# Intuitive solving

Intuitive solving consists in solving the Rubik's cube without using any algorithm that you do not understand. In most methods, for example for the last layer, most algorithm are used in such way that there is an input cube in some state, then you apply the appropriate algorithm that you learnt by heart, and quite magically, the cube is in the desired state.

## Contents

### Overview

Intutive solving can basically be broken into two parts :

- solving most of the cube with intuitive moves (first two layers or more)
- solving the remaining pieces with commutators

You can use any existing method, remove all algorithm and try to do each step with your intuition only. You should be able to complete at least two layers that way. The F2L methods (CFOP (AKA Fridrich method), Petrus) can be done intuitively. 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. It's ok if they are rotated, but in the correct order, because you will always be able to align them by just rotating the chosen face.

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.

#### Slots

After aligning the edges with the centers next to them, you will get four slots, one for each corner, that can contains two pieces : an edge piece and a corner piece. Notice that you can move some piece out one slot, for example the front-right-bottom slot (if you started with the bottom face), by doing R U' R or F' U F. This three moves are the following :

- Taking the piece out of the slot to the upper face
- Moving this piece out of the way
- Bring back the bottom edge at it's correct place (inverse of step 1)

Conversely, you can put a pair of pieces into one slot :

- Move the slot out, so that the destination is now on the scrambled face
- Move some piece into the destination
- Bring the destination back (inverse of step 1)

Of course, you will need to build pairs, so that you can insert them into the slots. To do so, notice that :

- You can break a pair when pieces are not well oriented relative to each other by hiding the corner piece from the scramble face by moving the appropriate slot out, moving the edge with the scrambled face, and the bring the slot back
- You can build one pair by hiding a corner by moving a slot out, bring an edge next to it, and then bring the slot back

If an edge or a corner is already in place, you can use the keyhole method, which can be done intuitively. That's all you need to know. 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. For example, if you want to flip the front-top edge using the front-right-bottom slot, you can do the following sequence : R U' R' then F' U F.

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. If it's in the other direction, you must take it out with the R 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.

So each orientation will be 3 or 4 moves long :

- move some edge out of the way (optional)
- take the edge out of the slot
- bring another edge instead
- put this edge in the slot (inverse of step 2)

You are done when all edges the belongs to the top layer and are in the top layer are oriented (yellow on top). If one edge of the top face remains the the slot, it's ok. You will only need to take care of using the face the brings it out in the right orientation when doing the last pair.

Finally, do the last pair using only two faces : the upper face and another face the allows to bring out the content of the slot.

### Last layer intutive solving

#### Rotating edges

Using the method above, the edges should be already oriented. If not, you will need a commutator. It can be composed with A = "flip an edge in the top face without changing anything else in the top face" and B = "rotate the top face to place another edge to be flipped at the intersection".

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. When you move the slot out, you can bring back the pair without breaking it and put it back in it's correct place.

For example, using the front-right-bottom slot, you can rotate the top-right edge, top-left edge and top-back edge like this : R U2 R' then U' then R U' R'.

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 commutator can be composed with A = "exchange an edge on the top face with an edge that is not on the top face, while keeping the rest of the top face unchanged" and B = "rotate the top face to put another edge in the intersection". The conjugation will used to place one of the three top edges at the location of the exchange.

You can also compose the commutator with A = "swap two edges on the top face" and B = "rotate the edges so that one swapped edge will be swapped with a third one". 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 orient corners by using a commutator like A = "rotate a corner without changing the rest of the top face" and B = "put another corner at the intersection".

To swap corners, use the same principle used for the commutator of edges : a conjugate to move a corner out of the top face, and a commutator with A = "exchange one corner of the top face with the corner not on the top face" and B = "move another corner in the intersection".

You can also rotate and orient corners at the same time by carefully choosing a conjugate and a commutator.

## See also

- Commutators and Conjugates
- Commutator
- Conjugate
- Intuitive Rubik's cube solution tutorial (uses interactive animated Rubik's cube simulators for better clarity)