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Here are my God's Algorithm results for the edges of the

3x3x3 cube. I explained in the last post what I mean by

1152-fold symmetry. All results below are for 1152-fold

symmetry. I am working on the 24-fold case, but I am not

quite done. The 24-fold case is just a matter of determining

the sizes of the equivalence classes in the 1152-fold case.

One item of terminology needs to be explained. Several

people, including myself, have posted results for the

2x2x2 cube and for the corners of the 3x3x3 cube. If you

take the term "corners of the 3x3x3 cube" absolutely

literally, it is completely isomorphic to the 2x2x2 cube.

When people have posted results for the "corners of the

3x3x3 cube", they all (including myself) really mean

"corners plus centers of the 3x3x3". See below:

-------------- --------------------- ------------------- | x | x | | x | | x | | x | | x | | | | | | | | | | | | |-----|------- -------|------|------ ------|-----|------ | x | x | | | | | | | x | | | | | | | | | | | | | -------------- -------|------|------ ------|-----|------ 2x2x2 | x | | x | | x | | x | | | | | | | | | --------------------- ------------------- Corners of 3x3x3 Corners + Centers

Thus, when I say I have solved the "edges of the 3x3x3", I need

to clarify what I mean. I have solved the "edges without the

centers". I suppose my next project will be "edges with the

centers". Unfortunately, "edges with the centers" is a twenty-four

times larger problem than is "edges without the centers". "Edges

without the centers" took about a year running 24 hours a day,

7 days a week, on two machines. I am going to have to rethink

"edges with the centers" before I start. I don't want it to take

24 years.

--------------------- ------------------- | | x | | | | x | | | | | | | | | | -------|------|------ ------|-----|------ | x | | x | | x | x | x | | | | | | | | | -------|------|------ ------|-----|------ | | x | | | | x | | | | | | | | | | --------------------- ------------------- Edges without Centers Edges with Centers

>Results using q-turns onlyDistance Number of from Start Nodes using 1152-fold Symmetry0 1 1 1 2 5 3 25 4 215 5 1,860 6 16,481 7 144,334 8 1,242,992 9 10,324,847 10 76,993,295 11 371,975,385 12 382,690,120 13 8,235,392 14 54 15 1

>Results using q-turns and h-turnsDistance Number of from Start Nodes using 1152-fold Symmetry0 1 1 2 2 9 3 75 4 919 5 11,344 6 139,325 7 1,664,347 8 18,524,022 9 167,864,679 10 582,489,607 11 80,930,364 12 314

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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?