Packetizer

Rubik's Revenge Solution

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|    RRRRRR    U     U   BBBBBB    III   K     K  /   SSSSS    |
|    R     R   U     U   B     B    I    K   K       S     S   |
|    R     R   U     U   B     B    I    K K         S         |
|    RRRRRR    U     U   BBBBBB     I    K            SSSSS    |
|    R R       U     U   B     B    I    K K               S   |
|    R   R     U     U   B     B    I    K   K       S     S   |
|    R     R    UUUUU    BBBBBB    III   K     K      SSSSS    |
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|    RRRRRR  EEEEEEE V     V EEEEEEE N     N   GGGG  EEEEEEE   |
|    R     R E       V     V E       NN    N  G    G E         |
|    R     R E        V   V  E       N N   N G       E         |
|    RRRRRR  EEEEE    V   V  EEEEE   N  N  N G       EEEEE     |
|    R R     E         V V   E       N   N N G  GGGG E         |
|    R   R   E         V V   E       N    NN  G    G E         |
|    R     R EEEEEEE    V    EEEEEEE N     N   GGGG  EEEEEEE   |
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|                 A Solution to Rubik's Revenge                |
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|                                     B                        |
|                 ________________________________________     |
|                /         /         /         /         /|    |
|               /  ULB    /   UBl   /   UBr   /   UBR   / |    |
|              /_________/_________/_________/_________/ R|    |
|             /         /         /         /         /| U|    |
|            /  ULb    /   Ulb   /   Ubr   /   URb   / | B|    |
|        L  /_________/_________/_________/_________/ R| /|    |
|          /         /         /         /         /| U|/ |    |
|         /   ULf   /   Ufl   /   Urf   /   URf   / | b/ R|    |
|        /_________/_________/_________/_________/ R| /| B|    |
|       /         /         /         /         /| U|/ | u| B  |
|      /   UFL   /   UFl   /   UFr   /   URF   / | f/ R| /|    |
|     /_________/_________/_________/_________/ R| /| u|/ |    |
|     |         |         |         |         | F|/ | b/ R|    |
|     |         |         |         |         | U/ R| /| B|    |
|     |   FLU   |   FUl   |   FUr   |   FUR   | /| f|/ | d|    |
|     |         |         |         |         |/ | u/ R| /|    |
|     |_________|_________|_________|_________/ R| /| b|/ |    |
|     |         |         |         |         | F|/ | d/ R|    |
|     |         |         |         |         | u/ R| /| B|    |
|     |   FLu   |   Flu   |   Fur   |   FRu   | /| d|/ | D/    |
|     |         |         |         |         |/ | f/ R| /     |
|   L |_________|_________|_________|_________/ R| /| D|/      |
|     |         |         |         |         | F|/ | b/       |
|     |         |         |         |         | d/ R| /        |
|     |   FLd   |   Fdl   |   Frd   |   FRd   | /| D|/         |
|     |         |         |         |         |/ | f/          |
|     |_________|_________|_________|_________/ R| /           |
|     |         |         |         |         | D|/  D         |
|     |         |         |         |         | F/             |
|     |   FDL   |   FDl   |   FDr   |   FRD   | /              |
|     |         |         |         |         |/               |
|     |_________|_________|_________|_________/                |
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|                         D                                    |
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|Written by     Jonathan Bowen                                 |
|               Programming Research Group                     |
|               Oxford University Computing Laboratory         |
|               8-11 Keble Road                                |
|               Oxford OX1 3QD                                 |
|               England                                        |
|                                                              |
|               Tel +44-865-273840                             |
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|Created        January 1983                                   |
|Updated        April 1985                                     |
|Issue          1.1                                            |
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|                           Notation                           |
|--------------------------------------------------------------|
|                                                              |
|1.  Description                                               |
|    -----------                                               |
|                                                              |
|    Rubik's Revenge is a cube  which may be  considered to    |
|    consist of 64 miniature  cubes or 'cubies'.  Each face    |
|    is divided into sixteen square segments.  Any face and    |
|    its  adjacent  segments  on  the other  faces  may  be    |
|    rotated relative to the rest of the cube. Additionally    |
|    the next level  of segments may  also be rotated  with    |
|    the face.                                                 |
|                                                              |
|2.  Faces                                                     |
|    -----                                                     |
|                                                              |
|    The following letters are used to denote the six faces    |
|    of the cube:                                              |
|                                                              |
|    U  for the upper face,                                    |
|    B  for the back face,                                     |
|    F  for the front face,                                    |
|    L  for the lefthand face,                                 |
|    R  for the righthand face,                                |
|    D  for the downward face.                                 |
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|    U  B  F  L  R  D   denote a clockwise rotation through    |
|                       90 degrees  of the face  indicated.    |
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|    U- B- F- L- R- D-  denote  an  anticlockwise  rotation    |
|                       through 90 degrees.                    |
|                                                              |
|    U2 B2 F2 L2 R2 D2  denote   a  rotation  through   180    |
|                       degrees.                               |
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|    A double letter (e.g. UU for the upper face) indicates    |
|    that  the  rotation is  to include  the next  level of    |
|    adjacent segments as well.                                |
|                                                              |
|3.  Segments                                                  |
|    --------                                                  |
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|    Each segment  of each face is represented  by a string    |
|    of three letters.  The first letter indicates the face    |
|    on  which  the  segment  is situated.  The  other  two    |
|    letters indicate  which adjacent faces  the segment is    |
|    nearest.  If the two  letters are  lowercase  then the    |
|    segment is  in the centre  of the face.  If one of the    |
|    letters is uppercase  and one lowercase then  it is on    |
|    the edge  of the  face.  In this  case  the  uppercase    |
|    letter  indicates the  immediately  adjacent face.  If    |
|    the two letters  are uppercase  then the segment is at    |
|    the corner  of the face.  Note that the  order of  the    |
|    last  two  letters  is  immaterial.  A  single  letter    |
|    indicates a combination of the four centre segments on    |
|    that face and  two letters indicates a  combination of    |
|    two  edge  segments.  The  following  are  examples of    |
|    segments and combinations of segments:                    |
|                                                              |
|    Ufl or Ulf  the  centre  segment  of  the  upper  face    |
|                nearest the front and lefthand faces.         |
|                                                              |
|    RFb or RbF  the segment at the centre of the righthand    |
|                face's edge which is adjacent to the front    |
|                face and nearest the back face.               |
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|    FDL or FLD  the corner segment on the front face which    |
|                is adjacent  to the lefthand  and downward    |
|                faces.                                        |
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|    R           a combination of centre segments Rfu, Rub,    |
|                Rbd and Rdf.                                  |
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|    FU          combination of edge segments  FUl and FUr.    |
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|                          Operation                           |
|--------------------------------------------------------------|
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|    Operation notation                                        |
|    ------------------                                        |
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|    Segments and  segment combinations  in brackets denote    |
|    movement  of the segments  and combinations specified.    |
|    Elements in the brackets are a cyclic group and rotate    |
|    round one place from right to left  when the operation    |
|    is  performed.   E.g.  (UF,BU,UL)  is  transformed  to    |
|    (BU,UL,UF).  Note that  the first element moves to the    |
|    last position.                                            |
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|1.  Get all the centre segments matching ensuring that the    |
|    positions are compatible with the corner segments.        |
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|2.  Get all the edge segments matching.                       |
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|3.  Get a cross on a face ensuring that the segments match    |
|    downwards.                                                |
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|4.  Complete  the face  ensuring  that  the corners  match    |
|    across.                                                   |
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|5.  Using  the completed face  as the bottom face complete    |
|    the middle slice  using either  of the following moves    |
|    for each  of the four segments depending  on which  is    |
|    required.                                                 |
|                                                              |
|    (i)    (UF,RF):  U  R  U- R- U- F- U  F                   |
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|    (ii)   (UF,FR):  F- U2 L- U  L  U2 F                      |
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|6.  Again using the completed face  as the bottom face now    |
|    get  a  cross  on  the  upper  face.  Do  not  try  to    |
|    orientate these downwards at first.  Use the following    |
|    two moves:                                                |
|                                                              |
|    (iii)  UB,UF flip  (UF,BU,UL):  B  L  U  L- U- B-         |
|           to flip the back and front segments.               |
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|    (iv)   UB,UL flip  (UF,UL,BU):  B  U  L  U- L- B-         |
|           to flip the back and lefthand segments.            |
|                                                              |
|7.  Now orientate the cross downwards:                        |
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|    (v)    (UR,UB):  F- U- F  U- F- U2 F  U-                  |
|           to swap the right and back segments.               |
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|8.  Get  the four  corners into  their  correct  positions    |
|    using either  of the following moves  depending on how    |
|    the cube has fallen out:                                  |
|                                                              |
|    (vi)   (UBR,LBU,LUF):  U  R  U- L- U  R- U- L             |
|           to rotate all but the front righthand corner.      |
|                                                              |
|    (vii)  (UFL,FUR) and (ULB,BRU):                           |
|               B  L  U  L- U- L  U  L- U- L  U  L- U- B       |
|           to swap front and back pairs.                      |
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|9.  Rotate  the  corners   so  that  they  are  orientated    |
|    properly using the following move:                        |
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|    (viii) (FLU,LUF,UFL) and (FDL,DLF,LFD):                   |
|               R  F  R- F  R  F2  R- L- F- L  F- L- F2 L      |
|           to move  the top and  downward segments  to the    |
|           front face.                                        |
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