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1、ThefirstquestionisabouttheGodSNumber.SotwewannaknowwhatistheGod,sNumber?IbelievethatmanyofsmayhaveplayedRubiksCube,andtheGod,SNumberisaboutthatcube.So,lookatthispictureontheleft.EvenifyouhaventplayedtheRubiksCube,youcaneasilyfindthatithasonlybeenrotatedtwice,soyouonlyneedtorotateittwiceinreverseorde
2、randthenyoucanrecoverit.Lookattherightone.Itwasrandomlyrotatedbysixsteps.Itseemsabitdifficulttoseehowtorecoveritataglance.However,ifweknowexactlyhowitwasrotated,wecanstillrotateitinreverseorder.Justneedsixstepswecanrecoverthiscomplicatedcube.ButisthereverseorderalwaysbeingthebestwaytorecovertheRbik,
3、scube?1.etuslookatthenextquestion.WhatifthestateofaRubiksCubeisobtainedbyrotatingitonethousandsteps?Howtorecoverit?Dowealsoneedtorotateinreverseorderonethousandsteps?Ofcausenot.PeoplewhohaveplayedRubiksCubemayknowthattherearesomespecificwaystosolverandomlyrotatingRubiksCube,withonlyalimitednumberofs
4、teps,(excepttheonewithtwistedcorners)Therefore,wewanttoknowwhetherexistanexactupperlimitnumberofsteps,nomatterwhatstatetheRubikscubeisrotatedinto,wecanrecoveritwithinthisnumberofsteps.AndthisnumberistheGodsNumber.Manymathematicianshaveresearchedintothisproblem.Theyusedthemathematicalprinciplesofsymm
5、etry,grouptheory,topology,andsoon.Mathematiciansadvancethisnumberverydifficult.Untiltwothousandandsix,theGod,sNumberwasprovedtobebetween20and27.Duringthisprocess,amathematiciandiscoveredaRbik,sCubestate,whichrequiresatleast20stepstorecover,justlikethispicture.Withthedevelopmentofcomputerscience,scie
6、ntistscontinuetoupdatethealgorithmtosolvetheRubiksCube,finallyintwothousandandten.ScientistshavecompletedthecalculationofthestateofallRubiksCubeswithcomputers.Andtallstatescanberesolvedwithin20steps.Atthattime,wecansaythattheGodsnumberis20.Isthisover?No,infact,weonlysolvedtheproblemofthethird-orderR
7、ubiksCubebybruteforce,notbytheoreticalproof.Weonlyknowthatitisindeed20.butwedontknowwhy.So,whataboutthefourth-orderRubiksCube?Wedontknow.AlthoughwehavesomegeneralwaystosolveanyRubiksCubeproblem,wedontknowwhetheritisthebest.Maybeoneday,whenwebuildaquantumcomputer,wecanalsogettheGodsNumberofthefourth-orderRubiksCubethroughbruteforcetbutwhataboutthefifth-orderRubiksCube?Westillneedtoresearch.
