Layer-by-layer methodLayer-by-layer methods are a family of methods for solving the 3×3×3 Rubik's Cube. Such methods are the most frequently known as beginners' methods, as they are the methods most cubers learn initially, before advancing to speedcubing methods such as CFOP. HistoryThe layer-by-layer approach was pioneered by David Singmaster in his 1980 book Notes on Rubik's "Magic Cube".[1][2] The same idea was adopted by James G. Nourse in his The Simple Solution to Rubik's Cube which became the bestselling book of 1981,[3] and similar approaches could be found in Don Taylor's Mastering Rubik's Cube and Cyril Östrop's Solving the Cube from the same era.[4] MethodLayer-by-layer methods typically begin with the following steps (numbered as per the diagram below):
The sequence of steps to complete the final layer varies between layer-by-layer methods.[4] The diagram illustrates one possible sequence:[5]
 Suitable algorithms to use in the final-layer phase of a layer-by-layer method depend on the sequence of steps, because many algorithms make other changes to pieces in the top layer as a side effect. For example, some corner-permutation algorithms (such as L' U R U' L U R' U) also rotate the corners, so can only be used in a method that permutes corners before rotating them. Some edge-flipping algorithms (such as F R U R' U' F') also rotate corners and rearrange both corner and edge pieces in the final layer, so are suitable only when flipping edges is the first of the final-layer steps to be performed. CFOP methodThe CFOP speedcubing technique, developed by Jessica Fridrich and others in the 1980s, combines into a single step each of steps 2 and 3, steps 5 and 6 and steps 4 and 7 in the above sequence. However, the method uses many more algorithms than most layer-by-layer methods, making it harder to learn, but faster to execute once mastered.[6] See alsoReferences
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