Harnessing parallel disks to solve Rubik’s cube

The number of moves required to solve any configuration of Rubik’s cube has held a fascination for over 25 years. A new upper bound of 26 is produced. More important, a new methodology is described for finding upper bounds. The novelty is two-fold. First, parallel disks are employed. This allows 1.4×1012 states representing symmetrized cosets to be enumerated in seven terabytes. Second, a faster table-based multiplication is described for symmetrized cosets that attempts to keep most tables in the CPU cache. This enables the product of a symmetrized coset by a generator at a rate of 10 million moves per second.