synth/games/tasks/number_wall/README.md

About

This folder is for generating Number Wall puzzle questions and answers.

To generate the puzzles, you can run the ./run.sh command.

Folder Structure

• ./scripts/number_wall.py: the core logic for generating Number Wall puzzles.
• ./scripts/number_wall_prompt.py: the prompt templates for generating Number Wall puzzle questions.
• ./scripts/number_wall_verifier.py: the verifier for validating Number Wall puzzle solutions.
• ./run.sh: a script for generating Number Wall puzzles with various configurations.

Game Rules

Number Wall is a logic puzzle where:

1. The grid must be divided into islands by placing walls (marked as 'A').
2. Each island must contain exactly one number.
3. The total number of cells in an island (including the number cell) must equal the value of that number.
4. All cells within an island must be connected horizontally or vertically.
5. Walls (marked as 'A') cannot form 2×2 or larger continuous rectangles.
6. All islands must be separated by walls, with no diagonal connections between islands.

Parameters

The puzzle generator supports the following parameters:

• n: Size of the grid (default: 5)
• number_rate: Probability of placing a number in the grid (default: 0.2)
• num_of_data: Number of puzzles to generate (default: 100)
• max_attempts: Maximum attempts to generate a valid puzzle (default: 1000)

PASSRATE

Current pass rates with deepseek-reasoner:

• 3×3 grid, number_rate=0.2: 0.6
• 3×3 grid, number_rate=0.25: 0.7
• 4×4 grid, number_rate=0.2: 0.2
• 4×4 grid, number_rate=0.25: 0.2
• 5×5 grid, number_rate=0.15: 0.2
• 5×5 grid, number_rate=0.2: 0.2
• 5×5 grid, number_rate=0.25: 0