Revenge

---------------------------------------------------------------| | | | | 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 | | | | | | 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 | | | | | | | | | | | | A Solution to Rubik's Revenge | | | | | | 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 | / | | | | | | |/ | | |_________|_________|_________|_________/ | | | | D | | | | | | | | | |Written by Jonathan Bowen | | Programming Research Group | | Oxford University Computing Laboratory | | 8-11 Keble Road | | Oxford OX1 3QD | | England | | | | Tel +44-865-273840 | | | |Created January 1983 | |Updated June 1997 | |Issue 1.2 | ------------------------------------------------------------------------------------------------------------------------------| 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. | | | | U B F L R D denote a clockwise rotation through | | 90 degrees of the face indicated. | | | | 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. |

| | | 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 | | -------| | | | 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. | | | | RFd or RdF the segment at the centre of the righthand | | face's edge which is adjacent to the front | | face and nearest the downward face. | | | | FDL or FLD the corner segment on the front face which | | is adjacent to the lefthand and downward | | faces. | | | | R a combination of centre segments Rfu, Rub, | | Rbd and Rdf. | | | | FU combination of edge segments FUl and FUr. | | | | | | | ------------------------------------------------------------------------------------------------------------------------------| Operation | |--------------------------------------------------------------| | | | Operation notation | | -----------------| | | | 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. |

| | |1. | | |2. | |3. | | |4. | | |5. | | | | | | | | |6. | | | | | | | | | | |7. | | | | |8. | | | | | | | | | | |9. | | | | | | | |

Get all the centre segments matching ensuring that the positions are compatible with the corner segments. Get all the edge segments matching. Get a cross on a face ensuring that the segments match downwards. Complete across.

the face

ensuring

that

the corners

match

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

(ii)

(UF,FR):

F- U2 L- U

L

F

U2 F

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- Bto flip the back and front segments.

(iv)

UB,UL flip (UF,UL,BU): B U L U- L- Bto flip the back and lefthand segments.

Now orientate the cross downwards: (v)

(UR,UB): F- U- F U- F- U2 F Uto swap the right and back segments.

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 to swap front and back pairs.

Rotate the corners so that they properly using the following move:

U are

L- U- B orientated

(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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