The Gilles Roux
method
The left block 
This block is going to be a 1x2x3 sized part on the cube, in case of right handed solution, on the left side.
So the following parts will be next to each other: edges BL, DL, FL, corners DBL, DFL and the center on the left. According to the other cubies (it also applies to the centers), it doesn’t matter where they are. A possible scrambled cube after the solution of the left block is shown on this figure.
There is no particular algorithm for the left block (from now on: LB), everything depends on the situation, and unfortunately you will have to find out many things by yourself. So I can provide only a short description.
The most frequent way of LB –building is made of two steps: first, solve one 1x2x2 block, then solve the remaining corner-edge pair, and then put them together. Those who know the Petrus-method have a little asset.
In rare cases (rather when the situation inspires it so much), it starts from a 1x1x3 block (the bottom of the LB), then insert the two edges, and then put them together. Anyway, this is usually not a good idea: a 1x1x3 block won’t give you too much freedom.
Solving the 1x2x2 block is usually done the following way: after you’ve spotted the 5 element (+ the center) of the LB, find a simple corner-edge pair. It doesn’t matter where it is. Next, put the suitable edge to the center, and then put the corner-edge and edge-center pairs together. The 1x2x2 is finished. Now solve the remaining corner-edge pair, and assemble the 1x2x3 – the LB is finished.
A possible series of moves can be seen on the following pictures.
The scrambled cube:
First corner-edge pair (move: UF, WhiteGreenRed-WhiteRed)
The edge that belongs to the first corner-edge pair is in place:
The 1x2x2 block (B2U2B):
The second corner-edge pair (L'FD2, RedBlueWhite-BlueWhite):
The left block (Lxy'):
Very rarely comes a 1x1x3 starting:
Assemble the 1x1x3 block: UD’
Move the other two edges in front of each other: F
Before assembling the two parts, the edges must be exchanged: RU2, and then R2.
(In the end, do y2z’ to take it to it’s place. It can be done before)
This kind of block-building should be missed when possible, because a 1x1x3 block really limits the number of moveable layers.
In the beginning it is advised that you work with one particular set of colors. Since 24 different blocks can be composed, it is quite difficult to choose the one that seems to be the best of them, in a few seconds. Later, when you are better at block-building, you can even start with the right block (so the block that would be RB by color, becomes LB and vice versa). Another way to speed up, is solving another corner-edge pair, after the first one (just don’t let it come apart too much in the meantime), and continue this way.
Lastly: It is advised to solve the left block slowly (very slowly!) as a practice, again an again. Later on, you will find many ways of simplifying. Also, it is worthwhile to see the block-building advices found on Lars Petrus’ website, it helps much if you inspect them exhaustively (http://www.lar5.com/cube/blox.html), or rather Roux’s website (http://grrroux.free.fr/). There are good strategies of block-building on Ryan Heise’s site (http://www.ryanheise.com/cube/method/stage1.html) (Building 1st square), just as in the full solution examples.
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