How to Solve the Rubik's Cube
For those of you who have a Rubik's Cube and can't figure out how to solve it, here's an easy to learn beginner solution that will let you solve the cube from any legal state (i.e. assuming you haven't changed the stickers around or taken it apart and reassembled it into an unsolvable state).
If you wish to become a speedcuber, this method is easily expanded to the more advanced layer by layer methods like the popular Fridrich method.
Getting to know the cube
Rather than thinking of the cube as 6 faces x 9 stickers per face = 54 colored squares to put in the right places, think of it as 20 moving pieces (8 corners each with three stickers + 12 edges each with 2 stickers) and 6 centers. While the center pieces can rotate about an axis, they are fixed and don't move with respect to the other centers. Therefore, the center piece of a face must define the color of that face when the cube is solved.
On my cube, white is opposite yellow, blue is opposite green, and red is opposite orange, so my diagrams will reflect that. If your cube was bought in the US yours will probably be the same. If you have an older cube or a Japanese cube, you may have a different color scheme. So when I refer to yellow stickers toward the end of the tutorial, just keep in mind that on your cube, it will be the color opposite of the side you started with.
A common beginner mistake is trying to solve the cube one face at a time. Not only is this highly inefficient, it is extremely difficult. There are many different methods to solve the cube. The system described here is an easy to learn layer by layer method with very few algorithms or movesets to memorize.
Notation
Moves and algorithms are described using standard cube notation. In standard cube notation, each of the 6 faces is described by its position with respect to you.
- F = front
- B = back
- R = right
- L = left
- U = up
- D = down
A letter by itself (e.g. F) means turn that face 90 degrees clockwise with respect to the center of the cube. A letter with an apostrophe (F') denotes a 90 degree counter-clockwise turn. A letter followed by the number 2 (F2) denotes 2 turns, i.e. a 180 degree turn.
Positions on the cube are denoted by two letters for edges and three letters for corners (e.g. FR = front right edge; UFL = upper front left corner).
Part 1: First Layer Edges
Pick a color to start with. I always start with white because it's the color that stands out the most on a scrambled cube. Your first objective is to solve the four white edges, building a cross on your first layer as shown below.
Note that each white edge piece has another color sticker on it. When the white cross is completed, this other color has to match the center piece it's adjacent to.
Your cross should look like this: | Not like this: |
This step should be pretty intuitive; however if you are having trouble or just starting out you may want to try the beginner's "daisy method" first. As you get used to the process you can skip the daisy and build the cross directly.
Daisy method for building the cross
Once you have finished the cross, keep the white cross on the bottom face for the rest of your solve.
Part 2: First Layer Corners
Your next step is to complete the first layer by filling in the corners. Locate a corner piece that has a white sticker on it. There are four of them, and they can be found on the top layer or bottom layer.
If the corner piece is on the top layer, rotate U until it is directly above where it needs to go. Hold the cube so that this corner is at the UFR position. Now check the position of the white sticker. You have three possible cases:
R U R' | |
F' U' F | |
Doing R U2 R' or F' U2 F will reduce this to one of the above cases. |
If the white corner piece is on the bottom layer, replace it with different corner piece from the top layer. The white corner piece will then be in the top layer and you can now deal with it using one of the cases indicated above.
Once you have done this with all four corners, you should be done with the first layer.
Part 3: Middle Layer Edges
Notice that the middle layer consists of just four edge pieces that need to be solved. An easy way to identify a middle layer edge is to look for edge pieces that have no yellow stickers on it.
If the middle layer edge is on the top layer, rotate U until it's matched with an adjacent center sticker. Hold the cube so that its target position (where you want to place that edge) is at the FR position. You have two possible cases:
U R U R' U' F' U' F | |
U' F' U' F U R U R' |
If the middle layer edge is in the middle layer but in the wrong position or orientation, replace it with a random edge piece from the top layer using the method above. After doing this, the middle layer edge you need will be on the top layer.
Notice that what you are doing each time you solve a middle layer edge is taking out a first layer corner and then putting it back in from the other side.
Once you're finished with all four middle layer edges, you are done with the first two layers. Congratulations, you're halfway done! From here on out things will get a little more complicated, as you'll have to fix what's left without messing up what you've already done. While the steps up to this point are pretty intuitive, subsequent steps involve memorizing algorithms.
For the last layer, diagrams will show a top-down view of what your top layer looks like. You will still be executing the algorithms with the top layer as the U face.
Part 4: Last Layer Cross
Your first objective is to orient the last layer edge pieces so they all have yellow facing up, forming a yellow cross on the last layer. The orientation of your last layer edges has three possible cases:
F R U R' U' F' | |
F U R U' R' F' | |
Do both of the above algorithms |
If you have exactly one edge oriented correctly or oriented incorrectly and your first two layers are completely solved, your cube is in an unsolvable state, which can happen if you rearrange stickers or disassemble the cube and reassemble it randomly. If you're in this situation, take apart your cube and reassemble it solved before doing anything else.
Part 5: Last Layer Corner Orientation
Complete the last layer orientation by orienting the corners so that they all have yellow facing up. You only need to learn two algorithms for this. In fact, it's really only one algorithm, because one is simply the mirror image of the other. In the diagrams, the dashes on the sides represent which side the yellow sticker is on.
Case 1: Exactly one corner is already correctly oriented (has yellow sticker on top). Determine which case it matches and apply the appropriate algorithm.
R U R' U R U2 R' | |
L' U' L U' L' U2 L |
Case 2: Exactly two corners are correctly oriented. Hold the cube so that the UFL corner needs to be rotated counter-clockwise (there should be a yellow sticker on the front face; see diagram) and do R U R' U R U2 R' to bring you to Case 1.
Hold the cube like this. |
Case 3: No corners are correctly oriented. Hold the cube so that the UFL corner needs to be rotated clockwise (there should be a yellow sticker on the left face; see diagram) and do R U R' U R U2 R' to bring you to Case 1.
Hold the cube like this. |
If you end up with exactly three corners correctly oriented, your cube is in an unsolvable state.
Part 6: Last Layer Permutation
You're almost done! Now all you have to do is position all the pieces where they need to go. Let's start with the corners. There's only one algorithm you need here, the two corner switch:
R B' R F2 R' B R F2 R2 U |
You may have to do this algorithm more than once (e.g. if two opposite corners need to be switched). Once all your corners are correctly positioned, you can move on to the edges:
F2 U R' L F2 R L' U F2 | |
F2 U' R' L F2 R L' U' F2 |
Note that these two algorithms are identical except for the direction in which to turn U. It's easy enough to remember: it's U to cycle edges clockwise and U' to cycle them counterclockwise.
You may have four edges that need to be positioned, in which case do the 3 edge cycle twice as needed. However if you've gotten this far and you only have two edges switched (and everything else is correct), it means your cube is unsolvable.
Now that you know how to solve the Rubik's cube, what's next? Want to learn how to get faster? Head over to the cubing tips page for ideas.