Update README.md

README.md

@@ -33,4 +33,170 @@ configs:
     path: data/train-*
   - split: test
     path: data/test-*
+license: mit
+tags:
+- countdown
+- math
+- reasoning
+pretty_name: Countdown Numbers Game (uniformly random puzzles using countdown rules)
+size_categories:
+- 100K<n<1M
 ---
+
+# Countdown Numbers Game Dataset
+
+This dataset contains configurations and solutions for variations of the Countdown numbers game. Each example comprises a sequence of numbers, a target number, the computed solution (closest value), the arithmetic expression that achieves that value, the difference between the target and the computed value, and the final Countdown score.
+
+
+## HuggingFace Download Links
+
+<div align="center">
+
+
+| **Dataset Variant** | **Dataset Name**           | **Download**                                                                            |
+| ------------------- | -------------------------- | --------------------------------------------------------------------------------------- |
+| Random              | `countdown-numbers-3-8`    | [🤗 HuggingFace](https://huggingface.co/datasets/alexjackson17/countdown-numbers-3-8)    |
+| Random Solvable     | `countdown-numbers-3-8-nz` | [🤗 HuggingFace](https://huggingface.co/datasets/alexjackson17/countdown-numbers-3-8-nz) |
+| Coundown Game Rules | `countdown-numbers-6-gr`   | [🤗 HuggingFace](https://huggingface.co/datasets/alexjackson17/countdown-numbers-6-gr)   |
+
+
+</div>
+
+
+---
+
+## Dataset Overview
+
+Each data point in the dataset includes:
+
+- **Numbers:**  
+  A sequence of $n$ integers $s_1, s_2, \ldots, s_n$ where $s_i \in \{1, 2, \ldots, 100\}$ for all $i \in \{1, 2, \ldots, n\}$, and $n \in \{3, 4, \ldots, 8\}$.
+  (Note: In the traditional Countdown game, the numbers are subject to more specific restrictions.)
+
+- **Target:**  
+  An integer $t \in \{1, 2, \ldots, 999\}$. (For context, the standard Countdown game usually features targets from 101 and above.)
+
+- **Closest:**  
+  The value computed by a solver $r \in \{1, 2, \ldots, 999\}$ that is closest to the target number.
+
+- **Expression:**  
+  The arithmetic expression used to compute the closest value.
+  For instance, $((2 + 48) \times 5) \div 10$
+
+- **Delta:**  
+  The absolute difference between the target and the closest value, i.e. $|t - r|$.
+
+- **Score:**  
+  The Countdown score calculated as $\max(0, 10 - |t - r|)$.
+  This score reflects how close the computed value is to the target.
+
+---
+
+## Dataset Variants
+
+This dataset is provided in three variants:
+
+1. **Random:**  
+ Configurations and solutions generated by uniformly sampling and solving one million game instances, without additional restrictions.
+
+1. **Random Solvable (Score > 0):**  
+ Configurations are generated by uniformly sampling numbers and then **rejecting** any sample that results in an unsolvable instance (i.e., a score of 0). This variant ensures that each instance has a solution that yields a positive score.
+
+1. **Countdown:**  
+ Configurations generated by sampling **6 numbers** in the style of the British TV show *Countdown*.
+
+
+### Score Distributions
+
+The following histograms show the distribution of scores for each dataset variant:
+
+#### Random Variant
+
+<img src="random_3_8_1m_score_distribution.png" width="600"/>
+
+
+#### Random Solvable (Score > 0) Variant
+
+<img src="random_solvable_3_8_1m_score_distribution.png" width="600" />
+
+#### Countdown Game Rules
+
+<img src="countdown_score_distribution.png" width="500"/>
+
+---
+
+## Generation Process
+
+The dataset was created by:
+- Uniformly sampling numbers within the specified ranges.
+- Solving each sampled instance to determine the closest value, the corresponding expression, the difference from the target, and the score.
+- For the **Random Solvable (Score > 0)** variant, rejection sampling was applied: instances that did not yield a positive score were discarded.
+
+The train and test splits were created by randomly partitioning the instances into 80% training and 20% testing, using a stratified split based on the score and number of starting values.
+
+
+### Split Score/Size Distributions
+
+The final distributions of scores and numbers are shown in the following histograms:
+
+#### Random Variant
+
+<img src="random_3_8_1m_distribution_comparison.png" width="600" />
+
+#### Random Solvable (Score > 0) Variant
+
+<img src="random_solvable_3_8_1m_distribution_comparison.png" width="600" />
+
+#### Countdown Game Rules
+
+<img src="countdown_random_1m_distribution_comparison.png" width="600" />
+
+---
+
+## How to Use the Dataset
+
+You can load and use this dataset with the Hugging Face `datasets` library. For example:
+
+```python
+from datasets import load_dataset
+
+dataset = load_dataset("alexjackson17/countdown-numbers-6-gr")
+
+# Example: Access the first entry in the training split
+example = dataset["train"][0]
+print("Numbers: ", example["starting"])
+print("Target: ", example["target"])
+print("Closest: ", example["closest"])
+print("Expression: ", example["expression"])
+print("Difference: ", example["delta"])
+print("Score: ", example["score"])
+```
+
+---
+
+## Citation
+
+If you use this dataset in your research or projects, please cite it as follows:
+
+```bibtex
+@misc{jackson2025countdown,
+  title = {Countdown Numbers Game Dataset},
+  author = {Alex Jackson},
+  year = {2025},
+  note = {Released under the MIT License},
+}
+```
+
+---
+
+## Funding Attribution
+
+This work was supported by UK Research and Innovation [grant number EP/S023356/1], in the UKRI Centre for Doctoral Training in Safe and Trusted Artificial Intelligence ([www.safeandtrustedai.org](https://www.safeandtrustedai.org)).
+
+---
+
+## License
+
+This dataset is released under the MIT License. See the [LICENSE](LICENSE) file for more information.
+
+For questions, feedback, or further information, please contact [Alex Jackson](mailto:mail@alexjackson.uk).