A Devil's Algorithm for a 3x3 Rubik's Cube refers to a sequence of moves that, when repeated, will always solve the cube, regardless of its initial scrambled state.
Understanding Devil's Algorithms
The core concept of a Devil's Algorithm is its deterministic nature. Unlike algorithms designed to solve specific parts of a cube, a Devil's Algorithm is guaranteed to eventually return the cube to its solved configuration. This is achieved by cycling through all possible configurations of the cube when applied continuously.
Key Characteristics:
- Guaranteed Solution: It promises to solve a Rubik's Cube from any configuration eventually.
- Repetitive Application: The algorithm may need to be applied numerous times for complete resolution.
- Cycle Through States: The algorithm essentially cycles through all possible states of the cube.
- Not Necessarily Efficient: Devil's Algorithms are generally not the most efficient way to solve a Rubik's cube.
Example of a Devil's Algorithm
While there isn’t one single universally agreed-upon "Devil's Algorithm", many algorithms can be used to achieve this effect. One of the most straightforward ones for the 3x3 is the sequence:
R U R' U'
This algorithm, when applied repeatedly, will eventually solve a 3x3 Rubik's cube.
Note: The above algorithm is often used to solve the white cross and is known as the "Right Hand Algorithm". It's quite effective and easy to execute.
How it Works
- Deterministic: The moves are deterministic, that means for every application, it follows a pattern.
- Long Cycle: Given a starting scrambled position, the algorithm will systematically cycle through all possible configurations of the Rubik's cube in the 3x3 permutation group and will eventually reach the solved state after many repetitions.
Why "Devil's Algorithm"?
- The name "Devil's Algorithm" probably implies the frustration that may come with the very large number of repetitions of the moves needed to solve a cube in a practical setting.
- It sounds like a “magical” algorithm that will always return the cube to the solved state.
Practical Use
While useful theoretically, practically it is much more efficient to use known algorithms for specific states of the cube, rather than relying on repetitions of a Devil's Algorithm.
Summary of Devil's Algorithm
The Devil's Algorithm, such as the sequence R U R' U', is a sequence of moves that, when applied enough times, will solve the Rubik’s Cube, no matter how scrambled it is. Although not the most efficient method to solve the Rubik’s cube, it demonstrates how a sequence of moves can cycle through all states of the cube and eventually lead to the solved state.
