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Invisible <voi### [at] dev null> wrote:
> 4.33 10^19 Number of valid combinations for a Rubik's Cube.
I think the correct term is permutations, rather than combinations.
(There *is* a difference between these two terms. They certainly are not
synonyms.)
Btw, the classic Rubik's Cube has about 4.33*10^19 permutations, but if
you mark the pieces such that their orientation becomes discernible and
thus part of the correct solution (relevant only with the center pieces,
but the other pieces also have to be marked in order to distinguish the
proper orientation for the center pieces), the total number of permutations
increases to 8.9*10^22. In other words, there will be a bit over 2000 times
the amount of permutations, making it slightly more difficult to solve.
The Rubik's Revenge has about 7.4*10^45 permutations, ie. about 10^26
times more than the Rubik's Cube. Curiously, though, it's only slightly
more difficult to solve. The solving difficulty is in no way related to
the increased number of permutations.
(The main reason why Rubik's Revenge is only slightly more difficult to
solve than the Rubik's Cube is that the former can be partially solved to
a state where it becomes completely equivalent to the latter, after which
Rubik's Cube solving techniques can be used to solve it. Thus all the
additional techniques you need to solve Rubik's Revenge are the ones needed
to make it equivalent to the Rubik's Cube. Then just solve the it like the
Rubik's Cube.)
(Ok, there's one slight difference: With the Rubik's Revenge it's possible
for a single "edge piece" (which in this case will be an edge piece pair) to
end up in the wrong orientation, which is impossible in the Rubik's Cube.
However, it can be turned around with a fixed sequence which you can
memorize.)
Likewise larger versions of the cube exhibit the same phenomenon: The
amount of permutations grows exponentially, but solving them doesn't
become significantly more difficult. Only the amount of rotations needed
increases with the size of the cube, but the same principles can be applied
to all cubes from 5x5x5 up.
--
- Warp
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> You know when somebody says that something is "astronomically big"?
>
> ...well, it turns out astronomers use some pretty freakin' big numbers!!
> o_O
Yeah, the US national debt is about $11.3*10^12 ...
or $113 for every star in the milky way,
or $1738 for every person alive on earth,
I guess that makes it astronomically big.
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Orchid XP v8 wrote:
> Number of atoms? (Or sometimes ions, or subatomic particles of some
> kind. Make sure you specify; it kinda makes a difference.)
12 grams of carbon-12. Avagadro's number is the number of neutrons in one
gram of neutrons. 1/A is the weight of a neutron.
They specify "carbon 12" because not all neutrons weigh the same amount, due
to E=Mc^2.
> There's a whole zoo of algebraic systems (I think that's the term) -
> monoids, semigroups, groupoids, groups, rings, fields, etc. They're all
> essentially the same "thing", just with differing numbers of properties
> guaranteed.
Right. I'd have to go look up the details.
> Personally, I only bother with fields and groups. A group is closed,
> associative, and possesses a unique identity element and an inverse
> element for every member. An Abelien group or commutative group is...
> self-explanatory, actually?
That was my memory, yes.
--
Darren New, San Diego CA, USA (PST)
Insanity is a small city on the western
border of the State of Mind.
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Orchid XP v8 wrote:
>>> 8.1 10^53 Number of elements in The Monster Group.
>>
>> I haven't any idea what this is. :-)
>>
>> <google> Oh, see, this is the sort of thing I'd have to spend a day
>> chasing references around to even figure out what this means.
>
> Apparently, there's a class of groups which can be completely classified
> into something like 6 different kinds, except for a small handful of
> unique groups that don't fit this classification. The "monster group" is
> the largest such - and it's frickin' HUGE!
oh good! I tried to mentally count the weight of Frankenstein, Medusa,
Hydra and others but quickly realized it wouldn't quite fit. :)
>>> 3 10^52 Kg Mass of the observable universe (exluding Dark Matter).
>>
>> I wonder if they're just talking about rest mass or what.
>
> I'm fairly sure it's rest mass, yes. Basically, number of atoms times
> mass of an atom.
It's quite heavy. Perhaps we should do a galaxy jump day to relief a
bit of that weight from Atlas' boss' shoulders. ;)
BTW, astromonical was truly devilish... :P
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Ken wrote:
>
> "Invisible" <voi### [at] devnull> wrote in message
> news:4a30e22e@news.povray.org...
>> 5 10^22 Number of stars in the universe.
>
> 5 10^30 Number of bacteria on the planet Earth
>
> Assuming bacteria is not unique to this planet how many bacteria inhabit
> the known universe?
According to the Hitchhiker's Guide to the Galaxy, the universe is
infinite so it's overall population is 0 because whatever astronomical
number n you put for the number of people/animal/bacteria/whatever it's
still n/universe_size, which turns in n/infinite, thus yielding 0 or
very close. :)
that's why it's so quiet out there... :P
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Tim Attwood wrote:
> Yeah, the US national debt is about $11.3*10^12 ...
>
> or $113 for every star in the milky way,
> or $1738 for every person alive on earth,
>
> I guess that makes it astronomically big.
Can debt be said to physically exist?
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Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> 4.33 10^19 Number of valid combinations for a Rubik's Cube.
>
> I think the correct term is permutations, rather than combinations.
Each side of the cube contains a combination of coloured squares. These
combinations are created by permutating the arrangements of squares on
the whole cube. So... whatever.
> Likewise larger versions of the cube exhibit the same phenomenon: The
> amount of permutations grows exponentially, but solving them doesn't
> become significantly more difficult. Only the amount of rotations needed
> increases with the size of the cube, but the same principles can be applied
> to all cubes from 5x5x5 up.
By complete coincidence:
http://arxivblog.com/?p=332
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Invisible <voi### [at] devnull> wrote:
> http://arxivblog.com/?p=332
Firefox warns about that website.
http://safebrowsing.clients.google.com/safebrowsing/diagnostic?client=Firefox&hl=en-US&site=http://arxivblog.com/?p=332
--
- Warp
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Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> http://arxivblog.com/?p=332
>
> Firefox warns about that website.
>
>
http://safebrowsing.clients.google.com/safebrowsing/diagnostic?client=Firefox&hl=en-US&site=http://arxivblog.com/?p=332
You know, I'd hate to be in charge of writing a program to do that sort of
detection. That just sounds like an awful, tedious, but nevertheless highly
valuable application.
--
Darren New, San Diego CA, USA (PST)
Insanity is a small city on the western
border of the State of Mind.
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On 06/13/09 13:06, Darren New wrote:
> Warp wrote:
>> Invisible <voi### [at] devnull> wrote:
>>> http://arxivblog.com/?p=332
>>
>> Firefox warns about that website.
>>
>>
http://safebrowsing.clients.google.com/safebrowsing/diagnostic?client=Firefox&hl=en-US&site=http://arxivblog.com/?p=332
>>
>
> You know, I'd hate to be in charge of writing a program to do that sort
> of detection. That just sounds like an awful, tedious, but nevertheless
> highly valuable application.
It's a helpful service. It's helpful as long as there are almost no
false positives - even if it's poor at detecting true positives.
I had a Wordpress blog on my site once. I stopped doing anything with
it, and someone pointed out that FF was giving this error (I hadn't gone
to it for months). Sure enough, there had been a WP exploit and the blog
had been hacked.
--
Psychoceramics: The study of crackpots.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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