Rubiks Cube/Numbers
From charlesreid1
Number of permutations
- 3 possible rotations of 8 corners, 7 corners determine the 8th = 3^7
- 2 possible rotations of 12 edges, 11 edges determine the 12th = 2^11
- 8 different corner pieces to be distributed to 8 locations = 8!
- 12 different edge pieces to be distributed to 12 locations = 12!
Furthermore, some of these possibilities are not possible. Only even parity cases can occur on the 3x3 cube, cutting the number of ways of distributing the corners and edges in half.
Total number of permutations of a 3x3 cube:
$ N = \dfrac{ 3^{7} \times 2^{11} \times 8! \times 12! }{ 2 } = 43,252,003,274,489,856,000 $
or about 43 quintillion permutations.