Contructing Algorithms (not a how to, sorry)

[rachmaninovian]

ah yes, thanks guys this has been interesting to me. thanks for all your help!

 

[Christopher Mowla]

and this - [Rw U2 Rw',R' U' R U]

This reminds me of something.

The 3-flip? lol, I was posting about it just recently in the FMC tread (in this subforum). Cmowla replied to there so he already did it

Kenneth, did you see my new "2-gen" 3-flipper and 5-flipper in the "A Collection of Algorithms" thread a few days ago?
Rw U2 Rw U2 Rw' U R U Rw U2 Rw' U' R' U' Rw R U R U Rw U2 Rw' U' R' U' Rw' U2 Rw' U2 Rw' (36 qtm, 30f)

Rw U2 Rw U' R U Rw U2 Rw' U' R' U' Rw U R U Rw U2 Rw' U' R' U' Rw' U R U Rw U2 Rw' U' R' U' Rw U R U Rw U2 Rw' U' R' U' R' U2 Rw' U2 Rw' (54 qtm, 47f)

 

[Kenneth]

Lol, no, I missed those, 47f! I won't even try it on a cube

 

[Christopher Mowla]

I don't know. I probably can't do better than cube explorer:

r F2 U2 r' B2 l B2 r D2 l' E2 B2 l' y2 (13)

, which is equal to what we can already do using "LU'F (PLL parity) F'UL'", assuming that we use a PLL parity algorithm like r2 F2 U2 r2 U2 F2 r2, so that it can be applied to all size cubes. If not, for the 4x4x4, 12 may be the minimum.

Sorry for the bump, but we were discussing the fewest moves for the case above, and I just found an interesting algorithm.

It's very horrible for speed, but it is 12 btm. It's actually pure too, and thus it can be applied to all big cube sizes, not just the 4x4x4. Hence the upper bound in btm for big cube sizes has just been lowered one btm. It appears to be optimal in quarter turns too. (E.G. L U' F r2 U2 r2 Uw2 r2 u2 F' U L' (18q, 12 btm) ).

F2 l E' F2 E l' r' E' F2 E r F2 (16q, 12 btm)
= [F2 r' E': [E r l E', F2]]