## Understand edge parity?

General discussions and topics

### Understand edge parity?

 Hi, I'm new to cubing and can easily complete my 3x3x3 and 4x4x4 cubes. The thrill for me is to understand how I'm doing the solve, not just performing the algorithms as fast as I can. I fully understand all my moves on the 3x3x3 but the algorithm of the revenge's edge parity fix is just a sequence of moves to me. Dose any one know of any websites that don't just list algs but actually explain why they work? ..... I mean what is parity? How is it created? And how dose the long alg fix the problem? Any help or ideas much appreciated. Cheers Danny
dannylaw

Posts: 5
Joined: Fri Mar 06, 2009 10:39 am

### Re: Understand edge parity?

As far as I know, a parity on the 4x4 is basically the effect of a misolved center piece on the edges. When you solve each center, notice how four cubies are identical. It they are solved in a certain way (I'm not sure how), they will change the edges.

When you do the parity algorithms, it switches two of the center pieces which leads to a change in the edge pieces.

For a better explanation, go here.

Poley

Posts: 7
Joined: Tue Oct 14, 2008 10:44 am

### Re: Understand edge parity?

[quote user='dannylaw']

 Hi, I'm new to cubing and can easily complete my 3x3x3 and 4x4x4 cubes. The thrill for me is to understand how I'm doing the solve, not just performing the algorithms as fast as I can. I fully understand all my moves on the 3x3x3 but the algorithm of the revenge's edge parity fix is just a sequence of moves to me. Dose any one know of any websites that don't just list algs but actually explain why they work? ..... I mean what is parity? How is it created? And how dose the long alg fix the problem? Any help or ideas much appreciated. Cheersnope Danny
[/quote]
cubingking77

Posts: 133
Joined: Fri Feb 20, 2009 2:08 pm

### Re: Understand edge parity?

I've been trying to figure this out as well...I refuse to memorize an "algorithm" because that is just allowing myself to be programmed like a robot to do a sequence of moves instead of truly understanding the problem.

I would like to know why the moves to resolve edge parity work....as any other sequence of moves to solve a 4X4 cube can easily be explained.
shane_delon

Posts: 1
Joined: Sat May 19, 2012 4:54 am

### Re: Understand edge parity?

(Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2 is the edge parity alg.
This alg uses single layer turns for UFB but double layer turns for LR
The combination probably causes the parity.
By the time you do F2 (Rr) F2 you can see on the D face the flipped piece.

If you want to use a longer but understandable algorithm, learn Rubik's Cube commutators.
lol, here to help ^_~
Sharkretriver

Posts: 367
Joined: Thu Jul 14, 2011 10:11 pm

### Re: Understand edge parity?

I have the same problem. I try to solve the cube without memorizing algorithms, but i couldn't find a way to solve the double edge orientation parity.
I found this algorithm that seems more logical that others to me, at least is more simetrical. Having the dedge parity on front top:

Rr U2 Rr
U2 r' U2 r
U2 l' U2 l
F2 r' F2
Rr' U2 Rr'

Try studying the algorithm, do it slowly, following the edges in order to understand what is really happening.
facutroche

Posts: 1
Joined: Wed Apr 24, 2013 6:42 pm

### Re: Understand edge parity?

About 2 years ago, I deciphered the common parity algorithms and made "derivation videos" for them on YouTube.

I started a thread on speedsolving.com around that time. For the links to the derivation videos I am talking about, see the first post.
This is the thread Methods for Forming 2-Cycle Odd Parity Algorithms for Big Cubes

I have packed a lot of original information in that thread (I didn't learn any content within from anywhere, and no one before me figured any of this out), so if you all have any questions, ask away. I probably should start making more videos, but I've been working on a huge Rubik's cube project lately that is eating up all of my spare time.

I have dumped all of the algorithms I have found for the 4x4x4 on this wiki page (my name is Christopher Mowla...I recently added authors names on that page, so every algorithm with my name to the right of it I have found without a computer solver...well there are a few exceptions but not many):
4x4x4 Parity Algorithms

Also, if anyone is curious, I believe out of all of the parity algorithms I have found, the following double parity algorithm, being just a conjugate, is probably the easiest OLL parity algorithm to understand, as it doesn't require any knowledge of commutators. It only requires that you know that all OLL parity algorithms have an odd number of inner layer quarter turns. That's about it. It's very straight forward.
(B Lw2 U' L' U r u2 b' r2 Bw2 E) r' (E' Bw2 r2 b u2 r' U' L U Lw2 B')

After the moves (B Lw2 U' L' U r u2 b' r2 Bw2 E) are executed, study the pattern of the center pieces in the inner layer right slice: only red and orange center pieces are in that slice AND they are in the formation that, if you do an inner layer quarter turn, they stay exactly the same. This way we can do whatever we want to that slice and, once we undo the moves (B Lw2 U' L' U r u2 b' r2 Bw2 E) with (E' Bw2 r2 b u2 r' U' L U Lw2 B'), then the centers will not be affected at all (well, on a picture cube they will be, but not on a 6 colored cube).

And, of course, the 4 edge pieces in the inner layer right slice are in the correct formation with respect to each other so that, once the inner layer quarter turn r' is executed, then they swap with each other to preserve the edges. To understand why this works, it's just a matter of understanding precisely which 4-cycle double parity is and then placing the edges in the correct locations (with respect to each other).

NOTE: It doesn't matter how many moves it takes you to create the same setup as (B Lw2 U' L' U r u2 b' r2 Bw2 E), only that you understand that setup. If you understand that setup, you're set. I just tried several paths to find the shortest sequence of moves to create that setup, so don't be hard on yourself or be the least bit intimidated by that move sequence.

For all other parity algorithm types (see the different categories I have made on the wiki page I linked to), they require more knowledge than the double parity conjugate above. If you want to create the single edge flip case from that, you just need to do PLL parity which is
r2 U2 r2 Uw2 r2 u2 = r2 U2 r2 U2 r2 + r2 u2 r2 u2
or, better yet, the conjugate (r2 F2 U2) r2 (U2 F2 r2).

I can understand why it is so hard to understand parity algorithms, but, at the same time, most short existing algorithms I have either made myself or have studied and understood to a level that I can see most of them share a similar "tactic". I explain quite a bit about various parity algorithms in the thread I linked to earlier.

However, if you can understand the conjugate I have show above, then you can truly say that you understand how one edge parity algorithm works without any doubt or pretending.
cmowla

Posts: 2
Joined: Fri May 10, 2013 4:41 am