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2x2 Pseudo Solving: Improving CLL and EG

Athefre

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http://sites.google.com/site/athefre/

The common way to start a 2x2 solve is by building a face or layer. To take this further, you can pseudo build so that they contain pieces from separate layers. At first it isn't that intuitive. A good strategy is to find a first pair and add to it. Below is a list of first pair types:
1. FDL+FRD opposite, DLF+RDF same, LFD+DFR opposite
2. FDL+FRD opposite, DLF+RDF opposite, LFD+DFR same
3. FDL+FRD opposite, DLF+DFR same, LFD+RDF same
4. FDL+FRD same, DLF+DFR same, LFD+RDF opposite
5. FDL+FRD opposite, DLF+DFR opposite, LFD+RDF opposite
6. FDL+RDF opposite, DLF+FRD same, LFD+DFR same
7. FDL+RDF opposite, DLF+FRD opposite, LFD+DFR opposite
8. FDL+RDF opposite, DLF+DFR same, LFD+FRD opposite
9. FDL+RDF opposite, DLF+DFR opposite, LFD+FRD same
10. FDL+RDF same, DLF+DFR opposite, LFD+FRD opposite
11. FDL+DFR opposite, DLF+FRD same, LFD+RDF opposite
12. FDL+DFR same, DLF+FRD opposite, LFD+RDF opposite
13. FDL+DFR same, DLF+RDF same, LFD+FRD opposite
14. FDL+DFR opposite, DLF+RDF opposite, LFD+FRD opposite

Some pairs equal another. Rotate the cube and its second identity is shown.

1=9, 2=10, 4=4, 5=5, 7=7, 11=11, and 12=12. The rest have no meaningful second form.
There are 14 options for the first pair. I haven't yet encountered a scramble where there wasn't already multiple usable pairs. Almost every two connected corners can be used.

With the first pair chosen, there are several possible pair combinations to complete the face or layer. They are listed below. Parentheses around a number means that pair needs swapped. Parentheses around the plus sign means one of the two unlabled pairs needs swapped.
(1)+(1)
(1)+12
(2)+(2)
(2)+11
(3)+(3)
(3)+4
4+4
5+5
(5)+5
(5)+(5)
6(+)14
7(+)13
8(+)8
9(+)10
11+11
12+12
Pretty much you can simplify all of this to a couple of rules. The face must have two or fewer D colors and the pairs must have opposite LR colors. In all of the above images, LR is blue/green.

Scramble: R U' F' R' U' F2 U' F2 R
Layer: y x' F2 U' R
CLL: U L' U L F' U2 L2 F' L' U L

Scramble: F2 R' F R' F2 U R F R2
Layer: x y U B'
CLL: U2 L U2 L' U2 L' B L B' U' R'

Scramble: R2 F2 R U R U2 F2 R' U'
Face: y' x' U' R'
EG1: U R' U2 R' U2 R' U' R2 U' R

Scramble: U F R F2 U2 F' U2 F U2
Face: x' U2 L'
EG1: R' U2 R U' R2 U R' U R2

Scramble: U' F2 U' F2 U R F2 R'
Face: y x2 U' R2
EG1: R' F U2 R2 F R' U' F'

Scramble: U R2 F2 R' F2 U2 R' U'
Face: x' y F'
EG1: U' R2 U R' U2 R2 F R

Scramble: F2 R F' R' U F' R' U
Face: x U R2
EG2: U F R F' U R2 F' R U'

Scramble: U2 R F U' F R' U2 R2 U'
Face: x' F
EG2: U R2 B2 R' U2 R' U' R U' R' U R'
As you can see, this increases your options during inspection to improve move count and help lead to one look solves. The time investment will be adjusting to a new type of recognition and learning to see various types of pairs.
 

Escher

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I've been doing this for double-layer only turns for a couple years, but I never branched out into your crazy non-matching system :p

Might take a look at doing this at some point.
 

CuberMan

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nice post! haha I also already discovered about pseudo first layer a couple months ago, but I think it was too hard to recognize and also hard to track one look solve under 15 seconds inspection using pseudo... it need LOTS of practice
 

Athefre

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Holy shiitake mushrooms! This looks fast.
But does this mean I need to learn EG all over again?
You can use all of your current algorithms. The big change is that you would need to associate additional recognition with each alg.


I've been doing this for double-layer only turns for a couple years, but I never branched out into your crazy non-matching system :p

Might take a look at doing this at some point.
I've been meaning to complete this for about five years, but I kept stupidly applying it to 3x3 and putting it off for whatever other reason.
 

Athefre

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I provided a link at the top of the first post.

If it isn't displaying correctly for you, let me know.
 
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Scramble: R U' F' R' U' F2 U' F2 R
Layer: y x' F2 U' R
CLL: U L' U L F' U2 L2 F' L' U L

My CLL would be RUR'URUL'UR'U'L but than I still need U2 R2 for separation,

So U L' U L F' U2 L2 F' L' U L is no CLL after all ... what is it that I don't understand?
 

Athefre

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Scramble: R U' F' R' U' F2 U' F2 R
Layer: y x' F2 U' R
CLL: U L' U L F' U2 L2 F' L' U L

My CLL would be RUR'URUL'UR'U'L but than I still need U2 R2 for separation,

So U L' U L F' U2 L2 F' L' U L is no CLL after all ... what is it that I don't understand?
L' U L F' U2 L2 F' L' U L' is the CLL. In my case, there was no final AUF and the last move of the CLL, L', canceled with the layer adjustment that would have been L2.
 
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