# 2x2x2 {RU} group method

#### Michal Robaczyk

##### Member
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

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#### 0r1

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

#### 0r1

##### Member
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.

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#### Michal Robaczyk

##### Member
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:

#### GodCubing

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

#### GodCubing

##### Member
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
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

##### Member
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

##### Member
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

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

#### GodCubing

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

#### Michal Robaczyk

##### Member
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

##### Member
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

##### Member
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.

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Great