Rubik's Cube Solution: "Most people solve the cube layer by layer. This is a simple way for the human mind to approach the problem, but it is useless for speed cubing. No matter how good you are, you will use more than 100 moves. Going for speed, I use 60 moves on average. Going for few moves, I average 45.
In the final of the Swedish championship, 8 of 11 competitors used a vanilla layer-by-layer method. The other 3 of us finished 1, 2 and 3!
The basic problem with the layer method is a big one, and it's obvious once you realize it. When you have completed the first layer, you can do nothing without breaking it up. So you break it, do something useful, then restore it. Break it, do something, restore it. Again and again. In a good solution you do something useful all the time. The first layer is in the way of the solution, not a part of it!"