The New Method / Substep / Concept Idea Thread

[dudefaceguy]

@dudefaceguy Here's some 4x4 example solves with your method-
"1. Solve two opposite centers.
2. Solve a 1x3x3 block and a 1x3x4 block (similar to Roux) on the opposite face.
3a. Solve two more corners such that the last 3 corners are out of place, then solve the last 3 corners using a commutator.
3b. Solve the last edge pair of the 1x3x3 block to extend it to a 1x3x4 block.
4. Extend one of the 1x3x4 blocks into a 2x3x4 block by solving one middle slice excluding the top layer.
5. Use the unsolved slice to solve exactly 7 of the remaining 10 edge pieces.
6. Solve the remaining 3 edge pieces and some center pieces with a commutator.
7. Solve the remaining center pieces with 2 or 3 commutators."

Scramble: D2 L R2 F2 L2 R2 D2 B L2 U2 B' U2 B2 F' U' F2 D2 L2 R' U' R Fw2 Rw2 R' B2 D2 Fw2 F L' B Uw2 F D2 B' Uw L2 Uw2 L' B2 Uw' B Rw Fw B Uw2 U Fw2
x2
R2 f r U2 r' U R' y r U2 r' z // 2 Opposite Centers (10)
R U R2 L U' r' U' F' L2 F // Red 1x3x3 (10)
R2 U' r L F' L D L2 U R' U' r2 R' F R2 F' R' U R2 U' R2 U' R U r' U2 R U R' U' R y D' R U' R' D // Orange 1x3x4 (36)
y U2 R' F2 R F' R' F2 R2 U R' // Corners (10)
U' R l L R2 D' R2 L2 U R' // Remaining Edge (10)
2R U 2R' m' U m' D2 U m' U m D2 2R U' 2L2 U2 m2 U 2L' U2 2L m U2 m' 2R2 U' 2R2 U m U2 m2 U2 m 2R2 U 2R2 U' m' U2 m // Left M slice (40)
U2 2R U2 2R2 U' 2R2' U2 2R U2 2R2 U 2R' r U R' U' 2R' U R U' R' // Solve 7/10 Edges (21)
// Non-Intuitive Near-Impossible L3E Commutator
// Non-Intuitive Near-Impossible Last 12 Centers Commutators
137 STM + ~40-50 for the rest = 180 ish

This method is extremely difficult to solve with, not for beginners whatsoever, requires a very high level understanding of the cube, many parts are too complex to do efficiently.
I spent actually over an hour on the solve, because how complicated it is.
Algorithms are easier to understand than commutators.
I actually know exactly how commutators work, and have lots of experience on 3x3, but I didn't grasp this.
Even in your own video you struggled near the end to solve using your own method.

This is an interesting method, maybe just not for me
Maybe other people will like it though

Wow, thank you very much for testing out this method! I agree that it is definitely not a beginner-friendly method. The intended audience is very specific and possibly includes only myself. It's not meant to be a generally popular or universal method, but rather to fill a specific niche for weirdos like myself by providing a couple of things that I couldn't find in other methods.

The ideal candidate would be someone like myself, who learns Heise for 3x3 because they really REALLY don't like learning algorithms, and then wants to try larger cubes without learning parity algorithms. It also helps if you really REALLY love commutators and enjoy spending lots of time to work out move-optimal solutions. I will often spend a few minutes on a single commutator, trying to save one or two moves or solve one extra piece. This is not necessary of course, but I really enjoy doing it.

I realize that most people will not be looking for these things when selecting a method. But, I couldn't find a method that satisfied by own weird criteria so I made one. I gave absolutely no regard for things that are very important in speedsolving methods, like minimizing rotations, avoiding slice moves, and other ergonomics. Making a big cube method intended for Heise mains is already restricting the intended audience to like 5 people in the world.

Thank you for linking the solve, because I am not good at following notation. The 3/4 slice step was definitely very difficult for me to figure out at first, but it can be done pretty easily. It looked like you were making bars and then pairing them with edge pieces and inserting them, which I tried to do at first also. I've found it to be a lot more efficient to build the 3/4 slice like this:

1. Place the edge in the top layer on the L or R side, oriented such that the color you want to pair is on the U face.
2. Rotate the slices (mostly just the unsolved slice) to join center pieces with the edge, making a bar that goes from the L to the R face - perpendicular to the slice where it will be inserted. Rotate the U layer 180 degrees to shift the edge piece between the L and R side, depending on where the center pieces are located. The 3 pieces can be joined with only U and r moves, and sometimes l moves if necessary.
3. Once the two center pieces are joined to the edge, rotate U 90 degrees to place the three pieces in the correct slice.

This was not clear in my video - I probably should have spent more time on this step.

As for L3E commutator, the moves will always be exactly the same, or mirrored, if the 3 edges are in the same slice. For example, if the unsolved slice is u and the unsolved edges are in the columns FL, FR, and BR, and the FL edge belongs in the FR column, use [L': [F' U' F, u]]. This, or it's mirror, will solve all cases of L3E in the same slice. I use this in my video. If instead the last edges are in different slices, the commutator can sometimes require an ugly conjugate, but it can be easier to include center pieces.

Thanks again for posting the solve and for linking it!

 

[ImmolatedMarmoset]

I’m sure this has been thought of before, but isn’t there a way to algorithmically combine steps 4b and 4c of roux? It doesn’t seem like there would be a ton of algs. Just want to get input; I couldn’t find this anywhere.

 

[PapaSmurf]

alg.cubing.net

It's all contained in the link.

I’m sure this has been thought of before, but isn’t there a way to algorithmically combine steps 4b and 4c of roux? It doesn’t seem like there would be a ton of algs. Just want to get input; I couldn’t find this anywhere.

Yeah. It's just called L6EP, and is useful in L7E or when you get an eoskip in LSE. Otherwise, just use EOLR.

 

[ImmolatedMarmoset]

alg.cubing.net

It's all contained in the link.



Yeah. It's just called L6EP, and is useful in L7E or when you get an eoskip in LSE. Otherwise, just use EOLR.

Thanks so much!
Do you know where any algs are? I know about EOLR, but I did a quick search on speedsolving wiki and a bit on google, and I couldn’t find anything. I just want to see how many there are and what they’re like.

 

[PapaSmurf]

Here they are un sorted.

There are 96 (including EPLL) and they're all probably very good. I don't know how many are trivial, but they'll be an easy set to learn. Average movecount is around 8.6 iirc.

 

[ImmolatedMarmoset]

Here they are un sorted.

There are 96 (including EPLL) and they're all probably very good. I don't know how many are trivial, but they'll be an easy set to learn. Average movecount is around 8.6 iirc.

Thanks so much! I’m more of a beginner so maybe I’ll look into simpler ways of doing that. Maybe getting l/r edges together in the bottom layer after EO and then apply an alg to solve the whole thing? I might put that into cube explorer because I’m pretty sure no one has tried that out and it shouldn’t be a lot of algs. I’d like to hear your thoughts on a beginner version of L6EP executed that way. In other words, algorithmically (or possibly intuitively) predicting 4c. Would that have any extra algs than just normal 4c or no? I’m a bit confused about that.

Edit: you can skip the 4c step with l/r edges on the bottom together, I randomly found one case while playing around with alg.cubing.net: https://alg.cubing.net/?setup=M2_U2_M2_U2_U_M2&alg=U_M2_U2_M2_U3_M2_U
Don’t know if this is even useful, but the alg I found doesn’t ever go into the 4c roux step.

 

[PapaSmurf]

You'll be better doing EOLR most of the time then L6EP when you get an eo skip, because it's more efficient. And Kian Mansour has a good video here and videos here.

 

[Sue Doenim]

Thanks so much! I’m more of a beginner so maybe I’ll look into simpler ways of doing that. Maybe getting l/r edges together in the bottom layer after EO and then apply an alg to solve the whole thing? I might put that into cube explorer because I’m pretty sure no one has tried that out and it shouldn’t be a lot of algs. I’d like to hear your thoughts on a beginner version of L6EP executed that way. In other words, algorithmically (or possibly intuitively) predicting 4c. Would that have any extra algs than just normal 4c or no? I’m a bit confused about that.

Edit: you can skip the 4c step with l/r edges on the bottom together, I randomly found one case while playing around with alg.cubing.net: https://alg.cubing.net/?setup=M2_U2_M2_U2_U_M2&alg=U_M2_U2_M2_U3_M2_U
Don’t know if this is even useful, but the alg I found doesn’t ever go into the 4c roux step.

In my opinion, 4c starts when LR edges (or FB edges if you're doing EOFB) are on the D layer and EO is solved. That way, you can make the solve better by implementing techniques like dots evasion when applicable. As a Roux solver, I know that as you get more experienced with L6E, it gets easier to predict 4c after EOLR is solved, and I bet that more experienced solvers can take that further and predict it earlier. At any rate, I don't think the bad recognition is worth it, and the speed gain would probably be negligible in cases where it applies.

 

[Umar Uzden]

Hello, guys. I'm new here and just finished reading this thread. Also I checked "List of methods". Is there any actual or work in progress algorithmic method to blockbuild to F2L - 1 slot state?

 

[WoowyBaby]

Hello, guys. I'm new here and just finished reading this thread. Also I checked "List of methods". Is there any actual or work in progress algorithmic method to blockbuild to F2L - 1 slot state?

I don't think blockbuilding could be algorithmic? I'm not quite sure what you are asking...

 

[xyzzy]

I'm new here and just finished reading this thread.

That must have taken you a whole day… (I've done it once before, but that was when the thread was only 100-ish pages long.)

Anyway, no, there isn't any work being done on "algorithmic" blockbuilding. The biggest obstacle is the sheer alg count; it's just not realistic to learn all of the different cases as separate algs. For example, starting with a 2×2×3 block, the number of cases to build an additional square is 3024; restricting this to the cases where there's already a pair built still has 323 cases. For this reason, blockbuilding outside of inspection is usually done by forming pairs and joining them up (relatively few cases), as opposed to directly solving a whole block at once. (If you have 15 seconds of inspection time, that can make it easier to plan out solutions that are better than just creating pairs separately and joining them.)

 

[Umar Uzden]

That must have taken you a whole day...

It took me way longer - three weeks or so )

I was thinking about lowering case count through restricting order of solve and corner position.
By order I mean, for example, 2x2x2 block in BDL, then square in FDL (FDL corner + FL and DF edges), then BDR square (BDR + BR and DR)
Any corner except BDL can be moved to FUR position by 1 move, so it will reduce cases by 7 times for front square, so there will be 864 cases, and by 6 times for right square leaving 504 cases.
I genned near 100 algs for front square, and average movecount was ~5.4 face turns. For right square movecount will be higher, but I doubt (don't have access for my pc for week or two) that average will be higher than 9 moves.
Also, for first square corner can be oriented and moved to FUR in 2 moves or less, for second square in 3 or less moves, reducing cases by 3 times, but increasing movecount.

 

[WoowyBaby]

2OP (said too-ahp) is an interesting 3x3 speedsolving method that is barely related to any other method, switches off between intuitive parts and algorithmic parts, high chance of lucky solves (see examples), low movecount, about 80% moves being RU, decent lookahead due to 2x2x2 being solved, and fast developed algs.
Cons are pause before EO and high algorithm count, but these can easily be overcome.

A little explanation of the Steps:
2x2x2- Just normal Petrus Block
(EO2x2x2)- This is much better, but harder to plan in inspection than just 2x2x2, so if you can do it, do it, if you can’t then that’s fine. I personally cannot do it.
EO- You have 9 edges and RUF moves, so you basically bring 4 bad edges to F layer using R and U moves, then F to flip those 4.
Koce. F2L-1- Short for Kociemba F2L minus 1 slot, you make F2L-1 so it looks like you’ve done Kociemba Phase 1. It sounds very confusing and complicated, but actually very simple and easy.
TSLE- Just from the ZZ-CT method, you orient remaining 5 corners and place last E edge. Algs: https://gyroninja.net/zzct/zzct-tsle.html
F2L-1- I think everyone knows what this is.
This step can be done entirely [R2,F2,U] if you want to, because Kociemba Phase 1 is already done.
By the way, you can have your slot any of three places, not just FR.
TTLL- Again, from ZZ-CT. Permutes your last 9 pieces, finishing your solve. 1/5 of the time your D corner will be solved, so it PLL time. Algs from same website as TSLE.
Basically how this method is
(kinda random notes):
- 2x2x2 and EO
- Part of Koce. Phase 1 intuitively
- Alg to finish Phase 1
- Part of Koce. Phase 2 intuitively
- Alg to finish Phase 2

EXAMPLE SOLVES:

Scramble: D2 L2 B2 U2 B2 D2 U F2 D' F' R' B2 D2 B2 F' D R2 B2 R2

U2 u R U D’ L2 // 2x2x2
R’ F2 R’ U’ F // EO
R L’ U L // Koce. F2L-1
R’ U R U2 R’ U2 R // TSLE
y’ R2 U2 R2 B2 R2 U R2 U’ R2 // F2L-1
R' U R' U R U' R U' R2 D R' U' R U D' R’ U2 // TTLL
48 moves, 83% of them RU moves

Scramble: U2 B2 U2 F2 R2 U' L2 D R2 F2 D' R F' L D L2 B U2 F2 R B'
x2
r’ U F r F’ U’ // 2x2x2
l2 F2 U F’ // EO
R’ U2 R // Koce. F2L-1
U’ L’ U2 L // TSLE
U’ R2 F2 U’ R2 // F2L-1
y R2 U2 R2 U’ R2 U’ R2 U // TTLL
30 HTM, just random scramble off cstimer, went through scramble only once, crazy, right?? (almost FMC PB!)

Scramble: F2 R2 F2 U' B2 L2 D' F2 U B2 U2 F R2 B' F2 L' F' L' R B'
(x)
R’ U’ R’ r U’ // 2x2x2
(x) U’ F R2 F’ // EO
U R2 U2 R’ // Koce. F2L-1
U’ L’ U’ L U2 L’ U L // TSLE
U2 R2 M’ U2 M U’ y’ M U2 M’ // F2L-1
x' y' D2 U R U' R' D2 R U R' U' // TTLL
40 STM, drilled solution to 7.20 seconds

More Example Solves!

Spoiler

Scramble: B' R2 D' B2 L2 B2 D2 L2 U2 B L2 R2 B' L' R2 U' L2 R2 B' R

R L’ U L y U2 R u’ // 2x2x2
F U’ F // EO
// Koce. F2L-1 Skip
U’ R U' R' U R U2 R' // TSLE
F2 R2 F2 R2 U’ R2 U’ R2 U2 R2 // F2L-1
U2 R U' R D R' U2 R D' R' U2 R' U' R U2 R' // TTLL
44 HTM

Scramble: B2 U' L' F L' D2 B' U2 L2 D2 B2 L2 D2 R B2 D2 L F2 D2 U L
y2 z
u U R’ U z x’ u’ // 2x2x2
R’ U R F’ // EO
L’ U2 L R2 // Koce. F2L-1
R’ U2 R U R’ U2 R // TSLE
U’ R2 U’ R2 // F2L-1
d’ R2 U2 R' U R2 U' R' U' R U2 R2 U2 R U' R2 U2 // TTLL
41 HTM

Scramble: L' U2 L' D2 U2 B2 F2 R U2 F2 L U F' U2 L D2 U' B' D F'

r u' r' U2 R' u2 // 2x2x2
z' U F' // EO
L' R U' R' // Koce. F2L-1
U' L' U' L' D' L U' L' D L U L // TSLE
F2 L2 U2 M' U2 M // F2L-1
R2 U2 R U' R' U R' U2 R2 U R U R' // TTLL
43 STM

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

U' R2 U' R' U2 // 2x2x2
x2 y' U R' F // EO
U' L' U2 L R' U L' U' R U' L // TSLE
F2 U' F2 U R2 U2 M' U2 M // F2L-1
F2 U' R2 u2 R2 F2 D R2 D r2 // TTLL
38 STM

Random notes:

Spoiler

- Using this for FMC, movecounts of steps are about:
2x2x2: 5 EO: 4
Koce. F2L-1: 4 TSLE: 7
F2L-1: 7 TTLL: 12
Total(FMC)- 39 moves
|In speedsolve: ~42-44 moves|

To be faster with this method,
- Plan your entire 2x2x2
- Track EO in inspection (or even solve it simultaneously w/ 2x2x2?)
- Learn all TSLE and TTLL algs and get recognition down
- Lookahead to F2L-1 during TSLE
————
The name 2OP comes from 2x2x2 -> Orient -> Permute, but also make 2x2x2 then do OverPowered stuff

OPTIMAL TTLL ALGORITHMS (useful for FMC)

Spoiler

The algorithms will be in the same order as this website:
Opposite Front:
1- (U) R2 U’ F2 r2 U F2 U’ r2 F2
2- R2 U2 R' U R2 U' R' U' R U2 R2 U2 R U' R2
3- (U) R U' R' U R U2 R' U' R U R’
4- R’ L’ F2 R L D’ F2 R2 U’ L2 B2 R2 U2 L2
5- F2 R2 U2 F2 U F2 U R2 F2
6- R L U2 R L’ B2 U’ F2 L2 D’ L2 F2 U R2
7- (U2) R2 U R2 U R2 U2 R2
8- (U2) F2 L2 D' B2 D' B2 D2 L2 F2
9- R2 U2 R2 U' R2 U' R2
10- (U2) F2 R2 U' F2 U' F2 U2 R2 F2
11- F2 L2 D2 B2 D B2 D L2 F2
12- R2 D2 B2 D' B2 D' R2 F2 U F2
Opposite Right:
1-
2-
3-
4-
5-
6-
7-
8-
9- F2 U2 F2 U F2 U F2
10-
11-
12-
Diagonal:
1-
2-
3-
4-
5-
6-
7-
8-
9-
10-
11- R2 U B2 U R2 U' R2 U' B2 R2
12-
All Bars:
1-
2-
3-
4-
5-
6-
7-
8- R U R' F2 L D' L D L2 F2
9-
10-
11-
12-
Bar Right:
1- D B2 D' F2 D B2 D' F2
2-
3-
4-
5-
6-
7-
8-
9-
10-
11-
12-
Bar Front:
1- D' r2 U R2 U' r2 D R2
2-
3-
4-
5-
6-
7-
8-
9-
10-
11-
12-

OPTIMAL PLL ALGORITHMS (useful for FMC)

Spoiler

Let’s go:
Aa- (x) R’ U R’ D2 R U’ R’ D2 R2
Ab- (x) R2 D2 R U R’ D2 R U’ R
E- L U' R D2 R' U R L' U' L D2 L' U R'
F- R2 F R F' R' U' F' U F R2 U R' U' R
Ga- F2 D R' U R' U' R D' F2 L' U L
Gb- R2 F2 U R2 D' R2 D B2 U' F2 B2 R2
Gc- B2 R2 L2 U' R2 U R2 D' R2 D L2 B2
Gd- L U L' B2 D' R U' R' U R' D B2
H- R2 F2 B2 L2 D' R2 F2 B2 L2
Ja- R2 D R D' R F2 L' U L F2
Jb- R2 D' R' D R' B2 L U' L' B2
Na- F2 U2 R2 U F2 U2 F2 R2 U R2 U2 R2 F2
Nb- R U' R2 F2 U' R F2 R' U F2 R2 U R'
Ra- R U2 R' U B L' B' R B L B' U R'
Rb- R2 F R U R U' R' F' R U2 R' U2 R
T- R2 U R2 D' F2 L2 U' L2 D F2
Ua- F2 U' R' L F2 R L' U' F2
Ub- F2 U R' L F2 R L' U F2
Y- R2 U' R2 U' R2 U F U F' R2 F U' F'
Z- R2 U' R2 U R2 B2 R2 U B2 U' R2 B2

I’ve been thinking whether this is actually useful for 3x3 2H speedsolves today, I should do some practice and testing speedsolving this, and if it’s not good, then it’s still useful for FMC.

 

[Deleted member 36445]

Promising

 

[dudefaceguy]

I wrote up an updated and simplified tutorial for my intuituve 4x4 method, incorporating the feedback and criticism from @PapaSmurf @WoowyBaby and @dbeyer. Thanks guys for all of the feedback!

Here's the updated tutorial: https://www.speedsolving.com/forum/threads/intuitive-4x4-method-with-parity-avoidance.73049/

 

[Skewbed]

The start of 2x2x2 + EO seems really good.

 

[PapaSmurf]

Just do eo2x2x2. Should be possible. Also, you could use a variation on OL5C from SSC to optimise steps 3 and 4. The last 2 steps should be good, although maybe weird ergonomics.
Very good idea though.

 

[WoowyBaby]

Yes, I was first thinking of EO2x2x2 but I thought it might be too much to plan in inspection so I split them up, if you guys day it’s possible then ok! (I’ll edit the post)
Edit: Just saying, In the random notes section, under the “To be faster with this method:” I said this about EO- “even solve it simultaneously w/ 2x2x2”

 

[PapaSmurf]

https://alg.cubing.net/?setup=B-_D2...0 U_x-_z_L-_U-_L_D2_L-_U_L_D2_F2//TTLL,_50/50
Here's a solve with the ideas I mentioned. This method seems quite nice.

 

[Imam Alam]

bismillaahir raHmaanir raHeem

Gilles Roux said:

Hey Ryan, you could be much faster.
You know what's the problem with you?
You think too much, you'll never be a speedcuber!

... P.S.: I've got the same problem...

([email protected])

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What This Post is About

Just sharing a bunch of simple methods and variants for solving the 3x3x3 cube in fun, novel and elegant ways.

I guess this is more of a concept idea post than a new method post.

Spoiler

The main goal is to solve the cube with more understanding, and rely less on rote memorization.

.
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Methods Overview

This is my collection of "mini-methods" that have only "mini-algs", along with other cubing concepts.

Feel free to add more methods or method variants to this list!

Spoiler

Spoiler: Mini-Methods

a mini-method is a stand-alone (complete) method that solves the entire 3x3x3 cube. It is not just a sub-step. I am calling it "mini" because it is based on a simple idea, and it is possible to boil it down to one or two core concepts.

Spoiler: Mini-Algs

a mini-alg (or a trigger) is a very short sequence of moves that is so easy to understand and implement that you may even choose to call it "intuitive".

Spoiler

I don't believe that any method or variant can ever be 100% intuitive, just more intuitive or less intuitive (that, too, varies person to person).

I am simply focusing on the ones that are more intuitive for me.

Spoiler: Disclaimer

I don't claim any credit for any of these methods.

Just trying to share and discuss methods invented by others.

My contribution (hopefully) is the way these methods are organized and modified to fulfill the requirements described below.

The methods outlined here would have the following properties:

- solving as fast as possible is not the goal, nor winning competitions (rather the goal of using these methods would be pure fun/enjoyment, or a better understanding of the cube, or both)

Spoiler

No, I am not against speedsolving and competitions (both have their places in cubing), just looking for ways to expand the horizon, and to try out new things.

- methods that require some intuitiveness are preferred (simplified versions of the popular methods are also welcome)

Spoiler

No, I am not against memorization and algorithms (both have their places in cubing).

In fact, the more you practice intuitively the more it becomes memorized/algorithmic, and vice versa.

We still use algorithms as beginners, in one form or another, but we keep on trying to understand how those algorithms actually work.

- have significantly different step(s) compared to more popular methods, and preferably do not end with LL (last layer) algorithms

Spoiler

Well, I am not against popular methods either.

It is just that popular methods are usually optimized for speedsolving, and here we are focusing more on other factors, such as fun, novelty, challenge, and elegance.

- diverse solving styles, fun new methods to try out (elegant, aesthetically pleasing solutions are a bonus)

Spoiler

Concepts are preferred over memorized algorithm sets.

Examples: freedom of movement, symmetry, parity and twist constraints, group theory.

In practice: block building, commutators, generator reduction (domino, 2-gen), EO and CP etc.

- relatively few (<10) algs, learning new algs with every new method is not desired (shorter and ergonomic algs are a bonus)

Spoiler

No, I am not against methods with large alg sets.

I just find a smaller alg set to be easier to digest, easier to understand thoroughly in less time, and easier to recall.

- relatively low (<70) move count STM/HTM

Spoiler

Here we are expressing move count in STM (Slice Turn Metric) and HTM (Half Turn Metric), i.e. these methods should not require more than 70 slice turns (and half turns) on average to solve the cube.

That's what I am aiming for.

Spoiler

Feel free to add to my list, your methods don't need to fulfill all of the above conditions, so if you think that you know of a method that goes with the general spirit, just go for it!

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Algorithms Overview

The algs should be easy to understand and easy to implement, i.e. it should be a nice alg set.

Hence shorter and simpler algorithms are preferred.

Spoiler

Spoiler

For the 15 mini-methods and variants I am sharing here, I propose an alg set of 9 triggers or mini-algs (yes, you read that correctly: 9 short algs for 15 methods combined!).

The algorithms included here would have the following properties:

- the alg set is short (<10 algs for one complete method)

Spoiler

I am using 9 algs for 15 methods, none of these methods require more than 8 algs, and there are one or two methods that virtually require 0 algs.

- each alg is short (3 ~ 6 moves HTM and STM)

Spoiler

The 9 triggers I am using have an average length of 4.89 moves HTM (4.11 moves STM), none of them is longer than 6 moves HTM (and 6 moves STM).

- the algs should be easy to understand and recall (the user of the method should know exactly what the algs do to which pieces)

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All of the 9 algs I am using can be considered as nice (usually symmetric), so they are even shorter, and easier to understand.

- additionally, the algs should be ergonomic if possible (preferably 2-gen)

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All of the 9 algs I am using are 2-gen.

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Methods List

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From here onward "methods" stands for "methods and variants".

The mini-methods that I am sharing may be put into the following groups:

Spoiler: Disclaimer

When I describe a method with the name of the inventor of that method, I do that only generally, sometimes only taking a method partially and simplifying the rest.

For example, when I describe a method as "Roux" I don't claim that this is exactly how Gilles Roux had proposed it.

So please take the method names with a grain of salt.

[2-Generator Methods]

Method 1. Wu

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- 1x1x3: EO (trigger 1 / trigger 2) then CP (trigger 8 / 2GR / others), or CP (trigger 8 / 2GR / others) then EO (trigger 2)

- 2x2x3 (blockbuild)

- 3x3x3: make 4 corner-edge pairs (2-gen blockbuild) while doing CO L6C (triggers 1 and 7 / trigger 1 + mirror / corner 3-cycle / sune), then EP (trigger 6), then permute last 2 layers (trigger 9)

Method 2. ZZ

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- EOline (trigger 1 / trigger 2)

- F2L (blockbuild), optional CO L4C

- L4C (trigger 1 + mirror / corner 3-cycle + sune), or CP L4C if CO L4C already done (trigger 1 + mirror / corner 3-cycle)

- EP L4E (triggers 3, 4 and 5 / trigger 1 + mirror + inverse / sune + mirror)

Method 3. Petrus

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- 2x2x3 (blockbuild)

- EP L7E (trigger 1 + mirror using F turns)

- F2L (blockbuild), optional CO L4C

- L4C (trigger 1 + mirror / corner 3-cycle + sune), or CP L4C if CO L4C already done (trigger 1 + mirror / corner 3-cycle)

- EP L4E (trigger 1 + mirror + inverse / sune + mirror)

[Edges First Methods]

Method 4. Heise

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- F2L-1 (blockbuild, then EO) (w/ or w/o pseudo blocks)

- L5E EP (w/ or w/o EC pairs)

- L5C or L3C (corner 3-cycle)

Method 5. Keyhole

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- F2L-1

- EO L5E (trigger 1 + mirror)

- EP L5E (trigger 1 + mirror)

- L5C (trigger 1 + mirror + inverse / corner 3-cycle)

Method 6. Coffer

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- F2L-1

- EP L5E (trigger 1 as R U2 R')

- EO L5E (trigger 1 as R U2 R')

- L5C (trigger 1 as R U2 R' + mirror / trigger 1 / corner 3-cycle)

[Corners First Methods]

Method 7. Sandwich

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- 8C (trigger 1 + mirror / corner 3-cycle)

- E slice and S slice

- EP L4E (triggers 3 and 4)

- EO L4E (edge flip commutator)

Method 8. Columns

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- 8C (trigger 1 + mirror / corner 3-cycle)

- E slice and DL+DR as 3 pairs or LMCF style E2L (trigger 5)

- EO L6E (trigger 2)

- EP L6E as 3 pairs (triggers 3 and 4)

Method 9. Roux

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- FB and SB (blockbuild)

- LLC (corner 3-cycle)

- EO L6E (trigger 2)

- EP L6E (triggers 3 and 4)

[Orient First Methods]

Method 10. Thistlethwaite

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- EO and separate E slice edges (trigger 1 / trigger 2)

- CO (triggers 1 and 7 / trigger 1 only)

- CP (trigger 8)

- EP (triggers 3, 4 and 6)

Method 11. Morozov OF

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- CO (triggers 1 and 7 / trigger 1 only)

- separate E slice edges (trigger 5) and EO L8E (trigger 2)

- CP (trigger 8)

- EP (triggers 3, 4 and 6)

Method 12. Morozov CF

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- CO (triggers 1 and 7 / trigger 1 only)

- CP (trigger 8)

- separate E slice edges (trigger 5) and EO L8E (trigger 2)

- EP (triggers 3, 4 and 6)

[Permute First Methods]

Method 13. Benek CF

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- CP (trigger 8 / 2GR / others)

- CO (triggers 1 and 7 / trigger 1 only)

- separate E slice edges (trigger 5) and EO L8E (trigger 2)

- EP (triggers 3, 4 and 6)

Method 14. Benek PF

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- CP (trigger 8 / 2GR / others)

- EO (trigger 2)

- CO (triggers 1 and 7 / trigger 1 only)

- separate E slice edges (trigger 5) and EP (triggers 3, 4 and 6)

Method 15. Benek 2GR

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- EO (trigger 1 / trigger 2)

- CP (trigger 8 / 2GR / others)

- CO (triggers 1 and 7 / trigger 1 only)

- separate E slice edges (trigger 5) and EP (triggers 3, 4 and 6)

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Algorithms List

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The mini-algs (triggers) for the above methods are:

Spoiler: Disclaimer

I don't claim to have generated any of these algs.

I have simply collected, compared and selected the algs to come up with a relatively nice alg set.

Trigger 1. R U* R' (U*) = [R: U] or [R, U]

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length: 3 or 4 HTM, 3 or 4 STM

application: this is the only alg required for method 5 (keyhole), it is also the only alg required for method 6 (coffer) as R U2 R', and it is useful for CO in methods 10 ~ 15 (OF and PF methods)

Trigger 2. M' U M* = [M': U]

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length: 5 HTM, 3 STM

application: EO alg in methods 7 ~ 15 (CF, OF and PF methods)

Trigger 3. U2 M2 U2 (M2) = [U2: M2] or [U2, M2]

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length: 4 or 6 HTM, 3 or 4 STM

application: EP alg in methods 7 ~ 15 (CF, OF and PF methods)

Trigger 4. M' U2 M (U2) = [M': U2] or [M', U2]

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length: 5 or 6 HTM, 3 or 4 STM

application: EP alg in methods 7 ~ 15 (CF, OF and PF methods)

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Instead of using 90 degree M slice turns, we can use R2 U2 R2 F2 R2 U2 R2 F2 = [[R2: U2], F2] (8 HTM, 8 STM), thus making the EP finish in methods 7 ~ 12 (OF and PF methods) purely with 180 degree turns.

In these methods we progressively reduce the cube to be solvable with 180 degree turns, so I find this alternative alg pretty elegant.

Although not a 2-gen alg, it is still quite ergonomic and short, and has some symmetry.

Trigger 5. U M2 U* = [U: M2]

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length: 4 HTM, 3 STM

may also be applied as R E2 R*

application: EP alg (M slice or E slice) in methods 7 ~ 15 (CF, OF and PF methods)

Trigger 6. R2 U2 R2 U2 R2 U2 = [R2 U2 R2, z' y2]

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length: 6 HTM, 6 STM

application: EP alg in methods 10 ~ 15 (OF and PF methods)

Trigger 7. (U) R2 U2 R* = [U R2, z' y2]

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length: 3 HTM, 3 STM

application: CO alg in methods 10 ~ 15 (OF and PF methods)

source: Morozov method

Trigger 8. R2 U R2 U' R2 = [R2 U: R2]

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length: 5 HTM, 5 STM

application: CP alg in methods 10 ~ 15 (OF and PF methods)

source: Morozov method

Trigger 9. R U R2 U' R' = [R U: R2]

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length: 5 HTM, 5 STM

application: this is the permutation alg for method 1 (Wu), and this is the main alg for that method

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Methods Comparison

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---------------------------------------------------------------------------------------------
   type    |             steps            |  #EO  |       features       |       redux
---------------------------------------------------------------------------------------------
           | Wu               EO CP BB BB |  12   | BB          OF    PF |                 RU
    2G     | ZZ               EO BB CS EP |  12   | BB          OF       |                 RU
           | Petrus           BB EO CS EP |   7   | BB                   |                 RU
---------------------------------------------------------------------------------------------
           | Heise            BB EO EP CS |   5   | BB                   |
    EF     | Keyhole             EO EP CS |   5   |                      |
           | Coffer              EP EO CS |   5   |                      |
---------------------------------------------------------------------------------------------
           | Sandwich            CS EP EO |   0   |       CF             | MU
    CF     | Columns             CS EO EP |   6   |       CF             | MU
           | Roux             BB CS EO EP |   6   | BB    CF             | MU
---------------------------------------------------------------------------------------------
           | Thistlethwaite   EO CO CP EP |   8   |       CF    OF       |      G1+G2+G3
    OF     | Morozov OF       CO EO CP EP |   8   |       CF    OF       | MU   G1+G2+G3   RU
           | Morozov CF       CO CP EO EP |   8   |       CF    OF       | MU   G1+G2+G3
---------------------------------------------------------------------------------------------
           | Benek CF         CP CO EO EP |  8/11 |       CF    OF    PF |      G1+G2+G3   RU
    PF     | Benek PF         CP EO CO EP |  8/11 |       CF    OF    PF |      G1+G2+G3   RU
           | Benek 2GR        EO CP CO EP | 11/12 |       CF    OF    PF |      G1+G2+G3   RU
---------------------------------------------------------------------------------------------

Spoiler: Comments

- Generally speaking, the earlier methods in the list (methods 1 ~ 6) have more of a blockbuilding/edges first/face turns/direct solve style, and later methods (methods 7 ~ 15) have more of a corners first/columns first/slice turns/reduction style

- Earlier methods in the list (methods 1 ~ 9) solve the corners relatively directly, later methods (methods 10 ~ 15) solve corners more indirectly.

- Number of edges to be oriented during the EO stage gradually decreases and then increases again as we progress through the list.

- For methods 7~ 9 and 10 ~ 15, each method builds upon the previous ones, hence they get more and more complex as we progress through the list.

- Generally speaking, methods 10 ~ 15 first reduce the cube to <F2, B2, R, L, U, D>, then to <F2, B2, R2, L2, U, D>, and then to <F2, B2, R2, L2, U2, D2>, before finally solving it with 180 degree turns only.

- Will add more methods to the list, that is when I find them.

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Yup, that's my first post in this forum!

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(Been lurking around for a long time...)

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Tony Fisher said:

Intuitive means you are fully aware of every move you are making and understand what each turn is doing.

(http://twistypuzzles.com/~sandy/forum/viewtopic.php?f=8&t=27543)

subHaanakallaahumma wa biHamdika ashhadu an laa ilaaha illaa anta astaghfiruka wa atoobu ilaika