problem_id string | dataset string | statement string | final_answer string | domain string | source string | country string | year int64 | date timestamp[s] | task string | answer_type string | subtopic null | url string | solutions list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
HMMT2025-FEB-ANT-01 | hmmt_feb_2025 | Compute the sum of the positive divisors (including $1$) of $9!$ that have units digit $1$. | 103 | number_theory | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-02 | hmmt_feb_2025 | Mark writes the expression $\sqrt{\underline{a b c d}}$ on the board, where $\underline{a b c d}$ is a four-digit number and $a \neq 0$. Derek, a toddler, decides to move the $a$, changing Mark's expression to $a \sqrt{\underline{b c d}}$. Surprisingly, these two expressions are equal. Compute the only possible four-di... | 3375 | number_theory | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-03 | hmmt_feb_2025 | Given that $x, y$, and $z$ are positive real numbers such that
$$
x^{\log _{2}(y z)}=2^{8} \cdot 3^{4}, \quad y^{\log _{2}(z x)}=2^{9} \cdot 3^{6}, \quad \text { and } \quad z^{\log _{2}(x y)}=2^{5} \cdot 3^{10}
$$
compute the smallest possible value of $x y z$. | \frac{1}{576} | algebra | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-04 | hmmt_feb_2025 | Let $\lfloor z\rfloor$ denote the greatest integer less than or equal to $z$. Compute
$$
\sum_{j=-1000}^{1000}\left\lfloor\frac{2025}{j+0.5}\right\rfloor
$$ | -984 | algebra | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-05 | hmmt_feb_2025 | Let $\mathcal{S}$ be the set of all nonconstant monic polynomials $P$ with integer coefficients satisfying $P(\sqrt{3}+\sqrt{2})=$ $P(\sqrt{3}-\sqrt{2})$. If $Q$ is an element of $\mathcal{S}$ with minimal degree, compute the only possible value of $Q(10)-Q(0)$. | 890 | algebra | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-06 | hmmt_feb_2025 | Let $r$ be the remainder when $2017^{2025!}-1$ is divided by 2025!. Compute $\frac{r}{2025!}$. (Note that $2017$ is prime.) | \frac{1311}{2017} | number_theory | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-07 | hmmt_feb_2025 | There exists a unique triple $(a, b, c)$ of positive real numbers that satisfies the equations
$$
2\left(a^{2}+1\right)=3\left(b^{2}+1\right)=4\left(c^{2}+1\right) \quad \text { and } \quad a b+b c+c a=1
$$
Compute $a+b+c$. | \frac{9 \sqrt{23}}{23} | algebra | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-08 | hmmt_feb_2025 | Define $\operatorname{sgn}(x)$ to be $1$ when $x$ is positive, $-1$ when $x$ is negative, and $0$ when $x$ is $0$. Compute
$$
\sum_{n=1}^{\infty} \frac{\operatorname{sgn}\left(\sin \left(2^{n}\right)\right)}{2^{n}}
$$
(The arguments to sin are in radians.) | 1-\frac{2}{\pi} | algebra | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-09 | hmmt_feb_2025 | Let $f$ be the unique polynomial of degree at most $2026$ such that for all $n \in\{1,2,3, \ldots, 2027\}$,
$$
f(n)= \begin{cases}1 & \text { if } n \text { is a perfect square } \\ 0 & \text { otherwise }\end{cases}
$$
Suppose that $\frac{a}{b}$ is the coefficient of $x^{2025}$ in $f$, where $a$ and $b$ are integers ... | 1037 | algebra | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-ANT-10 | hmmt_feb_2025 | Let $a, b$, and $c$ be pairwise distinct complex numbers such that
$$
a^{2}=b+6, \quad b^{2}=c+6, \quad \text { and } \quad c^{2}=a+6
$$
Compute the two possible values of $a+b+c$. In your answer, list the two values in a comma-separated list of two valid \LaTeX expressions. | \frac{-1+\sqrt{17}}{2}, \frac{-1-\sqrt{17}}{2} | algebra | HMMT 2025 ANT | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | set | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-ANT-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-COMB-01 | hmmt_feb_2025 | Compute the number of ways to arrange the numbers $1,2,3,4,5,6$, and $7$ around a circle such that the product of every pair of adjacent numbers on the circle is at most 20. (Rotations and reflections count as different arrangements.) | 56 | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-02 | hmmt_feb_2025 | Kevin the frog in on the bottom-left lily pad of a $3 \times 3$ grid of lily pads, and his home is at the topright lily pad. He can only jump between two lily pads which are horizontally or vertically adjacent. Compute the number of ways to remove $4$ of the lily pads so that the bottom-left and top-right lily pads bot... | 29 | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-03 | hmmt_feb_2025 | Ben has $16$ balls labeled $1,2,3, \ldots, 16$, as well as $4$ indistinguishable boxes. Two balls are \emph{neighbors} if their labels differ by $1$. Compute the number of ways for him to put $4$ balls in each box such that each ball is in the same box as at least one of its neighbors. (The order in which the balls are... | 105 | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-04 | hmmt_feb_2025 | Sophie is at $(0,0)$ on a coordinate grid and would like to get to $(3,3)$. If Sophie is at $(x, y)$, in a single step she can move to one of $(x+1, y),(x, y+1),(x-1, y+1)$, or $(x+1, y-1)$. She cannot revisit any points along her path, and neither her $x$-coordinate nor her $y$-coordinate can ever be less than $0$ or ... | 2304 | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-05 | hmmt_feb_2025 | In an $11 \times 11$ grid of cells, each pair of edge-adjacent cells is connected by a door. Karthik wants to walk a path in this grid. He can start in any cell, but he must end in the same cell he started in, and he cannot go through any door more than once (not even in opposite directions). Compute the maximum number... | 200 | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-06 | hmmt_feb_2025 | Compute the number of ways to pick two rectangles in a $5 \times 5$ grid of squares such that the edges of the rectangles lie on the lines of the grid and the rectangles do not overlap at their interiors, edges, or vertices. The order in which the rectangles are chosen does not matter. | 6300 | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-07 | hmmt_feb_2025 | Compute the number of ways to arrange $3$ copies of each of the $26$ lowercase letters of the English alphabet such that for any two distinct letters $x_{1}$ and $x_{2}$, the number of $x_{2}$ 's between the first and second occurrences of $x_{1}$ equals the number of $x_{2}$ 's between the second and third occurrences... | 2^{25} \cdot 26! | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-08 | hmmt_feb_2025 | Albert writes $2025$ numbers $a_{1}, \ldots, a_{2025}$ in a circle on a blackboard. Initially, each of the numbers is uniformly and independently sampled at random from the interval $[0,1]$. Then, each second, he \emph{simultaneously} replaces $a_{i}$ with $\max \left(a_{i-1}, a_{i}, a_{i+1}\right)$ for all $i=1,2, \ld... | \frac{2025}{101} | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-09 | hmmt_feb_2025 | Two points are selected independently and uniformly at random inside a regular hexagon. Compute the probability that a line passing through both of the points intersects a pair of opposite edges of the hexagon. | \frac{4}{9} | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-COMB-10 | hmmt_feb_2025 | The circumference of a circle is divided into $45$ arcs, each of length $1$. Initially, there are $15$ snakes, each of length $1$, occupying every third arc. Every second, each snake independently moves either one arc left or one arc right, each with probability $\frac{1}{2}$. If two snakes ever touch, they merge to fo... | \frac{448}{3} | combinatorics | HMMT 2025 COMB | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-COMB-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step ... |
HMMT2025-FEB-GEO-01 | hmmt_feb_2025 | Equilateral triangles $\triangle A B C$ and $\triangle D E F$ are drawn such that points $B, E, F$, and $C$ lie on a line in this order, and point $D$ lies inside triangle $\triangle A B C$. If $B E=14, E F=15$, and $F C=16$, compute $A D$. | 26 | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-02 | hmmt_feb_2025 | In a two-dimensional cave with a parallel floor and ceiling, two stalactites of lengths $16$ and $36$ hang perpendicularly from the ceiling, while two stalagmites of heights $25$ and $49$ grow perpendicularly from the ground. If the tips of these four structures form the vertices of a square in some order, compute the ... | 63 | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-03 | hmmt_feb_2025 | Point $P$ lies inside square $A B C D$ such that the areas of $\triangle P A B, \triangle P B C, \triangle P C D$, and $\triangle P D A$ are 1, $2,3$, and $4$, in some order. Compute $P A \cdot P B \cdot P C \cdot P D$. | 8\sqrt{10} | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-04 | hmmt_feb_2025 | A semicircle is inscribed in another semicircle if the smaller semicircle's diameter is a chord of the larger semicircle, and the smaller semicircle's arc is tangent to the diameter of the larger semicircle.
Semicircle $S_{1}$ is inscribed in a semicircle $S_{2}$, which is inscribed in another semicircle $S_{3}$. The r... | 20 | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-05 | hmmt_feb_2025 | Let $\triangle A B C$ be an equilateral triangle with side length $6$. Let $P$ be a point inside triangle $\triangle A B C$ such that $\angle B P C=120^{\circ}$. The circle with diameter $\overline{A P}$ meets the circumcircle of $\triangle A B C$ again at $X \neq A$. Given that $A X=5$, compute $X P$. | \sqrt{23}-2 \sqrt{3} | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-06 | hmmt_feb_2025 | Trapezoid $A B C D$, with $A B \| C D$, has side lengths $A B=11, B C=8, C D=19$, and $D A=4$. Compute the area of the convex quadrilateral whose vertices are the circumcenters of $\triangle A B C, \triangle B C D$, $\triangle C D A$, and $\triangle D A B$. | 9\sqrt{15} | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-07 | hmmt_feb_2025 | Point $P$ is inside triangle $\triangle A B C$ such that $\angle A B P=\angle A C P$. Given that $A B=6, A C=8, B C=7$, and $\frac{B P}{P C}=\frac{1}{2}$, compute $\frac{[B P C]}{[A B C]}$.
(Here, $[X Y Z]$ denotes the area of $\triangle X Y Z$ ). | \frac{7}{18} | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-08 | hmmt_feb_2025 | Let $A B C D$ be an isosceles trapezoid such that $C D>A B=4$. Let $E$ be a point on line $C D$ such that $D E=2$ and $D$ lies between $E$ and $C$. Let $M$ be the midpoint of $\overline{A E}$. Given that points $A, B, C, D$, and $M$ lie on a circle with radius $5$, compute $M D$. | \sqrt{6} | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-09 | hmmt_feb_2025 | Let $A B C D$ be a rectangle with $B C=24$. Point $X$ lies inside the rectangle such that $\angle A X B=90^{\circ}$. Given that triangles $\triangle A X D$ and $\triangle B X C$ are both acute and have circumradii $13$ and $15$, respectively, compute $A B$. | 14+4\sqrt{37} | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025-FEB-GEO-10 | hmmt_feb_2025 | A plane $\mathcal{P}$ intersects a rectangular prism at a hexagon which has side lengths $45,66,63,55,54$, and 77, in that order. Compute the distance from the center of the rectangular prism to $\mathcal{P}$. | \sqrt{\frac{95}{24}} | geometry | HMMT 2025 GEO | United States | 2,025 | 2025-02-15T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2025/blob/6fdc4277120810ff75aa22d2d5489b91f7a262a1 | [
{
"solution_id": "HMMT2025-FEB-GEO-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; final answer agrees with the pinned MathArena key. Solution, sketch, and three-step o... |
HMMT2025: solutions and oracle sketches
30 problems, with one GPT-6 Astra reference solution, an 18β24-word strategy sketch, and three 17β20-word outline steps per problem.
Source and selection
Statements and exact final-answer strings are copied from MathArena/hmmt_feb_2025, revision 6fdc4277120810ff75aa22d2d5489b91f7a262a1. Original numbering, diagram source, and whitespace are retained.
Round configurations are subsets of the default configuration:
ant: 10 problems.comb: 10 problems.geo: 10 problems.
Fields
Each JSONL record contains problem_id, dataset, statement, final_answer, domain, source, country, year, date, task, answer_type, subtopic, url, and solutions.
final_answer is a string retaining the exact source key, including LaTeX or comma-separated values. Each nested solution contains solution_id, role, source_type, source_url, generated_by, note, solution, sketch, and steps.
Construction and validation
GPT-6 Astra with high reasoning generated solutions from the statements, followed by separate solution reviews, sketch generation/review, and outline generation/review. Final-answer agreement uses the pinned MathArena parser, including its numerical tolerance and unordered-list behavior. Answer agreement alone does not establish proof validity.
Sketch prompts follow the same IMO-aligned examples and protocol used for our AIME datasets. Investigation-guided annotation repairs retain earlier attempts and use unchanged review criteria. Publication was explicitly approved by the curator. No independent expert-panel verification is claimed.
License and attribution
CC BY-NC-SA 4.0. Attribution: MathArena/hmmt_feb_2025; original contest organizers. This release adds generated solutions, sketches, outlines, metadata, and documented exclusions. See provenance.json for source/parser pins and answer-check records.
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