Rubik's Cube - Solution and Notation

Rubik's Cube is a famous puzzle cube invented by Ernö Rubik in 1974.

For those unfamiliar with the cube, the basic concept is that the cube is made up of 27 cubelets. The exposed faces of these each have a different colour. Rubik invented a mechanism whereby any layer of cubelets (i.e. 9 cubelets) can be rotated in a clockwise or an anticlockwise (counterclockwise) direction, independently of the other layers. By doing this many times at random, the colours displayed on the faces become jumbled up. The objective of the puzzle is to restore the initial position in which each side of the cube shows only one colour.

The approach to solving Rubik's Cube and the Wolstenholme notation and tools (sequences of twists) used are best seen in the Kublitz Cube application - an electronic version of the Cube. This is a version of the Cube in which you can effectively see, or know, the colours on all the cubelets without needing to turn the Cube around. This is effected by providing gaps between the 27 cubelets and by ensuring that the colours on any pair of opposite cubelet faces are identical; so, while you cannot see the colours on the back of the Cube, you can see those on the forward-facing sides of the back cubelets, which are the same.

You can find an online version of Kublitz Cube here. Tap on the Help button to see the approach to solving the Cube and the Wolstenholme notation. With the Kublitz Cube application you don't simply get the approach to solving the Cube, but a means of putting it into practice.

The online version of Kublitz Cube

Extended notation

The notation in Kublitz Cube was designed specifically for rotations of single outside layers of cubelets and of the entire cube. While all sequences can be specified using only this simple notation, more advanced puzzlers might wish to specify other moves more concisely. For example, they might want to refer to the rotation of the middle layer, between Front and Back, by 90 degrees clockwise as seen from the Front. Now this could be specified as three rotations using the simple notation: FOC FABO (i.e. rotate the complete cube clockwise then turn the Front and Back layers back again), but this is not concise.

The notation can be easily extended by references to the specific layers. In order to maintain the word-like notation, each layer reference begins with the letter E and is then followed by one or more of the following letters: N is the layer nearest to the face specified; M is the middle layer, i.e. the second layer back from the face spcified, and X is the extreme layer furthest from that face. The E followed by letters denoting the layer or layers to be rotated are specified between the face letter and the rotation direction letter. So, the rotation of the middle layer, between Front and Back, by 90 degrees clockwise as seen from the Front can be specified as FEMO (or as BEMA). The rotation of the top two layers in an anticlockwise direction as seen from the Top can be specified as TENMA (or DEXMO). The rotation of the Right layer by 180 degrees could be referred to as RENI or LEXI, but you would normally use the simple RI for this, unless the extended notation helps you to remember the move.