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2x2x2 {RU} group method

Joined
Sep 21, 2010
Messages
13
Location
Poznan, Poland
WCA
2006ROBA01
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:

VariantNumber of algs (for phase 2)Average move count
A5514.23
B12713.21
C (CLL)715.31
D (EG)1515.15
E (SS)10413.16
F7113.98

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
 
Last edited:

0r1

Member
Joined
Feb 25, 2020
Messages
7
Similar things have been done with BRASS method (which is basically Variant C). I made a video about BRASS here:

 

0r1

Member
Joined
Feb 25, 2020
Messages
7
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.
 
Last edited:
Joined
Sep 21, 2010
Messages
13
Location
Poznan, Poland
WCA
2006ROBA01
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
Joined
May 13, 2020
Messages
28
For variant E have you considered being DBR, DFR, UBL, UFL neutral? Also, is 1 looking possible for any of the variants?
 

GodCubing

Member
Joined
May 13, 2020
Messages
28
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:

VariantNumber of algs (for phase 2)Average move count
A5514.23
B12713.21
C (CLL)715.31
D (EG)1515.15
E (SS)10413.16
F7113.98

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
 

GodCubing

Member
Joined
May 13, 2020
Messages
28
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
 

GodCubing

Member
Joined
May 13, 2020
Messages
28
I respectfully disagree, from what I can tell the recognition is just shape and where the opposite sticker is
 

GodCubing

Member
Joined
May 13, 2020
Messages
28
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.
 
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