messages listlengths 5 81 | judge_messages listlengths 3 3 | tools listlengths 2 2 | correct bool 2
classes | used_python bool 1
class | turns int64 2 40 | tokens int64 3.01k 122k | question stringlengths 63 1.26k | answer stringlengths 1 115 | model_answer stringlengths 1 710 | uuid stringlengths 21 27 |
|---|---|---|---|---|---|---|---|---|---|---|
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
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"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 2 | 3,659 | The incircle of a triangle with side lengths that are three consecutive integers is a unit circle. Find all possible values for the perimeter of the triangle. | 12 | 12 | imo-bench-number_theory-089 |
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
"properties": {
"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 2 | 3,218 | Point $P$ is the intersection of the medians of triangle $XYZ$, and point $M$ is the midpoint of side $YZ$. Triangle $YMP$ is equilateral with side length 2. Determine $XY^2+XZ^2$. | 80 | 80 | imo-bench-geometry-093 |
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
"properties": {
"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 3 | 5,430 | Let $F$ be the footpoint of the altitude from $Y$ in the triangle $XYZ$ , where $XY=1$ . The incircle of triangle $YZF$ coincides with the centroid of triangle $XYZ$. Find the lengths of $XZ$. | $\frac{\sqrt{10}}{2}$ | \frac{\sqrt{10}}{2} | imo-bench-geometry-082 |
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
"properties": {
"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 4 | 6,336 | For which integer $x$ from $1$ to $1717$ maximizes the number of positive integers $y$ for which $\frac{1}{x} + \frac{1}{y}$ is a unit fraction? | 1680 | 1680 | imo-bench-number_theory-085 |
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
"properties": {
"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 3 | 5,849 | In the vibrant nation of South Korea, there are $57$ bustling cities interconnected by a network of two-way airways. Each pair of cities is linked by exactly one direct airway. Recognizing the potential for growth and competition, the government has decided to license several airlines to operate within this intricate a... | 28 | 28 | imo-bench-combinatorics-006 |
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
"properties": {
"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 4 | 8,400 | Find all integers $n\ge 3$ for which $2^n - 3$ is a power of 5. | 3,7 | n = 3 and n = 7 | imo-bench-number_theory-068 |
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
"properties": {
"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 5 | 8,198 | Find all positive integers $n\ge 2$ such that for any positive integer $k$ relatively prime to $n$, $k^2 - 1$ is a multiple of $n$. | 2, 3, 4, 6, 8, 12, 24 | n \in \{2, 3, 4, 6, 8, 12, 24\} | imo-bench-number_theory-041 |
[
{
"role": "system",
"content": "# Role\nYou are Terence Tao, the world-leading mathematician who is known as the Mozart of Math. You don't attempt to solve complex problems in 1 turn. You instead systematically break the problem down into subcomponents that can be solved over many turns by taking full advan... | [
{
"role": "system",
"content": "You are a judge whose job is to determine if a student's answer is mathematically equivalent to the provided ground truth. DO NOT attempt to solve the problem or manually re-verify if the student's answer is correct, only compare student's answer to the provided ground answer... | [
{
"type": "function",
"function": {
"name": "submit_answer",
"description": "Submit final solution to the problem.",
"parameters": {
"type": "object",
"properties": {
"answer": {
"type": "string",
"description": "Final mathematical answer w... | true | true | 5 | 10,122 | Let $g: \mathbb{Z}_{>0} \to \mathbb{Z}$ be a function satisfying the following conditions:
(i) $g(p) = p + 1$ for all prime numbers $p$,
(ii) $g(nm) + nm = ng(m) + mg(n)$ for all positive integers $n, m$.
Find all integers $1 \le n \le 4000$ satisfying $g(n) = 2n$. | 4, 27, 3125 | 4, 27, 3125 | imo-bench-number_theory-062 |
[{"role":"system","content":"# Role\nYou are Terence Tao, the world-leading mathematician who is kno(...TRUNCATED) | [{"role":"system","content":"You are a judge whose job is to determine if a student's answer is math(...TRUNCATED) | [{"type":"function","function":{"name":"submit_answer","description":"Submit final solution to the p(...TRUNCATED) | true | true | 6 | 10,517 | "For an arbitrary positive integer $m$, not divisible by $3$, consider the permutation $x \\mapsto 3(...TRUNCATED) | 197 | 197 | imo-bench-combinatorics-092 |
[{"role":"system","content":"# Role\nYou are Terence Tao, the world-leading mathematician who is kno(...TRUNCATED) | [{"role":"system","content":"You are a judge whose job is to determine if a student's answer is math(...TRUNCATED) | [{"type":"function","function":{"name":"submit_answer","description":"Submit final solution to the p(...TRUNCATED) | true | true | 6 | 10,219 | "Let $P$ and $Q$ be the circumcenter and incenter of triangle $DEF$. The perpendicular from $Q$ to $(...TRUNCATED) | 0.5 | 1/2 | imo-bench-geometry-017 |
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