Problem 931. Rubik's Mini-Cube: Solve Randomized Mini-Cube - Score : Moves

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.png"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId2","target":"/media/image2.png"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId3","target":"/media/image1.gif"}],"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>The Challenge is to Solve a thoroughly scrambled Mini-Rubik's Cube(2x2x2).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The Performance metric is average number of moves for solving 500 cubes.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A standard Mini-Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Moves are denoted as F for clockwise rotation of the Front face. F'(or FP) is CCW and F2 is F twice. The provided function r_new=rubick_rot_mini(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.</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: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=\"rId3\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Input: (rubik)\n\nrubik: row vector of size 24\n(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives forty face moves.\n\nOutput: move_vec (Numeric of moves to solve)\n move_vec:values 1:27 for UFDLBR U'F'D'L'B'R' U2F2D2L2B2R2 XYZX'Y'Z'X2Y2Z2]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>If the cube was randomized by [1 9] UD', one solution is [3 7] which are the complements in reverse order.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Scoring is average face moves for 500 cubes</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Cube Moves X, Y, and Z do not constitute a move but are needed in the vector</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>A string to numeric value function is provided in the template</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Verifications will be by executing your move vector against the provided Rubik and counting number of face moves.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The function rubik_rot_mini(mov,r) is provided in the template.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The Function Template Contains a 3D Cube Viewer and the first step in solving is at the bottom in a comment block.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:hyperlink w:docLocation=\"http://kociemba.org/cube.htm\"><w:r><w:t>Cube Theory: 20-moves Any Cube</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:hyperlink w:docLocation=\"http://peter.stillhq.com/jasmine/rubikscubesolution.html\"><w:r><w:t>General Cube Info and Middle Layer</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:hyperlink w:docLocation=\"http://www.speedcubing.com/final_layer_print.html\"><w:r><w:t>SpeedCube Bottom Sequences</w:t></w:r></w:hyperlink><w:r><w:t>(Note: Mini-Cube can use the full cube moves and ignore edge effects)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Coming Soon: The Mini-Cube (2x2x2): Full Random - Eleven or Less Moves</w:t></w:r></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.png","contentType":"image/png","content":"data:image/png;base64,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"},{"partUri":"/media/image2.png","contentType":"image/png","content":"data:image/png;base64,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"},{"partUri":"/media/image1.gif","contentType":"image/gif","content":"data:image/gif;base64,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"}]}

The Challenge is to Solve a thoroughly scrambled Mini-Rubik's Cube(2x2x2).The Performance metric is average number of moves for solving 500 cubes.A standard Mini-Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.The faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)Moves are denoted as F for clockwise rotation of the Front face. F'(or FP) is CCW and F2 is F twice. The provided function r_new=rubick_rot_mini(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.<img src="https://sites.google.com/site/razapor/matlab_cody/minicube2.png"><img src="https://sites.google.com/site/razapor/matlab_cody/miniCube_Map24_200.png"><img src="http://mathworks.com/matlabcentral/images/surf.gif"><pre class="language-matlab">Input: (rubik)
</pre><pre class="language-matlab">rubik: row vector of size 24
(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives forty face moves.
</pre><pre class="language-matlab">Output: move_vec (Numeric of moves to solve)
 move_vec:values 1:27 for UFDLBR U'F'D'L'B'R' U2F2D2L2B2R2 XYZX'Y'Z'X2Y2Z2
</pre><ul><li>Example:</li><li>If the cube was randomized by [1 9] UD', one solution is [3 7] which are the complements in reverse order.</li><li>Scoring is average face moves for 500 cubes</li><li>Cube Moves X, Y, and Z do not constitute a move but are needed in the vector</li><li>A string to numeric value function is provided in the template</li><li>Verifications will be by executing your move vector against the provided Rubik and counting number of face moves.</li></ul>The function rubik_rot_mini(mov,r) is provided in the template.The Function Template Contains a 3D Cube Viewer and the first step in solving is at the bottom in a comment block.<ul><li></li><li><a href="http://kociemba.org/cube.htm">Cube Theory: 20-moves Any Cube</a></li><li><a href="http://peter.stillhq.com/jasmine/rubikscubesolution.html">General Cube Info and Middle Layer</a></li><li><a href="http://www.speedcubing.com/final_layer_print.html">SpeedCube Bottom Sequences</a>
(Note: Mini-Cube can use the full cube moves and ignore edge effects)</li></ul>Coming Soon: The Mini-Cube (2x2x2): Full Random - Eleven or Less Moves

The Challenge is to Solve a thoroughly scrambled Mini-Rubik's Cube(2x2x2).

The Performance metric is average number of moves for solving 500 cubes.

A standard Mini-Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.

The faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)

Moves are denoted as F for clockwise rotation of the Front face. F'(or FP) is CCW and F2 is F twice.  The provided function r_new=rubick_rot_mini(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.

<<https://sites.google.com/site/razapor/matlab_cody/minicube2.png>>

<<https://sites.google.com/site/razapor/matlab_cody/miniCube_Map24_200.png>>

<<http://mathworks.com/matlabcentral/images/surf.gif>>

Input: (rubik)
  
  rubik: row vector of size 24
  (The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives forty face moves.

Output: move_vec (Numeric of moves to solve)
   move_vec:values 1:27 for UFDLBR U'F'D'L'B'R' U2F2D2L2B2R2 XYZX'Y'Z'X2Y2Z2

* Example:
* If the cube was randomized by [1 9] UD', one solution is [3 7]  which are the complements in reverse order. 
* Scoring is average face moves for 500 cubes
* Cube Moves X, Y, and Z do not constitute a move but are needed in the vector 
* A string to numeric value function is provided in the template
* Verifications will be by executing your move vector against the provided Rubik and counting number of face moves.

The function rubik_rot_mini(mov,r) is provided in the template.

The Function Template Contains a 3D Cube Viewer and the first step in solving is at the bottom in a comment block.

* 
* <http://kociemba.org/cube.htm Cube Theory: 20-moves Any Cube> 
* <http://peter.stillhq.com/jasmine/rubikscubesolution.html General Cube Info and Middle Layer>
* <http://www.speedcubing.com/final_layer_print.html SpeedCube Bottom Sequences>
(Note: Mini-Cube can use the full cube moves and ignore edge effects)

Coming Soon: The Mini-Cube  (2x2x2): Full Random - Eleven or Less Moves

Solve

Solution Stats

12 Solutions
2 Solvers

Last Solution submitted on Apr 07, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers2

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 931. Rubik's Mini-Cube: Solve Randomized Mini-Cube - Score : Moves

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers2

Suggested Problems

More from this Author247

Problem Tags

Community Treasure Hunt

Problem 931. Rubik's Mini-Cube: Solve Randomized Mini-Cube - Score : Moves

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers2

Suggested Problems

More from this Author247

Problem Tags

Community Treasure Hunt

Players