• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 35,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

Understanding Parity.

A

andyt1992

Guest
Thread starter #1
I often hear people say if you can understand why parity happens you can work out how to solve it, I am not just talking about 4x4's here but about any cube or non cube puzzle that can get parity.
The puzzles I am most interested in understanding why parity happens are:

SQ-1
Fisher Cube
4x4 and upwards
Void Cube - Shifted Centers?

The reason is I dont want to have to remember a load of algorithms and solve cubes in robot mode, I wish to have a greater understanding of the logic of each puzzle and be able to solve each intuitively.
 

cmhardw

Premium Member
Joined
Apr 5, 2006
Messages
4,106
Likes
134
Location
Atlanta, Georgia
WCA
2003HARD01
#4
First hint: Parity is the same concept on all puzzles. It refers to the parity of the permutation of the pieces. If the overall piece permutation parity is odd, then you have "parity error." If the overall piece permutation is even you do not have "parity error." Also, "parity error" is a very poor choice of wording, as the real concept behind what we term parity is really referring to odd parity permutations.

Search for parity on this forum for some other topics with much more detailed explanations. Consider this only a nudge in the right direction.

Chris
 

masterofthebass

Premium Member
Joined
May 13, 2007
Messages
3,923
Likes
3
Location
Denver, CO
WCA
2007COHE01
YouTube
masterofthebass
#5
Fisher Cube doesn't have parity, it only has rotated centers like a picture cube would have.

The case of a void cube parity is quite simple. If you were to take a 3x3, and solve your f2l with the Eslice centers cycled clockwise (red cross piece on the green center, green piece on the orange center, etc.) you would get the same scenario as you do on a void cube. This happens on the void cube quite easily, obviously, because you don't have the centers there to reference off of.

I personally still don't get how sq-1 parity works, and I'll let you search around for the bigcube edge parity.
 

Kirjava

Colourful
Joined
Mar 26, 2006
Messages
6,122
Likes
48
WCA
2006BARL01
YouTube
snkenjoi
#6
First hint: Parity is the same concept on all puzzles. It refers to the parity of the permutation of the pieces. If the overall piece permutation parity is odd, then you have "parity error." If the overall piece permutation is even you do not have "parity error." Also, "parity error" is a very poor choice of wording, as the real concept behind what we term parity is really referring to odd parity permutations.

Search for parity on this forum for some other topics with much more detailed explanations. Consider this only a nudge in the right direction.

Chris

Either cubers don't use this exact definition or "PLL Parity" is really badly named.
 
Joined
Oct 14, 2009
Messages
2,478
Likes
9
Location
Near Toronto
WCA
2009METH01
YouTube
simpsons36109
#7
PLL parity basically means a 2 cycle, so you switch only 2 corners or 2 edges (sq-1, even cubes 4x4+, etc.). On big cubes I think the OLL parity is caused by an odd number of twists in the inner layers like Rw, and the parity alg does another odd with makes the total even. I don't know but I think sq-1 parity happens while you get it into a cube.
 
Joined
Oct 14, 2009
Messages
2,478
Likes
9
Location
Near Toronto
WCA
2009METH01
YouTube
simpsons36109
#9
PLL parity basically means a 2 cycle, so you switch only 2 corners or 2 edges

PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.
Well, I meant i can be thought of like a 2 cycle. (or 4 cycle (O-Perm) and so fourth)

And, two 2 cycles isn't parity, a Z and H Perm arn't
 

Kirjava

Colourful
Joined
Mar 26, 2006
Messages
6,122
Likes
48
WCA
2006BARL01
YouTube
snkenjoi
#10
PLL parity basically means a 2 cycle, so you switch only 2 corners or 2 edges

PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.
Well, I meant i can be thought of like a 2 cycle. (or 4 cycle (O-Perm) and so fourth)

I'm specifically addressing Chris' definition here; you're forgetting that an edge pair is two pieces.

However, PLL parity is defintely not a 4 cycle.

And, two 2 cycles isn't parity, a Z and H Perm arn't

Nice edit. You do know that I stated exactly this in the post you replied to, right?
 
Last edited:
Joined
May 7, 2006
Messages
7,287
Likes
40
WCA
2003POCH01
YouTube
StefanPochmann
#11
Fisher Cube doesn't have parity, it only has rotated centers like a picture cube would have.
So... center orientation parity?

The case of a void cube parity is quite simple. If you were to take a 3x3, and solve your f2l with the Eslice centers cycled clockwise
More direct perspective, not talking about something that isn't there:
Turning an inner slice is a 4-cycle of edges, that's an odd permutation right there.

I personally still don't get how sq-1 parity works
Not even the setup-to-turn-six-corners solution?

Search for parity on this forum for some other topics with much more detailed explanations.
These are also good:
http://www.jaapsch.net/puzzles/theory.htm
http://en.wikipedia.org/wiki/Parity_of_a_permutation

PLL parity is not a single 2 cycle
It *is* from the perspective of solving as a 3x3x3, where it's a 2-cycle of dedges.
 

Kirjava

Colourful
Joined
Mar 26, 2006
Messages
6,122
Likes
48
WCA
2006BARL01
YouTube
snkenjoi
#14
Nice edit. You do know that I stated exactly this in the post you replied to, right?
No you said it
PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.

I don't know what this is supposed to mean, but here's what I meant that you didn't understand;

PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.

I'm saying PLL Parity is really two sets of 2 cycles. Which is not parity. (I thought this was obvious)

And, two 2 cycles isn't parity, a Z and H Perm arn't

And then you seem to tell me this as if I haven't already stated it.

Now, tell me how you think PLL Parity is a 4 cycle please.
 
Joined
Oct 14, 2009
Messages
2,478
Likes
9
Location
Near Toronto
WCA
2009METH01
YouTube
simpsons36109
#16
Nice edit. You do know that I stated exactly this in the post you replied to, right?
No you said it
PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.

I don't know what this is supposed to mean, but here's what I meant that you didn't understand;

PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.

I'm saying PLL Parity is really two sets of 2 cycles. Which is not parity. (I thought this was obvious)

And, two 2 cycles isn't parity, a Z and H Perm arn't

And then you seem to tell me this as if I haven't already stated it.

Now, tell me how you think PLL Parity is a 4 cycle please.
if your saying pll parity is really two 2 cycles, then what do you call it when 2 adjacent / opposite edges are switched on a 4x4?
 

Kirjava

Colourful
Joined
Mar 26, 2006
Messages
6,122
Likes
48
WCA
2006BARL01
YouTube
snkenjoi
#17
Chris' definition doesn't allow that abstraction, referring specifically to pieces.
I have no problem considering a dedge to be a piece.

I do, my problem is that it's two pieces.

if your saying pll parity is really two 2 cycles, then what do you call it when 2 adjacent / opposite edges are switched on a 4x4?

two 2 cycles (assuming you meant dedges and not edges, if you did mean edges (which I seriously doubt) I would simply call it a 2 cycle)
 
Last edited:

Kirjava

Colourful
Joined
Mar 26, 2006
Messages
6,122
Likes
48
WCA
2006BARL01
YouTube
snkenjoi
#19
Chris' definition doesn't allow that abstraction, referring specifically to pieces.
I have no problem considering a dedge to be a piece.
I do, my problem is that it's two pieces.
You're wrong, it's at least *four* pieces, don't forget the stickers!

Come on, you know what I mean. You do however make a valid point. It seems silly to me to think of it as a single piece when they weren't always a single one in the solve, and can return to being two.

It just irks me that it's universally referred to as "PLL Parity" when it's a matter of perspective. For example, vcuber doesn't even understand what I'm talking about.
 
Joined
May 7, 2006
Messages
7,287
Likes
40
WCA
2003POCH01
YouTube
StefanPochmann
#20
it's universally referred to as "PLL Parity"
Is it? Do *you* refer to it as that? Or is it just universally referred to that in the pseudo-3x3x3 context? There I think it's alright.

You do however make a valid point.
Yeah, I was hoping to :). What one considers a piece depends on the purpose and usage.

It seems silly to me to think of it as a single piece when they weren't always a single one in the solve, and can return to being two.
Good point, though if you insist that it shouldn't be called piece, you're just as stubborn as people who insist it should be. Like you said, matter of perspective. And neither is wrong except for calling the other wrong.
 
Top