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Kænguruen Danish Math Competition
A dataset of multiple-choice math problems from the Danish Kangaroo math competition (Matematikkens Kænguru), a popular international mathematics contest held annually in Denmark for students in grades 4–9.
Dataset description
Kænguruen originates from France (1991) and is now held in 100+ countries with around 6 million participants per year. In Denmark it is organized by Danmarks Matematiklærerforening and takes place on the third Thursday of March. Students have 60 minutes to answer 18–24 multiple-choice questions designed to be "small, different and challenging."
This dataset contains 106 problems drawn from the 2020–2024 competitions across three grade levels. All problems are in Danish.
Problems were originally presented as PDFs. Visual elements (diagrams, figures, grids) were converted to text where possible. Problems that could not be adequately represented in text form were excluded.
Dataset structure
| Field | Type | Description |
|---|---|---|
id |
string | Unique identifier: {year}_{grade}/{problem_number} |
input |
string | The problem statement |
choices |
list[string] | The five answer options (A–E) |
target |
string | The correct answer (full text, matching one entry in choices) |
solution |
string or null | Worked solution, if available |
percentage_correct |
float or null | Share of students who answered correctly, if available |
year |
int | Competition year (2020–2024) |
grade |
string | Grade level: 4-5-klasse, 6-7-klasse, or 8-9-klasse |
difficulty |
string | Difficulty based on question number: easy (1–10), medium (11–20), hard (21–30) |
Example
{
"id": "2020_6-7-klasse/21",
"input": "Et 3-cifret tal kaldes spektakulært, hvis dets midterste ciffer er større end summen\naf første og sidste ciffer. Fx er 360, 361 og 362 spektakulære tal og de kommer også\nlige efter hinanden i rækkefølge.\n\nHvad er det største antal spektakulære 3-cifrede tal, der kommer lige efter hinanden\ni rækkefølge?",
"choices": ["5", "6", "7", "8", "9"],
"target": "8",
"solution": "9 er det største mulige midterste tal og da tallet skal være 3 cifferet må det første tal være 1, dermed har vi:\n190, 191, 192, 193, 194, 195, 196, 197\n198 er ikke spektakulært da 1+8=9.\nSå svaret er 8.",
"percentage_correct": null,
"year": 2020,
"grade": "6-7-klasse",
"difficulty": "hard"
}
Loading the dataset
With 🤗 datasets
from datasets import load_dataset
dataset = load_dataset("danish-foundation-models/kaenguruen", split="test")
With inspect-ai
from inspect_ai.dataset import hf_dataset, FieldSpec
dataset = hf_dataset(
"danish-foundation-models/kaenguruen",
split="test",
sample_fields=FieldSpec(
input="input",
target="target",
choices="choices",
id="id",
metadata=["solution", "percentage_correct", "year", "grade", "difficulty"],
),
)
Model performance
Results below are for gpt-5.4-mini and gpt-5.4-nano evaluated with reasoning_effort=high,
and gpt-4.1-mini and gpt-4.1-nano evaluated with chain-of-thought prompting,
using inspect-ai.
By difficulty
Difficulty is assigned by question number following the competition convention: questions 1–10 are easy, 11–20 are medium, and 21–30 are hard.
| Difficulty | gpt-5.4-mini | gpt-5.4-nano | gpt-4.1-mini | gpt-4.1-nano | n |
|---|---|---|---|---|---|
| easy (1–10) | 91.7% | 88.9% | 86.1% | 63.9% | 36 |
| medium (11–20) | 95.7% | 91.3% | 82.6% | 37.0% | 46 |
| hard (21–30) | 91.7% | 91.7% | 66.7% | 45.8% | 24 |
Note: early questions (1–10) more frequently involve semi-visual or spatial elements, which may make them harder for language models despite being intended as easier for students.
By grade level
| Grade | gpt-5.4-mini | gpt-5.4-nano | gpt-4.1-mini | gpt-4.1-nano | n |
|---|---|---|---|---|---|
| 4-5-klasse | 88.9% | 88.9% | 77.8% | 66.7% | 9 |
| 6-7-klasse | 95.0% | 90.0% | 75.0% | 45.0% | 40 |
| 8-9-klasse | 93.0% | 91.2% | 84.2% | 47.4% | 57 |
Note: problems for lower grade levels more frequently contain visual or spatial elements, which may make them harder for language models despite being intended as easier for students.
By year
There is no consistent trend in model accuracy across competition years (2020–2024). Note that the number of problems per year is small (17–27), so individual year estimates carry substantial uncertainty.
Accuracy by year — data table
| Year | gpt-5.4-mini | gpt-5.4-nano | gpt-4.1-mini | gpt-4.1-nano | n |
|---|---|---|---|---|---|
| 2020 | 100.0% | 95.7% | 91.3% | 69.6% | 23 |
| 2021 | 90.5% | 85.7% | 85.7% | 57.1% | 21 |
| 2022 | 94.4% | 94.4% | 72.2% | 27.8% | 18 |
| 2023 | 94.1% | 94.1% | 82.4% | 52.9% | 17 |
| 2024 | 88.9% | 85.2% | 70.4% | 33.3% | 27 |
Evaluation
Evaluation scripts are in the scripts/ folder of this repository:
scripts/eval_kaenguruen.py— runs all models and writes results to thelogs/folderscripts/plot_kaenguruen_results.py— generates the accuracy-vs-cost and by-year plots
To reproduce the evaluation results:
# Install dependencies
pip install inspect-ai openai datasets
# Run evaluation (requires OPENAI_API_KEY)
python scripts/eval_kaenguruen.py
# Plot results
python scripts/plot_kaenguruen_results.py
Log files from the original evaluation runs are stored in the logs/ folder of this
repository as .eval files. They can be inspected using the inspect-ai log viewer:
inspect view --log-dir logs/
Curation
This dataset was curated by Kenneth Enevoldsen, Sofie Mosegaard, Nicolas Legrand, and Simon Enni. The source data files are available in the original repository: centre-for-humanities-computing/m-gsm-symbolic.
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