# Roux Misoriented Centers Table



## Athefre (Aug 17, 2012)

For years, on the official Roux site, there has been a short list of EO + LR cases that take advantage of misorienting the centers. I have completed a table for all of the cases. While it's always great for FM, of course you wouldn't memorize all of these for speedsolves. Many are easy to recognize and can take off as many as 4+ moves compared to the path you would normally take. Those are the ones you should learn. Not all will purposefully change the center orientation. The goal is to orient the edges and solve UL+UR in as few moves as possible. Sometimes it's possible to solve a case in fewer moves when R, r, or F are added, but for now I kept the table MU based. After performing each one the edges will be left in a three misoriented on U state or, in a few cases, all edges oriented. I have placed letter codes beneath each sequence to show the total move count not including the initial AUF. The G means the guaranteed length and P is for the potential length. This is because UL+UR will be slotted either with the final move or will require a placement on D then U2M2. The top row shows the edge orientation and the left column shows the UL+UR location.

2 Misoriented







a



b



c



d



e



f



g



h



i



1UM'UM
G9 P9M'UM'UM'
G11 P9MUM'UM'
G11 P9UMUM'UM
G11 P9U'MU'M'U'M
G11 P9UMUM
G9 P7UM'
G9 P9UM'UM'
G9 P7UM
G9 P9



2M'U2M'UM'
G11 P9M'UM
G9 P7UM'UMUM'
G11 P11M'UMUM'
G11 P9M'U'MU'M'
G11 P9M'UMU2M'
G11 P9MU'M'
G9 P9U2MUMU2M
G11 P11M'U'M
G9 P9



3MU2M'UM'
G11 P9UM'U2M'UM
G11 P11M'UM'
G9 P7UM'U'M'
G9 P7U'M'UM'
G9 P7M'UM'U2M
G11 P9UM'
G9 P9U2MUM'
G11 P11UM
G9 P9



4UM'UM
G9 P9M'U'M
G9 P7UM'
G7 P5M'UM'UM'
G11 P9UM'
G7 P7U'MU'M
G9 P7U2MUM'
G9 P9U2M
G7 P7U'M
G7 P5



5U'M'U'M
G9 P9M'UM
G9 P7U'M'
G7 P5U'M'
G7 P7M'U'M'U'M'
G11 P9UMUM'
G9 P7U'M'
G7 P5U2M
G7 P7M'U'M
G9 P9



6U'M'UM
G9 P9MU'M'
G9 P7U'M'
G7 P5UM'U'M'UM
G11 P9M'
G5 P5U2M'
G7 P7U'M'
G7 P5U'M'U'M'
G9 P7U2M'UM
G9 P9



7UM'U'M
G9 P9MUM'
G9 P7UM'
G7 P5M'
G5 P5U'M'UM'U'M
G11 P9U2M'
G7 P7MU'M'
G9 P9UM'UM
G9 P7U'M
G7 P5



8UM'
G7 P5MUM'
G9 P7MUM
G9 P7U2MUM'
G9 P9U2MU'M'
G9 P9U2M'UM
G9 P7U'M'U'M
G9 P9UM'UMUM
G11 P11U'M'
G7 P5



9U'M'
G9 P9M'
G7 P7U2M'UM'
G9 P7M'UM'
G9 P9UMUM
G9 P7U2M'U'M
G9 P7M
G5 P5U2M'
G7 P7UM2UM
G7 P7



10UM'
G7 P5U2MUM'
G9 P7U2MUM
G9 P7UM'
G9 P9U'M'
G9 P9UM'
G7 P7U'M'UM
G9 P9UM2UM
G7 P7U'M'
G7 P5



11UM'
G9 P9M'
G7 P7M'UM'
G9 P7U'MU'M
G9 P7M'U'M'
G9 P9U2M'UM
G9 P7U'M'UM
G9 P9U2M'
G7 P7M'U2MUM
G11 P9



12UM
G7 P5U2M'UM
G9 P7U2M'UM'
G9 P7M'UM'
G9 P9M'U'M'
G9 P9UM2UM'
G7 P7U'M
G7 P5UM
G7 P7U'MUM'
G9 P9



13UM'
G9 P9M
G7 P7MUM
G9 P7U2MUM'
G9 P9U2M2U'M
G9 P7U2M
G7 P7MU2M'UM'
G11 P9U2MUM'
G9 P7U'MUM'
G9 P9



14UM
G7 P5M'UM
G9 P7M'UM'
G9 P7U'MU'M'
G9 P7UMUM'
G9 P7UMUM'UM'
G11 P11U'M
G7 P5U2MUM'
G9 P7U'MU'M'
G9 P9



15U'M'
G9 P9M
G7 P7U2MUM
G9 P7U2M2UM
G9 P7U2MU'M'
G9 P9U2M
G7 P7UM2UM'
G7 P7U2MU'M'
G9 P7M'
G5 P5

4 & 6 Misoriented






j



k



l




m



n



o



p



q



r



s



1UM'
G5 P5M'UM'
G7 P7UM'UM'
G7 P7MUM
G7 P7UMUM
G7 P7M2UM'
G7 P7UM'U2M'
G13 P13UM'
G7 P5U'M'
G7 P5U'MU2M'UM'
G13 P13



2M
G7 P7M2UM'
G9 P7MU'M'
G9 P7M2UM
G9 P7M'U'M
G9 P7M'UM'U2M'UM'
G11 P9M2UM'
G7 P7M'
G7 P7M'
G7 P7M'UMUM'UM'
G13 P13



3M'U2M'
G11 P11UM
G7 P5UM'UM
G7 P7UM'
G7 P5U
G7 P7M'
G7 P7UM'
G5 P5M'UM'
G9 P7M'U'M'
G9 P7UM'U2M'UM'
G13 P13



4UM'U'M'U'M'
G11 P9UM'
G7 P7M'
G7 P5M
G5 P3UM
G5 P5M'U2M'
G9 P7U'M'U2M'
G9 P9UM2
G9 P9M2
G9 P9M
G9 P9



5U'M'UM'UM'
G11 P9U'M'
G7 P7UM'
G5 P5M
G5 P3U2M
G7 P5M'U2M'
G9 P7UM'U2M'
G9 P9M2
G9 P9U'M2
G9 P9M
G9 P9



6U'M'U'M'U'M'
G11 P9M'
G5 P3UM'
G5 P5UM
G7 P7M
G7 P5M'U2M'
G9 P7UM'U2M'
G9 P9M2
G5 P3M2
G9 P9M'
G9 P9



7UM'UM'UM'
G11 P9M'
G5 P3U2M'
G7 P5U'M
G7 P7UM
G5 P5M'U2M'
G9 P7U'M'U2M'
G9 P9M2
G9 P9M2
G5 P3M'
G9 P9



8UM'U2M'
G9 P9M
G3 P3UM'UM'
G7 P7MUM
G7 P7UM
G5 P5UM
G9 P9U2M'
G9 P9UM2UM'
G7 P5U'M2U'M'
G7 P5UM
G11 P11



9M'
G9 P9UM2U'M'
G9 P7UM'UM'
G7 P7M
G5 P3U
G7 P7UM'
G11 P11UM'UMUM
G11 P9U2M'
G7 P5UM
G7 P5M
G9 P9



10UM'U2M'
G9 P9UM'U2M
G9 P7UM'U'M'
G7 P7MUM
G9 P9UM
G5 P5UM
G9 P9M'
G9 P9U'M'
G7 P7UM'
G7 P7UM
G11 P11



11M'
G9 P9U'M2UM'
G9 P7U
G3 P1M
G5 P3U
G9 P9U'M'
G11 P11U'M'UMUM
G11 P9U'M
G7 P5U2M'
G7 P5M
G9 P9



12UM'U2M'
G9 P9M'UM'
G9 P9UM'
G5 P5UMU2M'
G9 P7UMU'M
G7 P7UM'
G9 P9M'
G9 P9UM2
G7 P5U'M2
G7 P5UM'
G11 P11



13M
G9 P9M'
G5 P3U
G9 P9U'M2UM
G9 P7U
G3 P1U'M'
G11 P11U'MUM'UM'
G11 P9M'
G7 P5U'M'
G7 P5M'
G9 P9



14UM'U2M'
G9 P9M'UM'
G7 P7UM'
G5 P5M'
G3 P3UMUM
G7 P7UM'
G9 P9U2M'
G9 P9UM'
G7 P7U'M'
G7 P7UM'
G11 P11



15M
G9 P9M'
G5 P3U
G7 P7UM2U'M
G9 P7UMUM
G7 P7UM'
G11 P11UMUM'UM'
G11 P9UM'
G7 P5M'
G7 P5M'
G9 P9


I found these by hand and spent a lot of time on each, but I think some can still be improved. I plan to run all of these through a solver and may add it to the wiki sometime soon. If you find a mistake or something better for a case, post to let me know.


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## Cool Frog (Aug 17, 2012)

I was actually working on this for a while (But you published it first!)

Will look over this in more detail/ trade and shtuff.


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## A Leman (Aug 17, 2012)

Great Work! You found 285 cases by hand. I am going to look through this although I always finish F2B with the centers correct or opposite (helps my recognition).


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## PandaCuber (Aug 17, 2012)

What, yesssssssssss.


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## waffle=ijm (Aug 18, 2012)

thanks athefre. I look forward to taking these in.


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## PandaCuber (Aug 18, 2012)

Example solve please. I dont understand.


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## pijok (Aug 18, 2012)

PandaCuber said:


> Example solve please. I dont understand.



Scramble: M' U M2 U2 M2 U M2 U M U' M U M2 U2 M U2 M U2 M2 U2 M' U' M U' M'
2 Misoriented:
AUF: U2
Alg from table: UM2UM'
Now all edges are oriented, continue with 4b

Scramble: U' M2 U2 M U' M U2 M U M' U' M' U M2 U2 M' U M U' M U2 M' U' M' U2
4 Misoriented:
AUF: U
Alg from table: M'
Now 3 edges on top are misoriented, continue with:
U M' U M'
4c


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## PandaCuber (Aug 18, 2012)

Im not seeing the solution...


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## Athefre (Aug 18, 2012)

pijok said:


> Scramble: M' U M2 U2 M2 U M2 U M U' M U M2 U2 M U2 M U2 M2 U2 M' U' M U' M'
> 2 Misoriented:
> AUF: U2
> Alg from table: UM2UM'
> Now all edges are oriented, continue with 4b



Close, but notice the orientation relative to the corners. The solution would instead be:

AUF: U
Alg: UM2UM' (notice this puts the LR edges in a better position than your solution)
Finish: UM'U2M UM2U2M



pijok said:


> Scramble: U' M2 U2 M U' M U2 M U M' U' M' U M2 U2 M' U M U' M U2 M' U' M' U2
> 4 Misoriented:
> AUF: U
> Alg from table: M'
> ...



AUF: U2
Alg: U'M'
Finish: UM'UM' UMU2M2U2


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## Renslay (Aug 18, 2012)

Aaaaaw... Now I see it!


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## 5BLD (Aug 18, 2012)

better alg for one of the cases RUr'MUM'U'rU'R' and inverse
i know more will post later maybe

thumbs up for putting the effort into that


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## Athefre (Aug 18, 2012)

Thanks. I added it to the table but it didn't look right. When I edit this into the wiki, I should be able to make this easier to understand and include both RrMU and MU. Also, the inverse has a 7 move MU solution.


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## 5BLD (Aug 19, 2012)

Yeah you're right about the inverse whoops
Also RU'r'U'M'UrUR' and inverse
R'FRU:M2 is same as optimal
Theres obviously M':B'RB or the A9 for the ELL etc


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## pijok (Aug 19, 2012)

Athefre said:


> Close, but notice the orientation relative to the corners. [..]


Wow, didn't noticed there are multiple AUF's including corner orientation


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## Athefre (Aug 19, 2012)

5BLD said:


> Yeah you're right about the inverse whoops
> Also RU'r'U'M'UrUR' and inverse
> R'FRU:M2 is same as optimal
> Theres obviously M':B'RB or the A9 for the ELL etc



These are showing their potential for fewest moves. Though R'FRU:M2 can be (U2)MUM'U2M'U2M' and M':B'RB is MU'M'UMUM'.

One thing I should note is that this is LR neutral. If you really cared about the individuality of the LR edges relative to the corners, there would be another set of cases sometimes slightly different. So far I'm unsure if it matters because any Roux user experienced enough to understand this would probably know to invert a U move.


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## Renslay (Jul 5, 2013)

Are you sure g1 is correct?


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## pijok (Jul 5, 2013)

Renslay said:


> Are you sure g1 is correct?



Set up: U M' U2 M2 U M' U M' U2 M U M U M U'

From the table:
U M' Three missoriented on top
U2 M U M orient
U' M' U2 M' Finish 4b


I would do:
U M U M'
U' M U' M'
U M2


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## Renslay (Jul 5, 2013)

pijok said:


> Set up: U M' U2 M2 U M' U M' U2 M U M U M U'
> 
> From the table:
> U M' Three missoriented on top
> ...



Exactly. I think some of the recommended solutions are long/wrong/weird/etc. I would check them all, but I'm not good in searching alternatives.


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## Athefre (Jul 6, 2013)

No. As I mentioned a couple times, many don't solve the orientation and instead just solve up to the three misoriented on U case. This is a good thing because it allows you to learn only what is necessary to get to the point where you make your decision for where to place the LR edges. Instead of finishing 4a+4b with M'UM', sometimes you want to do MU2M2(UM') or something similar.

When I find the time, I'll finish the other half of this so I'll no longer have to explain that this is LR neutral.


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## andrjob (Nov 28, 2013)

Great work! Today I try to use it when I was solving cube - fewes moves (with Roux). At the end I redused lse algorithm by 4 moves.

But I dont understand what explain G and P? (under algorithm). For example: G8 P7


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## TheNextFeliks (Dec 8, 2013)

I don't understand this. I do the alg but then what? It is confusing me a lot.


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## Athefre (Dec 8, 2013)

andrjob said:


> But I dont understand what explain G and P? (under algorithm). For example: G8 P7



G stands for Guaranteed. Meaning the alg will always solve the case in at least that number of moves. P is Potential, meaning if the UL and UR edges are in the right place the case will be solved in that smaller number of moves. You can actually ignore this G and P stuff. It's only there so I can keep track of how many moves in which my current alg solves the case.



TheNextFeliks said:


> I understand this. I do the alg but then what? It is confusing me a lot.



In the topic post I mention that it doesn't always simply solve the case. It often leaves you with a three misoriented on U state so you can finish UL and UR how you want.

If you have examples of what you are having an issue with, I would love to help.

Early next year I'll get started on simplifying this.


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## TheNextFeliks (Dec 8, 2013)

Athefre said:


> G stands for Guaranteed. Meaning the alg will always solve the case in at least that number of moves. P is Potential, meaning if the UL and UR edges are in the right place the case will be solved in that smaller number of moves. You can actually ignore this G and P stuff. It's only there so I can keep track of how many moves in which my current alg solves the case.
> 
> 
> 
> ...



Ok. I'll post an example tomorrow.


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## Renslay (Dec 8, 2013)

I don't understand a few things. For example, how is it possible that F3 and G3 differ so much? If I have an F3, and I do a U', I'll get G3, won't I?


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## pijok (Dec 8, 2013)

Renslay said:


> I don't understand a few things. For example, how is it possible that F3 and G3 differ so much? If I have an F3, and I do a U', I'll get G3, won't I?


Notice the relative position of the corners. (There are 4 possible positions of the corners but athefre reduced it to opposite neutral)

Here are all possible configurations. You can see what G/P means and how F3 and G3 differ:

1) Correct corners:
Setup for F3[G11]: U' M2 U M2 U M' U M' U2 M U M U M U2 M
Solution:* M' U M' U2 M* U' M' U' M' * U2 M2 (11)

2) U2 offset:
Setup for F3[P9]: U' M2 U' M2 U M' U M' U2 M U M U M U2 M
Solution: *M' U M' U2 M* U' M' U' M * (9)

3) U' offset
Setup for G3[P9]: M' U M' U2 M U M U M U2 M
Solution: *M' * U2 M' U M' * U M' U2 M (9)

4) U offset
Setup for G3[P9]: U' M2 U2 M2 U M' U M' U2 M U M U M U2 M
Solution: *M' * U2 M' U M' * U M U2 M (9)

* means that all edges are oriented
(Notice that in this examples UR always is on DF. However you don't have to care about that, because this system is opposite color neutral. If you have 3) with UL on DF just solve it like 4))

For G3 both possible corner configurations lead to a 9 move solution. Thats why G=P.
Since the EO for F3 and G3 is the same, you can also use G3 to solve the F3 case. But then you all the time need 2 extra moves to insert UL UR => F3 would have G=P=11.

If you understand how EO with misoriented centers is working, it shouldn't be a big problem to understand the table.

Well that was my way to look at this stuff. Hopefully it helps


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## Renslay (Dec 8, 2013)

pijok said:


> Notice the relative position of the corners. (There are 4 possible positions of the corners but athefre reduced it to opposite neutral)
> 
> Here are all possible configurations. You can see what G/P means and how F3 and G3 differ:
> 
> ...



Aaaaaw! Okay, now I understand it. So, technically, the corners have to be aligned to the blocks exactly or rotated by only a U2.



One more question: I assume it would be a hell of a work to learn all the cases. Which cases should I learn? For example, all the k,l,m,n?


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## Athefre (Dec 8, 2013)

Renslay said:


> One more question: I assume it would be a hell of a work to learn all the cases. Which cases should I learn? For example, all the k,l,m,n?



Only learn the ones that are easy to recognize. I made a quick list of some that are useful. Others not listed can be learned later as you get better at tracking LSE during CMLL.

a8, a10, a12, a14
c4-7
d5, d7
e4, e6
f6, f7, f10, f12, f13, f15
g5, g6, g9, g12, g14, g15
h4, h5, h9, h10, h11, h12
i4, i7, i8, i9, i10, i15
j1, j2
Be familiar with all of k, l, m, and n.
o1, o3
p2, p3, p8-p15
q1-7
r2, r4, r7

All of the s cases are useful, especially the ones that are easy to recognize and orient all six edges in just five moves. Those are s4-15.


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## Renslay (Dec 29, 2013)

Is N10 okay?

Here is a scramble:
U' M U2 M' U M U' M U

This is N10, which says: U M but I fail to see how it works.

However, if I do a U2, I get L8: U M' U M', which is indeed seems a good solution (continue with U' M U2 M' U).

So, shouldn't N10 be U' M' U M' ? Or do I misunderstood something again?

EDIT:
:facepalm: never mind. This is NOT N10... Mis-looked the orientation of DF.


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## Athefre (Mar 20, 2021)

*New Document*

I have transferred the table in this topic to a Google Sheets document. This topic is the first time that EOLR was developed. Back then I called it "Roux Misoriented Centers Table", which wasn't the perfect name. Misoriented centers was only in the name because it often take advantage of misoriented centers to find the best orientation. It sets up to an arrow to where the user either places the UL+UR edges on the D layer or directly solves the UL+UR edges. The algorithms in the tables could likely be better because I found them all without the use of a computer. Plus, there are a few more documents that have been developed by the community since then and given the name EOLR. Those surely have better algorithms. I just wanted to preserve this for historical reasons.

The images in the original post no longer work. Possibly because the forum now has a 20 image limit for individual posts. I would have edited the original post to avoid a multi-year bump, but wanted to preserve the post as it is and not have a "Last edited" note past the year that it was developed. Also to avoid it looking as if I added anything to the development.


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## abunickabhi (Apr 16, 2021)

Athefre said:


> *New Document*
> 
> I have transferred the table in this topic to a Google Sheets document. This topic is the first time that EOLR was developed. Back then I called it "Roux Misoriented Centers Table", which wasn't the perfect name. Misoriented centers was only in the name because it often take advantage of misoriented centers to find the best orientation. It sets up to an arrow to where the user either places the UL+UR edges on the D layer or directly solves the UL+UR edges. The algorithms in the tables could likely be better because I found them all without the use of a computer. Plus, there are a few more documents that have been developed by the community since then and given the name EOLR. Those surely have better algorithms. I just wanted to preserve this for historical reasons.
> 
> The images in the original post no longer work. Possibly because the forum now has a 20 image limit for individual posts. I would have edited the original post to avoid a multi-year bump, but wanted to preserve the post as it is and not have a "Last edited" note past the year that it was developed. Also to avoid it looking as if I added anything to the development.


Wow this project has been created 9 years back. The new document that you shared is not publicly shared, request access are to be pressed for every user.

The images in the original post of this thread do not load. EOLR is much easier to say, compared to the name Roux Misoriented Centers Table. Have you updated the algs as well?


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## Athefre (Apr 16, 2021)

abunickabhi said:


> Wow this project has been created 9 years back. The new document that you shared is not publicly shared, request access are to be pressed for every user.
> 
> The images in the original post of this thread do not load. EOLR is much easier to say, compared to the name Roux Misoriented Centers Table. Have you updated the algs as well?



Interesting. I just updated the permissions so everyone should be able to view now. I only transferred the table. The algs weren't updated. If someone wants to learn a lot of EOLR, there are more optimized resources now. I kept everything the way it originally was only for historical purposes. To preserve the first developed EOLR. Even if it didn't have that name back then.


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