2，3，4，5，6，7，8，9的其中一个数字。如下图所示，她把Kangaroo比赛的日期印了出来。请问她一共用了多少个图章？15032018(A)5(B)6(C)7(D)9(E)10#2.Thepictureshows3 yingarrowsand9xedballoons.Whenanarrowhitsaballoon,theballoonburstsandthearrow iesfurtherinthesamedirection.Howmanyballoonsintotalarehitbyarrows?Gambarberikutmenunjukkan3anakpanahyangberterbangandan9belonyangtidakbergerak.Apabilasuatuanakpanahmengenaisuatubelon,belontersebutakanpecahdananakpanahtersebutakanterusterbangpadaarahyangsama.Berapakahjumlahbilanganbelonyangakandipecahkanolehanakpanah?下图显示3支飞箭和9粒固定的气球。当一支箭击中一粒气球，那粒气球会爆裂，而箭会继续往同样的方向飞行。请问一共多少粒气球会被飞箭击中？(A)2(B)3(C)4(D)5(E)61,KangarooMathCompetition2018{Ecolier#3.Susanis6yearsold.Susan'sbrotherisoneyearolder.Susan'ssisterisoneyearyounger.Whatisthesumoftheagesofthethreesiblings?Susanberumur6tahun.AbangSusanadalahsetahunlebihtua.AdikperempuanSusanadalahsetahunlebihmuda.Apakahhasiltambahumurbagitigaadik-beradiktersebut?Susan今年6岁。Susan的哥哥比她大一岁。Susan的妹妹比她小一岁。请问三个兄弟姐妹的岁数之和为多少？(A)10(B)15(C)18(D)21(E)30#4.Thegureshowsvescrewsinawoodenblock.Fourofthescrewsarethesamelength,andtheotherscrewisshorter.Whichscrewistheshortest?Rajahberikutmenunjukkanlimaskrudalamsatublokkayu.Empatdaripadaskrutersebutadalahsamapanjang,manakalasatulagiskruadalahlebihpendek.Skrumanakahyangpalingpendek?下图显示一片木块里的五条螺丝。四条螺丝的长度是相同的，并且另外一条是较短的。请问哪一条螺丝最短？(A)1(B)2(C)3(D)4(E)5#5.HereisapictureofSophietheLadybird.WhichpictureisnotSophie?GambarinimenunjukkanSophiesangKumbang.GambarmanakahbukanmenunjukkanSophie?这是瓢虫Sophie的一张图片。请问下列哪项不是Sophie？(A)(B)(C)(D)(E)2,KangarooMathCompetition2018{Ecolier#6.Lucyfoldsasheetofpaperinhalf.Thenshecutsapieceoutofitasshown.Whatwillsheseewhensheunfoldsthepaper?Lucymelipatsekepingkertasmenjadiseparuh.Kemudiandiamemotongsebahagiandaripadakertastersebutsepertiditunjukkan.Apakahyangakandilihatolehnyaapabiladiamembukalipatankertastersebut?Lucy把一张纸对折一半。接着，她把纸上的一部分剪出来，如下图所示。请问她把纸打开后会看见什么？(A)(B)(C)(D)(E)#7.Dianatakespartinanarcherycontest.Onherrstturn,Dianascores12pointswiththreearrows(leftgure).Onhersecondturn,shescores15points(middlegure).Howmanypointsdoesshescoreonherthirdturn(rightgure)?Dianamengambilbahagiandalampertandinganmemanah.Padagiliranyangpertama,Dianamendapat12markahdengantigaanakpanah(rajahkiri).Padagiliranyangkedua,diamendapat15markah(rajahtengah).Berapakahmarkahyangdidapatinyapadagiliranyangketiga(rajahkanan)?Diana参加一个射箭比赛。在第一回合，Diana以三支箭得了12分（左图）。在第二回合，她得了15分（中图）。请问她在第三回合得了多少分（右图）？(A)18(B)19(C)20(D)21(E)223,KangarooMathCompetition2018{Ecolier#8.Mikesetsthetablefor8guests.Hewantstoserveeachguestwiththecorrectarrangement,whichmeansaforkontheleftofeachplateandaknifeontheright.Howmanyguestsgetthecorrectarrangement?Mikemenyiapkanmejamakanuntuk8orangtetamu.Diamahumenghidangkansetiaptetamudengansusunanyangbetul,iaitugarfudisebelahkiripinggandanpisaudisebelahkanan.Berapakahramaikahtetamuyangmendapatsusunanyangbetul?Mike为8位客人准备餐桌。他想要以正确的排列招待客人，那就是每个碟子的左边是个叉子，右边是把刀。请问多少位客人会拿到正确的排列？(A)2(B)3(C)4(D)5(E)6#9.Robertomakesdesignsusingtileslikethis.Howmanyofthedesignsbelowcanhemake?Robertomembuatpelbagairekabentukmenggunakanbeberapajubinsepertiberikut.Berapakahbilanganrekabentukdibawahyangbolehdibuatolehnya?Roberto使用以下的瓷砖制造图案。请问，在以下的图案之中，他能制造多少个？(A)1(B)2(C)3(D)4(E)54,KangarooMathCompetition2018{Ecolier#10.Albertllstheboxeswiththesevegures.Eachgureappearsonceineverycolumnandeveryrow.Someguresarenotshown.WhichguremustAlbertputintheboxwiththequestionmark?Albertmengisikotak-kotakberikutmenggunakanlimagambarberikut.Setiapgambarmunculsekalisahajapadasetiaplajurdansetiapbaris.Beberapagambartidakditunjukkan.GambarmanakahyangmestiAlbertisikanpadakotakdengantandasoal?Albert用以下五个图形填满格子。每个图形在每一行和每一列出现一次。一些图形没被显示。请问Albert必须把什么图形放进拥有问号的格子里？?(A)(B)(C)(D)(E)5,KangarooMathCompetition2018{Ecolier4points#11.Tomhastwotypesofpiecesasshowningray.WhatisthenumberofpiecesthatTomneedsinordertomaketheshapeoftheboatinthegurebelow?Tommempunyaiduajenisbentuksepertiyangditunjukkandenganwarnakelabu.BerapakahbilanganbentukyangdiperlukanolehTomuntukmembuatbentukbotsepertiditunjukkanpadarajahdibawah?Tom有两种板块，如下图中以灰色展示。请问Tom需要多少片板块，以制造下图中船的形状？(A)5(B)6(C)7(D)8(E)9#12.Thecoloursinthisgureareinverted.Thenthegureisrotatedaround.Whatdoesthenewgurelooklike?Rajahinitelahdisongsangkanwarnanya.Kemudian,rajahinitelahdiputarkan.Apakahruparajahbaruyangterhasil?图片中的颜色被调换。接着，图片被旋转。请问新的图片会是什么？(A)(B)(C)(D)(E)6111111,KangarooMathCompetition2018{Ecolier#13.PetatheRabbithas20carrots.Sheeats2carrotseveryday.Sheatethe12thcarrotonWednesday.Onwhichdaydidshestarteatingthecarrots?PetasangArnabmempunyai20bijilobak.Iamemakan2bijilobaksetiaphari.Iamemakanlobakke-12padahariRabu.Padahariapakahdiamulamemakanlobaktersebut?兔子Peta有20条胡萝卜。她每天吃2条胡萝卜。她在星期三吃了第12条胡萝卜。请问她在星期几开始吃胡萝卜？(A)Monday/Isnin/星期一(B)Tuesday/Selasa/星期二(C)Wednesday/Rabu/星期三(D)Thursday/Khamis/星期四(E)Friday/Jumaat/星期五#14.Thereare8 owersinagarden.Someinsects(butter iesanddragon ies)sitonthe owers.Thereisnomorethanoneinsectper ower.Morethanhalfofthe owersareoccupied.Thenumberofbutter iesonthe owersistwicethenumberofdragon iesonthe owers.Howmanybutter iessitonthe owers?Terdapat8bungadidalamsuatutaman.Beberapaserangga(rama-ramadanpepatung)telahhinggappadabunga-bungatersebut.Terdapattidaklebihdarisatuseranggapadasetiapbunga.Lebihseparuhdaripadabungatersebuttelahdihinggapiserangga.Bilanganrama-ramayanghinggappadabungaadalahduakalibilanganpepatungyanghinggappadabunga.Berapakahbilanganrama-ramayanghinggappadabunga?花园里有8朵花。一些昆虫（蝴蝶和蜻蜓）坐在花朵上。每朵花上不超过一只昆虫。多于一半的花朵被占据。花朵上的蝴蝶是花朵上的蜻蜓的两倍。请问多少只蝴蝶坐在花朵上？(A)2(B)3(C)4(D)5(E)67,KangarooMathCompetition2018{Ecolier#15.CaptainKooksailsfromEasterthrougheveryislandandbacktoEaster.Thetotaljourneyis100km.ThedistancebetweenDesertandLakeisthesameasthedistancebetweenEasterandFlowerviaVolcano.HowfarisitfromEastertoLake?KaptenKookberlayardariEastermelaluisemuapulaudankembalisemulakeEaster.Jarakperjalanantersebutialah100km.JarakantaraDesertdanLakeadalahsamadenganjarakantaraEasterdanFlowermelaluiVolcano.BerapakahjarakdariEasterkeLake?Kook船长从Easter驶过每座岛，再回去Easter。旅程一共为100km。Desert和Lake之间的距离与从Easter通过Volcano去Flower的距离一样。请问Easter和Lake之间的距离为多少？Flower15DesertVolcano1726EasterLake(A)17km(B)23km(C)26km(D)33km(E)35km#16.TheroomsinKanga'shousearenumbered.BabyRooentersthemaindoor,passesthroughsomeroomsandleavesthehouse.Thenumbersoftheroomsthathevisitsarealwaysincreasing.Throughwhichdoordoesheleavethehouse?SetiapbilikdidalamrumahKangaadalahbernombor.BabyRoomasukdaripintuutama,melaluibeberapabilikdankeluardarirumahtersebut.Nomborbagibilik-bilikyangdilaluinyasentiasameningkat.Daripintumanakahdiakeluardarirumahtersebut?Kanga的屋子里的房间都是被标上号码的。BabyRoo进入大门，通过一些房间，并离开屋子。他经过的房间的号码都一直在增加。请问他从哪一扇门离开屋子？(A)A(B)B(C)C(D)D(E)E8,KangarooMathCompetition2018{Ecolier#17.Fourballseachweigh10g,20g,30gand40g.Whichballweighs30g?Empatbolamempunyaiberat10g,20g,30gdan40g.Bolayangmanakahmempunyaiberat30g?四粒球的重量分别为10g，20g，30g，和40g。请问哪粒球的重量为30g？CDBDCAB(A)A(B)B(C)C(D)D(E)cannotbedetermined/tidakbolehditentukan/不能确定#18.Thebandshowninthegurecanbefastenedinveways.Forexample,thegurebelowshowsthebandfastenedinonehole.Howmuchlongeristhebandfastenedinoneholethanthebandfastenedinallveholes?Pitayangditunjukkanpadarajahberikutbolehdikancingdenganlimacara.Sebagaicontoh,rajahdibawahmenunjukkanpitatersebutdikancingpadasatulubang.Berapakahbezapanjangpitayangdikancingpadasatulubang,denganpitayangdikancingpadakesemualimalubang?图中显示的带有五种固定方法。举例来说，下图显示使用一个洞固定的带。请问，使用一个洞固定的带会比使用五个洞固定的带长多少？(A)4cm(B)8cm(C)10cm(D)16cm(E)20cm91,KangarooMathCompetition2018{Ecolier#19.Thelargerectangleiscutintosquaresofvarioussizes.Thethreesmallestsquareseachhaveanareaof1.Whatistheareaofthelargerectangle?Segiempattepatyangbesarberikutdibahagikankepadabeberapasegiempatsamadengansaizyangpelbagai.Tigasegiempatsamayangpalingkecilmasing-masingmempunyailuas1.Apakahluassegiempattepatyangbesartersebut?大长方形被切割成不同大小的正方形。三个最小的正方形的面积各为1。请问大长方形的面积为多少？(A)165(B)176(C)187(D)198(E)200#20.Inavideogame,thenalenemyisanevilrobotwithmanyheads.Todefeattherobot,wehavetocutallitsheads.Ifwecut3heads,onenewheadwillgrow.Wecanonlydefeattherobotbycuttingo13headsintotal.Howmanyheadsdidtherobothaveinthebeginning?Dalamsatupermainanvideo,musuhterakhirnyaialahsuaturobotdenganbeberapakepala.Untukmenewaskanrobottersebut,kitaperlumemotongsemuakepalanya.Jikakitamemotong3kepala,satukepalabaruakanmuncul.Kitahanyabolehmenewaskanrobottersebutdenganmemotong13kepalakesemuanya.Berapakahbilangankepalarobottersebutpadaawalnya?在电子游戏中，最后的敌人是一个有许多头的邪恶机器人。为了打败机器人，我们必须切断它所有的头。如果我们切断三个头，一个新的头会长出来。我们只能通过总共切断13个头来打败机器人。请问机器人一开始有多少个头？(A)8(B)9(C)10(D)11(E)12ENDOFPAPER答案：BECEDDDDDABEECDDCBDB10,,,,,,,,,,MathKangaroo2019AnswerKeyQuestion#Level1&2Level3&4Level5&6Level7&8Level9&10Level11&121DEBEDA2CCCEBE3CACCEE4EDEDCD5BAEDBC6CADDBB7ADDACB8CBCBBC9EBBDAD10BCAABD11ACCACD12EECBCB13BBCEEE14BABBBE15EDACDD16DDCCBC17DEBDAA18ACCBCB19DBACDA20BEDCEE21CBCBAB22DEEBEB23ABDCBC24CDCEDE25BECA26BACD27DCDE28AEBC29DEAB30CDCC,KangarooMathCompetition2020(China)–Ecolier?3points#1.Amushroomgrowseveryday.MarytakesapictureofthemushroomeachdayfromMondaytoFriday.WhichofthesepictureswastakenonTuesday?蘑菇每一天都在成长，小丽从星期一到星期五每天都会给蘑菇拍照，以下哪张照片是在星期二拍摄的？?(A)(B)(C)(D)(E)#2.Whichpiececompletesthepattern?以下哪一块拼图能够拼成完整的图案?1???1?1(A)(B)(C)(D)(E)#3.Timshadesallthesquaresinthegridwheretheresultis20.Whichpatterndoesheget?如图显示，小庭将答案为20的格子涂上阴影。以下哪一个是他的答案?16+419+128−812×1016−47×3(A)(B)(C)(D)(E)111,KangarooMathCompetition2020(China)–Ecolier#4.Whichofthefollowinggureshasthelargestshadedarea?如图显示，以下哪个图的阴影面积最大?(A)(B)(C)(D)(E)#5.Whichoneoftheguresbelowcanyoumakewiththesepieces?如图所示，用以下的图形碎片可以制作出哪个选项中的图形?(A)(B)(C)(D)(E)2,KangarooMathCompetition2020(China)–Ecolier#6.Ellidrawsthissquarewithchalkonthepavement.Shestartsjumpingfromnumber1.Eachtimeshejumps,shealwaysjumpstoanumberthatis3morethanthenumbersheisstandingon.WhatisthelargestnumberEllicanjumponto?小艾用粉笔在人行道上画了如以下图片中的大正方形。她从数字1开始跳跃。每当她跳跃时，她总是跳到比她之前站立的数字多3的位置。请问小艾可以跳到的最大数字是多少？158114710142423131821191620(A)11(B)14(C)18(D)19(E)24#7.Jorgegluesthese6stickerstothefacesofacube.Thepicturesshowsthecubeintwopositions.Whichstickerisontheoppositefacetotheduck?小乔将6个贴纸分别各自粘贴到一个立方体的表面。如图显示的是该立方体在两个不同的位置时的情况。请问哪个贴纸的图案会在鸭子贴纸的对面?(A)(B)(C)(D)(E)3,KangarooMathCompetition2020(China)–Ecolier#8.Casperhasthefollowing7shadedpieces.Heusessomeofthesepiecestofullycoverthiswhitegridwithoutoverlap.Heusesasmanydierentpiecesaspossible.HowmanypiecesdoesCasperuse?小贾有以下7个阴影碎片。他将在不重叠的情况下用其中一些阴影碎片把所有的白色网格完全覆盖。他用了尽可能多的不同的碎片。请问小贾将会用到多少块阴影部分的碎片?(A)3(B)4(C)5(D)6(E)74points#9.Cindycolourseachregiononthepatterneitherred,blueoryellow.Theregionsthattoucheachotherhavedierentcolours.Theouterregionofthepatterniscolouredred.Howmanyregionsiscolouredred?小迪将图案上的每个区域都分别涂上红色，蓝色或者黄色，且相邻的区域颜色不同，她将图案的外圈（区域）涂上红色。请问有多少个区域被涂上红色?(A)1(B)2(C)3(D)4(E)54,KangarooMathCompetition2020(China)–Ecolier#10.Loeslooksatthepyramidfromabove.WhatdoesLoessee?小卢从金字塔的上方往下看，她会看到什么？(A)(B)(C)(D)(E)#11.Dennistiesahorse1meterfromacornerofa7meterby5meterhouse,usingaropewithlength11meter.Dennisplaces5pilesofdrygrassesasshownbelow.Howmanyofthepilescouldthehorsereach?如图所示，小妮使用一根11米长的绳子将一匹马绑在7米x5米的小屋外，并且置放了5堆干草准备喂食马儿。捆绑着马儿的地方与小屋的角落之间的距离为1米。请问这匹马能够吃到多少堆的草?(A)1(B)2(C)3(D)4(E)55,KangarooMathCompetition2020(China)–Ecolier#12.Lonnekebuildsafenceusingpoleswithlength1meter.ThepictureshowsafencewithkSticlength4meter.HowmanypolesdoesLonnekeneedtobuildafencewithlength10meter?小罗用1米长的杆来搭建围栏,如右侧所示：kStic下图显示的是一个4米长的围栏。请问小罗要搭建一个10米长的围栏需要多少根杆?4米(A)22(B)30(C)33(D)40(E)42#13.Everytimethekangaroogoesup7steps,therabbitgoesdown3steps.图中的袋鼠每向上跳7层楼梯，兔子就会往下跳3层。Onwhichstepdotheymeet?请问它们会在哪一层见面？(A)53(B)60(C)63(D)70(E)736,KangarooMathCompetition2020(China)–Ecolier#14.Thesumofthreenumbersis50.Karinsubtractsasecretnumberfromeachofthesethreenumbers.Shegets24,13and7astheresults.Whichoneofthefollowingisoneoftheoriginalthreenumbers?有三个数字的总和是50。小凯用这三个数字分别减去了一个神秘的数字，得到的结果分别是24，13和7。以下哪一个数字是原本三个数字中的其中之一?(A)9(B)11(C)13(D)17(E)23#15.Ameliewantstobuildthefollowinggureusing10ofthesegivenshapes.Whentwoshapesshareaside,thecorrespondingnumbersmatch.Fourshapeshavealreadybeenplaced.WhichnumbergoesinthetrianglemarkedwithX?小米想用10个如下图左侧显示的五边形来拼成右侧的图形。当两个五边形共享同一边时，其相对应的数字是相同的。如图所示，已经有4个五边形摆放进图形里了。请问三角形中的X将会是数字几?X5142333224544511135451223(A)1(B)2(C)3(D)4(E)5#16.Faridhastwotypesofsticks:shortones,measuring1cmandlongones,measuring3cm.Withwhichofthecombinationsbelowcanhemakeasquare,withoutbreakingoroverlappingthesticks?小瑞有两种不同的棍子：短棍是1cm，长棍是3cm。在不折断棍子，也不重叠的情况下，他能用下列哪一种组合摆出一个正方形?(A)5shortand2long(B)3shortand3long(C)6short5根短棍和2根长棍3根短棍和3根长棍6根短棍(D)4shortand2long(E)6long4根短棍和2根长棍6根长棍7,KangarooMathCompetition2020(China)–Ecolier5points#17.Astandarddicehas7asthesumofthedotsonoppositefaces.Thediceisputontherstsquareasshownandthenrollstowardstheright.Whenthedicegetstothelastsquare,whatisthetotalnumberofdotsonthethreefacesmarkedwiththequestionmarks?一颗标准骰子的相对面点数的总和为7。如图显示，骰子被放在第一个正方形的上面，然后再依着次序向右滚动。当骰子被滚动到最后一个正方形的上面时，请问该骰子被标上问号的点数总和是多少????(A)6(B)7(C)9(D)11(E)12#18.6peopleeachorderonescoopoficecream.Theyorder3scoopsofvanilla,2scoopsofchocolateand1scoopoflemon.Theytoptheicecreamswith3cherries,2wafersand1chocolatechip.Theyuseonetoppingoneachscoop,suchthatnotwoicecreamsarealike.Whichofthefollowingcombinationsisnotpossible?6个人每人要买一勺冰淇淋。他们点了3勺香草，2勺巧克力和一勺柠檬。他们想在冰淇淋上搭配3个樱桃、2个华夫饼和1个巧克力碎。为了使冰淇淋两两互不相同，他们需要在每勺冰淇淋上搭配一种配料。请问以下哪一个组合是不可能的?(A)chocolatewithacherry(B)vanillawithcherry(C)lemonwithawafer巧克力冰淇淋和一个樱桃香草冰淇淋和一个樱桃柠檬冰淇淋和一个华夫饼(D)chocolatewithawafer(E)vanillawithachocolatechip巧克力冰淇淋和一个华夫饼香草冰淇淋和巧克力碎#19.TheQueentriestondoutthethreenamesofRumpelstiltskin'swife.Sheasksher:"AreyoucalledAdeleLillyCleo?""AreyoucalledAdeleLauraCora?""AreyoucalledAbbeyLauraCleo?"Eachtimeexactlyonenameanditspositionwasright.WhatisthenameofRumpelstiltskin'swife?王后试图找出侏儒怪妻子的名字（名字有3个组成部分）王后问她:“你是叫AdeleLillyCleo吗?”“你是叫AdeleLauraCora吗?”“你是叫AbbeyLauraCleo吗?”每次只有一个部分和它的位置是正确的。请问侏儒怪的妻子叫什么名字?(A)AbbeyLillyCora(B)AbbeyLauraCora(C)AdeleLauraCleo(D)AdeleLillyCora(E)AbbeyLauraCleo8,KangarooMathCompetition2020(China)–Ecolier#20.Ateacherwritesthenumbersfrom1to8onaboard.Theteacherthencoversthenumberswithtriangles,squaresandacircle.Ifyouaddthefournumberscoveredbythetriangles,thesumis10.Ifyouaddthethreenumberscoveredbythesquares,thesumis20.Whichnumberiscoveredbythecircle?老师在黑板上写下了1到8的数字。然后老师分别用三角形，正方形和圆形来遮盖这些数字。如果你把4个被三角形所遮盖的数字相加时，所得到的数字总和是10。如果你将3个被正方形所遮盖的数字相加时，所得到的数字总和是20。请问被圆形所遮盖的数字是多少?(A)3(B)4(C)5(D)6(E)7#21.Janehassomepicturesofparrots.Shewantstocolouronlythehead,tailandwingsofeachparroteitherred,blueorgreensothatallthreecoloursareusedoneachpicture.Shecoloursoneparrot'sheadred,itswingsgreenanditstailblue.Howmanymoreparrotscanshecoloursothatalltheparrotsarecoloureddierently?小珍有一个绘画本，里面有一些鹦鹉的图片。她想要将每一只鹦鹉的头，尾巴和翅膀都分别涂上红色，蓝色或者绿色，以便绘画本中每张鹦鹉图片都有这三种颜色。她先将一张鹦鹉图片中的鹦鹉的头涂上红色，将翅膀涂上绿色，将尾巴涂上蓝色。请问她还可以为多少只鹦鹉涂上颜色，以便让所有的鹦鹉都有不同的颜色?(A)1(B)2(C)4(D)5(E)99,KangarooMathCompetition2020(China)–Ecolier#22.SeveralteamscametothesummerKangaroocamp.Eachteamhas5or6members.Thereare43peopleintotal.Howmanyteamsareatthiscamp?有几支队伍来到了袋鼠夏令营。每支队伍会有5或6名队员。如果他们一共有43人。请问袋鼠夏令营里将会有多少支队伍?(A)4(B)6(C)7(D)8(E)9#23.Whichkeywoulditbeimpossibletocutintothreedierentguresofveshadedsquares?以下哪个选项不能被切成三个不同形状，且每个形状包含五个阴影正方形？(A)(B)(C)(D)(E)#24.AnnreplaceslettersinthecalculationKANROO+GAwithnumbersfrom1to9andthencalculatestheresult.Thesamelettersarereplacedbythesamenumbers.Dierentlettersarereplacedbydierentnumbers.Whatisthelargestpossibleresultshecouldget?小安用1到9的数字来替换KAN−ROO+GA中的字母，然后计算结果。相同的字母将会被相同的数字所替换，不相同的字母将会被不相同的数字所替换。她可能得到的最大结果是什么?(A)925(B)933(C)939(D)942(E)948ENDOFPAPER10,MathKangaroo2020AnswerKeyNo.Level0Level1&2Level3&4Level5&6Level7&8Level9&10Level11&121DDEEBBD2EEEEADB3AAADCEB4EEABAAA5AAEEEBC6DDDCECE7EEEADBD8DDCBBED9CCCCDCE10CCCEBAD11DEDAADE12DCEECBB13BDABBB14AABCBB15BDCCAB16DBCCCA17DBEAEB18DCDDDA19CABBAC20CDAEDB21BDBABD22EDEACE23CBBDED24BDCBDD25DCCE26DCCC27BECA28ADAA29EDBC30BCDC,-ScratchPaper-草稿纸,,?KSF2020{nalizedproblemsEcolier3points#1.Amushroomgrowseveryday.MarytakesapictureofthemushroomeachdayfromMondaytoFriday.WhichofthesepictureswastakenonTuesday??(A)(B)(C)(D)(E)Solution:#2.Whichpiececompletesthepattern?1???1?1(A)(B)(C)(D)(E)Solution:#3.Tysgershadesallthesquaresinthegridwheretheresultis20.Whichshapedoesheget?16+419+128−812×1016−47×3(A)(B)(C)(D)(E)16+419+128−812·1016−47·3Solution:Insteadof19+1somecountriesmightprefer40:2.Youcanalsoreplace19+1bytheanswer20instead.Inthatyoualsoreducethenumberofcalculations.Notethatinthatcasetheformulationmustalsobedierentbecause20isthennotananswer.#4.Whichofthefollowinggureshasthelargestpartshaded?(A)(1B)(C)(D)(E)1,KSF2020{nalizedproblemsEcolierSolution:Youcanusegardeninsteadofgures#5.Youcanmakedierentguresbyusingthesepieces:Whichoneoftheguresbelowcanyoumakewiththesepieces?(A)(B)(C)(D)(E)Solution:#6.Ellidrawsthebigsquarewithchalkonthepavement.Shestartsjumpingfromnumber1.Eachtimeshejumps,shealwaysjumpstoanumberthatis3morethanthenumbersheisstandingon.WhatisthelargestnumberEllicanjumponto?158114710142423131821191620(A)11(B)14(C)18(D)19(E)24Solution:#7.Jorgegluesthese6stickerstothefacesofacube:Thepicturesshowsthecubeintwopositions.Whichstickerisontheoppositefacetotheduck?(A)(B)(C)(D)(E)Solution:#8.Casperhasthefollowing7pieces:2,KSF2020{nalizedproblemsEcolier.Heusessomeofthesepiecestofullycoverthisgridwith-outoverlap.Heusesasmanydierentpiecesaspossible.HowmanypiecesdoesCasperuse?(A)3(B)4(C)5(D)6(E)7Solution:Somecountriesmightwanttostatethatthegridis17squareslong.4points#9.Cindycolourseachregiononthepatterneitherred,blueoryellow.Shecoloursregionsthattoucheachotherwithdierentcolours.Shecolourstheouterring(region)ofthepatternred.HowmanyregionsdoesCindycolourred?(A)1(B)2(C)3(D)4(E)5Solution:#10.Loeslooksatthepyramidfromabove.WhatdoesLoessee?(A)(B)(C)(D)(E)Solution:Mathematiciansmightprefer:Whatdoesthepictureofthepyramidlooklikewhentakenfromabove?#11.Dennistiesadog1metrefromacornerofa7metresby5metreshutasshowninthepictureusingan11metreslongleash.Dennisplaces5treatsasshown.Howmanyofthetreatscouldthedogreach?3,KSF2020{nalizedproblemsEcolier1114meter(A)1(B)2(C)3(D)4(E)5Solution:Notethatthedogisinperspectiveandthehutisnot.#12.Lonnekebuildsafenceusing1metrelongpoles.Thepictureshowsa4metresStick4metreslongfence.HowmanypolesdoesLonnekeneedtobuilda10metreslongfence?(A)22(B)30(C)33(D)40(E)42Solution:#13.Everytimethekangaroogoesup7steps,therabbitgoesdown3steps.Onwhichstepdotheymeet?(A)53(B)60(C)63(D)70(E)73Solution:#14.Thesumofthreenumbersis50.Karinsubtractsasecretnumberfromeachofthesethreenumbers.Shegets24,13and7astheresults.Whichoneofthefollowingisoneoftheoriginalthreenumbers?(A)9(B)11(C)13(D)17(E)234,KSF2020{nalizedproblemsEcolierSolution:24+13+7=44.50-44=66:3=2.Sothenumbersare24+2=26,13+2=15and7+2=9.45312#15.Ameliewantstobuildacrownusing10copiesofthistoken.Whentwotokensshareaside,thecorrespondingnumbersmatch.Fourtokenshavealreadybeenplaced.WhichnumbergoesinthetrianglemarkedwithanX?X51423332254411154523(A)1(B)2(C)3(D)4(E)5Solution:#16.Faridhastwotypesofsticks:shortones,measuring1cmandlongones,measuring3cm.Withwhichofthecombinationsbelowcanhemakeasquare,withoutbreakingoroverlappingthesticks?(A)5shortand2long(B)3shortand3long(C)6short(D)4shortand2long(E)6longSolution:5points#17.Astandarddicehas7asthesumofthedotsonoppositefaces.Thediceisputontherstsquareasshownandthenrollstowardstheright.Whenthedicegetstothelastsquare,whatisthetotalnumberofdotsonthethreefacesmarkedwiththequestionmarks????(A)6(B)7(C)9(D)11(E)12Solution:#18.6peopleeachorderonescoopoficecream.Theyorder3scoopsofvanilla,2scoopsofchocolateand1scoopoflemon.Theytoptheicecreamswith3cherries,2wafersand1chocolate5,KSF2020{nalizedproblemsEcolierchip.Theyuseonetoppingoneachscoop,suchthatnotwoicecreamsarealike.Whichofthefollowingcombinationsisnotpossible?(A)chocolatewithacherry(B)vanillawithcherry(C)lemonwithawafer(D)chocolatewithawafer(E)vanillawithachocolatechipSolution:#19.TheQueentriestondoutthethreenamesofRumpelstiltskin'swife.Sheasksher:"AreyoucalledAdeleLillyCleo?""AreyoucalledAdeleLauraCora?""AreyoucalledAbbeyLauraCleo?"Eachtimeexactlyonenameanditspositionwasright.WhatisthenameofRumpelstiltskin'swife?(A)AbbeyLillyCora(B)AbbeyLauraCora(C)AdeleLauraCleo(D)AdeleLillyCora(E)AbbeyLauraCleoSolution:#20.Theteacherwritesthenumbersfrom1to8ontheboard.Theteacherthencoversthenumberswithtriangles,squaresandacircle.Ifyouaddthefournumberscoveredbythetriangles,thesumis10.Ifyouaddthethreenumberscoveredbythesquares,thesumis20.Whichnumberiscoveredbythecircle?(A)3(B)4(C)5(D)6(E)7Solution:Thesumofalleightnumbersis1+2+...+8=36.Thesumofthosecoveredbysquaresandtrianglesis10+20=30.Sotheremainingnumberis36-30=6.Onewaytomaterializethisis2,3,5,1,4,7,8,6.#21.Janehassomepicturesofparrots.Shewantstocolouronlythehead,tailandwingsofeachparroteitherred,blueorgreensothatallthreecoloursareusedoneachpicture.Shecoloursoneparrot'sheadred,itswingsgreenanditstailblue.Howmanymoreparrotscanshecoloursothatalltheparrotsarecoloureddierently?(A)1(B)2(C)4(D)5(E)9Solution:6,KSF2020{nalizedproblemsEcolier#22.SeveralteamscametothesummerKangaroocamp.Eachteamhas5or6members.Thereare43peopleintotal.Howmanyteamsareatthiscamp?(A)4(B)6(C)7(D)8(E)9Solution:#23.Whichkeywoulditbeimpossibletocutintothreedierentguresofveshadedsquares?(A)(B)(C)(D)(E)Solution:#24.AnnreplaceslettersinthecalculationKANROO+GAwithnumbersfrom1to9andthencalculatestheresult.Thesamelettersarereplacedbythesamenumbersanddierentlettersbydierentnumbers.Whatisthelargestpossibleresultshecouldget?(A)925(B)933(C)939(D)942(E)948Solution:Theexpressionequalsto100
K+11
A+10
G+N100
R11
O.TomakeKAN+GAmaximalAnnshouldsuccessivelychoosemaximalK=9,thenA=8,G=7andnallyN=6.AtthesametimetheminimalpossiblevalueofROOis122.ThereforeAnn'smaximalresultequals986122+78=942.Youcanalsousedigitsfrom1-8andthenchangetheanswers.YoucanalsouseKAN+GA-ROO(whichwedidnottakeasthentheanswerofKAN+GA>1000).Insteadofthegivenanswer,thefollowinganswerscanbeused:A511,C941.Thisisbasedonwhatweexpectasoftenchosenwrongstrategies:A-takingallnumbersashighaspossible(soalsoforROO),B-switchthenumberforAandN//AnothersolutionclosertoEcolierstudents:ThenumberROOthatissubtractedshouldbeassmallaspossible,soitmustbe122.FromthenumbersKAN,GAadded,theonlyhundredsdigitisKsoitshouldbeK=9.ThenextlargestnumbersarethetensdigitsAandGsotheyshouldbeeitherA=8andG=7ortheotherwayround(wedecidelater),namelyA=7,G=8.Nextwelookattheunits,NandA.ThesecondoneisAforwhichatthisstagewehavetwochoicesbutNshouldbethelargestavailabledigit,soN=6.Usingtheseconclusionswehavetwooptions,a)KAN+GA=986+78=1064orb)KAN+GA=976+87=1063.Weprefertherstoneaslarger,sowenowhaveKAN+GA-ROO=986+78-122=942.7,考试说明/InstructionTimeallowed:75minutes考试时长：75分钟Language:English&Chinese试卷语言：英文和中文Thisisa24-questionmultiple-choicecompetition.考试包含24道单项选择题。Problems1to8areworth3pointseach.1-8题每题3分Problems9to16areworth4pointseach.9-16题每题4分Problems17to24areworth5pointseach.17-24题每题5分1pointwillbedeductedforanincorrectanswerandnopointforablankanswer.答错扣1分，不答不扣分。Thefullscoreis120(Startingpointis24)总分为120分（起始分数为24分）Donotopenthisbookletuntilyouaretoldtodoso.收到监考老师指令后，方可打开试卷册。Markyouranswersclearlyontheanswersheetusinga2Bpencil.务必使用2B铅笔在答题卡上正确填涂自己的答案。Year3Calculatorcannotbeusedduringthecompetition.&考试期间禁止使用计算器。Year4GoodLuck!预祝考试顺利,,KangarooMathCompetition2021(China)–Level23points#1.Erikhas4bricks:Erik有4块砖：Whichofthecubesshownbelowcanhemakewithhis4bricks?用这4块砖可以组成以下哪个立方体？(A)(B)(C)(D)(E)#2.Whenyouputthe4puzzlepiecestogethercorrectly,theyformarectanglewithacalculationonit.Whatistheresultofthiscalculation?将下列4个拼图碎片正确拼接在一起后，会出现写有一道算式题的矩形。请问这个算式的答案是多少?(A)6(B)15(C)18(D)24(E)33#3.Alayadrawsapictureofthesun.Alaya画了一个太阳。Whichofthefollowinganswersispartofherpicture?以下哪个选项是这个图画中的一部分？(A)(B)(C)(D)(E)1,KangarooMathCompetition2021(China)–Level2#4.Howmanyfishwillhavetheirheadspointingtowardstheringwhenwestraightentheline?把下面的鱼线拉直后，有多少个鱼头是朝着圆环的方向的？(A)3(B)5(C)6(D)7(E)8#5.Fiveboyscompetedinashootingchallenge.Rickyscoredthemostpoints.WhichtargetwasRicky’s?5个男孩进行射击比赛，Ricky的得分最高。请问下列哪个靶子是Ricky的？(A)(B)(C)(D)(E)#6.Ameasuringtapeiswrappedaroundacylinder.Whichnumbershouldbeattheplaceshownbythequestionmark?一把卷尺缠绕在一个圆柱体上。请问图中问号处标记的应该是哪个数？(A)33(B)42(C)48(D)53(E)692,KangarooMathCompetition2021(China)–Level2#7.Denisefiredasilverandagoldrocketatthesametime.Therocketsexplodedinto20starsintotal.Thegoldrocketexplodedinto6morestarsthanthesilverone.Howmanystarsdidthegoldrocketexplodeinto?Denise同时点燃一个银色烟花和一个金色烟花。两个烟花一共爆炸出20颗“星星”。其中金色烟花比银色烟花多爆炸出6颗“星星”。请问金色烟花爆炸出多少颗“星星”？(A)9(B)10(C)12(D)13(E)15#8.Rosanahassomeballsof3differentcolours.Ballsofthesamecolourhavethesameweight.Whatistheweightofeachwhiteball?Rosana有三种不同颜色的球。颜色相同的球重量也相同。请问白球的重量是多少？6kg14kg10kg(A)3kg(B)4kg(C)5kg(D)6kg(E)7kg4points#9.Nisahas3differenttypesofcardsinagame:apple,cherryandgrapes.Shechooses2cardsfromthesetandswapstheirplaces.Shewantstoarrangethecardssothatallthecardswiththesamefruitonarenexttoeachother.Forwhichsetisthisnotpossible?在一场游戏中，Nisa有三种不同类型的卡片：苹果卡片，樱桃卡片和葡萄卡片。然后她从以下卡组中选取了两张卡片并且交换了它们的位置，使得有相同水果图案的卡片彼此相邻。请问以下哪个卡组不可能实现上述要求？3,KangarooMathCompetition2021(China)–Level2(A)(B)(C)(D)(E)#10.18cubesarecolouredwhiteorgreyorblackandarearrangedasshown.有18个白色、灰色或黑色的立方体按右图所示进行组合。Thefiguresontherightshowthewhiteandtheblackparts.Whichofthefollowingisthegreypart?右图显示了其中白色和黑色部分的排列方式。请问以下哪个选项可以表示灰色部分的排列方式？(A)(B)(C)(D)(E)#11.Sofiewantstopick5differentshapesfromtheboxes.Shecanonlypick1shapefromeachbox.Whichshapemustshepickfrombox4?Sofie想要从下面盒子中取出5个不同的图形。她只能从每个箱子中取出一个图形。请问Sofie必须从箱子4中取出什么图形？箱子1箱子2箱子3箱子4箱子5(A)(B)(C)(D)(E)4,KangarooMathCompetition2021(China)–Level2#12.Inanicecreamshopthereissomemoneyinadrawer.Afterselling6icecreams,thereare70eurosinthedrawer.Aftersellingatotalof16icecreams,thereare120eurosinthedrawer.Howmanyeuroswerethereinthedraweratthestart?在一家冰淇淋店的收银柜里有一些钱。卖出6个冰淇淋之后，收银柜里一共有70欧元。卖出16个冰淇淋之后，收银柜里有一共120欧元。请问收银柜里原先有多少欧元？(A)20(B)30(C)40(D)50(E)60#13.The5ballsshownbegintomovesimultaneouslyinthedirectionsindicatedbytheirarrows.如图所示，5个球按照箭头所指的方向同时移动。Whentwoballsgoinginoppositedirectionscollide,thebiggerballswallowsthesmalleroneandincreasesitsvaluebythevalueofthesmallerball.Thebiggerballcontinuestomoveinitsoriginaldirection,asshowninthefollowingexample.当两个移动方向相反的球发生碰撞时，大球会吞掉小球，并将小球的值和它本身的值相加。然后大球继续朝着原来的方向移动，如下图所示。Whatisthefinalresultofthecollisionsofthe5ballsshown?请问上图显示的5个球互相碰撞后的最终结果是什么？4950484950(A)(B)(C)(D)(E)#14.Onatallbuildingthereare4fireescapeladders,asshown.Theheightsof3laddersareattheirtops.Whatistheheightoftheshortestladder?如图所示，在一座高楼中有4个消防逃生梯，其中有3个逃生梯的高度标在了梯子顶部。请问最短的逃生梯高度是多少？(A)12(B)14(C)16(D)20(E)225,KangarooMathCompetition2021(China)–Level2#15.TheKoalaatesomeleavesfrom3branches.Eachbranchhad20leaves.TheKoalaateafewleavesfromthefirstbranchandthenateasmanyleavesfromthesecondbranchaswereleftonthefirstbranch.Thenitate2leavesfromthethirdbranch.Howmanyleavesintotalwereleftonthe3branches?考拉吃了三根树枝上的一些叶子。每根树枝上有20片叶子。考拉先后吃了第一根和第二根树枝上的几片叶子。第二根树枝上被吃掉的叶子数量正好是第一根树枝上吃剩的叶子数量。接着考拉又吃了第三根树枝上的2片叶子。请问这三根树枝上一共剩下几片叶子？(A)20(B)22(C)28(D)32(E)38#16.Noraplayswith3cupsonthekitchentable.Shetakestheleft-handcup,flipsitover,andputsittotherightoftheothercups.Nora在餐桌上玩3只杯子。她拿起左手边的杯子，把它翻转过来然后放在了其他杯子的右边。Thepictureshowsthefirstmove.Whatdothecupslooklikeafter10moves?上述图片表示的是第一次移动杯子的情况。请问移动10次之后，三只杯子是怎么排列的？(A)(B)(C)(D)(E)5points#17.Evahasthe5stickersshown:Shestuckoneofthemoneachofthe5squaresofthisboardsothatisnotonsquare5,isonsquare1,andisadjacenttoand.OnwhichsquaredidEvastick?6,KangarooMathCompetition2021(China)–Level2Eva有5张贴纸，如图所示：她将这5张贴纸贴在右图中的五个方格里。不在第五个方格里，在第一个方格里，与和相邻。请问第几个方格里贴的是？(A)1(B)2(C)3(D)4(E)5#18.7cardsarearrangedasshown.Eachcardhas2numbersonwith1ofthemwrittenupsidedown.Theteacherwantstorearrangethecardssothatthesumofthenumbersinthetoprowisthesameasthesumofthenumbersinthebottomrow.Shecandothisbyturningoneofthecardsupsidedown.Whichcardmustsheturn?7张卡片按照下图所示排列。每张卡片上有2个数字，其中一个数字倒着写。老师想重新排列这些卡片，使得上面一行的数之和等于下面一行的数之和。她只需把其中一张牌翻转过来就可以实现。请问她必须翻转下面哪张牌？(A)A(B)C(C)D(D)F(E)G#19.Miathrowsdartsatballoonsworth3,9,13,14and18points.Shescores30pointsintotal.WhichballoondoesMiadefinitelyhit?Mia向分值为3、9、13、14和18分的气球投掷飞镖，最终她一共得了30分。请问她肯定击中了多少分的气球？39131418(A)3(B)9(C)13(D)14(E)187,KangarooMathCompetition2021(China)–Level2#20.Thenumbers1to9areplacedinthesquaresshownwithanumberineachsquare.Thesumsofallpairsofneighbouringnumbersareshown.将数字1到9放在如图所示的方格里，每个方格里都有一个数字。相邻两个数字的和如下图所示。Whichnumberisplacedintheshadedsquare?请问阴影方格内放入的数字是多少？(A)4(B)5(C)6(D)7(E)8#21.Aboxhasfewerthan50cookiesin.Thecookiescanbedividedevenlybetween2,3,or4children.However,theycannotbedividedevenlybetween7childrenbecause6morecookieswouldbeneeded.Howmanycookiesarethereinthebox?一个盒子里的饼干不到50块。这些饼干可以平均分给2个、3个或4个孩子。如果要平均分给7个孩子的话还差6块饼干。请问盒子里一共有多少块饼干？(A)12(B)24(C)30(D)36(E)48#22.Elenawantstowritethenumbersfrom1to9inthesquaresshown.Thearrowsalwayspointfromasmallernumbertoalargerone.Shehasalreadywritten5and7.Whichnumbershouldshewriteinsteadofthequestionmark?Elena想把数字1到9写在下面的方框里。箭头总是从较小的数指向较大的数。她已经写了5和7这两个数。请问问号处应该填写哪个数？(A)2(B)3(C)4(D)6(E)88,KangarooMathCompetition2021(China)–Level2#23.Eachofthe5boxescontainseitherapplesorbananas,butnotboth.Thetotalweightofallthebananasis3timestheweightofalltheapples.Whichboxescontainapples?在5个箱子，有的装着苹果，有的装着香蕉，但不会同时装两种水果。所有香蕉的总重量是所有苹果总重量的3倍。请问哪个箱子中装的是苹果？(A)1and2箱子1和2(B)2and3箱子2和3(C)2and4箱子2和4(D)3and4箱子3和4(E)1and4箱子1和4#24.Martinplaced3differenttypesofobjects,hexagons,squaresandtriangles,onsetsofscales,asshown.如图所示，Martin在一组天平上面放置了三种不同类型的物品：六边形，正方形和三角形。Whatdoesheneedtoputontheleft-handsideonthethirdsetofscalesforthesescalestobalance?他需要在第三个天平的左边再放哪些物品才能让这些天平都保持平衡？(A)1square1个正方形(B)2squares2个正方形(C)1hexagon1个六边形(D)1triangle1个三角形(E)2triangles2个三角形9,等级01-5EADBA6-10DEBDD11-12AD等级1-PreEcolier1-5EDABA6-10DEBDD11-15ECCAB16-20DDCAB21-24CECC等级2-Ecolier1-5CBBCE6-10CDCAE11-15ECCDE16-20BDEAD21-24DDEA等级3-Benjamin1-5DBDAE6-10CBEDE11-15BBBDA16-20ECDCB21-25ABCAC26-30EDBBE等级4-Cadet1-5AEBAD6-10BEABE11-15DCECD16-20BBCEC21-25CBBDD26-30CBADC等级5-Junior1-5CBBBC6-10BCCDE11-15BAAAC16-20EECCE21-25EAEBE26-30DDCDD,考试说明/InstructionTimeallowed:75minutes考试时长：75分钟Language:English&Chinese试卷语言：英文和中文Thisisa24-questionmultiple-choicecompetition.考试包含24道单项选择题。Problems1to8areworth3pointseach.1-8题每题3分Problems9to16areworth4pointseach.9-16题每题4分Problems17to24areworth5pointseach.17-24题每题5分1pointwillbedeductedforanincorrectanswerandnopointforablankanswer.答错扣1分，不答不扣分。Thefullscoreis120(Startingpointis24)总分为120分（起始分数为24分）Donotopenthisbookletuntilyouaretoldtodoso.收到监考老师指令后，方可打开试卷册。Markyouranswersclearlyontheanswersheetusinga2Bpencil.务必使用2B铅笔在答题卡上正确填涂自己的答案。Year3Calculatorcannotbeusedduringthecompetition.&考试期间禁止使用计算器。Year4GoodLuck!预祝考试顺利,,MathKangaroo2022(China)–Level23points1.Buzzthebeewantstoreachtheflower.Whichsetofdirectionswillgethimthere.蜜蜂按照下列哪组方向前进可以采到花蜜？(A)→↓→↓↓→(B)↓↓→↓↓(C)→↓→↓→(D)→→↓↓↓(E)↓→→↓↓↓2.Laserbeamsreflectinmirrorsinthewayshowninthepicture.Atwhichletterwillthislaserbeamend?激光束在镜׿中的反射情况如右图所示。那么下图中的激光束将从哪个字母的位置反射出来？(A)A(B)B(C)C(D)D(E)E3.Rossitzawantstoput2coinsineachrowandineachcolumnofthegrid.小萝想在网格的每行和每列都放上2枚硬币。Whichcoindoessheneedtomovetoanemptycell?请问她现在需要将哪枚硬币移动到其他空格中？(A)A(B)B(C)C(D)D(E)E1,MathKangaroo2022(China)–Level24.WhatisthesmallestnumberofboxesthatBillhastomovetobeabletoopenthedarkTRAINbox?小博至少要移动多少个盒׿，才能打开装着玩具火车的黑色盒׿？棋盘游戏乐谱床上用品书(A)3(B)4(C)5(D)6(E)75.Kengualwaysmakesonelargejumpfollowedbytwosmalljumpsonthenumberline,asshowninthepicture.Kengustartsat0andendson16.WhatisthenumberofjumpsthatKengumakes?如图所示，袋鼠总是按照先一大跳再两小跳的规律在一条数轴上跳跃。它从数字0开始，一直跳到数字16。请问袋鼠一共跳跃了多少次？(A)4(B)7(C)8(D)9(E)126.Annamakesajigsawwheretwosquareswithcommonsidesdonotcontainthesamenumber.Whichpieceshouldsheusetocompleteherjigsaw?安安制作了一个拼图，其中有公共边的两个小正方形内的数字都不相同。请问她应该用下面哪一块来完成她的拼图？(A)(B)(C)(D)(E)2,MathKangaroo2022(China)–Level27.2022+□=2020+□Whichtwonumberscanbewritteninthetwoboxestomakethestatementcorrect?下面哪两个数字可以填入两个方框中使等式成立？(A)3and53和5(B)4and14和1(C)3and43和4(D)7and27和2(E)9and89和88.Johnbuildsthetowershown.小吉搭了一座塔，如图所示。Whatwillheseeifhelooksathistowerfromabove?如果从上方看这座塔，可以看到下面哪个图案？(A)(B)(C)(D)(E)4points9.Fivecarsnumbered1,2,3,4and5aremovinginthesamedirection.五辆编号为1、2、3、4、5的汽车朝同一方向行驶。First,thelastcar(5)overtakesthetwocarsaheadofit.Next,thesecondlastcarovertakesthetwocarsaheadofit.Finally,themiddlecarovertakesthetwocarsaheadofit.Inwhatorderarethecarsnow?首先，最后一辆车(5)超过了它前面的两辆车。接下来，倒数第二辆车超过了它前面的两辆车。最后，中间的车超过了它前面的两辆车。请问现在汽车的编号顺序是什么？(A)1,2,3,5,4(B)2,1,3,5,4(C)2,1,5,3,4(D)3,1,4,2,5(E)4,1,2,5,33,MathKangaroo2022(China)–Level210.Theagesofafamilyofkangaroosare2,4,5,6,8and10years.Thesumoftheagesoffourofthemis22years.Whataretheagesoftheothertwokangaroos?袋鼠家族中的袋鼠年龄分别是2、4、5、6、8和10岁。其中四只袋鼠的年龄之和为22岁。那么另外两只袋鼠的年龄是多少？(A)2and82岁和8岁(B)4and54岁和5岁(C)5and85岁和8岁(D)6and86岁和8岁(E)6and106岁和10岁11.DuringmyholidayIsentthefivepostcardsshownbelowtomyfriends.TherearenoducksonMike’scard.Cara’scardhasthesunonit.ThereareexactlytwolivingcreaturesonPaula’scard.Lexi’scardhasadogonit.TherearekangaroosonHeather’scard.WhichcarddidMikeget?假期里，我把下面五张明信片寄给了我的朋友们。没有鸭׿的明信片是小麦的。拉拉收到的明信片上有太阳。只有两个ࣿ物的明信片是宝儿的。小雷收到的明信片上有一只狗。有袋鼠的明信片是希希的。请问小麦收到的是下面哪张明信片？(A)(B)(C)(D)(E)12.Mosifwantedthesumofthethreenumbersineachrowandineachcolumnofthegridtobethesame.Hemadeonemistake.Whichnumbermusthecorrect?小莫想让网格中每一行和每一列的三个数字之和都相同。但他犯了一个错误。请问他必须修改哪个数字？(A)1(B)3(C)oneofthe4s其中一个数字4(D)5(E)oneofthe7s其中一个数字74,MathKangaroo2022(China)–Level213.Aladdinhasasquarecarpet.Therearethesamenumberofdots,arrangedintwolines,alongeachsideofhiscarpet.Unfortunately,thecarpethasfolded.阿拉丁有一块正方形地毯。地毯每一侧都有两行相同数量的圆点。但地毯被折叠了。HowmanydotsarethereonAladdin’scarpet?请问阿拉丁的地毯上一共有多少个圆点？(A)48(B)44(C)40(D)36(E)3214.Joannafoldsthenumbersquaretwiceasshown.Thenshepunchesaholethroughtheblackspotshownbythearrow.Whichnumbersdoesshealsopunchthrough?小乔将数字方格纸按照如图所示的方式折叠了两次。然后她在箭头指向的黑点上打了一个洞。请问这个洞穿过了哪些数字？(A)8,11,26,29(B)14,17,20,23(C)15,16,21,22(D)14,16,21,23(E)15,17,20,225,MathKangaroo2022(China)–Level215.Thepupilsinaclasssitinrows.Therearethesamenumberofpupilsineachrow.Thereare2rowsofpupilsinfrontofRobertand1rowofpupilsbehindhim.Inhisrow,thereare3pupilsonhisleftand5pupilsonhisright.Howmanypupilsarethereinthisclass?某班的学ࣿ在教室排排坐。每排的学ࣿ人数相同。小罗前面有2排同学，后面有1排同学。在他那一排中，他的左边3名同学，右边有5名同学。请问这个班一共有多少名学ࣿ？(A)10(B)17(C)18(D)27(E)3616.Thecubeinthepictureisbuiltfromthethreekindsofwoodenblocksshown.Howmanywhitewoodenblocksareused?一个立方体由三种木块组成，如图所示。请问总共用了多少个白色木块？(A)8(B)11(C)13(D)16(E)195points17.Wandachoseafewofthefollowingshapesandsaid“AmongsttheshapesIhavechosen,thereare2colouredones,2largeonesand2roundones.”WhatisthesmallestnumberofthefollowingshapesthatWandacouldhavechosen?小达从以下形状中挑选出几个，然后说：“我选出的形状中有2个涂色的，2个大的，2个圆的。”请问小达最少可以从以下形状中选出几个？(A)2(B)3(C)4(D)5(E)66,MathKangaroo2022(China)–Level218.Threefootballteamsparticipateinasportstournament.Eachteamplaystheothertwoteamsexactlyonce.Ineachgame,thewinnergets3pointsandtheloserdoesn’tgetanypoints.Ifthegamefinishesinadraw,eachteamgets1point.Attheendofthetournament,whichnumberofpointsisitimpossibleforanyteamtohave?三支足球队参加体育比赛。每支球队与另外两支球队只交手一次。每场比赛中，胜方得3分，败方不得分。如果比赛以平局结束，每队得1分。在比赛结束时，任何球队都不可能得到的分数是？(A)1(B)2(C)4(D)5(E)619.Apyramidisbuiltfromcubeswithaside-length从上方看of10cm.Anantclimbedupandoverthepyramid,asshownbytheredline.Whatisthelengthofthepathwalkedbytheantacrossthepyramid?一个金字塔是由边长为10厘米的小立方体搭建而成的。一只蚂蚁爬上并越过金字塔，路径如图中红线所示。这只蚂蚁经过金字塔的路径长度是多少？(A)30cm30厘米(B)60cm60厘米(C)70cm70厘米(D)80cm80厘米(E)90cm90厘米20.AlmawantstoputoneofthepiecesshowninthemiddleofthepicturesothatachildinAisabletotraveltoBandtoE,butnottoD.Shecanrotatethepieces.小玛想把下图所示的其中一块碎片放在图片中间，这样A区的孩׿就可以去B区和E区游玩，但不能去D区。碎片可以旋转。Whichtwopiecescouldsheuse?请问她可以用哪两块碎片？(A)1and21和2(B)2and32和3(C)1and41和4(D)4and54和5(E)1and51和57,MathKangaroo2022(China)–Level25米21.AhmadandZhalehstartmovingfrompointAwiththesamespeed,inthedirectionsshown.Ahmadwalksaroundthesquare-shapedgardenandZhalehwalksaroundtherectangular-shapedone.10米TheymeetagainatA.Whatisthesmallestnumberoflapsaroundthesquare-shapedgardenthatAhmadcoulddotomeetZhalehthere?小艾和小扎从点A开始以相同的速度沿图中所示方向前进。小艾绕着正方形的花园走，小扎绕着长方形的花园走。他们在点A再次相遇。小艾最少要绕几圈正方形花园才能在点A遇见小扎？(A)1(B)2(C)3(D)4(E)522.Fivechildrenatesomeplums.LaurenatetwoplumsmorethanSophie.BettyatethreeplumsfewerthanLauren.ClaireateoneplummorethanBettyandthreeplumsfewerthanAlice.Whichtwogirlsatethesamenumberofplums?五个孩׿吃了一些李׿。L比S多吃了两颗李׿。B比L少吃了三颗李׿。C比B多吃一颗李׿，比A少吃三颗李׿。请问哪两个孩׿吃了相同数量的李׿？(A)ClaireandLauren.C和L(B)ClaireandSophie.C和S(C)LaurenandAlice.L和A(D)SophieandAlice.S和A(E)AliceandBetty.A和B23.Thesmallcaterpillarshowninthepicturecurlsuptosleep.图中的毛毛虫蜷缩起来睡觉。Whatmightthatlooklike?可能会是什么样׿的？(A)(B)(C)(D)(E)8,MathKangaroo2022(China)–Level224.Inthegrid,thesamenumberishiddenunderthesamecoloursquare.Totherightofeachrow,thesumofthenumbershiddenunderthesquaresinthatrowisgiven.Whichnumberishiddenundertheblacksquare?右图网格中，相同颜色的方块下面隐藏有相同的数字。每一行右边的数字表示隐藏在该行方块下的数字之和。请问哪个数字隐藏在黑色方块下面？(A)6(B)8(C)10(D)12(E)149,EcolierFinalized3points1(KW).Buzzthebeewantstoreachtheflower.Whichsetofdirectionswillgethimthere.(A)→↓→↓↓→(B)↓↓→↓↓(C)→↓→↓→(D)→→↓↓↓(E)↓→→↓↓↓Solution:Thecorrectansweris(A)-threemovesrightandthreemovesdown(right,down,right,down,down,right):2(DK).Laserbeamsreflectinmirrorsinthewayshowninthepicture.Atwhichletterwillthislaserbeamend?EDABC(A)A(B)B(C)C(D)D(E)ESolution:Thelaserbeamtravelsdown,thenright,up,right,down,left,downandendsupatpointB.3(DK).Rossitzawantstoput2coinsineachrowandineachcolumnofthegrid.ADBCESOLUTIONSINCLUDED-DONOTUSEFORCONTEST1,EcolierFinalizedWhichcoindoessheneedtomovetoanemptycell?(A)A(B)B(C)C(D)D(E)ESolution:Noticethatmostrowsandcolumnshavetwocoins,whilethefirstcolumnandthelastrowhave3coinseachforwhichthecommoncoinisthecoinC.Thiscoinneedstobemovedtothecolumn/rowwithonlyonecoinwhichisthesecondcolumnfourthrow(movingcoinCdiagonallynexttothecoinB:4(DE).WhatisthesmallestnumberofboxesthatBillhastomovetobeabletoopenthedarkTRAINbox?boardgamesbooksmusicsheetsstuffedanpuzzlesimalsbeddingclothsCDsBOOKSTRAIN(A)3(B)4(C)5(D)6(E)7Solution:Inordertoreachthetrainbox,Billmustmovetheboxeswithbooks,musicsheets,boardgames,stuffedanimalsandbedding-atotalof5boxes.OR:Hehastomove1.Books,2.MusicSheets,3.BoardGames,4.StuffedAnimalsand5.Bedding.Thetotalis5.Note:OnlydarkORtrainisneeded.Weleavebothfornowfortranslationreasons.5(NO).Kengualwaysmakesonelargejumpfollowedbytwosmalljumpsonthenumberline,asshowninthepicture.Kengustartsat0andendson16.0234WhatisthenumberofjumpsthatKengumakes?(A)4(B)7(C)8(D)9(E)12Solution:Thesumofthedistanceofonelargejumpandtwosmalljumpsis4.Itisrepeated.Therefore16÷4=4and4×3=12.SOLUTIONSINCLUDED-DONOTUSEFORCONTEST2,EcolierFinalized322541114433225514133222454411336(DK).Annamakesajigsawwheretwosquareswithcommonsidesdonotcontainthesamenumber.Whichpieceshouldsheusetocompleteherjigsaw?41223(A)123(B)423(C)134(D)341(E)124Solution:ThecorrectanswerisD.TopersuadeyourselfinthisitisenoughtocheckthateachsquarefromtheinsertedpieceDisnotneighbortothesquarewiththesamenumber.Ontheotherhand,allotheranswersarewrong.IfweputthepieceAthesquarewithnumber1wouldhaveaneighboronitsleftwiththesamenumber1.Forotherpiecesthesquareswiththesameneighborare:squarewithnumber2forpieceB,squarewithnumber4forpieceCandsquarewithnumber3forpieceE.Solution2:Theneighboringtilesoftheredcircleare2,3and5.Sotheredcirclehavetobe1or4.Thereisno1inthegivenanswers.Soitis4.Therearetwo4s(D)and(E).Theneighboringtilesofgreencircleare3and5.Sothegreencirclehavetobe1,2and4.Itis3inanswer(E)and2inanswer(D).7(CH).2022+!=2020+!Whichtwonumberscanbewritteninthetwoboxestomakethestatementcorrect?(A)3and5(B)4and1(C)3and4(D)7and2(E)9and8Solution:Noticethatthenumber2022islargerthan2020by2,henceinorderfortheequationtobecorrectthenumberinthefirstsquareshouldbesmallerthanthenumberinthesecondby2.Amongtheofferedpairsofnumbers,theonlytwonumbersthatcanbeputinsquaresare3and5.OR:2022+3=2020+5(=2025)Note:ifacountrythinksthisquestionisnotsuitablefor3pasnumbers¡1000areneeded,theycanchangethequestioninto20+(box)=22+(box)andswapallanswers(sothefirstansweristhen5and3,andsoon).Anotheroptionistomovethisquestiontothe4por5psectionasfor4por5ptheyearcanbeanexception.8(GR).Johnbuildsthetowershown.Whatwillheseeifhelooksathistowerfromabove?SOLUTIONSINCLUDED-DONOTUSEFORCONTEST3,EcolierFinalized(A)(B)(C)(D)(E)Solution:Inthepicture,fivesolidfiguresofdifferentsizesarestacked.Whenlookingdownatthesesolidfiguresfromabove,thethirdandfourthfiguresareinvisiblebecausetheyaresmallerthanthesecondfigure.4points9(PL).Fivecarsnumbered1,2,3,4and5aremovinginthesamedirection.12345First,thelastcar(5)overtakesthetwocarsaheadofit.Next,thesecondlastcarovertakesthetwocarsaheadofit.Finally,themiddlecarovertakesthetwocarsaheadofit.Inwhatorderarethecarsnow?(A)1,2,3,5,4(B)2,1,3,5,4(C)2,1,5,3,4(D)3,1,4,2,5(E)4,1,2,5,3Solution:Theorderofthecarschangeslikethis:1,2,3,4,5−→1,2,5,3,4−→1,3,2,5,4−→2,1,3,5,4Note:secondlast(=penultimate)10(GR).Theagesofafamilyofkangaroosare2,4,5,6,8and10years.524Thesumoftheagesoffourofthemis22years.Whataretheagesoftheothertwokangaroos?(A)2and8(B)4and5(C)5and8(D)6and86810(E)6and10Solution:Thesumofalltheagesis2+4+5+6+8+10=35sotheothertwoaddupto35−22=13.Thisisuniquely5+8(easytospotbecauseonlyoneofthegivennumbersisodd).11(DE).DuringmyholidayIsentthefivepostcardsshownbelowtomyfriends.TherearenoducksonMike’scard.Cara’scardhasthesunonit.ThereareexactlytwolivingcreaturesonPaula’scard.Lexi’scardhasadogonit.TherearekangaroosonHeather’scard.WhichcarddidMikeget?(A)(B)(C)(D)(E)Solution:Thedeductionis:MikeisnotD,HeatherisB,thenPaulaisC,thenCaraisAorD,SOLUTIONSINCLUDED-DONOTUSEFORCONTESTLexieisE.SincenowB,C,EandDareallexcludedforMike,MikecanonlybeA(andCarawillbe4,EcolierFinalizedD).Remark:Thereisalsoablack-and-whiteversionofthepictures.12(GR).Mosifwantedthesumofthethreenumbersineachrowandineachcolumnofthegridtobethesame.915Hemadeonemistake.376Whichnumbermusthecorrect?474(A)1(B)3(C)oneofthe4s(D)5(E)oneofthe7sSolution:Thesumsinmostrowsandcolumnsis15.Theexceptionsarethefirstcolumnandthesecondrowwherethesumis16.Sowemustchangethenumberattheirintersectionby1less.9151523761615474151615151513(PL).Aladdinhasasquarecarpet.Therearethesamenumberofdots,arrangedintwolines,alongeachsideofhiscarpet.Unfortunately,thecarpethasfolded.HowmanydotsarethereonAladdin’scarpet?(A)48(B)44(C)40(D)36(E)32Solution:Thesamenumberofdotsarrangedintworowsmeanstherearetworowsofsixdotsalongeachside,thereforetheunfoldedsquarecarpetshouldbeasfollows:.Thetotaldotsshouldbe4×6+8=32.SOLUTIONSINCLUDED-DONOTUSEFORCONTESTSolution2.5,EcolierFinalizedIfthewholecarpetwascoveredwithdots,itwouldbe6·6=36.Tworowsofdots(4dots)aremissinginthemiddle.Intotal36−4=32dots.Solution3.Ifthewholecarpetwascoveredwithdots,itwouldbe6·6=36.Thus,theonlypossibleanswerisE.14(GR).Joannafoldsthenumbersquaretwiceasshown.Thenshepunchesaholethroughtheblackspotshownbythearrow.Whichnumbersdoesshealsopunchthrough?123456789101112131415161718192021222324252627282930313233343536(A)8,11,26,29(B)14,17,20,23(C)15,16,21,22(D)14,16,21,23(E)15,17,20,22Solution:Thepictureshowsthepaperandtheholesasweunfoldittoitsoriginalshape.Thenumberspunchedareclear.123456789101112131415161718192021222324252627282930313233343536Note:Ifacountrydecidestouseadotted/dashedline,pleaseusetheofficialorigaminotation:seeYoshizawa-Randlettsystem.Herethatwouldmean:dashedlines(nodots).15(PH).Thepupilsinaclasssitinrows.Therearethesamenumberofpupilsineachrow.Thereare2rowsofpupilsinfrontofRobertand1rowofpupilsbehindhim.Inhisrow,thereare3pupilsonhisleftand5pupilsonhisright.Howmanypupilsarethereinthisclass?(A)10(B)17(C)18(D)27(E)36Solution:Asshowninthepicturebelow,thisrectangleformationhas3+1+5=9membersineachrow.Itfollowsthenumberofrowsintheformationis2+1+1=4rows.Therefore,thetotalnumberofpupilsis4×9=36pupilsinall.Note:Assomeregardthisproblemsimilartothecarproblem;itcanbereplacedwithaproblemfromreserved.16(PH).Thecubeinthepictureisbuiltfromthethreekindsofwoodenblocksshown.SOLUTIONSINCLUDED-DONOTUSEFORCONTESTHowmanywhitewoodenblocksareused?6,EcolierFinalized(A)8(B)11(C)13(D)16(E)19Solution:Thefirstlayerhasatotalof2whiteblocks,whilethesecondlayerhasatotalof6whiteblocksandthethirdlayerhasatotalof3whiteblocks.Therefore,thetotalnumberofwhitewoodenblocksinacubeis2+6+3=11.ORAlargecubecanbemadewithatotalof27smallwhitewoodenblocks(cubes).Greywoodenblockscanbeformedby5whitewoodenblocks,andblackwoodenblockscanbeformedby3whitewoodenblocks.Ifyoulookatthepicture,youcanseethat2greywoodenblocksand2blackwoodenblocksareusedtomakealargecube.Assumingalargecubewith27smallwhitewoodenblocksintotal,27−10(2greyblocks)−6(2blackblocks)=11,so11whitewoodenblockswereused.5points17(PL).Wandachoseafewofthefollowingshapesandsaid”AmongsttheshapesIhavechosen,thereare2colouredones,2largeonesand2roundones.WhatisthesmallestnumberofthefollowingshapesthatWandacouldhavechosen?(A)2(B)3(C)4(D)5(E)6Solution:Wandaselectsthetworoundones(circles);oneiscolouredandoneiswhite.Thenshehasalreadyonelargefigure.Shecouldchosetheotherlargecolouredpiece(square),andallconditionsaresatisfied.SotheminimumamountoffiguresthatWandaselectedisthree.18(IR).Threefootballteamsparticipateinasportstournament.Eachteamplaystheothertwoteamsexactlyonce.Ineachgame,thewinnergets3pointsandtheloserdoesn’tgetanypoints.Ifthegamefinishesinadraw,eachteamgets1point.Attheendofthetournament,whichnumberofpointsisitimpossibleforanyteamtohave?(A)1(B)2(C)4(D)5(E)6Solution:Aseveryteamhasjust2gamesandthepossibilitytoget0,1or3pointseachgame,theonlypossibilitiesare0+0=0points,0+1=1point,1+1=2points,1+3=4pointsand3+3=6points.Thereisnochancetoget5points-forthiscaseateamwouldhavetohaveatleast3gamesSOLUTIONSINCLUDED-DONOTUSEFORCONTEST(3+1+1points).7,EcolierFinalized19(SK).Apyramidisbuiltfromcubeswithaside-viewfromabovelengthof10cm.Anantclimbedupandoverthepyramid,asshownbytheredline.Whatisthelengthofthepathwalkedbytheantacrossthepyramid?(A)30cm(B)60cm(C)70cm(D)80cm(E)90cmSolution:Tothemiddleofthecubeinthetopofthepyramidtheanthastoclimb3cubesvertically(3·10cm=30cm)and3timeshalfacubelengthhorizontally(3·5cm=15cm).Thewayfromthetophasthesamelengthsincethepyramidissymmetric.Sointotaltheantwillclimb30cm+15cm+30cm+15cm=90cm.Alternativesolution(ifweassumethattehcubesarearrangedsymmetrically):Afterclimbingupthefirstcube(10cm)theanthastowalkhorizontallyalongtheredlineforthehalflengthofacube(5cm).Soitcaneasilybecounted:10(up)+5(horizontally)+10+5+10+10(straight,onthetop)+10(down)+5+10+5+10=90cm.Solution3.Theant’swayconsistsofsixverticalintervals(heightofacube)andis6·10=60cm.Intheviewfromabovewecanseethehorizontalpartofthewayoftheant,whichintotalisequaltothreeofthecube’sedge,i.e.3·10=30cm.Intotal60+30=90cm.Note:Ifyouprintinblack/whiteyouneedtochangethewordredline.PictureG15331-3iswithoutthe’viewfromabove’textsothatpeoplecanchoosethatfortheirownlanguage(fortranslationreasons).20(DK).AlmawantstoputoneofthepiecesshowninthemiddleofthepicturesothatachildinAisabletotraveltoBandtoE,butnottoD.Shecanrotatethepieces.EF123DA45BCWhichtwopiecescouldsheuse?(A)1and2(B)2and3(C)1and4(D)4and5(E)1and5Solution:1canbeputinsothatthestraightstreetleadsfromBtoE,thenA(andF,whatdoesn’tmatter)hasaconnectionaswell.2doesn’tworkbecausethispiececonnectsthreeneighboursandA,BandEaren’tthreeneighbours.3wouldconnectAwithCandE,sonottoB.4doesn’tworkbecauseassoonasAhasaccess,ithasaccessstraighttoD.5worksifyouputthe“lonely”endofthestreetstoE,soA,BandCareconnectedaswell,butnotD.Sowenotethat1and5aretheonlySOLUTIONSINCLUDED-DONOTUSEFORCONTESTtwopieceswhichcanbeputinthespacesothatAcantraveltoBandE,butnottoD.8,EcolierFinalized21(IR).AhmadandZhalehstartmovingfrompoint5mAwiththesamespeed,inthedirectionsshown.Ahmadwalksaroundthesquare-shapedgardenandZhalehwalksaroundtherectangular-shapedone.5m5mTheymeetagainatA.Whatisthesmallestnumberoflapsaroundthe10m5mAsquare-shapedgardenthatAhmadcoulddotomeetZhalehthere?5m5m(A)1(B)2(C)3(D)4(E)510mSolution:WhenAhmadhasreturnedtopointAforthefirsttime,hehaswalked4·5m=20m,butthenZhaledisnotatpointA,ashemustwalk2·5m+2·10m=30mforacompleteround.WhenAhmadhasreturnedtopointAforthesecondtime,hehaswalked2·20m=40mandZhaledhaswalkedmorethanonebutlessthan2rounds,soheisnotatpointA.WhenAhmadhasreturnedtopointAforthethirdtime,hehaswalked3·20m=60m.Since60m=2·30m,inthismomentZhalehhascompleted2fullroundsanisbackatpointA.Note:Wekeptthetextasshortaspossible.Tobeprecise,youmaywanttoadd:”forthefirsttimeafterthestart”inthelastsentence.(Sincetheymeetatthestartfirst,thecorrectanswerwouldbe0).However,thereisno0lapsasanoptionrightnowandthisclarificationisnotnecessaryifyoukeepthedistractorsasproposed(1,2,3,4,5).therefore,wedidnotaddthissentencenow.22(PL).Fivechildrenatesomeplums.LaurenatetwoplumsmorethanSophie.BettyatethreeplumsfewerthanLauren.ClaireateoneplummorethanBettyandthreeplumsfewerthanAlice.Whichtwogirlsatethesamenumberofplums?(A)ClaireandLauren.(B)ClaireandSophie.(C)LaurenandAlice.(D)SophieandAlice.(E)AliceandBetty.Solution:Note:Tosolvetheproblemitmaybehelpfultomarkthenumbersofplumsonanumberline.Laurenate2plumsmorethanSophie.BecauseBettyate3plumslessthanLauren,Bettyhad1plumlessthanSophie.SinceClaireate1plummorethanBetty,ClaireateasmanyplumsasSophie,so(B)iscorrect.(AsAliceate3plumsmorethanClaire,Aliceate1plummorethanLauren.AndBettyandClairedidnoteatthesamenumberofplums,SoallthenumbersaredifferentexceptforClaireandSophie.)23(DE).Thesmallcaterpillarshowninthepicturecurlsuptosleep.Whatmightthatlooklike?(A)(B)(C)(D)(E)Solution:Asyousee,thecaterpillarhasalternatelyoneyellowandoneblackcircle.Soyouhavetofindapossible“path”throughthesleepingcaterpillarwhereyoucandrawonelinefromtheheadtoablackcircle,thentoayellow,thentoablackandsoon.TheonlypossibilitytofindsuchawaySOLUTIONSINCLUDED-DONOTUSEFORCONTESTthroughwholethebodyofthecaterpillarisinoptionAasshown:or9,EcolierFinalized24(PL).Inthegrid,thesamenumberishiddenunderthesamecoloursquare.Totherightofeachrow,thesumofthenumbershiddenunderthesquaresinthatrowisgiven.Whichnumberishiddenundertheblacksquare?(A)6(B)8(C)10(D)12(E)14Solution:Thenumberhiddenbygreysquareplustwonumbershiddenbywhitesquaresaddup34,accordingtothefirstlineofthetable.Thenumberhiddenbywhitesquareplustwonumbershiddenbygreysquaresaddup26,accordingtothethirdlineofthetable.Thismeansthatthreenumbersundergreysquaresplusthreenumbersunderwhitesquaresaddup34+26=60(firstandthirdlines).Thus,thenumberunderwhitesquareplusthenumberundergreysquareequals60:3=20.Finally,ifthenumbersinthesecondlinesums32,thenumberunderblackmustbe32−20=12.SOLUTIONSINCLUDED-DONOTUSEFORCONTEST10,Level考试说明/InstructionTimeallowed:75minutes考试时长：75分钟Language:English&Chinese试卷语言：英文和中文Thisisa24-questionmultiple-choicecompetition.考试包含24道单项选择题。Problems1to8areworth3pointseach.1-8题每题3分Problems9to16areworth4pointseach.9-16题每题4分Problems17to24areworth5pointseach.17-24题每题5分1pointwillbedeductedforanincorrectanswerandnopointforablankanswer.答错扣1分，不答不扣分。Thefullscoreis120(Startingpointis24)总分为120分（起始分数为24分）Donotopenthisbookletuntilyouaretoldtodoso.收到监考老师指令后，方可打开试卷册。BMarkyouranswersclearlyontheanswersheetusinga2Bpencil.务必使用2B铅笔在答题卡上正确填涂自己的答案。Grade3Calculatorcannotbeusedduringthecompetition.&考试期间禁止使用计算器。Grade4GoodLuck!预祝考试顺利,,MathKangaroo2023(China)–LevelB3points1.Akiralits5identicalcandlesallatthesametime.Theystoppedburningatdifferenttimesandnowlookasshowninthepicture.Whichcandlestoppedburningfirst?ABCDE小安将5支相同的蜡烛同时点燃。蜡烛在不同的时间停止燃烧，现在看起来如图所示。哪支蜡烛最先停止燃烧？(A)A(B)B(C)C(D)D(E)E2.The2kangaroocoinswiththequestionmarkonhavethesamevalue.Whatisthisvalue?标注问号的两枚袋鼠硬币的面值相同。它们的面值是多少？20+10+10+?+?+1=51(A)1(B)2(C)5(D)10(E)203.Agraycirclewith2largeholesinitisputontopofaclock-face,asshown.1如图所示，将带有两个孔的灰色圆盘放在钟面上。12111121039486557Thegraycircleisturnedarounditscenter.Which2numbersisitpossibletoseeatthesametime?1灰色圆盘绕其中心旋转。哪两个数字可能同时被看到？(A)4and94和9(B)5and95和9(C)5and105和10(D)6and96和9(E)7and127和123,MathKangaroo2023(China)–LevelB4.Alicehasthesepuzzlepieces:小艾有以下拼图：1234Which2piecescansheputtogethertoformthissquare?她可以用哪两块拼成下方的正方形？1(A)1and21和2(B)1and31和3(C)1and41和4(D)2and32和3(E)2and42和415.Alightengineerinthetheatreturnsthelightsonandoff.Sheusestheplanshown.Howlongintotalareexactly2ofthelightsonatthesametime?剧院里的灯光工程师负责灯光的开关，她的开关计划如下图所示。恰好有2盏灯同时亮起的总时长是多少？Green绿色Orange橘黄色Blue0123456789101112蓝色minutes分钟(A)2minutes2分钟(B)6minutes6分钟(C)8minutes8分钟(D)9minutes9分钟(E)10minutes10分钟4,MathKangaroo2023(China)–LevelB6.Kristofferfoldsthetransparentpaperalongthedashedline.小凯沿着中间虚线折叠透明纸。Whatcanhethensee?他能看到什么图案？1(A)(B)(C)(D)(E)7.Annahas4discsofdifferentsizes.Shewantstobuildatowerof3discsso111thateverydiscissmallerthanthediscbelowit.HowmanydifferenttowerscanAnnamake?11小娜有4张大小不同的圆盘。她想建造一个由3张圆盘组成的塔，并且每张圆盘都比紧邻其下方的圆盘小。小娜能建造多少个不同的塔？(A)1(B)2(C)4(D)5(E)68.Dannygluedthe2piecesofpaperontopoftheblackcircleontheright.小丹把两张纸粘在右侧黑色圆上。Whatcanhenotobtain?他无法获得以下哪个图案？(A)(B)(C)(D)(E)5,MathKangaroo2023(China)–LevelB4points9.Theshapeontherightiscoveredwiththe5piecesbelow.Whichpiecewillcoverthedot?右侧图形正好可以被下方选项中的5个碎片覆盖住。哪个碎片将会覆盖在圆点上面？(A)(B)(C)(D)(E)10.Therearesixweightsof1,2,3,4,5and6kg.Rossitzaputsfiveofthemonthescalesandputsoneweightaside.Thescalesbalance.Whichweightdidsheputaside?有六个砝码，重量分别为1、2、3、4、5和6千克。小罗将其中五个砝码放在天平上，还剩一个砝码。天平保持平衡，剩下的砝码重量是多少？(A)1kg1千克(B)2kg2千克(C)3kg3千克(D)4kg4千克(E)can’tbesure无法确定11.Alihasa60cmruler.Unfortunately,someofthemarkingshavefadedaway.Heisabletomeasureanyofthelengths10,20,30,40,50and60cmusinghisruleronlyonce.WhichisAli’sruler?小力有一把60cm的尺子。但尺子上的一些刻度已经看不清了。每次他只用这把尺子量一回，就可以测出10、20、30、40、50和60cm中的任意长度。以下哪把是小力的尺子？10302040305010201040(A)60cm(B)60cm(C)60cm(D)60cm(E)60cm6,MathKangaroo2023(China)–LevelB12.Thereare7housesnorthofRoadA,8houseseastofRoadBand5housessouthofRoadA.RoadAHowmanyhousesarewestofRoadB?路A路A的北面有7栋房屋，路B的东面有8栋房North北屋，路A的南面有5栋房屋。路B的西面有多少栋BWest西East东房屋？RoadB路South南(A)4(B)5(C)6(D)7(E)813.Thereare8carswaitinginaqueuefortheferry.Everycarcontainseither2or3people.Thereare19peopleintotalwaitingfortheferry.Howmanycarscontainexactly2people?有8辆摆渡车在排队等候。每辆车可容纳2人或3人，一共有19人在等待摆渡。有多少辆车恰好只坐了两个人？(A)2(B)3(C)4(D)5(E)614.TheMetrolinehas6stations,A,B,C,WestEastD,E,andF.西东Thetrainstopsateverystation.ABCDEFWhenitreachesoneofthetwoendstations,itchangesitsdirection.ThetraindriverstarteddrivingatstationBandherfirststopwasstationC.Whichstationwillbeher96thstop?地铁线路有6个车站A、B、C、D、E和F。地铁每站都会停。当地铁到达两端的终点站时，就会改变方向。地铁司机从B站出发，到达的第一站是C站。那么第96站是哪一站？(A)A(B)B(C)C(D)D(E)E15.Haticewantstopaintthecirclesinthepicture.Shewantstopaintany2circlesconnectedwithalinedifferentcolours.Whatisthesmallestnumberofcolourssheneeds?小花想将图中的圆圈全部涂色，同一条线段连接的任意两个圆圈都涂上不同颜色。她最少需要多少种颜色？(A)2(B)3(C)4(D)5(E)67,MathKangaroo2023(China)–LevelB16.Samwalksthroughthetwo-storeymazefromtheentrancetotheexit,passing3wallstickers.Inwhatorderwillsheseethem?小莎从入口走到出口，会穿过两层楼的迷宫，路过三张贴纸。她会按照什么顺序看到这些贴纸？OUT出口INgroundfloor一楼入口firstfloor二楼(A)(B)(C)(D)(E)5points17.6beaversand2kangaroosarestandinginaline.12345678Amongstany3consecutivelynumberedanimals,exactly1isakangaroo.Whichnumberedanimalisakangaroo?6只海狸和2只袋鼠站成一排。任意3个编号连续的动物中，恰好有1只是袋鼠。以下哪个编号对应的是袋鼠？(A)1(B)2(C)3(D)4(E)518.Rebeccafoldsasquarepieceofpapertwice.Thenshecutsoffonecorner.Next,sheunfoldsthepaper.Whatdoesthepaperlooklikeonceunfolded?小瑞将一张正方形纸对折了两次，然后剪掉一个角，最后将这张纸展开。以下哪项是这张纸展开后的样子？(A)(B)(C)(D)(E)19.Hermione,HarryandRonalwayswalkintothecommonroomoneatatime.Hermioneisneverfirst,HarryisneversecondandRonisneverthird.Inhowmanydifferentorderscouldtheywalkin?赫敏、哈利和罗恩总是按照不同顺序走进公共休息室。赫敏从来不是第一个，哈利从来不是第二个，罗恩从来不是第三个。他们可以有多少种不同的顺序进入休息室？(A)1(B)2(C)3(D)4(E)68,MathKangaroo2023(China)–LevelB20.Therearefiveclocksonthewall.Itisknownthatoneclockisanhourfast,oneclockisanhourslow,oneclockshowsthecorrecttimeandtwoclockshavestopped.Whichclockshowsthecorrecttime?墙上挂着五个钟。已知有一个钟走快了一小时，一个钟走慢了一小时，一个钟显示正确的时间，两个时钟已停止工作，以下哪个钟显示的时间是正确的？(A)A(B)B(C)C(D)D(E)E21.AdamandBrendahave9marbleseach.Together,theyhave8redand10bluemarbles.Brendahastwiceasmanybluemarblesasredmarbles.HowmanybluemarblesdoesAdamhave?小亚和小布每人有9颗弹珠，两人的弹珠加起来一共有8颗红色弹珠和10颗蓝色弹珠。小布拥有的蓝色弹珠是红色弹珠的两倍。小亚有多少颗蓝色弹珠？(A)3(B)4(C)5(D)6(E)022.Elsehastwomachines.WhensheputsasquaresheetofpaperinmachineR,itturnsthepaper90◦clockwise,asshowninthepicture.WhensheputsthepaperinmachineS,itstampsthepaperwitha♣.小艾有两台机器。如图所示,当她把一张方形纸放进机器R时，它会把纸张顺时针旋转90◦；当把方形纸放进机器S时，它会在纸张上打印出图案♣。RS♣Inwhichorderarethemachinesusedtoproducetheresultshown?要在纸张上最终形成下图所示的图案，使用机器的顺序是什么？♣???(A)SRR(B)RSR(C)RSS(D)RRS(E)SRS9,MathKangaroo2023(China)–LevelB23.TeacherOlenawantstowritethenumbers1to7inthecircles.Insideeach78circleshewrites1number.Shewantsthesumofthenumbersin2circlesthat99arenexttoeachothertobeasshown.Whatnumbermustshewriteinsidethegreen/shadedcircle?869小欧老师想把数字1到7写在圆圈里，每个圆圈内写一个数字。她希望相邻圆圈中的数字之和如图所示。她必须在绿色/阴影圆圈内写的数字是多少？(A)1(B)2(C)3(D)4(E)524.Mariahasshadedexactly5cellsina4×4grid.Shechallenges5ofherfriendstoguesswhichcellsshehasshaded.Thegridstheyhavedrawnareshownbelow.Marialooksatthemandsays:“Oneofyouisrightandeachoftherestofyouhasfourcellscorrect.”Whichisthecorrectanswer?小玛在一个4×4网格中只给5个单元格涂上了阴影。她邀请5个朋友猜测涂上阴影的单元格有哪些。5个朋友绘制的网格如下所示。小玛看着他们说：“你们当中有一个是正确的，其余的每个人都猜对了四个阴影单元格。”以下哪个网格是正确的？(A)(B)(C)(D)(E)10,EcolierFinalizedEcolier3points1(France).Akiralits5identicalcandlesallatthesametime.Theystoppedburningatdifferenttimesandnowlookasshowninthepicture.Whichcandlestoppedburningfirst?ABCDE(A)A(B)B(C)C(D)D(E)ESolution:Sincetheyareinitiallyidenticalcandles,theonethatwentoutfirstistheonewhosesizehasdecreasedtheleast.2(Denmark).The2kangaroocoinswiththequestionmarkonhavethesamevalue.Whatisthisvalue?contest20+10+10+?+?+1=51for(A)1(B)2(C)5(D)10(E)20useSolution:Thevalueofthe2coinstogetheris51−20−10−10−1=10.Hencetheirvalueis5.3(Denmark).Agraycirclewith2largeholesinitisputontopofaclock-face,asshown.1not1211112do103-9486557Thegraycircleisturnedarounditscenter.1Which2numbersisitpossibletoseeatthesametime?included(A)4and9(B)5and9(C)5and10(D)6and9(E)7and12Solution:Thepictureshowsthatoneholewillshowatime4hoursaftertheother.ThisisonlytrueforB.4(Denmark).Alicehasthesepuzzlepieces:Solutions1234Which2piecescansheputtogethertoformthissquare?1(A)1and2(B)1and3(C)1and4(D)2and3(E)2and411,EcolierFinalizedSolution:15(Slovakia).Alightengineerinthetheatreturnsthelightsonandoff.Sheusestheplanshown.Howlongintotalareexactly2ofthelightsonatthesametime?GreenOrangeBluecontest0123456789101112minutesfor(A)2minutes(B)6minutes(C)8minutes(D)9minutes(E)10minutesuseSolution:Thediagramshowstwelveinstants(minutes),numberedfrom1to12,atwhichthelightsareturnedonorturnedoff.Thereareexactly2lightsonduringthefollowinginstants(minutes):2(greenandbluelights),4(greenandorangelights),5(greenandorangelights),6(orangeandbluenotlights),7(greenandbluelights),9(greenandorangelights),11(orangeandbluelights),and12(orangeandbluelights).Thus,thereare2lightsonfor8minutes.do-6(Denmark).Kristofferfoldsthetransparentpaperalongthedashedline.includedWhatcanhethensee?1Solutions(A)(B)(C)(D)(E)11111Solution:21,EcolierFinalized7(Slovenia).Annahas4discsofdifferentsizes.Shewantstobuildatowerof3discssothateverydiscissmallerthanthediscbelowit.HowmanydifferenttowerscanAnnamake?(A)1(B)2(C)4(D)5(E)6Solution:WecanuseA,B,CandDtodescribethe4discsorderdbysize.WithoutthediscAthereisexactly1waytocostructsuchatower:BCD.WithoutthediscBthereisexactly1waytocostructsuchatower:ACD.WithoutthediscCthereisexactly1waytocostructsuchatower:ABD.WithoutthediscDthereisexactly1waytocostructsuchatower:ABC.Therefore,Annacanmake4differenttowers.contestforuse8(Germany).Dannygluedthe2piecesofpaperontopoftheblackcircleontheright.Whatcanhenotobtain?notdo-(A)(B)(C)(D)(E)Solution:Answer:D.Dannycanobtainthecomposition(A)bygluingthegreypieceovertheblackpiece,andthewhitepieceoverthegreypiece.Healsocanobtainthecomposition(B)bygluingthewhitepieceovertheblackpiece,andthegreypieceovertheblackandthewhitepieces,asshownincludedbeside:Itispossibletoobtainthecomposition(C)bygluingthewhiteandgreypiecesovertheblackpiece.Finally,itispossibletoobtainthecomposition(D)bygluingthewhitepieceovertheblackpiece,andthegreypieceovertheblackandthewhitepieces,asshownbeside:SolutionsHowever,itisimpossibletoobtainthecomposition(E),becausethegreypieceisshapedliketwowhitepiecestogether,whilethisoptionshowstwogreypiecesseparated.4points3,EcolierFinalized9(Greece).Theshapeontherightiscoveredwiththe5piecesbelow.Whichpiecewillcoverthedot?(A)(B)(C)(D)(E)Solution:Firstly,wehavetochoosethepieceforthecorner.Cistheonlyoptiontoplace.contestNowthereare3andhalfsquaresonthehorizontalpositionand2andhalfontheverticalpositionarestillneededtofill.foruseCombinationofPieceBandPieceDcanmakethefigure:andcombinationofPieceAandPieceCcanmakethefigurenotSo,thepiecethatcoversthedotisA.(Or)doWecancoverthefigurewiththefivepiecesasbelow.-So,thepiecethatcoversthedotisA.included10(Russia).Therearesixweightsof1,2,3,4,5and6kg.Rossitzaputsfiveofthemonthescalesandputsoneweightaside.Thescalesbalance.Whichweightdidsheputaside?Solutions(A)1kg(B)2kg(C)3kg(D)4kg(E)can’tbesureSolution:Weights5and6kgarealreadyused.Ifwedonotuseweights2or4kgthetotalweightoftheremainingweightswillbeexpressedasanoddnumber(19and17kgaccordingly).Inthiscaseitisimpossibletodividetheweightssothatthescalescomeinbalance.Sotheansweris1or3kg.Let’scheckthem.Withouttheweight1kgthetotalweightwillbe2+3+4+5+6=20kg.Sooneachbowlofthescalesshouldbe10kg.Itispossibleifweput5+3+2ononebowland4+64,EcolierFinalizedontheotherbowl.Itmatcheswiththepicture.Withouttheweight3kgthetotalweightwillbe1+2+4+5+6=18kg.Sooneachbowlshouldbe9kg.Itispossibleifweput5+4ononebowland6+2+1ontheotherbowl.Butthatdoesnotmatchwiththepicture.11(Greece).Alihasa60cmruler.Unfortunately,someofthemarkingshavefadedaway.Heisabletomeasureanyofthelengths10,20,30,40,50and60cmusinghisruleronlyonce.WhichisAli’sruler?10302040305010201040(A)60cm(B)60cm(C)60cm(D)60cm(E)60cmSolution:WithE)hehasreadythelength10cm.Hecanmeasure20cmbyusingtheportionfromcontest40totheend,whichisoflength60-40=20cm.Hecanget30fromthemarksbyusing40-10=30cm.Thelength40cmisalreadymarked,50cmisfrom60-10=50cm.andthelength60cmistheforwholeruleruse12(Greece).Thereare7housesnorthofRoadA,8nothouseseastofRoadBand5housessouthofRoadA.RoadAHowmanyhousesarewestofRoadB?do(A)4-North(B)5WestEast(C)6RoadBSouth(D)7(E)8includedSolution:ThehousesnorthandsouthofRoadAareallthehouses.Soallthehousesare7+5=12.ThehouseseastandwestofroadBarealsoallthehouses(so12).Asthereare8houseseastofit,theremaining12-8=4housesarewestofroadB.(Notewecannotfindanexactnumberofhousesperquarter.GoingclockwisefromthefirstquadranttheyareN,8-N,N-3and7-NhousesrespectivelyastheparameterNcanvaryonanappropriaterange.)13(Norway).Thereare8carswaitinginaqueuefortheferry.SolutionsEverycarcontainseither2or3people.Thereare19peopleintotalwaitingfortheferry.Howmanycarscontainexactly2people?(A)2(B)3(C)4(D)5(E)6Solution:Answer:D.Since19isdivisibleneitherby3nor2,thereareatleast1carwith2peopleandatleast1carwiththreepeople.Iftherewereexactly1carwiththreepeople,therewouldbe7carswithtwopeopleeach.However,19-3=16,and2x7=14.Iftherewereexactly2carswiththreepeopleeach,therewouldbe6carswithtwopeopleeach.However,19-6=13,and2x6=12.Consideringthereareexactly3carswiththreepeopleeach,theremustbe5carswithtwopeopleeach.Also,19-9=10,and2x5=10.Thus,thereare5carswithtwopeopleeach.5,EcolierFinalized14(Greece).TheMetrolinehas6stations,A,B,C,D,E,andF.WestEastThetrainstopsateverystation.ABCDEFWhenitreachesoneofthetwoendstations,itchangesitsdirection.ThetraindriverstarteddrivingatstationBandherfirststopwasstationC.Whichstationwillbeher96thstop?(A)A(B)B(C)C(D)D(E)ESolution:Solution1:After10stopssheisatexactlythesamepositionandistravelingtoEast.Soweonlyneedtocalculateherlocationafter96-90=6stops.ThatbringshertoDandsheistravelingtowardstheWest.Solution2:ABCDEF12349876510111213141918171615Andcontinuethisuntilthenumber96isreached.Ornoticesomeregularityinhere,forexampleforF:4,14,24,34,44,54,64,74,84,94,andthentwomoretotheleftfromFsothatwillbeD.OrnoticethatforDineverysecondrowthereis6,16,26,36,andsoon,until96sotheanswerisD.Notethatcontestthisquestionallowsforsolutionsatmanydifferentlevels.for15(Hungary).Haticewantstopaintthecirclesinthepicture.Shewantstopaintany2circlesconnectedwithalinedifferentcolours.Whatisthesmallestnumberofcolourssheneeds?use(A)2(B)3(C)4(D)5(E)6notSolution:Namethecirclesasshowninfigure.doAB-CDEFGAmongthecircles,CircleDhasthehighestnumberofconnectionswiththeothercircles.So,wehavetostartwiththiscircletogetthecorrectanswer.Thequestionisthegetthesmallestnumberofincludedcolorstobeused.IfwepaintCircleDwithblue,wecanuseredinCircleFandgreeninCircleG.WecanchooseredorgreenforCircleA.IfwechooseredforCircleA,wecanusegreenforCircleCbecauseredisalsousedforCircleFanditisconnectedtoCircleC.WecanchooseredorgreenforCircleB.WehavetochoosegreenforCircleB,redforCircleEbecausegreenisalsousedforCircleGanditisconnectedtoCircleE.Therefore,thesmallestnumberofcolorsweneedis3;red,blueandgreen.(Or)Wecanpaintthecirclesasshowninthefollowingfigure.SolutionsThesmallestnumberofcolorsweneedis3;red,blueandgreen.16(Belgium).Samwalksthroughthetwo-storeymazefromtheentrancetotheexit,passing3wallstickers.Inwhatorderwillsheseethem?6,EcolierFinalizedOUTINgroundfloorfirstfloor(A)(B)(C)(D)(E)Solution:Samhastowalkalongthenumbersfromtheentrancetoexit.contestFirstly,hewillseethefroginnumber4,thenrhinoinnumber8andfinallysharkonnumber13.So,theansweris(A)frog,rhinoandshark.for5pointsuse17(Greece).6beaversand2kangaroosarestandinginaline.12345678notAmongstany3consecutivelynumberedanimals,exactly1isakangaroo.doWhichnumberedanimalisakangaroo?-(A)1(B)2(C)3(D)4(E)5Solution:Ifnumber1isakangaroothen2and3arebeavers.Butif2and3arebeavers,then4isakangaroo.Similarly5and6arebeaversand7isakangaroo.Thisisimpossiblebecauseweonlyhavetwokangaroosandwefoundat1,4and7.Similarly2cannotbeakangaroobecausebyavariantofthepreviousargumentitwouldfollowthatthe2,5and8are(three,nottwo)kangaroos.Number3isapossibility:Itfollows3and6arekangaroosandtherestarebeavers.Wecanrejectthecasewhereincludednumber4isakangarooasitforces1and7tobekangaroos.Also5isrejectedwithasimilarargument.12345678Weconcludethatnumbers3and6,andonlythem,arekangaroos.Solution2:Startingwithakangarooattheposition1wouldmeantherearekangaroosatpositions4and7,andthereareonlytwokangaroos;similarly,ifthefirstkangarooisattheposition2,wemusthaveoneatposition5andposition8whichisnotpossible.Therefore,kangaroosareatpositions3and6,sotheansweris3.Solutions18(Slovakia).Rebeccafoldsasquarepieceofpapertwice.Thenshecutsoffonecorner.Next,sheunfoldsthepaper.Whatdoesthepaperlooklikeonceunfolded?7,EcolierFinalized(A)(B)(C)(D)(E)Solution:Theupperrightquarterofthesquareretainsitspositionafterfolding,andithasatrianglecutoutatitsbottomleft,whichafterunfoldinggivesshape(B).19(Hungary).Hermione,HarryandRonalwayswalkintothecommonroomoneatatime.Hermioneisneverfirst,HarryisneversecondandRonisneverthird.Inhowmanydifferentorderscouldtheywalkin?(A)1(B)2(C)3(D)4(E)6Solution:IfHermioneissecond,RonmustbethirdandHarryfirst.IfHermioneisthird,HarrymustbefirstandRonsecond.Therefore,therearetwopossibleorders.contest20(Russia).Therearefiveclocksonthewall.forItisknownthatoneclockisanhourfast,oneclockisanhourslow,oneclockshowsthecorrecttimeandtwoclockshavestopped.Whichclockshowsthecorrecttime?usenotdo-(A)A(B)B(C)C(D)D(E)ESolution:Solution1:Ifoneclockshowsthecorrecttime,oneclockisinahurryforanhourandoneclockisanhourbehindthenthreeclocksshouldshowthetimewithadifferenceof1hour.Theclockintheworkshopshows6,2,4,3and7o’clock.Theonlysetthatfitstheconditionis2,3and4hours.Sothecorrecttime-3o’clock-isshownbyclockD.Solution2:Havingtwoclocksthatincludedareoffby1hourmeansthattogetherwiththeclockthatshowscorrecttimetheseclocksshowthreeconsecutivenumbers.Theclocksintheworkshopshow6,2,4,3,and7o’clock,hencethecorrecttimeis3o’clock.21(Brazil).AdamandBrendahave9marbleseach.Together,theyhave8redand10bluemarbles.Brendahastwiceasmanybluemarblesasredmarbles.SolutionsHowmanybluemarblesdoesAdamhave?(A)3(B)4(C)5(D)6(E)0Solution:Note:thepictureisnotnecessarybutcanbeused.Brendahas6blueand3redmarbleswhichmeansAdamhastheremaining10-6=4bluemarbles.22(Denmark).Elsehastwomachines.WhensheputsasquaresheetofpaperinmachineR,itturnsthepaper90◦clockwise,asshowninthepicture.8,EcolierFinalizedWhensheputsthepaperinmachineS,itstampsthepaperwitha♣.RS♣Inwhichorderarethemachinesusedtoproducetheresultshown?♣???(A)SRR(B)RSR(C)RSS(D)RRS(E)SRScontestforusenotdo-includedSolutionsSolution:Thepaperhasbeenturned90degreesclockwisetwice,butonlyonetimeafteritwasstamped.HenceRSR.9,EcolierFinalized23(Greece).TeacherOlenawantstowritethenumbers1to7inthecircles.78Insideeachcircleshewrites1number.Shewantsthesumofthenumbersin2circlesthatarenexttoeachothertobeas99shown.Whatnumbermustshewriteinsidethegreen/shadedcircle?869(A)1(B)2(C)3(D)4(E)5Solution:Note:thereisab/wversionwiththewordsuminitavailablecontestforuseNote.Alternativetext(LB)forthesecondlineoftext:Alongeachlineistheadditionofthenumbersinthe2circlesonthatline.Solution1:Theproblemcanbesolvedbyfiguringoutwherethenumber1goes.Noticethatnumber1cannotgivesum9togetherwithacirclenexttoitastheavailablenotnumbersarefrom1to7.Thereforenumber1mustgointhetopcircle,andfromthereit’squicktofigurethatthegreencircleisfilledwithnumber4.doThesolutioncanalsobeobtainedbycheckingallthepossiblesolutionsforthegreencircleonebyone.-Solution2:Weworkbycheckingsystematicallythecases.Forexamplea)supposeforthemomentthatthegreencirclecontainthenumber1.ThengoinganticlockwiseALLothernumberscanbefilledusingthegivensums.Forinstancethenextcircle(ontherightofthegreenone)must5sothatthesumis6.Thenextafterthatmustbe6-5=1,then9-1=8.Thiscannotbebecausethenumbersareupto7,sowestartagainsupposingforthemomentthatb)thegreencirclecontainthenumber2.Thiswillbefollowedby6-2=4,thenby9-4=5,thenby8-8=3thenby7-3=4.Thiscannotbebecausethenumber4hasalreadybeenused.Sonewstartwithc)with3atthegreencircle.Theincludednextnumberisagain3,whichwereject.Westartagainwith4.Thistimeitworksasshown,andwearedone.Ifwetried5itwillfailasinthecaseswealreadysaw.Notethatwecansavetimebydoingsomeadhoclittleargumentstorejectcases.Forexampleata)abovewestartedwiththenumber1.Thiscanimmediatelyberejectedbecausethenumberonitsleftwouldhavetobe9-1=8,whichis7186799Solutions328654notpermitted.Andsoon.924(Catalonia).Mariahasshadedexactly5cellsina4×4grid.Shechallenges5ofherfriendstoguesswhichcellsshehasshaded.Thegridstheyhavedrawnareshownbelow.Marialooksatthemandsays:”Oneofyouisrightandeachoftherestofyouhasfourcellscorrect.”Whichisthecorrectanswer?10,EcolierFinalized(A)(B)(C)(D)(E)Solution:Therearethreeshadedcellswhicharecommonforallgrids.Lookingatthedifferences,theonlygridwhichdiffersfromeachoftheothergridsbyexactlyonecellisgrid(E).contestforusenotdo-includedSolutions11