MagicSolver is a Machine Learning-based Rubik's Cube solver developed as a project for "Fondamenti di Intelligenza Artificiale" course at University of Salerno (UNISA).
Unlike traditional solvers that rely on complex, pre-computed lookup tables and mathematical group theory, MagicSolver learns to estimate the distance to the solution by observing millions of scrambled states. It effectively derives a heuristic function purely from data, guiding an adaptive search algorithm to solve the puzzle.
The system combines a Random Forest Regressor (acting as the learned heuristic function $h(s)$) with an Adaptive Beam Search algorithm to navigate the state space.
This project implements two distinct data representation pipelines to benchmark "Raw Learning" vs. "Domain Knowledge":
A pure data-driven approach that assumes zero prior knowledge of the cube's geometry.
- Input: The cube state is flattened into a sparse vector of 324 binary features (54 faces × 6 colors).
- Logic: The model must autonomously abstract spatial rules, piece interdependencies, and color relationships solely from bit patterns.
- Goal: To demonstrate that AI can learn complex combinatorial rules without manual feature engineering.
A hybrid approach that leverages geometric intuition to compress the input space.
- Input: The state is reduced to 7 continuous features, representing the 3D Manhattan Distance of corners and edges from their solved positions.
- Logic: The model acts as a "refiner," learning to correct the errors of the mathematical distance to provide a more accurate heuristic than the raw math alone.
- Goal: To optimize training efficiency and reduce memory footprint for constrained hardware.
Since no public dataset was suitable for this specific regression task, MagicSolver generates its own training data procedurally:
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Reverse Scrambling: Starting from a solved cube, the system applies
$k$ random moves (backward) to generate pairs of(State, Distance). - Dataset Size: 2,000,000 unique samples were generated to ensure statistical significance.
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Format: Data is serialized in compressed
.npzformat to handle large-scale I/O efficiently.
The models were evaluated on a held-out Test Set of 660,000 samples.
| Pipeline | MAE (Mean Absolute Error) | R² Score | Key Insight |
|---|---|---|---|
| Pipeline 1 (OHE) | 1.615 moves | 75.14% | Surprisingly, the raw data model matches the engineered one. |
| Pipeline 2 (Manhattan) | 1.624 moves | 74.80% | Highly efficient in memory, similar accuracy. |
Clone the repository and set up a Python environment:
Before training, you need to generate the dataset. You can generate it, running the DataSetGenerator.py file
You can choose which pipeline to train. The script will save the trained model as a .joblib file. You can run TrainModel.py and TrainModelManhattan.py, it depends on which pipeline you want to train
At this point you can run MagicSolverGUI.py and you can finally resolve the old cubes that that have been sitting on your shelf for years! :)
The autors of the project are:
- Gerardo Russo
- Giuseppe Sepe
- Andrea Stefanile
- Pasquale Tangredi