# [Help Thread]ZZ and ZB Discussion

#### DNFphobia

##### Member
EFPL Method

First of all, I did NOT create this method or any of the images. I only translated and posted this on the forums.
Second, Do NOT use the images without permission of the creator.

The 3x3x3 EFPL method ( Pronounced as "Apple method") is a ZZ variant method created by Korean speedcuber Do Hyun Kim and is composed of 4 steps and has 46 algs in total (Without counting rotatations, AUF, or skips).

1. EOline: Orient all 12 edges of the cube while solving the DF and DB edges.

2. F2LOS: Finish F2L while orienting at least 1 LL corner.

3. PS: Permute all the edges of the LL along with the oriented corner from step 2.

4. L3C: Solve the remaining 3 corners.

Step 1 and 2 should be easy for those who already know ZZ. There are better tutorials and guides for EOline and ZZF2L out there like http://cube.crider.co.uk/zz.php or Asmallkitten's youtube tutorials.

Step 3 has 23 cases in total without counting mirrored cases and it has an average of 11.39 moves.
Permute the oriented corner and move it to BUL before performing the algs. The black dots represent edges that are already permuted. The lines in the first chart shows how the edges are cycled and the lines on the second chart shows how the edges are swapped. The line in the first chart can be divided into 2 sets, clockwise and anticlockwise. The second chart shows what edge pieces needs to be swapped. The white dot from the first chart are used to tell if the case is clockwise or anticlockwise

Step 4 has 23 cases and has an average of 10.26 moves. For step 4, move the oriented corner to BUL and perform the alg. The chart contains 27 cases in which 1 is a skip and 3 are cube rotations. Step 4 can be divided into 3 sets, all correctly oriented, clockwise, and anticlockwise.
If don't get this, you could go look at the L3C on the speedsolving wiki.

For the cases with the Korean words in it, simply do a y' and the alg above it. For the case on the down left side, do a y' and the alg above it, but make sure to leave out the y.

Pros:
Somewhat low movecount
Algs are very easy to learn
Finger trick friendly algs
No orientation need for the LL edges due to EO
Fast F2L

Cons:
More algs compared to OCLL+PLL or CLL+EPLL
Tricky recognition for step 3 (Can be improved by practice)

Here's the WCA page for the creator of the EFPL method, Do Hyun Kim: http://worldcubeassociation.org/results/p.php?
i=2013KIMD01
If you have any questions or find mistakes, just reply to me.

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#### A Leman

##### Member
This has a higher movercount than Sune-PLL. All of the pros are generic for ZZ, but the F2L would be slower and It would have the same problem L3C has which is the chance of corner twists ruining a percentage of your solves. Step 3 looks very difficult actually. do-able, but difficult.

#### elrog

##### Member
I think orienting the top 4 edges at the same time as doing a pair as is done in the ZB method is very efficient. I was thinking that this should be done with the second to last pair rather than the last. The goal would be to get the pair solved and get all the edges oriented correctly so that no flipping of edges are required to solve the last pair. This would use all the same algorithms. The edge that goes into the last slot may be counted as a good or bad edge depending on making the number of good and bad edges even for the ones your working with, or by looking at how the edge in its place is flipped. If the edge that goes into the last slot is in the slot incorrectly, turn it up to the top layer with a single move and do the case before putting the cross back. I was also thinking that the cases for this may be reduced by how you put the pair before it into its slot just as in avoiding the OLL dot cases.

The number of cases for the second to last slot can be reduced down to 86 from 158 if you always have atleast 2 edges that fit into the top layer oriented correctly. You can use these algs for the 2nd slot to get it into such a position. While doing this, you would need only 86 algorithms rather than the 158, but you would use them for 2 different slots.

As for the last pair, I was thinking that you could orient the corners while placing it and finish with PLL. This would take 28 algs. This is called F2LL.

You could also place all of the edges at the same time as the last pair as is done in the 2nd approach for the Heise method (your pair would always be the F2L slot) and finish with L4C requiring 84 algs. Note that the 24 L3C cases can be done intuitively and you will memorise the cases and their quickest solutions with practice as in F2L, and learning the algs isn't necessary. This would still take more algs than doing the PLL approach, but also a few less moves on average. I'm not sure what the average recognition time is for L4C.

A third approach would be to solve a 1x2x2 block in the top layer and finish with L5P. L5P has 107 algs, but there are only 53 of them with edges already oriented and 24 of them are L3C. Creating such a block with the F2L pair could be done by creating a 1x2x2 block that fits into the top layer and placing it in the F2L slot. You would then continue to match it with its complementary edge while matching and placing the F2L pair. Getting the 1x1x2 block to place in the slot would be easier than getting the last F2L slot matched because you have more options. This would require 36 algs with edges already oriented.

You could use only 15 algs to solve the L5P. This is 15 not including mirrors. The number of algs is so low because the only possible permutations for the last 5 pieces when both edges need switched are the V-perm and J-perm. The V perm can also have many cases solved with a mirror of another alg.

Rather than doing the 36 algs for the last slot on my 3rd option, you could just get the corner and edge that go into the slot in the top layer and match the corner in the slot with its edges while creating and placing the pair leaving you with the F2L and a 1x2x2 block in the top layer. This would require 432 algs, but can be reduced to 144 by crontrolling the orientation of the corner in the slot. This could be reduced even further by excluding mirror cases.

Excluding mirror cases would be possible if you orient the corner in the slot to have the top color on bottom. If the corner in the slot doesn't have the top color on bottom, the mirror cases would be cases with the corner in the slot oriented differently, meaning that you could use 144 algs for 2 different orientations of the corner. It would require only 72 algs not including mirrors with the corner in the slot having the top color on bottom.

The chance for skipping the step of placing a corner in the slot in a usable position is increased from 26 and 2/3% for always putting the top color of a corner on bottom to 53 and 1/3% for having the top color of the corner in the slot not on the bottom. If you learned both the 72 and 144 algs, the last slot would take 216 algs, but you would have a corner in the slot in a usable position 80% of the time.

Getting a corner in the last slot with the top color on bottom while keeping the 2 pieces that go in the slot out can many times be done in 3 or 4 moves, but occasionaly require up to 8 moves. If you didn't worry about keeping the edge that fits in the slot out, you could do the last slot step with 90 algs (rather than 72) not including mirrors. It would ensure you a 3 or 4 move step of getting a corner in the slot with the correct orientation unless you get a very bad case which happens very seldom and uses 7 moves. This very bad case is eliminated if you use the 144 algs for the last slot that don't need the top color on bottom because you can place the corner in the slot 2 different ways.

If you were going to learn the 36 algs for putting a 1x1x2 block in the slot, this would not be reduced by inverses because of the orientation of the corner. If you were to get a top layer corner in the slot with the top color on bottom and have one of its edges by it, this would still require 36 algs because either edge that matches with it can go beside it. You could ignore the orientation of the corner in the slot and use 108 algs with a 40% chance to already have a case set up and usually 3 or 4 moves to get a case set up.

I think much more than 100 algs in 1 step lowers recognition time and reduces the effectiveness of it. I also think a method shouldn't use more than 300 total algs and preferably not even close to that. Because of this, I think the last slot step should be accomplished with these 108 algs, or by using 90 algs after a top layer corner is placed into the slot with the top color on bottom. Using the 108 algs would take a few less moves average to set up the case, but may take a bit more recognition time. This could just be improved with practice though. Using 86 of the ZBF2L algs, with the 15 algs for the last step, and with doing the 108 algs for the last slot, the total alg count would be 209 while it would be 191 if you used the 90 algs instead of the 108 algs. Either of these is a large improvement from the standard ZB method which uses nearly 500 algs for the last step alone.

I have been messing with an alg generater seeing how the algorithms for the last pair would turn out, and I have been compiling a list of the 15 L5P algorithms required for the last step. The last pair algorithms are extremely easy to generate if you use only R and U moves assuming the the pair is in the FR position and the edges are oriented such that they can be solved with only U and R moves. Using the restricted moveset adds a few more moves, but your saving moves by solving the last pair at the same time. The amount of moves from the last pair to solve should be about the same as doing the F2L pair normally, doing OLL, and finishing with PLL. What makes this better is that it is roughly the same amount of moves while including moves to set up the case, but it is much easier to preform quickly because of using only R and U moves. A con for this would be the alg count.

I dislike the ZZ F2L because it sacrifices move count to increase turn speed. My last slot step increases turn speed while not increasing move count. I did get to thining though, that if one were to use ZZ F2L and this last slot substep, the solve could be preformed extremely quickly.

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#### mDiPalma

##### Member
I dislike the ZZ F2L because it sacrifices move count to increase turn speed.
Explain.

#### Pyjam

Elrog, do you know "fish and chips" (search in this forum) ?
I could be wrong, but your idea seems similar.

#### elrog

##### Member
mDiPalma, I can consistantly solve F2L in less than 30 moves, and even sometimes under 20. When I try this with ZZ F2L, I find it hard to get below 30. I was plugging some scrambles into cubesolver having it solve a whole 1x2x3 block on the left side after the EO had been built, and it took between 8 and 16 moves. The right side takes just the same. Its over 20 moves for the blocks, and plus the EO it goes over 30. If you like ZZ F2L, great for you, but I personally suck with it.

Pyjam, I do not know/use synder (I'm a big Heise fan), though I can say that I've looked into it. I've been going through looking at many various methods seeing what they all do. I'm also working on 3 other methods I'd like to try atm. I actually came up with the tripod, HTA, and belt method on my own, then found out it had already been done. I used PBL rather than doing corner circuits in HTA though. I know that realistically, this method has alot of influence from the ZB/ZZ method because of the ZB F2L and the using a reduced move set. I like to think of this method as more of a last slot substep because F2L and ZB F2L have already been made up. One might even go so far to call it a ZB varient.

#### elrog

##### Member
mDiPalma, I can consistantly solve F2L in less than 30 moves, and even sometimes under 20. When I try this with ZZ F2L, I find it hard to get below 30. I was plugging some scrambles into cubesolver having it solve a whole 1x2x3 block on the left side after the EO had been built, and it took between 8 and 16 moves. The right side takes just the same. Its over 20 moves for the blocks, and plus the EO it goes over 30. If you like ZZ F2L, great for you, but I personally suck with it.

Pyjam, I do not know/use synder (I'm a big Heise fan), though I can say that I've looked into it. I've been going through looking at many various methods seeing what they all do. I'm also working on 3 other methods I'd like to try atm. I actually came up with the tripod, HTA, and belt method on my own, then found out it had already been done. I used PBL rather than doing corner circuits in HTA though. I know that realistically, this method has alot of influence from the ZB/ZZ method because of the ZB F2L and the using a reduced move set. I like to think of this method as more of a last slot substep because F2L and ZB F2L have already been made up. One might even go so far to call it a ZB varient.

Sorry, I didn't mean to post twice.

#### aznanimedude

##### Member
....

I think much more than 100 algs in 1 step lowers recognition time and reduces the effectiveness of it. I also think a method shouldn't use more than 300 total algs and preferably not even close to that. Because of this, I think the last slot step should be accomplished with these 108 algs, or by using 90 algs after a top layer corner is placed into the slot with the top color on bottom. Using the 108 algs would take a few less moves average to set up the case, but may take a bit more recognition time. This could just be improved with practice though. Using 86 of the ZBF2L algs, with the 15 algs for the last step, and with doing the 108 algs for the last slot, the total alg count would be 209 while it would be 191 if you used the 90 algs instead of the 108 algs. Either of these is a large improvement from the standard ZB method which uses nearly 500 algs for the last step alone.
so rather than sacrifice movecount to increase turn speed, as you claim is the problem with ZZF2L, you seek to remedy this by learning 90 or 108 algorithms just for last slot?

the idea is ok i suppose, although some of the cases you mention, like F2LL for example, people have shied away from iirc because some of the cases were awkward to execute anyway compared to normal insert -> OLL/PLL and so there was less gain for the OLL skip.

Perhaps i'm just being a stubborn person who doesn't want to accept something different, but i kinda fail to see the improvement here. I'm more than welcome to be proven wrong in this point though

#### elrog

##### Member
Just in my own defense, 108 algs is not Much more than 100 algs. I also think that learning the algs would be time consuming and a pain, but once you have it, you keep your move count while increasing turn speed. Note that there would be no awkard cases with only U and R moves. I understand If you don't see much improvement, but for setting a WR, you need all of the small things to be done right, not just the main concepts. I'm not saying that anyonees going to go around setting WR with this or any of my ideas. The only thing I can tell that OLL and PLL has better than this besides alg count, is easy recognition, however easy recognition doesn't necessarily mean faster.

#### aznanimedude

##### Member

Another has joined the ranks

#### elrog

##### Member
I've been thinking about what the best way to solve the last layer and the last slot in 2 algorithms would be when edges are already oriented. I found that solving corner permutation was just hard to recognise, while placing edges and orienting corners just used to many algorithms. I also considered solving a corner and edge in the top layer, but this too took too many algoritms for the F2L. What I finaly came up with was solving the F2L and orienting atleast 2 adjacent corners in the top layer, then finish with permuting the last layer and orienting the 2 remaining corners.

I came up with 74 cases for the last layer not including mirrors. For F2L cases, I used a variety of ways to recognise cases depending on where the edge and corner were to reduce the ruquired alg number. For instance, I came up with only 4 algorithms for cases with the corner in the slot oriented correctly and the edge in the top. This was accomplished by realizing that the headlights case can solve atleast 2 adjacent corners from and OCLL case, then always AUFing so that the corners are in a position to be solved with that case, and having 4 positions for the edge leaves you with 4 algorithms.

In the end, I had 39 (not including mirrors) algorithms for all cases except ones with both the corner and edge in the top layer. I couldn't find a good way to reduce for cases with the corner and edge both in the top layer, leaving me with 108 algorithms for those cases alone.You have a about a 1/3 chance to have a casewithout the edge or corner in the top layer, and an average of 3 mores to get it that way for when its not, giving you about 2 moves average added to your solve if you choose not to learn the 108 algorithms. If you were to learn the 108 algorithms, you would not need to do anything to reduce cases (besides AUF) before you preform the algorithms making this potentially better than CLS, CPLS, my previous idea, or any other idea for the last slot and top layer that I can think of.

The recognition for this may seem ify, but it wouldn't be that bad. You would just look at your corner and edge that go into the slot, and depending on where they are, look at 2 more corners to know the appropriate algorithm. You could also be finding out the case while doing the previous F2L pair.

I had the idea of solving one step of the last layer (corner orientation, corner permutation, edge permutation, edge orientation) with each F2L slot, but this was impractical because it eliminates extended cross possibilitties, requires vast amounts of algorithms and bad recognition for the first 2 slots, and both corner orientation and edge permutation could not be easily preserved while solving more F2L slots, meaning that they both need to be last.

#### aznanimedude

##### Member
i almost kinda wished you solved the CP detection and solving during F2L conundrum, then ZZ would love you forever

#### elrog

##### Member
Well, I had this idea about solving a 1x2x3 block and corner permutation during inspection to make up for the hard recognition of corner permutation. You would then orient edges using U Uw R RW M and E moves. You can many times avoid E or M moves with double turns. Because you never move the first to corner in relation to eachother, corner premutation would be preserved throughout the solve. The problem with this is not getting to use inspection time to find bad edges, and creating a 2x2x3 block is easier without starting with a 1x2x3.

I had an idea on how to solve corner permutation while solving the last slot that used a different recognition pattern than CPLS, but I'm not sure it would be much better. My idea was that if the corner that goes in the slot is in the top layer, you should put it into the position that the corner in the slot would go. You could then recognise the permutation case by looking at your other 3 corners and seeing which two need switched. To reduce the number of algorithms, you need to put the yellow corner back above the slot it goes in.

Example: The corner in the slot goes in LFU and the slot is the FR slot. You would AUF until the corner that goes in the slot is in LFU. Then if you need to switch RFU and RBU, you would AUF the corner back above the slot and apply an algorithm that puts the corner in the slot and swaps the UBR and UBL corners.

This would take 3x3x5 algorithms. The first 3 is for the orientation of the corner that goes in the slot. The second 3 is for the possible cases that your 3 corners (not the one in the slot or the one that goes in the slot) could be in. The 5 is for where the edge is placed. This bring you to a total of 40 algorithms, but it doesn't include cases that have the corner in the slot. I don't think this would work out well because of all the AUFing.

A better idea would be to solve the corner that goes in the slot and solve corner permutation while placing the edge. To do this you would need only 9 algorithms. My recognition system would be to AUF until you have 2 corners in their place, you may then havea diagnol corner swap, and adjacent corner swap, or no corners needing swapper. After you find which two need swapped, you could place the edge in a particular place and use an algorithm to swap whichever two need swapped. You may also always put the corners that need swapped in a particulay place and use an algorithm for each different place the edg can be. It makes no difference wether you AUF to place the edge or the corners, the number of cases stays the same. The 9 algorithms is including cases with the edge already in the slot.

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#### icecuber

##### Member
Hello,
I am a norwegian speedcuber, I average about 15 seconds but I am improving. Like most ZZ cubers I have read all I could find about 2gll and how to get there. Since I could not find any great complete list(except for Lars' site, but those are not fit for speedsolving), I decided to generagte my own algs. I made a program to pick the best algorithms(is this normal?) and sort them:

http://www.scribd.com/doc/132080393/2gll-speedcubing-algorithms

Some algs were bad, so I used some from the wikis and BOCA too. If you know nice algs for the ones I can't sub2 i would be grateful if you shared them.

Also, i had an idea to place opposite corners opposite while doing the last slot. Kind of like zz-b but with corners. This would result in 50% 2gll, and the rest diagonal swaps. Most diagonal swaps can be done using 2 F turns and RU without exceeding 16 moves. Has anyone thought of this?

#### elrog

##### Member
For your 22nd case, rather than a 12 move algorithm with alot of Bs, I think you should use this one: (U2) R' U2 R2 U' R U' R U' R U' R' U2 R2 U R2

If my thumb is on the top, I use it to bring the right side down. If my thumb is on front, I use my ring finger (which I keep under the cube) to bring the back of the right side up while lifting my thumb so it ends up on the front afterwards. I do both U2s with my right hand (using my pointer and middle finger) and the rest of the Us with my left pointer finger. After doing the first R2, I use my pointer and middle finger alternately to do the Rs by pushing the UDB corner towards the FRD corner.

I notice that Your case 34 algorithm is the inverse of this. I do find this a little harder to do than the other one. You could do the inverse of your 12 move alg for case 22 for this. You could also use U instead of B if you do an x' rotation.

For case 54, heres an alg that is a little longer and has more double moves, but I find it easier to preform. R U R2 U' R2 U R2 U2' R' U2' R' U2' R U2' R2 U2' R'

For your case 57, you could do your same alg, but like this: L' U L2 U L' U L U2 L U2 L U L' U L2. You could also do this from this angle: R' U R2 U R' U R U2 R U2 R U R' U R2.

I used CubeSolver to find these solutions. Your idea about having diagnal swaps also could be good, but you'll have to come up with some good recognition system for it. Other than that, if you could get good algs for it, I think it would be a good substep.

#### aznanimedude

##### Member
so i'm assuming you figured out how to detect edges and are having trouble orienting them?

if read a bit on edge orientation strategy. it usually just boils down to finding 4 edges, moving them to a F/B face, and then doing a F/B turn. Don't focus too much on doing the line at the same time, just work on orienting the edges then placing the line edges after orienting.

for 4 edges it's straight forward, just put them in Front or Back and then just do a F/B turn accordingly.

good way to check if you're done is form the EOLine and try to solve F2L without any cube rotations, only use <R,U,L>.

or if you're really really struggling, make an EOCross but try not to use that as a crutch if at all. In fact i'd recommend you don't even do a EOCross, gives you bad habits that will limit your block building and freedom during F2L.

#### Brest

##### Super Reconstructor
Staff member
Hi guys,
Im just starting to learn ZZ, but.. I cant learn EOLine...
Any tips?
(http://cube.crider.co.uk/, I just don't understand it.)

What I mean is, that I cant really orient the edges. (It looks like a freshly scrambled cube.)
Watch some of a small kitten.