4x4 Parity Algorithms

[whauk]

R2 D' x is a shorter setup

 

[chikato_tan]

R U R' U' r2 U2 r2 Uw2 r2 u2 U R U' R'

are you sure it`s the right one , because i follow the alg and it becomes a mess , BTW , what`s the difference between u and Uw ?

 

[Tentacius]

"u" is just the inner layer, and Uw is both the inner and outer layer. (WCA notation)

http://alg.garron.us/?alg=u_Uw&cube=4x4x4&notation=WCA

 

[ben1996123]

z Dw' m D Lw' Uw' r' Uw Lw Uw' Lw2 Bw' r' Bw Rw' R' u s Uw z'

 

[reThinking the Cube]

cuBerBruce's post shows the shortest 4x4x4 algorithms which convert a 4x4x4 with parity into a pseudo 3x3x3,...

I know you and CB already know this, but I feel obligated to say it anyway - that the shortest AND (IMO) best way to do this, is by the first 13 turns of reParity™ = Rw U2 Lw' U2 x' Rw' U2 Lw U2 Rw' U2 Lw U2 Lw'

 

[Cheese11]

http://www.youtube.com/user/Erickulchycki?feature=mhee#p/u/7/rx5YKIlgOhs

 

[Jorghi]

I've never done 4x4, but how many parity algorithms are there? Couldn't you do Parity + Edge Permutation then Corner permutation. That way if the corners are already permuted then you are lucky.

 

[Hershey]

I've never done 4x4, but how many parity algorithms are there? Couldn't you do Parity + Edge Permutation then Corner permutation. That way if the corners are already permuted then you are lucky.

You really need only 2-3 algs:
OLL parity
PLL 4 edge swap (aka PLL parity)
Double parity


PLL parity is technically not parity since there is an even number of swaps (2 swaps).

 

[uberCuber]

For purposes of normal reduction solving, I've never really seen the point in a "double parity" alg. For it to be useful, you would have to recognize if there is PLL parity before even beginning OLL. Since you can tell if you will have OLL parity or not before you even finish F2L, how are you supposed to recognize PLL quickly enough to make it worthwhile, considering that you have to recognize it without the LL correctly oriented?

 

[cubersmith]

You really need only 2-3 algs:
OLL parity
PLL 4 edge swap (aka PLL parity)
Double parity


PLL parity is technically not parity since there is an even number of swaps (2 swaps).

I didnt know it had to be an odd number of swaps to be parity?

 

[uberCuber]

I didnt know it had to be an odd number of swaps to be parity?

Define parity.

 

[reThinking the Cube]

PLL parity is technically not parity since there is an even number of swaps (2 swaps).

Technically, it will be parity (unable to solve as a reduced 3x3x3 without using slice turns) if the corner permutation does not match the dedge permutation. What is described as PLL parity is a double swap of 4x4x4 edge pieces, but is also a 2-cycle of 3x3x3 dedge (odd dedge permutation) in the reduction state. If the corners are already solved - then the corner permutation is even and does not match that dedge permutation, and this is an impossibility with an actual 3x3x3, and therefore it must also be parity.

 

[uberCuber]

Definitions of parity are so inconsistent. If using a direct-solve method, that exact same case would not be considered parity.

 

[Hershey]

I think Chris Hardwick said somewhere that PLL parity is only called a parity when using reduction or something like that?

anyway I thought in cubing, parity is an odd number of swaps for edges/corners.

Not sure if this is faster, but you might like it:
Rw' U R U Lw' U2 Rw' U2
r2
U2 Rw U2 Lw U' R' U' Rw

OMG alg.

 

[Rpotts]

Technically, it will be parity (unable to solve as a reduced 3x3x3 without using slice turns)

this is not a technical definition of parity.

 

[reThinking the Cube]

this is not a technical definition of parity.

Technically, it is.

 

[Hershey]

What is the definition of parity?

"Parity is a misnomer cubing term that is used colloquially to describe an odd permutation of pieces within a certain defined orbital"?

Technically, it is.

Oh really?

 

[reThinking the Cube]

Definitions of parity are so inconsistent. If using a direct-solve method, that exact same case would not be considered parity.

Show me a direct-solve parity case, so that I might define it consistently.

 

[Rpotts]

it's an swap of two pieces.

OLL parity is parity in direct solve methods, or K4 ELL, but PLL parity is not, as its two two swaps

 

[Hershey]

Show me a direct-solve parity case, so that I might define it consistently.

rU2r'U2r'U2lU2r'U2rU2F2r2F2l' is a direct solve parity.

rU2r'U2r'U2lU2r'U2rU2F2r2F2l'U2rU2r'U2r'U2lU2r'U2rU2F2r2F2l' is PLL parity done by doing direct solve parity case , U2, then the direct solve parity case again.


If you do OLL parity, U2, and then OLL parity again, you end up with two flipped edges (the <M,U> algorithm on 3x3).]
Basically doing an odd swap of edges then doing an odd swap again creates a case that is not parity.

OLL parity is parity in direct solve methods, or K4 ELL, but PLL parity is not, as its two two swaps

Why not be consistent with definitions and consider PLL "parity" not to be parity at all? Lets not relate 4x4 to 3x3?