# Question about placing stickers on the Rubik's cube



## Robert-Y (Mar 20, 2009)

If I peeled off every sticker of the Rubik's cube and then I placed them all back on the Rubik's cube at random, what are the chances that I will attain a legal cube position?


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## JohnnyA (Mar 20, 2009)

43 quintillion out of however many possible ways you can put the stickers on. So 54 stickers/places - (43quintillion)/(54!)

This is just off my head and I'm tired so sorry if it's wrong.


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## Gparker (Mar 20, 2009)

i really dont know, but itd be impossible if you had 2 of the same stickers on the same peice XD


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## speedcuber1355 (Mar 20, 2009)

Can a piece be flipped around, or does it have to be able to be solved from that position?


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## speedcuber1355 (Mar 20, 2009)

If its a solvable position around 1/5^51

position with pieces flipped around 1/4^50

these are obviously rounded and I may be way off so dont hate me if im wrong


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## Lucas Garron (Mar 20, 2009)

(43252003274489856000*(9!)^6)/(54!)
=278628139008/651266248090757461677878416625
≈4.27825*10^-19



(Reassemble-solvable: *12 it.)


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## Herbert Kociemba (Mar 21, 2009)

Lucas Garron said:


> (43252003274489856000*(9!)^6)/(54!)
> =278628139008/651266248090757461677878416625
> ≈4.27825*10^-19




I do not understand the (9!)^6.
There are 6! possibilities to put 6 colours onto the 6 centers, so I would prefer 43252003274489856000*6!/54!


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## Johannes91 (Mar 21, 2009)

Herbert Kociemba said:


> Lucas Garron said:
> 
> 
> > (43252003274489856000*(9!)^6)/(54!)
> ...


Stickers of the same color can be in any order. For every cube position, there are (9!)^6 sticker permutations that look like it.

So maybe Lucas' number should be:

(43252003274489856000*(9!)^6*6!) / (54!)
= (43252003274489856000*6!) / (54!/(9!)^6)
= 40122452017152/130253249618151492335575683325
≈ 3.08034*10^-16


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## Herbert Kociemba (Mar 21, 2009)

Johannes91 said:


> Herbert Kociemba said:
> 
> 
> > Lucas Garron said:
> ...



Oh yes, I hope we finally got the right number.


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## Lucas Garron (Mar 21, 2009)

Herbert Kociemba said:


> Johannes91 said:
> 
> 
> > Herbert Kociemba said:
> ...


Ah, indeed. If we go by WCA-legal, we should probably rescheming so I'd probably agree with the extra factor of 6! (Else just *24)


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