Solving Corners
1. Solve Four Bottom Corners
We will start by solving four corners of the cube that share one color (in this case we will select white color). You may try to complete this step on your own and look at the provided sequences only if stuck and frustrated for some time. This step can be solved intuitively if you invest some of your time.
Select one corner with white sticker and turn the whole cube so the white sticker of this corner is facing down. You have solved one of 4 corners this way. Now look for other corners with white sticker and put them to the bottom layer using the right one of the following sequences. Solve the corners one by one. When searching for the next corner to solve, you may freely turn the top layer to put the corners into the position in which you can apply the sequence.
Pay attention to align colors of the corners on sides, since if they do not match as well, the corners are not in correct places. The orange and green colors are just example, there can be other color combinations (like blue-red, green-red, ...) in the pictures instead, just the white sticker should be really white.
The cubie on top, bottom sticker on the front side:



The cubie on top, bottom sticker on the right side:



If you do not see any situation being similar to one of the first two above (remember that you can freely turn top layer to position the corner to the top-right-front position), the corners are in positions that are more difficult to solve. The following sequences will help you to transform such positions into the ones you should be familiar with already.
The bottom sticker on the top:





The cubie on bottom, bottom sticker on the front side:



The cubie on bottom, bottom sticker on the right side:



One possible way to remember the last two sequences is "bring white sticker to the top, put it back (inside layer you just turned), reverse the first step".
If you have no idea, what is going on when using these sequences, just go really slow and watch what is happening with the solved corners and the one being solved after each turn.
2. Place Four Top Corners
To solve the four top corners you will need to temporarily destroy the 4 bottom corners. The question is: How to destroy and restore the bottom corners so as the top corners become solved? The simplest idea is to remove one bottom corner from its position (using one of the sequences given earlier) and solve it in a different way. Let us look at an example showing the removing and restoring of the front-right-bottom corner:
Remove, position top layer, and restore corner (shown applied to a solved cube):





If you look at the result you may notice that the top corners changed. Two corners are twisted (orange-blue-yellow and red-blue-yellow) and two are swapped (top-right ones). If we select carefully how to turn the whole cube before applying this corner sequence to affect the right corners, we can solve the top corners just by this one sequence! In this step, we will only position the corners to their correct positions while ignoring the way how they are twisted. Thus our task is quite simple: apply the corner sequence (possibly more times) to place the corners to their correct positions (use the colors of side stickers of bottom corners to find the right ones).
As you can notice the corner sequence swaps the top-right-front and top-right-back corners. You just need to turn the top-layer and/or the whole cube (keeping top layer facing up) to a position where swapping these two top-right corners will place at least one corner to a correct position. You can always get one of the following cases when turning the top layer to place the corners:
- All corners are in their positions (althought probably twisted) - this step is finished.
- If two adjacent corners can be correctly positioned by turning the top face then only one swap of the other two corners is necessary (make sure that you turn the cube so that these two corners are in top-right positions when applying the sequence).
- If two (diagonally) opposite corners can be correctly positioned by turning the top face then perform a swap of any two top corners and you will obtain the previous situation.
3. Twist Four Top Corners
Now we are able to position the top corners using one (quite simple) corner sequence that is explained in the previous text, thus there is no magic here up to this point. Let us try to follow this way even for twisting the corners. We can twist (two) corners using the previous corner sequence, however, it also moves corners which is not good for this step. (Just reminding you that in this step, we want to twist corners and NOT move them, because they are already positioned in` the previous step.) The idea behind the corner sequence was to do some change and redo it in a different way, so the other parts of the cube became changed while everything solved before remains solved. Let us try the same idea in this step using our corner sequence: swap two corners using the corner sequence and swap them back from a different angle using the same corner sequence. If we can do so, the corners will be in their correct positions (swap + swap back = nothing), but will be somehow twisted. Let us try that, but before that I must say that swapping two corners back from a different angle requires left | right mirroring the corner sequence, which is shown below:
Mirror vesion of the corner sequence (shown applied to a solved cube):





Now you can try the presented idea of doing and redoing (in a different way) the corner swap to twist top corners:
Normal corner sequence, turn cube, mirrored corner sequence (shown applied to a solved cube):














You can see that this new twist sequence leaves all corners in their original positions and twists only two corners: the top-left-front corner is twisted clockwise and the top-left-back corner counter-clockwise. It is not difficult to twist all top corners in any orientation using this twist sequence. After performing consequent multiple application of the twist sequence to the corners, as soon as three corners become oriented correctly, the remaining corner has no chance to be twisted incorrectly (if you do not believe me, try it).
Examples
The following examples will show you what angle to choose for the twist sequence. After one application the orientation of top corners changes and you will get another that is also shown bellow. You will not get into an infinite cycle when followed correctly - I promise.
Two twisted, facing oposite sides - apply from this angle
Two twisted, facing the same side - apply from this angle
Two twisted, facing adjacent sides - apply from this angle
Three twisted, clock-wise - apply from this angle
Three twisted, counter clock-wise - apply from this angle
Four twisted, facing opposite sides - apply from this angle
Four twisted, facing three sides - apply from this angle
This step can look to be the most difficult at first, but it will become easy after some practicing. (This step may be quite long sometimes and you can do it much more efficiently - how to do so can be found on these pages in descriptions of other methods e.g. in Waterman method.)
Go to Solving Edges to continue.