# number of "solved" positions for 4x4



## mynameiswillem (Apr 27, 2009)

i recently got an eastsheen 4x4 and 5x5 with super stickers and that got me thinking. how many solved positions are there for a 4x4? if you are looking at the individual peices and no just the color on the piece itself then there will certainly be more than just a couple.

im somewhat math illiterate so any1 wanna figure that out?


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## ThatGuy (Apr 27, 2009)

http://speedcubing.com/chris/cubecombos.html
by super stickers you mean pictures? What do you mean by

"and no just the color on the piece itself then there will certainly be more than just a couple"
?


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## mynameiswillem (Apr 27, 2009)

but does that only count the inside pieces? because i care about number of "solved" positions for there to be. if you know what i mean


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## mynameiswillem (Apr 27, 2009)

ThatGuy said:


> http://speedcubing.com/chris/cubecombos.html
> by super stickers you mean pictures? What do you mean by
> 
> "and no just the color on the piece itself then there will certainly be more than just a couple"
> ?



and not*
http://9cube.net/syssite/home/shop/1/pictures/newsimg/1200139930.jpg


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## Ellis (Apr 27, 2009)

I'm not completely sure what you're asking here. There is one solved position on a 4x4 supercube. For a regular 4x4, I think there are (4!^6) possible solved states, but that could definitely be wrong, so don't quote me on that


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## mynameiswillem (Apr 27, 2009)

ya sorry i meant a regular 4x4


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## Ellis (Apr 27, 2009)

So you're just talking about the arrangement of indistinguishable center pieces in a solved state? I think it's 4!^6, unless someone wants to correct me. 191,102,976. Might not be right.


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## cmhardw (Apr 27, 2009)

Ellis said:


> So you're just talking about the arrangement of indistinguishable center pieces in a solved state? I think it's 4!^6, unless someone wants to correct me. 191,102,976. Might not be right.



(4!)^6 / 2

You have to divide that number in half because the parity of the center pieces (if they were distinguishable, as in a supercube) would have to match the, even, parity of the solved corners.

So if you solved your supercube disregarding the positions of the centers, and only making sure they were on the face with the correct color, then you could consider there to be 95 551488 solved states.

Chris


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## Ellis (Apr 27, 2009)

cmhardw said:


> Ellis said:
> 
> 
> > So you're just talking about the arrangement of indistinguishable center pieces in a solved state? I think it's 4!^6, unless someone wants to correct me. 191,102,976. Might not be right.
> ...



Ah ok, thanks for clearing that up. I knew I was forgetting something. It makes sense now.


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