Rubik's Cube for Beginners
Step 5: Orient Last Layer Corners
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.
3 Wrong Corners
These are the simplest. Just use the algorithm provided for the case you have. In the first state, the three corners need to be rotated clockwise. In the second, the three corners need the be rotated counterclokewise. Notice that the algorithm for state 2 is just the algorithm for state 1 backwards.
|State 1||State 2|
|R U R' U R U2 R'||R U2 R' U' R U' R'|
4 Wrong Corners
For these cases, two corners need to be rotated clockwise, while the other two need to be rotated counterclockwise. Hold the cube as shown in the diagrams for states 3 and 4. Notice the two yellow stickers on the top layer of the left face. Make sure they are, then do the algorithm for state 1. You should now have state 1.
|State 3||State 4|
2 Wrong Corners
For these cases, one corner needs to be rotated clockwise and the other needs to be rotated counterclockwise. Find the one that needs to be twisted counterclockwise. Hold the cube so that that corner is located at the bottom left corner of the top layer. There should be a yellow sticker on the front-face side of the front-up-left corner. If you have done the set-up correctly, your cube will match one of the three states below. Do the algorithm for state 1. Now it should have state 2.
|State 5||State 6||State 7|
When you are done, your cube should look like this: