The New Method / Substep / Concept Idea Thread

[TDM]

Here's a 2x2 method I've thought of a while ago but never posted because I didn't think it was going to be fast enough. But I might as well post it anyway even though I know it's not worth switching to, because it's quite fun.

ROP (reduce, orient, permute).

1- Reduce to 2-gen. Setup to a porky v2 case seems to be at most three moves, usually fewer. Add in finishing the block and it's usually <6 moves.
2- Orient
3- Permute (intuitive, just pair up the two D layer pieces)

Here are five example solves with the first five scrambles I got from qqTimer:

Spoiler

F2 R' U' R' U' F2 U' R' U
y' R U R' F R F' // R
R U' R' U2 R U2 R // O
U' R2 U // P (16)


F R U' R U' F' U2 F U'
y' U' R2 U' R F' // R
U R U2 R2 U R' // O
U2 R2 U' R2 U' // P (16)


U R2 U R' U' F U R' F
z R U2 R' F // R
U2 R' U2 R U' R U2 R // O
U R2 U' R2 U R2 U' R2 // P (20)


R' U' F2 U2 R' F' U2 F' U2
x' z2 U2 R' F // R
U R' U R' U R' U' R // O
U' R2 U R2 U' R2 // P (17)


U F2 U F' U2 F R' F' R' U'
y' F R U2 R' F // R
U' R2 U R' // O
U' R2 U' R2 U' // P (14)

Pros:
Reasonably efficient
Easy to fingertrick because mostly <R, U>

Cons:
Nobody cares about RU 2x2 solving since RUF is often better anyway
Inspection is hell. Trying to find a 1-2 move setup is usually quite tricky and takes me more than 15 seconds before I even start identifying CP.
72 algs for second step (though that's better than other 2x2 methods and can be reduced to 48 by mirroring. And that can be reduced further to ~30 by doing one move to orient a D layer corner, except the few cases for which you can't do that)

 

[crafto22]

Hawaiian Kociemba/L2S Combination:

1. Orient F2L edges and solve cross - RD edge
2. Solve a 2x2x3 using RUL
3. Solve CP and a pair (I have a good way to go about this, I'll explain later)
4. Solve LL EO with the last pair (modified VHLS that doesn't affect CP)
5. Solve the corners along with the two LL edges then insert the RD edge all in one look (same number of algs as for 2GLL)

Pros:
- Efficient
- 1LLL (in fact, 1 look last layer and RD)
- Algs already exist for VHLS and CPLS, they must simply be lightly modified
- Ignoring RD is efficient
- All 1LLL algs are already generated

Cons:
- I find it difficult to orient the F2L edges AND the semi-cross in one look, but I'm sure I'll get the hang of it
- Lots of new algs most people don't know
What else?

 

[TDM]

Hawaiian Kociemba/L2S Combination:

Looks like you've rearranged the steps of Petrus and added CP. The first two steps do definitely look less efficient than regular Petrus. Petrus+CP would probably be a bit better I think.

Though I don't see what you're doing at the end there. What do you mean, "the two LL edges"? Setting up to S' U2 S? That can't be fast...

 

[crafto22]

Looks like you've rearranged the steps of Petrus and added CP. The first two steps do definitely look less efficient than regular Petrus. Petrus+CP would probably be a bit better I think.

Though I don't see what you're doing at the end there. What do you mean, "the two LL edges"? Setting up to S' U2 S? That can't be fast...

No, I'll explain later. Also, it isn't always about efficiency, the goal with this method is good lookahead and rotationless F2L.

 

[wir3sandfir3s]

Hawaiian Kociemba/L2S Combination:

1. Orient F2L edges and solve cross - RD edge
2. Solve a 2x2x3 using RUL
3. Solve CP and a pair (I have a good way to go about this, I'll explain later)
4. Solve LL EO with the last pair (modified VHLS that doesn't affect CP)
5. Solve the corners along with the two LL edges then insert the RD edge all in one look (same number of algs as for 2GLL)

Pros:
- Efficient
- 1LLL (in fact, 1 look last layer and RD)
- Algs already exist for VHLS and CPLS, they must simply be lightly modified
- Ignoring RD is efficient
- All 1LLL algs are already generated

Cons:
- I find it difficult to orient the F2L edges AND the semi-cross in one look, but I'm sure I'll get the hang of it
- Lots of new algs most people don't know
What else?

Looks to me like the CP+EO variation, but an extra alg to orient the LL edges and a 1LLL... This can be achieved with normal CP+EO, I just thought people might like the low alg count.
Still a cool idea
Also, you may have gotten confused on my L2S idea, like many other people.
-Solve 2x2x3 block while orienting all edges.
-Solve RD edge
-Create both remaining pairs and put them in the U layer. The will either look like a Y or T perm (I can explain in more detail if you want). Make it so it looks like a T perm and put them both on the right.
-Solve the back one (for better recog) first in a single alg while orienting the corners (1/28), then solve the front one in a single alg to permute everything and solve the cube (1/around 80, probably less).

You can do CP as well to limit the PLLLS Algs to 1/44.
Should I make a thread on this?
Also HK is now on the wiki

 

[crafto22]

Looks to me like the CP+EO variation, but an extra alg to orient the LL edges and a 1LLL... This can be achieved with normal CP+EO, I just thought people might like the low alg count.
Still a cool idea
Also, you may have gotten confused on my L2S idea, like many other people.
-Solve 2x2x3 block while orienting all edges.
-Solve RD edge
-Create both remaining pairs and put them in the U layer. The will either look like a Y or T perm (I can explain in more detail if you want). Make it so it looks like a T perm and put them both on the right.
-Solve the back one (for better recog) first in a single alg while orienting the corners (1/28), then solve the front one in a single alg to permute everything and solve the cube (1/around 80, probably less).

You can do CP as well to limit the PLLLS Algs to 1/44.
Should I make a thread on this?
Also HK is now on the wiki

No no I understand your L2S idea very well, I simply meant it as the last layer is being almost entirely solved with the last two slots. anyway I'm working on improving this, hopefully I can find something that would work very well.

 

[Shiv3r]

Hey Guys, there's a new method gaining momentum very slowly but surely in the forum: ECE!
its very move-efficient(more so than roux) and also requires less algorithms than CFOP.
I am posting this because it seems like it will be very popular and so I want to get it some attention.
You can find the method proposal here

 

[wir3sandfir3s]

Hey Guys, there's a new method gaining momentum very slowly but surely in the forum: ECE!
its very move-efficient(more so than roux) and also requires less algorithms than CFOP.
I am posting this because it seems like it will be very popular and so I want to get it some attention.
You can find the method proposal here

L2S + ECE + HK?
Lol
Just throw in all the efficient methods

 

[Shiv3r]

L2S + ECE + HK?
Lol
Just throw in all the efficient methods

bbbut ECE's alg count is almost half that of CFOP and 5000 times less algs then hawaiian kociemba

 

[wir3sandfir3s]

bbbut ECE's alg count is almost half that of CFOP and 5000 times less algs then hawaiian kociemba

Yes, pure HK, take a more efficient variation, there are different alg counts for each variation.

 

[Teoidus]

Random idea I had for Roux: what if we left L and R centers unsolved as well? That is, you could potentially solve FB and SB around other centers, allowing you to take advantage of more free pairs and the like, and then solve the centers while doing EO with <M,U,u>. Would something like this be possible?

 

[JTWong71]

Yes, it is possible, but it would be harder, and it is hard to transition from u and U.

 

[PenguinsDontFly]

Random idea I had for Roux: what if we left L and R centers unsolved as well? That is, you could potentially solve FB and SB around other centers, allowing you to take advantage of more free pairs and the like, and then solve the centers while doing EO with <M,U,u>. Would something like this be possible?

Yes, it is possible, but it would be harder, and it is hard to transition from u and U.

Many people already do this, myself included. It does work for easy cases (like a skip but around the wrong center), but in most solves it ends up being a nuisance to have to go back and fix centers.

 

[JTWong71]

L2S + ECE + HK?
Lol
Just throw in all the efficient methods

I had a thought like your L2S idea using CFOP using all 4 Slots to help influence and skip the last layer. I have a solve I did a while ago on it.

z2 //Inspection
F2 D B' U R2 L D2 F L' //XXCross
B' R' U' R2 F R F' R' U' B //F2L-3 + EO + OLL
U F2 L' D2 F' R B2 R' F D2 L F2 U' //L5C
32 STM

Trying to put three methods together, each method will likely have to have a tiny portion of the solve. I am trying to combine HK and ECE(BA), although it is hard to equally combine them because I can build blocks to reduce the amount of possible cases to solve Permutation at the end (In BA). Or, I can build blocks, then orient like in BA, then solve the rest like HK. I see that L2S can work with the other two methods. Each method has something that is unique to itself. L2S is Highly Influencing the last step. HK is leaving one piece of F2L unsolved. BA is Orientating early to leave Permutation left to solve.

So, combining the three together, you can:
I. 2x2x2
II. 2x2x3 + EO
III. Solve DR Edge and Setup CE Pair
IV. Insert pair and Orient the Corners
V. Permute the rest of the pieces

I think that combining 3 methods comes out a little less efficient than combining 2 methods, as it is hard to include 3 different ways to solve a cube into 1.

 

[Teoidus]

Many people already do this, myself included. It does work for easy cases (like a skip but around the wrong center), but in most solves it ends up being a nuisance to have to go back and fix centers.

Interesting. Do you think, if EO algorithms were generated/an organized approach to resolving centers + EO at the same time came about, it could potentially be useful more often than it is awkward? Or is it just not worth the extra cost (awkward U/u, harder to force ULUR skips)?

 

[PenguinsDontFly]

Interesting. Do you think, if EO algorithms were generated/an organized approach to resolving centers + EO at the same time came about, it could potentially be useful more often than it is awkward? Or is it just not worth the extra cost (awkward U/u, harder to force ULUR skips)?

Rosstheboss will swear on his life that mismatched centres are worthwhile, but I don't think so (that is, until someone proves me wrong). If you think it has potential, go for it. Start experimenting or genning algs and let us know if you find something! Good luck!

 

[crafto22]

https://alg.cubing.net/?setup=B2_F2...d_here) M2_U_M-_U2_M_U_M2_U2_S-_U2_S_//_L5EP

I had a thought like your L2S idea using CFOP using all 4 Slots to help influence and skip the last layer. I have a solve I did a while ago on it.

z2 //Inspection
F2 D B' U R2 L D2 F L' //XXCross
B' R' U' R2 F R F' R' U' B //F2L-3 + EO + OLL
U F2 L' D2 F' R B2 R' F D2 L F2 U' //L5C
32 STM

Trying to put three methods together, each method will likely have to have a tiny portion of the solve. I am trying to combine HK and ECE(BA), although it is hard to equally combine them because I can build blocks to reduce the amount of possible cases to solve Permutation at the end (In BA). Or, I can build blocks, then orient like in BA, then solve the rest like HK. I see that L2S can work with the other two methods. Each method has something that is unique to itself. L2S is Highly Influencing the last step. HK is leaving one piece of F2L unsolved. BA is Orientating early to leave Permutation left to solve.

So, combining the three together, you can:
I. 2x2x2
II. 2x2x3 + EO
III. Solve DR Edge and Setup CE Pair
IV. Insert pair and Orient the Corners
V. Permute the rest of the pieces

I think that combining 3 methods comes out a little less efficient than combining 2 methods, as it is hard to include 3 different ways to solve a cube into 1.

That's an interesting idea, but what if we did this:

1. 2x2x2 in DBL + orient some edges if possible
2. 2x2x2 + EO
3. Place the E-slice edges in the E-slice + orient a D-layer corner
4. Use EJLS to orient the remaining corners (16 algs)
5. Permute the corners
6. L5EP

Example:
z2 // inspection
L2 U' L U' L2 B L' U2 L' // a very inefficient 2x2x2
R' U F2 U F' // EO
R' U R U R' U' R' F2 // 2x2x3
U2 R U R' U' R U R' U R // lucky cancel into an H OCLL
D' R2 U R2 U D R2 U2 D' R2 U' D // CP (algs would be used here)
M2 U M' U2 M U M2 U2 S' U2 S // L5EP

 

[Shiv3r]

I had a thought like your L2S idea using CFOP using all 4 Slots to help influence and skip the last layer. I have a solve I did a while ago on it.

z2 //Inspection
F2 D B' U R2 L D2 F L' //XXCross
B' R' U' R2 F R F' R' U' B //F2L-3 + EO + OLL
U F2 L' D2 F' R B2 R' F D2 L F2 U' //L5C
32 STM

Trying to put three methods together, each method will likely have to have a tiny portion of the solve. I am trying to combine HK and ECE(BA), although it is hard to equally combine them because I can build blocks to reduce the amount of possible cases to solve Permutation at the end (In BA). Or, I can build blocks, then orient like in BA, then solve the rest like HK. I see that L2S can work with the other two methods. Each method has something that is unique to itself. L2S is Highly Influencing the last step. HK is leaving one piece of F2L unsolved. BA is Orientating early to leave Permutation left to solve.

So, combining the three together, you can:
I. 2x2x2
II. 2x2x3 + EO
III. Solve DR Edge and Setup CE Pair
IV. Insert pair and Orient the Corners
V. Permute the rest of the pieces

I think that combining 3 methods comes out a little less efficient than combining 2 methods, as it is hard to include 3 different ways to solve a cube into 1.

for now, were calling it Briggs-Adam(easier to say I think)

 

[theradhaxor]

First of all, I think Adam-Briggs rolls of the tongue easier,
And I think we are veering away from the ECE method by trying to optimize different parts of the solve. Here's the method I currently use/made

1. Roux First block(on left)
2. Connect block to bottom center piece, and add 2x2x1 on the back
That connects to the first block and center, while simultaneously adding last f2l pair
Right now, the cube should look like f2l without two cross pieces
3. CMLL
4. Orient all remaining edges using U, M,D (similar to roux)
5. Place the two edges to finish f2l, then EPLL

A variant that I might use

1 and 2 are the same
3. Perform 1 of 7 algs that orient top corners, not permute(similar to 2 look cmll, but not permuting)
4. Orient all remaining edges using U,M,D same as above
5. Place two edges to finish f2l, then PLL

I am planning to post a new thread on the forum proposing this method, but just saying when I would orient the edges

 

[JTWong71]

That's an interesting idea, but what if we did this:

1. 2x2x2 in DBL + orient some edges if possible
2. 2x2x2 + EO
3. Place the E-slice edges in the E-slice + orient a D-layer corner
4. Use EJLS to orient the remaining corners (16 algs)
5. Permute the corners
6. L5EP

I like that idea, and I think we can add something to help influence more so EJLS won't be all that is influencing the Orientation.

So what if we changed it to:

I. 2x2x2 in DBL + Slight Influence on EO (For 6+ Bad edges)
II. 2x2x3 + EO + Set up easy Pseudo CE Pair
III. Insert the Pseudo CE Pair into an F2L-Slot while Orienting all of the Corners + Placing E-Slice Edges (One will already be in place from the CE Pair)
IV. CP+EP

This would have more algorithms, but I think it would be more efficient, influencing throughout most of the solve.

Example Solve:
x' z //Inspection
D2 l U2 u' L //2x2x2 + Orientation Influence
R2 U l' D R' D x' //2x2x3 + EO + E-Slice + Some Oriented Corners (Lucky)
R' U2 R U2 R2 U' R' U' R U R2 //CO + 1x1x2 (Cancelled 'R' Move)
D R' U' R D' R U R D' R U' R' D R //CP+EP
36 STM

Used the same scramble as Crafto.
I did something slightly different because of the D-Layer Orientation Skip.
I think it can have decent fingertricks, after 2x2x3 at least, 2G+3G Steps.