# AMC12 Dataset (Research-Oriented)

A structured dataset derived from the AMC 12 (American Mathematics Competitions), designed for **LLM training, evaluation, and reinforcement learning (RL)** on mathematical reasoning tasks.

This repository contains **all AMC 12 problems from 2000–2025**, making it one of the most complete AMC12 datasets available for research.

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## 📘 Introduction

The AMC 12 is a **25-question, 75-minute multiple-choice examination** aimed at high school students. Problems are designed to **increase in difficulty progressively**, requiring a combination of algebra, geometry, combinatorics, and number theory reasoning.

* **Format:** 25 multiple-choice questions (A–E)
* **Duration:** 75 minutes
* **Difficulty progression:** Problems 1 → 25 increase in complexity
* **Calculator policy:**

  * Since 2008, calculators are **not permitted**
  * Problems are designed to be solvable without computational aids

Top-performing students (~top 6%) are invited to participate in the AIME, making AMC 12 a strong proxy for **high-level mathematical reasoning ability**.

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## 📦 Dataset Overview

Each sample corresponds to a single AMC 12 problem.

### Example (JSONL)

```json
{
  "year": 2019,
  "problem_id": "2019A-15",
  "question": "...",
  "answer": "D",
  "difficulty": 3
}
```

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## 🧱 Schema

Each entry in the dataset follows this structure:

| Field        | Type   | Description                                                                       |
| ------------ | ------ | --------------------------------------------------------------------------------- |
| `problem_id` | string | Unique identifier in the format `{year}{A/B}-{problem_number}` (e.g., `2019A-15`) |
| `year`       | int    | Competition year (2000–2025)                                                      |
| `question`   | string | Full problem statement (including choices)                                        |
| `answer`     | string | Correct answer option (`A`–`E`)                                                   |
| `difficulty` | int    | Difficulty level derived from problem order                                       |

### 🔑 Problem ID Definition

The `problem_id` encodes the full provenance of each problem:

```
{year}{A/B}-{problem_number}
```

* `{year}` → competition year
* `{A/B}` → AMC12A or AMC12B
* `{problem_number}` → position in the exam (1–25)

#### Examples

* `2007B-5` → AMC 12B, 2007, Problem 5
* `2019A-15` → AMC 12A, 2019, Problem 15

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### Difficulty Structure

We adopt a coarse-grained difficulty approximation aligned with problem order:

| Problem Range | Difficulty      |
| ------------- | --------------- |
| 1–10          | Easy–Medium (2) |
| 11–20         | Medium–Hard (3) |
| 21–25         | Hard (4)        |

This structure enables:

* Curriculum learning
* Difficulty-aware evaluation
* Model capability stratification

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## 🚀 Why This Dataset?

### Compared to Other Math Datasets

* **Not heavily pretrained**
  Unlike datasets such as GSM8K, AMC-style problems are less likely to be memorized by models

* **Higher reasoning complexity**
  Problems typically require **multi-step, structured reasoning**, often exceeding datasets like MATH500

* **Clean evaluation signal**

  * Multiple-choice format eliminates ambiguity
  * No unit mismatch issues (e.g., “8 months vs 240 days”)

* **Fully verifiable**
  Every problem has a **unique, discrete answer**, ideal for RL reward design

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### Compared to Other AMC Datasets

* **Complete coverage (2000–2025)**
  Includes all AMC12A and AMC12B problems across 25 years

* **Fully indexed & traceable**
  Each problem maps directly to its original contest and position

* **Structured for ML pipelines**
  Ready for:

  * RL training (PPO / GRPO)
  * Pass@k evaluation
  * Verifier-based reward systems

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## 📚 Data Source & Attribution

This dataset is curated from publicly available resources, with primary reference to:

* Art of Problem Solving

All AMC problems are **copyrighted by the Mathematical Association of America (MAA)** under the American Mathematics Competitions program.

This repository does **not claim ownership** of the original problem statements and provides them solely for research and educational purposes.