# L8E on 3x3



## mk8 (Jul 21, 2022)

hello, i would like to ask if a situation, where the E slice and corners are solved, and all other edges are oriented, is solvable with a nice subset of moves (say like <M U D> or <R M U D>) in a tolerable amount of moves (preferrably under 10 STM)
if yes, do the algs exist or do i have to gen them myself? i use trangium's batch solver to gen all of my algs btw, so including a subset of moves to get all those cases would be helpful


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## Filipe Teixeira (Jul 21, 2022)

I remember that @Hazel had those algs, but I don't know how you can find them ATM because her site is down


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## Bruce MacKenzie (Jul 21, 2022)

There are 8! / 2 = 20,160 position permutations of the Up and Down edge cubies. With D4 symmetry these may be boiled down to 2644 cases. That's a lot of algorithms.


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## mk8 (Jul 22, 2022)

Bruce MacKenzie said:


> There are 8! / 2 = 20,160 position permutations of the Up and Down edge cubies. With D4 symmetry these may be boiled down to 2644 cases. That's a lot of algorithms.


well, someone in the Batch Solver thread gave me a nice subset that should include everything and the program found 98 cases... i suppose that's not all of them right?


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## Bruce MacKenzie (Jul 22, 2022)

mk8 said:


> well, someone in the Batch Solver thread gave me a nice subset that should include everything and the program found 98 cases... i suppose that's not all of them right?


Not by my reckoning. I sat down and wrote some code this evening and solved all 2644 of my cases. Here are the length 4 and 5 maneuvers I found (if you're not familiar with the notation it is outlined on Walter Randelshofer's site):



U2 MF2 U2 MF2​R2 MF2 R2 MF2​MU' MF2 MU MR2​MF2 D' MF2 D​MF2 D MF2 D'​MF' MU2 MF' MU2​L2 MF L2 MF'​D2 MF' D2 MF​D' MF2 D MF2​D MF2 D' MF2​U' MR2 MU' MF2 D • CU​U MR2 U2 MR2 U​U MR2 MU MF2 D' • CU'​R2 MU' MF2 MU L2 • CR2​F2 U' MF2 U B2 • CF2​F2 U MF2 U' B2 • CF2​D2 MF2 D' MF2 D'​D2 MF2 D MF2 D​D' MF2 D' MF2 D2​D' MF' D2 MF D'​D MF2 D MF2 D2​D MF' D2 MF D​

This is from the symmetry reduced set so each of these represents as many as eight distinct arrangements depending on the orientation of the cube to which they are applied.


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## mk8 (Jul 22, 2022)

Bruce MacKenzie said:


> Not by my reckoning. I sat down and wrote some code this evening and solved all 2644 of my cases. Here are the length 4 and 5 maneuvers I found (if you're not familiar with the notation it is outlined on Walter Randelshofer's site):
> 
> 
> 
> ...


but all of the cases can be achieved with this subset of moves: <M2, S2, M' U2 M, M U2 M', S' U2 S, S U2 S'>, right? for this exact generator, the batch solver gives 68 <M U D> cases with y rotations allowed
what could be wrong?


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## Bruce MacKenzie (Jul 22, 2022)

mk8 said:


> but all of the cases can be achieved with this subset of moves: <M2, S2, M' U2 M, M U2 M', S' U2 S, S U2 S'>, right? for this exact generator, the batch solver gives 68 <M U D> cases with y rotations allowed
> what could be wrong?


All the 20,160 position permutations of the UP+DOWN edge cubies may be found by closure of the group formed from the two generators R U L D F2 D' L' U' R' F2 and R' L' U D B2 R' B2 U' D' R L D'. If you can form these two generators using your subset of moves then your subset of moves can form all 20,160 U+D edge cubie position permutations. I have no idea what your batch solver is doing.

Addendum:

This morning I fired up GAP and found that one can close the group with three of the length 4 maneuvers:

MU' MF2 MU MR2
MF2 D' MF2 D
L2 MF L2 MF'

If you can show that your subset of moves can form these three elements then the subset can form the whole group.


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## PiKeeper (Jul 22, 2022)

mk8 said:


> but all of the cases can be achieved with this subset of moves: <M2, S2, M' U2 M, M U2 M', S' U2 S, S U2 S'>, right? for this exact generator, the batch solver gives 68 <M U D> cases with y rotations allowed
> what could be wrong?


I think you need to add U and D into those subsets to make it work. Otherwise there's no way to get a case where an s layer edge is in the m layer


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## Hazel (Jul 22, 2022)

I generated all the algorithms for EO in this state:


https://imgur.com/a/ANYPHN9


Some of the algs might not work though, I don't think I actually tested all of them


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