why parity?

[DeCubeRob]

why can't a 3x3 have parity, but a 2x2 can and a 4x4 and 5x5?
does it have something to do with the number of cuby's?

just something i notice

so why is the 3x3 holy, and doesn't have parity?

 

[Kirjava]

3x3x3 can have parity

 

[sa11297]

in bld it can. like an r perm situation. its just that most people learn 3x3 then 4x4 so it seems like the 3x3 parity is normal

 

[Kirjava]

It can have parity in normal speedsolving too.

 

[Kenneth]

The term parity is missused in cubing. From start it was the states you get when doing the '3x3x3 step' when using reduction on a 4x4x4 that you cannot get on a 3x3x3, the cases are not in parity with a real 3x3x3.

So far it is ok, but then all cases on all puzzles that are pure 2-cycles, single flips or twists are 'paritys' and that is not correct, these are something else...

 

[DeCubeRob]

so parity is also when i have two corners switched, and flipped the correct way, while the rest of the cube is solved?
(3x3 cube)

 

[Kirjava]

No, that case is impossible.

It depends how you define 'parity' really. There are a few different types of 3x3x3 parity.

 

[DeCubeRob]

yea i just realised what i said is bulsh@t

 

[Kirjava]

Trying to think of the different types of 3x3x3 parity situations.

I can think of Corner/Edge 2Cycle, Human Kociemba Half Turn Redux, Keychain and U/D CO.

 

[penfold1992]

2x2 doesnt really have a parity, the parity you come across is not actually a parity in terms of edges... as there are no edges.
a 3x3x3 cant have a parity as it comes with the rules of the rubiks cube (such as you cant rotate 2 corners only, the same direction) or only a 3 edges can be swapped with the same orientation...
a 4x4x4 has a parity because...i dno

 

[nitay6669]

im not sure why 4X4 can have oll parity, but the pll parity is actually 2 edges swapped and 2 center pieces ( from the same color) swapped. so you cant see it but there are 2 cycles and not just one.

 

[Kirjava]

Not really. I can perform PLL parity without swapping any centres.

 

[DeCubeRob]

I can think of Corner/Edge 2Cycle, Human Kociemba Half Turn Redux, Keychain and U/D CO.

don't use fancy words lol. i don't really understood what you said

 

[freshcuber]

I believe Roux has a parity so 3x3 does have parity outside blind. I'm not any sorts of a knowledgable person on Roux though.

4x4 OLL parity happens because you pair up an edge in the wrong orientation. Once it's like that you can't flip a single edge without the parity alg. If you're a white cross solver you always end up with a yellow edge that has the parity but in reality any edge can have the parity. You can just solve every edge in cross and F2L because the edge that originally has parity is correctly oriented while solving which then misorients another edge until you get to OLL at which point you can no longer continue the solve in a normal fashion until you apply the alg.

That's my understanding of it at least.

 

[Kirjava]

I believe Roux has a parity

Nope.

4x4 OLL parity happens because you pair up an edge in the wrong orientation.

Nope.

 

[RubikZz]

An void cube can get parity.

 

[freshcuber]

Then would you care to elaborate?

 

[Cool Frog]

Parity,two 2 cycles (edges and corners). non-parity, n 3 cycles on a 3x3. Yes?
What algorithm do you use to solve parity in human kociemba, Kirjava?

 

[Kirjava]

Then would you care to elaborate?

"The sun is green"

"No it isn't"

"Would you care to elaborate?"

"..."

 

[freshcuber]

I'll rephrase it.

Why is there 4x4 OLL parity? Anybody?