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1、RaymondSmullyanWhatisthenameofthisbook?ImagesbyM.C.EscherTHEISLANDOFKNIGHTSANDKNAVESThereisawidevarietyofpuzzlesaboutanislandinwhichcertaininhabitantscalled"knights"alwaystellthetruth,andotherscalled"knaves"alwayslie.Itisassumedthateveryinhabitantoftheislan
2、diseitheraknightoraknave.Ishallstartwithawellknownpuzzleofthistypeandthenfollowitwithavarietyofpuzzlesofmyown.26.Accordingtothisoldproblem,threeoftheinhabitants-A,B,andC-werestandingtogetherinagarden.AstrangerpassedbyandaskedA,"Areyouaknightoraknave?"Aanswe
3、red,butratherindistinctly,sothestrangercouldnotmakeoutwhathesaid.ThestrangerthanaskedB,"WhatdidAsay?"Breplied,"Asaidthatheisaknave."Atthispointthethirdman,C,said,"Don'tbelieveB;heislying!"Thequestionis,whatareBandC?solution26.Itisimpossibleforeitheraknighto
4、raknavetosay,"I'maknave,"becauseaknightwouldn'tmakethefalsestatementthatheisaknave,andaknavewouldn'tmakethetruestatementthatheisaknave.ThereforeAneverdidsaythathewasaknave.SoBliedwhenhesaidthatAsaidthathewasaknave.HenceBisaknave.SinceCsaidthatBwaslyingandBw
5、asindeedlying,thenCspokethetruth,henceisaknight.ThusBisaknaveandCisaknight.(ItisimpossibletoknowwhatAis.)26.Itisimpossibleforeitheraknightoraknavetosay,"I'maknave,"becauseaknightwouldn'tmakethefalsestatementthatheisaknave,andaknavewouldn'tmakethetruestateme
6、ntthatheisaknave.ThereforeAneverdidsaythathewasaknave.SoBliedwhenhesaidthatAsaidthathewasaknave.HenceBisaknave.SinceCsaidthatBwaslyingandBwasindeedlying,thenCspokethetruth,henceisaknight.ThusBisaknaveandCisaknight.(ItisimpossibletoknowwhatAis.)27.WhenIcameu
7、pontheaboveproblem,itimmediatelystruckmethatCdidnotreallyfunctioninanyessentialway;hewassortofanappendage.Thatistosay,themomentBspoke,onecouldtellwithoutC'stestimonythatBwaslying.Thefollowingvariantoftheproblemeliminatesthatfeature.Supposethestranger,instea
8、dofaskingAwhatheis,askedA,"Howmanyknightsareamongyou?"AgainAanswersindistinctly.SothestrangerasksB,"WhatdidAsay?Breplies,"Asaidthatthereisoneknightamongus."ThenCsays,"Don'tbelieveB;heislying!"Thequesti
