How to solve a 3x3x4 Cuboid?

 How to solve a 3x3x4 Cuboid?

Simple but amazing cubes to be introduced such as 3x3x4 cuboids. Here we are going to discuss the solution method of it.

there is a very simple method to fix it.

1. Fix the middle layers 

    First Layer 2 Then Layer 3

2. Fix the outer laters 

    First BOTTOM layer Then the UPPER layer

We cannot solve this as an ordinary 3x3x3 cube that starts to make the bottom layer cross, corners, then the second layer edges followed by the TOP layer cross and lastly, the TOP layer corners.

This should be started to solve from the middle layers which means starting from the second and third layers.

Here we have demonstrated how to solve a cuboid with the following colour pairs;

– Remember the Opposite colour pair –

Light-Blue with Light-Green

Orange with Pink

White with Yellow

An interesting thing is that we cannot mix the 1st layer with the second or third layers or the second layer with the 4^th layer. So mixing layers are 1^st and 4^th and 2^nd and 3^rd respectively.

Fixing the second layer first;

Take white as the bottom or 1^st layer.

Matching opposite colour pairs of the second layer,

To do that need a correct corner piece to identify the correct side colour and where it should be placed.

As an example, let us take the blue-pink-white corner, then place it at the bottom and find out where the two colours of the sides are other than white. 

Blue should be to the left and the pink should be to the right sides. So second layer centrepiece needs to be selected and placed according to this.

Then Green should be opposite to blue and the Orange should be opposite to the Pink.

Check whether any centre colour matches blue or pink in the second layer, and place it in to correct place.

Then check whether the other colour, if blue is matched and placed to the correct position, the pink colour piece needs to be fixed. 

So, find a pink colour centrepiece in the third layer. Then put it to the correct side but above the second layer then rotate that layer for the third to become the second. 

So, fix other centres of the second layer like that.

E.g., let’s take the blue-pink edge.

There are two edges like blue-pink.

If we want to fix that edge (in the second layer), one blue-pink edge should be in layer 3 and it needs to be flipped also. 

The correct edge orientation of the blue-pink edge is that the blue is to be the left side and pink is to be the right side. If flipped it should be the opposite. So before fixing the edge. 

It should be placed like the below image and follow the algorithm RURU’R

It will fix the edge.

Do not rotate the whole cuboid until all edges are in the second layer. 

Just hold the cuboid as it is rotate the second layer imparity edge to the right-front flip the correct edge to the third layer right-front and do the same algorithm. 

Likewise, we can fix all four edges of the second layer.

Fix the third layer

Check whether the two edges are the same colour matched correctly or not? If not, it should be diagonal swapped edges in the cuboid. 

If matched keep them to the left and do the following algorithm to fix the other two edges

RURU’R y’ RU’RUR or 

[RURU'RU'] [D] [RU'RUR] [D']

    U – means both upper layers

    D – means both down layers

Or we can use it only for the middle layers neglecting the upper and bottom layers in this case.

If diagonal swapped edges are there; keep the imparity edges to the front-right and the back-left;

Use the algorithm below – Take U for both upper layers and D for both down layers, or we can use Uu and Dd

[RU'RU'RU] [RD'] [RURU'R] [DR]

OR

R(Uu)'R(Uu)'R(Uu)R(Dd)'R(Uu)R(Uu)'R (Dd)R

After fixing the edges, sometimes we get an imparity centre issue, two, three or four centres can be swapped after fixing the edges. 

We can eliminate them by using the same algorithm one or several times according to centres are placed.

2[RU] 2[RU2] [RURU'R] – for adjacent centre swaps.

When expanding it; There are two parts;

Part 1

Rotate right layer

Rotate both upper layers

Repeat the same both once

Rotate right layer

Rotate both upper layers twice

Repeat the same movements once

Part 2: TOP and BOTTOM edge swapping

Rotate right layer

Rotate both upper layers

Rotate right layer

Rotate both upper layers anti-clockwise

Rotate right layer

Or we can use the following algorithm to fix opposite centre swaps. It will reduce the use of algorithms sometimes.

It is a very easy algorithm for opposite-centre swaps.

[ RU2 ] x3 

Run R UU three times to fix the opposite swapping issue

U – means both upper layers

Fixing the BOTTOM  Layer

After fixing the middle layers, time to go for the outer layers which are the TOP and the BOTTOM layers.

First, we need to fix the top and bottom cross. It is very easy.

BOTTOM layer – white

So, select one edge with white and any colour.

e.g., white-blue

If the selected edge is not correctly positioned and it is in the TOP layer, keep the white-blue edge away from the blue side. 

Then rotate the blue side once matches the white-blue edge with its colour and rotate back. Likewise, do for all other sides except already fixed, to fix the white and yellow cross on the BOTTOM and the TOP layers.

Next, fix the BOTTOM layer corners;

As usual, use RU RU’ R to fix corners.

Keep the corner that should be replaced with the wrong corner of the bottom layer to the TOP right corner and use the above algorithm.

Then do not rotate the whole cuboid, rotate only the bottom layer with the imparity corner that comes to the bottom right and rotate the upper layer correct corner to the TOP-Right and do the same algorithm. Likewise, do for the rest and the bottom layer will be fixed.

After fixing the BOTTOM layers, fix the TOP layer corners and Edges if there are; 

But sometimes we will have to face some parity issues for the edges (adjacent or opposite) in the TOP layer,

2[RU] 2[RU2] [RURU'R] – for adjacent corner swaps. 

[ RU2 ] x3  - opposite-edge swaps.

Even after fixing that, we will have to face another issue two adjacent edges of both middle layers swapped.

As shown in the image; the Green side and the Blue side edges are swapped.

So, by using the following algorithm, we can fix that issue. We just need to keep a cuboid that swapped edges to the FRONT layer's left and right sides.

(Uu)2 RF u2 FR (Uu)2

 

It will be the end of the story. Enjoy!