K4LL 2-Gen Algorithms

[cuBerBruce]

The mathematically inclined reader might take it as a challenge to come up with actual 2-gen algs (either <U, Rw> or <U, r> ) for all of these cases.

That's great! I want others to find good algs too. If anyone does find algorithms that are authentically 2-gen, it would be great if they posted them and the derivations here (well, unless they were found with a computer solver).

I rather assumed real 2-gen algs would be too long for speedsolving use. Nevertheless, I have used ksolve to generate solutions for <U, r>. The best I found was 15 moves. The <U, Rw> group is much larger than <U, r>, and with essentially, the same branching factor, I expect <U, Rw> solutions to be longer.

I used ksolve to find <U, r> solutions for one member of each of the seven groups. These should be the optimal algs for the specific cases, but not necessarily the best for each group.

First I list the pure versions (no centers permuted).

Group 1: 23 moves for the chosen case
r2 U r' U2 r' U r U r U2 r2 U2 r U2 r U r' U r' U2 r2 U r2
r2 U r' U2 r' U' r U' r U2 r2 U2 r U2 r U' r' U' r' U2 r2 U r2
r2 U' r U2 r' U2 r' U2 r2 U2 r2 U r U r' U2 r' U2 r2 U2 r' U r

Group 2: 24 moves for the chosen case
U' r2 U' r' U r' U r' U2 r U r' U r2 U' r U r U' r U' r' U2 r
r U' r2 U' r' U r' U r' U2 r U r' U r2 U' r U r U' r U' r' U2

Group 3: 22 moves for the chosen case
U r' U r2 U2 r2 U2 r U2 r U2 r' U' r U r U2 r2 U2 r U2 r

Group 4: 22 moves for the chosen case
U2 r' U2 r' U' r U' r2 U2 r2 U2 r' U2 r' U2 r U r' U' r' U2 r2
U2 r2 U2 r U' r U r' U2 r U2 r U2 r2 U2 r2 U' r' U' r U2 r

Group 5: 20 moves for the chosen case
r U2 r2 U2 r U2 r U r' U r' U2 r2 U2 r' U2 r' U r U
r U2 r2 U2 r U2 r U' r' U' r' U2 r2 U2 r' U2 r' U' r U'

Group 6: 22 moves for the chosen case
r U2 r2 U2 r U' r U r' U2 r U2 r U2 r2 U2 r2 U' r' U' r U2

Group 7: 22 moves for the chosen case
r U r' U r2 U2 r2 U2 r U2 r U2 r' U' r U r U2 r2 U2 r U2

Next I list the non-pure versions (same-color centers may be permuted).

Group 1: 19 moves for the chosen case
r U2 r' U r U r U' r' U r' U' r U' r U r' U r'

Group 2: 21 moves for the chosen case
U2 r U r U r' U' r' U' r U r U' r' U r' U r U2 r' U2

Group 3: 17 moves for the chosen case
U' r' U' r U2 r2 U r2 U r' U' r' U' r U' r U
U' r' U' r' U' r U' r U r2 U r2 U2 r' U' r U

Group 4: 19 moves for the chosen case
r2 U r U2 r U' r2 U' r2 U2 r' U2 r' U r U' r' U' r2

Group 5: 20 moves for the chosen case
Pure solutions were not improved.

Group 6: 17 moves for the chosen case for the chosen case
U2 r U' r' U2 r' U r U r U' r2 U' r2 U' r' U2

Group 7: 15 moves
r' U r2 U r2 U r U' r U' r' U2 r' U r

 

[Christopher Mowla]

I used ksolve to find <U, r> solutions for one member of each of the seven groups. These should be the optimal algs for the specific cases, but not necessarily the best for each group.

Thanks for your time; these algorithms are neat.

In my search for algorithms which do not require single slice turns, I could not find algorithms for 3-cycles. But, I found that 2 3-cycles are probably going to be briefer for <U, Rw>:
(Rw' U Rw U2 Rw' U' Rw U')4

Also, this is one of the 2 2-cycle algorithms listed below:
Rw' U2 Rw' U2 Rw U2 Rw U Rw' U2 Rw' U2 Rw U2 Rw U
=[Rw' U2 Rw' U2 Rw U2 Rw,U](U2)

http://alg.garron.us/?alg=[r-_U2_r-_U2_r_U2_r,U]_U2&cube=4x4x4And for <U,r>, I have some 2 2-cycle algorithms:
r' U r U2 r U2 r U2 r2 U2 r U2 r U2 r U2 r2 U r
r2 U2 r' U2 r2 U2 r2 U2 r' U2 r2 U2 (I think this has been known for a while).
[r' U2 r' U2 r U2 r,U]

 

[cuBerBruce]

In my search for algorithms which do not require single slice turns, I could not find algorithms for 3-cycles. But, I found that 2 3-cycles are probably going to be briefer for <U, Rw>:
(Rw' U Rw U2 Rw' U' Rw U')4

Well, using ksolve, I've found a 20-move 3-cycle in <U, Rw>. Around 25 moves seems more typical.

Rw U Rw' U' Rw U2 Rw U Rw' U Rw U Rw2 U Rw2 U Rw' U2 Rw' U

 

[Cool Frog]

Mind = Blown...
some of these are very nice, others are not so...
but that 3 gen 3 cycle...

I will play around with this until I get some nice Opposite only 3 cycles (for all the cases) because for me, those are particularly bad.

your diagram for that cycle is also wrong =P