completely algorithmic 2x2 method idea

[hiyouhavepolio]

step 1: solve cpline at DL (~100 cases)
step 2: 2gen finish (~1850 cases)
idk how optimal this is compared to other methods

cpline

Pattern Corner Permutation (PCP)

docs.google.com

2gen finish

https://docs.google.com/spreadsheets/d/1dX8hIRg0JYK5Yki3QUwWZORTZyqhkVgt7RjFP-3WwiI/edit?gid=351709441#gid=351709441

 

[bldcuber314]

step 1: solve cpline at DL (~100 cases)
step 2: 2gen finish (~1850 cases)
idk how optimal this is compared to other methods

cpline

Pattern Corner Permutation (PCP)

docs.google.com

2gen finish

https://docs.google.com/spreadsheets/d/1dX8hIRg0JYK5Yki3QUwWZORTZyqhkVgt7RjFP-3WwiI/edit?gid=351709441#gid=351709441

Can't access the doc, (you need to change the access settings)

 

[Kami]

why not just learn 2 billion algs and learn every case of 2x2

 

[CubeLite]

why not just learn 2 billion algs and learn every case of 2x2

actually, there are only 3.6 million cases on 2x2

 

[Garf]

actually, there are only 3.6 million cases on 2x2

doable. just have to commit a lifetime

 

[CubeLite]

doable. just have to commit a lifetime

Someone learnt all LL algs for 3x3, but then you remember, literally like zayn, he probably knows over 5000 algs, maybe less, and he can like cancel on any scrambles

 

[Herbert Kociemba]

actually, there are only 3.6 million cases on 2x2

Actually you can rotate the 2x2 to 24 different positions so presumably there are less than 200000 essential different cases. Peanuts!

 

[Garf]

Actually you can rotate the 2x2 to 24 different positions so presumably there are less than 200000 essential different cases. Peanuts!

Wait that’s actually doable. @abunickabhi

 

[Twisted101]

step 1: solve cpline at DL (~100 cases)
step 2: 2gen finish (~1850 cases)
idk how optimal this is compared to other methods

cpline

Pattern Corner Permutation (PCP)

docs.google.com

2gen finish

https://docs.google.com/spreadsheets/d/1dX8hIRg0JYK5Yki3QUwWZORTZyqhkVgt7RjFP-3WwiI/edit?gid=351709441#gid=351709441

This method except u have to learn ~2000 algs

 

[Averageof12]

step 1: solve cpline at DL (~100 cases)
step 2: 2gen finish (~1850 cases)
idk how optimal this is compared to other methods

cpline

Pattern Corner Permutation (PCP)

docs.google.com

2gen finish

https://docs.google.com/spreadsheets/d/1dX8hIRg0JYK5Yki3QUwWZORTZyqhkVgt7RjFP-3WwiI/edit?gid=351709441#gid=351709441

I thought up a method similar to this, except with a slightly different start. Honestly, just learning full LS might even be more practical.

 

[Discomantis]

step 1: solve cpline at DL (~100 cases)
step 2: 2gen finish (~1850 cases)
idk how optimal this is compared to other methods

cpline

Pattern Corner Permutation (PCP)

docs.google.com

2gen finish

https://docs.google.com/spreadsheets/d/1dX8hIRg0JYK5Yki3QUwWZORTZyqhkVgt7RjFP-3WwiI/edit?gid=351709441#gid=351709441

Is there a way to solve CP line (aka 2 gen reduction) without learning algs? I was wanting to learn how to for 2OH cause I think it could potentially be good

 

[Twisted101]

Is there a way to solve CP line (aka 2 gen reduction) without learning algs? I was wanting to learn how to for 2OH cause I think it could potentially be good

Ofc, with yash mehta’s tracing instead of pcp

 

[Discomantis]

Ofc

Would you have a tutorial to this perhaps?

 

[Twisted101]

Would you have a tutorial to this perhaps?

 

[qwr]

Actually you can rotate the 2x2 to 24 different positions so presumably there are less than 200000 essential different cases. Peanuts!

can you use Burnside's Lemma to count cases up to symmetry? as far as I remember, the 3 million number already includes cube rotations

Using Burnside's Lemma in GAP to handle special variations of the Rubik's Cube?

If you want to count the number of distinct positions of a standard 2x2x2 Rubik's Cube simple counting arguments will suffice: There are 8 corners, all distinct The 8 corners can be in any permutat...

math.stackexchange.com

 

[Herbert Kociemba]

can you use Burnside's Lemma to count cases up to symmetry? as far as I remember, the 3 million number already includes cube rotations

Using Burnside's Lemma in GAP to handle special variations of the Rubik's Cube?

If you want to count the number of distinct positions of a standard 2x2x2 Rubik's Cube simple counting arguments will suffice: There are 8 corners, all distinct The 8 corners can be in any permutat...

math.stackexchange.com

You get the three million by fixing for example the DBR corner and use only U, R and F moves so that there are 7! 3^6 =3674160 different cases. But still there are 24 ways which of the 8 corners is the DBR corner and 3 ways which is the D face of this corner so I still think a reduction by a factor of a bit less than 24 (less because of the symmetric positions) is possible. Though I am not 100% sure in the moment, the fixed corner irritates me a bit. But Polya Burnside Lemma would surely be a way to find the exact number of cases up to symmetry by hand.

 

[Athefre]

As pointed out, the method idea has been around for a long time. It is something that I have recently been occasionally thinking about. Below are some ideas that I have been collecting. They are also in the PCP doc.

1. I recently developed a way to intuitively solve the last six corners. It works like Roux LSE, where the corners are iteratively oriented then intuitively permuted. This is a two step process, but still very efficient and is likely pretty close in move count to the 1,800 alg one step version.
   • https://sites.google.com/site/athefre/other/iterative-corner-solving
2. The number of cases can be reduced, and probably ergonomics improved, by imagining a mirror along UR. If the cube is rotated by z x2, a different case can be seen. This means there is now the opportunity to choose between two cases.
3. Keeping the current corner at DBR, the last five corners can be solved relative to the corner at DBR. The sets would be L5C, NML5C, a new thing that would probably be called Conjugated L5C, or twisted versions of those three. The same cube rotation idea can be used here.
4. Really advanced, the last six corners can be solved with CPLine. This sets up the corners so that after the final CPLine moves all corners are solved. L5C, twisted L5C, and conjugated L5C, and rotations, can all be used to greatly reduce the cases.

I don't know if anyone has developed the full 2 gen last six corners alg set as listed in the main post. By that I mean a sorted algorithm sheet with the best algs chosen. It would be nice to have a move count for CPLine then 2Gen.