Rubik's Cube/Reference Summary

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 * HOW TO FIND YOUR VERY OWN PERSONAL WAYS TO SOLVE RUBIK'S CUBE                              |
 * (Preliminary April 20, 2007 version)            |
 * by Mr. Ray Calvin Baker                         |
 * FREE Public Domain Educational Material         |
 * Chapter Ten - - - - - - - - - - Reference Summary of Useful Operations                     |
 * In a "group", (and mathematical group theory is a part of finite discrete mathematics      |
 * relevant to the solution of Rubik's Cube and many other puzzles) every operation has an    |
 * inverse operation which undoes what that operation does. The most important operation in a |
 * group is the identity operation -- it does nothing at all! A Cube fresh from the factory   |
 * represents the identity operation. Scrambling the Cube is another operation. Applying the  |
 * inverse of that scrambling operation is your goal. It restores the Cube to its pristine    |
 * condition, as if nothing at all had been done.                                             |
 * Here is a reference summary of the most useful moves, as scribbled on my work sheets.      |
 * INTERCHANGE THREE CORNER CUBIES                                                            |
 * _ a _  (h)     _ a _   (*)                       _ g _   (*)      _ g _   (h)          |
 * b _ T _ c      * _ T _ *                         * _ T _ *        b _ T _ c              |
 * | F d R |      | F d R |      "Fv R^ F^ Rv T2"   | F a R |        | F a R |              |
 * e _ | _ f      * _ | _ *      --->   * _ | _ *        e _ | _ f              |
 * g              g                                 d                d                  |
 * INTERCHANGE TWO CORNER CUBIES                                                              |
 * 1st: "Fv R^ F^ Rv T2"                                    |
 * _ a _  (h)     _ * _   (*)   2nd: "L^"                 _ * _   (*)      _ a _   (h)    |
 * b _ T _ c      * _ T _ *       3rd: "Fv R^ F^ Rv T2"   * _ T _ *        b _ T _ c        |
 * | F d R |      | F d R |       4th: "Fv R^ F^ Rv T2"   | F g R |        | F g R |        |
 * e _ | _ f      * _ | _ *       5th: "Lv"               * _ | _ *        e _ | _ f        |
 * g              g           6th: "Rv Tv R^"             d                d            |
 * CHANGE ORIENTATION OF TWO CORNER CUBIES                              _ * _    Corner       |
 * * _ 1 _ * cubie        |
 * 1st: "Fv R^ Fv R^ Fv R^"                            | 3 * 2 |  before...    |
 * 0 0 0 0 0  2nd: "Fv R^ Fv R^ Fv R^"   0 + - 0 0                 * _ | _ *               |
 * 0 0 0 0 0  3rd: "Fv"                  0 0 0 0 0         _ * _       *       _ * _       |
 * [F] [k]  4th: "Fv R^ Fv R^ Fv R^"     [F] [K]       * _ 2 _ *           * _ 3 _ *     |
 * 5th: "F^"                                 | 1 * 3 |           | 2 * 1 |     |
 * -->                  * _ | _ *           * _ | _ *     |
 * ...after "+".      ...after "-".    |
 * INTERCHANGE THREE EDGE CUBIES                                                              |
 * | |  |#3|  |  |  |#2|       Down-slice: "2R^ Rv"       |  |  |#1|  |  |  |#3|         |
 * +--+--+--+--+--+--+--+--+--+   TOP twice:  "T2"        +--+--+--+--+--+--+--+--+--+      |
 * | | L|  | F|  | R|  | K|  |    Up-slice:   "2Rv R^"    |  | L|  | F|  | R|  | K|  |      |
 * +--+--+--+--+--+--+--+--+--+   TOP twice:  "T2"        +--+--+--+--+--+--+--+--+--+      |
 * | |  |  |  |  |  |#1|                   --->       |  |  |  |  |  |  |#2|         |
 * CHANGE ORIENTATION OF TWO EDGE CUBIES                                                      |
 * Down-slice: "2R^ Rv"      (Only the orientation of       |
 * Turn TOP:  "Tv"            marked edge cubies            |
 * Down-slice: "2R^ Rv"       is changed -- "flipped",)     |
 * +--+ +--+  +--+  +--+       Turn TOP:   "Tv"           +--+  +--+  +--+  +--+         |
 * | |  |#3|  |  |  |#2|       Down-slice: "2R^ Rv"       |  |  |#3|  |  |  |#2|         |
 * +--+--+--+--+--+--+--+--+--+   TOP twice   "T2"        +--+--+--+--+--+--+--+--+--+      |
 * | | L|  | F|  | R|  | K|  |    Up-slice:   "2Rv R^"    |  | L|  | F|  | R|  | K|  |      |
 * +--+--+--+--+--+--+--+--+--+   Turn TOP:   "Tv"        +--+--+--+--+--+--+--+--+--+      |
 * | |  |  |  |  |  |  |       Up-slice:   "2Rv R^"       |  |  |  |  |  |  |  |         |
 * +--+ +--+  +--+  +--+       Turn TOP:   "Tv"           +--+  +--+  +--+  +--+         |
 * Up-slice:  "2Rv R^"   (Rubik's Maneuver does not change  |
 * TOP twice: "T2"        position of any cubie.)           |
 * Don't forget that you can use the ideas in Chapter Six, "Customize Your Moves --           |
 * Commutation", to "customize" these fundamental operations for those situations where the   |
 * Cube you are working with doesn't quite agree with the diagrams!                           |
 * I hope this book has helped you to solve the Cube. But, even more, I hope it has           |
 * encouraged you to seek and find more efficient methods -- YOUR VERY OWN PERSONAL WAYS      |
 * TO SOLVE RUBIK'S CUBE.                                                                     |
 * By the way, if you ever get tired of plain colors on all six sides of your Cube, you can   |
 * look for "Pretty Patterns" to make your Cube look more decorative. Try                     |
 * "2R2 R2 2F2 F2 2T2 T2" for a start. Douglas Hofstadter invented an entire alphabet,        |
 * so you can even make your Cube spell out messages (or at least your initials).             |
 * Now you should be ready to write Chapter Eleven, "MY VERY OWN PERSONAL WAY TO SOLVE RUBIK'S |
 * CUBE"! Then we can all say,                                                                |
 * " The end. ".                                           |
 * Down-slice: "2R^ Rv"      (Only the orientation of       |
 * Turn TOP:  "Tv"            marked edge cubies            |
 * Down-slice: "2R^ Rv"       is changed -- "flipped",)     |
 * +--+ +--+  +--+  +--+       Turn TOP:   "Tv"           +--+  +--+  +--+  +--+         |
 * | |  |#3|  |  |  |#2|       Down-slice: "2R^ Rv"       |  |  |#3|  |  |  |#2|         |
 * +--+--+--+--+--+--+--+--+--+   TOP twice   "T2"        +--+--+--+--+--+--+--+--+--+      |
 * | | L|  | F|  | R|  | K|  |    Up-slice:   "2Rv R^"    |  | L|  | F|  | R|  | K|  |      |
 * +--+--+--+--+--+--+--+--+--+   Turn TOP:   "Tv"        +--+--+--+--+--+--+--+--+--+      |
 * | |  |  |  |  |  |  |       Up-slice:   "2Rv R^"       |  |  |  |  |  |  |  |         |
 * +--+ +--+  +--+  +--+       Turn TOP:   "Tv"           +--+  +--+  +--+  +--+         |
 * Up-slice:  "2Rv R^"   (Rubik's Maneuver does not change  |
 * TOP twice: "T2"        position of any cubie.)           |
 * Don't forget that you can use the ideas in Chapter Six, "Customize Your Moves --           |
 * Commutation", to "customize" these fundamental operations for those situations where the   |
 * Cube you are working with doesn't quite agree with the diagrams!                           |
 * I hope this book has helped you to solve the Cube. But, even more, I hope it has           |
 * encouraged you to seek and find more efficient methods -- YOUR VERY OWN PERSONAL WAYS      |
 * TO SOLVE RUBIK'S CUBE.                                                                     |
 * By the way, if you ever get tired of plain colors on all six sides of your Cube, you can   |
 * look for "Pretty Patterns" to make your Cube look more decorative. Try                     |
 * "2R2 R2 2F2 F2 2T2 T2" for a start. Douglas Hofstadter invented an entire alphabet,        |
 * so you can even make your Cube spell out messages (or at least your initials).             |
 * Now you should be ready to write Chapter Eleven, "MY VERY OWN PERSONAL WAY TO SOLVE RUBIK'S |
 * CUBE"! Then we can all say,                                                                |
 * " The end. ".                                           |
 * look for "Pretty Patterns" to make your Cube look more decorative. Try                     |
 * "2R2 R2 2F2 F2 2T2 T2" for a start. Douglas Hofstadter invented an entire alphabet,        |
 * so you can even make your Cube spell out messages (or at least your initials).             |
 * Now you should be ready to write Chapter Eleven, "MY VERY OWN PERSONAL WAY TO SOLVE RUBIK'S |
 * CUBE"! Then we can all say,                                                                |
 * " The end. ".                                           |
 * " The end. ".                                           |