# Another four interesting cosets

Submitted by rokicki on Fri, 02/03/2006 - 22:38.

These are the distributions of the optimal solution lengths for the cosets where the edges start at the given M-symmetric position, using the quarter turn metric. The first run took longer than the other three combined; not sure why. Only a handful of positions at length 24; none at 26 or higher. I'm currently running the coset where the edges begin in the known length-26 position. It's interesting to note that with the edges superflipped and reflected across the center, all solutions took either 18, 20, or 22 moves.

edges at identity: d pos M M + inv 0 1 1 1 8 240 5 3 10 288 6 3 12 8764 197 113 14 116608 2475 1303 16 1075761 22536 11588 18 9978950 208393 105516 20 30348006 633616 320955 22 2561302 53756 27942 44089920 920985 467424 edges at pons asinorum: d pos M M + inv 12 130 6 6 14 464 16 14 16 81548 1712 892 18 1945598 40755 20782 20 33790110 705339 357035 22 8272070 173157 88695 44089920 920985 467424 edges at superflip: d pos M M + inv 14 2184 47 26 16 69880 1468 763 18 2125879 44430 22592 20 28197210 588540 297654 22 13694720 286495 146384 24 47 5 5 44089920 920985 467424 edges at superflipped pons asinorum: d pos M M + inv 18 164140 3442 1766 20 18013361 375910 189872 22 25912419 541633 275786 44089920 920985 467424