# Efficiency of 5x5 edges methods



## mark49152 (Nov 23, 2015)

At UK Championships there were some discussions about 5x5 edges methods, and we agreed it would be interesting to study the relative move efficiency of different approaches. So, that’s the purpose of this thread. I’d like to see how you solve 5x5 edges and in particular, how efficient your method is. I’m also looking forward to learning a few things .

*Instructions: * Please use the scrambles in this post so that we can compare solutions. Scramble with your cross colour facing down. Then solve edges, and post your solution and your move count.

*Finished state is defined as follows:- *

All tredges formed, except you may leave 1-2 ready to be fixed by a parity or L2E alg (I’m not interested in counting moves in parity algs). 
Cross must be formed on bottom ready for F2L; other tredges can be in any permutation. 
Any centers that you usually fix mid-way through edges can be left broken (I’m not interested in counting moves to fix centers).

Scrambles are from qqtimer.net (5x5x5 edges under bigcube subsets, but with lower-case replaced with 'w' format to avoid any ambiguity about whether qqtimer.net intends these to be wide or slice moves).

1. Rw R Bw B Uw Dw2 R D2 R' Uw' L D L' Dw' F U F' Dw2 L D L' Uw L D L' Dw2 L' U' L Uw2 Dw2 F D F' Uw2 R U' R' Uw' Dw U D2 B' Bw' R' U2 Rw U2 Rw U2 Rw U2 Rw

2. Rw R Bw B Uw Dw F' U' F Uw' B D' B' Uw' Dw2 F' U F Uw R D2 R' Uw F' U2 F Dw' R D2 R' Uw2 Dw B' U2 B Dw F U2 F' Uw U2 D B' Bw' R' Rw'

3. Rw R Bw B Uw2 Dw2 L' D2 L Dw L D L' Dw' L U' L' Uw Dw2 F' D2 F Dw2 B U' B' Uw2 Dw B U2 B' Uw2 Dw' R U' R' Uw Dw B D B' Dw U D2 B' Bw' R' U2 Rw U2 Rw U2 Rw U2 Rw

4. Rw R Bw B Uw' Dw2 B' U2 B Uw' L' U L Uw2 Dw' F U F' Uw2 Dw' R' D R Uw Dw2 B U' B' Uw Dw F D F' Dw2 L' U' L Dw2 L D2 L' Dw U2 B' Bw' R' Rw' 

5. Rw R Bw B Uw Dw2 B D B' Dw' B' D B Dw' L U' L' Dw B U B' Uw' Dw' F U F' Uw' B' U2 B Uw2 Dw2 F' D F Uw2 Dw' B D2 B' Uw Dw' U D' B' Bw' R' Rw'


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## mark49152 (Nov 23, 2015)

My solution to scramble #1. Method: Hoya & AvG.

L F’ L’ B D L’ // midge cross = 6
U’ D Lw’ U Lw // DL half = 11
U2 Rw U’ Rw’ // DL = 15
U’ D’ Lw’ U Lw // DF half = 20
Rw U Rw’ // DF = 23
D’ Rw U Rw’ // DR half = 27
D’ B’ Lw’ U2 Lw U B // DB = 34
D Lw’ U Lw // DR = 38
F’ R’ // fill BR = 40
Lw’ U’ Lw // FR half = 43
L U’ L’ U Rw U’ Rw’ // FR = 50
F L // fill BL = 52
(would usually fix last 2 centers here)
F U F’ Uw // BR half = 56
L’ U2 L Uw’ // BL half = 60
F U F’ Uw // UF half = 64
F U F’ Uw’ // UL half = 68
U’ L’ U L Uw // UR half = 73
L’ U’ L F’ L F L’ Uw’ // FL half = 81
R U2 R’ Uw // UR = 85
L’ U’ L Uw’ // FL = 89
F’ // fill DF = 90
F U2 F’ Uw // UF = 94
F U F’ Uw2 // UB half = 98
R U R’ F R’ F’ R Uw // UB = 106
U2 R F L' D // fix cross and setup for L2E = 111
(now fix L2E)


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## yoinneroid (Nov 23, 2015)

this will probably be way more efficient per tredge formed than what I usually do in solves.
scramble 1
y' 3Uw' F' U F 3Uw Uw' R' D' R // 5
U R' U' R Uw y2 // 10
D F D' F' Uw' F' U' F Uw // 19
D' R' D R Uw' R U R' Uw // 28
R U R' U F' U' F Uw' F D F' Uw //40
R U' R' Uw L' U L Uw2 R U' R' Uw // 52
y' R' U2 R Uw R U R' U' F' U F Uw' y2 // 64
R U2 R' Uw' F' U' F Uw // 72
F D F' Uw L D L' Uw2 R U R' U' F' U F Uw // 88
L2 U' R2 F // 92 cross
flipped edge BL left


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## guysensei1 (Nov 23, 2015)

What if I use Yau5? There will be 2 F2L pairs solved after reduction...

EDIT: I was thinking perhaps take the move count I get after reduction, and subtract the moves I used to solve the 2 pairs?
EDIT2: Aah this isn't suitable for Yau5 at all, I can't do cross+centers my way as centers are already done.


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## Christopher Mowla (Nov 23, 2015)

Do you want us to interpret these scrambles as being in old WCA notation or in SiGN?


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## mark49152 (Nov 23, 2015)

yoinneroid said:


> this will probably be way more efficient per tredge formed than what I usually do in solves.


That's OK as long as the solution is what you might reasonably do in a speed solve if you "mastered" your method.



guysensei1 said:


> What if I use Yau5? There will be 2 F2L pairs solved after reduction...


Write down the full solution since it will affect other edges. For comparison of move counts, I suggest counting 6 moves total for those slots, as that's what it would cost to insert arbitrary solved tredges to knock out the unsolved ones. Is that fair?



guysensei1 said:


> Aah this isn't suitable for Yau5 at all, I can't do cross+centers my way as centers are already done.


Any centers that you usually fix mid-way through edges can be left broken (I’m not interested in counting moves to fix centers).



Christopher Mowla said:


> Do you want us to interpret these scrambles as being in old WCA notation or in SiGN?


Yes I noticed that when yoinneroid's solution did nothing but scramble my cube further . I've fixed the OP to explicitly show wide moves. (Interestingly, the qqtimer.net scrambles preserve centers using either interpretation.)


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## guysensei1 (Nov 23, 2015)

mark49152 said:


> Any centers that you usually fix mid-way through edges can be left broken (I’m not interested in counting moves to fix centers).


I get this, but the deal here is that the 4 cross tredges in Yau are solved before the last 4 centers, thus attempting to do Yau on a centers-solved 5x5 doesn't work well...


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## mark49152 (Nov 23, 2015)

guysensei1 said:


> I get this, but the deal here is that the 4 cross tredges in Yau are solved before the last 4 centers, thus attempting to do Yau on a centers-solved 5x5 doesn't work well...


You can break those centres. Solve the four cross dedges, breaking the centres, then skip fixing those centres and move on to solving the rest of the edges. (My Hoya solution messes up the F and U centres.)


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## ~Adam~ (Nov 23, 2015)

I've favourited this thread and will get round to it in the near future.


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## guysensei1 (Nov 23, 2015)

mark49152 said:


> You can break those centres. Solve the four cross dedges, breaking the centres, then skip fixing those centres and move on to solving the rest of the edges. (My Hoya solution messes up the F and U centres.)


Oh I see. I thought you were referring to 'break' as the simple misaligning of the center layers.
I'll do this ASAP.


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## Goosly (Nov 23, 2015)

Sorry, writing down my whole solution would take too much time. Just movecount + whether or not I left the L2E unsolved.

I setup to (Uw' R U R' Uw) to solve 2 half-edges or a whole edge if possible, until I get the 2-swap case for L2E (unless they're solved already). So that's reduction I guess.

1. 93 (L2E unsolved)
2. 100 (all edges solved)
3. 107 (L2E unsolved)
4. 107 (all edges solved)
5. 107 (all edges solved)


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## Christopher Mowla (Nov 23, 2015)

I am guessing that this is for speedsolving purposes, but I just wanted an excuse to practice my edge pairing method on the first scramble. (If I would have used a computer search to aid me, I of course would have gotten fewer moves. Also keep in mind that this took about 45 minutes to solve!)

74 OBTM, 62s (With all centers completed, one tredge incomplete, and four cross-edges solved in D layer).

EDIT: I just tried the 5th scramble, and it's harder for me, at least:

83 OBTM, 69s (With all centers completed, two tredges incomplete, and four cross-edges solved in U layer).


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## ~Adam~ (Nov 24, 2015)

Oh wow. So Hoya, middle 4 edges free slice, placed 2 solved in back then made 2 more and left last 2.

1. 91
2. 80
3. 80
4. 73 (no flipping algs required)
5. 82

I'll post an example solve when I have time.


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## Hssandwich (Nov 24, 2015)

With Hoya cross edges:
z2 y D2 Rw R' U' Rw' R U Rw U' Rw' //WO
R' D' F U F' Lw F' Lw' R' B Rw U2 Rw' //BW
D' U2 F2 Rw' Lw F Lw' Rw2 U2 Rw' U Rw U' Rw' //RW
R D' Rw' R F Rw R2 Rw' Lw F Rw Lw' R D' //GW
F L F' Rw' F' Rw2 U2 Rw' U Lw' U2 Lw U' Rw' Lw F2 Rw Lw' U Lw' U2 Lw L' F' //L2C
F' U2 F Uw' E R U R' F R' F' R Uw E' //RY
L' U L Uw2 L' U' L F' L F L' Uw2 //OG
U' R U R' y Uw' U F' U' F Uw //RB
Dw U R U' R' Dw' //RG
R' U R2 U' R' Uw F U F' Uw' //YO
F U2 F' E R U R' E' //YB&GY
z' Rw2 B2 U2 Lw U2 Rw' U2 Rw U2 F2 Rw F2 Lw' B2 Rw2 U2 z //Parity

https://alg.cubing.net/?puzzle=5x5x...w-_Dw_U_D2_B-_Bw-_R-_U2_Rw_U2_Rw_U2_Rw_U2_Rw


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## Dene (Nov 25, 2015)

I don't understand why cross has to be finished if you're looking for the most efficient edges method. I do straight redux, so that would be an extra step after doing edges.


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## ~Adam~ (Nov 25, 2015)

Because Yau and Hoya build these edges in place.

It wouldn't be a fair comparison if you don't get to the same point in the solve.


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## Meep (Nov 25, 2015)

1) 66 
2) 59
3) 67
4) 65
5) 69

Notes: http://pastebin.com/mN4ixgYR
I solved the last 2 edges before doing the cross, then subtracted the length of the L2E alg from the total move count. E moves were counted as 2 moves, and flipUF/flipFR is 7. The +x at the end is how many moves it took me for the cross - I didn't bother writing the moves down.


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## yoinneroid (Nov 25, 2015)

mark49152 said:


> Yes I noticed that when yoinneroid's solution did nothing but scramble my cube further . I've fixed the OP to explicitly show wide moves. (Interestingly, the qqtimer.net scrambles preserve centers using either interpretation.)



Sorry, fixed my solution, it should have been Uw at the third line (instead of Uw')


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## ryanj92 (Nov 25, 2015)

solution 1
solution 2
solution 3
solution 4
solution 5

i tried to stick to yau5 as much as possible - i included inserting the 2 F4L pairs, and i inserted the last cross edge like i would during a solve.

the steps in each solve are:
- 3 cross edges
- final cross edge
- 4 edges
- 2 F4L pairs
- 2 edges, setup to L2E

(i just realised i inserted the second f2l pair wrong on the first solve... )


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## ch_ts (Nov 25, 2015)

done by matching wing edges then center edges, then cross
1. 82 BTM
2. 79 BTM


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## Dene (Nov 25, 2015)

cube-o-holic said:


> Because Yau and Hoya build these edges in place.
> 
> It wouldn't be a fair comparison if you don't get to the same point in the solve.



That doesn't make sense as a fair comparison. Doing cross as part of edges is a restriction/benefit that is inherent in that method which isn't relevant to others. Furthermore, the OP specifically mentions not worrying about finishing the centres for certain methods, but having solved centres restricts what you can do with edges too. 

Ultimately in means the whole point of this thread is silly. You can't look at the "efficiency" of edge solving in isolation from the method. Maybe edge movecount is lower, but centre solving is significantly impaired. Maybe edge movecount is much higher, but the cross+F2L is completed at the end. Efficiency could only truly be looked at when comparing whole solves and looking at a range of factors.


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## ~Adam~ (Nov 25, 2015)

Dene said:


> Efficiency could only truly be looked at when comparing whole solves and looking at a range of factors.



By getting to the point where there is parity and a cross solved with 2 scrambled centres you are comparing everything which matters between Hoya and Redux (I don't know Yau well enough) barring 4 moves to setup to solving last 2 centres for Hoya.

The 1st 4 centres are solved the same in both methods so we are ignoring that part.

The last 2 centres adds 4 moves for Hoya so you can feel free to add those to the totals.

Since Hoya has the cross solved it only makes sense to get to that point with Redux solves, unless of course people are intentionally building X-crosses during Redux solves.


I don't see any problems with these comparisons.

Mark is mainly looking at whether the difference in move count for the different part of the solve is made up for in the better look ahead with Hoya (from our conversation at UKC).


Am I missing something?


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## Dene (Nov 26, 2015)

cube-o-holic said:


> By getting to the point where there is parity and a cross solved with 2 scrambled centres you are comparing everything which matters between Hoya and Redux (I don't know Yau well enough) barring 4 moves to setup to solving last 2 centres for Hoya.
> 
> The 1st 4 centres are solved the same in both methods so we are ignoring that part.
> 
> ...



Lookahead of centres matters, and could potentially be affected by whether you do all centres first, or whether you mix centres and edges. Also, lookahead into F2L could play a role: is time lost or gained (or neither) transitioning straight from last edges to CE pairs, as opposed to finishing centres then doing 3x3 as a whole? And potentially many other factors...

Personally I'm not really a fan of trying to compare methods that take different approaches in such simplistic terms as movecount.


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## mark49152 (Nov 26, 2015)

Thanks everyone for the solutions so far. I have a busy week but hope to find some time this weekend to go through them and do some initial comparison.

@Dene: Point taken, but please don't assume the results will be distilled down to a simple move count "score" with no other factors considered. I hope to learn something from the comparison and hope that it will be useful and interesting to other cubers too. I'm more interested in the solutions than purely move counts, and hope to see some more solutions posted. By going through different solutions I do believe it will be possible to make some quantitivative statements about the different approaches, but of course those would need to be set in the context not just of the overall methods, but the personal techniques/variations of different cubers, and the small sample set size. For example, both Adam and I would go in the simplistic "Hoya" bucket, but Adam solves four edges Hoya and the rest freeslice whereas I solve five edges Hoya and the rest AvG. So even Hoya solvers aren't directly comparable by total move count. By going through solutions I'd like to at least break it down to shorter phases and look at the efficiency of those individually.


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## Hssandwich (Nov 26, 2015)

You only need 2 moves to setup for L2C, L F, and then you can use Rw, F U and Lw to do the rest, or are you counting both the setup and the undo?


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## ~Adam~ (Nov 26, 2015)

Hssandwich said:


> You only need 2 moves to setup for L2C, L F, and then you can use Rw, F U and Lw to do the rest, or are you counting both the setup and the undo?



Yes. 4 total.


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