The New Method / Substep / Concept Idea Thread

[NizzyGG]

Not sure if this counts as a method, but ZZ-CT is technically a method, so I guess this counts.

If you don't know what the columns method is, it basically works like this. (Skip down if you don't want to know.)

- 4 Pairs
- Last Layer Corners (CMLL or LBL LL)
- Insert Edges
- Orient Edges
- LL Edge PLL

My variation is quite odd, I'll explain how it goes, then into how to solve using this.

- 4 Pairs
- Last Layer Corners (CMLL)
- Insert Edges & Orient All Edges (Bad/Good edges at the same time.)
- EPLL.

So lets get into it.

- The first two steps, (Pairs + Corners Is quite easy, if you can solve of course.)
- Insert + Orient. (M' U2 M) (U M' U' M) (U' M' U M) Until the last edge.
Here's the algorithmic part of this step.
Using the Roux Good/Bad edge technique, we can ignore the final edge and just focus on making the edges good. (M' U' M) Know you're left with one edge left. Insert it. (M' U2 M) (U M' U' M) (U' M' U M)
- EPLL.
- AUF.

Done.

My PB with the method - 32.24 (I avg sub 25, I suck.)

Leave your suggestions, or I could just be plain stupid and wrote this entire thing and it's just a whole other method.

 

[ShyGuy1265]

Hi guys, I've been tinkering with a 4x4 method lately that I think is more efficient than K4 and comparable to Yau. Substeps are as follows (Haven't got a fancy name or anything, I've just been calling it CFCE):

1. Cross: Centers + cross dedges, identical to Yau
2. F3L. Two substeps:
2a. Using F2L techniques, solve the 1st layer + at least 1 E wing piece for each F3L slot
2b. Using K4 techniques, complete F3L.
3. CLL
4. ELL: Solve last 8 wing pieces, identical to K4

This must be more efficient than K4:
Cross will take slightly less moves than Layer;
During 2a, each "F2L pair" takes moves less than or equal to moves needed to insert a wing during K4 F2L; and
2b, CLL, ELL are same as in K4.

Efficiency is comparable to Yau:
CFCE contains: cross, 3x3 style F2L, half of K4 F3L, K4 LL
Yau contains: cross, 3-2-3, 3x3 style F2L, CFOP LL, 1/2 parities
Since both contain cross and 3x3 style F2L, we only need to compare movecounts of (half k4 F2L + k4 LL) vs (3-2-3 + CFOP LL + 1/2 parities).

CFCE: 4 wing pieces * 8 moves per wing + 9 moves CLL + 3 ELL comms * ~10 moves per comm = 71 moves
Yau: ~33 moves 3-2-3 (from some counting on cubesolv.es) + 10 OLL + 13 PLL + 1/2 * (7 PLL parity + 17 OLL parity) = 68 moves

On paper, F3L lookahead is much easier than 3-2-3 lookahead (in F3L, you're looking for any E wing, just like in F2L, while in 3-2-3 you look for specific wing pieces based on whatever's currently in the E slice). I think this more than compensates for the small increase in movecount, especially if there exist ways to bring down F3L movecount further with special tricks.

This is very similar to what I just proposed. Someone told me that people have been using it for years.

 

[ShyGuy1265]

Not sure if this counts as a method, but ZZ-CT is technically a method, so I guess this counts.

If you don't know what the columns method is, it basically works like this. (Skip down if you don't want to know.)

- 4 Pairs
- Last Layer Corners (CMLL or LBL LL)
- Insert Edges
- Orient Edges
- LL Edge PLL

My variation is quite odd, I'll explain how it goes, then into how to solve using this.

- 4 Pairs
- Last Layer Corners (CMLL)
- Insert Edges & Orient All Edges (Bad/Good edges at the same time.)
- EPLL.

So lets get into it.

- The first two steps, (Pairs + Corners Is quite easy, if you can solve of course.)
- Insert + Orient. (M' U2 M) (U M' U' M) (U' M' U M) Until the last edge.
Here's the algorithmic part of this step.
Using the Roux Good/Bad edge technique, we can ignore the final edge and just focus on making the edges good. (M' U' M) Know you're left with one edge left. Insert it. (M' U2 M) (U M' U' M) (U' M' U M)
- EPLL.
- AUF.

Done.

My PB with the method - 32.24 (I avg sub 25, I suck.)

Leave your suggestions, or I could just be plain stupid and wrote this entire thing and it's just a whole other method.

I don't see the difference between this and PCMS.

 

[NizzyGG]

I don't see the difference between this and PCMS.

I changed it up a tad. It's hard to explain, i'd have to make a video tbh.

 

[Teoidus]

This is very similar to what I just proposed. Someone told me that people have been using it for years.

Really? Can you show me where this happened?

I'm surprised I haven't heard more of it--it seems pretty competitive.

 

[Thermex]

crafto and I are working on a potential way to do edges in WaterRoux that we could use some help on in making algs. Basically the DB and FR edges get solved while orienting the rest of the edges so it's possible to end in L5EP. The DB and FR edges get put in the redge slots with no regards to permutation/orientation. Anyone think they can help us out? Preferably keep the algs using M U and R/r moves. I know that the sets with both DB and FR oriented have 16 algs each and there'd be 8 sets so it's not a horribly large algset (120-130 is my guess)

Going along with many of the ideas posted here, maybe another variation of waterman similar to the one you just mentioned could go like this:

1. Solve every piece on a layer except one corner (12 moves)
2. Put the last corner in while orienting and permuting the u-layer corners (~10 moves, currently working on a 2×2 algset that does this)
3. Orient and pemute 3 edges on the u-layer, leaving only five unsolved edges left (~9 moves? not sure how this step works or how I'd generate algs for it, but there'd probably be around 100 algs and a lot of them already have all 3 edges in the u-layer)
4. Rotate the cube waterman style so that the "m-ring" and the FR edge are unsolved and use a last 5 edges algorithm (~9 moves, I'm pretty sure I saw someone somewhere create a set of algs for this, I would need the link to those)

All in all this method would be like 650 algorithms, but more than half come from the second step. To avoid learning those 350 second-step algs you could just insert the last corner and use a CMLL, which would only add on like 3 or 4 moves. I just need to finish generating the step 2 algs (~4 months?), figure out how to do step 3 and find the pdf that has the last 5 edges algorithms and this could be a seriously viable speedcubing method. If it all works out, the average movecount would 39-40 moves which is completely insane. What do you guys think?

 

[Neuro]

@Thermex What I would do is build an entire face but you can have EG-1, EG-2, or CLL. From there, do a rotation and do modified LMCF E2L to get to L5E and solve as normal. It seems to me that you want to keep this as close to Waterman as possible so I kept the built in rotation but TBH I probably won't use it due to that and the lookahead for face would be bad.

I think that the next step for WaterRoux would be FB, SB corners (can be EG-1), solve all corners, do E2L to get to L6E, CL2E(that's the new algset that I'm working on w/ crafto), L5E, L7E, or to LSE depending on preference. I'd only do this if SB is so bad that it's hard to find BR square. Oh and CL2E has 114 algs so it's not too bad and all can be done w/M,U,R/r and should all be pretty short.

 

[Thermex]

@Neuro the reason I thought of using a last 5 corners case is because when I averaged out the moves it was slightly less than solving a full side and using EG. It basically just cuts off like two moves per solve, but for people who don't feel like learning 350 algs they could easily just use EG and solve a full side instead. Also I thought about that same lookahead problem too, but I figured the solve would flow fairly well, here's my idea of how each step would kinda "flow" and how you would lookahead for it.

1. One-look the first block (just like a Roux solve) and try to see if you can look into the final corner-edge pair that goes in the D-layer.
2. Since you can one-look the first block and maybe even all 8 pieces that go on the D-layer, you can track your last D-layer corner and try to recognize your last 5 corners case as fast as you can. (The 2×2 last 5 corner algs I'm working on don't have great recognition, but I'm sure with LOTS of practice and some lookahead you could recognize the cases fairly quickly).
3. You would expect the hardest recognition to come in this step, but since you execute a corner-based algorithm and the edges don't move around a lot you could track the edges that would go on the U-layer while executing your last 5 corners algorithm. With practice this actually might flow pretty well.
4. I'm sure last 5 edges recognition isn't too bad, idk though I'd have to see the document with the algs and recognition.

Im really interested though in the LMCF E2L algs you mentioned for the three edges on u-layer step (from now on I'll abbreviate it to TEUL). So you're saying there's already algs for these cases? I kinda need some clarification on how E2L works (specifically how it would in this method) and also what the average movecount of an E2L alg would be in this method. WaterRoux still seems like a really good method and still probably close in movecount to this proposed method, but I feel like if the TEUL step works this method would probably be a little faster because TEUL would go faster than SB since it's algorithmic. Aside from that, whats CL2E? You didn't really explain what it was but it sounds interesting.

 

[Neuro]

efattah has posts about LMCF all over the forums, I'm pretty sure he also has a thread dedicated to it so it shouldn't be too hard to find. The algs would probably need to be modified to preserve the face though. CL2E solves FR and DB while orienting all of the edges so you just get either an EPLL or L5EP case. The edges are forced into the redge slots in any orientation/permutation. The main thing that's different in setup from say L6E is that the M slice needs to be solved otherwise DB won't insert correctly. It won't work with pure Waterman though, because it won't preserve UL.

 

[Thermex]

@Neuro oh ok I read that entire thread and closely reread his pdf, and now I understand this stuff a lot better. The E2L triplet stage solves the DF, UL, and UR edges, but I need to solve the UB, UL, and UR edges so I would need to generate my own algs for that. As for the L5E cases I was talking about, turns out about someone asked Efattah if he could generate those algs but he said it wouldnt work well with LMCF and that the recognition wouldnt be very good. I still think I might try to make the TEUL and L5E cases if I have time, but I'm pretty busy rn and don't know how Cube Explorer works. Do you think it's worth it to go on with this method? If not I still want to somehow contribute to some 3×3 method, I've been really interested in this stuff the last couple of weeks.

 

[Sue Doenim]

What if during a ZZ solve, you did F2L with the pieces in the correct sides (eg. R and L) but solved the corners right, did COLL, and used and algorithm to solve the rest. Actually, it might even be better if you did this style of F2L on just R, so the algs could be <R,U> or <R,r,U,M>, depending on preference. You could even mix this with ZZ-KA if you wanted (see post #3003).
Wait a second.
Actual new method time.
We could turn this into a sort of corners first method, but with EO first. So corners first but not actually.
I'm going to think about this and repost about it tomorrow.
Nobody post before then.
I want all the glory.
I should stop writing one sentence and starting a new paragraph.
But it helps establish the fact that I am having sudden epiphanies.
So I won't.

 

[2180161]

What if during a ZZ solve, you did F2L with the pieces in the correct sides (eg. R and L) but solved the corners right, did COLL, and used and algorithm to solve the rest. Actually, it might even be better if you did this style of F2L on just R, so the algs could be <R,U> or <R,r,U,M>, depending on preference. You could even mix this with ZZ-KA if you wanted (see post #3003).

I don't follow. Could you give an example solve?

 

[Sue Doenim]

I don't follow. Could you give an example solve?

I changed my mind about what to make the method, but here's an example solve anyway.
L B' D2 R F2 U' F R U F2 B2 L' F2 R U2 B2 L2 F2 U2 L2
x2
EOLine- R U B' L F R D' B2
Weird F2L- U2 R' L2 U' L' R' U R U' R' U' R U' R U2 R' U2 R U R' U R U R'
COLL- U2F R U' R' U R U2 R' U' R U R' U' F'
Edge permutation- cube explorer couldn't find anything under 19 moves for this (L,U,R) so I won't even bother. Only doing this with right side would probably be better. There would only be 18 algs, I think.

 

[2180161]

I changed my mind about what to make the method, but here's an example solve anyway.
L B' D2 R F2 U' F R U F2 B2 L' F2 R U2 B2 L2 F2 U2 L2
x2
EOLine- R U B' L F R D' B2
Weird F2L- U2 R' L2 U' L' R' U R U' R' U' R U' R U2 R' U2 R U R' U R U R'
COLL- U2F R U' R' U R U2 R' U' R U R' U' F'
Edge permutation- cube explorer couldn't find anything under 19 moves for this (L,U,R) so I won't even bother. Only doing this with right side would probably be better. There would only be 18 algs, I think.

There would be a decent number of algs with the first way. With the second, you would have less algs, but recognition would be trash (probably anyway)

What I like to do is:

Eoline
F2L-1E
COLL
L5E

There are ~160 algs to learn though, iirc. Although, some of them would just be conjugated PLL's.

 

[Sue Doenim]

I thought I was onto something huge with EO corners first, but I wasn't. This is the best I could come up with.
EOCF
1) EO
2) Build D face
3) Solve corners of U whilst permuting corners of D face keeping first face intact, basically EG
4) Permute D face edges and separate remaining edges into E slice or U face, this might be better after a z rotation, D, E, and U become L, M and R
5) Permute remaining edges

Sort of a Waterman variant. My second version would probably be better, and I thought of a new addition to it.
1) EOLine
2) Left block
3) Do the sort-of F2L, but you can ignore corners, just make sure the R face is solved

4) COLL and fix corners, again similar to EG (1)
5) Permute remaining edges- recognition wouldn't be bad, R face would just be solved, 3-cycle, other 3-cycle, opposite swap, adjacent, or other adjacent; U would just be Ua, Ub, H, Z, Opp, Adj, Oa, Ob, W, or solved.
There are 25 new cases, not including EPLL for the edge permutation, all of which are 2-gen.

During my search for an EOCF method, I thought of two things.
1- LMCF with EO- Would it have any effect? I don't know enough about the method to tell.
2- SSC is about as close to mixing EO and CF as you can get without sacrificing speed. My idea was when you have 3 white corners oriented on D, use TSLE to insert edge and then solve corners with one of I think 26 algs.

 

[crafto22]

Wait... Hexagonal Francisco is good?? Well, not quite, but if we change it up a bit it actually is:

1. Solve a 2x3x1 on DB, sorta like a Roux block but rotated to be on the D layer, plus one corner, ideally the DLF corner (10 moves)
2. Solve three E-slice edges. Super fast, awesome lookahead (12 moves)
3. Solve the last corner and edges of F2L (9 moves)
4. LL however you want. I'd just do OLL/PLL which would be ~24 moves.

Now I realize this isn't as efficient as many other methods in development right now, considering the average move count would be only slightly lower than ZZ (although still quite a bit lower than CFOP), but the true advantage of the method is how easy lookahead would be for the second step. If you one-look the first step, which is most certainly achievable, the rest of the solve is just fast recognition and spamming TPS. Additionally, the second step has no rotations and is entirely pseudo 2-gen.
Here's the reconstruction of a 10.91 solve I got:

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

x2 R' L' B F L D' L2 U D L y U2 R2 y // Super crappy FB+c (12/12)
r U r' u r U' M U' R' u2 // 3 E-slice edges (10/22)
U' R U' R' U' R U' R' U R U R' D2 // Last pair + OLL skip (13/35)
U R2 u R' U R' U' R u' R2 F' U F U // PLL (14/49)

Kinda lucky but still shows that this could have potential. I did sorta cheat by forcing that OLL skip and solving the last cross edge on purpose while inserting my third E-slice edge, but these are all things you could do using this method! I wasted like a solid 3 seconds being bad at FB so with practice that definitely could have been better.

 

[Teoidus]

Yeah, HXF is actually pretty decent. It's a joke method but it could certainly be good

 

[Neuro]

Yeah, HXF is actually pretty decent. It's a joke method but it could certainly be good

One thing I just noticed about HF is that it's actually a really nice way to get to L5E or L5EP. If you think about it, you can solve F2L, do CLL, and L5E which is all pretty efficient. Even better probably would be to implement TCLL algs. You could even finish off a solve using HK if you were super dedicated to the method.

Oh and one quick question: Why don't most alg makers include median movecount into their statistics? It seems like it'd be at least as if not more valuble than the average movecount of the algs because it shows us what to expect for that step (at least in the realm of probability). Therefore, we get a more accurate representation as to what to expect from the algset.

 

[Teoidus]

One thing I just noticed about HF is that it's actually a really nice way to get to L5E or L5EP. If you think about it, you can solve F2L, do CLL, and L5E which is all pretty efficient. Even better probably would be to implement TCLL algs. You could even finish off a solve using HK if you were super dedicated to the method.

Yup, it's quite nice. You can also solve CP with a 3x1x1 line to start and build up from there, and that basically lets you do TCLL with much less algs.

Oh and one quick question: Why don't most alg makers include median movecount into their statistics? It seems like it'd be at least as if not more valuble than the average movecount of the algs because it shows us what to expect for that step (at least in the realm of probability). Therefore, we get a more accurate representation as to what to expect from the algset.

Yeah, ideally, you'd want to use the expected value. Basically people use the mean because they make the simplifying assumption that probability for each case is equal (not exactly accurate, but oh well). You can use the median to kinda compensate for this, since it's less sensitive to outliers, but it's still not quite exactly what you want.

 

[Neuro]

Yeah, ideally, you'd want to use the expected value. Basically people use the mean because they make the simplifying assumption that probability for each case is equal (not exactly accurate, but oh well). You can use the median to kinda compensate for this, since it's less sensitive to outliers, but it's still not quite exactly what you want.

That's about what I thought. One thing about the median that I personally don't like is if there's an equal amount of 2 movecounts (i.e. same amount of 7's as 9's) and you get a median movecount that doesn't exist. What would you want to do to fix the problems of median? Look at the pool of highest probability cases and see the median from there so it's more exact?