nlile/24-game

Math Twenty Four (24s Game) Dataset

A comprehensive dataset for the classic math twenty four game (also known as the 4 numbers game / 24s game / Game of 24). This dataset of mathematical reasoning challenges was collected from 4nums.com, featuring over 1,300 unique puzzles of the Game of 24, with difficulty metrics derived from over 6.4 million human solution attempts since 2012.

In each puzzle, players must use exactly four numbers and basic arithmetic operations (+, -, ×, /) to construct an expression that evaluates to 24. For example, given the numbers "4 9 10 13", one valid solution is "(10 - 4) × (13 - 9) = 24".

Dataset Summary

This dataset contains 1,362 unique combinations of 24 numbers puzzles, specifically:

• Complete set of math puzzles using 4 numbers to make 24
• Performance data from over 6.4 million puzzle attempts (<3 4nums.com)
• Difficulty ratings based on real player solve times
• Multiple solution variations for each solvable puzzle
• Comprehensive coverage of all possible number combinations from playing cards (1-13)

Dataset Structure

Each entry in the dataset represents a unique math twenty four puzzle:

{
    "numbers": [n1, n2, n3, n4],        # Four numbers to make 24
    "solutions": ["expr1", "expr2",...], # Valid mathematical expressions
    "solvable": bool,                    # Whether 24 can be made
    "amt": float,                        # Adjusted Median Time (seconds)
    "solved_rate": float,                # Success rate for the 24s game
    "mean_time": float,                  # Average solve time
    "std_time": float                    # Standard deviation of solve times
}

Performance Metrics

Our 24 numbers game dataset includes comprehensive performance metrics from millions of puzzle attempts:

• AMT (Adjusted Median Time): Time at which survival rate crosses 50%
• Solved rate: Percentage of players who successfully solved the puzzle
• 1-sigma mean/std: Statistics for central 68% of solve times

Game Rules & Constraints

The math twenty four puzzle rules are simple:

• Use exactly 4 numbers from 1-13 (representing playing cards A-K)
• Basic arithmetic operations only (+, -, ×, /)
• Each number must be used exactly once
• The final result must equal 24
• All intermediate calculations must be valid

Example Puzzles

Here are some example puzzles with varying difficulty levels:

• Easy: {1, 1, 1, 8} with solution "(1 + 1 + 1) × 8"
• Medium: {4, 4, 10, 10} with solution "(10 × 10 - 4) / 4"
• Hard: {3, 3, 8, 8} with solution "8/(3 - 8/3)"
• Unsolvable: {1, 5, 11, 13}