Introduction: How to Solve the 3x3 Rubiks Cube
Welcome to my guide for solving the 3x3 Rubiks Cube. Though they may seem impossible at first, with a little bit of practice and some patience, anyone can solve it. The cube I use is the stickerless Dayan Zhanchi (Found here) with "Puzl" brand lubricant (Found here). Lubricant isn't required for your cube to work, but it allows faster turns and gives it a nicer feel overall. I will walk you through this methed by performing a solve myself, and commenting on and explaining each step required.
Please note: This method isn't designed to be fast, it's designed to get the job done. With some practice, you can achieve times under a minute, but any faster requires a different method. Onwards!
Edit: The pictures get a little darker as the Instructable goes on, sorry about that, they looked better on my iPad.
Step 1: Move Notation and Steps Required
The first thing we need to do before we start to solve (Besides owning a cube) is to understand what each algorithm means. The different moves you will use are as follows:
U, U2, U'
D, D2, D'
L, L2, L'
R, R2, R'
F, F2, F'
B, B2, B'
First, assume position the cube so a face points towards you, like picture 1. U and D stand for Up and Down, and represent turning either face 90° clockwise as though you were looking at it head-on. U2 and D2 require you to turn the face 180° in either direction and U' and D' are turns 90° anticlockwise as though you were looking at it head-on.
L and R are the left and right faces of the cube, and work exactly the same as U and D: 90° clockwise, a 180° turn or 90° anticlockwise.
Finally, F and B are the front and back faces of the cube. They work exactly the same as the rest, but remember that the back face is turned the opposite direction, because it points away from you.
In some guides, letters like Fi and Bi are used instead of F' and B'. The I stands for inverted, but means exactly the same thing.
These are each of the steps required to solve the cube. We'll go through each one later.
-The 1st layer corners
-The middle layer
-The top face
-The top corners
-The top edges
One final thing to note before we start is to always think of the cube as layers, NOT faces. This is a common mistake, and is one of the reasons why the puzzle seems so hard.
Step 2: Part 1: the Cross
The first thing we do when we start solving is the cross. I like to start on the orange face so I'll be doing that, but it's really a matter of personal preference.
Pictures 1 and 2 are our end result here. Notice how each edge on the top not only lines up with the orange side, but the face beneath it as well. There isn't much help I can really give you this step since we aren't using any algorithms, so just try to line up each edge then rotate the face to move it into place.
Step 3: Part 2: the First Corners
It's fine for our first algorithm. Hoorah! This step, we'll be moving the corners into place to complete the first layer (Not face). Here's the algorithm we'll be using: R' D' R D.
Firstly, look at the corner closest to the camera in photo 1. In this case, the corner we will put here needs to be orange, blue and white, so we need to find that. If it's on the bottom layer, just turn that layer so the corner is directly below where it needs to be. If the corner we need isn't on the bottom, we need to move it there. Find it, turn the cube so the corner is on the right, like in picture 2. Now it's time to use our first algorithm. Do R' D' R D. You should see the corner move to the bottom, and the cross not be broken.
Now that we have the corner at the bottom, turn the bottom layer so the corner is underneath where it needs to be. Next, use the R' D' R D algorithm to move it up into place. Chances are, once you've moved it into place, it won't be the right way round. We can fix this by repeating the R' D' R D algorithm a few times. Each time, it moves the shape to the bottom, and the next moves it back to the top. However, when it moves the corner to the top, it also turns it once so by repeating the algorithm a few times, we can get the corner the right way around. Keep doing this algorithm until the corner matches the faces it is adjacent to, as shown in picture 3.
Once you've got your first corner oriented, repeat this step to do the other 3 top corners; Get it to the bottom, get it underneath where it needs to be, keep using R' D' R D until it fits. When you've finished each corner, your cube should look a bit like picture 4.
Onto the middle layer!
Step 4: Part 3: the Middle Layer
The first thing we need to do for this step is flip the cube upside-down, so the side we created the cross on (In my case, the orange side) is facing the floor, like in picture 1.
Next, we need to rotate the top face until an inverted "T" shape is created, like picture 2. This "T" must NOT use the colour of the current top face (Red for me). Next, work out which side the top edge (The white-blue one) needs to move to. In this case, it needs to move to the left, between the white center and the blue center. We can move it here with the algorithm U' L' U L U F U' F'. You should see that the piece is now where it needs to be, as shown in picture 3. If you create the T and the top piece needs to move to the right, the algorithm U R U' R' U' F' U F will move it into place, like picture 4.
There are a couple of problems that we can encounter at this step. First, if no inverted "T" can be created without using the top face, then we need to move one of the middle edges to the top. Let's say we want the green-yellow edge in picture 5. The edge is on the right, so we use the U R U' R' U' F' U F algorithm to move it to the top. We can then use this piece to create the "T", then use the previous algorithms to move it to the right place. Alternatively, if the piece we want is on the left, we use the U' L' U L U F U' F' algorithm to move it to the top.
We also encounter a problem where the edge is in the right place, but flipped, like picture 6. The easiest way to solve this is to find which of the previous algorithms we need, use it to bring the edge to the top face then insert it correctly to where it needs to be.
Keep repeating this step until all 4 edges in the middle layer are in the right place, and the right way around, like in pictures 7 and 8.
-Create the "T" without the top colour
-Use U R U' R' U' F' U F or U' L' U L U F U' F' to move it right or left respectively
-Keep doing this until all 4 edges are complete.
Step 5: Part 4: the Top Face
Now we're going to make all of the top face the same colour, in this case red. Firstly, we need to construct a cross, as we did with layer 1. However, we do this slightly different. There are 4 different ways the top cross will be, when we start this step. These are shown in pictures 1, 2, 3 and 4. Remember that while constructing the top cross, corner colours are irrelevant.
-If the cross has nothing already constructed, except the center (Like picture 1): Use the algorithm F U R U' R' F'. This should create a line across the face.
-If the cross has an arrow shape (Like picture 2): Hold the cube so the "arrow" points to the bottom-right of the top face, and use the algorithm F U R U' R' F'. This should construct the whole cross.
-If the cross is a line (Like picture 3): Hold the cube so the line is horizontal across the top face and use the algorithm F R U R' U' F'. Don't get caught out - this algorithm is slightly different. This should construct the finished cross.
-If the cross is already completed (Like picture 4): Congratulations, you didn't have to do anything.
-If your top doesn't match any of these shown, you have either taken apart your cube and put it back together wrong, making it unsolvable, or you've missed out an edge in the middle layer. Look over your cube and make sure the first 2 layers are correct.
We should now have a cross on the top face. If you haven't, re-read the first part of this step. Now, it's time to solve the 4 corners of the top layer. There are several different possibilities here, so I'll go through each.
-If your top face has 2 corners adjacent to each other (Like picture 5) and the other 2 pieces facing away from each other, turn the top face so one of the top-coloured pieces faces towards you and is on the left (Picture 6). Then, use the algorithm R U R' U R U2 R'.
-If your top face has only 1 corner correct (Like picture 7), turn the top face so the correct corner is at the bottom-left (Picture 8) and use the same algorithm; R U R' U R U2 R'. Sometimes, this algorithm will not change the top face. You haven't done it wrong, so keep using these points until you have a completed top face.
-If your top face has 2 corners correct, and the other two facing towards you (Picture 9), hold the cube so they are both facing towards you (Also picture 9) and use R U R' U R U2 R'.
-If 2 opposite corners are solved (Like picture 10), position the cube so the red side is on the right (Picture 11) and use the algorithm R U R' U R U2 R'.
If you've used these correctly, you should have a completed top face, like in picture 12. Nearly done!
Step 6: Part 5: the Top Corners
This step is much simpler than last. There are 3 possible cases:
-All 4 edges line up perfectly, you'll know it when you see it. Move onto the next step.
-The corners on 1 face match up, but the others don't (Picture 1): Position the cube so the matching corners are at the back, and use the algorithm R' F R' B2 R F' R' B2 R2. This should fix all of the corners.
-None of your corners match (Picture 2). Use the previous algorithm, R' F R' B2 R F' R' B2 R2. This should fix 2 of your corners, then you can use the previous point to move on.
There aren't many pictures for this step, so here's a cat.
Step 7: Part 6: the Top Edges
THE FINAL STEP:
All we need to do now is move around the edges on the final layer. There are 4 different possibilities:
-None of the edges are in the right place (Picture 1): Use the algorithm F2 U L R' F2 L' R U F2. There should now be 1 edge solved, and 3 unsolved.
-One edge is solved and the other 3 need to move clockwise to solve the cube (Picture 2): With the solved edge at the back, use the algorithm F2 U L R' F2 L' R U F2. The cube should now be solved. If it isn't, you might have needed to use the next point.
-One edge is solved and the other 3 need to move anticlockwise to solve the cube (Picture 3): With the solved edge at the back, use the algorithm F2 U' L R' F2 L' R U' F2. The cube should now be solved
-All of the edges are solved: Congratulations, the cube is complete!
For your convenience, there is a list of the algorithms you used in this Instructable in the next step.
Step 8: Algorithm List
The pattern in picture 1 is created by doing F2 B2 L2 R2 U2 D2. Return the cube to normal by doing the same again.
-Move corner up and down, rotate corner: R' D' R D
-Move edge left: U' L' U L U F U' F'
-Move edge right: U R U' R' U' F' U F
-Arrow and dot on top face: F U R U' R' F'
-Line on top face: F R U R' U' F'
-Top corners: R U R' U R U2 R'
-Rotate top edges clockwise: F2 U L R' F2 L' R U F2
-Rotate top edges anticlockwise: F2 U' L R' F2 L' R U' F2