Layer by layer rubiks cube solution

Layer by Layer Solution
There are different approaches for solving the Rubik's Cube (layer by layer, solving the corners first, start with 2x2x2 block and expand). Each of these methods can be broken down into different levels of difficulty. For example, this solution uses a very easy way of solving it layer by layer that only requires a few algorithms. There exists a layer by layer method that requires over 50 algorithms that lets you solve the cube under 20 seconds

Notations
These terms will be used in algorithms of this solution.

U = Upper (top) face
D = Down (bottom) face
L = Left face
R = Right face
F = Front face
B = Back face
A letter by itself means to turn that face clockwise 90 degrees (e.g. F)
A letter with and apostophe after it means to turn that face counterclockwise 90 degrees (e.g. F')
A letter with a 2 after it means to turn that face 180 degrees (e.g. F2)
To decide whether to turn clockwise or counterclockwise, pretend that you are looking at the face you are turning. In the algorithms, the core of the cube should not be turned (unless you have x, y, or z in the algorithm, but those are not used in this beginner solution).

Speedcubing.com's notation page and Bob Burton's notation page explain this notation with pictures, and also has some notation not used in this solution, such as "x" or "f". Jon Morris's notation page has java applets with showing cubes being turned with this notation.

Cross

In this step, you have to form a cross on the D-face. I prefer to make a white cross because it stands out more from the other colors so it is easier to find. From now on, the rest of the guide will refer to white as the cross color. If you do a cross with a different color, just change "white" to your color.

FL Corners

The cross comprised the four edges of the first layer. In this step, you have to put in the corners. Just like the four edge pieces used to form the cross, the four corners have specific positions. Holding the cube so the cross is on the bottom, find a corner cubie in the top layer that has white on one of its three stickers. Look at the other two stickers of that corner piece to determine where in the bottom layer it has to go. Turn the top layer so that that corner is directly above its designated location. This is that start position.

You have to do this to all four corners. In all these five states, there is a solved cross in the D-face. These moves should not be considered algorithms. Do these moves slowly and watch carefully to see how the corner gets placed in.

2nd Layer

The cross comprised the four edges of the first layer. In this step, you have to put in the corners. Just like the four edge pieces used to form the cross, the four corners have specific positions. Holding the cube so the cross is on the bottom, find a corner cubie in the top layer that has white on one of its three stickers. Look at the other two stickers of that corner piece to determine where in the bottom layer it has to go. Turn the top layer so that that corner is directly above its designated location. This is that start position.

You have to do this to all four corners. In all these five states, there is a solved cross in the D-face. These moves should not be considered algorithms. Do these moves slowly and watch carefully to see how the corner gets placed in.

OLLE

From this step on, you will be using algorithms. Don't worry if you do not understand how they work. The important thing is that they work.

In this step, you have to form a cross on the U-face. Unlike the cross you made for the first layer, the position of the four the edges do not matter. There just has to be a cross.

OLLC

The goal for this step is to completely solve the top face so that it is all yellow. You do that by twisting the corners, three at a time. Don't worry about the sides of the top layer. That will be fixed in the next two steps.

There are seven possible orienting last layer corners states. The two algorithms for the first two states can turn three of the four corners clockwise or counterclockwise. For states 1 and 2, this step it easy. Just do the algorithm and move onto the next step. For the rest, it is a little more challenging.

The goal for states 3 to 7 is to strategically twist three corners, using one of the two algorithms, so that you result in state 1 or state 2. Then that can be solved using the algorithm for that state. The way to do so is explained below.

PLLC

I believed that the previous version of this page was a little too complicated. After having trouble explaining this step to someone at my school, I realized how much simpler it could be if I explained it the way I have now. Everything is kept the same. The same algorithm is used, but the step is presented in a more understandable and simple way.

Turn the top layer until exactly two of the corners are in their correct place. To the right is an example of a corner in the correct place. See how the color of each sticker of the corner matches the color of the center that sticker is on?

Now you will have one of the two states below. Either the two correct corners are adjacent to each other (and therefore the two that need to be swapped would be adjacent tool), or the two correct corners are diagonal from each other (and the two that need to be swapped would be diagonal too).

The corners that need to be swapped have arrows pointing to them. Therefore, the two correct corners in State 1 are the two on the right side, and the two correct corners in State 2 are the bottom-left and top-right ones. (Actually for state 2, the algorithm would still work if the two correct corners were at the top-left and bottom-right instead.)

PLLE

Yay! Last step! And this is proabably the easiest step too! The states are very straightforward.

There are 4 possible states for permuting the edges. Two algorithms are needed. The algorithm for state 2 is almost the same as the one for state 1, except for the second turn and second-to-last turn.

Be careful on the B and B' turns. Don't mix those two up. Remember that in the notation used, you pretend you are looking at the face you are turning to determine which way is clockwise and which is counterclockwise. Therefore, a B will look counterclockwise from the front, but if you were to turn the cube around and look at it from the back, the move would be clockwise. The same thing with B'.

this method but with pictures

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