"Every position of Rubik's Cube can be solved in twenty moves or less."

One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God's Algorithm [wiki]. The number of moves this algorithm would take in the worst case is called God's Number. At long last, God's Number has been shown to be 20.

It took fifteen years after the introduction of the Cube to find the first position that provably requires twenty moves to solve; it is appropriate that fifteen years after that, we prove that twenty moves suffice for all positions.

By 1980, a lower bound of 18 had been established for God's Number by analyzing the number of effectively distinct move sequences of 17 or fewer moves, and finding that there were fewer such sequences than Cube positions. The first upper bound was probably around 80 or so from the algorithm in one of the early solution booklets. This table summarizes the subsequent results.

Zaujimavosti:
- Rubikova kocka ma 43,252,003,274,489,856,000 roznych rozlozeni
- Distance-20 positions are both rare and plentiful; they are rarer than one in a billion positions


zdroj: http://www.cube20.org/ (tabulky lamania "rekordov", tabulka rozlozenia roznotahovych kociek, videa s najtazsou a prvou 20kovou kockou)