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APB - An algorithmic system for EO + RB after 2x2x3

Athefre

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Joined
Jul 25, 2006
Messages
1,128

Here I am presenting a method which algorithmically solves edge orientation and the final 1x2x3 after a 2x2x3 is built. I have always felt that the EO step of Petrus is a bit of an inefficiency. That there should be something more done while orienting the edges. So with APB, instead of separating EO and the last block, partial blockbuilding is performed while orienting the edges. The primary steps are:

Step 1: Build a 2x2x3
Step 2: Create an F2L pair. Or set up a pair so that the corner and edge can be paired in a single move.
Step 3: Orient all edges while inserting the pair. For each of the pair situations there are 31 or 32 cases.
Step 4: Solve the final three pieces. This step contains 116 algorithms averaging around 8 moves.

For 2x2x3 at dl, in step 2 above you create either the front (dFR) or back (dBR) pair. For 2x2x3 at db, it is recommended to create the left side pair (dFL). There are some add-ons to this method that I plan to develop. The biggest thing is the ability to create any of the four F2L pairs then in the last step solve the remaining corner and two edges. Another goal is to test the ergonomics and efficiency of the method if the pair is kept on the U layer while orienting the edges. More information about the add-ons can be viewed on the site.

Pros:
  • More efficient than EO + last block
  • No rotation
  • Can track EO while creating the pair
  • Algorithmic last step
Cons:
  • Memorization versus intuition
Block on Left Example:

Scramble:
B2 L2 B D2 F2 L2 F L2 B L2 R2 U2 R' D' B U' R2 B L2 R2 D'

2x2x2: y z D' B' M' B'
2x2x3: F' R2 U' R U R' F
Pair: R2 U' R
EOPair: U2 F' U F R
L3P: R' U' R U R U R U R'
ZBLL: F R' F2 R F R' F2 R U2 r U r' F' U'

View on alg.cubing.net

Block on Back Example:

Scramble:
D' R2 B R2 D B2 R' U D2 R' U2 L D2 R2 B2 L' F2 R F2 U2 B'

2x2x2: D' R' U2 R F R2
2x2x3: U' L' F2 L' U L'
Pair: R U R'
EOPair: U' R U' R' U' F'
L3P: r U2 r' U2' r U2 M U R'
ZBLL: R' U' R U R2 D' R U' R' D R2 U2 R' U2 R

View on alg.cubing.net
 
Last edited:
Joined
Oct 12, 2020
Messages
684
Location
In the park feeding ducks

Here I am presenting an alternative way of orienting all edges and solving the last block after the 2x2x3 is built in Petrus. I have always felt that the EO step of Petrus is a bit of an inefficiency. That there should be something more done while orienting the edges. So with APB, instead of separating EO and the last block, partial blockbuilding is performed while orienting the edges. The primary steps are:

Step 1: Build a 2x2x3 at db.
Step 2: Create the left side pair (dFL). Or set up the left side pair so that the corner and edge can be paired in a single move.
Step 3: Orient all edges while inserting the pair. For each of the pair situations there are 31 or 32 cases.
Step 4: Solve the final square (dFr). This step contains 116 algorithms averaging 8.27 moves.

Pros:
  • More efficient than EO + last block
  • No rotation
  • Can track EO while creating the pair
  • Algorithmic last step
Cons:
  • Slightly less ergonomic overall. This sometimes comes from the first step of creating the pair. And the final square step is R r U M versus R U.
An additional option is provided on the site for solving the 2x2x3 at dl. It works the same. You create the 2x2x3 on the left, create a pair, insert + EO, then solve the final square using R U based algorithms. However, the EOPair algorithms for block on left aren't very good. If you wanted, you could rotate after step 3 above then use all R U algs to solve the final square. But that may not be worth the rotation when the dFr algorithms are good. There are some add-ons to this method that I plan to develop. The biggest thing is the ability to create any of the four F2L pairs then in the last step solve the remaining corner and two edges. More information about the add-ons can be viewed on the site.

Example:

Scramble:
D' R2 B R2 D B2 R' U D2 R' U2 L D2 R2 B2 L' F2 R F2 U2 B'

2x2x2: D' R' U2 R F R2
2x2x3: U' L' F2 L' U L'
Pair: R U R'
EOPair: U' R U' R' U' F'
Square: r U2 r' U2' r U2 M U R'
ZBLL: R' U' R U R2 D' R U' R' D R2 U2 R' U2 R

View on alg.cubing.net
I'll have to take a look at it more in depth later but this definitely seems like an improvement for Petrus.
@PetrusQuber
 
Last edited:

xyzzy

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Joined
Dec 24, 2015
Messages
2,440
Step 3: Orient all edges while inserting the pair. For each of the pair situations there are 31 or 32 cases.
With the block at db, does EO here refer to EO along the F-B axis? (In other words, not the usual Petrus EO?)
 

Athefre

Member
Joined
Jul 25, 2006
Messages
1,128
With the block at db, does EO here refer to EO along the F-B axis? (In other words, not the usual Petrus EO?)
It's the EO used in most methods. F and B changes the edge orientation. L, U, R, and D only change their permutation. This way R r U M can easily be used during the square step. And I suppose this means rotating and using R U algs actually wouldn't work out so well. The L R EO would have to be used for that if someone really wants to rotate for R U algs. But possibly the f and S moves inclusion will improve the algs for dl block.
 
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Here I am presenting an alternative way of orienting all edges and solving the last block after the 2x2x3 is built in Petrus. I have always felt that the EO step of Petrus is a bit of an inefficiency. That there should be something more done while orienting the edges. So with APB, instead of separating EO and the last block, partial blockbuilding is performed while orienting the edges. The primary steps are:

Step 1: Build a 2x2x3 at db.
Step 2: Create the left side pair (dFL). Or set up the left side pair so that the corner and edge can be paired in a single move.
Step 3: Orient all edges while inserting the pair. For each of the pair situations there are 31 or 32 cases.
Step 4: Solve the final square (dFr). This step contains 116 algorithms averaging 8.27 moves.

Pros:
  • More efficient than EO + last block
  • No rotation
  • Can track EO while creating the pair
  • Algorithmic last step
Cons:
  • Slightly less ergonomic overall. This sometimes comes from the first step of creating the pair. And the final square step is R r U M versus R U.
An additional option is provided on the site for solving the 2x2x3 at dl. It works the same. You create the 2x2x3 on the left, create a pair, insert + EO, then solve the final square using R U based algorithms. However, the EOPair algorithms for block on left aren't very good. If you wanted, you could rotate after step 3 above then use all R U algs to solve the final square. But that may not be worth the rotation when the dFr algorithms are good. There are some add-ons to this method that I plan to develop. The biggest thing is the ability to create any of the four F2L pairs then in the last step then solve the remaining corner and two edges. More information about the add-ons can be viewed on the site.

Example:

Scramble:
D' R2 B R2 D B2 R' U D2 R' U2 L D2 R2 B2 L' F2 R F2 U2 B'

2x2x2: D' R' U2 R F R2
2x2x3: U' L' F2 L' U L'
Pair: R U R'
EOPair: U' R U' R' U' F'
Square: r U2 r' U2' r U2 M U R'
ZBLL: R' U' R U R2 D' R U' R' D R2 U2 R' U2 R

View on alg.cubing.net
An alternative to this would be the usual Petrus 223 in dl>EO>dBR>dfR square(for which the algs are genned but not yet formatted)
anyway, algorithmic blockbuilding is a really cool and underexplored concept.
 

PetrusQuber

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abunickabhi

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Here I am presenting an alternative way of orienting all edges and solving the last block after the 2x2x3 is built in Petrus. I have always felt that the EO step of Petrus is a bit of an inefficiency. That there should be something more done while orienting the edges. So with APB, instead of separating EO and the last block, partial blockbuilding is performed while orienting the edges. The primary steps are:

Step 1: Build a 2x2x3 at db.
Step 2: Create the left side pair (dFL). Or set up the left side pair so that the corner and edge can be paired in a single move.
Step 3: Orient all edges while inserting the pair. For each of the pair situations there are 31 or 32 cases.
Step 4: Solve the final square (dFr). This step contains 116 algorithms averaging 8.27 moves.

Pros:
  • More efficient than EO + last block
  • No rotation
  • Can track EO while creating the pair
  • Algorithmic last step
Cons:
  • Slightly less ergonomic overall. This sometimes comes from the first step of creating the pair. And the final square step is R r U M versus R U.
An additional option is provided on the site for solving the 2x2x3 at dl. It works the same. You create the 2x2x3 on the left, create a pair, insert + EO, then solve the final square using R U based algorithms. However, the EOPair algorithms for block on left aren't very good. If you wanted, you could rotate after step 3 above then use all R U algs to solve the final square. But that may not be worth the rotation when the dFr algorithms are good. There are some add-ons to this method that I plan to develop. The biggest thing is the ability to create any of the four F2L pairs then in the last step then solve the remaining corner and two edges. More information about the add-ons can be viewed on the site.

Example:

Scramble:
D' R2 B R2 D B2 R' U D2 R' U2 L D2 R2 B2 L' F2 R F2 U2 B'

2x2x2: D' R' U2 R F R2
2x2x3: U' L' F2 L' U L'
Pair: R U R'
EOPair: U' R U' R' U' F'
Square: r U2 r' U2' r U2 M U R'
ZBLL: R' U' R U R2 D' R U' R' D R2 U2 R' U2 R

View on alg.cubing.net
Really good work Athefre.

A lot of momentum is being put into making new methods and I like it in general. Makes cubing more creative.
 

Athefre

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Joined
Jul 25, 2006
Messages
1,128
An alternative to this would be the usual Petrus 223 in dl>EO>dBR>dfR square(for which the algs are genned but not yet formatted)
anyway, algorithmic blockbuilding is a really cool and underexplored concept.

That's definitely something that I considered. I even have the ZZ section on the page with algs that could be used. However, the primary goal with APB is to do something during EO. To have EO not be a step of its own.

Nautilus follows different first steps, and only one of the other variants is similar in finishing the EO, but yeah

There is at least one person that does Nautilus as 2x2x3 at db then add the pair at dFL. Then let's say that I or someone else would have eventually proposed EO + the dFL pair for those users. This shows that APB almost creates a kind of merged method of Nautilus and Petrus (There's even a section on the page that I call Nautrus). At least in most cases. For more advanced applications of APB where someone builds one of the D layer pairs it wouldn't look like Nautilus.

However, APB is developed for Petrus. So as long as users follow the steps of APB and don't do EOPair then some other Nautilus steps, I definitely classify it as Petrus.
 
Last edited:

Athefre

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Jul 25, 2006
Messages
1,128
I regenerated the EOPair algs for dl block. Incorporating f and S moves made a huge difference. A few cases still aren't great, but overall it is a much better move-count and no more repeating F and U moves. Though the new set contains a lot of S moves so users would have to practice the fingertricks. S moves can be fast but they aren't yet commonly used.

View algs (images will be added soon)

I want to eventually try generating EOPair which keeps the pair on the U layer. Just to see if there is even a small difference in ergonomics and how the last three pieces step compares to when the pair is placed in F2L.
 

Tao Yu

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I kind of like this method a lot. I'm a sucker for two things: methods that end with ZBLL, and algorithmic steps that feel intuitive... and this has both.

I'd really like to add these algs to my trainer and play around with it. Unfortunately, my interest in cubing in general is pretty low these days so idk if it will go much further than that.
 

Athefre

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Joined
Jul 25, 2006
Messages
1,128
I kind of like this method a lot. I'm a sucker for two things: methods that end with ZBLL, and algorithmic steps that feel intuitive... and this has both.

I'd really like to add these algs to my trainer and play around with it. Unfortunately, my interest in cubing in general is pretty low these days so idk if it will go much further than that.
That would be useful. If you get these added to your trainer, I'll link to it on my site.
 

Athefre

Member
Joined
Jul 25, 2006
Messages
1,128
APB is now fully usable! Adding in S and f moves into the moveset for the block on left algs completely changed everything. Block on left might be my recommended way to use APB now. It is efficient and maintains the R U ergonomics.

I have also created a dedicated website for APB.

 
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