How to solve the 2x2x4 Tower Cube
The 2x2x4 Tower Cube is a shape-shifting puzzle. This adds an extra element of confusion when compared to other puzzles such as the Pocket and Rubik's cube. However, if you've mastered the Pocket Cube (if not find out how to solve the Pocket cube here) you are in fact halfway to completing this puzzle! The other half is using algorithms from the 3x3x4 cube solution.
Notation
F = Front
B = Back
L = Left
R = Right
U = Up
D = Down
The following is new notation different from the normal cube notation thanks to the extra layers:
u = up
d = down
Part 1
Step 1 is to solved the top and bottom layers, i.e. the corner pieces. This can be done using the following two algorithms and picturing the cuboid as a 2x2x2 Pocket cube by considering each corner piece and the middle piece underneath it as one piece. First you need to get one end of corners in place and then orientate the other end. The pictures are taken directly from the guide on how to solve the Pocket cube found here.
First, pick the end you want to solve as your first layer, here we will solve the white layer first, and in particular pick a cube that belongs to that side as your reference point. Don't worry if the other end of your 2x2x4 tower cube is sticking out all over the place, we'll orientate those correctly in a moment
Aim
Soving the first layer is identical to solving the corners on a 3x3x3 Rubik's cube. Simply find the corner you want to move next to your reference piece, checking that the adjacent edges match, place it underneath where it needs to go and then perform the following algorithm (it may need to be performed multiple times and again don't worry if pieces are sticking out everywhere on the other end!):
Algorithm: R' D' R D
Step 2
For the other end the pieces need to first be orienated correctly
Aim
First, get the cube into one of the following positions. This can be done by performing the below algorithm. Once you have done this, position the cube as shown and perform the same algorithm, this may take several repetitions. After each repetition ensure you orientate the cube correctly before reapplying the algorithm.
Algorithm: R U R' U R U2 R'
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Part 2
Now that your shape is back in its correct shape we need to position the pieces correctly.
Step 3
The first step to solve the 3x3x4 cube is correctly placing the edge pieces in one of the middle two layers.
Aim
The first three edge pieces of the layer can be done intuitively. If you're lucky the fourth edge piece will also fall into place but if not to swap the front-right-top piece with the front-right-bottom piece, marked by an X each, do the following
Algorithm: F (Dd) F (Dd)' F
Part 3
Step 4
Step 4 is to solve the edge pieces in the other middle layer.
Aim
Solve the edge pieces in the other middle layer. To swap two pieces in the same layer, marked by an X each, arrange as follows. This diagram is a view from the back, so you will need to arrange it like this and then turn it round before performing the algorithm!
Algorithm: R F (Dd)' F (Dd) R (Dd)' F (Dd) R (Dd)'
Step 5
Now to place the corners onto the correct face. This can be done through intuition alone.
Aim
Step 6
Step 6 is the final step in this how to solve the 2x2x4 tower cube guide!
Aim
Then you need to move them into their correct positions. Use the below algorithm to swap the two corners in the bottom back marked with an X each. This diagram is a view from the back, so you will need to arrange it like this and then turn it round before performing the algorithm!
Algorithm: R F D' F D R D' F U F U'