2x2x2 {RU} group method

[Michal Robaczyk]

Hey, I want to share my 2x2x2 method (MRUG) which I've developed 11 years ago. The method consists of 2 phases:

PHASE 1:

• orient the cube so that DBL is solved (depending on what color you want to start with)
• solve DFL while reducing the cube to the {RU} group

Phase 1 has average of 3.52 moves (considering starting always from the same color, since you won't have much time in preinspection to pick shortest color to start with).

PHASE 2: rest of the cube. I've proposed 6 variants here. Each variant consists of 2 steps:

• Variant A:
  • Permute remaining 2 corners of first layer (ignore their orientation)
  • orient 6 corners (O6C)
• Variant B:
  • Put remaining 2 corners of first layer to their layer (ignore permutation and orientation)
  • orient 6 corners + swap DBR with DFR if needed
• Variant C (CLL):
  • solve first layer
  • solve LL (only 7 cases)
• Variant D (EG):
  • solve first face
  • solve LL + swap DBR with DFR if needed (only 15 cases)
• Variant E (SS):
  • solve DBR
  • Orient 5 corners and solve DFR
• Variant F:
  • orient 6 corners
  • solve first layer in {R2, U} group (the last layer will get automatically solved)

Stats:

Variant	Number of algs (for phase 2)	Average move count
A	55	14.23
B	127	13.21
C (CLL)	7	15.31
D (EG)	15	15.15
E (SS)	104	13.16
F	71	13.98

The details are on my old website here: http://2x2.great-site.net/ in the MRUG section. The website is only in Polish (unfortunately).
Reducing to the RU group can be easily done in the preinspection. First I'm putting DFL into UBR (0.83 moves average) then determining remaining D-corners positions and traversing the U-corners. There are 6 groups of 30 cases which can be solved by 18 short algorhitms (3 groups of 6 algorhitms depending on the DFL (which is now in UFR) orientation).
For speedcubing I think that the most potential is in the B and F variants, although they require a lot of algs to remember. In the F variant the O6C case can be determined during preinspection what makes that variant a 1-look method. The last step of F variant is very pretty in the {R2, U} group and the best part is when you finish the first layer the last layer is automatically solved!

Some example solves are here: http://2x2.great-site.net/zzprzyklady.html
On the site http://2x2.great-site.net/ there are also descriptions and algs for other 2x2x2 methods + some other stats and comparisons.

Feel free to comment.
Cheers

 

[0r1]

Similar things have been done with BRASS method (which is basically Variant C). I made a video about BRASS here:

 

[0r1]

Actually now that I'm thinking about it the original method 1 looked the 2-gen state (after orienting DRB). I think it was ~90 algorithms, but it had a dead-link so I was never able to use it.

 

[Michal Robaczyk]

BRASS method is actually very similar to variant E not C.
The difference is that in BRASS you do:
1. Bar + permute DBR
2. Reduce to {RU} +orient DBR

While in MRUG variant E you do:
1. Bar + reduce to {RU}
2. Permute and orient DBR

The last third step is the same for both methods and it has a total number of 104 algorhitms (including mirrors - maybe here is the difference between our numbers). All cases are here:

http://2x2.great-site.net/zz105.html

 

[GodCubing]

For variant E have you considered being DBR, DFR, UBL, UFL neutral? Also, is 1 looking possible for any of the variants?

 

[GodCubing]

Hey, I want to share my 2x2x2 method (MRUG) which I've developed 11 years ago. The method consists of 2 phases:

PHASE 1:

• orient the cube so that DBL is solved (depending on what color you want to start with)
• solve DFL while reducing the cube to the {RU} group

Phase 1 has average of 3.52 moves (considering starting always from the same color, since you won't have much time in preinspection to pick shortest color to start with).

PHASE 2: rest of the cube. I've proposed 6 variants here. Each variant consists of 2 steps:

• Variant A:
  • Permute remaining 2 corners of first layer (ignore their orientation)
  • orient 6 corners (O6C)
• Variant B:
  • Put remaining 2 corners of first layer to their layer (ignore permutation and orientation)
  • orient 6 corners + swap DBR with DFR if needed
• Variant C (CLL):
  • solve first layer
  • solve LL (only 7 cases)
• Variant D (EG):
  • solve first face
  • solve LL + swap DBR with DFR if needed (only 15 cases)
• Variant E (SS):
  • solve DBR
  • Orient 5 corners and solve DFR
• Variant F:
  • orient 6 corners
  • solve first layer in {R2, U} group (the last layer will get automatically solved)

Stats:

[TABLE=centered]
[TR]
[TD]Variant[/TD][TD]Number of algs (for phase 2)[/TD][TD]Average move count[/TD]
[/TR]
[TR]
[TD]A[/TD][TD]55[/TD][TD]14.23[/TD]
[/TR]
[TR]
[TD]B[/TD][TD]127[/TD][TD]13.21[/TD]
[/TR]
[TR]
[TD]C (CLL)[/TD][TD]7[/TD][TD]15.31[/TD]
[/TR]
[TR]
[TD]D (EG)[/TD][TD]15[/TD][TD]15.15[/TD]
[/TR]
[TR]
[TD]E (SS)[/TD][TD]104[/TD][TD]13.16[/TD]
[/TR]
[TR]
[TD]F[/TD][TD]71[/TD][TD]13.98[/TD]
[/TR]
[/TABLE]

The details are on my old website here: http://2x2.great-site.net/ in the MRUG section. The website is only in Polish (unfortunately).
Reducing to the RU group can be easily done in the preinspection. First I'm putting DFL into UBR (0.83 moves average) then determining remaining D-corners positions and traversing the U-corners. There are 6 groups of 30 cases which can be solved by 18 short algorhitms (3 groups of 6 algorhitms depending on the DFL (which is now in UFR) orientation).
For speedcubing I think that the most potential is in the B and F variants, although they require a lot of algs to remember. In the F variant the O6C case can be determined during preinspection what makes that variant a 1-look method. The last step of F variant is very pretty in the {R2, U} group and the best part is when you finish the first layer the last layer is automatically solved!

Some example solves are here: http://2x2.great-site.net/zzprzyklady.html
On the site http://2x2.great-site.net/ there are also descriptions and algs for other 2x2x2 methods + some other stats and comparisons.

Feel free to comment.
Cheers

Btw, I was trying to make a method just like variant E when I found this. Great minds think alike. I think this method is really cool

 

[Michal Robaczyk]

Hi. 1-look is definitely possible - the E variant is IMO the best for 1-look.

I don't understand what do you mean by "DBR, DFR, UBL, UFL neutral".

 

[GodCubing]

Hi. 1-look is definitely possible - the E variant is IMO the best for 1-look.

I don't understand what do you mean by "DBR, DFR, UBL, UFL neutral".

Solve any of the corners adjacent to the block instead of just solving DBR every time

 

[Michal Robaczyk]

OK I understand now. I think this would be very hard -> too many cases and much harder recognition.

 

[GodCubing]

I respectfully disagree, from what I can tell the recognition is just shape and where the opposite sticker is

 

[Michal Robaczyk]

That is correct, but you would have to recognize the shape not always in U-face + DFR but some other configurations too. And you would have to mirror the algs in all 3 axes.

 

[GodCubing]

Not quite. For solving DFR you simply mirror to the back. For UBL and UBR you are right, I did not consider some algs being not 2 gen. If all algs were 2 gen (which would be worse algs) then this concept would be much easier.

 

[Michal Robaczyk]

On http://2x2.great-site.net/zz105.html you have all algs for DBR. There is always a 2-gen alg and a 3-gen {FRU} when its shorter. If you find better algs or any mistakes please let me know The algs were generated by me and most probably there are better algs for speedcubing.

 

[GodCubing]

Great

 

[bcube]

Feel free to comment.

All right. I have no experience with methods like BRASS or MRUG, or the corner permutation step from a 3x3x3 cube, so CP is a mystery for me at the moment.

I have some experience with a zero-memorization variant of scrambled -> HTR through DR.

I was wondering if this is possible or is it just a nonsense? You choose the DBL corner and pair it up with 1 of the 4 corners to make DBL and a corner at DFL position to be in an HTR state relative to each other while making the rest of the corners to be solvable into HTR using only <R,U> moves. Then the solution is completed by an HTR finish, i.e using <R2, U2, F2> group.

 

[Michal Robaczyk]

That is kinda different from the MRUG, because you want to have {R, U, F2} moves after the first phase and DFL can be anywhere, right?

 

[bcube]

That is kinda different from the MRUG, because you want to have {R, U, F2} moves after the first phase and DFL can be anywhere, right?

The core idea would be to reach an HTR state. Since scrambled -> HTR in one step is difficult (see here until an HTR state is reached), I was wondering whether the <R,U> reduction could be implemented this way:

1. solve 2 corners into an HTR state relative to each other (i.e. 2 corners at DBL and DFL positions would share 2 pairs of same/opposite colors), and make the rest of 6 corners to be solvable into an HTR state using only <R,U> moves
2. get into an HTR state using only <R,U> moves, then finish using half-turns only

 

[bcube]

Here are some nice features for the proposed idea:

• The <R,U> reduction automatically eliminates fake HTR cases.
• Possibly lower move count than any other MRUG variant A-F (I love these stats and if you could make stats for the proposed idea, I would be very interested to see them).
• To me at the moment, <R,U> reduction recognition system alone is very difficult, and HTR recognition system alone is very difficult too (see the video below if interested). There is a hope that a recognition system for the proposed idea combining two theory-heavy areas wouldn´t have to be so difficult.

 

[bcube]

That is kinda different from the MRUG, because you want to have {R, U, F2} moves after the first phase and DFL can be anywhere, right?

I guess I didn't answer this in my previous post.

Well, from an HTR perspective, the DFL, URF, ULB and DRB corners are all the same, so it depends on whether we can figure out a recognition system regardless of what of these 4 corners ends up being at the DFL position after step 1.

If we can't figure out a recognition system for that, the DFL corner would end up at the DFL position after step 1 by default just like in other MRUG variants or CP-first methods in general. That would eliminate the F2 move from the half-turn step at the end of the solve.