Datasets:

lmms-lab
/

imo-2025

id stringclasses 6 values	problem stringclasses 6 values	solution stringclasses 0 values
2025-imo-p1	A line in the plane is called sunny if it is not parallel to any of the $x$-axis, the $y$-axis, and the line $x + y = 0$. Let $n \geq 3$ be a given integer. Determine all nonnegative integers $k$ such that there exist $n$ distinct lines in the plane satisfying both of the following: * for all positive integers ...	null
2025-imo-p2	Let $\Omega$ and $\Gamma$ be circles with centres $M$ and $N$, respectively, such that the radius of $\Omega$ is less than the radius of $\Gamma$. Suppose circles $\Omega$ and $\Gamma$ intersect at two distinct points $A$ and $B$. Line $MN$ intersects $\Omega$ at $C$ and $\Gamma$ at $D$, such that points $C, M, N$ and ...	null
2025-imo-p3	Let $\mathbb{N}$ denote the set of positive integers. A function $f: \mathbb{N} \to \mathbb{N}$ is said to be bonza if $$f(a) \text{ divides } b^a - f(b)^{f(a)}$$ for all positive integers $a$ and $b$. Determine the smallest real constant $c$ such that $f(n) \leq cn$ for all bonza functions $f$ and all positive in...	null
2025-imo-p4	A proper divisor of a positive integer $N$ is a positive divisor of $N$ other than $N$ itself. The infinite sequence $a_1, a_2, \ldots$ consists of positive integers, each of which has at least three proper divisors. For each $n \geq 1$, the integer $a_{n+1}$ is the sum of the three largest proper divisors of $a_n$...	null
2025-imo-p5	Alice and Bazza are playing the inekoalaty game, a two-player game whose rules depend on a positive real number $\lambda$ which is known to both players. On the $n^{\text{th}}$ turn of the game (starting with $n = 1$) the following happens: - If $n$ is odd, Alice chooses a nonnegative real number $x_n$ such that $$...	null
2025-imo-p6	Consider a $2025 \times 2025$ grid of unit squares. Matilda wishes to place on the grid some rectangular tiles, possibly of different sizes, such that each side of every tile lies on a grid line and every unit square is covered by at most one tile. Determine the minimum number of tiles Matilda needs to place to satisf...	null

IMO 2025 Problems Dataset

This dataset contains the 6 problems from the 2025 International Mathematical Olympiad (IMO). The problems are formatted with proper LaTeX notation for mathematical expressions.

Dataset Structure

Each example contains:

id: Problem identifier (e.g., "2025-imo-p1")
problem: The problem statement with LaTeX mathematical notation
solution: The solution (currently set to null)

Problem Types

The dataset includes problems covering various mathematical areas:

Problem 1: Combinatorial geometry (sunny lines)
Problem 2: Euclidean geometry (circles and triangles)
Problem 3: Number theory (bonza functions)
Problem 4: Number theory (proper divisors and sequences)
Problem 5: Game theory (inekoalaty game)
Problem 6: Combinatorial geometry (grid tiling)

Mathematical Notation

Mathematical expressions are formatted using LaTeX:

Variables and expressions: $x$ , $n \geq 3$
Display equations: $$f(a) \text{ divides } b^a - f(b)^{f(a)}$$
Sets: $\mathbb{N}$ , $\mathbb{R}$
Special formatting: sunny, bonza, proper divisor, inekoalaty game

Files

imo_2025.json: Full dataset in JSON format
README.md: This file

Usage

from datasets import load_dataset

# Load the dataset
dataset = load_dataset("lmms-lab/imo-2025")

# Access individual problems
for problem in dataset['train']:
    print(f"Problem: {problem['id']}")
    print(f"Statement: {problem['problem']}")
    print()

Or load directly from JSON:

import json

# Load from JSON
with open("imo_2025.json", "r") as f:
    problems = json.load(f)

# Access problems
for problem in problems:
    print(f"ID: {problem['id']}")
    print(f"Problem: {problem['problem']}")
    print(f"Solution: {problem['solution']}")
    print()

Citation

If you use this dataset in your research, please cite:

@dataset{imo2025,
  title={IMO 2025 Problems Dataset},
  author={LMMS Lab},
  year={2025},
  url={https://huggingface.co/datasets/lmms-lab/imo-2025}
}

Source

Problems are from the 2025 International Mathematical Olympiad. Original source: https://www.imo-official.org/problems.aspx

License

This dataset is released under the MIT License.

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