How to Solve a Rubik's Cube Using Commutators

Co-authored by Timothy Huynh

Last Updated: February 22, 2024

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

Please proceed to this Definitions section of another Rubik's solution page.
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.

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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.
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.
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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'.
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'.
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 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'
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.
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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'.
You have solved the Rubik's Cube using commutators!

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Question

What is an odd-numbered Rubik's cube?

Timothy Huynh
Rubik’s Cube Champion
Timothy Huynh is a Rubik’s Cube Artist & Champion based in Tampa, Florida. Timothy has been solving Rubik's Cubes professionally since 2016 and became a Guinness World Record Holder with advanced Rubik's cube-solving skills. Timothy has a follower base of over 8.6 million YouTube subscribers and 124k followers on Instagram. Internet celebrities including David Dobrik and Simu Liu have sung his praises, and Pixar has deemed his work "incredible."

Timothy Huynh

Rubik’s Cube Champion

Expert Answer

In odd-numbered Rubik's cubes, the absence of a fixed center distinguishes them from their even-numbered counterparts. Fixed centers in a Rubik's cube dictate the identity of each face, providing instant clues for solving a scrambled cube. However, in even-number cubes like the 4x4 and 6x6, the centers are not stationary; they shift positions. Consequently, arranging centers incorrectly can render the cube unsolvable. Contrastingly, in a 5x5 cube, a fixed center remains, ensuring that incorrect center placements never occur. The presence of this stable center reference point facilitates solving by providing a reliable guide for aligning colors and solving the cube accurately.

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What is the classic algorithm, not the layer method?

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There is no classic algorithm, because there are so many different combinations, each one with a different solution.

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The cross isn't working for me, help?

Community Answer

Try getting it done piece by piece. Find an edge, put it in the bottom, line it up with the corresponding center, and do F2 to place it properly.

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Tips

Once you get your time down to under one and a half or two minutes, consider switching to other, faster but more complicated methods.

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Carefully choose a good cube.

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Don't expect to get it right on the first try. Persevere, and you will get it eventually!

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