Problem 1123. Rubik's Cube: 30 Moves or Less : Minimum Moves

Created by Richard Zapor

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>This Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></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:jc w:val=\"center\"/></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=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"center\"/></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=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></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:jc w:val=\"left\"/></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:jc w:val=\"left\"/></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:jc w:val=\"left\"/></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:jc w:val=\"left\"/></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:jc w:val=\"left\"/></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:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Scoring:</w:t></w:r><w:r><w:t> Minimum number of moves</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></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:jc w:val=\"left\"/></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 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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 936.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 468.35px; transform-origin: 407px 468.35px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 308.633px 7.91667px; transform-origin: 308.633px 7.91667px; unicode-bidi: normal; "><span style="">This Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).</span></span></div><div style="block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 219.95px 7.91667px; transform-origin: 219.95px 7.91667px; unicode-bidi: normal; "><span style="">Rubik's Cube can be solved in 20 moves or less from any position. The</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "http://kociemba.org/cube.htm"><span style=""><span style="">Kociemba Two Phase algorithm</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7px 7.91667px; transform-origin: 63.7px 7.91667px; unicode-bidi: normal; "><span style=""> 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.</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "http://kociemba.org/math/CubeDefs.htm#faceturns"><span style=""><span style="">Definitions of Moves / Rotates / Flips for Corners and Edges</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 7.91667px; transform-origin: 151.317px 7.91667px; unicode-bidi: normal; "><span style="">. The Two-Phase algorithm typically solves in 24 moves or less.</span></span></div><div style="block-size: 134.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 67.4667px; text-align: center; transform-origin: 384px 67.4667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" 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" data-image-state="image-loaded"></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.667px 7.91667px; transform-origin: 376.667px 7.91667px; unicode-bidi: normal; "><span style="">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.</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 192.5px 7.91667px; transform-origin: 192.5px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; ">The </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 177.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 177.1px 7.91667px; ">color to numeric coding is [RWBYGO] [012345]. </span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 300.3px 7.91667px; transform-origin: 300.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; ">A </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 292.6px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 292.6px 7.91667px; ">solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4333px 7.91667px; transform-origin: 19.4333px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Input:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6833px 7.91667px; transform-origin: 18.6833px 7.91667px; unicode-bidi: normal; "><span style=""> Cube</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.25px 7.91667px; transform-origin: 146.25px 7.91667px; unicode-bidi: normal; "><span style="">Cube is a 48 long row vector of values 0 thru 5.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.91667px; transform-origin: 25.2667px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Output:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.8px 7.91667px; transform-origin: 42.8px 7.91667px; unicode-bidi: normal; "><span style=""> Move_Vector</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 189.433px 7.91667px; transform-origin: 189.433px 7.91667px; unicode-bidi: normal; "><span style="">Move_Vector is an empty to 30 element vector of values 1:18</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 7.91667px; transform-origin: 37.3333px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Constraint:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.917px 7.91667px; transform-origin: 108.917px 7.91667px; unicode-bidi: normal; "><span style=""> Solution must be 30 moves or less</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3833px 7.91667px; transform-origin: 28.3833px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Scoring:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.35px 7.91667px; transform-origin: 86.35px 7.91667px; unicode-bidi: normal; "><span style=""> Minimum number of moves</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><a target='_blank' href = "http://cube20.org/src/"><span style=""><span style="">Two Phase Source code</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 301.833px 7.91667px; transform-origin: 301.833px 7.91667px; unicode-bidi: normal; "><span style=""> is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><a target='_blank' href = "https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0&amp;d=1"><span style=""><span style="">30 move Cube Solution in Matlab (rought draft)</span></span></a></div></div></div>

This Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (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:* Minimum number of moves

<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)>

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Problem 1123. Rubik's Cube: 30 Moves or Less : Minimum Moves

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