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Renslay

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lol (dat meme). Almost, but not quite. The idea of this method is that orienting the edges becomes easier with the third available side.

How so? I cannot see that. Also don't forget that in Petrus, recognition of the EO is much easier.

lAnd steps 5 and 6 certainly aren't Petrus.

A CFOP solve with advanced techniques for the last slot / edge control / forcing partial skips / COLL/CLS/MGLS/whatsoever is still a CFOP solve. Same for Petrus.
 

goodatthis

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Method stuff

That is crazy, a few days ago I started writing up a method that is very similar to that, except the block does match and EO is done in a different way. When I do post it, please believe me that I came up with it before you posted this!

5- Insert the last F2L edge/corner pair (the orientation of the corner doesn't matter, allowing faster execution). (Use only <R, U> moves. 25 cases. Avg moves 7.5, rare worst case 12)
6- Perform CLS (24 algs (CLS: I/CLS: I(mirror)/OCLL). This orients the rest of the corners and leaves the edges oriented, skipping OLL)

Step 5 and 6 are basically just EJF2L
 
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Dane man

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Step 5 and 6 are basically just EJF2L
And EJF2L is just a subset of CLS. Doesn't make it worth any less.

If your just doing a 2x2x2 during inspection and your good at inspection, you should have insight as to what the EO case will be.
I was actually thinking of doing the edge orientation and block building at the same time. If you're up to that then go right ahead. Though, the EO-Block recognition difficulty becomes that of ZZ's EO-line.

A CFOP solve with advanced techniques for the last slot / edge control / forcing partial skips / COLL/CLS/MGLS/whatsoever is still a CFOP solve. Same for Petrus.
In that sense maybe, if you switched the steps, but they are intentionally not switched for the purpose I've already mentioned. Even if it could be called Petrus, then it is not "just Petrus".
 
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elrog

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That is crazy, a few days ago I started writing up a method that is very similar to that, except the block does match and EO is done in a different way. When I do post it, please believe me that I came up with it before you posted this!

I came up with it before I posted too ;).

Also, when comparing this method with Roux, I think you should be able to get the F2L done or just have one M edge to place by the time Roux finishes the second block. I think whether this is comparable with Roux in speed depends upon if the NMLL is comparable to CLL + L6E. I just did a solve and generated solutions to the NMLL cases as I went. The first step in NMLL seems great, but the second seems like it would have a high move count. I got an ugly 14 move optimal case. I am still working on making NMLL more efficient.
 

Tao Yu

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Well, I was thinking, and a very interesting method came to mind. It reduces the cube to , and solves the cube from there. Because it begins very similar to Petrus, I'd like to call it Pet rock. Here's the idea.

1- Solve the 2x2x2 block in the BDL corner.
2- Orient the edges relative to . The freedom of having a third side to turn without restriction should make this simpler to perform.
3- Extend from the original the 2x2x2 block to a 2x2x3 on the F side. This is done only using . With practice, this could become very efficient.
4- Extend from the original 2x2x2 block to a 2x2x3 on the R side. This in combination with step 3 should leave an F2L slot and all the edges oriented. (Use only moves)
5- Insert the last F2L edge/corner pair (the orientation of the corner doesn't matter, allowing faster execution). (Use only moves. 25 cases. Avg moves 7.5, rare worst case 12)
6- Perform CLS (24 algs (CLS: I/CLS: I(mirror)/OCLL). This orients the rest of the corners and leaves the edges oriented, skipping OLL)
7- Perform PLL. Done!

Because of the nature of the method, I don't have any way of discovering the avg move count besides actually performing it myself multiple times, so I have no idea how efficient it is yet, but what I do know is that it is very intuitive until steps 6 and 7. The total alg count is 55.

The combination of CLS and PLL has an avg move count of 22.3 (compared to the OLL/PLL avg move count of 21.5). Now the question is what the average moves are for steps 1-5. From what I've tested already, it seems not to be much more than what is already common for Cross+F2L or Petrus->F2L, though I'd like to test more, and see the possible situations.

It really depends on if steps 2-4 require less moves on average than 3 F2L slots. If I were good at block building, I could probably find out. Step 2 should be quick, though steps 3 and 4 will likely take more. Anyone already know or willing to give it a go?

What do you all think?


Moves required in step 5 cases
Code:
1/25 = 0 (done)
2/25 = 3 (connected correctly on top)
2/25 = 4

1/25 = 7 (disconnected left)
3/25 = 8

1/25 = 7 (disconnected right)
3/25 = 8

1/25 = 7 (edge in, corner on top)
3/25 = 8

1/25 = 7 (corner in, edge on top)
3/25 = 8

2/25 = 11 (connected incorrectly on top)
2/25 = 12
I won't comment on the movecount, but I think you need to ask yourself this: Is this faster than MGLS?

Two things to consider:

1. Your method skips ELS by doing EO in step 2. However, your EO step looks much harder than ELS, as you have 4 more edges to orient. The recognition of bad edges is also obviously worse; in ELS it's ridiculously easy. Not sure if the third side make up for that.

It doesn't look like a very fast step. But could there a fast way to do it?

2. The advantage your step 2 has over ELS however, is that it might make the blockbuilding easier. Step 1, 3 and 4 are basically solving F2Lminus1 using blockbuilding. However CFOP is pretty much the fastest known method for F2Lminus1 right now and it's use in MGLS will probably give it the edge. Will the EO in step 2 make steps 3 and 4 fast enough to make up for this difference? And what about the edge that ELS has over step 2?

Personally, I think it all rests on whether you can find a fast way to do step 2.

Not a bad idea though, I was pretty impressed anyway.
 

Dane man

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Personally, I think it all rests on whether you can find a fast way to do step 2.

Not a bad idea though, I was pretty impressed anyway.
Thank you.

When it comes to step two, It has only two extra edges to check when compared to the EO of normal Petrus. Those used to Petrus might find it to be very easy just checking the orientation of 2 more edges.

MGLS is a very fantastic LS method, and is one of the methods I refer to most as an efficient use of F2L slots to manipulate the last layer. I wouldn't be surprised if MGLS were faster than this method, but I still think this method has some potential.
 
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elrog

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I little while after my last post in this thread, I came up with what I believe to be a good NMLL system. Its movecount and recognition seem great, but its alg count is relatively high. I went about my search for a NMLL system by sorting out what could and could not be recognized with just the R and L colors. Turns out, Tripod LL is recognizable with just the R color if you 2x2x1 block contains an L corner and vice-versa.

Rather than placing 1 M layer edge after finishing the 1x2x3 on the right side, place 2.

Now you make a 2x2x1 block in the U layer. This requires 72 algorithms. To recognize this step, first determine the permutation and orientation of the URF corner. If it is an R layer corner, find the edge with the R color on it and not its permutation as well as its orientation. You can AML to have either the UF edge or the UB edge solved depending on the case.

The last step has 105 cases, but many are mirrors or can be turned into other cases easily. How to do recognition was stated in the first paragraph of this post.
 

guysensei1

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The somewhat recent discussion about WV+CP has got me thinking about ways to 'skip' OLL and permute corners. So here are the steps I thought up:
1)solve EO+ cross+3 f2l pairs however you want (no need to make the last pair!)
2)orient LL corners and insert the corner at the same time (WV/CLS stuff)
3)permute LL corners and insert the edge simultaneously
4)EPLL

Perhaps the order of 2 and 3 can be swapped around, or maybe CO+edge and CP+corner is better, not sure which is best in terms of number of algs/recognition/move count.

I also understand that, unless ZZ is used, EO is somewhat troublesome, so maybe you can just use this only when EO is done.
 

goodatthis

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Okay, so I just had an idea for LL that I think is pretty cool. So first off, I'm going to have you guys guess what this is.

What do all the PLLs except H, E and Z have in common?

Confused?
Its a physical type of block that these PLLs have in common.

Still confused:
Think F2L.

Okay, so I highly recommend you guess before opening this, but if you really have no clue, you can.

So what I am suggesting here is a sort of phasing for any kind of method that uses a LL. This can be used with Petrus, CFOP, ZZ, and many other methods.

So what is this mystery thing I'm talking about?

A pair. Just an oriented corner connected to its corresponding oriented edge. A pair is fairly easy and fairly intuitive to make during F2L, and creating one out of LL pieces isn't extremely hard either. Just like how the tripod method has an alg set that consists of 109 (maybe?) cases that all have a solved 2x2x1 in the back, this LL method consists of a 2x2x1 without the edge, which is considerably easier to make during the creation and/or insertion of the last F2L pair. Just like how there is phasing in the ZZ method which reduces the number of ZBLL cases to a much smaller number, there are fewer LL cases that have a solved pair.

Now to shows what exactly I mean by a solved pair, do the anti sune alg on a solved cube. Notice how there is a pair consisting of a correctly matched up oriented corner and edge in the UFL and UL position. This is the kind of pair that we are looking for. Now do the sexy sledge alg on a solved cube, and noticed how there is an unoriented pair in the FU and FUL position. This is not what we want.

Okay, so now for the important question, how many cases are there? This is what I'm proposing, to see if anyone is potentially interested in calculating the number of LL cases with a solved pair. Currently this is just an idea I'm bringing to the table, as an interesting concept I haven't seen before.


Okay, now for another LL proposal, I've seen some talk of one-look two-alg LL systems, and I was thinking, why not recognize OLL and PLL in one step, do the pure OLL that only flips edges and twists corners in their place, then immediately do PLL without having to recognize? Just a little wandering thought I had. I'm sure that all pure OLLs probably aren't very nice algs, but I wonder how much time it could save. And anyone with experience recognizing CP could easily determine the PLL case even when corners are twisted. Just a quick thought, and where would I find algs that are pure OLLs?
 

Dane man

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Okay, now for another LL proposal, I've seen some talk of one-look two-alg LL systems, and I was thinking, why not recognize OLL and PLL in one step, do the pure OLL that only flips edges and twists corners in their place, then immediately do PLL without having to recognize? Just a little wandering thought I had. I'm sure that all pure OLLs probably aren't very nice algs, but I wonder how much time it could save. And anyone with experience recognizing CP could easily determine the PLL case even when corners are twisted. Just a quick thought, and where would I find algs that are pure OLLs?
Unfortunately, this is much more difficult than it looks for one reason. OLL, and PLL are independant properties of a state, which means that it can get very complicated to try and combine them in any way.

For every PLL on OLL, there are 4 directions that the PLL can be rotated relative to the same OLL, meaning that, on an unoriented layer, it is extremely difficult and time consuming to recognize a PLL because there are four different directions for the PLL to be looked at, and will thus take much more time (recog/long-recog/alg/alg as opposed to recog/alg/recog/alg). It's especially difficult if your OLL algs affect permutation, and a lot of the good algs do. Even if you had "pure OLL" algs (which take more moves), the recog would be much less efficient, and take much more time than the standard method.


As for your mention of a solved pair on the last layer. I'm not exactly sure what you are proposing. Are you trying to suggest a 1LLL based on a solved pair? Are you trying to suggest that with preoriented edges and phasing, one could be left with a 1LLL for 3 corners? What exactly do you intend to do with this information?
 
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PJKCuber

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I got this weird idea.
1. Solve 3 cross edges and 2 F2L Pairs belonging to those 3 edges. Essentialy, it leaves 2 slots open.
2.Solve The last 2 slots and then the edge
3.Normal LL.
It sucks
 

Dane man

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I got this weird idea.
1. Solve 3 cross edges and 2 F2L Pairs belonging to those 3 edges. Essentially, it leaves 2 slots open.
2.Solve The last 2 slots and then the edge
3.Normal LL.
It sucks

Step one is just a 2x2x3 block like in Petrus, though the method of block building is a little different than usual.
Step two would be rather difficult, especially because of lack of edge orientation and solving the edge after the slots, instead of solving the edge first, then finishing like F2L.

It is an interesting method to solving F2L, though. Test it out, see how it goes.
 

PJKCuber

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Step one is just a 2x2x3 block like in Petrus, though the method of block building is a little different than usual.
Step two would be rather difficult, especially because of lack of edge orientation and solving the edge after the slots, instead of solving the edge first, then finishing like F2L.

It is an interesting method to solving F2L, though. Test it out, see how it goes.

Tried out a speedsolve 24.14 which is 2 seconds slower, but it was my 1st try.
As for Step 2, you can solve the edge 1st, but that would make this a double x cross F2L.
 

goodatthis

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Unfortunately, this is much more difficult than it looks for one reason. OLL, and PLL are independant properties of a state, which means that it can get very complicated to try and combine them in any way.

For every PLL on OLL, there are 4 directions that the PLL can be rotated relative to the same OLL, meaning that, on an unoriented layer, it is extremely difficult and time consuming to recognize a PLL because there are four different directions for the PLL to be looked at, and will thus take much more time (recog/long-recog/alg/alg as opposed to recog/alg/recog/alg). It's especially difficult if your OLL algs affect permutation, and a lot of the good algs do. Even if you had "pure OLL" algs, the recog would be much less efficient, and take much more time than the standard method.


As for your mention of a solved pair on the last layer. I'm not exactly sure what you are proposing. Are you trying to suggest a 1LLL based on a solved pair? Are you trying to suggest that with preoriented edges and phasing, one could be left with a 1LLL for 3 corners? What exactly do you intend to do with this information?

Well, I think that the fact that they are independent properties make them easier to distinguish.

Also, a good way to break this down is the same way one would recognize LLEF (which is included in your BLL method if I'm not mistaken?) by recognizing EP and EO. And CP is not had to recognize if you know CLL or COLL or OLLCP or CPEOLL or any sort of method that uses CP. Let's take this randomly generated LL scramble:

R2 B U2 B2 U2 F' D B' D L D2 F R' B2 R'

So first of all, I see that CP is correct, by recognizing the top layer corner colors. If I wanted to solve the CLL and be left with ELL, I would just do U2 sune. So the CP recog was very fast. So I now know that I have an EPLL as my PLL, and I can tell by the front 3 pieces that they are correctly permuted in relation to each other, so that is my bar for a U perm. If I just recognize the top and side colors of my edges, I see that the opposite edge is on the right from this angle), which is how I distinguish U perms. Now just twist your corners, and flip your edges, and you'll notice that I was correct, and we have a U perm.

Let's do another scramble: B2 U2 B' U2 B U2 L' R B R' B L B U

So immediately we recognize that the corners have to be diagonally swapped. Then, if we do a U' AUF to line up the pair of pieces in the back, we can easily see that the UB and UR edges need to be swapped, so we have a Y perm. Easy peasy. All this really is is a basic understanding of CP, and EP as well. It's basically OLLCP+EP recognition, and EP is really easy to recognize.

Another scramble: B2 D' F2 D B D' F2 D U' R' U R B
So immediately we see that the two corners in the back need to be swapped, but adjacently swapped corners also mean a 3 cycle of corners, which we can tell by the solved one in the back left. We also notice the solved edge on the left, and a 3 cycle of edges. So this is a G perm.

So overall, if you experiment a little, recognition is not hard. You probably thought that OCLL recognition was going to be hard at first, but then you realized it was actually really easy. It just takes a bit of open mindedness.

And with my idea with the pair in the LL, it's very self explanatory. You create a pair out of LL pieces during the insertion of your last F2L pair, and you are left with a LL subset with much less cases. I don't know where you're getting preoriented edges and a 3 corner LL from, but it's simple. I'll reiterate: Solved pair of LL pieces. Less cases. Think of the tripod method: there's a solved 2x2x1 in the LL, with this it's a solved 1x1x2.
 

Dane man

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So overall, if you experiment a little, recognition is not hard. You probably thought that OCLL recognition was going to be hard at first, but then you realized it was actually really easy. It just takes a bit of open mindedness.
I didn't say that the recognition was impossible, nor that it would take a long time to do. I meant that it takes significantly longer than just a glance at the sides to recognize PLL. What you have suggested is possible, but is exponentially more time consuming and requires much more thought than would be efficient in a speed solve. It works, it's just not efficient.
 
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