God's numbers for partial solves

[Cubenovice]

God's number for inserting edge/corner 5-cycle into a skeleton?? Hehe ... Move cancellations is the issue here!!

Per

God's "insertion cancellations" are opposite proportional to the quality of the skeleton ;-)

 

[Gaétan Guimond]

;-)

 

[Escher]

Has anybody calculated God's number for the F in CFOP, restricted to using a set of pre-determined, pair-solving algorithms (and mirrors)?

I know extremely little about programming, but I'm assuming it shouldn't be too hard to define a list of sequences that can be used to solve each pair sequentially and independently, and then brute-force solve all non-isomorphic positions on the 3x3 that have 4 edges solved around a face, and display the 'optimal' solution for each scramble (move distributions would be cool too).

Considering the computation would have to solve hundreds of different combinations for each cube I imagine it would be a big job.

I'm not that interested in the God's number itself but it would be interesting to study a bunch of the solutions, I'm currently trying to write down some ideas about pair selection and it would be nice to do a little analysis, though I don't really want to discuss my current thoughts here (or put my foot in anything pre-emptively).

If anybody has done this or wants to give it a go I'd be very grateful and it'd be cool to see the results.

Thanks,
Rowan.

 

[Stefan]

brute-force solve all non-isomorphic positions on the 3x3 that have 4 edges solved around a face

I think there are 914 million (24*21*18*15 * 16*14*12*10 / 4) positions to check, right?

Considering the computation would have to solve hundreds of different combinations for each cube I imagine it would be a big job.

After one slot is solved, there are only 9.5 million positions left, which could be precomputed. So for a given cube with cross solved, you could just try each of the four slots with each of its possible algs, and then look up the number of moves for the remaining three slots.

 

[reThinking the Cube]

...For the 2nd part, I assume you want these 5-cycles grouped in sets of 4 through conjugation by AUF moves, and only counting the shortest maneuver for each set of four configurations.

EDIT: Based upon the above assumptions, I've rerun the 1944 with the sets of 4 cases grouped together, and used a perl script to extract the best of each set of 4 configurations. The result I get is:

10f*: 16
11f*: 20
12f*: 186
13f*: 212
14f*: 52

Total cases: 486

By using conjugations without bothering to count the setup and undo setup moves, we get a "better than optimal" distance distribution.

Thanks Bruce, that is exactly what I wanted, and much quicker than I expected too. Possible orientation patterns for those 5-cycles of corners are too many (81), so I don't want to suggest burdening you with the task of analyzing them individually. But, it would be nice to know - the shortest manuever distributions for just the 6 (can be symmetrically reduced to 2 if you like) unique permutation patterns of those 486 5-cycle corner cases. That would be rather useful to me.

 

[Escher]

I think there are 914 million (24*21*18*15 * 16*14*12*10 / 4) positions to check, right?

Looks fine to me.

After one slot is solved, there are only 9.5 million positions left, which could be precomputed. So for a given cube with cross solved, you could just try each of the four slots with each of its possible algs, and then look up the number of moves for the remaining three slots.

Neat, I wasn't sure how to go about clever shortcuts, it actually sounds like quite a lot less work than I thought.

Would working 'backwards' from the shortest solution and cascading them make solving the longer cases trivial? Unless that's what you mean by 'precomputing'...

Also, if algorithms were included that changed another part of the f2l (i.e R2 U R U' R2'), would that make it much more complicated than solving them independently? I imagine you'd just have to specify for each algorithm whether it affected another slot and if so which in relation to it.

Thanks for answering, btw.