cube files
Indexed Cube Lovers Archive
Lower bounds for the 3x3x3 Super Group
Submitted by Walter Randelshofer on Tue, 07/22/2014 - 13:45.
For quite a while I was looking for an optimal solution for the 'Pure Superflip' (a Superflip pattern were all centers remain untouched). Such an algorithm would also allow to define the lower bound for the 3x3x3 Super Group. I don't know if there already exist lower and upper bounds for this cube group.
Years ago I computed all optimal solutions of the 'Superflip' pattern in ftm (face turn metric) to see if any of the 4416 algorithms may leave the centers unchanged. Unfortunately all these algorithms twist either 4 or 5 of the centers.
I figured out that such an algorithm must be within the range of 23 and 24 moves, but I never was able to prove it. It took just too long for solvers these days to compute a solution.
Nevertheless, in May 23, 2009, I found two short algorithms that seemed to be optimal:
B2 L2 B2 L' D2 F2 R' D B U L2 F2 R2 L' D' L F D' L D' R' B' U' F' (24 ftm, 32 qtm)
L2 D2 L2 D' B2 R2 U' B L F D2 R2 U2 D' B' D R B' D B' U' L' F' R' (24 ftm, 32 qtm)
I recently gave it another try and was finally lucky to prove that the 'Pure Superflip' can be solved optimally in 24 ftm. The algorithm I found was also more efficient in terms of quarter turn moves. The solver required 6 weeks, 6 days, 22 hours, 58 minutes and 34.1 seconds to find it:
New solution found in July 19, 2014:
B' L2 R U' B' D B2 R' L F2 D' F U R2 L' F (U L)2 (R' U')2 (24 ftm, 28 qtm)
There might a high chance that this algorithm is optimal in qtm (quarter turn metric) too. Maybe someone can be confirmed that.
I also discovered an optimal solution in ltm (layer turn metric):
CR2 MF' MR2 MD MF' R U B L U MR F' MR B MR F' L' U' R' U' (19 ltm, 26 ftm, 28 qtm)
Note, that in SSE notation a prepending C describes a 'Cube rotation'. CR means to rotate the whole cube in clockwise direction as seen form the right face.
And a prepending M describes a 'Mid-layer twist'. MR means to twist the middle layer in clockwise direction as seen from the right face.
See also this description to learn more about the SSE notation.
Cheers,
Walter Randelshofer
Years ago I computed all optimal solutions of the 'Superflip' pattern in ftm (face turn metric) to see if any of the 4416 algorithms may leave the centers unchanged. Unfortunately all these algorithms twist either 4 or 5 of the centers.
I figured out that such an algorithm must be within the range of 23 and 24 moves, but I never was able to prove it. It took just too long for solvers these days to compute a solution.
Nevertheless, in May 23, 2009, I found two short algorithms that seemed to be optimal:
B2 L2 B2 L' D2 F2 R' D B U L2 F2 R2 L' D' L F D' L D' R' B' U' F' (24 ftm, 32 qtm)
L2 D2 L2 D' B2 R2 U' B L F D2 R2 U2 D' B' D R B' D B' U' L' F' R' (24 ftm, 32 qtm)
I recently gave it another try and was finally lucky to prove that the 'Pure Superflip' can be solved optimally in 24 ftm. The algorithm I found was also more efficient in terms of quarter turn moves. The solver required 6 weeks, 6 days, 22 hours, 58 minutes and 34.1 seconds to find it:
New solution found in July 19, 2014:
B' L2 R U' B' D B2 R' L F2 D' F U R2 L' F (U L)2 (R' U')2 (24 ftm, 28 qtm)
There might a high chance that this algorithm is optimal in qtm (quarter turn metric) too. Maybe someone can be confirmed that.
I also discovered an optimal solution in ltm (layer turn metric):
CR2 MF' MR2 MD MF' R U B L U MR F' MR B MR F' L' U' R' U' (19 ltm, 26 ftm, 28 qtm)
Note, that in SSE notation a prepending C describes a 'Cube rotation'. CR means to rotate the whole cube in clockwise direction as seen form the right face.
And a prepending M describes a 'Mid-layer twist'. MR means to twist the middle layer in clockwise direction as seen from the right face.
See also this description to learn more about the SSE notation.
Cheers,
Walter Randelshofer
