Understanding and Solving the Rubik's Cube Without Algorithms
4. Back and Forth
In this chapter, we will explore the concept of "Back and Forth," a fundamental principle that allows us to manipulate specific parts of a layer on the Rubik's Cube while preserving the rest of the puzzle. By understanding this principle, we can apply logic-based movements to solve the cube without relying on move algorithms.
The Back and Forth principle is based on the observation that certain movements, such as U U' (or any reverse combination), return a layer to its original position. This basic principle is crucial for selectively affecting specific parts of a layer while keeping the rest intact.
Visual representation is helpful in understanding the Back and Forth principle. Figure 4.1 illustrates the concept through a step-by-step sequence. Click forward (⧐) at each movement or click play (▷) to see the sequence with short pauses between rotations.
To demonstrate the application of the Back and Forth principle, let's consider the R' movement ("Go") that places the green corner on the down layer. Rotating the down layer (D') will not affect the upper layer but moves the green corner away from its original position. To bring the upper layer back to its normal state, we use the "Come Back" movement (R), which returns everything except the green corner to its original condition.
The Back and Forth principle can be extended to more complex movements. By applying a sequence of moves and then performing the exact opposite sequence, we can restore the cube to its initial state, except for intentional changes made during the process.
It is important to remember that in order to affect specific parts of a desired layer, we utilize the back and forth movement of a perpendicular layer. This principle allows for precise manipulation while minimizing the impact on other parts of the cube.
Key Knowlege: In order to affect specific parts of a desired layer use the back and forth movement of a perpendicular layer.
App source: animcubejs.cubing.net/animcubejs.html