# Cubeshape Last Square-1 Method



## Kirjava (Nov 12, 2015)

Hey guys.

I've not been around much recently. I got a really cool new job and I've been focused on my career. I do a lot of programming now.

The ideas in this thread have been around for years, but I never posted because it wasn't complete. I realised the nature of the method is going to require anyone wanting to learn it to do their own development. I'm not going to learn it anytime soon, so I'm committing my ideas here to see if anyone can do something with them.

There are some attributes of this system that make me think it's a contender against cubeshape-first methods, but I don't know. There are a few issues that need to be worked out before we really know for sure.

Anyone wanting to learn this should know that it is going to end up being pretty alg heavy if you want to get fast.

However, you should be able to get decent with just one CO shape, a few edge algs and PBL.

I've been told doing algs in non-cubeshape is weird for people experienced in square-1.

Be warned, my documentation of this is very unclear and incomplete.

This pretty much exists because solving cubeshape last is my kind of idea of a kind of holy grail for methods. However, I don't solve square-1. In fact, a large amount of time during development I couldn't solve a square-1 at all - which didn't help. Andrew Nelson helped me a lot working on this. cubizh made a definition file and possibly generated some algs. Meep might've done something too.

Now, just making a method that circumvents cubeshape for the sake of it is cheating. If there's a point where 'just going to cubeshape and continuing' is obviously a better solution it doesn't really count.

There are of course variations of this method that will solve cubeshape + some other stuff to solve. The best is definitely cubeshape + COCP leaving you with edges to solve. This might defeat my cheating clause, but then you'd be missing out on the lovely way to deal with parity...

Here are the steps;


Edge Deisolation
Corner Orbit Resolution
Corner-Edge Block Pairing (& Parity)
Cancel into PBL

Edge Deisolation

The idea of this step is to ensure edges are always located in groups of two. This puts you in a state that more easily allows you to manipulate pieces in non-cubeshape.

Here's an image showing all valid and invalid shapes;







After this step you end up with 12 corners from 8 real corners and 4 pseudo corners.

This step is intuitive.

Corner Orbit Resolution

In this step, the plan is to fix corner orbits such that on return to cubeshape, corners will be separated correctly and in their respective layers. The algs need to get you to a known shape for step 3.

The thing about cubeshape last is that there will be no end of algs to learn. So far because of the sheer size of it we have only explored a single shape for step 3 and a few different types of shapes for step 2 /for/ that step 3 shape. This step is very alg heavy.

It's probably smarter to learn certain shapes first to reduce twistcount. Shield/Scallop seems a good starting point. Many different tricks and techniques in this stage are able to be explored. If you can work out a way of detecting parity here, you can solve it in a single twist. (!)

Corner-Edge Block Pairing

The aim of this step is to reduce to 2x2x1. So far I have only researched a single shape so I'll talk about that, but others may be feasible.

Currently my system for this is solve 3/4 edges (surprisingly these usually take a single twist or so because of the freedom) first, then solve the rest 2/3/4 edges at a time with algs.

This step has a bit of a mix of algs and intuition. Someone wanting to use this system will want to create a strong edge solving structure.

Since we've not resolved cubeshape yet, we can take a advantage of a few things that would not be possible otherwise. Corners are not fixed to their positions, this makes algs very short. I have found 3 twist 3cycles and 2 twist 2x2cycles.

This and the inherent nature of the shape makes solving parity a lot easier.

In this shape parity is 3 twists, and the pure version is 5.

Cancel Into PBL

Now cancel into PBL.

What follows are all the resources I and Andrew have collected so far. Algs, ksolve definition files, and an example solve.

KSolve Definitions


```
Name Preisolation

# CW from UF then DB
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Set EDGES 24 1

Solved
EDGES
1 1 1 1 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 1 1 1 1
End

Move U
EDGES
12 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24
End

Move D
EDGES
1 2 3 4 5 6 7 8 9 10 11 12 24 13 14 15 16 17 18 19 20 21 22 23
End

Move /
EDGES
1 2 3 4 5 6 19 20 21 22 23 24 13 14 15 16 17 18 7 8 9 10 11 12
End

Block
EDGES
2 3
End
```


```
HTM

Scramble test2
EDGES
1 1 1 1 2 3 2 3 2 3 2 3 2 3 2 3 2 3 1 1 1 1 2 3
End
```


```
Name Sq1_deisolated

# CW from UF then DB
# 3 3 2 1 2 1 2 1 2 1 3 3
# 1 3 3 2 1 2 3 3 2 1 2 1
# Kirjava
Set CORNERS 12 1

Solved
CORNERS
3 3 2 1 2 1 2 1 2 1 3 3
End

Move U
CORNERS
6 1 2 3 4 5 7 8 9 10 11 12
End

Move D
CORNERS
1 2 3 4 5 6 12 7 8 9 10 11
End

Move /
CORNERS
1 2 3 10 11 12 7 8 9 4 5 6
End

Ignore
CORNERS
1 1 0 0 0 0 0 0 0 0 1 1
End
```


```
#?3 ?3 2 1 2 1 2 1 2 1 ?3 ?3

HTM
Scramble test1
CORNERS
2 ?3 ?3 1 2 2 1 2 ?3 1 1 ?3
End
```


```
Name Sq1_barrel

# def-file by cubizh ?
# Layout: http://i.imgur.com/tMCVYzA.png
Set EDGES 24 1

Solved
EDGES
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
End

Move U
EDGES
12 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24
End

Move D
EDGES
1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 13
End

Move /
EDGES
1 2 3 4 5 6 24 23 22 21 20 19 13 14 15 16 17 18 12 11 10 9 8 7
End

Block
EDGES
2 3
End

Block
EDGES
4 5
End

Block
EDGES
8 9
End

Block
EDGES
10 11
End

Block
EDGES
14 15
End

Block
EDGES
16 17
End

Block
EDGES
20 21
End

Block
EDGES
22 23
End

Ignore
EDGES
1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1
End
```


```
HTM

Scramble test2
EDGES
13 2 3 4 5 ?6 1 8 9 10 11 ?12 7 14 15 16 17 ?18 7 20 21 22 23 ?24
End
```


```
Name Sq1_pbl

# 12 56
# 43 87
# Kirjava
Set CORNERS 8 1

Solved
CORNERS
1 2 3 4 5 6 7 8
End

Move U
CORNERS
4 1 2 3 5 6 7 8
End

Move D
CORNERS
1 2 3 4 8 5 6 7
End

Move /
CORNERS
1 6 7 4 5 2 3 8
End
```


```
#?3 ?3 2 1 2 1 2 1 2 1 ?3 ?3

QTM
Scramble test1
CORNERS
1 2 4 3 5 6 7 8
End
```

Algs

Step 2;

(this is very unclear, I know)


```
a)     YWY at DL

b)     W at DF (33XXXX Scallop on top)

        YWYW Solved
        YWWY U / U' / U2' /
        WYYW U' / U2 / U' /
        WYWY U' / D2' U2 / U2' /
        WWYY / D / U2' / D' /
        YYWW / U / U2' /

    Y at DF (33XXXX Scallop on top)

        YWWW U / U2 / U2' /
        WYWW / U2 / U2 / U2 /
        WWYW U3 / U2 / U
        WWWY D' / D / U2'

    W at DF (3X3XXX Shield on top)

        Y WYW D' U2' / D / U' /
        Y WWY D2' / U / U2 /
        W YYW U' / U2 / U / U2' /
        W YWY / U' / U / U2 /
        W WYY D / U' / U2' /
        Y YWW U2' / D2 / D /

    Y at DF (3X3XXX Shield on top)
    time
        Y WWW U' / U' / U' /
        W YWW D' U2 / D U2 /
        W WYW U2 / U' / U / U2 /
        W WWY / U' / U' / U

    W at DF (XX3XX3 Barrel on top)
    Y at DF (XX3XX3 Barrel on top)
```

Step 3;

-1,1 / -2,2 / 2,-1 / <- parity

(-1,1) / (-4,2) / (4,-2) / (1,-1) / (-5,1) / <- pure parity

D' / D / U' / (U) - 3 cycle (UFL - UFR - DBL)

U / D' U' / (D) - 2x2 cycle (UBL - UFR / etc)







```
cw U perms
6->7->12
1,0 / -1,5 / 1,0 / 0,-1 / 0,1 / 0,-5 / -1,0
7->12->1
-1,0 / 0,-5 / 0,1 / 0,-1 / 1,0 / -1,5 / 1,0
12->1->6
1,0 / 5,-1 / 1,0 / -1,0 / 0,1 / -5,0 / 1,0
1->6->7
-1,0/ -5,0 / 0,1 / -1,0 / 1,0 / 5,-1 / 1,0

ccw U perms

(Just reverse the previous algs)


6<->7; 1<->12 (E perm)

1,0 / -1,-1 / 0,1 / -1,-1 / 2,1 / -1,-1 /

  U / U' / U' / U / D' / U / U' / D /
  U / D' U' / U' / D U / U / D' U' / D
  U / D' U' / U' / D U / D' / D U / U'
  U / D' U' / D / D' U' / U / D U / U'
  U / D' / U' / D / D' / D / U' / U /
  U' / U / U / U' / D / U' / U / D' /
  U' / D U / U / D' U' / U' / D U / D'
  U' / D U / U / D' U' / D / D' U' / U
  U' / D U / D' / D U / U' / D' U' / U
  U' / D / U / D' / D / D' / U / U' /
  D U / D' U' / U' / D U / U / D' U' /
  D / D' U' / U / D U / U' / D' U' / U
  D' U' / D U / U / D' U' / U' / D U /
  D' / D U / U' / D' U' / U / D U / U'
  / U / U' / U' / D U / U' / U / D' /
  / U / U' / D / D' U' / D / U / D' /
  / U / U' / D / D' / D / U' / D' / U
  / U' / U / U / D' U' / U / U' / D /
  / U' / U / D' / D U / D' / U' / D /
  / U' / U / D' / D / D' / U / D / U'
  / D U / U' / D' U' / U / D U / D' U'
  / D U / U' / D' U' / D U2 / D' U' /
  / D U / D' U2' / D U / U / D' U' /
  / D / U' / U / D' U' / U / U / U' /
  / D / U' / U / D' / U / U' / U' / U
  / D / U' / D' / D U / D' / U / U' /
  / D' U' / U / D U / U' / D' U' / D U
  / D' U' / U / D U / D' U2' / D U /
  / D' U' / D U2 / D' U' / U' / D U /
  / D' / U / U' / D U / U' / U' / U /
  / D' / U / U' / D / U' / U / U / U'
  / D' / U / D / D' U' / D / U' / U /


6<->12; 1<->7 (X perm)

  D U / U5 / D' / U / U2' / D / D' / D U4' / D' U'
  D U / D4 U' / D / U' / U2 / D' / D / D5' / D' U'
  D U / D5 / D' / D / U2' / U / D' / D4' U / D' U'
  D U / D' U4 / D / D' / U2 / U' / D / U5' / D' U'
  D / U5 / D2 U / D' / U' / D / D2' / U5' / D'
  D / U5 / D2 / D' / U / D / D2' U' / U5' / D'
  D / D5 / D2 U / U' / U' / U / D2' / D5' / D'
  D / D5 / D2 / U' / U / U / D2' U' / D5' / D'
  D' U' / U5' / D / U' / U2 / D' / D / D' U4 / D U
  D' U' / D U4' / D' / D / U2' / U / D' / U5 / D U
  D' U' / D5' / D / D' / U2 / U' / D / D4 U' / D U
  D' U' / D4' U / D' / U / U2' / D / D' / D5 / D U
  D' / U5' / D2' U' / D / U / D' / D2 / U5 / D
  D' / U5' / D2' / D / U' / D' / D2 U / U5 / D
  D' / D5' / D2' U' / U / U / U' / D2 / D5 / D
  D' / D5' / D2' / U / U' / U' / D2 U / D5 / D
  / D U / U5 / D' U' / U6 / D U / U / D' U' /
  / D U / U' / U6 / D' U' / D U5' / U / D' U' /
  / D U / U' / D5 U' / D U / D6 / U / D' U' /
  / D U / U' / D6 / D' U' / D5' U / U / D' U' /
  / D U / U' / D' U5 / D U / U6 / U / D' U' /
  / D U / U' / D' U' / U6 / D U / U5' / D' U' /
  / D U / U' / D' U' / D U5' / D' U' / D U4' / D' U' /
  / D U / D' U4 / D U / D' U5 / D U / U / D' U' /
  / D' U' / U / U6 / D U / D' U5 / U' / D U /
  / D' U' / U / D U / U6 / D' U' / U5 / D U /
  / D' U' / U / D U / D' U5 / D U / D' U4 / D U /
  / D' U' / U / D U5' / D' U' / U6 / U' / D U /
  / D' U' / U / D6 / D U / D5 U' / U' / D U /
  / D' U' / U / D5' U / D' U' / D6 / U' / D U /
  / D' U' / U5' / D U / U6 / D' U' / U' / D U /
  / D' U' / D U4' / D' U' / D U5' / D' U' / U' / D U /
```







```
4->10->9 (Ccw U perm)
/ 2,-3 / 0,1 / 0,-1 / 1,0 / -3, 3 /

4->9->10 (Cw U perm)
/ 3,-3 / -1,0 / 0,1 / 0,-1 / -2.3 /

3<->4; 9<->10 (Vertical E perm)
/ 3,3 / 1,0 / -1,-1 / 0,1 / -3,-3 /
/ 3,3 / 0,-1 / 1,1 / -1,0 / -3.-3 /
/ -3,-3 / -1,0 / 1,1 / 0,-1 / 3,3 /
/ -3,-3 / 0,1 / -1,-1 / 1,0 / 3,3 /

4<->9; 3<->10 (E perm)

  / D2 U3' / D / U' / D U / U' / U / D4' U3 /
  / D2 U3' / D / D / D' U' / D / U / D4' U3 /
  / D3 U4' / U / U / D' U' / U / D / D3' U2 /
  / D3 U4' / U / D' / D U / D' / D / D3' U2 /
  / D3 U2' / D' / U' / D U / U' / U' / D3' U4 /
  / D3 U2' / D' / D / D' U' / D / U' / D3' U4 /
  / D4 U3' / U' / U / D' U' / U / D' / D2' U3 /
  / D4 U3' / U' / D' / D U / D' / D' / D2' U3 /
  / D4' U3 / U / U' / D U / U' / D / D2 U3' /
  / D4' U3 / U / D / D' U' / D / D / D2 U3' /
  / D3' U2 / D / U / D' U' / U / U / D3 U4' /
  / D3' U2 / D / D' / D U / D' / U / D3 U4' /
  / D3' U4 / U' / U' / D U / U' / D' / D3 U2' /
  / D3' U4 / U' / D / D' U' / D / D' / D3 U2' /
  / D2' U3 / D' / U / D' U' / U / U' / D4 U3' /
  / D2' U3 / D' / D' / D U / D' / U' / D4 U3' /


4<->10; 3<->9 (X perm)

  / -3,2 / 0,1 / -1,0 / 2,0 / 0,-1 / 0,1 / 2,-3 /
  / -2,3 / 0,-1 / 0,1 / -2,0 / 1,0 / 0,-1 / 3,-2 /
  / 2,-3 / 0,1 / 0,-1 / 2,0 / -1,0 / 0,1 / -3, 2 /
  / 3,-2 / 0,-1 / 1,0 / -2,0 / 0,1 / 0,-1 / -2,3 /


 / -1,0 / 1,0 / 1,0 /
```

Example Solve


```
(3,-1) / (0,1) / (-3,6) / (2,1) / (-2,-3) / (2,6) / (0,6) / (-2,-1) / (-4,2) / (-2,6) / (1,2) / (-1,0) / (0,-3) / (-2,5) / (-2,-3) /

edge deisolation:

6,2 / -5,4 / -3,-2 / 0,2 / 1,0

corner orbit resolution (+ reaching selected pairing state)

/ 2,0 / 0,-2 / 4,-2 / 4,0 /

edge pairing (stage needs most improvement)

parity
/ 2,-4 / -2,4 /
easy
4,1 / 1,1 / 1,-1 / -1,-1 /
2-2 cycle
-3,4 / -4,3 / 1,0 / 1,0 /
3 cycle
-1,6 /
1,0 / 5,-1 / 1,0 / -1,0 / 0,1 / -5,0 / -1,0

mini domino esque 2x2x1 pbl

/ -3,0 / 3,-3 / 6,0 / -1,-5

22:59 < Kirjava_> so doing an example solve in a method that doesn't exist on a puzzle you can't solve
22:59 < Kirjava_> is ****ing hard
```


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## bobthegiraffemonkey (Nov 13, 2015)

I remember you talking about this at some comp a while back, always wondered what it would look like in full. I'd be interested to see someone fill in the details, I would do it myself but I'm already invested in a different type of sq-1 experimental method to solve parity and cubeshape from inspection. Maybe it would be useful to combine the ideas, to get to (say) barrel/barrel and already know what parity you will get there?


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## shadowslice e (Nov 13, 2015)

This looks interesting. I will probably look into this once I've finished the new 3x3x3 method I making (just videos to go tho)

How do you think this will go combined with CP? I think it will be hell to execute but potentially pretty efficient.


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## stoic (Nov 13, 2015)

Hey look!
Kir's not dead after all.







Cool idea, too.


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## shadowslice e (Nov 13, 2015)

An interesting simplification of this method could be to reduce to a certain shape (or set of shapes) and then solve it like that before cubing it.

For clarification, we would have to go through each of the shapes in a similar way to RoFL before coming out with perhaps the best variation of them like how TCLL was decided on.

This will probably take a fair bit of work but would drastically reduce the alg count of this method As well as potentially being a lot more efficient than standard cube shape.

Just a thought that may be worth investigation. What does everyone else think?


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## BananaSlayer64 (Nov 14, 2015)

Kir's back! [emoji14]
This looks like a really interesting method.


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## Praetorian (Nov 14, 2015)

is the idea of making new methods to be different or to be more efficient


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## shadowslice e (Nov 14, 2015)

Praetorian said:


> is the idea of making new methods to be different or to be more efficient


Both. If you are going to convince anyone to use a new method it must be more efficient than the previous ones or provide some other benefit like increased ergonomics/freduced alg sets etc.

I guess most method creators also want to be different in some way.

Sent from my M1005D using Tapatalk


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