From:

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I performed a Local Maxima analysis. (This is for Q-turns only.) The Local

Maxima are in column 4. The shortest local maxima (six of them) are of

length 12. Interestingly, this is the same length which is suspected of

being the shortest Q-turn length for a local maximum in the full cube group.

Is there any connection? Also, the global maxima are of length 25. Does

this tell us anything about the Q-turn length of the global maxima for the

full cube group? Finally, pick any cube X in <U,R>. We know

|X| in G <= |X| in <U,R>. Can anybody find a cube X such that

|X| in G < |X| in <U,R>? Alternatively, can anybody prove

|X| in G = |X| in <U,R> for all X in <U,R>? (This assumes Q-turns only in

all cases. The questions would all have to be asked again for Q+H-turns.)

Number of Moves Which Go Closer to StartLevel Total 0 1 2 3 4 Cubes0 1 1 0 0 0 0 1 4 0 4 0 0 0 2 10 0 8 2 0 0 3 24 0 20 4 0 0 4 58 0 48 10 0 0 5 140 0 116 24 0 0 6 338 0 280 58 0 0 7 816 0 676 140 0 0 8 1,970 0 1,632 338 0 0 9 4,756 0 3,940 816 0 0 10 11,448 0 9,448 1,996 4 0 11 27,448 0 22,584 4,836 28 0 12 65,260 0 53,236 11,862 156 6 13 154,192 0 125,196 28,616 360 20 14 360,692 0 289,908 69,196 1,472 116 15 827,540 0 652,792 168,008 6,180 560 16 1,851,345 0 1,428,560 398,634 21,860 2,291 17 3,968,840 0 2,938,808 934,908 84,312 10,812 18 7,891,990 0 5,422,844 2,109,480 309,916 49,750 19 13,659,821 0 8,065,268 4,288,796 1,068,480 237,277 20 18,471,682 0 7,948,748 6,625,644 2,947,320 949,970 21 16,586,822 0 3,485,748 5,507,066 4,831,060 2,762,948 22 8,039,455 0 286,176 1,165,888 2,665,080 3,922,311 23 1,511,110 0 740 15,202 156,432 1,338,736 24 47,351 0 0 8 332 47,011 25 87 0 0 0 0 8773,483,200 1 30,736,780 21,331,532 12,092,992 9,321,895

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU

If you don't have time to do it right today, what makes you think you are

going to have time to do it over again tomorrow?