# Megaminx ULL Method and ELL Algs, EPLL+1

#### Delta Phi

##### Member
Being a Roux solver, I am not a huge alg-learning machine, instead preferring intuition, blockbuilding, and commutators. Megaminx last layer is not particularly conducive to this approach with the conventional methods. I know that efattah and some others have worked on tripod LL for megaminx, but I have developed my own approach that I believe works well. I have termed this approach "ULL", for U Last Layer, because the last layer pieces that need to be solved after LS form a U or V shape. Basically, you solve F2L and S2L normally up until last slot, where you then solve a 1x2x2 block in the top layer, and then solve the last slot. Then, you use one of the 11 following ELL algs to solve edges, leaving 4 corners to be solved using commutators. Obviously, an advantage this shares with @efattah 's method is reduced alg numbers from the OLL/PLL approach due to more blockbuilding. I think the main advantage this has over efattah's method is that you dont need to solve a specific block in the U layer, instead being able to use whatever pairs show up. A drawback I see is that the algs may not be as good, but I'm not certain about this.

I generated these algs because my previous (current, really, I just came up with these today) approach is to solve the U block, then LS, then do EO and EP separately, which takes only 4 easy algs virtually everyone knows already. In the future, I would like to investigate an additional set of ELL algorithms that together would guarantee at least one of the last 4 corners is solved using the cycle union system, changing the looks from 2.5 (cases with 4 corners needing 2 comms) to 2 flat.

All algs start with the U block in the back. There are three possible EPs, solved (0), clockwise (+), and counterclockwise (-), and there are 4 different EOs, solved (0), left edge good (L), middle edge good (M), and right edge good (R).

0+: y2' R U R' F' R U R' U' R' F R2 U' R' (J perm)
0-: y2' R U R2' F' R U R U' R' F R U' R' (inverse J perm)
L0: F2 DR' DL' F2 U F2' DL DR F2'
L+: L F R' F R F2' L' (Fat sune)
L-: R U' F' U F R
M0: y F2 DR' DL' F2 U2 F2' DL DR F2'
M+: R' F' U' F U R
M-: L F U F' U' L'
R0: F2' DL DR F2' U' F2 DR' DL' F2
R+: L U F U' F' L'
R-: L F2 R' F' R F' L' (Fat antisune)

I credit the pure flips to this video by Brandon Menrigh, it seems like he resides moreso on the twistypuzzles forum than here. I probably would have never finished if I hadn't seen his commutator idea.

EO+EP approach movecount: 0.75*6+0.67*13 (J perm) = 13.21 average movecount
ELL approach movecount: (3*9 (pure flips) + 2*13 (J perms) + 2*7 (fat sunes) + 4*6)/11 = 8.27 average movecount
saves almost 5 moves or nearly 40% on average!

#### OreKehStrah

##### Member
Being a Roux solver, I am not a huge alg-learning machine, instead preferring intuition, blockbuilding, and commutators. Megaminx last layer is not particularly conducive to this approach with the conventional methods. I know that efattah and some others have worked on tripod LL for megaminx, but I have developed my own approach that I believe works well. I have termed this approach "ULL", for U Last Layer, because the last layer pieces that need to be solved after LS form a U or V shape. Basically, you solve F2L and S2L normally up until last slot, where you then solve a 1x2x2 block in the top layer, and then solve the last slot. Then, you use one of the 11 following ELL algs to solve edges, leaving 4 corners to be solved using commutators. Obviously, an advantage this shares with @efattah 's method is reduced alg numbers from the OLL/PLL approach due to more blockbuilding. I think the main advantage this has over efattah's method is that you dont need to solve a specific block in the U layer, instead being able to use whatever pairs show up. A drawback I see is that the algs may not be as good, but I'm not certain about this.

I generated these algs because my previous (current, really, I just came up with these today) approach is to solve the U block, then LS, then do EO and EP separately, which takes only 4 easy algs virtually everyone knows already. In the future, I would like to investigate an additional set of ELL algorithms that together would guarantee at least one of the last 4 corners is solved using the cycle union system, changing the looks from 2.5 (cases with 4 corners needing 2 comms) to 2 flat.

All algs start with the U block in the back. There are three possible EPs, solved (0), clockwise (+), and counterclockwise (-), and there are 4 different EOs, solved (0), left edge good (L), middle edge good (M), and right edge good (R).

0+: y2' R U R' F' R U R' U' R' F R2 U' R' (J perm)
0-: y2' R U R2' F' R U R U' R' F R U' R' (inverse J perm)
L0: F2 DR' DL' F2 U F2' DL DR F2'
L+: L F R' F R F2' L' (Fat sune)
L-: R U' F' U F R
M0: y F2 DR' DL' F2 U2 F2' DL DR F2'
M+: R' F' U' F U R
M-: L F U F' U' L'
R0: F2' DL DR F2' U' F2 DR' DL' F2
R+: L U F U' F' L'
R-: L F2 R' F' R F' L' (Fat antisune)

I credit the pure flips to this video by Brandon Menrigh, it seems like he resides moreso on the twistypuzzles forum than here. I probably would have never finished if I hadn't seen his commutator idea.

EO+EP approach movecount: 0.75*6+0.67*13 (J perm) = 13.21 average movecount
ELL approach movecount: (3*9 (pure flips) + 2*13 (J perms) + 2*7 (fat sunes) + 4*6)/11 = 8.27 average movecount
saves almost 5 moves or nearly 40% on average!
I’ll have to check it out once I finish learning full Tripod LL algs for 3x3

#### xyzzy

##### Member
My megaminx LL method is also sorta like this, although I have EO solved earlier (during last two faces, like in Petrus) which simplifies things.

0+: y2' R U R' F' R U R' U' R' F R2 U' R' (J perm)
0-: y2' R U R2' F' R U R U' R' F R U' R' (inverse J perm)
You can just use Sunes here. Also, inverse J perm is the same thing as normal J perm, just from a different angle.

L0: F2 DR' DL' F2 U F2' DL DR F2'
R0: F2' DL DR F2' U' F2 DR' DL' F2
Alternative: R U R2' F R F2' U F.

For that matter, some possibly useful notes for forcing L3C (assuming EO is done):

Sune (R U R' U R U2' R'), back Sune (R' U' R U' R' U2 R), Antisune (R U2 R' U' R U' R') and back Antisune (R' U2' R U R' U R) all permute corners like an X perm. These also all move a corner-edge pair by two places, so it's very easy to recognise in those scenarios that you can just do a Sune variant to go to L3C immediately.

(On the other hand, if you have a corner-edge pair that needs to move by only one place, then you can solve that with a J perm.)

Double Sune etc. all preserve corner permutation, while also twisting all four corners. If the corner permutation is a 3-cycle and the permuted corner is twisted, you can always do a double Sune variant to twist that corner while solving EP. Bruno (R U2 R2' U' R2 U' R2' U2 R and inverse) also preserves corner permutation while twisting all corners, but they're not as versatile and it might be harder to recognise when Bruno can be used.

U perms (R U R' U R' U' R2 U' R' U R' U R and inverse) are useful when you have an already-solved corner.

If the corner permutation is two 2-cycles and not an X perm, then Sune/double Sune/Bruno will leave the corner permutation as two 2-cycles (and still not an X perm). This means you'll never get L3C by doing one of the aforementioned short algs in this case.

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#### abunickabhi

##### Member
Being a Roux solver, I am not a huge alg-learning machine, instead preferring intuition, blockbuilding, and commutators. Megaminx last layer is not particularly conducive to this approach with the conventional methods. I know that efattah and some others have worked on tripod LL for megaminx, but I have developed my own approach that I believe works well. I have termed this approach "ULL", for U Last Layer, because the last layer pieces that need to be solved after LS form a U or V shape. Basically, you solve F2L and S2L normally up until last slot, where you then solve a 1x2x2 block in the top layer, and then solve the last slot. Then, you use one of the 11 following ELL algs to solve edges, leaving 4 corners to be solved using commutators. Obviously, an advantage this shares with @efattah 's method is reduced alg numbers from the OLL/PLL approach due to more blockbuilding. I think the main advantage this has over efattah's method is that you dont need to solve a specific block in the U layer, instead being able to use whatever pairs show up. A drawback I see is that the algs may not be as good, but I'm not certain about this.

I generated these algs because my previous (current, really, I just came up with these today) approach is to solve the U block, then LS, then do EO and EP separately, which takes only 4 easy algs virtually everyone knows already. In the future, I would like to investigate an additional set of ELL algorithms that together would guarantee at least one of the last 4 corners is solved using the cycle union system, changing the looks from 2.5 (cases with 4 corners needing 2 comms) to 2 flat.

All algs start with the U block in the back. There are three possible EPs, solved (0), clockwise (+), and counterclockwise (-), and there are 4 different EOs, solved (0), left edge good (L), middle edge good (M), and right edge good (R).

0+: y2' R U R' F' R U R' U' R' F R2 U' R' (J perm)
0-: y2' R U R2' F' R U R U' R' F R U' R' (inverse J perm)
L0: F2 DR' DL' F2 U F2' DL DR F2'
L+: L F R' F R F2' L' (Fat sune)
L-: R U' F' U F R
M0: y F2 DR' DL' F2 U2 F2' DL DR F2'
M+: R' F' U' F U R
M-: L F U F' U' L'
R0: F2' DL DR F2' U' F2 DR' DL' F2
R+: L U F U' F' L'
R-: L F2 R' F' R F' L' (Fat antisune)

I credit the pure flips to this video by Brandon Menrigh, it seems like he resides moreso on the twistypuzzles forum than here. I probably would have never finished if I hadn't seen his commutator idea.

EO+EP approach movecount: 0.75*6+0.67*13 (J perm) = 13.21 average movecount
ELL approach movecount: (3*9 (pure flips) + 2*13 (J perms) + 2*7 (fat sunes) + 4*6)/11 = 8.27 average movecount
saves almost 5 moves or nearly 40% on average!
Interesting approach! I too come from a Roux background, so I do not find that much motivation to do megaminx as it is CFOP like block building and LL for the most part.

#### Delta Phi

##### Member
You can just use Sunes here. Also, inverse J perm is the same thing as normal J perm, just from a different angle.
Dang, I guess that changes the movecount numbers a bit I definitely should have realized that, I use Sune for the same situation when I do Heise

My megaminx LL method is also sorta like this, although I have EO solved earlier (during last two faces, like in Petrus) which simplifies things.
For what its worth, I try to influence EO all along the way, from solving the last Balint block, to forming the 1x2x2, to insertion.

I like your Sunes idea, seems very practical as well as efficient. I will add in your pure flip algs to my list, so I have more algs for changing C while solving E. I think theres something wrong with your U perm alg, but that should be an easy thing to find. I'll play more with algs to find something that deals with = perms (2-2 swaps that arent X perms).

After having done this method for a while, I think the recognition potential is far better than conventional OLL/PLL, while also being much more efficient.

#### xyzzy

##### Member
I think theres something wrong with your U perm alg, but that should be an easy thing to find.
That's what I get for trying to type it out from memory, ha. Should be correct now.

#### Delta Phi

##### Member
I have now figured out ELL+1 cases for oriented cases aka EPLL+1, which are easy to force with an EO step before solving the last Balint block.
Starting orientation is the same as the previous algs.

If you already have a solved corner somewhere, you can immediately do a U perm.
Clockwise: R' U' R U' R U R2' U R U' R U' R'
Counterclockwise: y2' R U R' U R' U' R2 U' R' U R' U R

If you have any corner solved but misoriented, you can use one of two algs for a particular permutation.
Clockwise:
y2' R U R' U R U' R' U R U2 R'
I call this double headlights for recog, the alg is a double Sune. Twists FR and BL counterclockwise, BR and FL clockwise.
????
I call this split headlights, twists FR and BL clockwise, BR and FL counterclockwise.

Counterclockwise:
y2' R U2 R' U' R U R' U' R U' R' (double Antisune)
????

If you have any two-two swaps, it is sufficient to do a 3-cycle during EP to leave a 3-cycle.
Any oriented besides BL: J perm/inv J perm (0+ 0- algs above)
CCW edge cycle, CW twist and cycle BR/BL/FL: R' U2' F' R U R' U' R' F R U2 R
CW edge cycle, CCW twist and cycle BR/BL/FL: R' U2' R' F' R U R U' R' F U2 R
CCW edge cycle, CCW twist and cycle : ????
CW edge cycle, CW twist and cycle : ????

I haven't been able to generate algs for these cases, doing megaminx LL algs by hand is making my brain explode, but all of the cases I've listed in this post will be able to solve any EO-ULL case into L3C.
CCW edge cycle, CCW twist and cycle : ????
CW edge cycle, CW twist and cycle : ????

#### A2021

##### Member
Being a Roux solver, I am not a huge alg-learning machine, instead preferring intuition, blockbuilding, and commutators. Megaminx last layer is not particularly conducive to this approach with the conventional methods. I know that efattah and some others have worked on tripod LL for megaminx, but I have developed my own approach that I believe works well. I have termed this approach "ULL", for U Last Layer, because the last layer pieces that need to be solved after LS form a U or V shape. Basically, you solve F2L and S2L normally up until last slot, where you then solve a 1x2x2 block in the top layer, and then solve the last slot. Then, you use one of the 11 following ELL algs to solve edges, leaving 4 corners to be solved using commutators. Obviously, an advantage this shares with @efattah 's method is reduced alg numbers from the OLL/PLL approach due to more blockbuilding. I think the main advantage this has over efattah's method is that you dont need to solve a specific block in the U layer, instead being able to use whatever pairs show up. A drawback I see is that the algs may not be as good, but I'm not certain about this.

I generated these algs because my previous (current, really, I just came up with these today) approach is to solve the U block, then LS, then do EO and EP separately, which takes only 4 easy algs virtually everyone knows already. In the future, I would like to investigate an additional set of ELL algorithms that together would guarantee at least one of the last 4 corners is solved using the cycle union system, changing the looks from 2.5 (cases with 4 corners needing 2 comms) to 2 flat.

All algs start with the U block in the back. There are three possible EPs, solved (0), clockwise (+), and counterclockwise (-), and there are 4 different EOs, solved (0), left edge good (L), middle edge good (M), and right edge good (R).

0+: y2' R U R' F' R U R' U' R' F R2 U' R' (J perm)
0-: y2' R U R2' F' R U R U' R' F R U' R' (inverse J perm)
L0: F2 DR' DL' F2 U F2' DL DR F2'
L+: L F R' F R F2' L' (Fat sune)
L-: R U' F' U F R
M0: y F2 DR' DL' F2 U2 F2' DL DR F2'
M+: R' F' U' F U R
M-: L F U F' U' L'
R0: F2' DL DR F2' U' F2 DR' DL' F2
R+: L U F U' F' L'
R-: L F2 R' F' R F' L' (Fat antisune)

I credit the pure flips to this video by Brandon Menrigh, it seems like he resides moreso on the twistypuzzles forum than here. I probably would have never finished if I hadn't seen his commutator idea.

EO+EP approach movecount: 0.75*6+0.67*13 (J perm) = 13.21 average movecount
ELL approach movecount: (3*9 (pure flips) + 2*13 (J perms) + 2*7 (fat sunes) + 4*6)/11 = 8.27 average movecount
saves almost 5 moves or nearly 40% on average!

#### A2021

##### Member
Se può interessare io il megaminx lo risolvo in modo completamente intuitivo se vuole questo è il link del video su yutube penso si riesca a capire la logica di risoluzione

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#### A2021

##### Member
Being a Roux solver, I am not a huge alg-learning machine, instead preferring intuition, blockbuilding, and commutators. Megaminx last layer is not particularly conducive to this approach with the conventional methods. I know that efattah and some others have worked on tripod LL for megaminx, but I have developed my own approach that I believe works well. I have termed this approach "ULL", for U Last Layer, because the last layer pieces that need to be solved after LS form a U or V shape. Basically, you solve F2L and S2L normally up until last slot, where you then solve a 1x2x2 block in the top layer, and then solve the last slot. Then, you use one of the 11 following ELL algs to solve edges, leaving 4 corners to be solved using commutators. Obviously, an advantage this shares with @efattah 's method is reduced alg numbers from the OLL/PLL approach due to more blockbuilding. I think the main advantage this has over efattah's method is that you dont need to solve a specific block in the U layer, instead being able to use whatever pairs show up. A drawback I see is that the algs may not be as good, but I'm not certain about this.

I generated these algs because my previous (current, really, I just came up with these today) approach is to solve the U block, then LS, then do EO and EP separately, which takes only 4 easy algs virtually everyone knows already. In the future, I would like to investigate an additional set of ELL algorithms that together would guarantee at least one of the last 4 corners is solved using the cycle union system, changing the looks from 2.5 (cases with 4 corners needing 2 comms) to 2 flat.

All algs start with the U block in the back. There are three possible EPs, solved (0), clockwise (+), and counterclockwise (-), and there are 4 different EOs, solved (0), left edge good (L), middle edge good (M), and right edge good (R).

0+: y2' R U R' F' R U R' U' R' F R2 U' R' (J perm)
0-: y2' R U R2' F' R U R U' R' F R U' R' (inverse J perm)
L0: F2 DR' DL' F2 U F2' DL DR F2'
L+: L F R' F R F2' L' (Fat sune)
L-: R U' F' U F R
M0: y F2 DR' DL' F2 U2 F2' DL DR F2'
M+: R' F' U' F U R
M-: L F U F' U' L'
R0: F2' DL DR F2' U' F2 DR' DL' F2
R+: L U F U' F' L'
R-: L F2 R' F' R F' L' (Fat antisune)

I credit the pure flips to this video by Brandon Menrigh, it seems like he resides moreso on the twistypuzzles forum than here. I probably would have never finished if I hadn't seen his commutator idea.

EO+EP approach movecount: 0.75*6+0.67*13 (J perm) = 13.21 average movecount
ELL approach movecount: (3*9 (pure flips) + 2*13 (J perms) + 2*7 (fat sunes) + 4*6)/11 = 8.27 average movecount
saves almost 5 moves or nearly 40% on average!
Se può interessare io il megaminx lo risolvo in modo completamente intuitivo se può interessare allego il link del mio video su yutube .

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