• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 35,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

Question about positions of the Rubik's cube

Joined
Jan 21, 2009
Messages
3,287
Likes
73
Location
England
WCA
2009YAUR01
YouTube
Robert271291
Thread starter #1
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?
 

AvGalen

Premium Member
Joined
Jul 6, 2006
Messages
6,857
Likes
87
Location
Rotterdam (actually Capelle aan den IJssel), the N
WCA
2006GALE01
YouTube
arnaudvg
#2
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?
12 times the normal amount

Or are you allowing positions where not all corners and/or edges are place back after the poppingout
 
Joined
Jan 21, 2009
Messages
3,287
Likes
73
Location
England
WCA
2009YAUR01
YouTube
Robert271291
Thread starter #3
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

Moderator
Staff member
Joined
Jul 6, 2007
Messages
3,555
Likes
88
Location
California
WCA
2006GARR01
YouTube
LucasGarron
#5
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
 
Last edited:
Top