Rubik's Cube/Moving Edge Cubies

 +-+ +-+ 
 * 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.                |
 * 1) If you suceeded in getting all twelve edge cubies properly located, there are only          #
 * 2) ((2 to the 12th power) / 2) = 4,096 / 2 = 2,046 ways these edge cubies can be oriented. We  #
 * 3) are closing in on the final, complete solution -- all siz sides -- of the Cube!             #
 * |   |    | #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.                |
 * 1) If you suceeded in getting all twelve edge cubies properly located, there are only          #
 * 2) ((2 to the 12th power) / 2) = 4,096 / 2 = 2,046 ways these edge cubies can be oriented. We  #
 * 3) are closing in on the final, complete solution -- all siz sides -- of the Cube!             #
 * __ 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.                |
 * 1) If you suceeded in getting all twelve edge cubies properly located, there are only          #
 * 2) ((2 to the 12th power) / 2) = 4,096 / 2 = 2,046 ways these edge cubies can be oriented. We  #
 * 3) are closing in on the final, complete solution -- all siz sides -- of the Cube!             #
 * 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.                |
 * 1) If you suceeded in getting all twelve edge cubies properly located, there are only          #
 * 2) ((2 to the 12th power) / 2) = 4,096 / 2 = 2,046 ways these edge cubies can be oriented. We  #
 * 3) are closing in on the final, complete solution -- all siz sides -- of the Cube!             #
 * 1) ((2 to the 12th power) / 2) = 4,096 / 2 = 2,046 ways these edge cubies can be oriented. We  #
 * 2) are closing in on the final, complete solution -- all siz sides -- of the Cube!             #