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Cube puzzle move notation is used to denote a sequence of moves (an algorithm) to be performed in order to manipulate a cube-shaped combination puzzle – most notably the Rubik's Cube and its variations. The goal of this manipulation would generally be to solve the puzzle, but could also be done to create aesthetically or mathematically interesting patterns.

For example, one popular algorithm, as written in Singmaster notation, is: R U R' U R U2 R'

Singmaster notation
Many cube enthusiasts use a notation known as "Singmaster notation" that was originally proposed by David Singmaster and further developed by others.

Letters, numbers and other symbols are used to indicate which layer/s of the cube should be turned, as well as the direction and distance it/they should be turned.

The notation is mostly used in relation with 3 x 3 cubes, but may be also used with smaller or larger cubes sizes.

Cube layers
The 3 x 3 cube layers (also called 'faces') are labeled as follows:

F = front, B = back, R = right, L = left, U = up, D = down, M = middle, E = equator, S = side

Turn direction
Turn direction is normally clockwise (judged as if facing the layer).

For example, R U indicates that the right hand layer should be turned once clockwise, followed by a clockwise turn of the upper layer.

The prime symbol (') is used to indicated that the layer in question should be turned counterclockwise, rather than clockwise.

For example, U' R indicates that the upper layer should be turned once counterclockwise, followed by a clockwise turn of the right layer.

Turn distance
Turn distance is normally a 90 degree turn, also known as a quarter turn.

The number two (2) is used to indicate that turn should be 180 degrees – the equivalent of 2 quarter turns.

For example, R' U2 indicates the right hand layer should be turned 90 degrees counterclockwise, followed by a 180 degree turn of the upper later.

Multiple layer turns
Singmaster originally proposed that lower case letters be used to indicate when a turn involves the layer, plus the layer next to it, at the same time.

However, a different way of notating such moves is now considered standard.

This notation uses the lower case letter 'w' (for 'with') next to the main letter to indicate the layer next to it should also be turned with it.

Other sized cubes
The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. As with the 3 x 3 cube, the letters F B R L U D refer to the outermost faces. Lowercase letters (f b u d l r) refer to the inner portions of the cube (called slices). An asterisk (L*), a number in front of it (2L), or two layers in parenthesis (Ll), means to turn the two layers at the same time (both the inner and the outer left faces).

For example: (Rr) ' l2 f ' means to turn the two rightmost layers anticlockwise, then the left inner layer twice, and then the inner front layer anticlockwise. By extension, for cubes of 6x6 and larger, moves of three layers are notated by the number 3, for example 3L.

Wolstenholme notation
An alternative to Singmaster notation, Wolstenholme notation, is designed to make memorising sequences of moves easier for novices.

This notation uses the same letters for faces except it replaces U with T (top), so that all are consonants. The key difference is the use of the vowels O, A and I for clockwise, anticlockwise and 180-degree turns, which results in word-like sequences such as LOTA RATO LATA ROTI (equivalent to LU′R′UL′U′RU2 in Singmaster notation). Addition of a C implies rotation of the entire cube, so ROC is the clockwise rotation of the cube around its right face.