The original Square-1 notation, created by Jaap Scherphuis, uses moves of the form (x,y) and moves of the form /. In an (x,y) twist, x indicates the number of 30-degree increments that the top layer should be twisted clockwise (an edge is 30 degrees and a corner is 60 degrees), and y indicates the number of 30-degree increments that the bottom should be twisted clockwise. A / twist simply refers to turning the entire right half of the puzzle by 180 degrees.
It is important to note that in this notation the puzzle must be held so that the layers containing the corners and edges are on the top and bottom, and the middle layer should be in a position so that, on the front side, the shorter middle-layer sticker should be on the left. Thus, from a solved state, the turn (1,-1)/ is possible, but (-1,1)/ is not.
In the newer official notation, adopted by the WCA, there is no /. The WCA regulations (version 2008 v1) say: "(x,y) means: turn upper layer x stickers clockwise, turn bottom layer y stickers clockwise, turn right half of the puzzle 180 degrees. Stickers are counted on the outside of the upper slice." Thus, every (x,y) move is considered to be followed by a / move.
The following examples illustrate the older notation, which is still useful for algorithms (since they may start with a / move or may not end with a / move).
Example 1: /(3,0)/(-3,-3)/(0,3)/
This example illustrates a situation where all top- and bottom-layer twists are in multiples of 90 degrees. (Algorithms like this also work on a 2x2x2 cube, if you perform the / turn as a R2.) If you perform this algorithm correctly it should do a J permutation on both the top and bottom layer.
Example 2: (1,0)/(-1,-1)/(0,1)
In this example, all top- and bottom-layer twists are only 30 degrees, which must be one edge. If you perform this algorithm correctly you should end up with two D edges on the U layer and two U edges on the D layer.
Karnaukh notation was invented by and is named after Daniel Karnaukh. The aim of Karnaukh notation is to make writing, learning and sharing Square-1 algorithms easier. It is based on standard Square-1 notation, with three major changes:
- Parentheses and commas are omitted
- Slashes are replaced with spaces
- Letters are assigned to common pairs of moves
For the letters, there are three types: U, D and E. Each can be written lowercase and inversed by appending a ', yielding twelve possibilities. The following table shows all abbreviations and their meanings in standard Square-1 notation:
Although not officially included, other move abbreviations such as M may be used as well.
It should be noted that Karnaukh notation is only supposed to be used for algorithms, not scrambling (for which standard notation should be used).