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1、BrainTeasersAPracticalGuideToQuantitativeFinanceInterviewsIftwopeopleinthisgroupmeteachother,youandthepair(3people)meteachother.Ifweonlyuse2coinsfrombag2,thefinalsumforIcoinfrombag1and2coinsfromnopairamongthesepeoplemeteachother,thenthesepeople(>3people)didnotmeetbag2rangesfrom-3to3(7pigeonho
2、les).Atthesametimewehave9(3x3)possibleeachother.Ineithersub-case,theconclusionholds.combinationsfortheweightsofcoinsinbag1andbag2(9pigeons).SoatleasttwoCase2:Supposeatleast3peoplehavenotmetyoubefore.combinationswillyieldthesamefinalsum(9)7,soatleasttwopigeonsneedtoshareonehole),andwecannotdis
3、tinguishthem.Ifweuse3coinsfrombag2,then.thesumIftwopeopleinthisgroupdidnotmeeteachother,youandthepair(3people)didnotrangesfrom-4to4,whichispossibletocoverall9combinations.Thefollowingtablemeeteachother.Ifallpairsamongthesepeoplekneweachother,thenthesepeople(;:::3exactlyshowsthatallpossiblecom
4、binationsyielddifferentsums:people)meteachother.Again,ineithersub-case,theconclusionholds.Sumtcoin,bag1AntsonasquareNI~-I01CO"•Thereare51antsonasquarewithsidelengthof1.Ifyouhaveaglasswitharadiusof-I-4-3-2,;;117,canyouputyourglassatapositiononthesquaretoguaranteethattheglassc'00-I01encompasses
5、atleast3ants?'!U~1234Solu'io~:Toguaranteethattheglassencompassesatleast3ants,wecanseparatetheelandC2representtheweightsofcoinsfrombag1and2respectively.squaremto25smallerareas.ApplyingthegeneralizedPigeonHolePrinciplewecan3showthatatleastoneoftheareasmusthaveatleast3ants.Soweonlyneed'tomakeThe
6、nhowabout3bags?Wearegoingtohave3=27possiblecombinations.Surelyansurethat.theglassislargeenoughtoCoveranyofthe25smallerareas.Simplyseparateindicatorrangingfrom-13to13willcoveritandwewillneed9coinsfrombag3.Thethe.areaInto5x5smallersquareswithsidelengthof1/5eachwilldosinceacirclewithpossiblecomb
7、inationsareshowninthefollowingtable:radiusof1/7cancoverasquare'?withsidelength115.SumC2-IC2=OC21~I~-t01-I01-I01CounterfeitcoinsIIee"CO-I-13-12-II-10-9-8-7-6-5,;;Thereare5bagswith~00c~insineachbag.Acoincanweigh9grams,10gramsorIIc'00-4-3-2-I012
