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
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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): $43,252,003,274,489,856,000$