Parity Issue of a Rubik's Cube

 How to solve Rubik'd Cube - Parity Issue? 

Normally, the edge imparity issue is not happening with a traditional 3x3x3 cube. so Let's Start with a 4x4x4 Rubik's Cube. 

4x4x4 Rubik's Cube

Edge's Imparity - Part 01

Following images shows Edge's im-parity issues that can be aries when 4x4x4 Rubik's cube solving.

By using algorithms and traditional methods to solve a 4x4x4 cube, we came across some sort of difficulties shown in the above image which is a parity issue ( edge parity issue) - Here We face edges in the form of an L-shape, in other words, an adjacent sides. 

Edges Swapped in an L shape

When Cube is fixing and comes across a circumstance like an edge parity of L shape as shown in the below image, how to fix that issue?

By keeping the cube imparity edges to FRONT and RIGHT, do the following algorithm

r2 U2 r2 (Uu)2 r2 u2

r - Inner right side layer -clockwise rotation

Uu - Both upper layers -clockwise rotation  

u - Inner upper layer -clockwise rotation 

    

By doing this, we get three out of four edges are mismatched but in a pattern which can be solved by doing them either clockwise or anti-clockwise movement by using the algorithms.

The below image shows three edges swapped as shown after the above moments.  

but it is easily solved as a 3x3x3 cube using one of the below methods;

    1. Clockwise Rotation 

        - We use this rotation if edges should be moved clockwise

        - Use the following algorithm to fix edges.

    RR  URU R'U'R'U'R' UR'

    2. Anti-Clockwise Rotation 

        - We use this rotation if edges should be swapped anti-clockwise

        - Then, We Use the following algorithm to fix edges.

RU' RURUR U'R'U' R'R'

The solved side should be kept to Backside

Here, Edges should be swapped clockwise rotation.

So, Use the following algorithm and the cube will be fixed.

    RR  URU R'U'R'U'R' UR'

Edge's Imparity - Part 02

Following images shows Edge's im-parity issues that can be aries when 4x4x4 Rubik's cube solving.

Here two out or four TOP layer edges are swapped.

We can easily fix that as shown below;

Hold the cube as shown above and do the same algorithm that we have used in part 01, with adjacent edges swapped. 

r2 U2 r2 (Uu)2 r2 u2

When we use the above algorithm, the Cube will be solved. if any case, edges are mismatched as in part 1, use the same algorithms used there to solve.

or we use alternative algorithms as we desire. if the above is unfamiliar or difficult; use 

2(Uu)   2(Ll)   2U 2l 2U   2(Ll)   2(Uu) 

Edge's Imparity - Part 03 Single edge Issue

Here We are going to show how to fix a single Edge imparity issue. All ok but one edge is flipped. Why this is happening? it is because when we make centre pieces they are not placed correctly. we cannot identify it but if they are placed correctly, the parity issue never happens.

 how to fix that with a single algorithm.

Here we can see a T shape on the yellow side.  Just focus edges and centre. we need to make a cross to solve the cube. 

After making the cross, it is easy to fix the cube.

4x4x4 TOP Layer cross-making algorithm

(Rr)2 B2 - (U2  Ll  U2)  (Rr)'

(U2  Rr  U2)

(F2   Rr  F2)  (Ll)'  - B2   (Rr)2

Keep the imparity issue towards us ( as FRONT) and do the above algorithm.

Keep the imparity edge facing you and do the mentioned algorithm to make a cross in the TOP layer

Then Edge parity issue will be fixed. 

after that solve as a normal 3x3x3 cube

    - OLL - use one oll method or use the traditional way to fix OLL and all yellow on the upper side.

    - PLL - use one of the PLL methods 

or use edges first and then corners. no need for OLL or PLL. need a good eye for colour recognition for speed cube solving. 

Edge's Imparity - Part 04 -Double Edge Imparity

What is meant by that? 

It is actually double-edge swaps. 

Two adjacent edges and the TOP layer and two opposite edges in the Right or left side layers are swapped. 

When we are going to solve a 4x4x4 cube, due to incorrectly placed centre pieces( we could not find them until the last because of pieces are square) some edges are not oriented correctly. some of the are flipped or swapped. here 4 edges of two sides are swapped.

We can fix that with a single algorithm.

Keep the Cube according to the above image (Imparity edges to Front, Back and Right as shown)

Use the following algorithm to fix this.

2R U 2R U

2R 2U 2R 2U

2R U 2R

U' 2R U'

if the cube is held as opposite as the above image; The algorithm also must be opposite. otherwise, the cube will not be fixed.

Suppose the cube holds FRONT-BACK with LEFT-BACK!

The algorithm should be like 

2L U' 2L U'

2L 2U' 2L 2U'

2L U' 2L

U 2L U

2L OR 2L' - both are the same- use them at your convenience. 

after following the above algorithm, we can fix the 4x4x4 cube as a normal 3x3x3. no parity issue then.

Part 05 - Corner Imparity

Sometimes when We are going to solve a cube specially 4x4x4 and above, we come across such a situation like corners are swapped. or flppied. this is known as the corner imparity issue and that can be solved. 

Case 1: Two Corners Swaps - TOP Layer

FRONT-TOP-Right  & BACK-TOP-Left

 corners can be swapped when trying to solve a 4x4x4  Rubik's cube. it can be solved but first, we need to unfix edges and then fix both edges and corners as well. 

By keeping the cube, as shown above, do the following algorithm;

There are two parts to the following algorithm,

Part 1 - use to swap the FRONT & Back edges 

Part 2 - fix both edges and corners at once.

Part 1 -  2(Uu)   2(Ll)   2U 2l 2U   2(Ll)   2(Uu) 

Part 2 - RU'  L 2U  R'UR  L'U'L   2UR'  UL'U 

The Cube will be fixed.

or you can use the below algorithm also to fix the cube.

Part 1 - r2 U2 r2 (Uu)2 r2 u2

Part 2 - RU'  L 2U   R'UR    L'U'L    2UR'   UL'U

Part 1 - use to swap the FRONT & Back edges

Part 2 - fix both edges and corners at once.

Case 2: Two Corners Swaps - TOP Layer

FRONT corners

Here also like the above method. there are two parts of the algorithm used here.

Part 1 - use to swap the FRONT & Back edges

Part 2 - fix both edges and corners at once.

Part 1 - 2Uu 2Ll 2U 2l 2U 2Ll 2Uu

Part 2 - F'U'FUF R'2F UFU F'U' FR

L - Left side outer layer clockwise rotation

l -  Left side inner layer clockwise rotation

another method for fixing the FRONT corner imparity issue is that, use one of the above part 1 to swap edges.

then the cube turns y' - anti-clockwise rotation along the y-axis and, use the following part 2 algorithm

Part 1 - r2 U2 r2 (Uu)2 r2 u2

Then y'

Part 2 - RUR'U' R'F 2R U'R'U'R  U R'F'