# New Speed Method for 2x2x3 (Mini Tower)

#### Ian Brown

##### Member
Hello, I'm new to this forum but thought this would be a good place to share my new speed method for the 2x2x3 cuboid. Some things to know about this method are that it relies heavily on algorithms, and that it is possible and encouraged to use this method for one-looking solves.

The solve has three stages:

1. Squares: Solve the square faces intuitively

2. CP: Corner permutation [ 5 cases ]

Adjacent swap on U layer: R U' (R D R D') R (U' D R U' R)
Diagonal swap on U layer: (R U D R U')2 (R U D R)
Adjacent swap on both layers: (R U R U') (D' R D R)
Diagonal swap on both layers: (R U D R) U2 (R U' D' R)
Diagonal swap on U layer and Adjacent swap on D layer: (R U R U R) U2 (R U' R U' R)

3. EP: Equator/Edge permutation [ 7 cases ]

Front Right with Back right swap: (R U2)3
Front left with front right, back left with back right: R E2 R
3 edge cycle clockwise, front left piece is correct: (R E R E')
3 edge cycle counterclockwise, front left piece in correct: (E R E' R)
Diagonal swap: (R E R E') (R U2)3
4 edge cycle clockwise: (R E R E) (R U2)2 (R D2)
4 edge cycle counterclockwise: (R E R E) (R U2)3

One thing you may notice is that the CP algs are not like those from SQ-1 or other algs for 2x2x3, this was done on purpose. The CP algorithms do not affect the equator layer and that is why it is possible to one look with this method.

I have attached a pdf detailing the method and algorithms, please try this method out and tell me what you think or how it can improve, I was partly inspired to explore this puzzle because I think it should become a WCA event.

Edit: After discussion, it has been determined that this method is much better when The equator layer is solved while also solving the square faces in the beginning of the solve. In this way, only 5 algorithms, all which are CP cases, are the only algs in this method.

The method would then go as follows

1.) Solve Square faces and equator simultaneously (done intuitively)

2.) Permute corners [5 cases]

for details see AC.pdf

#### Attachments

• SCE.pdf
144.6 KB · Views: 25
• AC.pdf
96.7 KB · Views: 20
Last edited:

#### Ian Brown

##### Member
How many algs would it be to solve a face then solve the rest?
After solving the square faces, there would be two algorithms to finish, one for CP, then one for EP

Last edited:

#### Ian Brown

##### Member
But how many algs would it take to do the square faces then do one alg to solve the rest? I.e: how big would the alg set be
I apologize but I'm a bit confused as to what you mean. If you're wondering how many total algorithms there are, its 14. There are 5 for corner permutation, and 7 for solving the equator layer.

#### ProStar

##### Member
I apologize but I'm a bit confused as to what you mean. If you're wondering how many total algorithms there are, its 14. There are 5 for corner permutation, and 7 for solving the equator layer.

Think of the cube like the LL on a 3x3. First you do OLL, which takes 57 algorithms, and then you do PLL, which takes 21 algorithms. But if you wanted to do the entire thing in one alg, it takes 3915 algorithms. That's kind of what I'm saying, except CP=OLL and EP=PLL. I'm asking how many algorithms you would need to be able to solve both CP and EP at once(with squares already finished), or like 1lll in my example

#### Ian Brown

##### Member
Think of the cube like the LL on a 3x3. First you do OLL, which takes 57 algorithms, and then you do PLL, which takes 21 algorithms. But if you wanted to do the entire thing in one alg, it takes 3915 algorithms. That's kind of what I'm saying, except CP=OLL and EP=PLL. I'm asking how many algorithms you would need to be able to solve both CP and EP at once(with squares already finished), or like 1lll in my example
Ok, sorry for the confusion. So I may be wrong but I'm pretty sure there would only be 35 unique cases. Since there is no parity or mirrored cases, and not counting layer adjustment and rotational variation. I think it's just (number of CP cases) * (number of EP cases) = 5 * 7 = 35.

edit: *the only thing is, to narrow it down to 35, you would have to set up the equator layer in the correct orentation for EP after solving the square faces so that you could flow from CP into EP without needing layer adjustment to make it work.*

Think of the cube like the LL on a 3x3. First you do OLL, which takes 57 algorithms, and then you do PLL, which takes 21 algorithms. But if you wanted to do the entire thing in one alg, it takes 3915 algorithms. That's kind of what I'm saying, except CP=OLL and EP=PLL. I'm asking how many algorithms you would need to be able to solve both CP and EP at once(with squares already finished), or like 1lll in my example
Just thinking out loud here: if we say there are 4 cases for equator layer adjustment between Cp and Ep, which are: E, E', E2, or no moves, then it might be (number of CP cases) * (number of equator adjustment cases) * (number of EP cases) = 5 * 4 * 7 = 140.

Last edited:

#### Billabob

##### Member
How many algs would it be to solve a face then solve the rest?

Not counting algs for the first face as it is easy enough to solve intuitively. The total number of cases is 35, 6 PBL cases multiplied by 6 equator cases and excluding the solved case.

The 6 PBL cases are the same as those used in Ortega for the 2x2, plus the case for all corners permuted. Ignoring the corners there are 3 equator cases can each be solved with either ( ), (R) or (F R), but if you solve the equator while preserving corner permutation there is a 1/2 chance you will have a "parity" of sorts where the corners are on the wrong end of the puzzle. This can be solved with R E2 R or avoided by learning an alternate set of PBL+equator algorithms. I'm not sure how to recognise that you have parity before permuting all these pieces but if a method for that is devised it would be possible to plan face+parity in inspection rather than just planning the face. With this you could one-look the puzzle using 17 algorithms.

#### Ian Brown

##### Member
Not counting algs for the first face as it is easy enough to solve intuitively. The total number of cases is 35, 6 PBL cases multiplied by 6 equator cases and excluding the solved case.

The 6 PBL cases are the same as those used in Ortega for the 2x2, plus the case for all corners permuted. Ignoring the corners there are 3 equator cases can each be solved with either ( ), (R) or (F R), but if you solve the equator while preserving corner permutation there is a 1/2 chance you will have a "parity" of sorts where the corners are on the wrong end of the puzzle. This can be solved with R E2 R or avoided by learning an alternate set of PBL+equator algorithms. I'm not sure how to recognise that you have parity before permuting all these pieces but if a method for that is devised it would be possible to plan face+parity in inspection rather than just planning the face. With this you could one-look the puzzle using 17 algorithms.
What do you mean by equator cases? Also, the CP algorithms in the first post (also in the pdf) preserve the equator layer pieces, so equator cases can be predicted before Corner Permutation.

##### Member
I see some similarities between this and a .pdf I put together named: MiniTowerCuboid
(though I oriented it with an M layer instead of an E layer)

I'll check out your algs and dig out my 2x2x3 again! Thanks!

I am also interested in a low count one-look set of algs, if discussion on that continues.

#### Ian Brown

##### Member
I see some similarities between this and a .pdf I put together named: MiniTowerCuboid
(though I oriented it with an M layer instead of an E layer)

I'll check out your algs and dig out my 2x2x3 again! Thanks!

I am also interested in a low count one-look set of algs, if discussion on that continues.

Hello, glad to know who created that document because I remember seeing it after creating my speed method and noticed similarities as well. The approach seems similar but I notice that those corner permutation algorithms affect the middle layer which unfortunately means it’s nearly impossible to 1-look. also there seems to be no Algorithm for the case where a diagonal swap occurs on one face, and an adjacent swap occurs on another. I would love to hear further suggestions and encourage everyone visiting this thread to view the pdf.

#### WoowyBaby

##### Member
I have made a method that people have told me is much better than orient, CP, E-layer, which most people think of.

From the New Method / Concept Thread, back in April 2019.
Here I present a method way better than what is currently done....... for the Tower Cube 2x2x3 lol.

Seriously though, most people do Seperate -> PBL -> E-layer which is not as good as this method I made-

Steps:
Left Block-
A 1x2x2 block, 2 corners 2 edges, on the down-left. Looks sort of like Roux FB. This is pretty easy to see in inspection, average ~3 moves. You can even predict the next step, which is:
R Pair- Simply a pair. Usually RB. Can be RF pair as well, but you would have to rotate before final step. After this step it should look like F2L-1. This step is actually really easy to recognize, averages ~3 moves, and is entirely 2-gen
-Combining these steps in one makes this a two step method
PL5C- Permute Last Five(5) Pieces. This step only has 8 total algorithms, which means its very realistic to learn, even for puzzle that's not official. Most of these are somewhat short. I should note that this step has WAY easier recognition than E-layer, the last step of the method most people use.
PL5C Algs:
Diag Top- R2 U' R2' U' R2 U R2' D' R2 U R2' U' R2 D R2'
Adj. Top- R2 U R2' U' R2 U' D R2' U' R2 U R2' D'
Opp. Front- R2 U2 R2' U' R2 U' R2'
Opp. Right- y' R2' U2 R2 U R2' U R2
Bar Front- D' R2 U R2’ U' R2 D R2’
Bar Right- (U) R2' D' R2 U R2' U' R2 D
Diagonal- R2 U R2' F2 U' R2 U R2' U F2
Basically Solved- R2 U R2' U' R2 D R2' u' R2 U R2'
Average movecount: 9.033

Pros:
- movecount <16
- algcount <10
- Fast recognition
- Fairly easy to predict R Pair in inpection
- Great ergonmics, R Pair is 2-gen and PL5C has fast algs.
- PL5C is better than PBL
- Cool blocks (subjective)
- Rotationless solve

EXAMPLE SOLVES:
Scrambles from cstimer, under LxMxN

Scr: D2 F2 D' F2 U R2 U' F2 D F2 U'
z2
u2 R2 D' // Left Block + R Pair (3)
U2 R2 D' R2 U R2 U' R2 D // PL5C (9)

Scr: R2 U2 R2 U R2 D F2 U' R2 D F2
y’
u’ R2 u R2 u’ // Left Block + R Pair (5)
R2 U R2 U R2 U2 R2 U // PL5C (7)

Scr: R2 U R2 U F2 U2 R2 D' R2
z2
u R2 u2 // Left Block (3)
R2 U R2 // R Pair (3)
U’ R2 U R2 U' R2 U' D R2 U' R2 U R2 D’ U’ // PL5C (15)

Scr: U' R2 U D2 R2 U' F2
y’
E2 R2 D’ // Left Block (3)
R2 U2 R2 U R2 U2 R2 U’ // Pair + PL5C (8)

I am aware this isn't an official event, but it can still be fun to be fast. Have fun with this method!

Main points:
- Only 8 algorithms
- Very good look lookahead/recog
- Two-lookable
- Great ergonomics
- Completely rotationless

----------------------------------------------------------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------------------------------------------------------------------------------------------------

More related to your own idea (I'll stop being arrogant about my own ideas lol),
I am able to generate all of these algorithms for this 1-step idea you have.

Here they are: (Well, except not)

E-Layer Solved:
Solved Corners - Done!
Double Diagonal - F2 U2 R2 U2 R2 U2 F2
Double Adjacent - R2 U R2 U' D' R2 D R2
Diag Top Adj Bot - R2 U R2 U2 R2 U' R2 U' R2 U R2
Top Diagonal - R2 U' R2 U' R2 U R2 D' R2 U R2 U' R2 D R2
Top Adjacent - R2 U R2 U' R2 U' D R2 U' R2 U R2 D'
E-Layer off by an R2 Move:
Solved Corners - R2 U2 R2 U2 R2
Double Diagonal - F2 U' D F2 R2
Double Adjacent - R2 U F2 D2 R2 U R2 F2
Diag Top Adj Bot - R2 U' R2 U R2 U' R2 U R2
Top Diagonal - R2 U R2 U' R2 U2 D' R2 U R2 U' R2 D R2
Top Adjacent - R2 U R2 U' F2 U R2 U R2 U2 F2 R2
Tip: Do the reverse of the alg to see what it looks like when you do it.

I only genned 2 out of the 6 or so sets because I don't feel like doing them all now, but still, I hope this is helpful in some way!

If you want me to make the rest of them just ask, and have fun with tower cube!

#### Ian Brown

##### Member
I have made a method that people have told me is much better than orient, CP, E-layer, which most people think of.

From the New Method / Concept Thread, back in April 2019.

Main points:
- Only 8 algorithms
- Very good look lookahead/recog
- Two-lookable
- Great ergonomics
- Completely rotationless

----------------------------------------------------------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------------------------------------------------------------------------------------------------

More related to your own idea (I'll stop being arrogant about my own ideas lol),
I am able to generate all of these algorithms for this 1-step idea you have.

Here they are: (Well, except not)

E-Layer Solved:
Solved Corners - Done!
Double Diagonal - F2 U2 R2 U2 R2 U2 F2
Double Adjacent - R2 U R2 U' D' R2 D R2
Diag Top Adj Bot - R2 U R2 U2 R2 U' R2 U' R2 U R2
Top Diagonal - R2 U' R2 U' R2 U R2 D' R2 U R2 U' R2 D R2
Top Adjacent - R2 U R2 U' R2 U' D R2 U' R2 U R2 D'
E-Layer off by an R2 Move:
Solved Corners - R2 U2 R2 U2 R2
Double Diagonal - F2 U' D F2 R2
Double Adjacent - R2 U F2 D2 R2 U R2 F2
Diag Top Adj Bot - R2 U' R2 U R2 U' R2 U R2
Top Diagonal - R2 U R2 U' R2 U2 D' R2 U R2 U' R2 D R2
Top Adjacent - R2 U R2 U' F2 U R2 U R2 U2 F2 R2
Tip: Do the reverse of the alg to see what it looks like when you do it.

I only genned 2 out of the 6 or so sets because I don't feel like doing them all now, but still, I hope this is helpful in some way!

If you want me to make the rest of them just ask, and have fun with tower cube!
Thanks for sharing this. This looks like a really good speed method yet I suppose an advantage of mine is the one-look ability and perhaps slightly more intuitive nature. Anyway, I wasn’t even aware of this method so it looks like there are 2 good alternatives to the bad way most people solve 2x2x3, further reason to add this as WCA event.

#### ProStar

##### Member
Thanks for sharing this. This looks like a really good speed method yet I suppose an advantage of mine is the one-look ability and perhaps slightly more intuitive nature. Anyway, I wasn’t even aware of this method so it looks like there are 2 good alternatives to the bad way most people solve 2x2x3, further reason to add this as WCA event.

You didn't actually invent a new method, everyone does white/yellow, permute top/bottom layers, permute middle layer. And multiple methods isn't a real reason to add it to the WCA, you can come up with different methods for any puzzle.

#### Ian Brown

##### Member
You didn't actually invent a new method, everyone does white/yellow, permute top/bottom layers, permute middle layer. And multiple methods isn't a real reason to add it to the WCA, you can come up with different methods for any puzzle.
No, the algorithms are different (arguably faster because no F moves) and and they also preserve the equator, so it’s possible to one-look. Also on 2x2x3 CP is typically done on each of the outer layers separately as opposed to both simultaneously, somtimes CP is only done for one layer, while the other layer is solved fully while doing the square faces. Further, all 7 possible EP cases are not recognized with their own algorithms by standard. This new method is about as different from the origianl way of solving 2x2x3 as Ortega is from LBL on a 2x2. Anyway I guess you can refrain from calling it a new method if you don’t want to, but it really is different.

Also this thread isn't a serious call to have 2x2x3 added to the WCA, I just thought I’d mention that I’d like to see it added eventually.

Last edited:

#### Ian Brown

##### Member
I just thought I'd mention this: To avoid ever having the diagonal top - diagonal bottom CP case, you can make sure to make a correct pair of corners on either yellow or white when initially solving the square faces. This takes more planning but reduces CP from 5 cases to 4.

#### ProStar

##### Member
I just thought I'd mention this: To avoid ever having the diagonal top - diagonal bottom CP case, you can make sure to make a correct pair of corners on either yellow or white when initially solving the square faces. This takes more planning but reduces CP from 5 cases to 4.

Diagonal top diagonal bottom is the best case ever, it's just R F R. Predicting E layer is still easy because it's just a flipped version

#### Ian Brown

##### Member
Diagonal top diagonal bottom is the best case ever, it's just R F R. Predicting E layer is still easy because it's just a flipped version
It’s not RFR, it’s (R U D R) U2 (R U’ D’ R). Doing this algorithm is better than RFR because it preserves the equator layer, the algorithm is also faster than it may seem because U and D moves would ideally be performed simultaneously. Plus, even having the equator pieces flipped with RFR like you said is still bad because it’s difficult to predict the more complicated EP cases.

Also, you don't have to do the technique in order to avoid the case, however some people may want to trade extra initial move prediction in exchange for lessening the number of possible CP cases.

Last edited:

#### ProStar

##### Member
I still think doing "squares"->cube wouldn't be that hard or take too many algs, and it would be simple to 1-look. Also the problem of having AUF cases is easily solved by just doing a couple E moves.

#### seagullboy225

##### Member
this is true, real cubers know when to simplify a method. Or you could do the Schrodinger cube method which actually would lower your cube outtake to 27 mph instead of having to deal with AUF cases. Clearly none of you have been to the Blingingsmith International Academy of Cubing.