## Line Charts: Algorithm Accuracy Across Puzzle Games
### Overview
The image contains three line charts comparing the accuracy of four algorithms (Few-Shot, Logic-LM, PAL, SymPro-LM) across different puzzle board sizes for Sudoku, Sujiko, and Magic-Square games. Accuracy is measured on a 0-100% scale, with SymPro-LM consistently achieving perfect scores.
### Components/Axes
- **X-Axes (Board Size)**:
- Sudoku: 4x4, 9x9, 16x16, 25x25
- Sujiko: 3x3, 4x4, 5x5
- Magic-Square: 3x3, 4x4, 5x5
- **Y-Axes (Accuracy %)**: 0-100% scale
- **Legends**: Located on the right of each chart, with color-coded labels:
- Orange: Few-Shot
- Purple: Logic-LM
- Blue: PAL
- Green: SymPro-LM
### Detailed Analysis
#### Sudoku
- **SymPro-LM**: Flat line at 100% across all board sizes.
- **Logic-LM**: Starts at ~60% (4x4), drops sharply to ~5% (9x9), and plateaus near 0% for larger boards.
- **Few-Shot**: Begins at ~55% (4x4), plummets to 0% by 9x9, remaining at 0% for larger boards.
- **PAL**: Starts at ~95% (4x4), declines to ~60% (25x25).
#### Sujiko
- **SymPro-LM**: Flat line at 100% across all board sizes.
- **Logic-LM**: Starts at ~65% (3x3), declines to ~50% (4x4), and drops to ~10% (5x5).
- **Few-Shot**: Begins at ~45% (3x3), declines to ~20% (4x4), and drops to 0% (5x5).
- **PAL**: Starts at ~95% (3x3), declines to ~80% (5x5).
#### Magic-Square
- **SymPro-LM**: Flat line at 100% across all board sizes.
- **Logic-LM**: Starts at ~65% (3x3), declines to ~30% (4x4), and drops to ~5% (5x5).
- **Few-Shot**: Begins at ~20% (3x3), declines to ~0% (4x4), and remains at 0% (5x5).
- **PAL**: Starts at ~95% (3x3), drops sharply to 0% (4x4), and remains at 0% (5x5).
### Key Observations
1. **SymPro-LM Dominance**: Achieves 100% accuracy universally, indicating perfect performance across all games and board sizes.
2. **Logic-LM Degradation**: Shows strong initial performance but degrades significantly with increasing board complexity.
3. **PAL Instability**: Performs well initially but collapses entirely for larger boards in Magic-Square and Sujiko.
4. **Few-Shot Limitations**: Struggles across all games, with near-zero accuracy for boards larger than 4x4.
### Interpretation
The data suggests SymPro-LM is the most robust algorithm, maintaining perfect accuracy regardless of puzzle complexity. Logic-LM and PAL exhibit initial competence but fail to scale, while Few-Shot demonstrates the poorest performance. This pattern implies that SymPro-LM's design inherently handles complexity better, whereas other algorithms may lack adaptive mechanisms for larger problem spaces. The sharp declines in Logic-LM and PAL for Magic-Square (5x5) highlight particular vulnerabilities to high-dimensional constraint satisfaction problems.
