Well I decided to pull a "Jerry Byran" and take another look at
some cube results, plus take a look at some new groups.
Analysis of the 3x3x3 squares group -----------------------------------
(h only) branching Moves Deep arrangements factor loc max (h only)
0 1 -- 0 1 6 6 0 2 27 4.5 0 3 120 4.444 0 4 519 4.325 0 5 1,932 3.722 0 6 6,484 3.356 1 (6 X pattern) 7 20,310 3.132 0 8 55,034 2.709 65 9 113,892 2.069 1,482 10 178,495 1.567 7,379 11 179,196 1.004 25,980 12 89,728 0.501 50,320 13 16,176 0.180 11,328 14 1,488 0.092 912 15 144 0.096 144 ------- ------ 663,552 97,611Analysis of the 3x3x3 <U, R> group ----------------------------------
branching Moves Deep arrangements (q only) factor
0 1 -- 1 4 4 2 10 2.5 3 24 2.4 4 58 2.416 5 140 2.413 6 338 2.414 7 816 2.414 8 1,970 2.414 program starts to really bog down after this...
I leave it to Jerry or Dan to check my results. I checked up to 2
moves deep by hand and verified 10 different positions. What I don't
understand is how Jerry manages to look at so many cube positions:
On full 3x3x3 cube, 7 100,803,036 13.231 (new)
Using 10 bytes to store a single cube position would still
need over 1 billion bytes, or am I missing something?
I also used GAP (quite a good program) to calculate the size of < U1, R1 > on the magic dodecahedron: 7,999,675,084,800.Once again, I welcome any verification.
-> Mark <-