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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
HMMT2026-FEB-ANT-01 | hmmt_feb_2026 | A line intersects the graph of \( y = x^2 + \frac{2}{x} \) at three distinct points. Given that the \( x \)-coordinates of two of the points are 6 and 7, respectively, compute the \( x \)-coordinate of the third point. | -\frac{1}{21} | algebra | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-02 | hmmt_feb_2026 | Compute the second smallest positive integer \( n \) such that
- \( n \) is divisible by 101, and
- the decimal representation of \( n \) contains the number 2026 as a consecutive sequence of digits. | 420261 | number_theory | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-03 | hmmt_feb_2026 | Compute the sum of all positive integers \( n \) such that \( n \) has at least 6 positive integer divisors and the 6th largest divisor of \( n \) is 6. | 48 | number_theory | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-04 | hmmt_feb_2026 | Let \( a, b, \) and \( c \) be pairwise distinct complex numbers such that
\[
a^2 + ab + b^2 = 3(a + b),
\]
\[
a^2 + ac + c^2 = 3(a + c),
\]
\[
b^2 + bc + c^2 = 5(b + c) + 1.
\]
Compute \( a \). | \frac{7}{2} | algebra | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-05 | hmmt_feb_2026 | Compute the largest positive integer \( n \) such that
\[
n \text{ divides } (\lfloor \sqrt{n} \rfloor)!^{n!} + 450.
\] | 1230 | number_theory | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-06 | hmmt_feb_2026 | The numbers 1, 2, ..., 2100 are written on a board. Every second, Mark takes two numbers on the board, \( a \) and \( b \), erases them, and replaces them with \( \gcd(a, b) \) and \( \operatorname{lcm}(a, b) \). Mark stops once any move he makes will not change the numbers written on the board. Compute the number of d... | 3840 | number_theory | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-07 | hmmt_feb_2026 | Positive real numbers \( x, y, \) and \( z \) satisfy the following equations:
\[
xyz = 3,
\]
\[
(x-y)(y-z)(z-x) = 4,
\]
\[
(x+y)(y+z)(z+x) = 40.
\]
Compute the minimum possible value for \( x \).
Give the minimum value of x as an exact expression using only integers, rational numbers, and radicals (no trigonometric... | (3+\sqrt{6})^{-1/3} | algebra | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-08 | hmmt_feb_2026 | Let \( a_0, a_1, a_2, \ldots \) be the unique sequence of nonnegative integers less than 397 with \( a_0 = 1 \) and
\[ a_{n+1}(a_n + 1)^2 \equiv a_n \pmod{397} \]
for all nonnegative integers \( n \). Given that \( a_{2026} = 9 \), compute the remainder when \( a_0 + a_1 + \cdots + a_{2026} \) is divided by 397. | 279 | number_theory | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-09 | hmmt_feb_2026 | Compute
\[ \sum_{k=1}^{\infty} \left( 2^{-\lfloor 101k/1 \rfloor} + 2^{-\lfloor 101k/2 \rfloor} + \cdots + 2^{-\lfloor 101k/100 \rfloor} \right). \] | 50(1 - \frac{1}{2^{101} - 1}) | algebra | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-ANT-10 | hmmt_feb_2026 | Let
\[ S = \sum_{k=0}^{2026} k \binom{2k}{k} 2^k. \]
Compute the remainder when \( S \) is divided by 2027. (Note that 2027 is prime.) | 289 | number_theory | HMMT 2026 ANT | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-COMB-01 | hmmt_feb_2026 | A math test has 4 questions. The topic of each question is randomly and independently chosen from algebra, combinatorics, geometry, and number theory. Given that the math test has at least one algebra question, at least one combinatorics question, and at least one geometry question, compute the probability that this te... | \frac{2}{5} | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-02 | hmmt_feb_2026 | Jacopo is rolling a fair 4-sided die with faces labeled 1, 2, 3, and 4. He starts with a score of 0. Every time he rolls a face with label $i$, he adds $i$ to his score, and then replaces the label of that face with 0. Compute Jacopo's expected score after 4 rolls. | \frac{875}{128} | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-03 | hmmt_feb_2026 | The numbers 1, 2, 3, 4, 5, 6, and 7 are written on a blackboard in some order. Jacob repeatedly swaps numbers at adjacent positions on the blackboard until the numbers are sorted in ascending order.
Compute the number of initial orderings for which it is possible that the number 4 was included in a swap at most once. | 324 | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-04 | hmmt_feb_2026 | Sarunyu has a stick of length 1 with one endpoint marked in red. Every minute, he picks one of his sticks uniformly at random and breaks it into two halves of equal length. Compute the expected length of the stick with the red endpoint after 5 minutes. | \frac{63}{256} | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-05 | hmmt_feb_2026 | Let $S$ be the set of positive integer divisors of $10^9$. Compute the number of subsets $T$ of $S$ such that
- for every element $s$ of $S$, exactly one of $s$ and $10^9/s$ is in $T$, and
- for every element $t$ of $T$, all positive integer divisors of $t$ are in $T$. | 252 | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-06 | hmmt_feb_2026 | Derek currently owes $\pi$ units of a currency called Money of Indiscrete Type, or MIT for short. Every day, the following happens:
- He flips a fair coin to decide how much of his debt to pay. If he flips heads, he decreases his debt by 1 MIT. If he flips tails, he decreases his debt by 2 MITs. If Derek's debt ever b... | 2 - \frac{\pi}{2} | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-07 | hmmt_feb_2026 | Let $S$ be the set of vertices of a right prism whose bases are regular decagons $A_1A_2 \ldots A_{10}$ and $B_1B_2 \ldots B_{10}$. A plane, not passing through any vertex of $S$, partitions the vertices of $S$ into two sets, one of which is $M$. Compute the number of possible sets $M$ that can arise out of such a part... | 1574 | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-08 | hmmt_feb_2026 | A regular hexagon with side length 4 is subdivided into a lattice of 96 equilateral triangles of side length 1. Let $S$ be the set of all vertices of this lattice. Compute the number of nondegenerate triangles with vertices in $S$ that contain the center of the hexagon strictly in their interior. | 6992 | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-09 | hmmt_feb_2026 | Let \( A_1, A_2, A_3, \ldots \) be a sequence of finite nonempty sets of positive integers. Given that \( |A_i \cap A_j| = \gcd(i, j) \) for all (not necessarily distinct) positive integers \( i \) and \( j \), compute the minimum possible value of
\[
\sum_{d|250} \max A_d,
\]
where the sum ranges over all positive i... | 499 | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-COMB-10 | hmmt_feb_2026 | Let \(S\) be the set of all ordered pairs \((x, y)\) of nonnegative integers \(0 \leq x \leq 19\) and \(0 \leq y \leq 2\). Compute the number of permutations \((x_1, y_1)\), \((x_2, y_2)\), ..., \((x_{60}, y_{60})\) of the elements of \(S\) such that
- \(y_1 = 2\) and \(y_{60} = 0\);
- for all nonnegative integers \(1... | 20460 | combinatorics | HMMT 2026 COMB | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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 ... |
HMMT2026-FEB-GEO-01 | hmmt_feb_2026 | Let $ABCD$ and $WXYZ$ be squares such that $W$ lies on segment $\overline{AD}$, $X$ lies on segment $\overline{AB}$, and points $Y$ and $Z$ lie strictly inside $ABCD$. Given that $AW = 4$, $AX = 5$, and $AB = 12$, compute the area of triangle $\triangle BCY$.
| 18 | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-02 | hmmt_feb_2026 | Let $HORSE$ be a convex pentagon such that $\angle EHO = \angle ORS = \angle SEH = 90^\circ$ and $\angle HOR = \angle RSE = 135^\circ$. Given that $HO = 20$, $SE = 26$, and $OS = 10$, compute the area of $HORSE$. | 191 | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-03 | hmmt_feb_2026 | Let \( ABCD \) be a rectangle with \( AB = 12 \) and \( BC = 16 \). Points \( W, X, Y, \) and \( Z \) lie on sides \( \overline{AB}, \overline{BC}, \overline{CD}, \) and \( \overline{DA} \), respectively, such that \( WXYZ \) is a rhombus with area 120. Compute \( XY \). | 5\sqrt{5} | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-04 | hmmt_feb_2026 | Let \( ABC \) be a triangle with \( \angle BAC = 90^\circ \). Points \( X \) and \( Y \) are such that \( B, X, Y, \) and \( C \) lie on segment \( \overline{BC} \) in that order, \( BX = 4, XY = 5, \) and \( YC = 3 \). Let \( T \) be a point lying on segment \( \overline{AC} \) such that \( TA = TX = TY = \ell \) for ... | \frac{7}{3}\sqrt{3} | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-06 | hmmt_feb_2026 | Let \(ABC\) be a triangle, and \(M\) be the midpoint of segment \(\overline{BC}\). Points \(P\) and \(Q\) lie on segments \(\overline{AB}\) and \(\overline{AC}\), respectively, so that \(\angle PMB = \angle QMC = \frac{1}{2}\angle BAC\). Given that \(AP = 1\), \(AQ = 3\), and \(BC = 8\), compute \(BP\). | \sqrt{17} - 1 | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-07 | hmmt_feb_2026 | Let \( ABC \) be an isosceles triangle with \( AB = AC \). Points \( P \) and \( Q \) are located inside triangle \( ABC \) such that \( BP = PQ = QC \). Suppose that \( \angle BAP = 20^\circ \), \( \angle PAQ = 46^\circ \), and \( \angle QAC = 26^\circ \). Compute the measure of \( \angle APC \) in degrees. | 74^\circ | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-08 | hmmt_feb_2026 | Let $ABC$ be a triangle with orthocenter $H$. The internal angle bisector of $\angle BAC$ meets the circumcircles of triangles $ABH$, $ACH$, and $ABC$ again at points $P$, $Q$, and $M$, respectively. Suppose that points $A$, $P$, $Q$, and $M$ are distinct and lie on the internal angle bisector of $\angle BAC$ in that o... | \sqrt{69} | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-09 | hmmt_feb_2026 | Let $ABC$ be triangle with incenter $I$ and incircle $\omega$. The circumcircle of triangle $BIC$ intersects $\omega$ at points $E$ and $F$. Suppose that $\Gamma \neq \omega$ is a circle passing through $E$ and $F$ and tangent to lines $AB$ and $AC$. If $AB = 5$, $AC = 7$, and $\Gamma$ has twice the radius of $\omega$,... | 3 + \sqrt{11} | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-GEO-10 | hmmt_feb_2026 | Let $ABC$ be a triangle with centroid $G$ and circumcenter $O$. Suppose that the orthocenter of triangle $AGO$ lies on line $BC$. Given that $AB = 11$ and $AC = 13$, compute $BC$. | \frac{\sqrt{1740}}{3} | geometry | HMMT 2026 GEO | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-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... |
HMMT2026-FEB-TEAM-02 | hmmt_feb_2026 | Jessica the jackrabbit wants to climb down a wall. The wall consists of 2026 horizontal layers stacked vertically. The $n$th layer from the top is partitioned into $2^n - 1$ identical rectangular bricks arranged side by side. Jessica begins in the topmost layer, which contains a single brick. A move consists of Jessica... | 3^{2025} | combinatorics | HMMT 2026 TEAM | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-FEB-TEAM-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 ... |
HMMT2026-FEB-TEAM-03 | hmmt_feb_2026 | Let $\alpha$ and $\beta$ be complex numbers such that $\alpha\beta + \alpha + \beta + 100 = 0$. Suppose that $|\alpha| = |\beta| = M$ for some nonnegative real number $M$. Determine, with proof, all possible values of $M$.
Output your answer as a comma-separated list of all possible values of $M$. For instance, if you... | 10 | algebra | HMMT 2026 TEAM | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-FEB-TEAM-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 ... |
HMMT2026-FEB-TEAM-05 | hmmt_feb_2026 | The numbers 1, 2, ..., 2026 are written on a blackboard. An operation consists of replacing any number on the blackboard with the positive difference between the largest and smallest numbers currently on the blackboard. Determine, with proof, the least number of operations required to make all the numbers on the blackb... | 3037 | combinatorics | HMMT 2026 TEAM | United States | 2,026 | 2026-02-14T00:00:00 | compute_and_prove | number | null | https://huggingface.co/datasets/MathArena/hmmt_feb_2026/blob/02fba4f74d8e68e73e66a02d540fd979c05c274c | [
{
"solution_id": "HMMT2026-FEB-TEAM-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 ... |
HMMT2026: solutions and oracle sketches
32 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_2026, revision 02fba4f74d8e68e73e66a02d540fd979c05c274c. Original numbering, diagram source, and whitespace are retained.
Round configurations are subsets of the default configuration:
ant: 10 problems.comb: 10 problems.geo: 9 problems.team: 3 problems.
Excluded problems:
HMMT2026-FEB-GEO-05: User excluded this problem because the omitted official diagram supplies necessary placement conditions.
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_2026; 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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