Rubik's Cube Results

These results were obtained without the necessity of storing the individual positions. The key problem in enumerating cube space in a depth first fashion is that the same positions occur multiple times - the duplicate position problem. The standard way to detect duplicate positions is to store the positions. Rather than storing positions as the way to detect duplicates, these results were obtained by producing the positions in lexicographic order.

These results were calculated on my standard desktop PC, which is now pretty old (2.8GHz Pentium). The face turn results required about three months. The quarter turn results required about five months.

Since these results were posted, Tom Rokicki has calculated the face turn metric out to 13f and the quarter turn metric out to 15q. Tom used a totally different algorithm.

Distance from Start, Standard 3x3x3 Rubik's Cube
Quarter Turn Metric Distance Patterns Unique Positions from up to Symmetry Start 0 1 1 1 1 12 2 5 114 3 25 1068 4 219 10011 5 1978 93840 6 18395 878880 7 171529 8221632 8 1601725 76843595 9 14956266 717789576 10 139629194 6701836858 11 1303138445 62549615248 12 12157779067 583570100997 13 113382522382 5442351625028		Face Turn Metric Distance Patterns Unique Positions from up to Symmetry Start 0 1 1 1 2 18 2 9 243 3 75 3240 4 934 43239 5 12077 574908 6 159131 7618438 7 2101575 100803036 8 27762103 1332343288 9 366611212 17596479795 10 4838564147 232248063316 11 63818720716 3063288809012	These results were obtained without the necessity of storing the individual positions. The key problem in enumerating cube space in a depth first fashion is that the same positions occur multiple times - the duplicate position problem. The standard way to detect duplicate positions is to store the positions. Rather than storing positions as the way to detect duplicates, these results were obtained by producing the positions in lexicographic order. These results were calculated on my standard desktop PC, which is now pretty old (2.8GHz Pentium). The face turn results required about three months. The quarter turn results required about five months. Since these results were posted, Tom Rokicki has calculated the face turn metric out to 13f and the quarter turn metric out to 15q. Tom used a totally different algorithm.

Rubik's Cube Results

Distance from Start, Standard 3x3x3 Rubik's Cube