Rubiks Cube

3x3 Rubiks Cube

The standard Rubiks Cube size is a 3x3.

Solving

A basic, layer-by-layer Rubiks Cube solution technique: Rubiks Cube/Layer Method

There are other, more advanced techniques:

Friedrichs Method (CFOP) - https://ruwix.com/the-rubiks-cube/advanced-cfop-fridrich/

2x2 Method -

Blindfolded - https://ruwix.com/the-rubiks-cube/how-to-solve-the-rubiks-cube-blindfolded-tutorial/

Empirical Investigations

Combinatorics and various numbers related to the Rubiks Cube: Rubiks Cube/Numbers

Theoretical Investigations

Notes on group theory and Rubiks Cube patterns: Rubiks Cube/Patterns

4x4 Rubiks Revenge

Solving

For the most part, solving the 4x4 is a lot like solving the 3x3, but complicated by two initial steps that need to happen first - arranging the center 2x2 cubies of each face, then orienting the two edge pairs of cubies of each of the twelve sides of the cube to match up.

Then you can think of these edge pairs as sticking together, and the whole thing becomes a 3x3 cube, but with 2 rows/columns instead of a single middle row/column.

However, the parity case complicates things. Whereas the 3x3 cube has a few ending scenarios with regard to the parity of the top layer and how the squares are oriented (memorizing these becomes crucial to fast solves), the 4x4 cube has some situations that are impossible on a 3x3 cube (such as two corner cubies being swapped) or a cube that's entirely solved except for two inside-out cubies on one of the top edges.

See Rubiks Revenge page for pictures.

Refs

• https://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms
• https://ruwix.com/twisty-puzzles/4x4x4-rubiks-cube-rubiks-revenge/parity/
• https://ruwix.com/twisty-puzzles/4x4x4-rubiks-cube-rubiks-revenge/
• http://web.mit.edu/sp.268/www/rubik.pdf
• http://web.mit.edu/sp.268/www/2010/rubikSlides.pdf
• https://math.stackexchange.com/questions/332146/efficient-method-to-determine-the-order-of-a-permutation-in-s-n