Kare
Member
After some serious computations I have found the following parity algs for 4x4 solved using the reduction method. The algs should be the shortest possible using only R, Rw & U while preserving the lower layers.
The move count is higher than the well known parity alg, but this might still be faster. I will leave it to the speed freaks to try out how fast the algs can be executed.
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Flip UB
Depth: 19
Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U R Rw2 U Rw U' Rw
Depth: 20
R Rw' U2 R' Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 R Rw2 U' R' U Rw
Rw2 U' Rw2 U2 Rw' U R U R' Rw' U2 R' Rw2 U R Rw U2 Rw' U2 Rw'
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Flip UR
Depth: 19
Rw U' Rw U R Rw2 U Rw U R2 U2 R Rw U Rw U2 Rw U2 Rw
Rw' U Rw' U' R' Rw2 U' Rw' U' R2 U2 R' Rw' U' Rw' U2 Rw' U2 Rw'
Depth: 20
Rw U R' U' R Rw2 U2 Rw2 U Rw U2 Rw' U2 Rw U' R' Rw2 U2 R Rw'
Rw U2 Rw U2 R' Rw' U' R Rw2 U2 R Rw U' R' U' Rw U2 Rw2 U Rw2
Rw' U' R U R' Rw2 U2 Rw2 U' Rw' U2 Rw U2 Rw' U R Rw2 U2 R' Rw
Rw' U2 Rw' U2 R Rw U R' Rw2 U2 R' Rw' U R U Rw' U2 Rw2 U' Rw2
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Flip UF
Depth: 19
Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' R' Rw2 U' Rw' U Rw'
Depth: 20
R' Rw U2 R Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 R' Rw2 U R U' Rw'
Rw2 U Rw2 U2 Rw U' R' U' R Rw U2 R Rw2 U' R' Rw' U2 Rw U2 Rw
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I have also been looking for algs for those who like to have one flipping three pieces. The shortest seems to be 22 moves and I have yet to compute all of them. Here is one such alg.
Flip all but UL
Depth: 22
Rw U Rw U2 Rw U2 Rw U Rw' U2 R Rw' U2 Rw' U Rw U2 Rw U2 Rw U Rw
I have loads of more algs that solves the parities but mess up one or more of the DR corners. If anyone would find that useful I can post those too, including an 18 move alg.
The move count is higher than the well known parity alg, but this might still be faster. I will leave it to the speed freaks to try out how fast the algs can be executed.
*************************************************************
Flip UB
Depth: 19
Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U R Rw2 U Rw U' Rw
Depth: 20
R Rw' U2 R' Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 R Rw2 U' R' U Rw
Rw2 U' Rw2 U2 Rw' U R U R' Rw' U2 R' Rw2 U R Rw U2 Rw' U2 Rw'
*************************************************************
Flip UR
Depth: 19
Rw U' Rw U R Rw2 U Rw U R2 U2 R Rw U Rw U2 Rw U2 Rw
Rw' U Rw' U' R' Rw2 U' Rw' U' R2 U2 R' Rw' U' Rw' U2 Rw' U2 Rw'
Depth: 20
Rw U R' U' R Rw2 U2 Rw2 U Rw U2 Rw' U2 Rw U' R' Rw2 U2 R Rw'
Rw U2 Rw U2 R' Rw' U' R Rw2 U2 R Rw U' R' U' Rw U2 Rw2 U Rw2
Rw' U' R U R' Rw2 U2 Rw2 U' Rw' U2 Rw U2 Rw' U R Rw2 U2 R' Rw
Rw' U2 Rw' U2 R Rw U R' Rw2 U2 R' Rw' U R U Rw' U2 Rw2 U' Rw2
*************************************************************
Flip UF
Depth: 19
Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' R' Rw2 U' Rw' U Rw'
Depth: 20
R' Rw U2 R Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 R' Rw2 U R U' Rw'
Rw2 U Rw2 U2 Rw U' R' U' R Rw U2 R Rw2 U' R' Rw' U2 Rw U2 Rw
*************************************************************
I have also been looking for algs for those who like to have one flipping three pieces. The shortest seems to be 22 moves and I have yet to compute all of them. Here is one such alg.
Flip all but UL
Depth: 22
Rw U Rw U2 Rw U2 Rw U Rw' U2 R Rw' U2 Rw' U Rw U2 Rw U2 Rw U Rw
I have loads of more algs that solves the parities but mess up one or more of the DR corners. If anyone would find that useful I can post those too, including an 18 move alg.