# About the number of permutations of MC4D calculating



## charliemckiz (May 1, 2012)

Rules that MC4D obey:
Position: 
4-color pieces: The permutation of 4-color pieces is always even
2/3-color pieces: The net permutation of 3-color and 2-color is always even.
Orientation: Consider rotation of a piece is a permutation of shading sides of that piece. So:
4-color pieces: The permutation of rotation of a 4-color piece is always even. Besides, the net rotation of all 4-color pieces is 0. 
3-color pieces: The net permutation of rotation of all 3-color pieces is even.
2-color pieces: The net permutation of rotation of all 2-color pieces is even.
Number of different kinds of pieces:
4-color pieces: 16
3-color pieces: 32
2-color pieces: 24

Based on the rules above:
Permutation of 4-color pieces: 16! ÷2
Orientation of 4-color pieces: (4! ÷2) 15 ×3
Permutation of 2/3-color pieces: 32! ×24! ÷2
Orientation of 3-color pieces: (3!) 32 ÷2
Orientation of 2-color pieces: (2) 24 ÷2
Total: 16! ÷2×(4! ÷2) 15 ×3×32! ×24! ÷2×(3!) 32 ÷2×(2) 24 ÷2

This number is not same as what is posted in website http://www.superliminal.com/cube/cube.htm. Who wants to check for us??


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