Understanding the Origin of Parity Errors and Solving by Logic
1. Introduction
This guide aims to provide insights into the origins of parity errors that commonly occur in cubes of size 4x4x4 or larger. By understanding these origins, individuals experienced in using commutators and conjugates will be able to solve them without the need to memorize specific move algorithms.
While this guide presents some example solutions, it is important to note that they are not necessarily the shortest or most efficient methods. They are intended to serve as starting points for you to explore and develop your own approaches. These solutions may not be suitable for speed cubing purposes. However, by understanding the logic behind them, you can gain a logical perspective and potentially make the process of memorizing speed cubing algorithms easier. Links will be provided to renowned algorithms for further reference and study.
Please note that this guide assumes you are already familiar with the use of commutators and conjugates and are capable of solving the 3x3x3 cube without relying on algorithms. If you need assistance with understanding and solving the Rubik's Cube without algorithms, please refer to the guide: "Understanding and Solving the Rubik's Cube Without Algorithms"
Additionally, it is assumed that you are familiar with the structure of the 4x4x4 or larger cubes, as well as the move notations according to the standard adopted by the World Cube Association (WCA), as well as the older notation that employs modifiers such as n, m, and c. For more details on move notations for solving big cubes, please refer to the guide "Solving Big Cubes by Logic".
You may wonder why, if you already have a good understanding of commutators and conjugates, you would need a guide to help solve the 4x4x4 or larger cubes. While it is indeed possible to find your own method for solving any NxNxN cube, there are certain situations or configurations that may appear impossible to solve. These configurations are known as parity errors, which arise from combinations of errors that partially "cancel out", creating the illusion of an absurd configuration. This guide addresses the following cases of parity errors:
Case 1 in Figure 1.1: PLL (Permutation of Last Layer) parity error involving "permutation of edge pairs."
Case 2 in Figure 1.2: PLL (Permutation of Last Layer) parity error involving "2-corner permutation."
Case 3 in Figure 1.3: PLL (Permutation of Last Layer) parity error involving "2-edge permutation."
Case 4 in Figure 1.4: OLL (Orientation of Last Layer) parity error involving "2-edge misorientation."
It is important to note that these denominations do not indicate the actual origins of the errors but rather describe how they appear on the cube.
App source: animcubejs.cubing.net/animcubejs.html