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Question about positions of the Rubik's cube

Robert-Y

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How many possible positions can be attained by the Rubik's cube, assuming that you can pop out the corners and edges and place them where you like but not the centres?
 

Robert-Y

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Yes, all the corners and edges must be placed back into the cube. Is the answer really that simple? I thought maybe I was being simple minded when I thought it was just 12 x 43 quintillion
 

Lucas Garron

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Since someone's gonna ask what happens when you're allowed to move centers:

Fix a corner.
(7!*3^7)*(12!*2^12)*(6!)
=15570721178816348160000

And because math is so beautiful: Fix an edge.
(8!*3^8)*(11!*2^11)*(6!)
=15570721178816348160000

(Extra factor of 360.)

EDIT:
While we're at it, fix a center.
(8!*3^8)*(12!*2^12)*(5!)/4
=15570721178816348160000
 
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