Understanding and Solving the Rubik's Cube Without Algorithms
6. Frey and Singmaster's strategy
Now that you can solve one layer of the cube with ease, it's time to learn a strategy or method for solving the entire cube. There are several methods available, but one of the oldest is the layer-by-layer method. In this approach, you solve the cube in three consecutive layers, typically starting with the bottom layer, then moving through the middle, and finally completing the upper layer.
The method we will be using here is a modification of the layer-by-layer method originally published by Frey and Singmaster (Alexander H. Frey, Jr. and David Singmaster, Handbook of Cubik Math, Hillside, New Jersey: Enslow Publishers, 1982, 193 p.). This method was later posted on the internet by Mark Jeays (http://jeays.net/rubiks.htm), which is why it is sometimes referred to as the Jeays' method.
We have chosen this strategy because it allows for the solution of 21 out of 26 cubelets (approximately 80%) using the "go, swap and back" movement that you are already familiar with. Additionally, the general strategy is easy to understand and remember.
The idea behind this method is to solve the cube layer by layer, always leaving a "free space" for the "go, swap and back" movement. However, as the cube gets closer to being solved, the available movements become increasingly limited. In the end, we will be forced to employ other techniques, but these techniques are essentially derived from the old and well-known "go, swap and back" movement.
Now, let's delve into the details of this method below.