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 Post subject: Every Cube has 24 solutions!
PostPosted: Mon Dec 24, 2001 8:43 am 
every cube has 24 "solutions" because the middles can be oriented differently, however they cannot be permuted differently.
4!= 4x3x2x1 = 24
You can demonstrate this on a cube with pictures on the middle piece on each face.

Therefore, the slogan that says "Billions of cominations! Only One Solution!" is FALSE
tell me if my math is correct

 Post subject: Not quite...
PostPosted: Tue Dec 25, 2001 8:43 am 

Joined: Sun May 27, 2001 7:03 pm
...but you have the right idea. like you said, each centre has 4 possible rotations and the best way to see this is to look at a cube with pictures. however there is a lot more possibilities than you thought. it is possible for each centre to be rotated by 180 degrees independently of the others, and also for two centres to be rotated 90 degrees each (in either the same direction, or in opposite directions). using these combinations of moves, this means that 5 of the centres are free to have any orientation, while the 6th centre has only two choices of orientation after we have chosen the orientations of the first 5. this means there are 4x4x4x4x4x2 = 2048 "solutions" of the cube.

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