Solving Rubik's Cube

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3x3x3 Solution

WARNING! My complete solution for the Rubik's Cube is on this page. If you haven't already solved it yourself then I recommend that you skip this page.

Step 1: Solve one complete row.

Anyone with a little patience should be able to correctly solve a single side of the Rubik's Cube. Remember that it isn't enough to get just one face all the same color; you must also get all the side colors of that first row of sub-cubes to line up properly.

This section is so easy that I'm not going to list any move sequences for it. Just keep at it and I'm sure that you'll get it.

Step 2: Put opposite corners in the correct location.

Now that you've solved one row, turn the cube upside down so that face is now in the D (or down) orientation and look at the four corners on the U side. Now imagine what they would look like if they were all oriented so that they all had the same color on the U face. Rotate the U face until you can get as many of the corners as possible in the correct location (refer to the colors in the center of the L, R, F and B faces).

If they are all in the correct location then you can skip this step but odds are pretty high that at least two of them will be in the wrong location. To set them right you can use the following move to swap the UFR corner with the URB corner.

2 corner swap

R U R' U' F' U' F

The grey colored markings in the diagram tell you what other pieces will be affected by this maneuver. They're grey because I don't care about them. I've only made a note of them to be complete. The only thing I really care about here is what happens to the two corners since all the other grey pieces are messed up anyway.

I find the easiest way to remember this move is to watch what happens to the FDR corner during the move. The first three twists pull out the FDR corner and put it in the UFL position. The last four twists return it to the lower corner using a different sequence of moves. That results in the other pieces moving in a set pattern while the bottom layer remains undisturbed.

You may have to execute this move twice or not at all but most of the time you only need to do it once.

Step 3: Put opposite corners in the correct orientation.

Once the corners are all in the correct position, they need to be oriented correctly. Look at each corner carefully and make a note of where the U color is. There are only three possible orientations for each piece: either the piece needs to rotate clockwise one position, or it needs to rotate counterclockwise one position, or it doesn't need to be rotated at all.

To correct their rotation, I use the following move, which rotates every U corner clockwise except for the UFL corner, which remains unchanged.

3 corner rotation

Full: R U R’ U R U2 R’ U2
+ f U’ f’ U2 f U’ f’
Simplified: R U R’ U R U2 R’

The full move does exactly what's shown in the diagram but since we haven't placed any edge pieces yet we can get by with using the simplified move which will also scramble the edge pieces a bit.

Again, watch what happens to the FDR corner when you do this move. The R U R' sequence is exactly the same as the start of the 2 corner swap move. The U R U2 R' puts the FDR corner back using a different sequence and rotates the corners in the process.

You may need to execute this move more than once. Your final goal is to get all four corners oriented properly but your first goal should be to get just one corner oriented properly. Once you've done that the other three corners will be oriented such that you can use this move to set them right.

Also, note that you can sometimes save yourself a move by using the mirror image of this sequence: L' U' L U' L' U2 L which will rotate all but the UFR corner counter clockwise.

Step 4: Solve opposite edges.

Once all eight corners are correctly positioned and oriented, I next set about completing the opposite side. When you're done with this step, the U layer and the D layer will be completely solved, leaving just the four edge pieces about the middle layer left.

The sequence that moves the edges works using the same basic principal as the earlier moves: remove one of the edge pieces from the bottom and then put it back in a different way, causing it to bring with it one of the other pieces from the middle layer into the top layer.

To set this move up, rotate the cube until you have an edge piece at the RB position with the U color on the R face. Then rotate the U face until the location for that piece is in the UF position. Finally use the edge move listed below to pull the RB piece into the UF location.

edge mover

Full: F u’ F2 u’ F r2 u’ r2 u
Simplified: F u’ F2 u’ F

As before, the full move does exactly what the diagram shows but since you don't care about the pieces in the middle layer, just use the simplified move. It will scramble the middle layer a bit but at this point you don't care.

If you have an edge piece that's oriented incorrectly, use the mirror image move: F' u F2 u F' instead. That will pull the piece from LB instead of the piece from RB.

Watch what happens to the FB piece as you execute this sequence.

Repeat that move for all four edge pieces in the U layer. If you have an edge piece that's incorrectly placed in the U layer then use the edge mover to pull another piece into its place and kick it out to the middle layer.

Step 5: Put middle row edges in the correct location.

At this point you should have all of the top layer and all of the bottom layer complete. That just leaves the four edge pieces in the middle layer.

Rotate the top and bottom layers so that all the corners line up with the center sub-cube on the front face. Now note the position of the remaining edge pieces. Ignore their orientation for now. There are only three possibilities at this point: either they're all in the correct position or one of them is in the correct position or none of them are in the correct position.

One of the following two moves should set things right:

4 mid-piece swap	3 mid-piece swap

(R2 u2)x2	R2 u’ R2 u

Note that you might also find it useful to use the mirror image of the 3 mid-piece swap: L2 u L2 u'.

Step 6: Put middle row edges in the correct orientation.

By now you have all of the pieces in their correct locations. At this point there is a 25% chance that you'll be completely done. Unfortunately, there is a 50% chance that two of the edges will be twisted 180° and there is a 25% chance that all four of them will be twisted.

This is where I got stuck when I first learned to solve the cube. The earlier moves were reasonably obvious. To me, this one was not. I could see no simple way to untwist those last cubes without disturbing the rest of the cube. Originally, my only recourse was to scramble the cube and solve it again. One out of four times I would get lucky. That wasn't a very satisfying solution. Luckily I didn't give up. I continued playing and twisting until one day I stumbled upon the following move quite by accident.

2 edge rotation

(r U)x4 (U r)x4

I discovered that repeating the r U pattern four times resulted in a cube that looked nearly solved except that the DF, DB, UL and UB edges were twisted. So by turning the U face one extra turn and repeating the pattern I could untwist all the faces but one while twisting one additional face. It's a bit long but it's very easy to remember, quick to do and it's really fun to watch people's reaction when they think that you're totally messing up a nearly-solved cube only to see it magically all fall into place with that last twist.

Congratulations! You're done!

Now on to bigger challenges!

By the way, I have consolidated all of these 3x3x3 moves onto a single printed sheet. Click here to see it.

<Professor's Cube>