I'll run those cases too.

I've finally got my "untwister" working, and usually there are multiple

solution sequences that it finds; I don't know which might be easiest

for speedsolvers so I'm dumping them all (at least the ones that

preserve overall cube orientation).

Here are the current set of solutions to the sequences you've posted.

I've given each a unique number.

(Note that I'm using the JavaScript alg.cubing.net and not the

Java applet, so I change r to 2R and so on.)

Spoiler

Almost all of these optimal solves show significant structure.

I should probably make my untwister recognize and reformat explicit

commutators and conjugates.

I've finished depth 15 for a few of these positions, and am starting

depth 16. I don't think I will be able to complete a depth-16 solve for

any of these in any reasonable amount of time; my depth-15 searches

for some of these took about half a day, and the others may take

longer.

I've finally got my "untwister" working, and usually there are multiple

solution sequences that it finds; I don't know which might be easiest

for speedsolvers so I'm dumping them all (at least the ones that

preserve overall cube orientation).

Here are the current set of solutions to the sequences you've posted.

I've given each a unique number.

(Note that I'm using the JavaScript alg.cubing.net and not the

Java applet, so I change r to 2R and so on.)

For (seq1002): F2 U' 2L' 2R' U F' L U' F 2L 2R F' U L' F'

Uw2 Fw D2 R' B' L Dw2 U2 R' F L D2 Bw' Dw2

Uw2 Fw D2 R' B' L Uw2 U2 L' B R D2 Fw' Uw2

Uw2 Bw R2 U' B' D Lw2 L2 D' B U R2 Bw' Uw2

Dw2 Bw D2 L' F' R Dw2 U2 L' B R D2 Fw' Uw2

Dw2 Bw D2 L' F' R Uw2 U2 R' F L D2 Bw' Dw2

Dw2 Fw L2 U' F' D Rw2 R2 D' F U L2 Fw' Dw2

For (seq1003): 2R2 U' B2 U' F L F' 2R2 F L' F' U B2 U 2R2

Rw2 U L B' Lw Dw2 Fw2 B2 Dw2 Lw' F L' D' Lw2

Rw2 U L B' Lw Dw2 Bw2 B2 Dw2 Lw' B L' U' Rw2

Rw2 U L B' Lw Uw2 Bw2 F2 Uw2 Lw' F L' D' Lw2

Rw2 U L B' Lw Uw2 Fw2 F2 Uw2 Lw' B L' U' Rw2

Rw2 U L B' Rw Fw2 Uw2 D2 Fw2 Rw' F L' D' Lw2

Rw2 U L B' Rw Fw2 Dw2 D2 Fw2 Rw' B L' U' Rw2

Rw2 U L B' Rw Bw2 Dw2 U2 Bw2 Rw' F L' D' Lw2

Rw2 U L B' Rw Bw2 Uw2 U2 Bw2 Rw' B L' U' Rw2

Lw2 D L F' Lw Uw2 Bw2 F2 Uw2 Lw' B L' U' Rw2

Lw2 D L F' Lw Uw2 Fw2 F2 Uw2 Lw' F L' D' Lw2

Lw2 D L F' Lw Dw2 Fw2 B2 Dw2 Lw' B L' U' Rw2

Lw2 D L F' Lw Dw2 Bw2 B2 Dw2 Lw' F L' D' Lw2

Lw2 D L F' Rw Bw2 Dw2 U2 Bw2 Rw' B L' U' Rw2

Lw2 D L F' Rw Bw2 Uw2 U2 Bw2 Rw' F L' D' Lw2

Lw2 D L F' Rw Fw2 Uw2 D2 Fw2 Rw' B L' U' Rw2

Lw2 D L F' Rw Fw2 Dw2 D2 Fw2 Rw' F L' D' Lw2

For (seq1006): R2 2R' F' L R F 2R' F' R' F 2R2 F' L' F R2

U F B' Dw B U' B' Dw2 U F' U' F Dw F' B

U F B' Uw R U' R' Uw2 U R' U' R Uw F' B

For (seq1007): 2R2 U F2 U B' R B 2R2 B' R' B U' F2 U' 2R2

R U' Fw2 B L2 Fw2 U Fw2 L2 Fw2 U B' U R'

R U' Fw2 B L2 Fw2 U Bw2 R2 Bw2 U B' U R'

R U' Fw2 B L2 Bw2 D Fw2 R2 Bw2 U B' U R'

R U' Fw2 B L2 Bw2 D Bw2 L2 Fw2 U B' U R'

R U' Bw2 B R2 Fw2 D Fw2 R2 Bw2 U B' U R'

R U' Bw2 B R2 Fw2 D Bw2 L2 Fw2 U B' U R'

R U' Bw2 B R2 Bw2 U Fw2 L2 Fw2 U B' U R'

R U' Bw2 B R2 Bw2 U Bw2 R2 Bw2 U B' U R'

For (seq1016): 2L2 2R2 U 2R2 F2 2R2 F2 U' 2L2 2U2 2R2 2U2

F2 B2 D Dw2 B2 R2 Fw2 U2 Uw2 B2 L2 Fw2 D F2 B2

F2 B2 D Dw2 B2 R2 Bw2 D2 Dw2 B2 R2 Bw2 D F2 B2

F2 B2 D Uw2 F2 L2 Bw2 U2 Dw2 B2 L2 Fw2 D F2 B2

F2 B2 D Uw2 F2 L2 Fw2 D2 Uw2 B2 R2 Bw2 D F2 B2

For (seq1017): 2L2 2R2 U' 2R2 F2 2R2 F2 U 2L2 2U2 2R2 2U2

F2 B2 D' Dw2 F2 L2 Fw2 D2 Dw2 F2 L2 Fw2 D' F2 B2

F2 B2 D' Dw2 F2 L2 Bw2 U2 Uw2 F2 R2 Bw2 D' F2 B2

F2 B2 D' Uw2 B2 R2 Bw2 D2 Uw2 F2 L2 Fw2 D' F2 B2

F2 B2 D' Uw2 B2 R2 Fw2 U2 Dw2 F2 R2 Bw2 D' F2 B2

For (seq1018): 2R2 U' 2R2 F2 2R2 F2 U2 F2 2R2 F2 2R2 U' 2R2

R2 Fw2 Rw2 U' R2 F2 R2 U2 R2 F2 R2 U' Rw2 Fw2 R2

R2 Fw2 Lw2 D' R2 B2 R2 D2 R2 B2 R2 D' Lw2 Fw2 R2

R2 Bw2 Lw2 D' L2 F2 L2 D2 L2 F2 L2 D' Lw2 Bw2 R2

R2 Bw2 Rw2 U' L2 B2 L2 U2 L2 B2 L2 U' Rw2 Bw2 R2

For (seq1019): F' R' 2D R U R' 2D' 2U' R U' R' 2U R F

F2 Rw2 U R2 U' R2 L2 D R2 D' R2 Rw2 L2 F2

F2 Lw2 D R2 D' R2 L2 U R2 U' R2 Lw2 L2 F2

For (seq1020): R2 D' F2 2F' U 2F U2 2F' U F2 U' 2F U2 2F' U' 2F D R2

Fw2 R2 F' Fw Rw2 F L F' Rw2 F Fw' R2 Fw L' Fw

Fw2 R2 F' Fw Rw2 F L F' Rw2 F Bw' D2 Fw U' Bw

Fw2 R2 F' Fw Rw2 F L F' Rw2 F Bw' D2 Bw L' Fw

Fw2 R2 F' Fw Lw2 B L B' Lw2 F Fw' R2 Fw L' Fw

Fw2 R2 F' Fw Lw2 B L B' Lw2 F Bw' D2 Fw U' Bw

Fw2 R2 F' Fw Lw2 B L B' Lw2 F Bw' D2 Bw L' Fw

Fw2 R2 F' Bw Uw2 F D F' Uw2 F Bw' R2 Fw L' Fw

Fw2 R2 F' Bw Dw2 B D B' Dw2 F Bw' R2 Fw L' Fw

Bw2 L2 F' Fw Lw2 F R F' Lw2 F Fw' L2 Bw U' Bw

Bw2 L2 F' Fw Rw2 B R B' Rw2 F Fw' L2 Bw U' Bw

Bw2 L2 F' Bw Dw2 F U F' Dw2 F Fw' D2 Fw U' Bw

Bw2 L2 F' Bw Dw2 F U F' Dw2 F Fw' D2 Bw L' Fw

Bw2 L2 F' Bw Dw2 F U F' Dw2 F Bw' L2 Bw U' Bw

Bw2 L2 F' Bw Uw2 B U B' Uw2 F Fw' D2 Fw U' Bw

Bw2 L2 F' Bw Uw2 B U B' Uw2 F Fw' D2 Bw L' Fw

Bw2 L2 F' Bw Uw2 B U B' Uw2 F Bw' L2 Bw U' Bw

For (seq1021): R2 2R2 U2 R2 U' 2R U2 2L 2R U' R2 U 2L' 2R' U2 2R' U' R2 2R2

F2 Rw2 U' F2 U F2 B2 D' F2 D F2 B2 Rw2 F2

F2 Lw2 D' B2 D B2 F2 U' B2 U B2 F2 Lw2 F2

For (seq1026): 2L2 2R2 U' 2L' 2R U2 F2 2L 2R F2 D2 F2 2L2 F2 2L2 D2 2R2 U' 2L2 2R2

Fw2 U2 Rw2 D B2 L2 Fw2 U2 B2 Bw2 U' Fw2 D2 B2 Rw2

Fw2 U2 Rw2 D B2 L2 Fw2 U2 B2 Fw2 D' Bw2 D2 B2 Rw2

Fw2 U2 Rw2 D B2 L2 Bw2 D2 B2 Bw2 D' Bw2 D2 B2 Rw2

Fw2 U2 Rw2 D B2 L2 Bw2 D2 B2 Fw2 U' Fw2 D2 B2 Rw2

Fw2 U2 Lw2 U F2 L2 Bw2 D2 F2 Fw2 D' Bw2 U2 F2 Lw2

Fw2 U2 Lw2 U F2 L2 Bw2 D2 F2 Bw2 U' Fw2 U2 F2 Lw2

Fw2 U2 Lw2 U F2 L2 Fw2 U2 F2 Fw2 U' Fw2 U2 F2 Lw2

Fw2 U2 Lw2 U F2 L2 Fw2 U2 F2 Bw2 D' Bw2 U2 F2 Lw2

Bw2 D2 Lw2 U B2 R2 Fw2 D2 B2 Bw2 D' Bw2 D2 B2 Rw2

Bw2 D2 Lw2 U B2 R2 Fw2 D2 B2 Fw2 U' Fw2 D2 B2 Rw2

Bw2 D2 Lw2 U B2 R2 Bw2 U2 B2 Bw2 U' Fw2 D2 B2 Rw2

Bw2 D2 Lw2 U B2 R2 Bw2 U2 B2 Fw2 D' Bw2 D2 B2 Rw2

Bw2 D2 Rw2 D F2 R2 Bw2 U2 F2 Fw2 U' Fw2 U2 F2 Lw2

Bw2 D2 Rw2 D F2 R2 Bw2 U2 F2 Bw2 D' Bw2 U2 F2 Lw2

Bw2 D2 Rw2 D F2 R2 Fw2 D2 F2 Fw2 D' Bw2 U2 F2 Lw2

Bw2 D2 Rw2 D F2 R2 Fw2 D2 F2 Bw2 U' Fw2 U2 F2 Lw2

For (seq2000): Rw2 Uw U S Lw2 2U2 2R 2U2 Lw2 S' U' Uw' Rw2

Rw2 U2 R2 Rw' U2 D2 L' Lw U2 D2 Rw' U2 Rw2

Rw2 U2 R2 Rw' U2 D2 L' Rw B2 F2 Lw' D2 Lw2

Rw2 U2 R2 Lw' B2 F2 L' Lw B2 F2 Lw' D2 Lw2

Rw2 U2 R2 Lw' B2 F2 L' Rw D2 U2 Rw' D2 Lw2

Lw2 D2 R2 Rw' D2 U2 L' Lw D2 U2 Rw' D2 Lw2

Lw2 D2 R2 Rw' D2 U2 L' Rw F2 B2 Lw' U2 Rw2

Lw2 D2 R2 Lw' F2 B2 L' Lw F2 B2 Lw' U2 Rw2

Lw2 D2 R2 Lw' F2 B2 L' Rw U2 D2 Rw' U2 Rw2

Uw2 Fw D2 R' B' L Dw2 U2 R' F L D2 Bw' Dw2

Uw2 Fw D2 R' B' L Uw2 U2 L' B R D2 Fw' Uw2

Uw2 Bw R2 U' B' D Lw2 L2 D' B U R2 Bw' Uw2

Dw2 Bw D2 L' F' R Dw2 U2 L' B R D2 Fw' Uw2

Dw2 Bw D2 L' F' R Uw2 U2 R' F L D2 Bw' Dw2

Dw2 Fw L2 U' F' D Rw2 R2 D' F U L2 Fw' Dw2

For (seq1003): 2R2 U' B2 U' F L F' 2R2 F L' F' U B2 U 2R2

Rw2 U L B' Lw Dw2 Fw2 B2 Dw2 Lw' F L' D' Lw2

Rw2 U L B' Lw Dw2 Bw2 B2 Dw2 Lw' B L' U' Rw2

Rw2 U L B' Lw Uw2 Bw2 F2 Uw2 Lw' F L' D' Lw2

Rw2 U L B' Lw Uw2 Fw2 F2 Uw2 Lw' B L' U' Rw2

Rw2 U L B' Rw Fw2 Uw2 D2 Fw2 Rw' F L' D' Lw2

Rw2 U L B' Rw Fw2 Dw2 D2 Fw2 Rw' B L' U' Rw2

Rw2 U L B' Rw Bw2 Dw2 U2 Bw2 Rw' F L' D' Lw2

Rw2 U L B' Rw Bw2 Uw2 U2 Bw2 Rw' B L' U' Rw2

Lw2 D L F' Lw Uw2 Bw2 F2 Uw2 Lw' B L' U' Rw2

Lw2 D L F' Lw Uw2 Fw2 F2 Uw2 Lw' F L' D' Lw2

Lw2 D L F' Lw Dw2 Fw2 B2 Dw2 Lw' B L' U' Rw2

Lw2 D L F' Lw Dw2 Bw2 B2 Dw2 Lw' F L' D' Lw2

Lw2 D L F' Rw Bw2 Dw2 U2 Bw2 Rw' B L' U' Rw2

Lw2 D L F' Rw Bw2 Uw2 U2 Bw2 Rw' F L' D' Lw2

Lw2 D L F' Rw Fw2 Uw2 D2 Fw2 Rw' B L' U' Rw2

Lw2 D L F' Rw Fw2 Dw2 D2 Fw2 Rw' F L' D' Lw2

For (seq1006): R2 2R' F' L R F 2R' F' R' F 2R2 F' L' F R2

U F B' Dw B U' B' Dw2 U F' U' F Dw F' B

U F B' Uw R U' R' Uw2 U R' U' R Uw F' B

For (seq1007): 2R2 U F2 U B' R B 2R2 B' R' B U' F2 U' 2R2

R U' Fw2 B L2 Fw2 U Fw2 L2 Fw2 U B' U R'

R U' Fw2 B L2 Fw2 U Bw2 R2 Bw2 U B' U R'

R U' Fw2 B L2 Bw2 D Fw2 R2 Bw2 U B' U R'

R U' Fw2 B L2 Bw2 D Bw2 L2 Fw2 U B' U R'

R U' Bw2 B R2 Fw2 D Fw2 R2 Bw2 U B' U R'

R U' Bw2 B R2 Fw2 D Bw2 L2 Fw2 U B' U R'

R U' Bw2 B R2 Bw2 U Fw2 L2 Fw2 U B' U R'

R U' Bw2 B R2 Bw2 U Bw2 R2 Bw2 U B' U R'

For (seq1016): 2L2 2R2 U 2R2 F2 2R2 F2 U' 2L2 2U2 2R2 2U2

F2 B2 D Dw2 B2 R2 Fw2 U2 Uw2 B2 L2 Fw2 D F2 B2

F2 B2 D Dw2 B2 R2 Bw2 D2 Dw2 B2 R2 Bw2 D F2 B2

F2 B2 D Uw2 F2 L2 Bw2 U2 Dw2 B2 L2 Fw2 D F2 B2

F2 B2 D Uw2 F2 L2 Fw2 D2 Uw2 B2 R2 Bw2 D F2 B2

For (seq1017): 2L2 2R2 U' 2R2 F2 2R2 F2 U 2L2 2U2 2R2 2U2

F2 B2 D' Dw2 F2 L2 Fw2 D2 Dw2 F2 L2 Fw2 D' F2 B2

F2 B2 D' Dw2 F2 L2 Bw2 U2 Uw2 F2 R2 Bw2 D' F2 B2

F2 B2 D' Uw2 B2 R2 Bw2 D2 Uw2 F2 L2 Fw2 D' F2 B2

F2 B2 D' Uw2 B2 R2 Fw2 U2 Dw2 F2 R2 Bw2 D' F2 B2

For (seq1018): 2R2 U' 2R2 F2 2R2 F2 U2 F2 2R2 F2 2R2 U' 2R2

R2 Fw2 Rw2 U' R2 F2 R2 U2 R2 F2 R2 U' Rw2 Fw2 R2

R2 Fw2 Lw2 D' R2 B2 R2 D2 R2 B2 R2 D' Lw2 Fw2 R2

R2 Bw2 Lw2 D' L2 F2 L2 D2 L2 F2 L2 D' Lw2 Bw2 R2

R2 Bw2 Rw2 U' L2 B2 L2 U2 L2 B2 L2 U' Rw2 Bw2 R2

For (seq1019): F' R' 2D R U R' 2D' 2U' R U' R' 2U R F

F2 Rw2 U R2 U' R2 L2 D R2 D' R2 Rw2 L2 F2

F2 Lw2 D R2 D' R2 L2 U R2 U' R2 Lw2 L2 F2

For (seq1020): R2 D' F2 2F' U 2F U2 2F' U F2 U' 2F U2 2F' U' 2F D R2

Fw2 R2 F' Fw Rw2 F L F' Rw2 F Fw' R2 Fw L' Fw

Fw2 R2 F' Fw Rw2 F L F' Rw2 F Bw' D2 Fw U' Bw

Fw2 R2 F' Fw Rw2 F L F' Rw2 F Bw' D2 Bw L' Fw

Fw2 R2 F' Fw Lw2 B L B' Lw2 F Fw' R2 Fw L' Fw

Fw2 R2 F' Fw Lw2 B L B' Lw2 F Bw' D2 Fw U' Bw

Fw2 R2 F' Fw Lw2 B L B' Lw2 F Bw' D2 Bw L' Fw

Fw2 R2 F' Bw Uw2 F D F' Uw2 F Bw' R2 Fw L' Fw

Fw2 R2 F' Bw Dw2 B D B' Dw2 F Bw' R2 Fw L' Fw

Bw2 L2 F' Fw Lw2 F R F' Lw2 F Fw' L2 Bw U' Bw

Bw2 L2 F' Fw Rw2 B R B' Rw2 F Fw' L2 Bw U' Bw

Bw2 L2 F' Bw Dw2 F U F' Dw2 F Fw' D2 Fw U' Bw

Bw2 L2 F' Bw Dw2 F U F' Dw2 F Fw' D2 Bw L' Fw

Bw2 L2 F' Bw Dw2 F U F' Dw2 F Bw' L2 Bw U' Bw

Bw2 L2 F' Bw Uw2 B U B' Uw2 F Fw' D2 Fw U' Bw

Bw2 L2 F' Bw Uw2 B U B' Uw2 F Fw' D2 Bw L' Fw

Bw2 L2 F' Bw Uw2 B U B' Uw2 F Bw' L2 Bw U' Bw

For (seq1021): R2 2R2 U2 R2 U' 2R U2 2L 2R U' R2 U 2L' 2R' U2 2R' U' R2 2R2

F2 Rw2 U' F2 U F2 B2 D' F2 D F2 B2 Rw2 F2

F2 Lw2 D' B2 D B2 F2 U' B2 U B2 F2 Lw2 F2

For (seq1026): 2L2 2R2 U' 2L' 2R U2 F2 2L 2R F2 D2 F2 2L2 F2 2L2 D2 2R2 U' 2L2 2R2

Fw2 U2 Rw2 D B2 L2 Fw2 U2 B2 Bw2 U' Fw2 D2 B2 Rw2

Fw2 U2 Rw2 D B2 L2 Fw2 U2 B2 Fw2 D' Bw2 D2 B2 Rw2

Fw2 U2 Rw2 D B2 L2 Bw2 D2 B2 Bw2 D' Bw2 D2 B2 Rw2

Fw2 U2 Rw2 D B2 L2 Bw2 D2 B2 Fw2 U' Fw2 D2 B2 Rw2

Fw2 U2 Lw2 U F2 L2 Bw2 D2 F2 Fw2 D' Bw2 U2 F2 Lw2

Fw2 U2 Lw2 U F2 L2 Bw2 D2 F2 Bw2 U' Fw2 U2 F2 Lw2

Fw2 U2 Lw2 U F2 L2 Fw2 U2 F2 Fw2 U' Fw2 U2 F2 Lw2

Fw2 U2 Lw2 U F2 L2 Fw2 U2 F2 Bw2 D' Bw2 U2 F2 Lw2

Bw2 D2 Lw2 U B2 R2 Fw2 D2 B2 Bw2 D' Bw2 D2 B2 Rw2

Bw2 D2 Lw2 U B2 R2 Fw2 D2 B2 Fw2 U' Fw2 D2 B2 Rw2

Bw2 D2 Lw2 U B2 R2 Bw2 U2 B2 Bw2 U' Fw2 D2 B2 Rw2

Bw2 D2 Lw2 U B2 R2 Bw2 U2 B2 Fw2 D' Bw2 D2 B2 Rw2

Bw2 D2 Rw2 D F2 R2 Bw2 U2 F2 Fw2 U' Fw2 U2 F2 Lw2

Bw2 D2 Rw2 D F2 R2 Bw2 U2 F2 Bw2 D' Bw2 U2 F2 Lw2

Bw2 D2 Rw2 D F2 R2 Fw2 D2 F2 Fw2 D' Bw2 U2 F2 Lw2

Bw2 D2 Rw2 D F2 R2 Fw2 D2 F2 Bw2 U' Fw2 U2 F2 Lw2

For (seq2000): Rw2 Uw U S Lw2 2U2 2R 2U2 Lw2 S' U' Uw' Rw2

Rw2 U2 R2 Rw' U2 D2 L' Lw U2 D2 Rw' U2 Rw2

Rw2 U2 R2 Rw' U2 D2 L' Rw B2 F2 Lw' D2 Lw2

Rw2 U2 R2 Lw' B2 F2 L' Lw B2 F2 Lw' D2 Lw2

Rw2 U2 R2 Lw' B2 F2 L' Rw D2 U2 Rw' D2 Lw2

Lw2 D2 R2 Rw' D2 U2 L' Lw D2 U2 Rw' D2 Lw2

Lw2 D2 R2 Rw' D2 U2 L' Rw F2 B2 Lw' U2 Rw2

Lw2 D2 R2 Lw' F2 B2 L' Lw F2 B2 Lw' U2 Rw2

Lw2 D2 R2 Lw' F2 B2 L' Rw U2 D2 Rw' U2 Rw2

Almost all of these optimal solves show significant structure.

I should probably make my untwister recognize and reformat explicit

commutators and conjugates.

I've finished depth 15 for a few of these positions, and am starting

depth 16. I don't think I will be able to complete a depth-16 solve for

any of these in any reasonable amount of time; my depth-15 searches

for some of these took about half a day, and the others may take

longer.

Last edited by a moderator: May 4, 2014