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Pseudo 3x3 shorter than 3x3?

Joined
May 7, 2006
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2003POCH01
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StefanPochmann
Thread starter #1
Everything you can do on a real 3x3 you can also do on a pseudo 3x3 (let's say on a 4x4). But a pseudo 3x3 allows more moves than a real 3x3. Can this save moves? Is there a 3x3 case that can be solved on a pseudo 3x3 in fewer moves than on a real 3x3?
 
Joined
Aug 4, 2012
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2009ADLA01
#2
If there is one I can't see it, any non-3x3 move done on a pseudo3x3 state will incorporate some 3x3 moves but also require something else to be undone. So it's ultimately going to be less efficient.
 
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Sep 17, 2009
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4EverTrying
#12
I'm glad you guys bumped this thread because I remembered it the other day when I found the shortest PLL parity algorithm in qtm.

When I combined my PLL parity alg (Rw' S2 U D R2 U D Rw') with the PLL parity algorithm (Rw2 U2 Rw2 Uw2 r2 Uw2), the resulting pseudo 3x3x3 algorithm was shorter in both ftm and stm than the optimal 3x3x3 algs.
Rw' S2 U D R2 U D Rw U2 Rw2 Uw2 r2 Uw2 (15 ftm, 13 stm)
z2 x' B2 L U D R2 B E' M' B' U' D' L' S' U2
(17 ftm, 14 stm) (example optimal 3x3x3 alg in both ftm and stm)


We have another example if we combine my PLL parity algorithm with Rw2 F2 U2 r2 U2 F2 Rw2:
Rw' S2 U D R2 U D Rw F2 U2 r2 U2 F2 Rw2 (16 ftm)
U' R' U B F' R2 B' D L R' D' B' F2 D' U2 R D' (17 ftm)(example optimal 3x3x3 alg)

So we now have two more examples besides Stefan's.


EDIT:
I used cuBerBruce's single slice turn 4x4x4 optimal solver with my PLL parity algorithm as a setup, and it gave the following unique solutions (which are all related to my alg):

Rw' S2 U D L2 U D Rw'
Rw S2 U D L2 U D Rw

Rw' S2 U D R2 U D Rw'
Rw S2 U D R2 U D Rw

Rw U D L2 U D S2 Rw
Rw' U D L2 U D S2 Rw'

Rw U D R2 U D S2 Rw
Rw' U D R2 U D S2 Rw'
 
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