Total Number of Reachable Positions on Rubik's Cube

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


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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $43,252,003,274,489,856,000$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $43,252,003,274,489,856,000$
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