Total Number of Reachable Positions on Rubik's Cube

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Theorem

The total number $N$ of reachable positions on Rubik's cube is:

\(\ds N\) \(=\) \(\ds 43 \, 252 \, 003 \, 274 \, 489 \, 856 \, 000\)
\(\ds \) \(=\) \(\ds \dfrac {8! \times 12! \times 3^8 \times 2^{12} } {2 \times 3 \times 3}\)


Proof



Sources