[Help Thread] 4x4 Discussion

[joey]

Parity in cage: Doing the algoritm that swaps two adjacent wings or swaps two dedges, or both.
Parity in reduction: Fixing the orientation and permutation of the cube so that it becomes solvable with only 3x3 moves.

So.. cage does have parity

 

[cmhardw]

Just to nitpick, because this does bug me a bit. The "PLL parity" is a parity, I don't see why people are saying it's not. However, it is not a parity in the same sense as the "OLL parity".

The OLL parity is a parity in the edge pieces of a 4x4x4, when trying to solve it as a 4x4x4.

The PLL parity is a parity in the solved edge groups of a 4x4x4, when trying to solve it as a 3x3x3.

Both are parites, but for different reasons. You can't say the OLL parity is a parity and the PLL parity is not, that is incorrect. You are comparing situations when trying to view the cube as either a 4x4x4 or a 3x3x3, so those are not comparable in a sense. They are both parities, but for different reasons.

Chris

 

[trying-to-speedcube...]

Cage method means centers last, right?
So when there is a 2-cycle of edges left, just do a slice move, and then you have a 3-cycle left. Cage doesn't have to have parity.

And Chris, the OLL parity is a single 2-cycle, so parity.
The PLL parity is a double 2-cycle, so no real parity.

 

[nitrocan]

Parity: A case that cannot occur on a 3x3, but can occur on bigger cubes.

PLL PARITY = PARITY.

 

[cmhardw]

And Chris, the OLL parity is a single 2-cycle, so parity.
The PLL parity is a double 2-cycle, so no real parity.

With all due respect, this post illustrates exactly my point in my first post.

The OLL parity is a parity in the edge pieces of a 4x4x4, when trying to solve it as a 4x4x4.

The PLL parity is a parity in the solved edge groups of a 4x4x4, when trying to solve it as a 3x3x3.

So when you have PLL parity, you have 4 pieces to swap in two 2-cycles. This is not a parity when viewing the puzzle as a 4x4x4 cube. However this is a parity when viewing the puzzle as a 3x3x3 cube.

I'm not trying to be rude, but this kind of distinction gets passed over all the time, and I find it absolutely incorrect to say the PLL parity is not a parity. It's not a parity when viewing the puzzle as a 4x4x4, true. Hopwever, it is certainly a parity when viewing the puzzle as a 3x3x3, which is the intention of solving via the reduction method.

Respectfully,
Chris

 

[Kirjava]

'PLL parity' is is a parity in the same way that the TPerm is a parity on 3x3x3 - in a specific situation.

Since most people use reduction on 4x4x4 and most use a none-BLD method for 3x3x3 speedsolving, I can see how the naming scheme arose - popularity. However, I solve my 4x4x4 as a 4x4x4 - not a 3x3x3. Excuse me if I don't recognise your abstraction at times.

As for cage varients - parity exists, but can also be completely avoided.

 

[joey]

Hah, I like how 'trying-to-speedcube' tried to argue with cmhardw :|

As for cage varients - parity exists, but can also be completely avoided.

Can be avoided with reduction too

 

[Lt-UnReaL]

If you want to cheat, count the number of slice turns you make in a normal 4x4 scramble. If that number is:
1) Even
- Solve centers with an even number of slice turns. (even+even=even)
2) Odd
- Solve centers with an odd number of slice turns. (odd+odd=even)

Double turns count as 2. Ultimately you want an even number of slice turns before you get to the 3x3 stage.

In case some people didn't notice, that ^ is for avoiding OLL parity.

 

[fanwuq]

If you want to cheat, count the number of slice turns you make in a normal 4x4 scramble. If that number is:
1) Even
- Solve centers with an even number of slice turns. (even+even=even)
2) Odd
- Solve centers with an odd number of slice turns. (odd+odd=even)

Double turns count as 2. Ultimately you want an even number of slice turns before you get to the 3x3 stage.

In case some people didn't notice, that ^ is for avoiding OLL parity.

Do you mean inner slice turns are just turns by STM?

 

[cmhardw]

'PLL parity' is is a parity in the same way that the TPerm is a parity on 3x3x3 - in a specific situation.

Since most people use reduction on 4x4x4 and most use a none-BLD method for 3x3x3 speedsolving, I can see how the naming scheme arose - popularity. However, I solve my 4x4x4 as a 4x4x4 - not a 3x3x3. Excuse me if I don't recognise your abstraction at times.

I agree that naming the PLL parity as "the parity that only exists as a parity when viewing it as a 3x3x3 after reduction" would be ridiculous ;-) However, the blanket statement: "the PLL parity is not really a parity" is simply a false statement without further qualification. That was my original point.

Chris

 

[Stefan]

Parity: A case that cannot occur on a 3x3, but can occur on bigger cubes.

AAAAAHHHHHH
(yes, this actually made me scream)

 

[IamWEB]

Parity: A case that cannot occur on a 3x3, but can occur on bigger cubes.

AAAAAHHHHHH
(yes, this actually made me scream)

It'll be ok. We'll get through Stefan, don't worry.

 

[fanwuq]

Parity: A case that cannot occur on a 3x3, but can occur on bigger cubes.

AAAAAHHHHHH
(yes, this actually made me scream)

I demand a video!

 

[Kirjava]

"the parity that only exists as a parity when viewing it as a 3x3x3 after reduction"

I call it an X-Perm

 

[jambob28]

Hi, if you lern 2 look oll and then this method of pll http://www.youtube.com/watch?v=g8_jKjwNkeY you will ony have to learn the long alg, ive solved the 4x4x4 this way like 100 times and ive never got the other one. i know its a 3x3x3 tutorial but it does help me

 

[Mike Hughey]

Parity: A case that cannot occur on a 3x3, but can occur on bigger cubes.

AAAAAHHHHHH
(yes, this actually made me scream)

I demand a video!

I think it would be tremendously useful to have a video of this to use as a stock answer for all kinds of questions. We really need this video!

(And it's funny, because the first thing I thought of when I read that post from nitrocan was a mental image of Stefan having a fit.)

 

[qqwref]

I'll put in my vote for also wanting a video. I can totally see this being the most-embedded video on speedsolving in a matter of weeks.

 

[TheJoker]

hello sir... since you are all talking... i might as well add this... and ask a question if it is consider cheating...

i solve 4x4 as regular solver here... reduction method... center, edge, 3x3...

i do encounter "parity" from OLL and PLL... actually 1 OLL parity... edge flip... then 4 OLL parity... adjacent edge, horizontal edge, horizontal corner and diagonal corner... can't explain it but i guess you know what i'm saying...

then i have a very loose over worn ES 4x4... it is loosely no matter how i tried to tighten the screw... so what i did is ... solve the ES 4x4... then i put a WHITE mark on screw inside where is the white face... then put a RED mark on screw inside where the red face is...

since it is loosely... although a tremendous lockups... it can still be speedsolve... so when i want to impress other cuber here in my country... i used that old loose es 4x4...

then in the inspection i look for the the white mark screw... then look for the white... i know where i want to put my white face now... then solve the yellow... turn the cube... then inspect the cube as if i'm looking for blue,red,green,orange... but i'm actually looking for my red screw mark... when i found it... i solve the red face there...

by doing this... i never encounter any parity at all... so my time drop considerably with this cube... and my fellow cuber here was amazed how fast i am...

well as far as i'm using this cube... i never did encounter parity yet...

is this consider CHEATING...???

thanks a lot... heheheheheheheh...

 

[Neroflux]

can 4x4 parity be avoided by using a different way to pair up the last 2 edges?

 

[Stefan]

is this consider CHEATING...???

It would be if it worked.

can 4x4 parity be avoided by using a different way to pair up the last 2 edges?

Sure. It's just not exactly easy to recognize.