Layer-by-layer method: Difference between revisions

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{{Short description|Method of solving the Rubik's Cube}}

{{about|the Rubik's Cube method|the thin film fabrication technique|Layer by layer}}

The '''Layer -by-layer Layer methodmethods''', also known as the '''beginners method''', isare a methodfamily of methods for solving the 3x3x33×3×3 [[Rubik's Cube]]. Many Such methods are the most frequently known as '''beginners' methods''', useas thisthey approach,are andthe itmethods alsomost formscubers thelearn basisinitially, ofbefore theadvancing to [[CFOPspeedcubing]] speedcubingmethods techniquesuch as [[CFOP]].

==History==

The Layer layer-by-layer Layer Methodapproach was pioneered by [[David Singmaster]] in his 1980 book ''Notes on Rubik's "Magic Cube"''.<ref name="linkedresources">{{cite web |url = http://www.linkedresources.com/teach/rubik/solution.php |title = A Step by Step Solution of Rubik's "Magic Cube" |author = David Singmaster |date = 1980-08-06 |publisher = Jeffrey W Baumann & LinkedResources |archiveurl = https://web.archive.org/web/20060304183050/http://www.linkedresources.com/teach/rubik/solution.php |archivedate = 2006-03-04}}</ref><ref name="ryanheise-beginner">{{cite web |url = http://www.ryanheise.com/cube/beginner.html |title = Beginner's Rubik's Cube Solution |quote = The general layer-by-layer approach described above is credited to mathematician David Singmaster and was first published in his 1980 book "Notes on Rubik's Magic Cube" |author = Ryan Heise |archiveurl = https://web.archive.org/web/20150926083418/http://www.ryanheise.com/cube/beginner.html |archivedate = 2015-09-26}}</ref> 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,<ref name="upi">{{Cite news|url=http://www.upi.com/Archives/1982/01/05/BEST-SELLER/3264379054800/|last=Hanauer|first=Joan|title=The man who wrote the best-selling book of 1981|date=5 January 1982|publisher=United Press International}}</ref> 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.<ref name="phil">[http://helm.lu/cube/MarshallPhilipp/page_1.htm A Comparison of Various Methods], Philip Marshall, 2005</ref>

== Method ==

Layer-by-layer methods typically begin with the following steps (numbered as per the diagram below):

The method begins with the puzzle solver making a cross on one face with the edge pieces ensuring that all edge colors match the adjacent center colors (step 1 in the diagram below), then putting the corners into position between the edges (step 2). By then, the layer should be solved. In step 3, the four edge pieces of the middle layer are solved. At this point, the first two layers are solved. In step 4, a cross of the opposite color is made on the last layer. For step 5, the last layer edges are permuted (swapped around). In step 6, the last layer corners are permuted. Finally, the last layer corners are oriented.<ref>[http://www.learnhowtosolvearubikscube.com/how-to-solve-a-rubiks-cube-solution-overview/ Eight steps: layer by layer method to the Rubik's cube]</ref>

# Forming a cross on one face, ensuring that all edge colours match the adjacent centre colours

[[File: Rubik's Cube layer by layer solution overview.jpg|thumb|center|400px|An overview of the layer by layer method for Rubik's Cube. The cube has been turned over in the third step.]]

# Inserting the corners of the same face between the edges, thereby completing one layer

# Inserting the edge pieces of the middle layer

The sequence of steps to complete the final layer varies between layer-by-layer methods.<ref name="phil"/> The diagram illustrates one possible sequence:<ref>[http://www.learnhowtosolvearubikscube.com/how-to-solve-a-rubiks-cube-solution-overview/ Eight steps: layer by layer method to the Rubik's cube]</ref>

Most Layer by Layer beginners' methods solves the first two layers using the same technique. However, there are many variant techniques for the final layer, depending on whether the corner or edge pieces are solved first.<ref name="phil"/> For example:

{{ordered list|start=4

# Top layer "white cross": F' U L' U' or F R U R' U' F'

| Flipping the edges, thus forming a cross on the face

# Top layer left corner: D L D' L’ / right corner: D' R' D R

| Permuting the edges

# Second layer right edge: U R U' R' U' F' U F / Left edge: U' L' U L U F U' F'

| Permuting the corners

# Final layer cross (edge orientation): F R U R' U' F'

| Rotating the corners

# Final layer edge permutation: R U R' U R U U R'

}}

# Final layer corner orientation: U R U' L' U R' U' L

[[File: Rubik's Cube layer by layer solution overview.jpg|thumb|center|400px|An overview of the layer by layer method for Rubik's Cube. The cube has been turned over in the third step.]]

# Final layer corner permutation: R' D' R D

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 method==

{{Main|CFOP method}}

The 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.<ref>{{Cite web |url=http://ukcubestore.com/cfop-tutorial.html |title=CFOP tutorial: UKCubeStore |access-date=2017-01-02 |archive-date=2021-06-08 |archive-url=https://web.archive.org/web/20210608131350/http://ukcubestore.com/cfop-tutorial.html |url-status=dead }}</ref>

The CFOP speedcubing

technique, developed by [[Jessica Fridrich]] and others in the 1980s, similarly divides the puzzle into layers to be solved. However, the method uses far more algorithms and shortcuts than the beginners' methods.<ref>

==See also==

[http://ukcubestore.com/cfop-tutorial.html CFOP tutorial: UKCubeStore]</ref>

* [[CFOP method]]

* [[Rubik's Cube]]

==References==