Message #500

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Re: Magic120Cell Realized
Date: Tue, 06 May 2008 23:43:00 -0700

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
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> 13427043475236100473238801150143720068671986307968791851735260237830993
> 59283951655340545557118534217560207955199404424096337283839953943573882
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> 51846977682603655222729137145829356583863818649600000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 00000000000000000000000000000000000000000000000000000000000000000000000
> 000000000000000000000000000000000
>
> What a number!
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