VH System (Level 5)
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This method is newer than the Fridrich method. Keep in mind that it is possible to "get lucky" and skip any of the steps (if they are already done). By using this method, you should be able to do the Rubik's Cube in anywhere from a minute to under twenty seconds, but if it takes you a minute to do the Rubik's Cube, then it would probably be a waste of time for you to learn this system.
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Step 1
Step 2
Step 3
Step 4
Step 5
Step 1
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Form a cross on one of the faces, like this:

Whatever color you choose for the cross will be your bottom color. I recommend using white, because the edge pieces you'll need will be easier to spot on the cube. You want your cube to look like this:

Practice making a cross while paying attention to most of the four pieces at the same time. Try to learn how to deal with flipped edges (edges that won't go into the cross correctly in one turn). Just practice, and you will learn for yourself how to do this step efficiently (usually in 5-8 turns). An optional variation of this step is called the extended cross, which is where you solve a 2x2x2 block and then the other two cross edges, but you solve the block in such a way that the other two edges are as easily solved as possible. This is the equivalent of solving a cross and then the first corner/edge pair, but it is quicker. You could even try to solve a 2x2x3 block and then the remaining corner/edge pair, called a double extended cross.


Step 2
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In this step, you will find a bottom layer corner (a corner with white on it, if you are taking my advice), and the edge that goes with it, and put them together into their correct location. You will do this three times, leaving one slot open. It is much more efficient to do this than to put the corners in, then put the edges in. Below are all of the situations that you could run into, except ones where both the corner and edge are in the first two layers but in different slots, and ones where the corner and edge are together in the wrong slot. Next to the cases are the algorithms for solving them, which are optimized for execution. These algorithms assume that the slot that the corner edge pair goes into is the only one that is free, so you should try out some stuff on your own if you have more than one free slot, or if you want to intentionally disturb a slot because there are pieces in there that have long solution algorithms.
If, after one of the algorithms, you see "reflection F/R", that means that this algorithm is a reflection of the previous one, and you probably won't have to memorize it, because you will see that the two algorithms are very similar. The F/R means that the algorithm is reflected across this line:

L/R would mean that it is a reflection from left to right, or a horizontal reflection, and F/B would be a vertical reflection.
R U' R' U F' U2 F U2 F' U F
R2 U2 R' U' R U' R' U2 R'
F2 U2 F U F' U F U2 F (reflection F/R)
F' U F R B U2 B' R'
R U' R' F' L' U2 L F (reflection F/R)
U R U' R' U' F' U F
U' F' U F U R U' R' (reflection F/R)
F' U' F U F' U' F
R U R' U' R U R' (reflection F/R)
F' U2 F R U2 R'
R U2 R' F' U2 F (reflection F/R)
U' F' U' F U2 F' U' F
U R U R' U2 R U R' (reflection F/R)
U2 R U R' U' F' U F
U2 F' U' F U R U' R' (reflection F/R)
R U R' U' R U R' U' R U R'
R U' R' F' U2 F
F' U2 F U F' U' F
R U2 R' U' R U R' (reflection F/R)
U2 R2 U2 R' U' R U' R2
U2 F2 U2 F U F' U F2 (reflection F/R)
R U' R' U2 F' U' F
F' U F U2 R U R' (reflection F/R)
U' R U' R' U R U R'
U F' U F U' F' U' F (reflection F/R)
U' F' U F
U R U' R' (reflection F/R)
U F' U2 F U' R U R'
U' R U2 R' U F' U' F (reflection F/R)
U' F' U2 F U' F' U F
U R U2 R' U R U' R' (reflection F/R)
U2 R U R' U R U' R'
U2 F' U' F U' F' U F (reflection F/R)
U F' U2 F U2 F' U F
U' R U2 R' U2 R U' R' (reflection F/R)
R U R'
F' U' F (reflection F/R)
U F' U' F U2 F' U F
U' R U R' U2 R U' R' (reflection F/R)
U' R U R' U R U R'
U F' U' F U' F' U' F (reflection F/R)
Now you will do the last c/e pair in a special way.


Step 3
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In this step, you will solve the last c/e pair such that when it is solved, you already have a cross on the U face, like this:

If you have one of the cases below, do the appropriate algorithm.
R B U2 B2 R B R2 U R U R'
F' L' U2 L2 F' L' F2 U' F' U' F (reflection F/R)
R U2 R U2 F R F' U2 R2
F' U2 F' U2 R' F' R U2 F2 (reflection F/R)
R U' R' U' R U B U' B' U R'
F' U F U F' U' L' U L U' F (reflection F/R)
R2 U2 R' U' R U' R' U2 R'
F2 U2 F U F' U F U2 F (reflection F/R)
F' L' U2 L F R U R'
R B U2 B' R' F' U' F (reflection F/R)
R U' R U B U' B' R2
F' U F' U' L' U L F2 (reflection F/R)
R B L U L' U B' U R'
F' L' B' U' B U' L U' F (reflection F/R)
F' U L' U L F R U R'
R U' B U' B' R' F' U' F (reflection F/R)
U' F' U' F' L F L' U2 F
U R U R B' R' B U2 R' (reflection F/R)
U2 R' F R F' U' F' U' F
U2 F R' F' R U R U R' (reflection F/R)
F' L' U L F R U R'
R B U' B' R' F' U' F (reflection F/R)
B' R' U' R U B R U R'
L F U F' U' L' F' U' F (reflection F/R)
U R B U B2 R B R2
U' F' L' U' L2 F' L' F2 (reflection F/R)
U F2 U2 F U F' U F2
U' R2 U2 R' U' R U' R2 (reflection F/R)
If you don't have any of those cases, begin to do the c/e pair as you normally would, but do not do the entire algorithm. Stop when you arrive at either of the two situations below (or their reflections):

If you have the first situation (or its reflection), identify which case you have for the last layer edges and do the appropriate algorithm. If you have the second situation (or its reflection), scroll down.
U F' U' F
U' R U R' (reflection F/R)
U2 R U2 R' U' F' U F
U2 F' U2 F U R U' R' (reflection F/R)
U' F' U' L' U L U F
U R U B U' B' U' R' (reflection F/R)
U F' U2 L' U L F
U' R U2 B U' B' R' (reflection F/R)
U F' U' L' U' L U F
U' R U B U B' U' R' (reflection F/R)
U' F' U' L' U2 L F
U R U B U2 B' R' (reflection F/R)
U' B' R B U B' R' B
U L F' L' U' L F L' (reflection F/R)
U F D B' R' B D' F2 U' F
U' R' D' L F L' D R2 U R' (reflection F/R)
If you had the second situation or its reflection, identify which case you have for the last layer edges and do the appropriate algorithm.
U' F' U F
U R U' R' (reflection F/R)
F R' F' R
R' F R F' (reflection F/R)
U2 F' U L' U L F
U2 R U' B U' B' R' (reflection F/R)
F R' F2 U' F U R
R' F R2 U R' U' F' (reflection F/R)
U' F' U' F U2 F R' F' R
U R U R' U2 R' F R F' (reflection F/R)
U2 R2 B' R' B R'
U2 F2 L F L' F (reflection F/R)
U' R B U B' R'
U F' L' U' L F (reflection F/R)
U2 R B U2 B' R' F' U2 F
U2 F' L' U2 L F R U2 R' (reflection F/R)
You are now finished the first two layers, with a beginning on the last layer.


Step 4
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This step is known as coll, which means you will permute and orient the last layer corners without disturbing the orientations of the last layer edges. All that will remain will be to permute the edges after this step.

There are seven cases, called H, T, U, L, Pi, S, and As. They are given names to help you remember and identify them. Each of these cases has six subcases, except H, which has only four since it is vertically symmetrical, for a total of forty cases. Look at where your last layer stickers are to identify your lettered case. To identify your subcase, you will look at four specific positions and find out what colors those stickers are. Those stickers will be given names relative to each other. For example, if they are green, green, blue, red, they will be called F, F, B, L, even if green doesn't happen to be the front color. To know which four positions to look at, refer to the specific case. It really, truly, in all seriousness, is much easier than it sounds, because your brain can group memories very easily. Think of this step as a folder on a computer called "COLL", inside of which are seven other folders, called H, T, U, L, Pi, S, and As, inside each of which are the algorithms.
"H"

On the U face, look at the four corner stickers:


"T"

On the U face, look at the two back corners, and on the F face, look at the two top corners:


"U"

On the U face, look at the two back corners, and on the F face, look at the two top corners:


"L"

On the U face, look at the front left corner and the back right corner, and on the F face, look at the top two corners:

To make it less confusing, if you want, in the "L" case ONLY, you can cover up the top left sticker on the F face because it is always L. You can't, however, cover up the front left sticker on the U face, even though it is always F, because it gives you your F color to work with.

"Pi"

On the U face, look at the four corner stickers:


"S"

On the U face, look at the front left, back right, and front right corners, and on the F face, look at the top left corner:


"As"

On the U face, look at the back left, front right, and front left corners, and on the F face, look at the top right corner:


You are almost done, and chances are that you already know the algoritms in the next step.


Step 5
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Here you will permute the last layer edges. Very often, you will only have to do a quick 3-cycle. Only sometimes will you have to do one of two other possibilities. It is also much more likely to skip this step compared to any other step in this method or in the Fridrich method. Identify your case and do the appropriate algorithm.
R2 U F B' R2 F' B U R2
R2 U' F B' R2 F' B U' R2 (reflection F/B)
R B' R' B F R' F B' R' B R F2 U
U R2 B2 F2 L2 D' R2 B2 F2 L2
You have now finished.