Problem 1138. Rubik's Cube: 30 Moves or Less: Minimum Avg Time

Created by Richard Zapor

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId1","target":"/media/image1.gif"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId2","target":"/media/image1.png"}],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This Challenge is to solve a thoroughly scrambled Rubik's cube in the minimum time (30 moves max).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Rubik's Cube can be solved in 20 moves or less from any position. The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://kociemba.org/cube.htm\"><w:r><w:t>Kociemba Two Phase algorithm</w:t></w:r></w:hyperlink><w:r><w:t> can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://kociemba.org/math/CubeDefs.htm#faceturns\"><w:r><w:t>Definitions of Moves / Rotates / Flips for Corners and Edges</w:t></w:r></w:hyperlink><w:r><w:t>. The Two-Phase algorithm typically solves in 24 moves or less.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Rubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[The color to numeric coding is [RWBYGO] [012345]. \nA solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Input:</w:t></w:r><w:r><w:t> Cube</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Cube is a 48 long row vector of values 0 thru 5.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Output:</w:t></w:r><w:r><w:t> Move_Vector</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Move_Vector is an empty to 30 element vector of values 1:18</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Constraint:</w:t></w:r><w:r><w:t> Solution must be 30 moves or less</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Scoring:</w:t></w:r><w:r><w:t> Average Time of Cubes 2 thru 4 (msec)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"http://cube20.org/src/\"><w:r><w:t>Two Phase Source code</w:t></w:r></w:hyperlink><w:r><w:t> is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0&amp;d=1\"><w:r><w:t>30 move Cube Solution in Matlab (rought draft)</w:t></w:r></w:hyperlink></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"},{"partUri":"/media/image1.gif","contentType":"image/gif","content":"data:image/gif;base64,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"},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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"}]}

This Challenge is to solve a thoroughly scrambled Rubik's cube in the minimum time (30 moves max).Rubik's Cube can be solved in 20 moves or less from any position. The <a href="http://kociemba.org/cube.htm">Kociemba Two Phase algorithm</a> can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2. <a href="http://kociemba.org/math/CubeDefs.htm#faceturns">Definitions of Moves / Rotates / Flips for Corners and Edges</a>. The Two-Phase algorithm typically solves in 24 moves or less.<img src="https://sites.google.com/site/razapor/matlab_cody/cube_small.gif"><img src="https://sites.google.com/site/razapor/matlab_cody/Cube_Map48_200.png">Rubik's Cube has 48 faces that are assigned to a vector as in the above figure.
U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.<pre class="language-matlab">The color to numeric coding is [RWBYGO] [012345]. 
A solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]
</pre>Input: CubeCube is a 48 long row vector of values 0 thru 5.Output: Move_VectorMove_Vector is an empty to 30 element vector of values 1:18Constraint: Solution must be 30 moves or lessScoring: Average Time of Cubes 2 thru 4 (msec)<a href="http://cube20.org/src/">Two Phase Source code</a> is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.<a href="https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0&amp;d=1">30 move Cube Solution in Matlab (rought draft)</a>

This Challenge is to solve a thoroughly scrambled Rubik's cube in the minimum time (30 moves max).

Rubik's Cube can be solved in 20 moves or less from any position. The <http://kociemba.org/cube.htm Kociemba Two Phase algorithm> can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2. <http://kociemba.org/math/CubeDefs.htm#faceturns Definitions of Moves / Rotates / Flips for Corners and Edges>. The Two-Phase algorithm typically solves in 24 moves or less.

<<https://sites.google.com/site/razapor/matlab_cody/cube_small.gif>>

<<https://sites.google.com/site/razapor/matlab_cody/Cube_Map48_200.png>>

Rubik's Cube has 48 faces that are assigned to a vector as in the above figure.
U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.

The color to numeric coding is [RWBYGO] [012345]. 
  A solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]

*Input:* Cube

Cube is a 48 long row vector of values 0 thru 5.
  
*Output:* Move_Vector

Move_Vector is an empty to 30 element vector of values 1:18

*Constraint:* Solution must be 30 moves or less

*Scoring:* Average Time of Cubes 2 thru 4 (msec)

<http://cube20.org/src/ Two Phase Source code> is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.

<https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0&d=1 30 move Cube Solution in Matlab (rought draft)>

Solve

Solution Stats

5 Solutions
1 Solvers

Last Solution submitted on Mar 17, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers1

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 1138. Rubik's Cube: 30 Moves or Less: Minimum Avg Time

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers1

Suggested Problems

More from this Author254

Problem Tags

Community Treasure Hunt

Problem 1138. Rubik's Cube: 30 Moves or Less: Minimum Avg Time

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers1

Suggested Problems

More from this Author254

Problem Tags

Community Treasure Hunt

Players