Easy EKA (corners)

[m0nkiem0nkie]

If there’s one thing I’m appreciative of in this cubing community is the willingness to share knowledge with each other with the common goal to unlock the secrets of solving the cube.

I myself have been privileged to be part of the 1st generation Rubik’s Cube rage back in the 80’s and have recently found a renewed interest in this puzzle; most particularly in 3BLD.

While I originally used the M2/OP-method, probably like many I became mentally stuck in-between the repetitive OP-corners method and facing the unsurpassable task of learning 378 3-style corner algorithms.

Thanks to this tutorial: http://twistypuzzles.ru/forum/index.php?topic=994.0 combined with Google translate I started to understand the EKA corners-method. However, the tutorial uses FDR as the helper piece, whereas I wanted to keep the UBL-RDF combo, to maintain use of the good old OP-corner alg. (in case of parity, for instance).

Understandably, most algorithms found on the Internet are full of speedy, but sometimes long algorithms containing only R-, D- and U-moves, to maintain regripless movements.

However, being a recreational cuber with an appreciation for simplicity and elegance, my goal was to collect sets of similar algorithms which could be grouped together, thereby making it easy to remember, turning it into an “easy-EKA”-method.

As a result, here is a set of algorithms I compiled from various sources and wish to share, using the UBL-RDF combo:

[F L2 F', R%]
RBD -> [F L2 F', R] -> (F L2 F') R (F L2 F') R'
RFU -> [F L2 F', R'] -> (F L2 F') R' (F L2 F') R
RBU -> [F L2 F', R2] -> (F L2 F') R2 (F L2 F') R2

[R' D' R, U%]
UFR -> [R' D' R, U2] -> (R' D' R) U2 (R' D R) U2
UBR -> [U: [R' D' R, U]] -> U: (R' D' R) U (R' D R) :U2
UFL -> [U': [R' D' R, U']] -> U': (R' D' R) U' (R' D R) :U2

[F' U2 F, D%]
FDL -> [F' U2 F, D] -> (F' U2 F) D (F' U2 F) D'
BDR -> [F' U2 F, D'] -> (F' U2 F) D' (F' U2 F) D
LBD -> [F' U2 F, D2] -> (F' U2 F) D2 (F' U2 F) D2

(R2 U R2 U' R2)
DBR -> [x: [R2 U R2 U' R2, D2]] -> x: (R2 U R2 U' R2) D2 (R2 U R2 U' R2) D2 :x'
LFU -> [x' y': [D2, R2 U R2 U' R2]] -> x' y': D2 (R2 U R2 U' R2) D2 (R2 U R2 U' R2) :y x

Misc. pure Commutators
BDL -> [L, B' R2 B] -> L (B' R2 B) L' (B' R2 B)
FLU -> [U' R U, L] -> (U' R U) L (U' R' U) L'
DFL -> [D R D', L2] -> (D R D') L2 (D R' D') L2

Misc. with Conjugates
DBL -> [D: [L2 , U R' U']] -> D: L2 (U R' U') L2 (U R U') : D'
LDF -> [L: [R U' R', D2]] -> L: (R U' R') D2 (R U R') D2 :L'
FRU -> [U': [D' L D, R2]] -> U': (D' L D) R2 (D' L' D) R2 :U
BRU -> [L2: [L B2 L', F]] -> Rw': U2 (L' D L) U2 (L' D' L) :Rw

As can be seen, similar algorithms have been grouped together, to ease the way to memorize these 18 algorithms.

Note: I am aware that for instance for BDR there is the [D, R' U R]-alg., yet for now I prefer the above as the particular logic of that group made memorizing those 3 [F' U2 F, D%]-alg’s much easier.

For those that are still a bit confused about the EKA corners-method:

1. As this is a 3-style method, group targets in letter pairs.
2. Setup the location of the first letter to the helper position (RDF); same as the OP-method.
3. The setup move(s) may relocate the position of the second letter. It is the (relocated) position of this second letter that determines which of the 18 algorithms to use.*
4. Perform algorithm, undo setup and voilà, you just solved 2 corners with only 1 algorithm!

*Tip: I place one of my fingers on the initial position of the second letter to physically follow its final position while performing the setup of the first letter to RDF.

All in all, for those who, like me, wanted to join the fun of using 3-style on corners, but have no intention to learn all 378 corner algorithms, this may work out for you. At least it did for me.

Of course, the above list is just my current personal preference. Who knows, there may be even more easy-EKA alg-groups to be discovered.

Have fun!

 

[guelda]

Hi m0nkiem0nkie!

"Being a a recreational cuber with an appreciation for simplicity and elegance" too , I find your idea very appealing.

I managed to perform my first 3BLD yesterday thanks to Jack Cai's OP tutorial (what a joy!) after about a week, I guess I will practice some time just to make sure the lettering is automatic and practice memorization as well, but the concept of 3-style looks like the Holy Grail in order to always understand what you do. I also read that Chris Hardwick was able to perform the needed commutators "on the fly" which sounds magical when blindfolded!

The method you mention and the way you present it seems to fit my needs of an intermediate method to reach (probably in a loooong time!) 3-style, as most people seem to think that it is too hard to jump directly from OP/M2 (I don't even do M2 but will most likely skip it thanks to you).

Thanks again and hopefully I'll get back to you after practicing a bit, sorry: a lot!

 

[m0nkiem0nkie]

Hi guelda,

Thanks for your feedback.

Indeed I would classify EKA as an intermediate method, with the added advantage that it brings more fun than just performing OP on corners, yet does not require a full knowledge of all 378 3-style corner alg's.

I do still use M2, yet where possible an advanced version of it, as it allows quite a few groups to solve 2 edges at the same time.

You may want to check my next post as well, as I have discovered another group of easy-EKA corner alg's.

 

[m0nkiem0nkie]

As a follow-up to my original post, although I promoted the initial 18 alg’s as easy to remember, for the life I myself still had trouble remembering the last 4 with the conjugates. I also was not fond of the 2 alg’s requiring the cube to rotate.

So in my quest to make things even easier, and with the help of the following website: http://csclub.uwaterloo.ca/~krmatthe/3-style-corners.cgi (Thanks, Kevin!), I started to search for alternatives, and lo and behold, particularly for these 6 I found a whole group of associated commutators:

[R' D' R, U%]
BRU -> [D’ R’ D: [R’ D’ R, U2]] -> D’ R’ D: (R' D' R) U2 (R' D R) U2 : D' R D
DBL -> [D’ R2 D: [R’ D’ R, U2]] -> D’ R2 D: (R' D' R) U2 (R' D R) U2 : D' R2 D
LFU -> [R’ U’ R U: [R’ D’ R, U2]] -> R’ U’ R U: (R' D' R) U2 (R' D R) :U R’ U R
FRU -> [L R U’ R’: [R’ D’ R, U2]] -> L R U’ R’: (R' D' R) U2 (R' D R) U2 :R U R’ L’
DBR -> [R2 U2 F: [R’ D’ R, U2]] -> R2 U2 F: (R' D' R) U2 (R' D R) U2 :F’ U2 R2
LDF -> [R2 U2 F: [R’ D’ R, U’]] -> R2 U2 F: (R' D' R) U’ (R' D R) U :F' U2 R2

For those that are using the other easy-EKA alg’s may notice that these new alg’s basically belong to the group solving the U-layer using [R’ D’ R, U%].

Memorizing the above took me less than a day, as now I only had to memorize the conjugate part, which by themselves are quite logic.

Once again, they may not be the fastest algorithms at hand, but do provide an easy set to memorize and utilize 3-style on corners. Of course, you may have found your own set of alg’s that appeal to you.

At least now I do not have to walk around with a cheat sheet in my pocket anymore.

Have fun!

 

[dudefaceguy]

This is a great approach - very similar to the way I started with intuitive 3 style. It probably results in much faster solves too, since you can actually learn and practice these 18 algs, and you will end up seeing the same comms over and over again.

I started by always conjugating one of the two letter pairs to the same layer as the buffer, and interchanging it with the buffer. I did one of 4 insertions from the third piece to the interchange layer. This made 4 types of commutators for each piece type, but I still had to construct them on the fly.

I will try a few solves always conjugating to the same exact sticker - this is a great way to practice new types of commutators and interchange groups.

 

[Moreno van Rooijen]

Hey,
This looks great! I was working on somewhat like this myself.
You might like this group for the following cases:
Instead of [F L2 F', R%] you use [R2 : [U' L' U, R%]]

RUF

RUB

RDB

[TD valign="top"] [R2 : [U' L' U, R']] [/TD]

[TD valign="top"] [R2 : [U' L' U,R2]] [/TD]

[TD valign="top"] [R2 : [U' L' U, R]] [/TD]

This is a bit faster and easier to execute than using F moves, at least it is for me.

 

[m0nkiem0nkie]

Although in my original post I choose to ignore the shorter BDR-alg, turns out that this one is quite a gem, as it can be the basis for a few other positions that do not have a 'clean' commutator (i.e. without a conjugate), providing another nice EKA-grouping:

[D%, R' U R]:
BDR -> [D, R' U R]
BRU -> R D' R': [D, R' U R]
DBL -> R D2 R': [D, R' U R]
UFR -> U2 R': [D, R' U R]
DBR -> D' R': [D2, R' U R]

I have been using these for a while now and besides easy to remember, they can be executed quite fast as well.