The New Method / Substep / Concept Idea Thread

[AHornbaker]

Method System: Block => CP => EOF2L => 2GLL

I have been fascinated by the idea of solves using CP. Unfortunately, recognition is usually not very good or move efficient. There is speculation whether CP solves are more efficient than traditional CP at the end as part of PLL. There is no doubt that a solve with early CP can lower the move count overall, and make the solve more efficient in cases and move sets, but is it viable for speedcubing?

The main problem in my opinion is the slow setup and recognition of CP early in the solve. I have come up with a fairly easy recognition system for CP with only 2 setup moves and 5 algs to learn, which could make CP viable for speedcubing.

I am classifying this as a method system because there are too many possible substeps and variations for a single method. I believe it should start off with a block; something simple and efficient that can be planned out during inspection. Two block approaches I will talk about are the 1x2x3 or Roux block, and the 2x2x3, or Petrus block.

Next is the distinguishing step: CP. After solving two of the corners in the initial block, you have 6 corners left to look at, which translates to 720 permutations. By placing the two remaining corners in the ULB and DRB spots, the perm count is reduced to 48 (24 times 2 if DRB is right/wrong corner). This setup takes only 2 moves, and may also be part of inspection. At this point there are 6 distinct cases to recognize, which can be solved in an average of 3 moves. This step is useful for the Roux block, because EO can later be solved using <R,U,r,M> without breaking up the block. In the case of the Petrus block, a single EO/CP step would be more efficient than using EO algs that preserve CP afterward, or the other way around. However, this step is very complicated, and is not yet viable for speedcubing. It may be a very useful FMC step.

CP Algs:

Spoiler

CP + EO Algorithms - Austin Hornbaker

CP Recognition:
1. Place 2 D corners in UBL and DBR (2 moves)
........-Make note of the corner in DBR
2. Examine colors on FRU corner
........-Find the other two corners with the same colors
........-This will make an L shape on either the F, R, or U face
........-Determine if the end corners of the L are permuted c-correct, or s-swapped

D Corners Correct CP (2.8 HTM)
Fc: (f R' f') or (d R' U' R d')
Fs: Correct CP
Rc: (f R f') or (d R' U R d')
Rs: (R F R F') or (R2 d R' U' R d')
Uc: (f U2 f') or (d' L' U L d)
Us: (U f R f') or (d R' U2 R d')

D Corners Swapped CP (2.8 HTM)
Fc: Correct CP
Fs: (f R' f') or (d R' U' R d')
Rc: (R F R F') or (R2 d R' U' R d')
Rs: (f R f') or (d R' U R d')
Uc: (U f R f') or (d R' U2 R d')
Us: (f U2 f') or (d' L' U L d)

12 EO Cases: (5.4 HTM).....U Edges......Alg:
0 Edges Misoriented-............-...............None
2 Edges Misoriented-
........L on U.......................F,R............r U R' U' M
........Line on U ..................L,R............R U' M' U R' U M
........Both on F ..................-...............r U R' U R U r'
........FR 1 on U...................F..............M' U R U r'
........FB 1 on U...................B..............M' U M U M' U M
4 Edges Misoriented-
........Cross on U.................-...............M' U2 M U2 M' U M
........FR, 3 on U..................F,R,B.........r U2 r' U2 M' U M
........FB, 3 on U..................L,F,R.........M' U M
........Line on U...................F,B............R U M' U' r'
........L on U.......................L,F............r U r'
6 Edges Misoriented-
........All flipped..................-...............r U R' U M U M' U M

Next is the EOF2L stage. Again, there are many ways to do this. In the case of the Roux block, I would solve a 2x2x2 block on BR. This reduces the cases for EO, which would only have 12 distinct cases. After EO, I would then fill in the last slot and proceed to 2GLL. There are many other ways to do EOF2L. An experienced cuber ideally could solve F2L while subsequently orienting the edges. The move count of the Roux block method comes down to how good you are at this step. In the case of the Petrus block, EO is already solved, and F2L would be finished with <R,U>.

The last step is 2GLL. This has 85 different cases to orient corners and permute edges. There are two possible ways to solve this. The first is learning all 84 algorithms and solving in one look. An alternate method is to learn 7 COLL algs and the remaining 4 edge perm algs and solve LL 2-Look.

2GLL Algs: (post wont let me indent or attach files, sorry for bad format, these algs can be found elsewhere)

Spoiler

2GLL Algorithms - Stachu Korick
________________________________________________________________________________
Corners Solved UUUU (5 cases) [39/5 moves]
- 0 -
+ 7 M2 U M2 U2 M2 U M2
Z 10 M2 U M2 U M' U2 M2 U2 M' U2
Bc 11 R2 U R U R' U' R' U' R' U R'
Ba 11 R U' R U R U R U' R' U' R2

Double-sune RLLR (8 cases) [107/8 moves]
- 18 y' F R U R' x U R' U' R x' U' R U R' x U R' U' R x' U' F'
+ 15 y2 R' U' R U' R' U2 R U R U2 R' U' R U' R'
Zr 15 y R U2 R' U' R U' R' U' R' U' R U' R' U2 R
Zl 15 R' U2 R U R' U R U R U R' U R U2 R'
Fa 11 y' R U2 R' U' R U R' U' R U' R'
Ba 11 y2 L' U' L U' L' U L U' L' U2 L
Lc 11 y' L' U2 L U L' U' L U L' U L
Bc 11 y2 R U R' U R U' R' U R U2 R'

T UULR (12 cases) [172/12 moves]
- 15 R' U' R U' R' U2 R U2 R U R' U R U2 R'
+ 15 R U2 R2 U R' U R' U R' U R U2 R2 U' R2
Zr 13 R U2 R' U' R U' R2 U2 R U R' U R
Zl 13 y2 R' U2 R U R' U R2 U2 R' U' R U' R'
Fa 15 y' R U R' U R U2 R' U' R U2 R' U' R U' R'
La 15 R U' R U2 R U2 R' U R U R' U' R' U R'
Ba 13 y' R U R2 U' R2 U' R2 U2 R U' R U' R'
Ra 15 y2 R' U2 R U R' U R U' R' U' R U' R' U2 R
Fc 15 y' R' U' R U' R' U2 R U R' U2 R U R' U R
Lc 15 R U2 R' U' R U' R' U R U R' U R U2 R'
Bc 13 y' R' U' R2 U R2 U R2 U2 R' U R' U R
Rc 15 L' U L' U2 L' U2 L U' L' U' L U L U' L

Headlights UUBB (12 cases) [172/12 moves]
- 15 y R' U2 R U R' U R U2 R U2 R' U' R U' R'
+ 15 R2 U R2 U2 R' U' R U' R U' R U' R2 U2 R'
Zr 13 R' U' R U' R' U2 R2 U R' U R U2 R'
Zl 13 y2 R U R' U R U2 R2 U' R U' R' U2 R
Fa 15 R U2 R' U2 R2 U R' U R' U' R U R U2 R2
La 15 y R U2 R' U' R U' R' U' R U R' U R U2 R'
Ba 13 R' U' R U' R U2 R2 U' R2 U' R2 U R
Ra 15 y R U2 R2 U' R2 U' R' U R' U' R U R' U R
Fc 15 y2 R U R' U R U2 R' U R U2 R' U' R U' R'
Lc 15 y R U' R U R U' R' U' R U2 R' U2 R' U R'
Bc 13 L U L' U L' U2 L2 U L2 U L2 U' L'
Rc 15 y R' U2 R U R' U R U R' U' R U' R' U2 R

L ULUB (12 cases) [180/12 moves]
- 15 R U2 R' U2 R' U' R U R U' R' U2 R' U2 R
+ 15 R U R' U R U' R' U R U' R' U R U2 R'
Zr 15 y2 R U2 R' U' R U' R' U2 R U R' U R U2 R'
Zl 15 y2 R U R' U R U2 R' U2 R U2 R' U' R U' R'
Fa 15 y2 R U2 R' U' R U' R' U R' U2 R U R' U R
La 15 y2 R U R' U R U2 R' U R' U' R U' R' U2 R
Ba 15 y L' U2 L' U' L2 U' L U L' U' L U2 L U' L
Ra 15 y L2 U' L U' L U L' U L U L' U' L' U L2
Fc 15 R2 U R' U R' U' R U' R' U' R U R U' R2
Lc 15 R U2 R U R2 U R' U' R U R' U2 R' U R'
Bc 15 y R' U' R U' R' U2 R U' R U R' U R U2 R'
Rc 15 y R' U2 R U R' U R U' R U2 R' U' R U' R'

Pi FLLB (12 cases) [161/12 moves]
- 15 R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R'
+ 15 y R U R' U R U2 R' U R U R' U R U2 R'
Zr 15 y R U2 R' U' R U' R' U R U2 R' U' R U' R'
Zl 12 f R U R' U' f' F R U R' U' F'
Fa 13 y L' U2 L U L' U L2 U L' U L U2 L'
La 15 y2 R' U' R U R2 U' R U' R' U2 R2 U R' U' R
Ba 9 y2 L' U2 L2 U L2 U L2 U2 L'
Ra 15 L U' L' U L2 U2 L' U' L U' L2 U L U' L'
Fc 9 R U2 R2 U' R2 U' R2 U2 R
Lc 15 L U L' U' L2 U L' U L U2 L2 U' L U L'
Bc 13 y R U2 R' U' R U' R2 U' R U' R' U2 R
Rc 15 L' U L U' L2 U2 L U L' U L2 U' L' U L

Sune ULBR (12 cases) [143/12 moves]
- 15 R' U R2 U R' U R U2 R U2 R U R' U R2
+ 11 R' U2 R2 U R2 U R U' R U' R'
Zr 13 R2 U' R' U' R2 U R U R2 U R' U R
Zl 14 L' U' L U' L' U2 L y' L U2 L' U' L U' L'
Fa 13 R' U2 R2 U R U' R' U R U R2 U' R'
La 13 R2 U R U' R' U' R U2 R U' R2 U' R2
Ba 13 R2 U' R2 U' R U2 R U' R' U' R U R2
Ra 11 y R U R2 U' R2 U' R2 U2 R2 U2 R'
Fc 7 y R U R' U R U2 R'
Lc 13 R2 U R' U' R' U' R U2 R' U' R2 U' R2
Bc 13 R2 U' R2 U' R' U2 R U' R' U' R' U R2
Rc 7 R' U2 R U R' U R

Antisune RULB (12 cases) [146/12 moves]
- 15 L U' L2 U' L U' L' U2 L' U2 L' U' L U' L2
+ 11 L U2 L2 U' L2 U' L' U L' U L
Zr 15 R U R' U R U2 R' U R' U2 R U R' U R
Zl 13 L2 U L U L2 U' L' U' L2 U' L U' L'
Fa 7 y R' U' R U' R' U2 R
La 7 L U2 L' U' L U' L'
Ba 13 L2 U L2 U L U2 L' U L U L U' L2
Ra 13 L2 U' L U L U L' U2 L U L2 U L2
Fc 13 L U2 L2 U' L' U L U' L' U' L2 U L
Lc 13 R' U2 R U2 R U2 R' U' R U' R2 U2 R
Bc 13 R2 U' R U' R2 U R2 U' R' U R2 U R2
Rc 13 L2 U' L' U L U L' U2 L' U L2 U L2

________________________________________________________________________________
(85 cases) [1120/85 moves]

Notation:
- Edges correct
+ L-R, B-F
Zr B-L, F-R
Zl B-R, F-L

Anticlockwise:
Fa L->R->B->L no F
La B->F->R->B no L
Ba R->L->F->R no B
Ra F->B->L->F no R

Clockwise:
Fc L->B->R->L no F
Lc B->R->F->B no L
Bc R->F->L->R no B
Rc F->L->B->F no R

Here are the two potential methods I outlined above:

Roux Block:
-1x2x3 ......~7
-CP..............5
-2x2x2.......~8
-EO + Pair..~10
-2GLL...........13
................~43 moves

Petrus Block:
-2x2x3
-EO/CP
-2GF2L
-2GLL

At the moment, I have finished the CP and EO algs for the Roux block method. However, I have not completed one-look EO/CP yet for the Petrus block method. The main problem with EO/CP is that both EO and CP interact with each other. In short, you cannot do one without messing up the other. Although there are only 6 cases for CP, there are 64 unique EO cases, which makes learning a set of algs unfeasible. Also, turning the U and R faces to position the edges for EO changes the CP. It would theoretically take 24 algs: (6 CP) X (4 EO: correct, 2, 4, or 6 misoriented). There is a pattern to track CP this way, but again, it would be infeasible for speedsolving.

A different way of doing this step is to orient edges while placing the corners for recognition, then creating a new set of CP algs that preserve EO. Unfortunately, this step would probably require too much thinking and be very inefficient.

Currently I am testing out the Roux block method the way I have outlined to see if it is viable for speedcubing. At the very least, I have developed a low move count CP recog/solve method. Let me know what kind of potential you think this system has and/or ways to improve it. All criticism is welcome.

-Austin

 

[rj]

~snip~

Nice concept. I will try this.

 

[elrog]

I think the 1x2x3 is more practical for speed. By doing all of this, you are increasing your understanding of how CP works. I hope you can eventually find a way to solve it during inspection with a 1x2x3 block or something of the sort.

 

[AHornbaker]

Another similar method that could also be viable is 1x2x3 => EOF2L => Winter Variation/OLL => PLL
Again, the biggest factor is the efficiency of EOF2L

 

[BoBoGuy]

3x3 method: X-CELL

X-CELL

Okay, I don't know if this is a new method, but I decided to make a new F2L method for beginners and intermediates.

Steps:
X-Cross
First layer corners
3 E-Layer edges
LL

Step 1: X-Cross

This step is pretty simple. Just make a 2x2x2 block, like in the petrus method, and then finish the cross edges.
Or, you can do cross+first pair.
For beginners, do cross+corner+edge (in the same slot).

Step 2: Corners of First Layer

This is a fairly intuitive step.
Finish the first layer with R U R', U R U' R', or R U2 R' U' R U R'.

Step 3: E-Layer

In this step, we will finish the E-Layer in only 2 , at most 3 looks.
It's easier to explain with just examples. Scramble with:
R U R' F U' F' R' U F2 L F2 L' U2 R U2 R U' R' L F' L' F R' U' R2 B' R' B U L' U' L
Sorry for the long scramble.

Anyway, U2 L' U L pairs up a F2L slot.Then you finish up the other 2 edges without ruining the pair with keyhole.
If you don't know what Keyhole F2L is, check out the wiki.
What you do is D R U R' D R' U' R D' F' U' F D'. Now you can insert the last pair easily.
We solved the E-layer in 17 moves, so it is pretty efficient.

Note: For the last layer, you can use partial edge control, or VH.

LL: Solve the last layer. OLL/PLL, CLL/ELL, EOEPCPCO, 4LLL, 3LLL, 1LLL, ZBLL, OLLCP, EO COLL/EPLL, etc. etc. etc.

And that's it.
Average move count: 60ish

 

[Lapinsavant]

Looks like an intermediate method which consist to solve the e layer (3 edges only) with the corner unsolved of the first layer, then you have to solve the last slot to finish f2l

 

[BoBoGuy]

Just got a 11.98 NL solve with X-CELL and a low 16 average.
Sub-15 can definitely be reached.

 

[scottishcuber]

Your scramble + solution isn't working for me.

 

[BoBoGuy]

Sorry. I'll fix it.

 

[AvGalen]

Sounds like a very slow way to do keyhole

 

[CubezUBR]

When solving edges on the 4x4, I place the edge oriented correctly while I swap it for another edge. This makes EO complete when I finish the edges. I solve the last 2 edges into correct orientation usually with a 3-cycle commutator. I'm sure others have thought of this, but does anyone do it?

Another Idea I've had is to just not pair the last 2 edges and save them for the very last part of the solve so you solve both parities and pair the last 2 edges in one step.

I do that first one out of bad habbit! I do white pairs then f2l pairs (non white or yellow) then yellow pairs in the right(ish) spot

 

[cubacca1972]

Just a random idea I had:

For those of you who like to solve using Fridrich (CFOP for you youngsters), there are 57 possible orientation cases for the last layer when the F2L stage is complete. I hate that number. That number is the specific reason I never bothered to learn Fridrich.

So I had a random thought-What if while you were about to slot the last corner-edge pair, you were able to orient 2 corners and one edge, and jam them together on the last layer (adjacent to each other, as in UFL-UL-UBL)? You would be able to reduce the total possible orientation cases to 11, one of which is an OLL skip, and four of the cases are a pair of mirrored algorithms.

In theory, there would be lots of freedom in slotting the last CE pair, as it doesn't really matter which last layer cubies make up the C-E-C cluster. Consider your standard issue slotting of your last CE pair, paying no attention to what that does to the last layer (R U' R', R U2 R', Sledgehammer, etc.) Intuitively, if you were to apply the inverse to a solved cube, you can see that the standard slotting algorithm can be applied to four unique C-E-C cases.

The potential problems would be recognition, and possible move count issues. Recognition could be tricky, as you would have four candidate edges to focus on, and what corners to go with it. I don't know how many cases there are outside of the ones that can be done using the standard CE pair slotting algorithms, and finding the optimal algorithms for those cases is a rather tedious process. On the other hand, each found algorithm can be used for four unique cases.

If this idea has legs (and hasn't been proposed before), I will add it to my list of obscure sub-step variations (WV, some non-useful Roux LSE ideas, and so on).

 

[mark49152]

Just a random idea I had:

I like the idea of simple, intuitive last slot inserts that reduce the number of OLL cases. They have to simple enough that they don't cause a recognition pause and become a slower version of 2-look OLL though.

One idea I briefly explored is manipulating corners to always get a sune or antisune case, with any orientation of edges. I like those OLL cases (squares, small lightning bolts, etc.) because many of them are easy to learn and execute as sunes with set-up moves. It has the same advantage that you have several cases to aim for and that freedom can result in shorter and easier algs. I didn't get very far with it though.

Here's a similar idea but working on edges to force a "bar" OLL case, where the freedom to create the bar either way around means fewer and shorter algs than full VHLS: http://www.speedsolving.com/forum/showthread.php?39278-Another-last-slot-method-F2L-to-bar-OLL-case

 

[Dapianokid]

My friend, Zach, is a speecuber. He's the one who interested me in this hobby. He doesn't really seriously focus on it, though. He is trying to learn Waterman and we discussed different methods wayy back before I even had a cube and he said something about a method which "cretes 6 crosses first." After some research, I found that no such method exists (I tried learning as many as I could in a short amount of time and found MANY methods, but no Edges First except for maybe Pochmann, but it's not a speedcubing method).

So, I decided to attempt solving a cube with edges first. I am adept at ZZ, so I thought perhaps EO would be a good first step. So far, this is the first out of two steps I have actually successfully completed. Intuitively solving all edges is as far as I've gotten. I would like help with this, because I've learned I can solve all edges in about the same amount of time it takes me to get the 2x2x3 block + EO in Petrus. This is blazingly fast for a new method, and I'm hoping that maybe the rest of the method would lead to a very nice solve.

Step one: EO +Line. Tip: Solve it exactly as you would in ZZ. Make sure it's on the bottom.

Step two: Intuitively solve the middle layer edges. If white is on bottom, which it normally is for me, then you are solving all edges without yellow or white.

Step three: Use PLL algorithms to permute the (if correctly executed, already oriented) LL edges. If white is on bottom, you should be going for the yellow edges to be solved. I use your classic R U R' U R U'2 R', A.K.A. your good friend, Sune!

Step four: Now you have a nice design with many twisted and misplaced corners. It is very likely you have a 2x2x2 or 3x3x3 block solved, and that you have many 2x1x1 blocks to move around. Go ahead and use Petrus or Roux to finish this one off.

Or, if you want to help me out, take advantage of the many algorithms which permute and orient corners without disturbing edges. I know very few of these. I don't want there to be a true LL or F2L in this, unless that is simply how it turns out. One should be able to solve the edges with any color on top or bottom at this point, because the corners are all fair game. This method could be a very speedy one! Help guys!

 

[Renslay]

My friend, Zach, is a speecuber. He's the one who interested me in this hobby. He doesn't really seriously focus on it, though. He is trying to learn Waterman and we discussed different methods wayy back before I even had a cube and he said something about a method which "cretes 6 crosses first." After some research, I found that no such method exists (I tried learning as many as I could in a short amount of time and found MANY methods, but no Edges First except for maybe Pochmann, but it's not a speedcubing method).

Of course there are edge first methods.
http://www.speedsolving.com/wiki/index.php/EF
However:
"EF is not well suited for advanced speedsolving, the first step is very easy but the corners needs a unplesant number of moves to be solved after that in most cases."
It is highly recommended inserting some corners before you solve all the edges - that's why you can't find many pure edge first variants.
For example, the 8355 method (or the Sexy Method) is almost a pure edge first method, but it inserts 3 corners in the middle of the solving of the edges, just to make the solving easier.
A simplified Belt method can be an edge first method.
The "Ultimate Method" (if I recall the name well) is an edge first method, where you solve the corners with commutators. It is very slow (high move count).
And as you said, almost every BLD method is technically an edge first (or equivalently, a corner first) method.

EDIT:
So far you worked out the easiest part of an edge first method: solving the edges (here, with ZZ).
Edge first solving is fun, but it won't be an efficient speedcubing method - why wouldn't you solve some of the corners in an earlier, easier sub-step before finishing the edges?

 

[Dapianokid]

Thanks, Renslay
Very informative. I think I was mostly excited about the possibilities of the cube once all edges have been solved. I also have a very quick way of doing so, which I like. Getting the corners may just be a step that nobody has really perfected yet. I hate corners first methods, though. I'll work on it and either give up, or contribute a practical speedsolving edges first method for the ZZ-apt mind.

I can solve all edges in less than 20 moves, easily, without the aid of algorithms or anything of the sort. So, the human mind of even a beginner speedcuber is capable of it. I think tackling the corners with a strategy would be effective. Something with few moves and yields pleasantly easy to recognize cases and paths to solving. Like treating it as two LLs. Hmmmmmm.

 

[Renslay]

Thanks, Renslay
Very informative. I think I was mostly excited about the possibilities of the cube once all edges have been solved. I also have a very quick way of doing so, which I like. Getting the corners may just be a step that nobody has really perfected yet. I hate corners first methods, though. I'll work on it and either give up, or contribute a practical speedsolving edges first method for the ZZ-apt mind.

I can solve all edges in less than 20 moves, easily, without the aid of algorithms or anything of the sort. So, the human mind of even a beginner speedcuber is capable of it. I think tackling the corners with a strategy would be effective. Something with few moves and yields pleasantly easy to recognize cases and paths to solving. Like treating it as two LLs. Hmmmmmm.

Your welcome.
Experimenting around the cube is fun and you can learn many thing. Just don't think you invent something groundbreaking.
Yes, solving the edges alone (or the corners alone) is easy enough so a beginner can figure out them by him/herself - that's the reason why most of the beginners (who don't learn the solving itself) came up with an EF or CF method first, or their variants.

If you want to solve the corners after an "edge first" step, I suggest you search after BH and TuRBo method (or any 3-cycle corner solving BLD method). BLDs are good in solving corners withouth mixing up the edges. However, they require fully understand the different type of commutators (BH), or learning many algorithms (TuRBo).
See:
http://www.speedsolving.com/wiki/index.php/BH
and
http://www.speedsolving.com/wiki/index.php/TuRBo
Or you can just solve them with free-style 3-cycling (look up for commutators). But again, this requires lots of practice, and the recognition still can be slow.

An other way for finishing the corners is the Belt method (or its variant), where you deal with the up layer and down layer corners separatedly. Think of it as a separation(up layer corners to up layer, down layer corners to down layer), OLL(up), PLL(up), OLL(down), PLL(down), or any other LL variant. However, the recognition can be awful, and there are two kind of parity cases (orientation parity and permutation parity, when you can't do a pure OLL or PLL on one side without touching the other side).
http://www.speedsolving.com/wiki/index.php/Belt

 

[Dapianokid]

Brilliant, Renslay! Yes, Belt method. How could I have skipped over it? I've brushed up on cube theory and the terms and logic behind commutors and conjugates and such, as BLD requires knowing quite a bit about the cube. This is good stuff! the "Moore Method" (my last name) is still something that isn't happening yet. Hrmm. Try new things!

 

[cubacca1972]

They have to simple enough that they don't cause a recognition pause and become a slower version of 2-look OLL though.

Very true. I was trying to think this through before burning too much energy looking up algorithms. Unless the cases are remarkably easy to identify, this idea may be DOA. Also, all cases would need to be bounded by an acceptably low number of algorithms, all of which would need to be of an acceptable length (maybe 7 moves at most?).

Oh well.

 

[BluShehn]

Is there a method of reduction for the 4x4 where you do edge pairing a little different and instead of solving it like a 3x3 you can solve it like a 2x2? I'd like to see something like this.