How to Solve a Rubik's Cube Using Commutators

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posted on 17 years ago — updated on 1 second ago

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There are many methods to solve a Rubik's Cube. This centers-edges-corners method is one of the simplest and most popular. It is excellent for beginners, although not as fast as certain other methods. For the sake of simplicity,
R means right face clockwise,
F means front face clockwise,
U means above (or up) face clockwise,
L means left face clockwise.
Also, if an apostrophe (') is added, it will signify counterclockwise.

If you're curious, the word "commutators" refers to a method in which only very small parts of the cube are moved at a time.

Steps

Understand the different terms used in this article. Please proceed to this Definitions section of another Rubik's solution page.

Pick a color to be the up face. Try to make a "+" sign using the center and edges of the face, which may be scattered around the cube. If one of the edges is incorrectly oriented, face that side towards you and apply FU'RU.

Rotate the cube so that the plus sign is now the left face. You will put the UF edge in place first. If that edge is in the right face, turn the right face to put that edge in FR position. Then apply U'RUR'. Do the same thing, rotating the cube down each time, until all four edges are in place.

Orient the middle edges. Put each incorrectly oriented cube closest to you, one at a time, and apply R'FRF'UF'U'F. The plus sign should still be in position, on the left face.

Rotate the cube so that the right face is now the up face. If the edges are all in place, go to the next step. If they aren't, there are two situations: If the left edge "wants" to switch with the back edge and the front edge wants to switch with the right edge, apply RUUR'U'RU'R'. Otherwise, correctly place exactly one edge by rotating the face and put it closest to you. If the other three want to rotate clockwise, apply RUUR'U'RU'R'. If they want to move counterclockwise, apply RUR'URU'U'R'.

Orient the last four edges. If all four are incorrectly oriented, apply R'FRF'UF'U'F. If two edges are incorrectly oriented and adjacent to each to each other, put the incorrectly oriented edges in the UF and UR positions and apply R'FRF'UF'U'F. If two edges are incorrectly oriented and opposite from each other, put the incorrectly oriented edges in the UR and UL positions and apply LFR'FRF'UF'U'L'.

Put the UFR corner in place. If the necessary block is in the front face, choose another corner to start with. The corner should be in the back face. Turn that face back to put the UFR corner in the UBR position and apply R'URU'R'URU'R'URU'. Then turn the back face back to its proper orientation. Keep repeating this move with each corner until all four Front corners are in place. If the corner is stuck in the front face, you can apply the same move to get it into the back face.

Put the remaining corners in place. Put the back face up so that the remaining "wrong" corners are in the up face. If all four corners are wrong, apply L'URU'LUR'U' and now one should be correctly placed. If three are wrong, put the correct one in the UFR position, closest to you. If the other three want to rotate clockwise, apply L'URU'LUR'U'. If they want to rotate counterclockwise, apply URU'L'UR'U'L'

Orient the corners in the right face. Do the UFR corner first. If it wants to rotate clockwise, apply FR'URU'R'URU'F'UR'U'RUR'U'RF'. If it wants to rotate counterclockwise, apply R'URU'R'URU'FUR'U'RUR'U'RF'. Repeat this for all the incorrectly oriented corners in the right face.

Orient the remaining corners. To start, put the left face up. If all 4 corners are incorrectly oriented, look at the UFR corner. If it wants to rotate clockwise, apply FR'URU'R'URU'F'UR'U'RUR'U'RF'. If it wants to rotate counterclockwise, apply R'URU'R'URU'FUR'U'RUR'U'RF'. If 3 corners are incorrectly oriented, place the correct one in the UBR position. Look at the UFR corner. If it wants to move clockwise, apply FR'URU'R'URU'F'UR'U'RUR'U'RF'. If it wants to move counterclockwise, apply R'URU'R'URU'FUR'U'RUR'U'RF'. If 2 corners are incorrectly oriented and they are adjacent, put the incorrect ones in the UFR and UFL positions. Look at the UFR corner. If it wants to move clockwise, apply FR'URU'R'URU'F'UR'U'RUR'U'RF' and if it wants to move counterclockwise, apply R'URU'R'URU'FUR'U'RUR'U'RF'. If 2 corners are incorrectly oriented and they are opposite each other, put the incorrect ones in the UFR and ULB positions. Apply L and then look at the UFR corner. If it wants to move clockwise, apply FR'URU'R'URU'F'UR'U'RUR'U'RF' and if it wants to move counterclockwise, apply R'URU'R'URU'FUR'U'RUR'U'RF'. Then apply L'.