Rubik's Cube Solution
---------------------------------------------------------------- | | | | | | | TTTTTTT H H EEEEEEE | | T H H E | | T H H E | | T HHHHHHH EEEEE | | T H H E | | T H H E | | T H H EEEEEEE | | | | | | RRRRRR U U BBBBBB III K K | | R R U U B B I K K | | R R U U B B I K K | | RRRRRR U U BBBBBB I K | | R R U U B B I K K | | R R U U B B I K K | | R R UUUUU BBBBBB III K K | | | | | | CCCC U U BBBBBB EEEEEEE | | C C U U B B E | | C U U B B E | | C U U BBBBBB EEEEE | | C U U B B E | | C C U U B B E | | CCCC UUUUU BBBBBB EEEEEEE | | | | | | | | | | A Solution to the Rubik Cube | | | | | | | | B | | _________________________________ | | / / / /| | | / ULB / UB / UBR / | | | /__________/__________/__________/ R| | | / / / /| U| | | L / UL / U / UR / | B| | | /__________/__________/__________/ R| /| | | / / / /| U|/ | | | / UFL / UF / URF / | / R| B | | /__________/__________/__________/ R| /| B| | | | | | | F|/ | | | | | | | | U/ R| /| | | | FLU | FU | FUR | /| |/ | | | | | | |/ | / R| | | |__________|__________|__________/ R| /| B| | | | | | | F|/ | D| | | | | | | / R| / | | L | FL | F | FR | /| D|/ | | | | | |/ | / | | |__________|__________|__________/ R| / | | | | | | D|/ D | | | | | | F/ | | | FDL | FD | 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 October 1981 | |Updated April 1985 | |Issue 1.1 | ---------------------------------------------------------------- ---------------------------------------------------------------- | Notation | |--------------------------------------------------------------| | | |1. Description | | ----------- | | | | The Rubik Cube is a cube which may be considered to | | consist of 27 miniature cubes or 'cubies'. Each face | | is divided into nine square segments. Any face and | | its adjacent segments on the other faces may be | | rotated relative to the rest of the cube. | | | |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. | | | |3. Segments | | -------- | | | | Each segment of each face is represented by a string | | of one to three letters. The first letter indicates | | the face on which the segment is situated. If this is | | the only letter in the string then the segment is in | | the centre of the face. If one letter follows then the | | segment is in the centre of one of the edges of the | | face and the second letter indicates the adjacent | | face. If two letters follow then the segment is in one | | of the corners of the face and the two letters | | indicate the two adjacent faces. Note that the order | | of the last two letters is immaterial. The following | | are examples of segments: | | | | U the centre segment of the upper face. | | | | RF the segment at the centre of the righthand | | face's edge which is adjacent to the front | | face. | | | | FDL or FLD the corner segment on the front face which | | is adjacent to the lefthand and downward | | faces. | | | |4. Operation notation | | ------------------ | | | | Segments in brackets denote movement of the segments | | 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. | | | | | | | | | | | | | | | | | | | ---------------------------------------------------------------- ---------------------------------------------------------------- | Operation | |--------------------------------------------------------------| | | |1. Get a cross on a face ensuring that the segments match | | downwards. | | | |2. Complete the face ensuring that the corners match | | across. | | | |3. 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 | | | | (ii) (UF,FR): F- U2 L- U L U2 F | | | |4. 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- | | | | (iv) UB,UL flip (UF,UL,BU): B U L U- L- B- | | | |5. Now orientate the cross downwards: | | | | (v) (UR,UB): F- U- F U- F- U2 F | | | |6. 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 | | | | (vii) (UFL,FUR) and (ULB,BRU): | | B L U L- U- L U L- U- L U L- U- B | | | |7. Rotate the corners so that they are orientated | | properly using the following move: | | | | (viii) (FLU,LUF,UFL) and (FDL,DLF,LFD): | | R F R- F R F2 R- L- F- L F- L- F2 L | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ----------------------------------------------------------------