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''' isare a methodfamily of methods for solving the 3x3x33×3×3 [[Rubik's Cube]]. Many beginner'sSuch methods useare thisthe approach,most butfrequently itknown alsoas forms'''beginners' themethods''', basisas ofthey are the methods most cubers learn initially, before advancing to [[CFOPspeedcubing]] speedcubingmethods such as [[CFOP]].

technique.

==History==

The layer-by-layer approach 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>

The Layer by Layer Method 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):

It starts by making a cross on one face with the edge pieces, then putting the corners into position between the edges. By then the layer should be solved. Third, the four edge pieces of the middle layer are solved. At this point the first two layers are solved. Fourth, a cross of the opposite color is made on the last layer. Fifth, the last layer edges are permuted. Sixth, 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]]

# 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 beginner's methods solve the first two layers using the same technique. However, there are many variations for the final layer, depending on whether the corner or edge pieces are solved first.

{{ordered list|start=4

<ref name="phil"/>

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

| Permuting the edges

| Permuting the corners

| Rotating the corners

}}

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

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==

{{Main|CFOP}}

The ==CFOP speedcubingmethod==

{{Main|CFOP method}}

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 beginner's methods.<ref>

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>

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

==See also==

* [[CFOP method]]

* [[Rubik's Cube]]

==References==

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[[Category:Rubik's Cube]]

{{Game-stub}}