Test-Time and Training-Time Reasoning with Code Interpreter
Collection
Model weights and dataset for the paper "Exploring Extrinsic and Intrinsic Properties for Effective Reasoning with Code Interpreter" (TMLR'26) • 8 items • Updated
messages listlengths 4 20 | tools listlengths 1 1 |
|---|---|
[
{
"content": "There are 152 students at Dala High School. Assume the following: \n- 100 students take a Math class \n- 94 students take a Science class \n- 57 students take an English class \n- 73 students take a Math class and a Science class \n- 24 students take a Math class and an English class \n- 27 ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "What is the smallest positive integer that leaves a remainder of 4 when divided by 5 and a remainder of 6 when divided by 7?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Find all triples of three-digit positive integers $x < y < z$ with $x, y, z$ in arithmetic progression and $x, y, z + 1000$ in geometric progression. The original answer is in the form of (k, m, n), please give the value of k + m + n.\n\n[i]For this problem, you may use calculators or computers to... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Let\n$a=\\frac{1^2}{1} + \\frac{2^2}{3} + \\frac{3^2}{5} + \\; \\dots \\; + \\frac{1001^2}{2001}$\nand\n$b=\\frac{1^2}{3} + \\frac{2^2}{5} + \\frac{3^2}{7} + \\; \\dots \\; + \\frac{1001^2}{2003}.$\nFind the integer closest to $a-b$.\n\nRemember to place the final answer in the last part using the... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Find the greatest integer less than $\\sqrt{10} + \\sqrt{80}$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content": "<think>\nI need to find the greatest integer le... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "The legs of a right triangle measure 6 inches and 8 inches. Find the greatest area of a rectangle that can be inscribed in the right triangle( square inches). Give the exact answer\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "ABCDE is a pyramid with square base ABCD. Point E is directly above A with AE = 1024 and AB = 640. The pyramid is cut into two pieces by a horizontal plane parallel to ABCD. This horizontal plane is a distance h above the base ABCD. The portion of ABCDE that is above the plane is a new pyramid. Fo... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "How many pairs of positive integers $(a,b)$ with $a + b \\le 100$ satisfy the equation \\( \\frac{a + \\frac{1}{b}}{\\frac{1}{a} + b} = 13 \\)?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_call... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "When the roots of the polynomial \n\n\\[P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \\cdot \\cdot \\cdot (x-10)^{10}\\]\n\nare removed from the number line, what remains is the union of $11$ disjoint open intervals. Find the number of these intervals on which \\( P(x) \\) is positive.\n\nRemember to place the... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Let $a + \\frac{1}{b} = 8$ and $b + \\frac{1}{a} = 3$. Find the sum of the two possible real values for $a$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content": "<... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "In the figure below, choose point \\(D\\) on \\(\\overline{BC}\\) so that \\(\\triangle ACD\\) and \\(\\triangle ABD\\) have equal perimeters. What is the area of \\(\\triangle ABD\\)?\n\n[asy]draw((0,0)--(4,0)--(0,3)--(0,0)); label(\"$A$\", (0,0), SW); label(\"$B$\", (4,0), ESE); label(\"$C$\", (... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "On the trip home from the meeting where this $AMC~10$ was constructed, the Contest Chair noted that his airport parking receipt had digits of the form $bbcac,$ where $0 \\le a < b < c \\le 9,$ and $b$ was the average of $a$ and $c.$ How many different five-digit numbers satisfy all these propertie... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "What are all values of $p$ such that for every $q>0$, we have $$\\frac{3(pq^2+p^2q+3q^2+3pq)}{p+q}>2p^2q?$$ Express your answer in interval notation in decimal form as [a, b). Please give the value of 2a + 2b.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'T... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "A finite sequence of positive integers $ m_i$ for $ i=1,2,...,2006$ are defined so that $ m_1=1$ and $ m_i=10m_{i-1} +1$ for $ i>1$. Let $ k$ be the number of these integers that are divisible by $ 37$. Find the value of $ k$.\n\nRemember to place the final answer in the last part using the format... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "In a triangle $ABC$, point $D$ lies on $AB$. It is given that $AD = 25$, $BD = 24$, $BC = 28$, and $CD = 20$. Find the length of $AC$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "How many three-digit numbers leave a remainder of $2$ when divided by $5$ and a remainder of $7$ when divided by $9$?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"con... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "How many positive integers not exceeding $2001$ are multiples of $3$ or $4$ but not $5$? Provide your answer as an integer.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "The roots of the polynomial \\[x^3 - 52x^2 + 581x - k\\]are distinct prime numbers. Find $k.$\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content": "<think>\nLet me ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Find the minimum value of $n$ such that, among any $n$ integers, there are three whose sum is divisible by $3$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content":... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Two circles have radii of 5 and 26, respectively. The smaller circle passes through the center of the larger one. What is the difference between the lengths of the longest and shortest chords of the larger circle that are tangent to the smaller circle?\n\nRemember to place the final answer in the ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Find the value of \\(i + 2i^2 + 3i^3 + \\ldots + 2002i^{2002}\\). The original answer is in the form of \\(k + mi\\), please give the value of \\(k + m\\).\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Find the largest constant $m,$ so that for any positive real numbers $a,$ $b,$ $c,$ and $d,$\n\\[\\sqrt{\\frac{a}{b + c + d}} + \\sqrt{\\frac{b}{a + c + d}} + \\sqrt{\\frac{c}{a + b + d}} + \\sqrt{\\frac{d}{a + b + c}} > m.\\]\n\nRemember to place the final answer in the last part using the format... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Let $S$ be the set of 10-tuples $(a_0, a_1, \\dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples. For each 10-tuple $s = (a_0, a_1, \\dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that\n\\[p_s(n) = a_n\\]for $0 \\le n \\le 9.$ For example, $... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Find all functions f from the set of real numbers into the set of real numbers which satisfy for all real $x,y$ the identity\n$f(xf(x+y))=f(yf(x))+x^2.$\nThe original answer is in the form of af(x) and bf(x), please give the value of a + b.\n\nRemember to place the final answer in the last part us... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "99 dwarfs stand in a circle. Some of them wear hats. There are no adjacent dwarfs wearing hats, and no two dwarfs wearing hats have exactly 48 dwarfs standing between them. What is the maximal possible number of dwarfs wearing hats?\n\nRemember to place the final answer in the last part using the ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "How many pairs of positive integers $(a,b)$ are there such that ${gcd}(a,b)=1$ and $\\frac{a}{b} + \\frac{14b}{9a}$ is an integer?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "A fair, twenty-faced die has $19$ of its faces numbered from $1$ through $19$ and has one blank face. Another fair, twenty-faced die has $19$ of its faces numbered from $1$ through $8$ and $10$ through $20$ and has one blank face. When the two dice are rolled, what is the probability that the sum ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "A circular grass plot with a diameter of 12 feet is intersected by a straight gravel path that is 3 feet wide. One edge of the path passes through the center of the plot. Calculate the number of square feet in the remaining grass area. The original answer is in the form $k\\pi - m\\sqrt{n}$, pleas... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Let $\\varphi$ be the positive solution to the equation $x^2 = x + 1$. For $n \\ge 0$, let $a_n$ be the unique integer such that $\\varphi^n - a_n \\varphi$ is also an integer. Compute $\\sum_{n=0}^{10} a_n$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'Th... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "The base of isosceles $\\triangle ABC$ is $24$ and its area is $60$. What is the length of one of the congruent sides?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"co... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Given that $a_{i} \\in \\{0,1,2,3,4\\}$ for every $0 \\le i \\le 9$, if $6\\sum_{i=0}^{9}a_{i} 5^{i} \\equiv 1 \\pmod{5^{10}}$, find the value of $a_{9}$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Let $x^2+bx+c = 0$ be a quadratic whose roots are each two more than the roots of $3x^2-5x-7$. What is $c$?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content": "<t... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "What is the smallest positive integer $n$ for which $9n-2$ and $7n + 3$ share a common factor greater than $1$?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content":... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "If $a, b, c \\ge 4$ are integers, not all equal, and $4abc = (a+3)(b+3)(c+3)$, then what is the value of $a+b+c$?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "For each integer $n \\ge 1$ define $a_n = \\left[\\frac{n}{\\left[\\sqrt{n}\\right]}\\right]$ (where $[x]$ denoted the largest integer not exceeding $x$, for any real number $x$). Find the number of all $n$ in the set $\\{1, 2, 3, \\cdots , 2010\\}$ for which $a_n > a_{n+1}$\n\nRemember to place t... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Pieck the Frog hops on Pascal’s Triangle, where she starts at the number $1$ at the top. In a hop, Pieck can hop to one of the two numbers directly below the number she is currently on with equal probability. Given that the expected value of the number she is on after $7$ hops is $\\frac{m}{n}$ , ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "In the coordinate plane, let $F = (5,0).$ Let $P$ be a point, and let $Q$ be the projection of the point $P$ onto the line $x = \\frac{16}{5}.$ The point $P$ traces a curve in the plane, so that\n\\[\\frac{PF}{PQ} = \\frac{5}{4}\\] for all points $P$ on the curve. Find the equation of this curve i... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Let $f(x) = x^3 + ax^2 + bx + c$ have solutions that are distinct negative integers. If $a+b+c = 2014$, find $c$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"role": "user",
"tool_calls": null
},
{
"content... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
[
{
"content": "Suppose $a_{1} < a_{2}< \\cdots < a_{2024}$ is an arithmetic sequence of positive integers, and $b_{1} <b_{2} < \\cdots <b_{2024}$ is a geometric sequence of positive integers. Find the maximum possible number of integers that could appear in both sequences, over all possible choices of the two se... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... |
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