Jump to content

Rubik's Cube/Reference Summary

From Wikiversity
+---------------------------------------------------------------------------------------------+
| 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. ".                                            |
|                                                                                             |
+---------------------------------------------------------------------------------------------+