Rubik's Cube/Rubik's Maneuver

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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 Nine - - - - - - - - - - Rubik's Maneuver -- How to Flip Two Edge Cubies           |
 * Goal Four is to orient each of the twelve edge cubies at its proper location. This will    |
 * finish a solution of the Cube! (This is the only elaborate operation I actually memorized  |
 * (and still remember) from some of the books I have read.)                                   |
 * _ * _     (t)                                                            |
 * _ * _TOP_ * _ /                                                              |
 * _ * _TOP_ * _ k _ * _                                                            |
 * * _TOP_ * _TOP_ * _TOP_ *   A Cube                 Notice that the edge cubies     |
 * |  * _ f _ * _TOP_ *   |    in need of             which need to be "flipped"      |
 * | F |  * _TOP_ *   | R |    Rubik's                correspond to edge cubie #2     |
 * * _ | t |  *   | R | _ *    Maneuver               and edge cubie #3 as            |
 * |  * _ | F | R | _ *   |                           described in Chapter Eight.     |
 * | F |  * _ | _ *   | R |                                                           |
 * * _ | F |  *   | R | _ *    The edge cubies                                        |
 * |  * _ | F | R | _ *   |    at BACK TOP                                            |
 * | F |  * _ | _ *   | R |    and FRONT TOP                                          |
 * * _ | F |  *   | R | _ *    need to be                                             |
 * * _ | F | R | _ *       "flipped".                                             |
 * * _ | _ *                                                                  |
 * DIAGRAM 9-1. A Cube in Need of Rubik's Maneuver                                    |
 * Rubik's Maneuver "flips" two edge cubies at the BACK TOP and FRONT TOP locations. You will |
 * need to use the "slice" moves ("down-slice" and "up-slice"), which were described in       |
 * Chapter Eight, "". Here is the recipe. (I memorized this -- you can, too.)                 |
 * Down-slice (2R^ Rv).                                                                   |
 * Turn the top (always in the same direction (T^ or Tv, it doesn't matter as long as     |
 * you are consistent) .                                                    |
 * Down-slice.                                                                            |
 * Turn the top.                                                                          |
 * Down-slice.                                                                            |
 * Turn the top twice (T2).                                                               |
 * Up-slice (2Rv R^).                                                                     |
 * Turn the top (still in the same direction).                                            |
 * Up-slice.                                                                              |
 * Turn the top.                                                                          |
 * Up-slice.                                                                              |
 * Turn the top twice (T2).                                                               |
 * DIAGRAM 9-2. Instructions for Rubik's Maneuver                                         |
 * And what if you need to "customize" your moves to "flip" two edge cubies which are NOT at  |
 * the FRONT TOP and BACK TOP positions? You have already been able to juggle THREE edge      |
 * cubies, following the directions in Chapter Eight, "". Just rotate the entire Cube until   |
 * one of the edge cubies to be flipped is at the BACK TOP position. (This corresponds to     |
 * edge cubie #2 as discussed in Chapter Eight, "".) Then use part two of the instructions of |
 * Chapter Eight to position another edge cubie that needs to be flipped. (This corresponds to |
 * edge cubie #3, as discussed in Chapter Eight.) Do Rubik's Maneuver, then undo the moves    |
 * you used to "customize" the locations of those two edge cubies that got flipped.           |
 * Don't worry about "edge cubie #1" -- Rubik's Mauever (if done correctly) only flips the two |
 * edge cubies at FRONT TOP and BACK TOP. The edge cubie at BOTTOM BACK should be completely  |
 * unaffected by Rubik's Maneuver.                                                            |
 * There is one special case not handled by the instructions in Chapter Eight. Can you figure |
 * out what needs to be done for this special situation?                                      |
 * __ This is where we want #3.                               |
 * |   |    |    |    |    |    | #2 |                                        |
 * |   | L  |    | F  |    | R  |    | K  |    |  Customizing Move:                |
 * ++++++++++ "3R^".                           |
 * |   |    |    |    |    |    | #3 |                                        |
 * DIAGRAM 9-3. Special Case Not Handled by Instuctions in Chapter Eight                  |
 * In the worst case, you will need to do Rubik's maneuver six times to flip 12 edge cubies.  |
 * (In the best case, you won't need to do it at all.)                                        |
 * ... And after all that work, the result is ....                                            |
 * |TOP|TOP|TOP|                                                  |
 * |TOP|TOP|TOP|                                                  |
 * |TOP|TOP|TOP|                                                  |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * DIAGRAM 9-3. The Unscrambled Cube                                          |
 * ++++++++++ "3R^".                           |
 * |   |    |    |    |    |    | #3 |                                        |
 * DIAGRAM 9-3. Special Case Not Handled by Instuctions in Chapter Eight                  |
 * In the worst case, you will need to do Rubik's maneuver six times to flip 12 edge cubies.  |
 * (In the best case, you won't need to do it at all.)                                        |
 * ... And after all that work, the result is ....                                            |
 * |TOP|TOP|TOP|                                                  |
 * |TOP|TOP|TOP|                                                  |
 * |TOP|TOP|TOP|                                                  |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * DIAGRAM 9-3. The Unscrambled Cube                                          |
 * |TOP|TOP|TOP|                                                  |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | L | L | L | F | F | F | R | R | R | K | K | K |                          |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * DIAGRAM 9-3. The Unscrambled Cube                                          |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * | B | B | B |                                                  |
 * DIAGRAM 9-3. The Unscrambled Cube                                          |
 * | B | B | B |                                                  |
 * DIAGRAM 9-3. The Unscrambled Cube                                          |
 * DIAGRAM 9-3. The Unscrambled Cube                                          |
 * DIAGRAM 9-3. The Unscrambled Cube                                          |

