From beginner level to pro level, F2L is usually the step with the most room for improvement because it requires recognizing and tracking multiple pieces at once, while having quite a lot of freedom. In other words, you know how F2L works logically. In theory, there are so many unique F2L cases that memorizing them all would be a very slow way to learn it. Once you understand the intuitive concepts from this tutorial, you should practice it until it feels somewhat natural, before moving on.
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You should be able to complete at least two layers that way. Note that before doing the last pair, you have an opportunity to orient the edges. Finally you will need to do the last layer, essentially with commutators. The Heise Method is an intuitive method for solving the whole cube, but is very difficult to understand. Nevertheless you can use part of it to solve the first two layers minus one pair. Intuitive F2L Cross Place four edges of one face, at their correct location and orientation.
You can notice that if an edge is on the opposite face in the correct orientation, you can move it to the correct face with the correct orientation with a half turn. If an edge is in the slice between those faces, you can always move it to the correct face with the right orientation with one quarter turn. Of course, you may need to rotate the destination face so that the edge arrives at the desired location, relative to other edges you have already placed.
You will obtain a cross. Turn the cube so that it is at the bottom. There are shortcuts of course, notably when you can form the pair and put it in the slot in three moves see F2L 4. Orienting edges before last F2L pair To orient remaing edges, notice that if you store an edge in a slot, and take it out using the adjacent face, it will be rotated.
By doing so, you will flip other edges too, so you must take into account the orientation of the edge currently in the slot so that you bring it out of the slot to the top face with the right orientation yellow on top if the last layer is yellow.
So if you have in the front-right-bottom an edge the has its yellow color to the right, the you must take it out with the F face. When you take the edge out, you must take care that it does not replace the other edge that you will place back in the slot. You may need to rotate the upper face to move it out of the way. You will only need to take care of using the face the brings it out in the right orientation when doing the last pair.
Last layer intutive solving Rotating edges Using the method above, the edges should be already oriented. If not, you will need a commutator. If you do not care about the orientation of corners, you can still rotate three edges without using a commutator. So you can place the edges correctly. By rotating the last layer, you can obtain one of these situations: all edges are already placed correctly three edges need to be rotated two pair of edges need to be swapped The third one can be solved by rotating any three edges, and then you are back in situation 2.
To rotate edges, notice that when you take one solved pair out of its slot, you can move it out of the way by rotating the upper face and put the slot back to its position. Then, you can turn the upper face to replace it with the edge currently in the slot. By doing this, you will rotate corners, so if they are alread correctly oriented, you need to use a conjugate of commutator to flip the edges without disturbing the corners.
The conjugation will used to place one of the three top edges at the location of the exchange. In this case, you need to be able to rotate those edges, so they must be either on the same face, or on the same slice. Solving corners You will need commutators to solve the corners.
You can also rotate and orient corners at the same time by carefully choosing a conjugate and a commutator. See also.
How To Solve The Second Layer Of The Rubik's Cube (F2L)