Solving Big Cubes by Logic
4.c. Solving the centers of 3 side faces
In a manner similar to the method devised by Frey and Singmaster for the 3x3x3 cube, we will utilize "free spaces" to execute "go, swap, and back" movements. Setups will also be necessary.
The approach is essentially the same as that used for solving the equator edges of the 3x3x3 cube. The difference lies in the fact that instead of a "free edge" on the side, which is employed for the "back and forth" movements, we will have an entire "free layer." The upper layer will continue to be utilized for "swaps." Consequently, we rotate the cube with the centers already solved downwards, positioning the unsolved edge of the first layer in front of us.
Refer to the schematic in Figure 4.7, where the "swap layer" and the "free layer" are indicated in pink. Click the play button (▷) to observe animations showcasing the "swap layer" and the layers employed for the "back and forth" movements involving the "free layer."
Take a look at Figure 4.8 for an example of utilizing the "free space" to solve the center of a side face.
The same approach can be applied to remove a piece from a side face and relocate it to the top face, followed by swapping it with the correct position on another side face.
If there are multiple pieces of the same color grouped in rows or columns, it is possible to execute more than one swap simultaneously.
Upon completing this step, only two faces will have some of the centers swapped, while the rest will be correctly positioned.
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