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

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.