CFOP efficiency and multi-slotting

[elrog]

Whut? If you're gonna say stuff like this at least describe your idea.




I actually don't agree with this. Expansion from a 1x2x3 can be extremely inefficient (consider what you have to destroy to place your edges) in comparison to how many other pieces on the cube you can usefully solve in the same number of moves.

I have described my idea pretty in depth in the New Method/Concept/Idea Thread. It is the last post on page 11 assuming you have 10 posts per page.

Expanding from a 1x2x3 to a 2x2x3 does not take many moves. If you make the 1x2x3 block on the left like in Roux, you can easily place the DF and DB edges using R, U, Rw, and M moves. It is very quick to do.

 

[mark49152]

In theory, if multi-slotting could be useful in ~50% of cases, when setting up the last three pairs, and if in each case it eliminates 3 moves from the setup of the next pair without adding additional moves to the insertion, that’s an average saving of 4.5 moves/solve reducing typical F2L pairs to 24.5 moves or ~3.1 moves/piece. So multi-slotting is not a holy grail, just an interesting idea that given the inefficiency of F2L, might be worthy of further development.

I started playing with multi-slotting again with the intention of seeking out the most useful cases and validating the assumptions above. Although I haven't changed my view that the overall potential of multi-slotting is well short of block building, it turns out that some cases can save a significant number of moves and it could be worth learning those selectively.

I broke the cases down similarly to the Absolute F2L site, as pairs of simple inserts with different AUFs in between. For each insert-AUF-insert sequence, I looked at what the move count would be if you instead did the simplest (naive) insert on the first pair with no regard to the second pair. Then I ranked the cases by the difference between these move counts (using predicted ETM). Obviously the worst scenarios are where a simple insert of the first pair sets the second pair up into a nasty 11-move case such as #23/24 (wiki numbering).

Just looking at connected first pairs, so far, I found 11 cases that potentially save 7 or more moves, with an average saving of 8.4 moves. This excludes the "obvious" cases where when the second pair is already made and you just try to preserve it when inserting the first. When I get time, I will also look at the split first pair cases.

So how useful is it likely to be? The probability of getting any one specific configuration of the second pair depends on how many slots are unsolved. I make it 1/98, 1/108 and 1/150 when solving the 1st, 2nd and 3rd slots respectively. Assuming roughly 50% of F2L pairs are connected before insertion and the cuber learns all these 11 cases, there is a better than 1/8 chance per solve of hitting one of these cases and being able to benefit from an ~8 move saving. That seems pretty worthwhile to me.

If anyone's interested in this, let me know and I'll post them in a PDF.

 

[CriticalCubing]

I started playing with multi-slotting again with the intention of seeking out the most useful cases and validating the assumptions above. Although I haven't changed my view that the overall potential of multi-slotting is well short of block building, it turns out that some cases can save a significant number of moves and it could be worth learning those selectively.

I broke the cases down similarly to the Absolute F2L site, as pairs of simple inserts with different AUFs in between. For each insert-AUF-insert sequence, I looked at what the move count would be if you instead did the simplest (naive) insert on the first pair with no regard to the second pair. Then I ranked the cases by the difference between these move counts (using predicted ETM). Obviously the worst scenarios are where a simple insert of the first pair sets the second pair up into a nasty 11-move case such as #23/24 (wiki numbering).

Just looking at connected first pairs, so far, I found 11 cases that potentially save 7 or more moves, with an average saving of 8.4 moves. This excludes the "obvious" cases where when the second pair is already made and you just try to preserve it when inserting the first. When I get time, I will also look at the split first pair cases.

So how useful is it likely to be? The probability of getting any one specific configuration of the second pair depends on how many slots are unsolved. I make it 1/98, 1/108 and 1/150 when solving the 1st, 2nd and 3rd slots respectively. Assuming roughly 50% of F2L pairs are connected before insertion and the cuber learns all these 11 cases, there is a better than 1/8 chance per solve of hitting one of these cases and being able to benefit from an ~8 move saving. That seems pretty worthwhile to me.

If anyone's interested in this, let me know and I'll post them in a PDF.

A PDF would be nice and the thread seems really interesting. I can say anything about f2l and multi slotting and my look ahead is not only great. Haha but still getting to know these stuff is good enough!

 

[abunickabhi]

I think Free Fop is the solution.Roux is hard to implement and moves/ piece is more in standard CFOP.so Free FOP will give more degree of freedom.CFOP is the key for next 5 years.i don't see any breakthroughs coming.CFOP is like English not the most pure and oldest language but has too many resources and tricks

 

[mark49152]

After a break of a few weeks I'm back looking at multi-slotting, and following my earlier study of different inserts, decided to tackle the following more general question: Given a pair already set up to insert, what good shortcuts exist to both insert that pair and set up the next pair at the same time?

Ignoring slots other than the target slot, and for a single configuration of the first pair, there are 96 possible configurations for the second pair pieces.

I wrote some code to generate all 96 cases (when first pair set up for R U' R'), feed them into ksolve+ and filter and format the results. In the spoiler below you will find all cases/solutions that take less than 6 moves, or optimal+1 moves, whichever is shortest. For each case, I generated four sets of solutions, forming both connected (R U' R') and split (R U R') insertion patterns, and both preserving and flipping the orientation of the second edge.

Some of these solutions are obvious, some are not really finger-friendly, but some are really neat tricks. Some of my favorites include A24, A28, A45 and A54. There were also some nice ones of length 7+ but also lots of junk so I've filtered out all >6. Cases with no <7 solutions also aren't shown.

I will also define groups B, C, etc. with different configurations of the first pair and generate solutions for those too.

EDIT: Updated with solutions to set up split pairs.

Enjoy

Spoiler

Case A02
Leave the pair split, preserving the edge
(U) B' R U' R' U B (U2 B' U' B) [6]
L' U R U' L R' (U' B' U' B) [6]

Case A03
Leave the pair split, flipping the edge
(U2) R U' B U' B' R' (U2 B' U' B) [6]

Case A05
Connect the pair, preserving the edge
R' F R F' (U L U2 L') [4]

Case A06
Connect the pair, flipping the edge
(U2) R U' B U' B' R' (L U2 L') [6]

Case A07
Connect the pair, preserving the edge
(U) B' R U' R' U B (L U2 L') [6]
L' U R U' L R' (U L U2 L') [6]
Leave the pair split, flipping the edge
R' F R F' (U' B' U' B) [4]

Case A09
Leave the pair split, preserving the edge
(U) R B U' B' R' (L U L') [5]
(U) F' U F R U' R' (U' L U L') [6]
(U) F' U' L' U' L F (U L U L') [6]
(U') F' U' F R U2 R' (L U L') [6]

Case A10
Connect the pair, preserving the edge
(U) R2 B' R' B U' R' (B' U2 B) [6]
(U2) F R' F' R2 U2 R' (B' U2 B) [6]
Leave the pair split, flipping the edge
L R' F R F' L' (U L U L') [6]

Case A11
Leave the pair split, preserving the edge
(U) F' L' U2 L U F (U' L U L') [6]

Case A12
Connect the pair, preserving the edge
(U) R U' R' (U' B' U2 B) [3]
(U2) R U2 R' (U B' U2 B) [3]
Leave the pair split, flipping the edge
(U) R2 B' R' B U' R' (U2 L U L') [6]
(U) F' U2 F R U' R' (U2 L U L') [6]
(U) F' L' U' L F (L U L') [5]
(U2) F R' F' R2 U2 R' (U2 L U L') [6]

Case A13
Leave the pair split, preserving the edge
(U) R U' R' (U L U L') [3]

Case A14
Connect the pair, preserving the edge
(U) F' U2 F R U' R' (B' U2 B) [6]
(U) F' L' U' L F (U2 B' U2 B) [5]
B' R' F R B F' (U2 B' U2 B) [6]
Leave the pair split, flipping the edge
(U2) F2 L F L' F (U' L U L') [5]
(U) R' F R F2 U F (U' L U L') [6]

Case A15
Connect the pair, flipping the edge
(U) F' L' U2 L U F (U B' U2 B) [6]
Leave the pair split, preserving the edge
(U2) R U2 R' (U' L U L') [3]

Case A16
Leave the pair split, flipping the edge
B' R' F R B F' (L U L') [6]

Case A17
Connect the pair, preserving the edge
(U) R U' R' (U' L U2 L') [3]
Connect the pair, flipping the edge
R' F R F' (U B' U2 B) [4]
Leave the pair split, flipping the edge
B' R' F R B F' (B' U' B) [6]

Case A18
Connect the pair, preserving the edge
(U2) R U' B U' B' R' (B' U2 B) [6]
Leave the pair split, preserving the edge
(U2) R U2 R' (U' B' U' B) [3]

Case A19
Connect the pair, preserving the edge
B' R' F R B F' (U2 L U2 L') [6]
Leave the pair split, preserving the edge
R' F R F' (U' L U L') [4]

Case A21
Connect the pair, preserving the edge
(U2) R U2 R' (U L U2 L') [3]
Leave the pair split, flipping the edge
(U) R2 B' R' B U' R' (U2 B' U' B) [6]
(U2) F R' F' R2 U2 R' (U2 B' U' B) [6]
(U) F' L' U2 L U F (U' B' U' B) [6]

Case A22
Connect the pair, flipping the edge
(U) R B U' B' R' (U2 L U2 L') [5]
(U) F' U F R U' R' (U L U2 L') [6]
(U) F' U' L' U' L F (U' L U2 L') [6]
(U') F' U' F R U2 R' (U2 L U2 L') [6]
Connect the pair, preserving the edge
(U) B' R U' R' U B (B' U2 B) [6]
L' U R U' L R' (U B' U2 B) [6]
Leave the pair split, preserving the edge
L R' F R F' L' (U B' U' B) [6]

Case A23
Connect the pair, preserving the edge
(U) R2 B' R' B U' R' (L U2 L') [6]
(U2) F R' F' R2 U2 R' (L U2 L') [6]
Leave the pair split, preserving the edge
(U2) R U' B U' B' R' (U2 L U L') [6]
Leave the pair split, flipping the edge
(U) R B U' B' R' (B' U' B) [5]
(U) F' U2 F R U' R' (U2 B' U' B) [6]
(U) F' L' U' L F (B' U' B) [5]
(U2) F2 L F L' F (U' B' U' B) [5]
(U) R' F R F2 U F (U' B' U' B) [6]
(U) F' U F R U' R' (U' B' U' B) [6]
(U) F' U' L' U' L F (U B' U' B) [6]
(U') F' U' F R U2 R' (B' U' B) [6]

Case A24
Connect the pair, flipping the edge
L R' F R F' L' (U' L U2 L') [6]
Leave the pair split, preserving the edge
(U) R U' R' (U B' U' B) [3]

Case A25
Leave the pair split, preserving the edge
(U) R2 B' R' B U' R' (L U L') [6]
(U2) R U' B U' B' R' (L U L') [6]
(U2) F R' F' R2 U2 R' (L U L') [6]

Case A26
Leave the pair split, flipping the edge
B' R' F R B F' (U L U L') [6]
Leave the pair split, preserving the edge
(U) F' L' U' L F (U2 B' U' B) [5]
(U2) F2 L F L' F (U B' U' B) [5]
(U) R' F R F2 U F (U B' U' B) [6]
(U) F' U2 F R U' R' (B' U' B) [6]

Case A27
Connect the pair, flipping the edge
(U) R2 B' R' B U' R' (U2 B' U2 B) [6]
(U2) F R' F' R2 U2 R' (U2 B' U2 B) [6]
Leave the pair split, preserving the edge
(U2) R U2 R' (U L U L') [3]

Case A28
Connect the pair, preserving the edge
B' R' F R B F' (U' B' U2 B) [6]
(U) F' L' U2 L U F (U' B' U2 B) [6]

Case A29
Leave the pair split, flipping the edge
(U) R B U' B' R' (U2 B' U' B) [5]
(U') F' U' F R U2 R' (U2 B' U' B) [6]

Case A32
Connect the pair, flipping the edge
(U) R B U' B' R' (L U2 L') [5]
(U) F' L' U' L F (L U2 L') [5]
(U2) F2 L F L' F (U' L U2 L') [5]
(U') F' U' F R U2 R' (L U2 L') [6]
(U) R' F R F2 U F (U' L U2 L') [6]
(U) F' U2 F R U' R' (U2 L U2 L') [6]
Connect the pair, preserving the edge
(U2) R U2 R' (U' B' U2 B) [3]
Leave the pair split, flipping the edge
(U) F' L' U2 L U F (U L U L') [6]

Case A33
Connect the pair, preserving the edge
(U2) R U2 R' (U' L U2 L') [3]
Connect the pair, flipping the edge
L R' F R F' L' (U B' U2 B) [6]
Leave the pair split, preserving the edge
L' U R U' L R' (L U L') [6]
(U) B' R U' R' U B (U' L U L') [6]

Case A34
Leave the pair split, preserving the edge
(U) F' L' U2 L U F (U B' U' B) [6]

Case A35
Leave the pair split, preserving the edge
(U) R U' R' (U' L U L') [3]

Case A36
Connect the pair, flipping the edge
(U2) R U' B U' B' R' (U2 L U2 L') [6]

Case A37
Leave the pair split, flipping the edge
(U2) R U' B U' B' R' (B' U' B) [6]

Case A38
Connect the pair, flipping the edge
(U) R2 B' R' B U' R' (U2 L U2 L') [6]
(U) F' L' U2 L U F (U' L U2 L') [6]
(U2) F R' F' R2 U2 R' (U2 L U2 L') [6]
Connect the pair, preserving the edge
(U) R U' R' (U B' U2 B) [3]
R' F R F' (U2 B' U2 B) [4]
Leave the pair split, flipping the edge
(U) F' U F R U' R' (U2 L U L') [6]
(U) F' U' L' U' L F (L U L') [6]
Leave the pair split, preserving the edge
(U2) R U2 R' (U B' U' B) [3]

Case A39
Connect the pair, flipping the edge
(U) F' U F R U' R' (B' U2 B) [6]
(U) F' U' L' U' L F (U2 B' U2 B) [6]

Case A40
Connect the pair, flipping the edge
B' R' F R B F' (U' L U2 L') [6]
Connect the pair, preserving the edge
L' U R U' L R' (U2 B' U2 B) [6]
(U) B' R U' R' U B (U B' U2 B) [6]
Leave the pair split, flipping the edge
R' F R F' (L U L') [4]
Leave the pair split, preserving the edge
(U) R2 B' R' B U' R' (B' U' B) [6]
(U2) F R' F' R2 U2 R' (B' U' B) [6]

Case A41
Leave the pair split, flipping the edge
R' F R F' (B' U' B) [4]

Case A42
Connect the pair, preserving the edge
(U) R B U' B' R' (B' U2 B) [5]
(U') F' U' F R U2 R' (B' U2 B) [6]
Leave the pair split, preserving the edge
(U) R U' R' (U' B' U' B) [3]

Case A43
Connect the pair, preserving the edge
R' F R F' (U2 L U2 L') [4]
Connect the pair, flipping the edge
(U) F' L' U' L F (B' U2 B) [5]
(U) F' U2 F R U' R' (U2 B' U2 B) [6]
Leave the pair split, preserving the edge
(U) R B U' B' R' (U2 L U L') [5]
(U2) F2 L F L' F (U L U L') [5]
(U') F' U' F R U2 R' (U2 L U L') [6]
(U) R' F R F2 U F (U L U L') [6]

Case A45
Connect the pair, preserving the edge
L R' F R F' L' (U L U2 L') [6]
Connect the pair, flipping the edge
(U2) F2 L F L' F (U' B' U2 B) [5]
(U) R' F R F2 U F (U' B' U2 B) [6]
Leave the pair split, preserving the edge
(U) F' L' U' L F (U2 L U L') [5]
(U) F' U2 F R U' R' (L U L') [6]

Case A46
Leave the pair split, preserving the edge
L' U R U' L R' (B' U' B) [6]
(U) B' R U' R' U B (U' B' U' B) [6]

Case A47
Connect the pair, preserving the edge
(U) R U' R' (U L U2 L') [3]
Leave the pair split, flipping the edge
L R' F R F' L' (U' B' U' B) [6]

Case A49
Connect the pair, preserving the edge
(U) R B U' B' R' (U' L U2 L') [5]
L' U R U' L R' (U' L U2 L') [6]
(U) B' R U' R' U B (U2 L U2 L') [6]
(U') F' U' F R U2 R' (U' L U2 L') [6]
Leave the pair split, preserving the edge
(U) R U' R' (L U L') [3]

Case A50
Leave the pair split, preserving the edge
(U2) R U' B U' B' R' (U' B' U' B) [6]

Case A51
Connect the pair, preserving the edge
(U2) R U2 R' (L U2 L') [3]

Case A52
Connect the pair, flipping the edge
(U) F' L' U' L F (U' L U2 L') [5]
(U) F' U2 F R U' R' (U L U2 L') [6]
Leave the pair split, preserving the edge
(U) R B U' B' R' (U B' U' B) [5]
(U) F' L' U2 L U F (U2 B' U' B) [6]
(U') F' U' F R U2 R' (U B' U' B) [6]

Case A53
Leave the pair split, flipping the edge
(U) F' U F R U' R' (U B' U' B) [6]
(U) F' U' L' U' L F (U' B' U' B) [6]

Case A54
Connect the pair, preserving the edge
L R' F R F' L' (U2 B' U2 B) [6]
Leave the pair split, flipping the edge
(U) R2 B' R' B U' R' (U' L U L') [6]
(U2) F R' F' R2 U2 R' (U' L U L') [6]
Leave the pair split, preserving the edge
R' F R F' (U B' U' B) [4]
(U) F' L' U' L F (U B' U' B) [5]

Case A55
Connect the pair, preserving the edge
(U2) R U' B U' B' R' (U L U2 L') [6]

Case A56
Connect the pair, flipping the edge
R' F R F' (U' L U2 L') [4]
Connect the pair, preserving the edge
(U) R U' R' (U2 B' U2 B) [3]
Leave the pair split, flipping the edge
L R' F R F' L' (L U L') [6]
Leave the pair split, preserving the edge
(U2) R U2 R' (U2 B' U' B) [3]

Case A57
Connect the pair, flipping the edge
B' R' F R B F' (U B' U2 B) [6]
Leave the pair split, preserving the edge
(U2) F2 L F L' F (U2 L U L') [5]
(U) R' F R F2 U F (U2 L U L') [6]
Leave the pair split, flipping the edge
L R' F R F' L' (B' U' B) [6]

Case A58
Leave the pair split, preserving the edge
(U) R2 B' R' B U' R' (U' B' U' B) [6]
(U2) F R' F' R2 U2 R' (U' B' U' B) [6]

Case A59
Connect the pair, preserving the edge
(U) R U' R' (U2 L U2 L') [3]
Leave the pair split, preserving the edge
B' R' F R B F' (U' L U L') [6]

Case A60
Connect the pair, flipping the edge
(U) R2 B' R' B U' R' (U L U2 L') [6]
(U2) F R' F' R2 U2 R' (U L U2 L') [6]

Case A62
Leave the pair split, preserving the edge
(U) R U' R' (B' U' B) [3]

Case A63
Connect the pair, flipping the edge
(U2) F2 L F L' F (B' U2 B) [5]
(U) R' F R F2 U F (B' U2 B) [6]

Case A65
Leave the pair split, preserving the edge
(U) F' L' U2 L U F (U2 L U L') [6]

Case A66
Connect the pair, preserving the edge
(U2) R U2 R' (B' U2 B) [3]
Leave the pair split, flipping the edge
R' F R F' (U L U L') [4]

Case A67
Connect the pair, preserving the edge
(U2) F2 L F L' F (L U2 L') [5]
(U) R' F R F2 U F (L U2 L') [6]
Leave the pair split, preserving the edge
(U) F' U F R U' R' (U L U L') [6]
(U) F' U' L' U' L F (U' L U L') [6]

Case A68
Connect the pair, preserving the edge
R' F R F' (U' B' U2 B) [4]
Leave the pair split, flipping the edge
(U2) R U' B U' B' R' (U' L U L') [6]

Case A69
Connect the pair, preserving the edge
B' R' F R B F' (U L U2 L') [6]
Connect the pair, flipping the edge
(U) R B U' B' R' (U' B' U2 B) [5]
(U) F' L' U2 L U F (B' U2 B) [6]
(U2) R U' B U' B' R' (U B' U2 B) [6]
(U') F' U' F R U2 R' (U' B' U2 B) [6]
Leave the pair split, preserving the edge
(U2) R U2 R' (U2 L U L') [3]
Leave the pair split, flipping the edge
(U2) F2 L F L' F (U2 B' U' B) [5]
(U) R' F R F2 U F (U2 B' U' B) [6]

Case A71
Leave the pair split, flipping the edge
B' R' F R B F' (U' B' U' B) [6]

Case A72
Leave the pair split, flipping the edge
(U) R B U' B' R' (U L U L') [5]
(U) F' L' U' L F (U L U L') [5]
(U) F' U2 F R U' R' (U' L U L') [6]
(U') F' U' F R U2 R' (U L U L') [6]

Case A73
Leave the pair split, preserving the edge
(U) F' L' U' L F (U' L U L') [5]
(U) F' U2 F R U' R' (U L U L') [6]

Case A74
Connect the pair, preserving the edge
(U) R U' R' (B' U2 B) [3]

Case A75
Connect the pair, preserving the edge
(U) F' L' U2 L U F (U2 L U2 L') [6]

Case A76
Leave the pair split, preserving the edge
(U2) R U2 R' (B' U' B) [3]

Case A77
Leave the pair split, preserving the edge
R' F R F' (U2 L U L') [4]

Case A78
Leave the pair split, flipping the edge
(U) R B U' B' R' (U' L U L') [5]
(U') F' U' F R U2 R' (U' L U L') [6]

Case A79
Connect the pair, preserving the edge
(U2) R U2 R' (U2 L U2 L') [3]
Connect the pair, flipping the edge
R' F R F' (B' U2 B) [4]
(U) R B U' B' R' (U B' U2 B) [5]
(U) F' L' U' L F (U B' U2 B) [5]
Leave the pair split, preserving the edge
(U) R U' R' (U2 L U L') [3]
Leave the pair split, flipping the edge
(U) F' L' U2 L U F (B' U' B) [6]

Case A82
Connect the pair, flipping the edge
R' F R F' (L U2 L') [4]
Connect the pair, preserving the edge
(U2) F2 L F L' F (U2 B' U2 B) [5]
(U) R' F R F2 U F (U2 B' U2 B) [6]
Leave the pair split, preserving the edge
(U) R B U' B' R' (U' B' U' B) [5]
(U') F' U' F R U2 R' (U' B' U' B) [6]

Case A83
Connect the pair, preserving the edge
(U) R B U' B' R' (U L U2 L') [5]
(U') F' U' F R U2 R' (U L U2 L') [6]
Connect the pair, flipping the edge
(U2) R U' B U' B' R' (U' B' U2 B) [6]
Leave the pair split, flipping the edge
(U) F' L' U' L F (U' B' U' B) [5]
(U) F' U2 F R U' R' (U B' U' B) [6]

Case A84
Leave the pair split, preserving the edge
(U) R U' R' (U2 B' U' B) [3]
R' F R F' (U2 B' U' B) [4]

Case A85
Connect the pair, preserving the edge
(U) R U' R' (L U2 L') [3]
Connect the pair, flipping the edge
(U) F' U' L' U' L F (B' U2 B) [6]
(U) R2 B' R' B U' R' (U' B' U2 B) [6]
(U) F' U F R U' R' (U2 B' U2 B) [6]
(U2) F R' F' R2 U2 R' (U' B' U2 B) [6]

Case A86
Leave the pair split, flipping the edge
(U2) R U' B U' B' R' (U L U L') [6]

Case A87
Leave the pair split, preserving the edge
(U) R2 B' R' B U' R' (U L U L') [6]
(U2) F R' F' R2 U2 R' (U L U L') [6]

Case A88
Leave the pair split, flipping the edge
(U) F' U' L' U' L F (U2 L U L') [6]
(U2) F2 L F L' F (L U L') [5]
(U) R' F R F2 U F (L U L') [6]
(U) F' U F R U' R' (L U L') [6]

Case A89
Connect the pair, preserving the edge
(U) F' U' L' U' L F (L U2 L') [6]
(U) R2 B' R' B U' R' (U' L U2 L') [6]
(U) F' U F R U' R' (U2 L U2 L') [6]
(U2) R U' B U' B' R' (U' L U2 L') [6]
(U2) F R' F' R2 U2 R' (U' L U2 L') [6]
Leave the pair split, preserving the edge
(U2) R U2 R' (L U L') [3]

Case A90
Connect the pair, preserving the edge
(U) F' L' U2 L U F (U2 B' U2 B) [6]

Case A91
Leave the pair split, flipping the edge
(U) R2 B' R' B U' R' (U B' U' B) [6]
(U2) F R' F' R2 U2 R' (U B' U' B) [6]

Case A92
Leave the pair split, preserving the edge
(U) F' U' L' U' L F (U2 B' U' B) [6]
(U2) F2 L F L' F (B' U' B) [5]
(U) R' F R F2 U F (B' U' B) [6]
(U) F' U F R U' R' (B' U' B) [6]

Case A94
Connect the pair, flipping the edge
(U2) F2 L F L' F (U2 L U2 L') [5]
(U) R' F R F2 U F (U2 L U2 L') [6]
Connect the pair, preserving the edge
(U2) R U2 R' (U2 B' U2 B) [3]
Leave the pair split, flipping the edge
(U) F' L' U2 L U F (L U L') [6]

Case A96
Leave the pair split, preserving the edge
(U2) R U' B U' B' R' (U B' U' B) [6]

 

[Stefan]

I just had a look at the first case (Case A05). Why is the solution R' F R F' (U L U2 L') and not R' F R F' (L U' L')?

 

[mark49152]

I just had a look at the first case (Case A05). Why is the solution R' F R F' (U L U2 L') and not R' F R F' (L U' L')?

Hi Stefan - the objective is to set the second pair up, not solve it directly. The second could be any of the other three pairs, not necessarily back left. I only chose the orange/green pair for clearest distinction from the first pair, and I only provided the insertion part (in parentheses) to help set up the cases.

The reason the insertion part isn't optimized is due to the way I set the solved state up in ksolve+. I solved the pairs to UFR/UF or UFR/UR, then separately appended insertions from there.

 

[Robert-Y]

Thanks for these, looking forward to the RUR' set.

 

[mark49152]

Thanks for these, looking forward to the RUR' set.

Added setups to RUR'-type second pair, to post above . Next up will be the B cases, with RUR' first pair.