# Pseudo 3x3 shorter than 3x3?



## Stefan (Sep 14, 2013)

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?


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## Hypocrism (Sep 14, 2013)

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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## rj (Sep 14, 2013)

On 5x5 centers, yes.


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## googlebleh (Sep 14, 2013)

I saw a 3x3x3 alg qq found for 4x4x4 a long time ago and spent the last 20 mins finding it



qqwref said:


> 4x4x4 <R,r,U> stuff found by hand:
> 
> an OLL
> Rw U2 Rw' U' R U r U2 Rw'



:/ too bad it's longer than the regular 3x3x3 alg


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## Stefan (Sep 14, 2013)

rj said:


> On 5x5 centers, yes.



Which one?

I just found one for 4x4:


Spoiler



Rw2 U2 D2 F2 B2 Rw2 (or Rw2 E2 S2 Rw2 if you allow slice moves). Two moves shorter than on a real 3x3.


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## ben1996123 (Sep 14, 2013)

thought about this before, specifically superflip on a 4x4. dno if ittuce less moves though


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## Stefan (Sep 14, 2013)

ben1996123 said:


> dno if ittuce less moves



You misspelled "fewer".

Superflip would be very interesting, yes.


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## windhero (Sep 14, 2013)

Stefan said:


> Which one?
> 
> I just found one for 4x4:
> 
> ...



I'm pretty sure he meant just doing 5x5 redux centers only, which wouldnt count as pseudo 3x3. Like you could have a red/red/red corner for example.


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## ncube (Sep 15, 2013)

It would be interesting if there could be better OLLs and PLLs on pseudo 3x3.


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## TiLiMayor (Jan 2, 2014)

I immediately thought of this: Rw U2 Rw2' F2 Rw F2 Rw U2 Rw2' F2 Rw
But seems like its the same move count for the real 3x3 alg..


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## Logical101 (Jan 2, 2014)

there is the fact that if you practice one alg you will get faster at it than if you practice 2 algs, yet this is a good idea


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## Christopher Mowla (Jan 2, 2014)

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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## Christopher Mowla (May 23, 2021)

In January, I was chatting with @mrCage on the twistypuzzles forum (who isn't active on this site anymore), and he found an algorithm which rotates two opposite (composite) centers on a 4x4x4 supercube which is 3 half turns less than the optimal algorithm to rotate two opposite fixed centers on a 3x3x3 supercube!
2R2 2F2 m2 2F2 2L2

Original post.


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