The first question is about the God’s Number.docx

ThefirstquestionisabouttheGod'SNumber.SotwewannaknowwhatistheGod,sNumber?IbelievethatmanyofsmayhaveplayedRubik'sCube,andtheGod,SNumberisaboutthatcube.So,lookatthispictureontheleft.Evenifyouhaven'tplayedtheRubik'sCube,youcaneasilyfindthatithasonlybeenrotatedtwice,soyouonlyneedtorotateittwiceinreverseorderandthenyoucanrecoverit.Lookattherightone.Itwasrandomlyrotatedbysixsteps.Itseemsabitdifficulttoseehowtorecoveritataglance.However,ifweknowexactlyhowitwasrotated,wecanstillrotateitinreverseorder.Justneedsixstepswecanrecoverthiscomplicatedcube.ButisthereverseorderalwaysbeingthebestwaytorecovertheRbik,scube?1.etuslookatthenextquestion.WhatifthestateofaRubik'sCubeisobtainedbyrotatingitonethousandsteps?Howtorecoverit?Dowealsoneedtorotateinreverseorderonethousandsteps?Ofcausenot.PeoplewhohaveplayedRubik'sCubemayknowthattherearesomespecificwaystosolverandomlyrotatingRubik'sCube,withonlyalimitednumberofsteps,(excepttheonewithtwistedcorners)Therefore,wewanttoknowwhetherexistanexactupperlimitnumberofsteps,nomatterwhatstatetheRubik'scubeisrotatedinto,wecanrecoveritwithinthisnumberofsteps.AndthisnumberistheGod'sNumber.Manymathematicianshaveresearchedintothisproblem.Theyusedthemathematicalprinciplesofsymmetry,grouptheory,topology,andsoon.Mathematiciansadvancethisnumberverydifficult.Untiltwothousandandsix,theGod,sNumberwasprovedtobebetween20and27.Duringthisprocess,amathematiciandiscoveredaRbik,sCubestate,whichrequiresatleast20stepstorecover,justlikethispicture.Withthedevelopmentofcomputerscience,scientistscontinuetoupdatethealgorithmtosolvetheRubik'sCube,finallyintwothousandandten.ScientistshavecompletedthecalculationofthestateofallRubik'sCubeswithcomputers.Andtallstatescanberesolvedwithin20steps.Atthattime,wecansaythattheGod'snumberis20.Isthisover?No,infact,weonlysolvedtheproblemofthethird-orderRubik'sCubebybruteforce,notbytheoreticalproof.Weonlyknowthatitisindeed20.butwedon'tknowwhy.So,whataboutthefourth-orderRubik'sCube?Wedon'tknow.AlthoughwehavesomegeneralwaystosolveanyRubik'sCubeproblem,wedon'tknowwhetheritisthebest.Maybeoneday,whenwebuildaquantumcomputer,wecanalsogettheGod'sNumberofthefourth-orderRubik'sCubethroughbruteforcetbutwhataboutthefifth-orderRubik'sCube?Westillneedtoresearch.