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README.md
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---
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dataset_info:
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features:
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- name: Rank
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dtype: int64
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- name: Puzzles
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dtype: string
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- name: AMT (s)
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dtype: float64
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- name: Solved rate
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dtype: string
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- name: 1-sigma Mean (s)
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dtype: float64
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- name: 1-sigma STD (s)
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dtype: float64
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splits:
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- name: train
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num_examples: 1362
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task_categories:
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- question-answering
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- text-generation
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language:
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- en
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tags:
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- mathematical-reasoning
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- tree-of-thoughts
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- test-time-compute
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- game-of-24
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size_categories:
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- 1K<n<10K
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license: mit
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---
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> **Bud Ecosystem mirror** of [`test-time-compute/game-of-24`](https://huggingface.co/datasets/test-time-compute/game-of-24) — a verbatim copy for offline, reproducible model evaluation. License **unchanged (MIT (test-time-compute/game-of-24); Apache-2.0 (nlile/24-game))**; all rights remain with the original authors.
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# Game of 24 Dataset
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## Dataset Description
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The Game of 24 is a mathematical reasoning puzzle where players must use four numbers and basic arithmetic operations (+, -, *, /) to obtain the result 24. Each number must be used exactly once.
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This dataset contains 1,361 unique Game of 24 puzzles ranked by difficulty based on human performance from Amazon Mechanical Turk studies.
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### Example
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**Input:** `4 5 6 10`
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**Output:** `(5 * (10 - 4)) - 6 = 24`
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**Step-by-step solution:**
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```
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10 - 4 = 6 (left: 5 6 6)
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5 * 6 = 30 (left: 6 30)
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30 - 6 = 24 (left: 24)
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Answer: (5 * (10 - 4)) - 6 = 24
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```
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## Dataset Structure
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### Data Fields
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- `Rank`: Difficulty ranking (1 = easiest, 1361 = hardest)
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- `Puzzles`: Four numbers separated by spaces (e.g., "4 5 6 10")
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- `AMT (s)`: Average time for humans to solve (seconds)
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- `Solved rate`: Percentage of humans who successfully solved the puzzle
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- `1-sigma Mean (s)`: Mean solving time within 1 standard deviation
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- `1-sigma STD (s)`: Standard deviation of solving time
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### Data Splits
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The original Tree of Thoughts paper uses indices 900-1000 (100 puzzles) for evaluation.
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- **Easy puzzles** (rank 1-300): 95-99% human solve rate, ~4-6 seconds
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- **Medium puzzles** (rank 300-900): 85-95% human solve rate, ~6-10 seconds
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- **Hard puzzles** (rank 900-1100): 80-90% human solve rate, ~10-15 seconds
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- **Very hard puzzles** (rank 1100-1361): 20-80% human solve rate, 15-200+ seconds
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## Source Data
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This dataset is from the official Tree of Thoughts (ToT) repository:
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- Paper: [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://arxiv.org/abs/2305.10601)
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- Repository: https://github.com/princeton-nlp/tree-of-thought-llm
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- Authors: Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, Karthik Narasimhan
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### Human Performance Collection
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Puzzles were ranked based on human performance data collected via Amazon Mechanical Turk, measuring:
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- Success rate (percentage of correct solutions)
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- Solving time (average time to solution)
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## Usage
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### Loading the Dataset
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```python
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from datasets import load_dataset
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dataset = load_dataset("test-time-compute/game-of-24")
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```
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### Paper Evaluation Subset
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To replicate the Tree of Thoughts paper evaluation:
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```python
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# Load indices 900-1000 (100 hard puzzles)
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eval_subset = dataset['train'].select(range(900, 1000))
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```
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### Task Format
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Each puzzle requires:
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1. **Input**: Four numbers (e.g., "4 5 6 10")
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2. **Output**: A valid mathematical expression using each number exactly once that equals 24
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3. **Verification**: Check that all four numbers are used and the expression evaluates to 24
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## Benchmark Results
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From the Tree of Thoughts paper (indices 900-1000):
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| Method | Success Rate | Model |
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|--------|-------------|-------|
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| IO (100 samples) | 7.3% | GPT-4 |
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| CoT (100 samples) | 4.0% | GPT-4 |
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| ToT (b=5) | 74.0% | GPT-4 |
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Where:
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- **IO**: Input-output prompting with 100 samples
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- **CoT**: Chain-of-thought prompting with 100 samples
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- **ToT**: Tree of Thoughts with beam width 5
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## Citation
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If you use this dataset, please cite the original Tree of Thoughts paper:
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```bibtex
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@article{yao2023tree,
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title={Tree of Thoughts: Deliberate Problem Solving with Large Language Models},
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author={Yao, Shunyu and Yu, Dian and Zhao, Jeffrey and Shafran, Izhak and Griffiths, Thomas L and Cao, Yuan and Narasimhan, Karthik},
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journal={arXiv preprint arXiv:2305.10601},
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year={2023}
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}
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```
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## License
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MIT License (same as original Tree of Thoughts repository)
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