Message #502

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: Magic120Cell Realized
Date: Wed, 07 May 2008 10:16:10 -0500

You guys will likely find this article interesting and a fun read:

http://www.scottaaronson.com/writings/bignumbers.html

Charlie shared it with me some time ago and it discusses truly unbelievably
unimaginably big numbers (not that the number David presented doesn’t fall
into this category ;))

David, thank you *so much* for your writeup on this!! I fixed my incorrect
listing of the number of pieces on the site (I apparently accidentally
multiplied by 2 instead of dividing by 2 when calculating the number of 2C
pieces, which is also why my quick permutation estimate was so far off).
For the total I wrote there, I also included the 0C (120-cell shaped)
interior and hidden piece of the puzzle.

Roice

On Wed, May 7, 2008 at 1:43 AM, Melinda Green <melinda@superliminal.com>
wrote:

> What a number indeed!
>
> So let me get this straight. If you imagine all the particles in the
> universe, and then imagine that each one really consists of another
> entire universe, and for each particle in those universes, another
> universe, and so on ten times, you would still not have enough particles
> so that each one could represent one unique state of this puzzle? OK, I
> suppose that counts as a big number. :-)
>
> BTW, don’t worry about the length of your posts David. It’s easy enough
> for anyone who’s not interested to just delete them. Any subject even
> remotely on-topic should be fair game. Even if the posts become too
> frequent for some people, they can choose to get daily digests or even
> no email at all and just read the messages on the web site when they
> feel like it.
>
> -Melinda
>
>
> David Smith wrote:
> > Hi everyone,
> >
> > I have just finished calculating an upper bound for the number
> > of permutations of the 120-Cell. To establish it is the exact answer
> > (which I am virtually certain of), we will have to find a number
> > of algorithms which I will describe in my explanation.
> >
> > The calculation was only difficult in one aspect, namely the
> > possible orientations of the corners. Here is the upper bound:
> >
> > (600!/2)*(1200!/2)*(720!/2)*((2^720)/2)*((6^1200)/2)*((12^600)/3)
> >
> > To answer Roice’s question, I did find an arbitrary-precision
> > calculator (Googol+, trial version) that displays the entire
> > number in its full glory:
> >
> > 23435018363697222779126210606140343600982219866708667227704291465940007
> > 37743198001537086016413748065359228217622633869330769129523601891497799
> > 90823414733250819032377663096727895392891107724676361939174468537213471
> > 84699260131924584724938945790242680862147295113762851571432130901040238
> > 96149551266842769465158629370618815995041314328829732432057176063611161
> > 23422302770133676753359134856348612503635674252607065815753807941966366
> > 98057536512196715919594180779891338303538085006270891583549467992567391
> > 85180535778985103137974951114346934416286264525322532242698044327455362
> > 45594013789336900464999769975314632465421639791307831594564938014806846
> > 43170816415770010483963217284920963354265992129473309221874222731561178
> > 16542353296798264919536869373254412130565886195935986667368898349834998
> > 21329543130389608025077440970771216857898162084209764122888617411552472
> > 35969553038560987694512525780640891845410615026444483377179855326132898
> > 75234261959552618641928258383934632570287455387991780347467121010722113
> > 61928836844443707162412473785444967682885281547729595860180055748863425
> > 82987146883285105106538113133816701062677558383952546932927579065352378
> > 01699938857635611816907866063280477566711511600651402621287007177419657
> > 47137395706297269591116929204261763967322064643743204180740840609622274
> > 50477533328851963152796037024975768039218238701900252954269938177351575
> > 02677389416404108346187189424180896325665818763923753999882873138580846
> > 77228966566309226326618668840915289587325249776450099751298794240127365
> > 82338830099863762586940626070992713912334648392737597361950653986530252
> > 30327207836333881250393819594360829900032177090494274930448392889865527
> > 16614065052187986459391365691818487107035801789611790557625739664732160
> > 65851938727927023709296602229334790711981400149187774330090686038188693
> > 91261606235286494542181170865114851849953373717543236061723434256780261
> > 70547107650201457180103595669061215322965129698879686174938686442023883
> > 00748340309101390837462739717879861015966407725537701315760595302551716
> > 71986415959726651855198833270638521668923163972072488967633862968020464
> > 59857154591489337994834077319666200102594473324166310981151194815089205
> > 57151182894539191982468293894472660275087710846277134524865818266133054
> > 42334380903271185037626999712118120957184637997454373033536708899691932
> > 67133888402013848180589600375369501541798982850283307728992349369110105
> > 46520467826426004880473115209607600645972315535718172987982451474844986
> > 38207939550826131991321502334364118044702920268720341762396367094618866
> > 13506333873119893045317942691097910138170606688929064386560230196639558
> > 14850013029742851991570001253742052023463664478943640221712458729805575
> > 31060005263175107421358143058444429499655242088655206273565212573195537
> > 60877333581750403698478423610827287681768029874613544014049713469388295
> > 71527311448542611407166314396015388432540041818749117638737494542689341
> > 11177171793223712397899145235623177290619123784817857187575278090251642
> > 14840994381181018155477448811016038175506185165844643664291009318841540
> > 44262379730778251303396955855695117379535034691606466408011495289375314
> > 79718119837237414217144612432890362908806009419290522751980178308626097
> > 82557352902277742867710678069168798437309117460470080742233210420451923
> > 51892222110034306764675636566213792404505572865844730850823909858221035
> > 85434125488705753096939302756128054596976405648147286686571256428614441
> > 70150339281973567744826847917503807378348535977716210565251241466128121
> > 27489744510755607030104354706835298463258585993214964912284096487358233
> > 65511645083418224779444054273548541176504221269485074946310915002488718
> > 06278368621631798236853973136155878954455605260743873955312576387057492
> > 91464434261509507888671511637033790932545587351156241243113539812047803
> > 32568991232059877343852662991568615775896662637181748468409947337080580
> > 40572024450182896514659885925637625707421001762988412973222775700881854
> > 24686720928281296902412091261171945310151555961276870291126372512436270
> > 06952830074271589382737534210078713204605113743280142889267219197170354
> > 89582163680862223974028925034235784987192176322008136686679929878224156
> > 10403264150753927641888742398755843764458442462577801213007109287401551
> > 75841278684502282053918624209180100149726514306210673113609117091246135
> > 65223035254373475279222721857792173328260547996939875237576837159815118
> > 68437995628528234082912911481312451144148067422323644080656449490476178
> > 69974972208660720805312515123592330897469991534040275425615810166559862
> > 90453613626399014292854794414276344511148330328685197189376868495672292
> > 92219730863040706516534661225522594916193135982360752630702024083643694
> > 98309370698498093084824000430278614244379613737044583505562135097992678
> > 05260822568001712636170958894341958120566294218192269192589063843887982
> > 76399691863692115560126140715610109114003149849449412445547918396053785
> > 42102203322863117771608181202015567452798664995683183676667131261081040
> > 30610697346947842941118989099929505001072885907143020380705671971970771
> > 74641197649400613289762440747999594711818677478380093322693390443497615
> > 06790858102509872412149022901579978879595015323736540446504645407248271
> > 24442974862512599608887589752218559193144931596281284315382618742792620
> > 66616881593787942961115669105927538622586908510205223079160329890976613
> > 24318437454227007437361053657522104635365530904941109094426111379946913
> > 71854373062622155659107585797616686931874970164036381491924856162327083
> > 87215983278489287122517383893445550987886905214362677925682743059318092
> > 90715982378923238819174377671246115948128333247228319128499096287090364
> > 06418925007261761200623236257957747401814104819201322380783299932882694
> > 97705069648412898606682892058216414535137703172325349226036435233500060
> > 08811101917211049364489819890827973553466812312700794247970136249599713
> > 68830975248367892523082396738072274831267273049793679458450960225575330
> > 90840325055925127369491405078011569600959829055592354981900265212992888
> > 74537523085955044911868546931655826676111114140917917721449373043059908
> > 24075969774780698659600903247322382509271117981454345778343923721701140
> > 34040387142730946291948768518544291460594918104272439297270660195239204
> > 69851212038726474485921192066725395225842350618752505691550098017532445
> > 29742915483006071654290990776376332377597123229369363319211034520828156
> > 16383626599751692734054125142693424208441259140739967321942103460390485
> > 73512549204538199361441602981588922796564372729802637150967463996220269
> > 92509662606254579651749991204772662937610983604733514590588466763484779
> > 75336521786978901110936704729127455396942554264720541493172351367586278
> > 52118009553781736752460941012653895714556808971968820220233708185524289
> > 26324734529251413367934964381909880343066993726638347012446562279909471
> > 00665871099287936575368913555297252102692185719691751527961183922455231
> > 72371787084227168597930766375481134730976264840880937562376002100356262
> > 35107696623982892463214959186113390887996406714662349935032809366747705
> > 65928739057221107528446966775483155772142995330294320084551917275407602
> > 87830218813852897349462068161826723496382625465167461901840049431850524
> > 89018407136301332421978685188429040584176333209422917640992438642326814
> > 48471988797114061727140678598275664209888253021405519815632168746508451
> > 06268660985414101246860290152701992710734632469139060273152361598118124
> > 26751417487110100479881455904096718779749277515897027333976945734065218
> > 13427043475236100473238801150143720068671986307968791851735260237830993
> > 59283951655340545557118534217560207955199404424096337283839953943573882
> > 77230454238664055061747285720327136114251359554586129278357158728391085
> > 51846977682603655222729137145829356583863818649600000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 00000000000000000000000000000000000000000000000000000000000000000000000
> > 000000000000000000000000000000000
> >
> > What a number!
> […]
>
>
>