Brute force: One way to solve a Rubik's Cube is through brute force, where the computer systematically tries all possible combinations until it finds the solution. This method is time-consuming and computationally expensive, but it guarantees a solution
Heuristic Algorithms: There are several heuristic algorithms, such as the Fridrich method, Kociemba's algorithm, and the CFOP method, that can be programmed to solve Rubik's Cubes efficiently. These algorithms use a combination of predefined moves and patterns to find the solution.
Genetic Algorithms: Genetic algorithms simulate the process of natural selection to find an optimal solution. In the context of Rubik's Cube, the computer generates a population of random solutions and evolves them over generations by applying crossover and mutation operations until it finds the best solution.
Neural Networks: Neural networks can be trained to solve Rubik's Cubes by providing them with a large dataset of solved cubes and their corresponding moves. The network learns to recognize patterns and generate the correct moves to solve the cube.
Pattern Databases: Pattern databases store precomputed solutions for specific patterns or subproblems of the Rubik's Cube. By using these databases, a computer can quickly look up solutions for smaller portions of the cube and combine them to solve the entire cube.
Optimization Algorithms: Optimization algorithms, like simulated annealing or tabu search, can be used to iteratively improve a partially solved Rubik's Cube. These algorithms explore the solution space by making small changes to the cube's configuration and accepting moves that lead to a better solution.
Monte Carlo Tree Search: Monte Carlo Tree Search is a simulation-based algorithm that builds a search tree by randomly exploring the possible moves and their outcomes. By iteratively expanding and exploring the tree, the computer can find an optimal solution for the Rubik's Cube.
Group Theory: Group theory provides a mathematical framework for analyzing the Rubik's Cube. By representing the cube's state as a permutation of its pieces, a computer can use group theory algorithms to manipulate and solve the cube efficiently.
Constraint Satisfaction: Constraint satisfaction algorithms can be used to model the Rubik's Cube as a set of constraints and variables and solve it by finding assignments that satisfy all constraints. This approach allows the computer to solve the cube using logical deductions.
Deep Reinforcement Learning: Deep reinforcement learning combines neural networks and reinforcement learning to train an agent to solve the Rubik's Cube. The agent learns to make optimal moves by receiving rewards or penalties based on the quality of its solutions.

These are just a few examples of how a computer can be programmed to solve Rubik's Cubes. Each approach has its own advantages and challenges, and the choice of method depends on factors such as computational resources, time constraints, and desired level of optimality.

References:

Fridrich, J. (1997). Method for Solving Rubik's Cube. Retrieved from https://www.cubezone.be/method.php
Kociemba, H. (1992). Optimal Solutions for Rubik's Cube. Retrieved from https://kociemba.org/cube.htm
Rokicki, T., Davidson, R., & Dethridge, J. (2010). The Diameter of the Rubik's Cube Group is Twenty. Retrieved from https://www.cube20.org/

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