---
pretty_name: Combi-Puzzles Dataset
license: mit
language:
- en
size_categories:
- n<1K
task_categories:
- text-generation
tags:
- maths
- combinatorics
- llms
---

# Combi-Puzzles Dataset

[![Paper](https://img.shields.io/badge/Paper-arXiv%3A2412.11908-B31B1B)](https://arxiv.org/abs/2412.11908)
[![Hugging Face Dataset](https://img.shields.io/badge/Hugging%20Face-Dataset-blue)](https://huggingface.co/datasets/andynik/combi-puzzles)
[![GitHub Repo](https://img.shields.io/badge/GitHub-Repository-181717?logo=github)](https://github.com/andynik/combi-puzzles)

This repository contains the Combi-Puzzles dataset used in the research paper titled "Can Language Models Rival Mathematics Students? Evaluating Mathematical Reasoning through Textual Manipulation and Human Experiments." These variations are designed to evaluate problem-solving strategies across different formats.

## Dataset Description

The Combi-Puzzles dataset includes 125 problems:
- **25 Base Combinatorial Problems**: Covers permutations, combinations, rules of addition/multiplication, and object arrangements.
- **5 Variations per Problem**:
  - **Common**: Standard textbook form.
  - **Mathematical**: Academic, technical presentation.
  - **Adversarial**: Includes additional irrelevant numerical information.
  - **Parameterisation**: Altered numerical parameters.
  - **Linguistic Obfuscation**: Narrative fictional stories with problem context and irrelevant information.

## JSON file structure

| Field                          | Type                    | Description                                                                                       |
|--------------------------------|-------------------------|---------------------------------------------------------------------------------------------------|
| `id`                           | integer                 | Unique identifier for this problem entry.                                                         |
| `versions`                     | array of object         | All textual variants of the problem.                                                              |
| `versions[].version`           | string                  | Label for the problem variant.                                                                    |
| `versions[].problem_statement` | string                  | The problem text or template; may contain `$paramX$` placeholders.                                |
| `parameters`                   | array of object         | Concrete parameter-sets to fill into templates in some versions.                                  |
| `parameters[].group_id`        | integer                 | Identifier grouping together sets of `param1`–`param4` values.                                    |
| `parameters[].param1`          | integer or string       | First placeholder value.                                                                          |
| `parameters[].param2`          | integer or string       | Second placeholder value.                                                                         |
| `parameters[].param3`          | integer or string       | Third placeholder value.                                                                          |
| `parameters[].param4`          | integer or string       | Fourth placeholder value.                                                                         |


## Problem Example

![Problem Example](p10.png)

The image above illustrates an example of a combinatorial problem and its variations. The highlighted text indicates content modifications based on the common version. The mathematical and linguistic obfuscation variations constitute the new text.

## Additional Information

The Combi-Puzzles dataset contains problems that have parameters expressed in string format (e.g. 12 as "twelve"):

- **Problems' ID with String Parameters**: 6, 12, 19, 20.

## Usage

You are encouraged to use this dataset to further evaluate problem-solving strategies in LLMs or other domains. Please cite our paper if you publish material based on this dataset.

## License

This dataset is licensed under the MIT License. See the `LICENSE` file for more details.

## Citation

Please cite the following if you use the dataset in your work:

```bibtex
@misc{nikolaiev2024languagemodelsrivalmathematics,
  title={Can Language Models Rival Mathematics Students? Evaluating Mathematical Reasoning through Textual Manipulation and Human Experiments},
  author={Andrii Nikolaiev and Yiannos Stathopoulos and Simone Teufel},
  year={2024},
  eprint={2412.11908},
  archivePrefix={arXiv},
  primaryClass={cs.CL},
  url={https://arxiv.org/abs/2412.11908},
}
```