# Edge parity on 4x4 BLD



## Nghia (Apr 3, 2008)

Hello,

I'm currently practicing 4x4 BLD and have this little question.
I'm in this case where there is an edge parity bUL <-> fUR and every other edges on the U layer are solved. 
My idea is to cycle bUL -> bUR -> fUR so that there will only be a pair of disoriented edges to fix with a regular parity fix algorithm.

The first question will be : is that, well, the "optimal" solution ?

And second question : can we solve any edge parity with that method ? I believe yes, since most of the cases I've encountered are solvable, but, who knows ?

Thank you guys ,

Nghia


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## Lucas Garron (Apr 3, 2008)

Nghia said:


> The first question will be : is that, well, the "optimal" solution ?


Definitely not




Nghia said:


> And second question : can we solve any edge parity with that method ?


Your approach is general, so yes.


However, I recommend learning a parity alg for opposite edges (I use l' U2 l' U2 (l'r) U2 l' U2 l U2 r' U2 l2). Setups are easy (3x3x3-style)...


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## masterofthebass (Apr 3, 2008)

the way I would to it... is the do a y' rotation. then set-up the "normal" parity algorithm with an r'. Then you preform the alg, r2 B2 U2... then, because that algorithm rotates the centers 180 degrees, you need to do an algorithm, that rotates them back. *from chris hardwick* R L U2 R' L' U R L U2 R' L' U. then undo the r' and you're done 

-EDIT-
Darn lucas, posting before me... People do that way too often now. Either way, these are 2 options to solve it.


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## Lucas Garron (Apr 3, 2008)

masterofthebass said:


> the way I would to it... is the do a y' rotation. then set-up the "normal" parity algorithm with an r'. Then you preform the alg, r2 B2 U2... then, because that algorithm rotates the centers 180 degrees, you need to do an algorithm, that rotates them back. *from chris hardwick* R L U2 R' L' U R L U2 R' L' U. then undo the r' and you're done
> 
> -EDIT-
> Darn lucas, posting before me... People do that way too often now. Either way, these are 2 options to solve it.


Conjugating is faster, I think.
(say, y B' l U'R'U)


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## cmhardw (Apr 3, 2008)

To be honest I would probably do:
y' r B2 r U2 r U2 F2 r F2 l' U2 l U2 r2 R L U2 L' R' U' R L U2 L' R' U' B2 r' y

Also fast is:
L F' D' L2 y' l' U2 l' U2 F2 l' F2 r U2 r' U2 l2 y L2 D F L'

--edit--
Wow Lucas nice alg, I'll have to learn that!

Chris


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## Lucas Garron (Apr 3, 2008)

cmhardw said:


> Also fast is:
> L F' D' L2 y' l' U2 l' U2 F2 l' F2 r U2 r' U2 l2 y L2 D F L'


LU'F. 



cmhardw said:


> Wow Lucas nice alg, I'll have to learn that!


Why, thank you! I learned the alg from the famous cuber Erik Akkersdijk and amazing BLD cuber Chris Hardwick here. 

It's the same alg, I just added an extra move to keep it <l,r,U2>.
Note that there are several ways to use it on 5x5x5 - I do l' U2 l' U2 (l'm'r) U2 l' U2 (lm) U2 r' U2 l2 (sorry for abusing my r2 animation page, but I don't have a 5x5x5 sim up yet. )

I find it easier to keep track of (no tilting ), and to do things like mirroring.
(l up, l up, l up, both up, l up, l down, r down, l2 - it's got a nice rhythm. )


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## dbeyer (Apr 4, 2008)

http://cube.garron.us/BLD/r2/r2anim.htm?alg=rU2rU2xU2rU2x'l'U2lU2r2

http://cube.garron.us/BLD/r2/r2anim.htm?alg=R2x2Ur2U2xU2r2U2x'U2r2U'x2R2

Some nice algs that I use 

For me if I got my buffer (URb) and it's opposite on the U, ULf, which I would try to avoid by the way, by picking another location to kick to for starting/ending my second cycle on wings (There are normally 2 cycles for wings).

But if I got that parity fix, I'd do
http://cube.garron.us/BLD/r2/r2anim.htm?alg=fU'x'r2B2U2lU2r'U2rU2F2rF2l'B2r2xUf' 

With centers solved of course. With a buffer there are only 23 swaps that you have to take into consideration.

Swapping the URb wing with the wings on the l slice is as simple as setting the wing to the BDl, then doing U'x'

general practice
l slice - multislice-deepL U'x' (preserving centers)
r slice - multislice-deepL Ux (preserving centers)
f slice - pair with the buffer then do U'x' and do the OLL parity fix like on 4x4 as shown above in the one applet
u/d slice pretty straight forward doing either a slice, blockturn, or 3x3 setup with some cube rotations 2-3 moves max

The only hard one that I haven't given much thought to is URb->DLb


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## Lucas Garron (Apr 4, 2008)

dbeyer said:


> The only hard one that I haven't given much thought to is URb->DLb


I just came up with lF2rB2U2lU2r'U2rU2F2rF2l'B2r'F2l' for such a swap (pseudo-2 setup moves).

Also, what do you do for the supercube "PLL parity" ?
I currently use r UR'U'B'R2B r'l' B'R2BURU' l
(Yes, I know the flip is sub-optimal, but I don't like the 5-mover as much.)


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## Nghia (Apr 4, 2008)

Lucas Garron said:


> However, I recommend learning a parity alg for opposite edges (I use l' U2 l' U2 (l'r) U2 l' U2 l U2 r' U2 l2). Setups are easy (3x3x3-style)...



Wow, that's one beautiful and very useful algorithm, thanks much Lucas ! 

***



masterofthebass said:


> the way I would to it... is the do a y' rotation. then set-up the "normal" parity algorithm with an r'. Then you preform the alg, r2 B2 U2... then, because that algorithm rotates the centers 180 degrees, you need to do an algorithm, that rotates them back. *from chris hardwick* R L U2 R' L' U R L U2 R' L' U. then undo the r' and you're done



Thanks masterofthebass (what's your real name ?), but I don't understand how that could work ? (I'm not saying that it shouldn't, but I'd like to have a more in-depth explanation of how it actually works)

***



Lucas Garron said:


> Conjugating is faster, I think.
> (say, y B' l U'R'U)



I understand how conjugating works, but I don't get what you're saying...

***



cmhardw said:


> To be honest I would probably do:
> y' r B2 r U2 r U2 F2 r F2 l' U2 l U2 r2 R L U2 L' R' U' R L U2 L' R' U' B2 r' y
> 
> Also fast is:
> L F' D' L2 y' l' U2 l' U2 F2 l' F2 r U2 r' U2 l2 y L2 D F L'





dbeyer said:


> http://cube.garron.us/BLD/r2/r2anim.htm?alg=fU'x'r2B2U2lU2r'U2rU2F2rF2l'B2r2xUf '





Lucas Garron said:


> Also, what do you do for the supercube "PLL parity" ?
> I currently use r UR'U'B'R2B r'l' B'R2BURU' l



Seriously, where do you guys get those algorithms ? With a computer program, or by just with your cube and a piece of paper ?

***



dbeyer said:


> With centers solved of course. With a buffer there are only 23 swaps that you have to take into consideration.
> 
> Swapping the URb wing with the wings on the l slice is as simple as setting the wing to the BDl, then doing U'x'
> 
> ...



Thanks Daniel,
If I understand correctly, when you're using a buffer, you must sometimes break into new cycles to keep that buffer "active" ?

And what's the general practice part about ?

***

Thank you guys for answering so nicely, I really didn't expect that 
And yeah, I've got so many questions, I just hope they don't annoy you guys


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## masterofthebass (Apr 4, 2008)

Nghia, my real name is Dan Cohen. Basically, if you speedsolve the 4x4, (I assume you do) most people use the standard parity fix if r2 B2 U2 (rest of alg here...) That algorithm rotates the centers 180 degrees, so you need to apply an algorithm to correct that. If you look at chris' first algorithm it's basically the same concept...


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## Nghia (Apr 4, 2008)

Hey Dan,

Yes I know that parity fix algorithm, but I wanted to understand the fact that by combining that with an r' as setup move, you can resolve this parity. Actually I think I understood :

When you do r', fUR goes to fUL. Then we do the parity fix algorithm, which twist bUL and fUL (where fUR is). And since on the 4x4, the edge's orientation is linked to its position on the cube, the parity fix algorithm also switches bUL and fUL, by twisting them ! But what's with Lucas' conjugate here ?

Ok It's the switching part that I didn't notice, now I can reasonably solve the 4x4 with this method with my eyes open, and I think that's it for the execution part. Now I must get onto the memorization part.

Does everybody here use the letter pair system from Chris Hardwick (Pedro told me he still uses his imagery system) ? And so how long did it take you guys to elaborate the pairs ?


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## Nghia (Apr 4, 2008)

Hey there,

I just got a very close DNF with 2 pairs of centers switched (on F and D), it's so unfair when you take off your blindfold, see the U face entirely solved, and then notice those switched pairs ! 

anyway, I'll remake an attempt tomorrow. I currently use a simple lettering system (consecutive letters on each face for centers and clockwise lettering for edges) and I think it's working pretty well. For the letter pairs, I just create them on the go for now


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## dbeyer (Apr 5, 2008)

It took me about a month to learn an image system, very closely modeled to Hardwicks original 506 image list. I used about 70-80% of his stuff, when I first learned my letter pair system. Now I feel as though he and I have almost completely unique lists, mind you we do have some of the same images, but that just goes to show we have some of the same interests. 

Such as DW, he picked Darkwing Duck (right?) and of course so did I, I love that series!

Chris has a larger memory system than I do though, he's learned one-syllable nouns, and is now breaking into learning one syllable verbs.

I made an attempt or two on 4x4 blindfolded, before I realized I needed a condensed system like letter pairs before I could bare to make another attempt.

I know what you mean when you say how unfair it is, to see a few pieces swapped when you see your cube had solid color faces on the first 4 sides you look at ...

the one alg that I gave you with the pure parity fix, with some random turns. Its a concept that Chris showed me at Gwiz '06. 
Pair the pieces with a slice turn (f)
Make sure the U center (relative to applying the parity fix) is solved. (U'x')
Parity Fix
Undo the setups 

The other alg that I gave that does a wing parity fix, that swaps them on the UFr and BUr is the pure version of Frank's one alg on Bigcubes.com, the one where you have 2 blocks on the tredges, and two wings have to be swapped on the same slice.

Yes, I did play with and manipulate the algs though so that they were comfortable and fast for big cubes bld.


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## Nghia (Apr 5, 2008)

Hey guys,

I couldn't hold this any longer: I just succeeded my first 4x4 BLD !!!!!!!
I'm so excited right now !!!

Ok, this was today's second attempt, the first one was a real bad DNF, it discouraged me a bit, but not enough to stop me  So I tried another one, and it worked !! 

The scramble is F2 D' u U' F2 u2 L r R' D2 B r' B' f F L B' r' B2 f2 F D2 f2 r2 B' f' F u2 R U R2 F u2 F2 L' U' f D' R U' (this week's second). The time was about 40-50 minutes (what were your times back then ?) mainly because I was really tired during the memorization phase (headache) and so I took much time to verify this and that, etc...But I'm overall very proud of this achievement 

Thank you guys one more time for helping me !!

***

Hey Daniel,

Now that I'm pretty much settled into BLD, I think I'll spend some time making my own letter pair system. I'm actually planning to use 3 languages (4 if I can get some words in German ) to build these letter pairs nouns (Vietnamese, French and English). I don't know yet if that will be an advantage or not (I could somehow get confused) but I've began doing so, and it works reasonably well.

I tried your alg, but it appraently has some side effects : 2 edge pairs swapped, 2 centers swapped and 2 corners as well. I don't know where I went wrong in it, but :confused:

Thanks


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## Mike Hughey (Apr 7, 2008)

Congratulations on your first 4x4x4 BLD! I'm very happy for you! Hopefully you'll get nice and addicted to it now (like me), and start doing them in competition. (I want to make sure the event gets so popular that they start having it at every competition!)

How fast was your first one?


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## Nghia (Apr 8, 2008)

Hey Mike,

Thank you very much, I really appreciate feedbacks like that, at least I can share my joy with people who understand the rubik's cube and not regular guys at school 

I'm addicted to BLD in general right now, but I'll have to be a little patient for my memo list/method to build up. So this first successful attempt was about 40-50 minutes, hope that's not to bad, but anyway I did it and that's what counts !!!  

And how fast was yours ?


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## RobinBloehm (Apr 8, 2008)

my very first successful one was about one hour, but I really double-checked everything over and over because of two DNFs a week before that. I just wanted a successful one.

But the next time I tried, I started speeding my memo and the time dropped to 33 minutes, I think.


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## Mike Hughey (Apr 8, 2008)

Nghia, your first one was substantially faster than mine. My first one was 63:42.73. My first attempt was over 88 minutes. So you're off to a nice start.

I wasn't patient with my memo list. I just solved a bunch making up memory images as I went. Like Robin, my time went down to 33 minutes (33:35.56, to be precise) by my sixth attempt (third successful solve), although that was a somewhat easy scramble. Then eventually I got serious and learned a memo list, but I was sub-20 before I ever did that. But memorizing a list of images really sped me up, so it's worth doing that at some point.

And I agree with you that the best part is simply that you did it! It's still a thrill every time for me when I pull off the blindfold and see the cube solved.


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## Nghia (Apr 8, 2008)

Hey Mike and Robin,

Thank you for the encouraging comments  I'm currently building my letter pairs list, I definitely reckon that a prepared list should speed up my memo a lot. At the same time, I'm finding a way to customize my 3x3 BLD memo method so that I won't really have to "think" much while memorizing.

For this first successful attempt, I don't remember how many times I had to check my memo, I was so tired and at some point even believed my memo was entirely wrong  Plus I had to fix some execution errors, so I was quite amazed to see a solved cube when I took off my blindfold !

I don't really remember my first attempt, but I think it was around the same time and I had 4 center pieces swapped (arghh! ). 

I'll make some filmed attempts this weekend if homeworks don't eat my time.


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## Lucas Garron (Apr 8, 2008)

Mike Hughey said:


> My first attempt was over 88 minutes. So you're off to a nice start.


90 minutes here, so I agree. However, I didn't try another one until a year later, and I suggest that you keep going, unlike me.
(Note: That attempt was actually closer than most of mine have been this year.  I still have the exec video on a backup hard-rive...)


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## Nghia (Apr 10, 2008)

Hey Lucas,

Thanks for the encouragement, I'm willing very much to try another one, but currently I think I'll have to make words and sentences on the go for a while (because the letter pairs list is huge !)

Thanks again ,


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