problem_id string | dataset string | statement string | domain string | source string | country string | year int64 | date string | task string | answer_type string | subtopic string | url string | solutions list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
AIME2026-I-01 | aime2026 | Patrick started walking at a constant rate along a straight road from school to the park. One hour after Patrick left, Tanya started running along the same road from school to the park. One hour after Tanya left, Jose started bicycling along the same road from school to the park. Tanya ran at a constant rate of $2$ mil... | algebra | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Equations | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-01:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-02 | aime2026 | Find the number of positive integer palindromes written in base $10$ with no zero digits, and whose digits add up to $13$. For example, $42124$ has these properties. Recall that a palindrome is a number whose representation reads the same from left to right as from right to left. | combinatorics | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Enum. combinatorics | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-02:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-03 | aime2026 | A hemisphere with radius $200$ sits on top of a horizontal circular disk with radius $200,$ and the hemisphere and disk have the same center. Let $\mathcal T$ be the region of points P in the disk such that a sphere of radius $42$ can be placed on top of the disk at $P$ and lie completely inside the hemisphere. The are... | geometry | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Solid geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-03:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-04 | aime2026 | Find the number of integers less than or equal to 100 that are equal to $a+b+ab$ for some choice of distinct positive integers a and b. | number_theory | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Factorization | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-04:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-05 | aime2026 | A plane contains points $A$ and $B$ with $AB = 1$. Point $A$ is rotated in the plane counterclockwise through an acute angle $\theta$ around point $B$ to point $A^\prime$. Then $B$ is rotated in the plane clockwise through angle $\theta$ around point $A^\prime$ to point $B^\prime$. Suppose that $AB^\prime = \frac{4}{3}... | geometry | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Trigonometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-05:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-06 | aime2026 | A real number $x$ satisfies $\sqrt[20]{x^{\log_{2026}x}}=26x$. What is the number of positive divisors of the product of all possible positive values of $x$? | algebra | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Logarithms | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-06:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-07 | aime2026 |
Find the number of functions $\pi$ mapping the set $A =\{1,2,3,4,5,6\}$ onto $A$ such that for every $a \in A,$
\[
\pi(\pi(\pi(\pi(\pi(\pi(a)))))) = a.
\] | combinatorics | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Permutations | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-07:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-08 | aime2026 | Let $N$ be the number of positive integer divisors of $17017^{17}$ that leave a remainder of $5$ when divided by $12$. Find the remainder when $N$ is divided by $1000$. | number_theory | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Divisibility | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-08:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-09 | aime2026 | Joanne has a blank fair six-sided die and six stickers each displaying a different integer from 1 to 6. Joanne rolls the die and then places the sticker labeled 1 on the top face of the die. She then rolls the die again, places the sticker labeled 2 on the top face, and continues this process to place the rest of the s... | combinatorics | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Probability | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-09:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-10 | aime2026 | Let $\triangle ABC$ have side lengths $AB = 13, BC = 14,$ and $CA = 15.$ Triangle $\triangle A'B'C'$ is obtained by rotating $\triangle ABC$ about its circumcenter so that $\overline{A'C'}$ is perpendicular to $\overline{BC},$ with $A'$ and $B$ not on the same side of line $B'C'.$ Find the integer closest to the area o... | geometry | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Analytic geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-10:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-11 | aime2026 | The integers from $1$ to $64$ are placed in some order into an $8 \times 8$ grid of cells with one number in each cell. Let $a_{i,j}$ be the number placed in the cell in row $i$ and column $j,$ and let $M$ be the sum of the absolute differences between adjacent cells. That is,
\[
M = \sum^8_{i=1} \sum^7_{j=1} (|a_{i,j+... | combinatorics | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Optimization | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-11:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-12 | aime2026 | Triangle $\triangle ABC$ lies in plane $\mathcal P$ with $AB = 6, AC = 4,$ and $\angle BAC = 90^\circ.$ Let $D$ be the reflection across $\overline{BC}$ of the centroid of $\triangle ABC. {}$ Four spheres, all on the same side of $\mathcal P,$ have radii $1, 2, 3,$ and $r$ and are tangent to $\mathcal P$ at points $A, ... | geometry | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Solid geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-12:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-13 | aime2026 | For each nonnegative integer $r$ less than $502,$ define
\[
S_r=\sum_{m\ge 0}\dbinom{10000}{502m+r},
\]
where $\binom{10000}{n}$ is defined to be $0$ when $n>10000.$ That is, $S_r$ is the sum of all binomial coefficients of the form $\binom{10000}{k}$ for which $0\le k\le 10000$ and $k-r$ is a multiple of $502.$ Find t... | number_theory | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Binomial coefficients | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-13:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-14 | aime2026 | In an equiangular pentagon, the sum of the squares of the side lengths equals $308,$ and the sum of the squares of the diagonal lengths equals $800.$ The square of the perimeter of the pentagon can be expressed as $m \sqrt n,$ where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. ... | geometry | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Euclidean geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-14:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-I-15 | aime2026 | Let $a, b,$ and $n$ be positive integers with both $a$ and $b$ greater than or equal to $2$ and less than or equal to $2n$. Define an $a \times b$ cell loop in a $2n \times 2n$ grid of cells to be the $2a + 2b - 4$ cells that surround an $(a - 2) \times (b - 2)$ (possibly empty) rectangle of cells in the grid. For exam... | combinatorics | AIME I | United States | 2,026 | 2026-02 | compute_and_prove | number | Enum. combinatorics | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-I-15:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-ste... |
AIME2026-II-01 | aime2026 | Find the sum of the $10$th terms of all arithmetic sequences of integers that have first term equal to $4$ and include both $24$ and $34$ as terms. | number_theory | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Arithmetic sequences | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-01:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-02 | aime2026 | The figure below shows a grid of $10$ squares in a row. Each square has a diagonal connecting its lower left vertex to its upper right vertex. A bug moves along the line segments from vertex to vertex, never traversing the same segment twice and never moving from right to left along a horizontal or diagonal segment. Le... | combinatorics | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Paths | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-02:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-03 | aime2026 | Let $ABCDE$ be a nonconvex pentagon with internal angles $\angle A = \angle E = 90^\circ$ and $\angle B = \angle D = 45^\circ.$ Suppose that $DE < AB, AE = 20, BC = 14\sqrt2,$ and points $B,C,$ and $D$ lie on the same side of line $AE.$ Suppose further that $AB$ is an integer with $AB < 2026$ and the area of pentagon $... | geometry | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Analytic geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-03:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-04 | aime2026 | For each positive integer $n$ let $f(n)$ be the value of the base-ten numeral $n$ viewed in base $b$, where $b$ is the least integer greater than the greatest digit in $n$. For example, if $n=72$, then $b=8$, and $72$ as a numeral in base $8$ equals $7\cdot 8+2=58$; therefore $f(72)=58$. Find the number of positive int... | number_theory | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Representation | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-04:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-05 | aime2026 | An urn contains $n$ marbles. Each marble is either red or blue, and there are at least $7$ marbles of each color. When $7$ marbles are drawn randomly from the urn without replacement, the probability that exactly $4$ of them are red equals the probability that exactly $5$ of them are red. Find the sum of the five least... | combinatorics | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Probability | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-05:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-06 | aime2026 | Find the sum of all real numbers $r$ such that there is at least one point where the circle with radius $r$ centered at $(4, 39)$ is tangent to the parabola with equation $2y = x^2 - 8x + 12.$ | geometry | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Analytic geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-06:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-07 | aime2026 | A standard fair six-sided die is rolled repeatedly. Each time the die reads 1 or 2, Alice gets a coin; each time it reads 3 or 4, Bob gets a coin; and each time it reads 5 or 6, Carol gets a coin. The probability that Alice and Bob each receive at least two coins before Carol receives any coins can be written as $\tfra... | combinatorics | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Probability | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-07:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-08 | aime2026 | Isosceles triangle $\triangle ABC$ has $AB = BC.$ Let $I$ be the incenter of $\triangle ABC.$ The perimeters of $\triangle ABC$ and $\triangle AIC$ are in the ratio $125:6,$ and all the sides of both triangles have integer lengths. Find the minimum possible value of $AB.$ | geometry | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Euclidean geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-08:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-09 | aime2026 | Let $S$ denote the value of the infinite sum
\[
\frac{1}{9} + \frac{1}{99} + \frac{1}{999} + \frac{1}{9999} + \cdots
\]
Find the remainder when the greatest integer less than or equal to $10^{100} S$ is divided by $1000.$ | number_theory | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Series | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-09:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-10 | aime2026 | Let $\triangle ABC$ be a triangle with $D$ on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Let $\omega$ be the circle that passes through $A$ and is tangent to segment $\overline{BC}$ at $D.$ Let $E \neq A$ and $F \neq A$ be the intersections of $\omega$ with segments $\overline{AB}$ and $\overline{A... | geometry | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Euclidean geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-10:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-11 | aime2026 | Find the greatest integer $n$ such that the cubic polynomial
\[
x^{3} - \displaystyle\frac{n}{6}x^{2} + (n - 11)x - 400
\]
has roots $\alpha^{2}$, $\beta^{2}$, and $\gamma^{2}$, where $\alpha$, $\beta$, and $\gamma$ are complex numbers, and there are exactly seven different possible values for $\alpha + \beta + \gamma$... | algebra | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Polynomial | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-11:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-12 | aime2026 | Consider a tetrahedron with two isosceles triangle faces with side lengths $5\sqrt{10}, 5\sqrt{10},$ and $10$ and two isosceles triangle faces with side lengths $5\sqrt{10}, 5\sqrt{10},$ and $18.$ The four vertices of the tetrahedron lie on a sphere with center $S,$ and the four faces of the tetrahedron are tangent to ... | geometry | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Solid geometry | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-12:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-13 | aime2026 | Call finite sets of integers $S$ and $T$ cousins if
- $S$ and $T$ have the same number of elements,
- $S$ and $T$ are disjoint, and
- the elements of $S$ can be paired with the elements of $T$ so that the elements in each pair differ by exactly $1$.
For example, $\{1,2,5\}$ and $\{0,3,4\}$ are cousins. Suppose that the... | combinatorics | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Enum. combinatorics | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-13:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-14 | aime2026 | For integers $a$ and $b,$ let $a \circ b = a - b$ if $a$ is odd and $b$ is even, and $a+b$ otherwise. Find the number of sequences $a_1, a_2, a_3, \ldots, a_n$ of positive integers such that
\[
a_1 + a_2 + a_3 + \cdots + a_n = 12 \quad \text{and} \quad a_1 \circ a_2 \circ a_3 \circ \cdots \circ a_n = 0
\]
where the ope... | combinatorics | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Enum. combinatorics | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-14:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME2026-II-15 | aime2026 | Find the number of ordered 7-tuples $(a_1, a_2, a_3, \ldots, a_7)$ having the following properties:
- $a_k \in \{1,2,3\}$ for all $k.$
- $a_1+a_2+a_3+a_4+a_5+a_6+a_7$ is a multiple of $3.$
- $a_1a_2 a_4 + a_2a_3a_5 + a_3a_4 a_6 + a_4 a_5 a_7 + a_5 a_6 a_1 + a_6 a_7 a_2 + a_7 a_1 a_3$ is a multiple of $3.$ | combinatorics | AIME II | United States | 2,026 | 2026-02 | compute_and_prove | number | Graph theory | https://huggingface.co/datasets/math-ai/aime26/blob/79037aebdb6580008fb960d17cb21fd3099083e3/aime2026.jsonl | [
{
"solution_id": "AIME2026-II-15:reference",
"role": "reference",
"source_type": "ai_generated",
"source_url": null,
"generated_by": "GPT-6 Astra",
"note": "Generated and model-reviewed by GPT-6 Astra; answer matches the imported key. Strategy sketch approved by the dataset curator. Three-st... |
AIME 2026 with Oracle Strategy Sketches
Thirty problems from the American Invitational Mathematics Examination (AIME) 2026 I and II, with GPT-6 Astra solutions, curator-approved strategy sketches, and three load-bearing solution steps. Records use the same field names and nested solution format as AOBench and its IMO-ProofBench subset.
Configurations and loading
| Configuration | File | Problems |
|---|---|---|
aime2026 (default) |
aime2026.jsonl |
30 |
aime2026_i |
aime2026_i.jsonl |
15 |
aime2026_ii |
aime2026_ii.jsonl |
15 |
All configurations use a test split. The default configuration concatenates
AIME I and II in exam/problem order, preserving stable IDs such as AIME2026-I-01.
from datasets import load_dataset
problems = load_dataset("kumarjau1998/AIME2026", "aime2026", split="test")
problem = problems[0]
reference = problem["solutions"][0]
statement = problem["statement"]
solution = reference["solution"]
sketch = reference["sketch"]
steps = reference["steps"]
Record format
| Field | Meaning |
|---|---|
problem_id |
Stable exam/problem identifier. |
dataset |
aime2026. |
statement |
Imported problem statement, with documented corrections to transcription errors. |
domain |
algebra, combinatorics, geometry, or number_theory. |
source |
AIME I or AIME II. |
url |
Pinned upstream problem-file URL. |
country, year, date |
United States, 2026, 2026-02. |
task |
compute_and_prove: compute the requested answer and justify it in the provided reference solution. |
answer_type |
number; AIME answers are integers from 0 through 999. |
subtopic |
One primary mathematical subtopic assigned by the curator. |
solutions |
List containing one AI-generated reference solution. |
The term reference identifies the route used to prepare the oracle sketch; it
does not mean an official contest solution. Numerical answers occur in the full
solutions. There is no additional top-level answer field, matching AOBench's schema.
| Solution field | Meaning |
|---|---|
solution_id |
Stable problem-prefixed route ID. |
role |
reference. |
source_type |
ai_generated. |
source_url |
null: solutions were generated, not imported from a published proof. |
generated_by |
GPT-6 Astra, using model ID gpt-6-astra. |
solution |
Complete generated mathematical solution. |
sketch |
One strategy sketch of 18–24 whitespace-delimited words. |
steps |
Three ordered load-bearing steps, each 17–20 whitespace-delimited words. |
note |
Generation and review provenance. |
Unlike the non-geometry AOBench/IMO-ProofBench collections, this release includes all AIME 2026 problems, including geometry. Its domains are:
| Domain | Problems |
|---|---|
algebra |
3 |
combinatorics |
11 |
geometry |
10 |
number_theory |
6 |
Generation and review
- GPT-6 Astra generated complete solutions from the statements alone using high reasoning effort through a Codex-subscription gateway.
- Each final answer was checked against the imported answer key. A fresh GPT-6 Astra request reviewed each complete solution.
- The reviewed route was compressed into an 18–24-word sketch, matching the mathematical prose/notation style used for the study's IMO sketches.
- A fresh GPT-6 Astra request reviewed each sketch for route fidelity, mathematical usefulness, and answer leakage. Rejected sketches were revised and reviewed again before inclusion.
- The dataset curator reviewed and approved all thirty sketches for publication.
- Three-step outlines were extracted from the checked solutions and reviewed in fresh GPT-6 Astra requests.
Full solutions and outlines have model-assisted review, using the same model
family as the generator. Correlated model errors remain possible. Curator
approval applies to the sketches; no independent expert-panel review of the
full solutions or outlines is claimed. Agreement with the answer key alone
does not certify every proof step. Provenance is recorded in provenance.json.
Intended use and limitations
Use for no-sketch versus oracle-sketch comparisons, strategy-conditioned execution, and test-time compute experiments. Keep full solutions and source metadata outside the solver's accessible inputs when measuring sketch assistance. The three-step outlines are a richer assistance condition and should be reported separately. Freeze the strategy annotations before comparing target-model outcomes.
AIME 2026 is public and may occur in model training data. This dataset is not a
clean unseen-problem generalization test. Upstream statements are reproduced as text, with source normalization documented in provenance.json. AIME I #10 restores primes on the rotated segment, and I #13 corrects the summation index and includes zero among the residue indices. Private answer keys were normalized to integers from 0 through 999.
Attribution and licensing
Problems originate from the Mathematical Association of America's AIME 2026
examinations. Statements and answer keys were obtained from
Math-AI's AIME26 dataset,
at revision 79037aebdb6580008fb960d17cb21fd3099083e3. That upstream dataset declares the Apache 2.0 license.
Its attribution and applicable third-party terms are retained; the upstream
metadata is not a claim that this curator owns the contest statements.
The new solution annotations and compilation are released under
CC BY 4.0, matching the annotation license used for AOBench.
See provenance.json for source URLs, checksums, normalization, and review details.
For the associated discovery/execution study, see the AOBench dataset card. When using this release, cite this dataset repository and credit MAA and Math-AI for the original problems and upstream transcription.
MathArena statement alignment
Released statements and diagram source are aligned with pinned MathArena datasets. AIME2026 I #10 retains the corrected rotated segment A'C'; I #13 retains nonnegative r and the summation index m. Original generation requests are preserved: the solutions and sketches were generated before this wording update. No solutions, sketches, or outlines were regenerated. Source revisions and per-problem changes are recorded in provenance.json.
MathArena statement transcriptions are licensed CC BY-NC-SA 4.0: https://creativecommons.org/licenses/by-nc-sa/4.0/ Attribution: MathArena, https://huggingface.co/MathArena. The aligned release is distributed under CC BY-NC-SA 4.0. Original annotation licensing and source attributions below remain recorded for provenance.
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