#### ch_ts

##### Member
I’m really interested in Kociemba related ideas, but I can’t find anywhere to explore them. Could you explain how Kociemba works or show me somewhere I could learn more?
You can try searching out Attila's domino reduction solves, but they're a bit difficult to understand imo

#### Cale S

##### Member
I’m really interested in Kociemba related ideas, but I can’t find anywhere to explore them. Could you explain how Kociemba works or show me somewhere I could learn more?
I use domino reduction in about a third of my FMC solves, and these are the main approaches I have to the reduction phase:

1. EO -> place 3 E edges in the E layer and orient all but 3 corners -> setup to R U R' or R U' R' type insert
2. EO -> place 3 E edges in the E layer and orient all but 4 corners -> setup to R U2 R' type insert
3. EO -> place 2 E edges in the E layer and orient all but 4 corners --> setup to single move

E layer can also be the M layer since you have two axes to choose from after EO

Here are examples of each:
R' U' F U2 F2 D2 R' D2 L B2 R' D2 F2 B R' D' L B' R2 F D R2 F2 R' U' F

B2 D B // EO
R (U' D' L D' L') // Domino

R' U' F U' F2 U R B L' U L' U' R2 D' R2 U L2 U F2 R2 U L2 D B' R' U' F

U L' F' B R' // EO
(L2 B') // sq
(F2 D2) // sq
(U B' D' B') // Domino

R' U' F D' R B2 D' F2 D' U2 L2 U' R2 B2 U' B2 L2 B' U L2 B2 F L U R' U' F

R' (B' U2 F' R) // EO
B (U2 L2 U' F' U F) // Domino
R' U' F R U R2 D' L2 R2 D2 L2 U' B2 U R' F D' R2 F2 D' U2 R U R' U' F

F (L U' D' B) // EO
(F2 U L2 U' D' R' F2 R') // Domino

here, R' F2 R' is an alternate way to do L' D2 L ending

R' U' F U2 F2 U2 F L2 B D2 B' L2 R2 F2 D2 L' R2 D' B2 R' D' L' D' U2 R' U' F

(R') F R' B2 U' L // EO
F2 D' B2 U' D' F' U2 F // Domino

R' U' F R2 U' R2 F2 D2 B2 U' F2 U F2 U' F' L2 D U2 R' B L' R' U' F

(U' F) U2 F // EO
R D' L2 D U2 R' D2 R' // Domino
R' U' F R2 D2 U B2 D R2 U' R2 B2 L R' B D2 L D U2 B' U L2 B2 F' R' U' F

D F' (L' D2 B) // EO
(D) R' D2 R' D2 R2 D // Domino

R' U' F D' B2 D' F2 D2 B2 U2 F2 R2 U B' U F' L D' F2 L D' L R U' R' U' F

D2 B R D F // EO
D' B2 L2 U' L2 D' L' // Domino

R' U' F L2 U2 L F2 D2 R B2 U2 L2 B2 U2 R' U' L' F' R D' B' U R F2 R' U' F

D2 R' B' // EO
D' (R' F2 U2 L D') // Domino

R' U' F U' F' D2 F2 B U' F' L F2 L2 B2 L2 F' U2 F D2 F D2 R2 B R' U' F

B D' F L // EO
(B F' L2 U2 F' B2 U') // Domino

For finishing after reducing to domino, it mostly comes down to trying several ways of making blocks until you get lucky, and it helps to know things like TTLLs and 2e2e algs. Also keep in mind that corner comm insertions with domino are not very good, but edge insertions can be good (especially E slice edges, which add like 1 move on average for insertions which is why you should focus more on solving the U and D layer pieces).

#### ImmolatedMarmoset

##### Member
I use domino reduction in about a third of my FMC solves, and these are the main approaches I have to the reduction phase:

1. EO -> place 3 E edges in the E layer and orient all but 3 corners -> setup to R U R' or R U' R' type insert
2. EO -> place 3 E edges in the E layer and orient all but 4 corners -> setup to R U2 R' type insert
3. EO -> place 2 E edges in the E layer and orient all but 4 corners --> setup to single move

E layer can also be the M layer since you have two axes to choose from after EO

Here are examples of each:
R' U' F U2 F2 D2 R' D2 L B2 R' D2 F2 B R' D' L B' R2 F D R2 F2 R' U' F

B2 D B // EO
R (U' D' L D' L') // Domino

R' U' F U' F2 U R B L' U L' U' R2 D' R2 U L2 U F2 R2 U L2 D B' R' U' F

U L' F' B R' // EO
(L2 B') // sq
(F2 D2) // sq
(U B' D' B') // Domino

R' U' F D' R B2 D' F2 D' U2 L2 U' R2 B2 U' B2 L2 B' U L2 B2 F L U R' U' F

R' (B' U2 F' R) // EO
B (U2 L2 U' F' U F) // Domino
R' U' F R U R2 D' L2 R2 D2 L2 U' B2 U R' F D' R2 F2 D' U2 R U R' U' F

F (L U' D' B) // EO
(F2 U L2 U' D' R' F2 R') // Domino

here, R' F2 R' is an alternate way to do L' D2 L ending

R' U' F U2 F2 U2 F L2 B D2 B' L2 R2 F2 D2 L' R2 D' B2 R' D' L' D' U2 R' U' F

(R') F R' B2 U' L // EO
F2 D' B2 U' D' F' U2 F // Domino

R' U' F R2 U' R2 F2 D2 B2 U' F2 U F2 U' F' L2 D U2 R' B L' R' U' F

(U' F) U2 F // EO
R D' L2 D U2 R' D2 R' // Domino
R' U' F R2 D2 U B2 D R2 U' R2 B2 L R' B D2 L D U2 B' U L2 B2 F' R' U' F

D F' (L' D2 B) // EO
(D) R' D2 R' D2 R2 D // Domino

R' U' F D' B2 D' F2 D2 B2 U2 F2 R2 U B' U F' L D' F2 L D' L R U' R' U' F

D2 B R D F // EO
D' B2 L2 U' L2 D' L' // Domino

R' U' F L2 U2 L F2 D2 R B2 U2 L2 B2 U2 R' U' L' F' R D' B' U R F2 R' U' F

D2 R' B' // EO
D' (R' F2 U2 L D') // Domino

R' U' F U' F' D2 F2 B U' F' L F2 L2 B2 L2 F' U2 F D2 F D2 R2 B R' U' F

B D' F L // EO
(B F' L2 U2 F' B2 U') // Domino

For finishing after reducing to domino, it mostly comes down to trying several ways of making blocks until you get lucky, and it helps to know things like TTLLs and 2e2e algs. Also keep in mind that corner comm insertions with domino are not very good, but edge insertions can be good (especially E slice edges, which add like 1 move on average for insertions which is why you should focus more on solving the U and D layer pieces).
YAY! Thx. Now I just have to learn EO.

#### WoowyBaby

##### Member
YAY! Thx. Now I just have to learn EO.
Just search up any ZZ EOline tutorial! (just ignore the line part of course)

In short, an edge is oriented if it can be solved using only RULD moves, and doing a quarter turn F or B flips the 4 edges on that face.
Sramble: L' D' L2 D' F2 R' D R L' D2 F R2 U2 L2 B2 U2 F L2 F2 B
y' U2 R L' F // EO
In this, I did U2 R L' to bring my 4 bad edges to F face, then did an F move to turn them good (oriented).
If you don't understand just from this, that's totally fine, an EOline tutorial goes more in depth

#### ImmolatedMarmoset

##### Member
Just search up any ZZ EOline tutorial! (just ignore the line part of course)

In short, an edge is oriented if it can be solved using only RULD moves, and doing a quarter turn F or B flips the 4 edges on that face.
Sramble: L' D' L2 D' F2 R' D R L' D2 F R2 U2 L2 B2 U2 F L2 F2 B
y' U2 R L' F // EO
In this, I did U2 R L' to bring my 4 bad edges to F face, then did an F move to turn them good (oriented).
If you don't understand just from this, that's totally fine, an EOline tutorial goes more in depth
I understand already how EO works, I just have to learn the rules. I use roux, so I at least understand it somewhat.

#### WoowyBaby

##### Member
I understand already how EO works, I just have to learn the rules. I use roux, so I at least understand it somewhat.
I don't get what you mean... the rules?
Well when you have EO solved, then you can do any moves besides quarter F/B turns. (so R R' R2 L L' L2 U U' U2 D D' D2 F2 B2)
If you've never done a ZZ solve, then you won't understand EO. Knowing Roux EO doesn't help you at all...
Scramble: D' R D2 B' R B U2 F B2 D F2 D2 F2 U2 B' R2 U2 R2 B U2 R2
y'
L U R F // EO

Scramble: R F' B2 D' L2 U' L2 U' B2 R2 D F2 R2 U F' U' F' R' U F R'
y z2
U' F // EO

Scramble: U' B' L2 U' L U' B L' B' L2 F' D2 F2 D2 F' D2 B' L2 U
L R' D' F' // EO

#### ImmolatedMarmoset

##### Member
I don't get what you mean... the rules?
Well when you have EO solved, then you can do any moves besides quarter F/B turns. (so R R' R2 L L' L2 U U' U2 D D' D2 F2 B2)
If you've never done a ZZ solve, then you won't understand EO. Knowing Roux EO doesn't help you at all...
Scramble: D' R D2 B' R B U2 F B2 D F2 D2 F2 U2 B' R2 U2 R2 B U2 R2
y'
L U R F // EO

Scramble: R F' B2 D' L2 U' L2 U' B2 R2 D F2 R2 U F' U' F' R' U F R'
y z2
U' F // EO

Scramble: U' B' L2 U' L U' B L' B' L2 F' D2 F2 D2 F' D2 B' L2 U
L R' D' F' // EO
Sorry, I wasn’t clear. I know how EO works. I know what it does. I haven’t done a ZZ solve, but I know that an oriented edge is one that can be solved RLUD, and I have tried this out to see if it works (spoiler: it does). I’ve even played with EO ideas on pyra, trying to come up with a better system than the one currently in place. However, I don’t know the rules for recognizing what EO you have quickly w/ ZZ in inspection, and I know that it’s much easier in FMC to know that. (I’ve tried just using an RLUD move set to find EO in FMC, but I don’t like it as it’s clunky and hard to realize which pieces are unoriented.) Hope that clears things up.

#### asacuber

##### Member
Does anyone have a good continuation?

R' U' F U F R2 D2 R2 B' L2 F R2 F' R2 F D' F' U' L F' U R B' L2 R' U' F

(R' F U' D' B')//EO+sq
(L')//123

My continuation was:
(D' R' U' R' D2)//223
(L' U2)//psF2L-1
U2 L U' L//AB5C in 17
Final solution was a 26: first 6 cancel then 1 cancel lol
this is just a random scramble btw

#### Lvl9001Wizard

##### Member
(I’ve tried just using an RLUD move set to find EO in FMC, but I don’t like it as it’s clunky and hard to realize which pieces are unoriented.)
Yeh watch any ZZ tutorial and you can do it faster.
Alternatively searching around there's some written explanations but I think learning with a video is faster

#### WoowyBaby

##### Member
FMC PB
Scramble: R' U' F L U2 F2 L F2 L U2 R' B2 R2 D2 U' R U' L' B' L2 F U B2 R' D R' U' F
(z)
B' R2 D F' D F2 // EO + Kociemba 2x2x3
R' U' R2 U2 R' // CO + Last 2 E Edges
r2 U S2 U' // Edge Circuits
L2 D2 R2 // Half-Turn-Only Finish
19 HTM, 18 STM
I love Kociemba/Domino, I don’t think I’d get this without it! (also I’m just bad at the normal way xd)
Also if anyone wants to learn Kociemba/Domino ideas from this solve then go ahead
Mark Boyanowski 26.3 mean:
23,37,19
Oof that 37, but GJ for a 26 mean!

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#### ImmolatedMarmoset

##### Member
FMC PB
Scramble: R' U' F L U2 F2 L F2 L U2 R' B2 R2 D2 U' R U' L' B' L2 F U B2 R' D R' U' F
(z)
B' R2 D F' D F2 // EO + Kociemba 2x2x3
R' U' R2 U2 R' // CO + Last 2 E Edges
r2 U S2 U' // Edge Circuits
L2 D2 R2 // Half-Turn-Only Finish
19 HTM, 18 STM
I love Kociemba/Domino, I don’t think I’d get this without it! (also I’m just bad at the normal way xd)
Also if anyone wants to learn Kociemba/Domino ideas from this solve then go ahead

Oof that 37, but GJ for a 26 mean!
Hey, I now have gotten EO down pretty well, but I’m having trouble doing CO intuitively for some reason. Could you help? GJ on the pb btw!

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#### WoowyBaby

##### Member
Hey, I now have gotten EO down pretty well, but I’m having trouble doing CO intuitively for some reason. Could you help? GJ on the pb btw!
Edit from future: TL;DR Setup to one of the 3 move insert cases or the single move case

Thanks! One super basic yet still optimal way of doing CO is to literally try every possible sequence of moves of increasing length.
Now this way is obviously inefficient time-wise, and only works if you want your solution to be 2-gen RU, so here’s kind of what I do:
Reduce it to one of the 3-move cases, R U R’, R U’ R’, R U2 R’. Just memorize these 3 cases and know how they can look. I can’t really explain it but you kinda just do it....
Here’s an example on 2x2-
Scr: R2 F2 R F R' F U2 F R U
I see red/orange is bad because it’s the L OLL case which takes 5 moves (z’ y F’ L’ U2 L F) so I notice white/yellow, the pattern looks just like the R U2 R’ case, so, I do R U2 R’ and that’s my CO.
A note about CO is that for he final move, it doesn’t matter if you do R or R’, so find which one influences Phase 2 better.
So for that 2x2 example, R U2 R does it as well as R U2 R’.
On 2x2, almost every time I do one of the 3-move cases if I do CO, so I’m pretty used to them.
Because they’re only 3 moves, you can easily find an optimal CO solution doing this, and in fact, basically all CO cases to a 3-move case and maybe cancel an R move or something.
R2 U2 R’ is just R to setup to R U2 R’ then cancel R’s to get R2 U2 R’
A simple sune (do R’ U’ R U’ R’ U2 R to setup this example) is just R2, now it’s a 3-move case, so you do U’ R U’ R’, so your CO solution for Sune is R2 U’ R U’ R’

But for 3x3, 2-gen CO just doesn’t work out, because during Phase 1 you may have EO and E edges solved so everything will break your E-layer edges.
So a trick is to make a “commutator”(not really) by doing stuff like R U’ L’ F2 L U R’ and now you’ve just made an alg that flips 2 corners and preserves EO and E Edges. R U D’ R2 U’ D R’ is another I just made up right now in 10 seconds.
Also, if you only have corners to twist in Phase 1, you can freely do any Half-Turns to change the unsolved corners positions but not affect EO or E Edges.

Hope this helped!

I know Kociemba is the best FMC method because the speedsolving logo is in G1. Lol
Lol yep it is, it’s also in a Half-Turn-Only state too.
One day I should FMC the speedsolving logo xD I’m pretty sure I can tell the entire state, because if it’s in HTO state then I don’t think you can have just 3 adj. sides solved but the other part not solved, so I’m gonna give it a shot sometime lolz

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#### ImmolatedMarmoset

##### Member
Thanks! One super basic yet still optimal way of doing CO is to literally try every possible sequence of moves of increasing length.
Now this way is obviously inefficient time-wise, and only works if you want your solution to be 2-gen RU, so here’s kind of what I do:
Reduce it to one of the 3-move cases, R U R’, R U’ R’, R U2 R’. Just memorize these 3 cases and know how they can look. I can’t really explain it but you kinda just do it....
Here’s an example on 2x2-
Scr: R2 F2 R F R' F U2 F R U
I see red/orange is bad because it’s the L OLL case which takes 5 moves (z’ y F’ L’ U2 L F) so I notice white/yellow, the pattern looks just like the R U2 R’ case, so, I do R U2 R’ and that’s my CO.
A note about CO is that for he final move, it doesn’t matter if you do R or R’, so find which one influences Phase 2 better.
So for that 2x2 example, R U2 R does it as well as R U2 R’.
On 2x2, almost every time I do one of the 3-move cases if I do CO, so I’m pretty used to them.
Because they’re only 3 moves, you can easily find an optimal CO solution doing this, and in fact, basically all CO cases to a 3-move case and maybe cancel an R move or something.
R2 U2 R’ is just R to setup to R U2 R’ then cancel R’s to get R2 U2 R’
A simple sune (do R’ U’ R U’ R’ U2 R to setup this example) is just R2, now it’s a 3-move case, so you do U’ R U’ R’, so your CO solution for Sune is R2 U’ R U’ R’

But for 3x3, 2-gen CO just doesn’t work out, because during Phase 1 you may have EO and E edges solved so everything will break your E-layer edges.
So a trick is to make a commutator(?) by doing stuff like R U’ L’ F2 L U R’ and now you’ve just made an alg that flips 2 corners and preserves EO and E Edges. R U D’ R2 U’ D R’ is another I just made up right now in 10 seconds.
Also, if you only have corners to twist in Phase 1, you can freely do any Half-Turns to change the unsolved corners positions but not affect EO or E Edges.

Hope this helped!

Lol yep it is, it’s also in a Half-Turn-Only state too.
One day I should FMC the speedsolving logo xD I’m pretty sure I can tell the entire state, because if it’s in HTO state then I don’t think you can have just 3 adj. sides solved but the other part not solved, so I’m gonna give it a shot sometime lolz
I suck at comms, but I think I could get used to them. Thanks so much!

#### asacuber

##### Member
@WoowyBaby So is your general approach like:
EO+Kociemba block
CO
DR
finish?

Also can you link some other websites through which you learnt this? Thanks!
But for 3x3, 2-gen CO just doesn’t work out, because during Phase 1 you may have EO and E edges solved so everything will break your E-layer edges.
So a trick is to make a commutator(?) by doing stuff like R U’ L’ F2 L U R’ and now you’ve just made an alg that flips 2 corners and preserves EO and E Edges. R U D’ R2 U’ D R’ is another I just made up right now in 10 seconds.
Also, if you only have corners to twist in Phase 1, you can freely do any Half-Turns to change the unsolved corners positions but not affect EO or E Edges.
Conjugate

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#### Cale S

##### Member
23.67 tied pb mean again

cool solutions on 2 and 3

R' U' F D2 R2 B2 R2 B2 F D2 U2 L' R U' R' B2 D B' F2 D' U2 R' U' F

D B L' U2 // 222
(B' R' B2) // 223
R2 F D' F' // F2L - 1
F' R' F // F2L
(F D R D' R' F' R') // 20 to 3e

D B L' U2 R2 F D' F2 R' F R F R D R' ^ D' F' B2 R B
^ = F2 L2 B2 U B2 L2 F2 D
Solution: D B L' U2 R2 F D' F2 R' F R F R D R' F2 L2 B2 U B2 L2 F B2 R B (25)
R' U' F U2 F R2 D2 F R2 F U2 F2 L2 U2 B' U' L' D' U L' U' B' D2 R' U' F

(B F R' F) // EO
(L' U B2 R' B2 D) // Domino
F2 U2 (L U2) // OBL
D2 L' D2 L2 B2 L' D2 L2 // PBL, 22 to 3e

F2 U2 D2 @ L' D2 ^ L2 B2 L' D2 L2 U2 % L' D' B2 R B2 U' L F' R F' B'
@ = M'
^ = M2
% = M'

Solution: F2 U2 D2 Lw' D2 Lw2 B2 L' D2 L2 U2 Lw' D' B2 R B2 U' L F' R F' B' (22)
R' U' F R2 U' B2 D U2 B2 L2 U' R2 D2 F U' R' B D' R B' D2 F L' R' U' F

L U2 F' R // EO
(R2 D') // 222
(U2 B' R2) // F2L - 1 with two corners swapped
U B' U' B // Domino + OBL
F2 U2 R2 U' R2 U' F2 R2 U2 R2 U' // PBL

Solution: L U2 F' R U B' U' B F2 U2 R2 U' R2 U' F2 R2 U2 R2 U' R2 B U2 D R2 (24)

#### asacuber

##### Member
R' U' F U2 F R2 D2 F R2 F U2 F2 L2 U2 B' U' L' D' U L' U' B' D2 R' U' F

(B F R' F) // EO
(L' U B2 R' B2 D) // Domino
F2 U2 (L U2) // OBL
D2 L' D2 L2 B2 L' D2 L2 // PBL, 22 to 3e

F2 U2 D2 @ L' D2 ^ L2 B2 L' D2 L2 U2 % L' D' B2 R B2 U' L F' R F' B'
@ = M'
^ = M2
% = M'

Solution: F2 U2 D2 Lw' D2 Lw2 B2 L' D2 L2 U2 Lw' D' B2 R B2 U' L F' R F' B' (22)

Woah what did you do there? i know the slice to 4centres4e then conjugate, but you seem to be doing something different here

F2 U2 R2 U' R2 U' F2 R2 U2 R2 U' // PBL
Did you just try matching up blocks randomly for this one?

GJ!

#### Cale S

##### Member
Woah what did you do there? i know the slice to 4centres4e then conjugate, but you seem to be doing something different here
With domino solutions, you can make any combination of U and D moves wide and it will affect the E slice pieces without adding moves, and this is the same as inserting slices that cancel 2. Here I found a combination of inserted slices that solved the 3e case

Did you just try matching up blocks randomly for this one?

GJ!
That PBL is one that I happen to know, I found it by hand once and then learned a few of the others that are PLL + 2 adjacent swapped corners