Rubik's Cube/Moving Edge Cubies

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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 Educational Material                        |
|                                                                                             |
| Chapter Eight  - - - - - - - - - Moving Edge Cubies                                         |
|                                                                                             |
| Goal Three is to locate each of the twelve edge cubies at the proper edge of the Cube. This |
| is going to take some different moves that leave the locations and orientations of the      |
| corner cubies unchanged. We will be using some two-layer turns that move some of the        |
| centers of several faces as well. Consequently, we will need some new landmarks.            |
|                                                                                             |
| This is not as difficult as it sounds, because, at this stage, all of the corner cubies     |
| should be properly located and oriented. Here is what is called the "down-slice" move.      |
| (It's called a "down-slice" because the three cubies on the FRONT move DOWN.)               |
|                                                                                             |
|             _ * _     (1)                 _ * _     (7)                  _ * _     (7)      |
|         _ * _ T _ * _ /               _ * _ T _ * _ /                _ * _ T _ * _ /        |
|     _ * _ ? _ * _ 2 _ * _         _ * _ ? _ * _ 8 _ * _          _ * _ ? _ * _ 8 _ * _      |
|   * _ T _ * _ T _ * _ T _ *     * _ T _ * _ k _ * _ k _ *      * _ T _ * _ k _ * _ T _ *    |
|   |   * _ 3 _ * _ ? _ *   |     |   * _ 1 _ * _ ? _ *   |      |   * _ 1 _ * _ ? _ *   |    |
|   | F |   * _ T _ *   | R |     | F |   * _ k _ *   | R |      | F |   * _ T _ *   | R |    |
|   * _ | 4 |   *   | ? | _ *     * _ | 2 |   *   | ? | _ *      * _ | 2 |   *   | ? | _ *    |
|   |   * _ | F | R | _ *   |     |   * _ | t | R | _ *   |      |   * _ | F | R | _ *   |    |
|   | ? |   * _ | _ *   | ? |     | ? |   * _ | _ *   | ? |      | ? |   * _ | _ *   | ? |    |
|   * _ | F |   *   | R | _ * 2R^ * _ | t |   *   | R | _ *  Rv  * _ | t |   *   | R | _ *    |
|   |   * _ | ? | ? | _ *   | --> |   * _ | ? | ? | _ *   | -->  |   * _ | ? | ? | _ *   |    |
|   | F |   * _ | _ *   | R |     | F |   * _ | _ *   | R |      | F |   * _ | _ *   | R |    |
|   * _ | 5 |   *   | ? | _ *     * _ | 3 |   *   | ? | _ *      * _ | 3 |   *   | ? | _ *    |
|       * _ | F | R | _ *             * _ | t | R | _ *              * _ | F | R | _ *        |
|         / * _ | _ *                   / * _ | _ *                    / * _ | _ *            |
|       (6)     *                     (4)     *                      (4)     *                |
|                                                                                             |
|   DIAGRAM 8-1. The Down-Slice Move                                                          |
|                                                                                             |
| Notice the new landmarks in this process -- the LEFT and RIGHT sides, and the BOTTOM,       |
| FRONT, BACK, and TOP edges of the LEFT layer have all stayed neatly arranged. The change to |
| the BOTTOM, FRONT, BACK, and TOP was only temporary. (I used "t" and "k" to indicate those  |
| faces that started on TOP or on the BACK; notice how they ended up exactly where they       |
| started.)                                                                                   |
|                                                                                             |
| Next, I will show you how a simple move (T2) and the "up-slice" can be used together to     |
| create a very useful three way shuffle of edge cubies.                                      |
|                                                                                             |
|             _ * _     (7)                 _ * _     (2)                                     |
|         _ * _ T _ * _ /               _ * _ T _ * _ /                                       |
|     _ * _ ? _ * _ 8 _ * _         _ * _ ? _ * _ 1 _ * _                                     |
|   * _ T _ * _ k _ * _ T _ *     * _ T _ * _ k _ * _ T _ *                                   |
|   |   * _ 1 _ * _ ? _ *   |     |   * _ 8 _ * _ ? _ *   |                                   |
|   | F |   * _ T _ *   | R |     | k |   * _ T _ *   | l |                                   |
|   * _ | 2 |   *   | ? | _ *     * _ | 7 |   *   | ? | _ *                                   |
|   |   * _ | F | R | _ *   |     |   * _ | k | l | _ *   |                                   |
|   | ? |   * _ | _ *   | ? |     | ? |   * _ | _ *   | ? |                                   |
|   * _ | t |   *   | R | _ * T2  * _ | t |   *   | R | _ *                                   |
|   |   * _ | ? | ? | _ *   | --> |   * _ | ? | ? | _ *   |                                   |
|   | F |   * _ | _ *   | R |     | F |   * _ | _ *   | R |                                   |
|   * _ | 3 |   *   | ? | _ *     * _ | 3 |   *   | ? | _ *                                   |
|       * _ | F | R | _ *             * _ | F | R | _ *                                       |
|         / * _ | _ *                   / * _ | _ *                                           |
|       (4)     *                     (4)     *                                               |
|                                                                                             |
|   DIAGRAM 8-2. Turn the TOP Layer Twice                                                     |
|                                                                                             |
|             _ * _     (2)                 _ * _     (8)                  _ * _     (8)      |
|         _ * _ T _ * _ /               _ * _ T _ * _ /                _ * _ T _ * _ /        |
|     _ * _ ? _ * _ 1 _ * _         _ * _ ? _ * _ 7 _ * _          _ * _ ? _ * _ 7 _ * _      |
|   * _ T _ * _ k _ * _ T _ *     * _ T _ * _ T _ * _ k _ *      * _ T _ * _ T _ * _ T _ *    |
|   |   * _ 8 _ * _ ? _ *   |     |   * _ 3 _ * _ ? _ *   |      |   * _ 3 _ * _ ? _ *   |    |
|   | k |   * _ T _ *   | l |     | k |   * _ f _ *   | l |      | k |   * _ T _ *   | l |    |
|   * _ | 7 |   *   | ? | _ *     * _ | 4 |   *   | ? | _ *      * _ | 4 |   *   | ? | _ *    |
|   |   * _ | k | l | _ *   |     |   * _ | b | R | _ *   |      |   * _ | k | l | _ *   |    |
|   | ? |   * _ | _ *   | ? |     | ? |   * _ | _ *   | ? |      | ? |   * _ | _ *   | ? |    |
|   * _ | t |   *   | R | _ * 2Rv * _ | F |   *   | R | _ *  R^  * _ | F |   *   | R | _ *    |
|   |   * _ | ? | ? | _ *   | --> |   * _ | ? | ? | _ *   | -->  |   * _ | ? | ? | _ *   |    |
|   | F |   * _ | _ *   | R |     | F |   * _ | _ *   | l |      | F |   * _ | _ *   | R |    |
|   * _ | 3 |   *   | ? | _ *     * _ | 5 |   *   | ? | _ *      * _ | 5 |   *   | ? | _ *    |
|       * _ | F | R | _ *             * _ | b | R | _ *              * _ | F | R | _ *        |
|         / * _ | _ *                   / * _ | _ *                   /  * _ | _ *            |
|       (4)     *                     (6)     *                     (6)      *                |
|                                                                                             |
|  DIAGRAM 8-3. The Up-Slice Move                                                             |
|                                                                                             |
|             _ * _     (8)                 _ * _     (4)                  _ * _     (1)      |
|         _ * _ T _ * _ /               _ * _ T _ * _ /                _ * _ T _ * _ /        |
|     _ * _ ? _ * _ 7 _ * _         _ * _ ? _ * _ 3 _ * _          _ * _ ? _ * _ 2 _ * _      |
|   * _ T _ * _ T _ * _ T _ *     * _ T _ * _ T _ * _ T _ *      * _ T _ * _ T _ * _ T _ *    |
|   |   * _ 3 _ * _ ? _ *   |     |   * _ 7 _ * _ ? _ *   |      |   * _ 3 _ * _ ? _ *   |    |
|   | k |   * _ T _ *   | l |     | F |   * _ T _ *   | R |      | F |   * _ T _ *   | R |    |
|   * _ | 4 |   *   | ? | _ *     * _ | 8 |   *   | ? | _ *      * _ | 4 |   *   | ? | _ *    |
|   |   * _ | k | l | _ *   |     |   * _ | F | R | _ *   |      |   * _ | F | R | _ *   |    |
|   | ? |   * _ | _ *   | ? |     | ? |   * _ | _ *   | ? |      | ? |   * _ | _ *   | ? |    |
|   * _ | F |   *   | R | _ * T2  * _ | F |   *   | R | _ *      * _ | F |   *   | R | _ *    |
|   |   * _ | ? | ? | _ *   | --> |   * _ | ? | ? | _ *   |      |   * _ | ? | ? | _ *   |    |
|   | F |   * _ | _ *   | R |     | F |   * _ | _ *   | R |      | F |   * _ | _ *   | R |    |
|   * _ | 5 |   *   | ? | _ *     * _ | 5 |   *   | ? | _ *      * _ | 5 |   *   | ? | _ *    |
|       * _ | F | R | _ *             * _ | F | R | _ *              * _ | F | R | _ *        |
|         / * _ | _ *                   / * _ | _ *                    / * _ | _ *            |
|       (6)     *                     (6)     *                      (6)     *                |
|                                 Compare this...             ... with the starting position. |
|                                                                                             |
|  DIAGRAM 8-4. Exchanging Three Edge Cubies                                                  |
|                                                                                             |
| After doing T2 a second time, all corner cubies have been restored to their places, with    |
| the correct orientation. The edge cubie marked "5" and "6" is also back where it started.   |
| But the edge cubie marked "1" and "2" has gone to the BOTTOM BACK location. The edge cubie  |
| marked "7" and "8" has gone to the FRONT TOP location, and the cubie marked "3" and "4" has |
| gone to the BACK TOP location. We have a very useful 3-cycle!                               |
|                                                                                             |
| In fact, this three-way shuffle is so simple, easy, and effective that you should memorize  |
| it (forwards and backwards, if you would like!).                                            |
|                                                                                             |
| You may use customization to shuffle any three edge cubies, but be careful -- many a Cube   |
| has gotten re-scrambled because someone forgot (or messed up) step 3 of the customization   |
| process. You can proceed one edge cubie at a time, until only three edge cubies are out of  |
| place. (One final three-way shuffle will put these three cubies into their proper places.)  |
| I suggest that you line up (1) one edge cubie (#1) which is out of place, (2) the edge      |
| cubie which belongs in the space occupied by edge cubie #1, and (3) any other edge cubie    |
| which is out of place (#3). Then the three way shuffle (if done in the proper direction)    |
| will restore one edge cubie (#2) to its proper location. Do not forget step 3 of the        |
| customizing process!                                                                        |
|                                                                                             |
|                               _ * _     (1)                                                 |
|                           _ * _ T _ * _ /...........Locate the edge cubie which belongs     |
|                       _ * _ ? _ * _ 2 _ * _         in the BOTTOM BACK location "#2"        |
|                     * _ T _ * _ T _ * _ T _ *       here at the BACK TOP edge.              |
| Locate any other ........._ 3 _ * _ ? _ *   |                                               |
| out-of-place edge   | F |   * _ T _ *   | R |                                               |
| cubie "#3" here     * _ | 4 |   *   | ? | _ *                                               |
| at the FRONT TOP    |   * _ | F | R | _ *   |                                               |
| edge.               | ? |   * _ | _ *   | ? |                                               |
|                     * _ | F |   *   | R | _ * ..... Locate an out-of-place edge cubie "#1"  |
|                     |   * _ | ? | ? | _ *   |       at the BOTTOM BACK edge.                |
|                     | F |   * _ | _ *   | R |       (it's hidden in back.)                  |
| The edge cubie      * _ | 5 |   *   | ? | _ *                                               |
| at BOTTOM FRONT..........._ | F | R | _ *           This is another view of the starting    |
| gets returned to          / * _ | _ *               position for shuffling three edge       |
| this position.          (6)     *                   cubies.                                 |
|                                                                                             |
|                     DIAGRAM 8-5. Recommended Way to Position Edge Cubies                    |
|                                                                                             |
| Let's try to develop another type of diagram to showw all twelve edge cubies. This may make |
| "customization" easier to visualize, as we put all twelve edge cubies into their proper     |
| places. I start with diagram 5-6, but, instead of emphasizing the corner cubies, I          |
| concentrate on the twelve edge cubies. The result is diagram 8-6. Leaving out a few more    |
| lines results in diagram 8-7.                                                               |
|                                                                                             |
|  *          This is a repeat         *                                                      |
|  |\         of diagram 5-6F         /|                                                      |
|  | *        from Chapter Five.     * |                                                      |
|  *d|\                             /|d*                                                      |
|  | | *                           * |/|                                                      |
|  | *?|                         /|?* |                                                       |
|  * |\|  \_                   _/  |/| *                                                      |
|  |\| *     * _           _ *     * |/|                  Exploded TOP Side                   |
|  | *?|\ A  |   * _   _ *   |  3 /|?* |                                                      |
|  *?|\| * _ | ? |   -   | ? | _ * |/|?*    vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv   |
|  |\| *a|   * _ |   B   | _ *   |c* |/|   | d | ? |   A   | ? |   B   | | |   3   | ? | d |  |
|  | *L|\| 1 |   * _   _ *   | C |/|K* |   +---+---+---+---+---+---+---+---+---+---+---+---+  |
|  *\|?* _ | ? |   *   | ? | _ * |/| * |   | ? | a | 1 | ? | 2 | b | ? | C | c | ? |   |   |  |
|  | \| * |   * _ | 2 | b | _ *  |?* |/|   +---+---+---+---+---+---+---+---+---+---+---+---+  |
|  | *?|\| ? |   * _ | _ *   | ? |/|?* |   | ? | L | ? | ? FRONT ? | ? RIGHT ? | ? | K | ? |  |
|  * |\| * _ FRONT   *   RIGHT _ * |/| *   +---+---+---+---+---+---+---+---+---+---+---+---+  |
|   \| *E|   * _ | ? | ? | _ *   |7* |/    |   | ? | E | e | ? | 6 | f | ? | g | 7 | ? |   |  |
|    *?|\| e |   * _ | _ *   | g |/|?*     +---+---+---+---+---+---+---+---+---+---+---+---+  |
|     \| * _ | ? |   *   | ? | _ * |/      |   | ? |   5   | ? |   F   | ? |   G   | ? |   |  |
|      *     * _ | 6 | f | _ *     *        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^   |
|       \ 5  |   * _ | _ *   |  G /                                                           |
|         \_ | ? |   *   | ? | _/                         Exploded BOTTOM Side                |
|            * _ |   F   | _ *                                                                |
|                * _   _ *                 This time, we will ignore the corner cubies...     |
|                    -                                                                        |
|                                                                                             |
|  We Are Unwrapping the Cube (Again!)                                                        |
|                                                                                             |
|  DIAGRAM 8-6A.                           DIAGRAM 8-6B.                                      |
|                                                                                             |
|                                        (exploded TOP)                                       |
|                      +----+         +----+         +----+         +----+                    |
|                      | lt |         | ft |         | rt |         | kt |                    |
|                 +  --+----+--  +  --+----+--  +  --+----+--  +  --+----+--  +               |
|                 |    | lt |    |    | ft |    |    | rt |    |    | kt |    |               |
|            +----+----+----+----+----+----+----+----+----+----+----+----+----+----+          |
|            | kl | kl |LEFT| fl | fl |FRONT fr | fr |RIGHT kr | kr |BACK| kl | kl |          | 
|            +----+----+----+----+----+----+----+----+----+----+--=-+----+----+----+          |
|           /     |    | bl |    |    | bf |    |    | br |    |    | bk |    |     \         |
|    Overlap      +  --+----+--  +  --+----+--  +  --+----+--  +  --+----+--  +      Note     |
|                      | bl |         | bf |         | br |         | bk |          the       |
|                      +----+         +----+         +----+         +----+         overlap.   |
|                                       (exploded BOTTOM)                                     |
|                                                                                             |
|            DIAGRAM 8-6C. ... and emphasize the edge cubies.                                 |
|                                                                                             |
|  DIAGRAM 8-6. A New Type of Diagram Emphasizes the Edge Cubies                              |
|                                                                                             |
| Eventually, you will line up the last three corner cubies, shuffle them into place, and     |
| undo the moves you made to line up those three edge cubies for the shuffle. That should     |
| complete the accomplishment of goal three for you! (Yes, it is possible that all twelve     |
| edge cubies were already in their correct locations. You don't need to use Chapter Eight at |
| all when that happens!)                                                                     |
|                                                                                             |
| For the sake of completeness, here is a discussion of a way to position the three cubies    |
| (#1,#2, and #3) as indicated in diagram 8-5. I am going to assume that you can identify one |
| edge cubie (#1) which is not in the correct location, then rotate the entire Cube until #1  |
| is positioned at the BOTTOM BACK edge of the Cube. You may want to keep careful notes as    |
| you proceed. You will need to remember how to undo both parts of this two-part              |
| customization process.                                                                      |
|                                                                                             |
|          After we have rotated the Cube to get the #1 edge cubie into the BOTTOM BACK       |
|          position, there are eleven possible places to find edge cubie #2.                  |
|                                                                                             |
| Part 1 Case 1.  +----+    +----+    +----+    +----+                                        |
|                 | #2 |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Move:                |
|            +----+----+----+----+----+----+----+----+----+  "Tv".                            |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 2.  +----+    +----+    +----+    +----+                                        |
|                 |    |    | #2 |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Move:                |
|            +----+----+----+----+----+----+----+----+----+  "T2".                            |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 3.  +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    | #2 |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Move:                |
|            +----+----+----+----+----+----+----+----+----+  "T^".                            |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 4.  +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  none needed for part one.        |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 5.  +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            | #2 | L  |    | F  |    | R  |    | K  | #2 |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "Lv Tv".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 6.  +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  | #2 | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "L^ Tv".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 7.  +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  | #2 | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "F^ T2".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 8.  +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  | #2 | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "R^ T^".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 9.  +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "L2 Tv".                         |
|                 | #2 |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 10. +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "F2 T2".                         |
|                 |    |    | #2 |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| Part 1 Case 11. +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    |    |<--This is where we want #2.            |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "R2 T^".                         |
|                 |    |    |    |    | #2 |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| DIAGRAM 8-7. Positioning Cubie #2 Without Disturbing #1                                     |
|                                                                                             |
| Now we need to position any other out-of-place edge cubie (#3), without disturbing either   |
| edge cubie #1 or edge cubie #2. This is the second part of the two-part customization       |
| process. You should be able to find an out-of-place edge cubie (#3) in one of the ten       |
| locations shown in diagram 8-8.                                                             |
|                                                                                             |
|          After we have rotated the Cube to get the #1 edge cubie into the BOTTOM BACK       |
|          position, and we have done Part 1 customizing moves to get the #2 edge cubie       |
|          into the BACK TOP position, there are ten possible places to find edge cubie #3.   |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 1.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 | #3 |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "Lv Fv".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 2.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    | #3 |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  none needed for part two.        |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 3.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    | #3 |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "R^ F^".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 4.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            | #3 | L  |    | F  |    | R  |    | K  | #3 |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "L2 Fv".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 5.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  | #3 | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "Fv".                            |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 6.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  | #3 | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "F^".                            |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 7.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  | #3 | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "R2 F^".                         |
|                 |    |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 8.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "L^ Fv".                         |
|                 | #3 |    |    |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 9.                /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "F2".                            |
|                 |    |    | #3 |    |    |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
|                                 __ This is where we want #3.                                |
| Part 2 Case 10.               /                                                             |
|                 +----+    +----+    +----+    +----+                                        |
|                 |    |    |    |    |    |    | #2 |                                        |
|            +----+----+----+----+----+----+----+----+----+                                   |
|            |    | L  |    | F  |    | R  |    | K  |    |  Customizing Moves:               |
|            +----+----+----+----+----+----+----+----+----+  "Rv F^".                         |
|                 |    |    |    |    | #3 |    | #1 |                                        |
|                 +----+    +----+    +----+    +----+                                        |
|                                                                                             |
| DIAGRAM 8-8. Positioning Cubie #3 Without Disturbing #2 Or #1                               |
|                                                                                             |
| When edge cubies #1, #2, and #3 are in position, do the three-way shuffle of edge cubies,   |
| just as we developed it earlier in this chapter. Then undo the customization process you    |
| used to get the three edge cubies into position. Be sure to undo part two (the part which   |
| positioned edge cubie #3) first, then undo part one (the part which positioned edge         |
| cubie #2) second.                                                                           |
|                                                                                             |
| Let's just check to see if you really understand how to "undo" the "customization" process  |
| whenn there are two parts to it, such as we have in this chapter. Here is an example.       |
| Suppose, after manipulating the entire Cube to get edge cubie #1 into position, we find     |
| that "Part 1 Case 11" is our situation, according to diagram 8-7. We apply the customizing  |
| moves, "R2 T^". Then suppose we find that "Part 2 Case 10" is our situation for positioning |
| cubie #3. The customizing moves are "Rv F^", so we make these moves. Having gotten all      |
| three edge cubies where we want them, we do the three-way shuffle, "Down-slice, TOP twice,  |
| Up-slice, TOP twice", or "2R^ Rv T2 2R^ Rv T2". How do we "undo" the customization?         |                                            |                                                                                             |
| Answer for the example: the entire customization, both part one and part two, is this:      |
| "R2 T^ Rv F^". So, to undo this. the moves are: "Fv R^ Tv R2".                              |
|                                                                                             |
| Common sense should allow you to correctly position all twelve edge cubies, using all of    |
| the directions which I have given you in this chapter. However, you will need to be         |
| careful, especially in selecting ways to "customize", and in "undoing" your customizations. |
|                                                                                             |
| Careful attention to the details of the 3-way shuffle may help you orient all edge cubies   |
| as you go along, but Chapter Nine, "Rubik's Maneuver -- How to Flip Two Edge Cubies", is    |
| provided just in case some edge cubies do not have the correct orientation.                 |
|                                                                                             |
# If you suceeded in getting all twelve edge cubies properly located, there are only          #
# ((2 to the 12th power) / 2) = 4,096 / 2 = 2,046 ways these edge cubies can be oriented. We  #
# are closing in on the final, complete solution -- all siz sides -- of the Cube!             #
|                                                                                             |
+---------------------------------------------------------------------------------------------+