Christopher Mowla
Premium Member
I just wanted to mention that I used the classic 3x3x3 setup R2 B2 U2 L U2 R' U2 R U2 F2 R F2 L' B2 R2, in Cube Explorer to find single dedge flip algorithms, and I found over a 100 more 23 single slice quarter turn solutions. I only searched through depth 18 (it took my PC 4 days to do that...I did let my PC rest every once in a while though), and thus I suspect that there are more 23q algorithms which can be created using this 3x3x3 setup, let alone with an optimal 4x4x4 solver in the single slice quarter turn metric.
If anyone has searched at a higher depth and has the 3x3x3 solutions, post them in a .txt file, and I will extract more 23qs and look again for any 21qs. Speaking of which, it's interesting to note that I found only 1 21q which was very close to being a single dedge flip algorithm: r' F l' F2 r F r' F2 D F' D l D' F D' l F2 r.
And two of the 23q's I found cancel to 22 block quarter turns
Rw' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 B' Rw (22,17)
Rw' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 B' Rw (22,17)
Which means that we could have just used the classic setup to find 22q algorithms all along!
Lastly, to Ed and Tom, I have added the (15,9) checkboard algorithm as well as the adjacent 4-cycle cases to the 4x4x4 parity algorithms page in the wiki, I have credited you guys, and I have updated the table which summarizes the move counts of 2-cycle and 4-cycle algorithms in 2 dedges.
For those who see that wiki page, you will notice that I added a lot more single dedge flip algorithms, including a bunch of 23qs, algorithms which just use two faces, and wide turn OLL parity algorithms which just use wide turns (that cannot be converted to single dedge flips simply by changing wide turns into inner slice turns).
If anyone has searched at a higher depth and has the 3x3x3 solutions, post them in a .txt file, and I will extract more 23qs and look again for any 21qs. Speaking of which, it's interesting to note that I found only 1 21q which was very close to being a single dedge flip algorithm: r' F l' F2 r F r' F2 D F' D l D' F D' l F2 r.
And two of the 23q's I found cancel to 22 block quarter turns
Rw' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 B' Rw (22,17)
Rw' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 B' Rw (22,17)
Which means that we could have just used the classic setup to find 22q algorithms all along!
Lastly, to Ed and Tom, I have added the (15,9) checkboard algorithm as well as the adjacent 4-cycle cases to the 4x4x4 parity algorithms page in the wiki, I have credited you guys, and I have updated the table which summarizes the move counts of 2-cycle and 4-cycle algorithms in 2 dedges.
For those who see that wiki page, you will notice that I added a lot more single dedge flip algorithms, including a bunch of 23qs, algorithms which just use two faces, and wide turn OLL parity algorithms which just use wide turns (that cannot be converted to single dedge flips simply by changing wide turns into inner slice turns).
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