2x2x2x2 Speed Cubing Algorithms

[connor]

For a while I have been working on a document that has a bunch of algorithms for speed solving the 2x2x2x2 (47 of them!). I personally haven't memorized all of them nor even half of them, but after seeing all the discussion on the 2x2x2x2 surrounding canonical moves I wanted to put out there what I have come up with to help solve the puzzle. These algorithms go along with a method I have been working on but I feel like they could help anyone who is trying to speed solve and is taking a similar approach to me. I also clarified the notations I used for the puzzle so hopefully its clear what all of the document is about. 

Any critique or suggestions are welcome!

- Connor Lindsay

[scarecrowfish]

This is very interesting. I'd never thought that trying to permute all four layers at once would be viable, but I guess it is.

I did notice what I think are a few mistakes in the pdf. I seems to be drawn as I' in the definitions, and some of the PAL cases seem to be missing a U* setup move, such as BBSS. Also, SXBB, XBXX, and SXXS have E* moves in their algorithms, which weren't defined. I presume you mean I*, but it's unclear.

Otherwise, I really like this idea, and I think I'll try to use some of these algorithms in my own solves.

~Luna

[Matthew Hinton]

I'm very glad to see someone put these ideas down on paper, especially since it uses the same kind of system as the Ortega method, which makes a world of sense to me. This is the method I'm going to use, if I can get a physical 2x2x2x2.

[Connor Lindsay]

Thanks for pointing out the mistakes! Halfway through I changed what I was using for the I moves, initially I labeled them E for equatorial like on a 3x3x3 but later changed to I for Inner face to match the other names. 

And yes I’d would happily adapt all the nomenclature to whatever or generally accepted I don’t if there Is any generally accepted nomenclature yet, if there is please let me know so I can adjust the document. I also want to go back through to make all my nomenclature more clear in general that was the last thing I added to the document so it needs the most work. I think what would help most for clarity is a short explanation of what each letter means and why I chose it, so that it makes sense how it relates to the simple rotation it represents. 

Also I’m so glad that it is of some help to people! I haven’t made anything for the full method but hopefully I will soon, Because to me at least this makes the most logical sense. 

On May 28, 2020, at 12:47 PM, Matthew Hinton <mtt...@gmail.com> wrote:



I'm very glad to see someone put these ideas down on paper, especially since it uses the same kind of system as the Ortega method, which makes a world of sense to me. This is the method I'm going to use, if I can get a physical 2x2x2x2.

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[carl.n.hoff]

Regarding nomenclature... I did a little research back in 2016 when I wrote this article for Game & Puzzle Design.   The 6 directions/faces on a 3x3x3 are named:

R=Right

L=Left

F=Front

B=Back

U=Up

D=Down

These equate to the plus and minus directions on the x, y, and z axes.  One of the first books to name the plus and minus directions on the w-axis was "A New Era of Thought" by Charles Howard Hinton in 1888.  He named the positive w-direction as Ana and the negative w-direction as Kata so I've adopted A and K into my own 4D nomenclature.  Not certain how generally this is accepted but its the best thing I found at the time.  By the way, this book is also where the term tesseract first originated.

Carl

On Thursday, May 28, 2020 at 5:42:53 PM UTC-7, connor wrote:

Thanks for pointing out the mistakes! Halfway through I changed what I was using for the I moves, initially I labeled them E for equatorial like on a 3x3x3 but later changed to I for Inner face to match the other names. 

And yes I’d would happily adapt all the nomenclature to whatever or generally accepted I don’t if there Is any generally accepted nomenclature yet, if there is please let me know so I can adjust the document. I also want to go back through to make all my nomenclature more clear in general that was the last thing I added to the document so it needs the most work. I think what would help most for clarity is a short explanation of what each letter means and why I chose it, so that it makes sense how it relates to the simple rotation it represents. 

Also I’m so glad that it is of some help to people! I haven’t made anything for the full method but hopefully I will soon, Because to me at least this makes the most logical sense. 

On May 28, 2020, at 12:47 PM, Matthew Hinton <mtt...@gmail.com> wrote:



I'm very glad to see someone put these ideas down on paper, especially since it uses the same kind of system as the Ortega method, which makes a world of sense to me. This is the method I'm going to use, if I can get a physical 2x2x2x2.

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[Raymond Zhao]

Hi Carl,

I ended up naming the two additional faces T for top and K for kata when I was writing down a 4D CFOP solution with RKT for the 3^4 in MC4D.

In that solution, I would use T to refer to the "inner cell", and K to refer to the "hidden cell".

A and K instead of T and K could work, though I'm wondering which cell would be A, and which one would be K? I arbitrarily chose K to be the hidden cell in my case.

Thanks,

Raymond

[carl.n.hoff]

Raymond,

   Not certain there is one universally accepted standard but this is what I settled on in my paper:

+x / R=Right
-x / L=Left
+y / F=Front
-y / B=Back
+z / U=Up
-z / D=Down
+w / A=Ana
-w / K=Kata

I've not written code to simulate a 3x3x3x3 before and I don't know if the 4 axes are defined this way in MC4D or not.  I was about to suggest that we could use the right-hand rule to differentiate the +w from the -w direction but the more I think about it that likely doesn't make sense.  Your right hand looks just like your left hand under a 4D rotation.  An arbitrary choice may be as good as anything else.  Keep in mind that a global rotation of the 3x3x3x3 can easily swap the "inner cell" with the "hidden cell".

I hope this helps,

Carl

[scarecrowfish]

I've always used I=in and O=out when notating my own algorithms. The advantage of this for me is that in both MC4D and the physical 2^4 it's immediately clear which cell is "in" and which is "out", so it's both easy to explain and easy to remember, and neither letter is used in standard 3D notation.

~Luna