Solving without R face turns

[Mikel]

y2 L

 

[kcl]

A while back I heard something like this about doing a U2 on 2x2 and solving without any 180˚ turns. My solution was U D lol.. My non cheating solution was to do sexy move*6 with a U instead of U' at the end.. As for this one, again I find loopholes haha.. Do a Y rotation, F or F', and then Y'. Loopholes are so nice

EDIT: yeah Mikel just posted that and I didn't see it..

 

[TMOY]

Just rotate your cube by 45° around either the y or the z axis. Then you can solve your cube with any method without having to apply R face turns since the R face doesn't exist anymore

 

[Stefan]

When you solved this with Cube Explorer, did you use the optimal solver or the two-phase solver?

Hmm, good question. I used the "incomplete cubes" solver and both output and runtime make me think it's optimal, but I didn't find anything about it in the documentation, so I'm not sure.

Spoiler: the output

computation started...

Searching depth 7

Searching depth 8

Searching depth 9

Searching depth 10

Searching depth 11

Searching depth 12

Searching depth 13

U D F2 B2 U' D' R' U D F2 B2 U' D' (13f*)
U D F2 B2 U' D' R' U' D' F2 B2 U D (13f*)
U D' F2 B2 U D' R' U D' F2 B2 U D' (13f*)
U D' F2 B2 U D' R' U' D F2 B2 U' D (13f*)

Your 100 billion nodes do seem excessive, given that you only need to go about half way, and there are only about 100 million nodes reachable in seven moves even if you allow all six sides (see cube20.org).

I just tried with ACube searching for optimal sequences:

java -cp ACube3.jar ACube f o
760 UF BR UB UL DF FR DB DL UR FL DR BL BUR BRD UBL ULF FRU DFL DLB FDR

On my old laptop, it takes 8 seconds to prepare the tables and then 6 seconds for the search.

 

[elrog]

I've done this before. I don't use one side while I solve my jupiter mf8 cube. After matching up the corners and edges, I solved the cube CFOP style without using the bottom face (the side that the center doesn't turn).

 

[cannon4747]

first off, I'd just not use D face turns. And something I've tried for fun recently is doing left-handed solves (i'm righty). If i get a T-perm I do L' U' L U L F' L2...etc. and the same for OLL. I'd insert and build F2l pairs on the left as well. It was actually an interesting challenge attempting to flip an alogorithm i know solely by muscle memory. For some cases I just used 2-look lol.

 

[unixpickle]

I finally optimized my cube solver for restricted movesets. I then ran a couple of statistical analyses on the cube without R turns. Here's what I found:

- maximum moves to orient all edges is 9 (usual maximum is 7, worst case is the only good edges at FR and BR, fix with F L F U' D2 B2 L F B)
- maximum moves to solve a specific cross is 10 moves (usual maximum is 8, for all 190080 crosses)
- maximum moves to solve a specific 2x2x2 block is 9 moves (usual maximum is 8, 7 configurations actually take 9 moves)

Some neat sequences without R turns:
R U R' = U2 F' L' U L U2 F [7 moves]
R2 U2 R2 U2 R2 U2 = U B2 L2 D2 F2 D2 L2 B2 U [9 moves]
superflip = L B F' U' F2 D2 L' B D' U2 F2 D' L' F' L2 F2 L2 D F2 U F2 U2 B2 [23 moves, may not be optimal]

 

[cuBerBruce]

- maximum moves to orient all edges is 9 (usual maximum is 7, worst case is the only good edges at FR and BR, fix with F L F U' D2 B2 L F B)

If you're not allowing a certain face to be turned, it presumably matters what EO scheme you are assuming, <U,D,R,L,F2,B2>, <U,D,R2,L2,F,B>, or <U2,D2,R,L,F,B>. That is, it presumably matters whether or not the restricted layer is one of the layers that can affect the orientation with a quarter turn.

- maximum moves to solve a specific cross is 10 moves (usual maximum is 8, for all 190080 crosses)

If you're not allowing a certain face to be turned, it presumably matters which face you're making the cross on. For example, if you're not allowing R turns, it probably matters whether cross is on R, L, or U/D/F/B.

- maximum moves to solve a specific 2x2x2 block is 9 moves (usual maximum is 8, 7 configurations actually take 9 moves)

If you're not allowing allowing a certain face to be turned, it presumably matters whether or not the 2x2x2 block includes pieces on that face.

 

[unixpickle]

I will address your questions with more numbers.

If you're not allowing a certain face to be turned, it presumably matters what EO scheme you are assuming, <U,D,R,L,F2,B2>, <U,D,R2,L2,F,B>, or <U2,D2,R,L,F,B>

It certainly does matter. I use the <U,R,L,D,F2,B2> scheme. My original number was based on restricting turns of the R face. If you restrict R, U, D, or L, the maximum moves to orient all edges is 9 with 1 taking 9 moves. Interestingly enough, if you restrict F or B, the maximum is 11 with 7 taking 11 moves.

If you're not allowing a certain face to be turned, it presumably matters which face you're making the cross on. For example, if you're not allowing R turns, it probably matters whether cross is on R, L, or U/D/F/B.

Here's what I found while restricting the R face. The F, U, D, and B crosses take 10 moves max with 4 that actually take 10 moves. The right cross takes 10 moves max with 792 that take 10 moves. The left cross, interestingly enough, still takes 8 moves with 1324 crosses which actually require a full 8 moves.

If you're not allowing allowing a certain face to be turned, it presumably matters whether or not the 2x2x2 block includes pieces on that face.

Any 2x2x2 block which does not intersect with the R face takes a maximum of 9 moves with 7 configurations that actually require 9 moves. Any 2x2x2 block which intersects with the R face still takes a maximum of 9 moves, but with 2452 configurations that actually require such a number.

 

[cuBerBruce]

I use the <U,R,L,D,F2,B2> scheme. My original number was based on restricting turns of the R face. If you restrict R, U, D, or L, the maximum moves to orient all edges is 9 with 1 taking 9 moves. Interestingly enough, if you restrict F or B, the maximum is 11 with 7 taking 11 moves.



Here's what I found while restricting the R face. The F, U, D, and B crosses take 10 moves max with 4 that actually take 10 moves. The right cross takes 10 moves max with 792 that take 10 moves. The left cross, interestingly enough, still takes 8 moves with 1324 crosses which actually require a full 8 moves.



Any 2x2x2 block which does not intersect with the R face takes a maximum of 9 moves with 7 configurations that actually require 9 moves. Any 2x2x2 block which intersects with the R face still takes a maximum of 9 moves, but with 2452 configurations that actually require such a number.

I confirm from my own independent breadth-first searches that your results are correct.

 

[Herbert Kociemba]

Hmm, good question. I used the "incomplete cubes" solver and both output and runtime make me think it's optimal, but I didn't find anything about it in the documentation, so I'm not sure.

Yes, the "incomplete solver" uses iterative deepening and the first solution found is guaranteed to be optimal.