4x4x4 Rubiks Cube strategy

With a 4x4x4 cube, it's possible to apply the same strategies as for a 3x3x3, either treating it as a 3x3x3 with a double-width middle or else as a 2x2x2 and just working on the corner "quadrants". Centres of each face can also be handled as a 2x2x2 cube, ignoring the outer layers entirely.

Is it better to apply those strategies in one order rather than the other?

Answer

Notation

We need to have some notation for the algorithms. We use:

• $U$ for the upper layer and $u$ for the middle upper layer.


• $R$ for the right layer and $r$ for the middle right layer.


• $L$ for the right layer and $l$ for the middle left layer.


• $F$ for the front layer and $f$ for the middle front layer.


• $?^2$ for turning a layer twice


• $?'$ for turning counter clockwise

Example: $(Uu)^2 ~ l'$ is turning the upper half of the cube twice and turning the middle left layer counter clockwise.

Solving
Note that you need the same colours as on the 3x3x3, but with the 4x4x4 you can mix them up and later on while solving you have a problem when yours centers doesn't have the same colours as the 3x3x3. So it easier to reduce to a 3x3x3 than a 2x2x2.

1. Solve the centers, by bringing two times two pieces together and then bring those pieces together and you have a solved center: (this can mostly done by intuition)
   
   
   
   • White Up, Red Front, Blue Right,
   
   
   • Yellow opposite to White
   
   
   • Red opposite to Orange
   
   
   • Blue opposite to green
   
   
   
   
   


2. Solve the edges (watch the video linked below and this becomes intuition)


3. Solve it as a 3x3x3


4. Solve the parities:
   
   
   
   • Edge parity: you want to flip one edge. $r' ~ U^2 ~ l ~ F^2 ~ l' ~ F^2 ~ r^2 ~ U^2 ~ r ~ U^2 ~ r' ~ U^2 ~ F^2 ~ r^2 ~ F^2$
   
   
   • Corner parity you want to swap two corners. $U^2 ~ r^2 ~ U^2 ~ r^2 ~ (Uu)^2 ~ r^2 ~ (Uu)^2$
     Note: Actually you swap two edges, so you need to do some more solving after you have performed this algorithm.
   
   
   
   



5. 
   

   Finish the cube and profit!

   
   

   Corner parity and edge parity

   
   

And I want to show you a good YouTube tutorial. (in this video he never mentioned a 2x2x2, but he did find it necessary to master the 3x3x3)