Datasets:
data_source stringclasses 5
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Every morning Aya goes... | math | {
"ground_truth": "204",
"style": "rule"
} | {
"index": 0,
"question": "Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes h... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "There exist real numbe... | math | {
"ground_truth": "025",
"style": "rule"
} | {
"index": 1,
"question": "There exist real numbers $x$ and $y$, both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$. Find $xy$.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Alice and Bob play the... | math | {
"ground_truth": "809",
"style": "rule"
} | {
"index": 2,
"question": "Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take turns with Alice going first. On each turn, the player removes either $1$ token or $4$ tokens from the stack. Whoever removes the last token wins. Find the number of positive integers $n$ less ... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Jen enters a lottery b... | math | {
"ground_truth": "116",
"style": "rule"
} | {
"index": 3,
"question": "Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers are randomly chosen from $S.$ She wins a prize if at least two of her numbers were $2$ of the randomly chosen numbers, and wins the grand prize if all four of her numbers were the randomly ... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Rectangles $ABCD$ and ... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"index": 4,
"question": "Rectangles $ABCD$ and $EFGH$ are drawn such that $D,E,C,F$ are collinear. Also, $A,D,H,G$ all lie on a circle. If $BC=16$,$AB=107$,$FG=17$, and $EF=184$, what is the length of $CE$?\n[asy] import graph; unitsize(0.1cm); pair A = (0,0);pair B = (70,0);pair C = (70,16);pair D = (0,16);pair ... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Consider the paths of ... | math | {
"ground_truth": "294",
"style": "rule"
} | {
"index": 5,
"question": "Consider the paths of length $16$ that follow the lines from the lower left corner to the upper right corner on an $8\\times 8$ grid. Find the number of such paths that change direction exactly four times, as in the examples shown below.\n[asy] size(10cm); usepackage(\"tikz\");label(\"\\b... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Find the largest possi... | math | {
"ground_truth": "540",
"style": "rule"
} | {
"index": 6,
"question": "Find the largest possible real part of \\[(75+117i)z+\\frac{96+144i}{z}\\]where $z$ is a complex number with $|z|=4$.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Eight circles of radiu... | math | {
"ground_truth": "197",
"style": "rule"
} | {
"index": 7,
"question": "Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ and $BC$ of triangle $ABC$, respectively. $2024$ circles of radius $1$ can be arranged in the same manner. The inradius of triangle $ABC$ can be expressed as $\\frac{m}{n}$, where $m$ and $n$... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $A$, $B$, $C$, and... | math | {
"ground_truth": "480",
"style": "rule"
} | {
"index": 8,
"question": "Let $A$, $B$, $C$, and $D$ be point on the hyperbola $\\frac{x^2}{20}- \\frac{y^2}{24} = 1$ such that $ABCD$ is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than $BD^2$ for all such rhombi.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangl... | math | {
"ground_truth": "113",
"style": "rule"
} | {
"index": 9,
"question": "Let $ABC$ be a triangle inscribed in circle $\\omega$. Let the tangents to $\\omega$ at $B$ and $C$ intersect at point $D$, and let $\\overline{AD}$ intersect $\\omega$ at $P$. If $AB=5$, $BC=9$, and $AC=10$, $AP$ can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Each vertex of a regul... | math | {
"ground_truth": "371",
"style": "rule"
} | {
"index": 10,
"question": "Each vertex of a regular octagon is independently colored either red or blue with equal probability. The probability that the octagon can then be rotated so that all of the blue vertices end up at positions where there were originally red vertices is $\\tfrac{m}{n}$, where $m$ and $n$ ar... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Define $f(x)=|| x|-\\t... | math | {
"ground_truth": "385",
"style": "rule"
} | {
"index": 11,
"question": "Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$. Find the number of intersections of the graphs of \\[y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 g(f(\\cos (3 \\pi y))).\\]\nGraph\nhttps://www.desmos.com/calculator/wml09giaun",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $p$ be the least p... | math | {
"ground_truth": "110",
"style": "rule"
} | {
"index": 12,
"question": "Let $p$ be the least prime number for which there exists a positive integer $n$ such that $n^{4}+1$ is divisible by $p^{2}$. Find the least positive integer $m$ such that $m^{4}+1$ is divisible by $p^{2}$.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a tetrah... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"index": 13,
"question": "Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$, $AC=BD= \\sqrt{80}$, and $BC=AD= \\sqrt{89}$. There exists a point $I$ inside the tetrahedron such that the distances from $I$ to each of the faces of the tetrahedron are all equal. This distance can be written in the form $\\fra... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $\\mathcal{B}$ be ... | math | {
"ground_truth": "721",
"style": "rule"
} | {
"index": 14,
"question": "Let $\\mathcal{B}$ be the set of rectangular boxes with surface area $54$ and volume $23$. Let $r$ be the radius of the smallest sphere that can contain each of the rectangular boxes that are elements of $\\mathcal{B}$. The value of $r^2$ can be written as $\\frac{p}{q}$, where $p$ and $... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Among the 900 resident... | math | {
"ground_truth": "073",
"style": "rule"
} | {
"index": 15,
"question": "Among the 900 residents of Aimeville, there are 195 who own a diamond ring, 367 who own a set of golf clubs, and 562 who own a garden spade. In addition, each of the 900 residents owns a bag of candy hearts. There are 437 residents who own exactly two of these things, and 234 residents w... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "A list of positive int... | math | {
"ground_truth": "236",
"style": "rule"
} | {
"index": 16,
"question": "A list of positive integers has the following properties:\n$\\bullet$ The sum of the items in the list is $30$.\n$\\bullet$ The unique mode of the list is $9$.\n$\\bullet$ The median of the list is a positive integer that does not appear in the list itself.\n Find the sum of the squares ... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Find the number of way... | math | {
"ground_truth": "045",
"style": "rule"
} | {
"index": 17,
"question": "Find the number of ways to place a digit in each cell of a 2x3 grid so that the sum of the two numbers formed by reading left to right is $999$, and the sum of the three numbers formed by reading top to bottom is $99$. The grid below is an example of such an arrangement because $8+991=99... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $x,y$ and $z$ be p... | math | {
"ground_truth": "033",
"style": "rule"
} | {
"index": 18,
"question": "Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations: \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\]\\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\]\\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] Then the value of $\\left|\\... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let ABCDEF be a convex... | math | {
"ground_truth": "080",
"style": "rule"
} | {
"index": 19,
"question": "Let ABCDEF be a convex equilateral hexagon in which all pairs of opposite sides are parallel. The triangle whose sides are extensions of segments AB, CD, and EF has side lengths 200, 240, and 300. Find the side length of the hexagon.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Alice chooses a set $A... | math | {
"ground_truth": "055",
"style": "rule"
} | {
"index": 20,
"question": "Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$. Bob's list has 2024 sets. Find the sum of the elements of A.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $N$ be the greates... | math | {
"ground_truth": "699",
"style": "rule"
} | {
"index": 21,
"question": "Let $N$ be the greatest four-digit positive integer with the property that whenever one of its digits is changed to $1$, the resulting number is divisible by $7$. Let $Q$ and $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$. Find $Q+R$.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Torus $T$ is the surfa... | math | {
"ground_truth": "127",
"style": "rule"
} | {
"index": 22,
"question": "Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$. When $T$ rests on the inside of $S$, it is internally tangent ... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "There is a collection ... | math | {
"ground_truth": "902",
"style": "rule"
} | {
"index": 23,
"question": "There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of a $5\\times5$ grid such that:\neach cell contains at most one chip\nall chips in the same row and all chips i... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $\\triangle ABC$ h... | math | {
"ground_truth": "468",
"style": "rule"
} | {
"index": 24,
"question": "Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\overline{IA}\\perp\\overline{OI}$, circumradius $13$, and inradius $6$. Find $AB\\cdot AC$.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Find the number of tri... | math | {
"ground_truth": "601",
"style": "rule"
} | {
"index": 25,
"question": "Find the number of triples of nonnegative integers \\((a,b,c)\\) satisfying \\(a + b + c = 300\\) and \\begin{equation*} a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000. \\end{equation*}",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let \\(O=(0,0)\\), \\(... | math | {
"ground_truth": "023",
"style": "rule"
} | {
"index": 26,
"question": "Let \\(O=(0,0)\\), \\(A=\\left(\\tfrac{1}{2},0\\right)\\), and \\(B=\\left(0,\\tfrac{\\sqrt{3}}{2}\\right)\\) be points in the coordinate plane. Let \\(\\mathcal{F}\\) be the family of segments \\(\\overline{PQ}\\) of unit length lying in the first quadrant with \\(P\\) on the \\(x\\)-ax... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $\\omega\\neq 1$ b... | math | {
"ground_truth": "321",
"style": "rule"
} | {
"index": 27,
"question": "Let $\\omega\\neq 1$ be a 13th root of unity. Find the remainder when \\[\\prod_{k=0}^{12}(2-2\\omega^k+\\omega^{2k})\\] is divided by 1000.",
"split": "test"
} |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let \\(b\\ge 2\\) be a... | math | {
"ground_truth": "211",
"style": "rule"
} | {
"index": 28,
"question": "Let \\(b\\ge 2\\) be an integer. Call a positive integer \\(n\\) \\(b\\text-\\textit{eautiful}\\) if it has exactly two digits when expressed in base \\(b\\) and these two digits sum to \\(\\sqrt n\\). For example, \\(81\\) is \\(13\\text-\\textit{eautiful}\\) because \\(81 = \\underline... |
test-math-aime24 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Find the number of rec... | math | {
"ground_truth": "315",
"style": "rule"
} | {
"index": 29,
"question": "Find the number of rectangles that can be formed inside a fixed regular dodecagon ($12$-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles.\n[asy] unitsize(0.6 inch); for(int i=0; i<360; i+=30) { d... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Find the sum of all in... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"index": 0,
"question": "Find the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "On $\\triangle ABC$ po... | math | {
"ground_truth": "588",
"style": "rule"
} | {
"index": 1,
"question": "On $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflect... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The 9 members of a bas... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"index": 2,
"question": "The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Find the number of ord... | math | {
"ground_truth": "117",
"style": "rule"
} | {
"index": 3,
"question": "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "There are $8!=40320$ e... | math | {
"ground_truth": "279",
"style": "rule"
} | {
"index": 4,
"question": "There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "An isosceles trapezoid... | math | {
"ground_truth": "504",
"style": "rule"
} | {
"index": 5,
"question": "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The twelve letters $A,... | math | {
"ground_truth": "821",
"style": "rule"
} | {
"index": 6,
"question": "The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result ... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $k$ be real number... | math | {
"ground_truth": "77",
"style": "rule"
} | {
"index": 7,
"question": "Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.",
"... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The parabola with equa... | math | {
"ground_truth": "62",
"style": "rule"
} | {
"index": 8,
"question": "The parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The 27 cells of a $3\\... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"index": 9,
"question": "The 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 ... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "A piecewise linear per... | math | {
"ground_truth": "259",
"style": "rule"
} | {
"index": 10,
"question": "A piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at fin... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The set of points in 3... | math | {
"ground_truth": "510",
"style": "rule"
} | {
"index": 11,
"question": "The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form ... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Alex divides a disk in... | math | {
"ground_truth": "204",
"style": "rule"
} | {
"index": 12,
"question": "Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting thos... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $ABCDE$ be a conve... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"index": 13,
"question": "Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $N$ denote the num... | math | {
"ground_truth": "735",
"style": "rule"
} | {
"index": 14,
"question": "Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Six points $ A, B, C, ... | math | {
"ground_truth": "468",
"style": "rule"
} | {
"index": 15,
"question": "Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Find the sum of all po... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"index": 16,
"question": "Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Four unit squares form... | math | {
"ground_truth": "82",
"style": "rule"
} | {
"index": 17,
"question": "Four unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The product $ \\prod_{... | math | {
"ground_truth": "106",
"style": "rule"
} | {
"index": 18,
"question": "The product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is eq... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Suppose $ \\triangle A... | math | {
"ground_truth": "336^\\circ",
"style": "rule"
} | {
"index": 19,
"question": "Suppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangl... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Circle $\\omega_1$ wit... | math | {
"ground_truth": "293",
"style": "rule"
} | {
"index": 20,
"question": "Circle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ i... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $ A $ be the set o... | math | {
"ground_truth": "237",
"style": "rule"
} | {
"index": 21,
"question": "Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively pri... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "From an unlimited supp... | math | {
"ground_truth": "610",
"style": "rule"
} | {
"index": 22,
"question": "From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value tha... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "There are $ n $ values... | math | {
"ground_truth": "149",
"style": "rule"
} | {
"index": 23,
"question": "There are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Sixteen chairs are arr... | math | {
"ground_truth": "907",
"style": "rule"
} | {
"index": 24,
"question": "Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $ S $ be the set o... | math | {
"ground_truth": "113",
"style": "rule"
} | {
"index": 25,
"question": "Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.",
"split": "test"
} |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $ A_1A_2 \\ldots A... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"index": 26,
"question": "Let $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 ... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let the sequence of ra... | math | {
"ground_truth": "248",
"style": "rule"
} | {
"index": 27,
"question": "Let the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $ \\triangle ABC $... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"index": 28,
"question": "Let $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive intege... |
test-math-aime25 | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "There are exactly thre... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"index": 29,
"question": "There are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.",
... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "$\\frac{m}{n}$ is the ... | math | {
"ground_truth": "142",
"style": "rule"
} | {
"index": 0,
"question": "$\\frac{m}{n}$ is the Irreducible fraction value of \\[3+\\frac{1}{3+\\frac{1}{3+\\frac13}}\\], what is the value of $m+n$?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "How many ways are ther... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"index": 1,
"question": "How many ways are there to split the integers $1$ through $14$ into $7$ pairs such that in each pair, the greater number is at least $2$ times the lesser number?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "What is the product of... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"index": 2,
"question": "What is the product of all real numbers $x$ such that the distance on the number line between $\\log_6x$ and $\\log_69$ is twice the distance on the number line between $\\log_610$ and $1$?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $M$ be the midpoin... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 3,
"question": "Let $M$ be the midpoint of $\\overline{AB}$ in regular tetrahedron $ABCD$. $\\frac{p}{q}=\\cos(\\angle CMD)$ is irreducible fraction, what is the value of $p+q$?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $\\mathcal{R}$ be ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"index": 4,
"question": "Let $\\mathcal{R}$ be the region in the complex plane consisting of all complex numbers $z$ that can be written as the sum of complex numbers $z_1$ and $z_2$, where $z_1$ lies on the segment with endpoints $3$ and $4i$, and $z_2$ has magnitude at most $1$. What integer is closest to the a... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "What is the value of \... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 5,
"question": "What is the value of \\[(\\log 5)^{3}+(\\log 20)^{3}+(\\log 8)(\\log 0.25)\\] where $\\log$ denotes the base-ten logarithm?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The roots of the polyn... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 6,
"question": "The roots of the polynomial $10x^3 - 39x^2 + 29x - 6$ are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each edge of the original box by $2$\nunits. What is the volume of the new box?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "A $\\emph{triangular n... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 7,
"question": "A $\\emph{triangular number}$ is a positive integer that can be expressed in the form $t_n = 1+2+3+\\cdots+n$, for some positive integer $n$. The three smallest triangular numbers that are also perfect squares are\n$t_1 = 1 = 1^2$, $t_8 = 36 = 6^2$, and $t_{49} = 1225 = 35^2$. What is the... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Suppose $a$ is a real ... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"index": 8,
"question": "Suppose $a$ is a real number such that the equation \\[a\\cdot(\\sin{x}+\\sin{(2x)}) = \\sin{(3x)}\\]\nhas more than one solution in the interval $(0, \\pi)$. The set of all such $a$ that can be written\nin the form \\[(p,q) \\cup (q,r),\\]\nwhere $p, q,$ and $r$ are real numbers with $p ... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $T_k$ be the trans... | math | {
"ground_truth": "359",
"style": "rule"
} | {
"index": 9,
"question": "Let $T_k$ be the transformation of the coordinate plane that first rotates the plane $k$ degrees counterclockwise around the origin and then reflects the plane across the $y$-axis. What is the least positive\ninteger $n$ such that performing the sequence of transformations $T_1, T_2, T_3,... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Suppose that $13$ card... | math | {
"ground_truth": "8178",
"style": "rule"
} | {
"index": 10,
"question": "Suppose that $13$ cards numbered $1, 2, 3, \\ldots, 13$ are arranged in a row. The task is to pick them up in numerically increasing order, working repeatedly from left to right. In the example below, cards $1, 2, 3$ are picked up on the first pass, $4$ and $5$ on the second pass, $6$ on... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The sum of three numbe... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 11,
"question": "The sum of three numbers is $96.$ The first number is $6$ times the third number, and the third number is $40$ less than the second number. What is the absolute value of the difference between the first and second numbers?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Isosceles trapezoid $A... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 12,
"question": "Isosceles trapezoid $ABCD$ has parallel sides $\\overline{AD}$ and $\\overline{BC},$ with $BC < AD$ and $AB = CD.$ There is a point $P$ in the plane such that $PA=1, PB=2, PC=3,$ and $PD=4.$ Let $\\frac{r}{s}=frac{BC}{AD}$ is irreducible fraction, what is the value of $r+s$?",
"split":... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $c$ be a real numb... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 13,
"question": "Let $c$ be a real number, and let $z_1$ and $z_2$ be the two complex numbers satisfying the equation\n$z^2 - cz + 10 = 0$. Points $z_1$, $z_2$, $\\frac{1}{z_1}$, and $\\frac{1}{z_2}$ are the vertices of (convex) quadrilateral $\\mathcal{Q}$ in the complex plane. When the area of $\\mathc... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $h_n$ and $k_n$ be... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 14,
"question": "Let $h_n$ and $k_n$ be the unique relatively prime positive integers such that \\[\\frac{1}{1}+\\frac{1}{2}+\\frac{1}{3}+\\cdots+\\frac{1}{n}=\\frac{h_n}{k_n}.\\] Let $L_n$ denote the least common multiple of the numbers $1, 2, 3, \\ldots, n$. For how many integers with $1\\le{n}\\le{22}... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "How many strings of le... | math | {
"ground_truth": "1296",
"style": "rule"
} | {
"index": 15,
"question": "How many strings of length $5$ formed from the digits $0$, $1$, $2$, $3$, $4$ are there such that for each $j \\in \\{1,2,3,4\\}$, at least $j$ of the digits are less than $j$? (For example, $02214$ satisfies this condition\nbecause it contains at least $1$ digit less than $1$, at least ... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "A circle with integer ... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"index": 16,
"question": "A circle with integer radius $r$ is centered at $(r, r)$. Distinct line segments of length $c_i$ connect points $(0, a_i)$ to $(b_i, 0)$ for $1 \\le i \\le 14$ and are tangent to the circle, where $a_i$, $b_i$, and $c_i$ are all positive integers and $c_1 \\le c_2 \\le \\cdots \\le c_{14... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The least common multi... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 17,
"question": "The least common multiple of a positive integer $n$ and $18$ is $180$, and the greatest common divisor of $n$ and $45$ is $15$. What is the sum of the digits of $n$?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The $\\textit{taxicab ... | math | {
"ground_truth": "841",
"style": "rule"
} | {
"index": 18,
"question": "The $\\textit{taxicab distance}$ between points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane is given by \\[|x_1 - x_2| + |y_1 - y_2|.\\]\nFor how many points $P$ with integer coordinates is the taxicab distance between $P$ and the origin less than or equal to $20$?",
"split":... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "A data set consists of... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"index": 19,
"question": "A data set consists of $6$ (not distinct) positive integers: $1$, $7$, $5$, $2$, $5$, and $X$. The average (arithmetic mean) of the $6$ numbers equals a value in the data set. What is the sum of all possible values of $X$?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The infinite product\n... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 20,
"question": "The infinite product\n\\[\\sqrt[3]{10} \\cdot \\sqrt[3]{\\sqrt[3]{10}} \\cdot \\sqrt[3]{\\sqrt[3]{\\sqrt[3]{10}}} \\cdots\\]\nevaluates to a real number $\\sqrt{m}$. What is the value of m?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "On Halloween $31$ chil... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 21,
"question": "On Halloween $31$ children walked into the principal's office asking for candy. They can be classified into three types: Some always lie; some always tell the truth; and some alternately lie and tell the truth. The alternaters arbitrarily choose their first response, either a lie or the ... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Define $x\\diamond y$ ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 22,
"question": "Define $x\\diamond y$ to be $|x-y|$ for all real numbers $x$ and $y.$ What is the value of \\[((1\\diamond2)\\diamond3)-(1\\diamond(2\\diamond3))?\\]",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $f(n) = \\left( \\... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 23,
"question": "Let $f(n) = \\left( \\frac{-1+i\\sqrt{3}}{2} \\right)^n + \\left( \\frac{-1-i\\sqrt{3}}{2} \\right)^n$, where $i = \\sqrt{-1}$. What is $f(2022)$?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Kayla rolls four fair ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 24,
"question": "Kayla rolls four fair $6$-sided dice. What is the denominator minus the numerator of the probability that at least one of the numbers Kayla rolls is greater than 4 and at least two of the numbers she rolls are greater than 2?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The diagram below show... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 25,
"question": "The diagram below shows a rectangle with side lengths $4$ and $8$ and a square with side length $5$. Three vertices of the square lie on three different sides of the rectangle, as shown. What is the numerator of the simplest fraction that represents the area of the region inside both the... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The graph of $y=x^2+2x... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 26,
"question": "The graph of $y=x^2+2x-15$ intersects the $x$-axis at points $A$ and $C$ and the $y$-axis at point $B$. What is the numerator of the simplest fraction that represents $\\tan(\\angle ABC)$?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "How many $4 \\times 4$... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"index": 27,
"question": "How many $4 \\times 4$ arrays whose entries are $0$s and $1$s are there such that the row sums (the sum of the entries in each row) are $1, 2, 3,$ and $4,$ in some order, and the column sums (the sum of the entries in each column) are also $1, 2, 3,$ and $4,$ in some order? Output the re... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Each square in a $5 \\... | math | {
"ground_truth": "22",
"style": "rule"
} | {
"index": 28,
"question": "Each square in a $5 \\times 5$ grid is either filled or empty, and has up to eight adjacent neighboring squares, where neighboring squares share either a side or a corner. The grid is transformed by the following rules:\n\nAny filled square with two or three filled neighbors remains fill... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "In $\\triangle{ABC}$ m... | math | {
"ground_truth": "44",
"style": "rule"
} | {
"index": 29,
"question": "In $\\triangle{ABC}$ medians $\\overline{AD}$ and $\\overline{BE}$ intersect at $G$ and $\\triangle{AGE}$ is equilateral. Then $\\cos(C)$ can be written as $\\frac{m\\sqrt p}n$, where $m$ and $n$ are relatively prime positive integers and $p$ is a positive integer not divisible by the sq... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "In rhombus $ABCD$, poi... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 30,
"question": "In rhombus $ABCD$, point $P$ lies on segment $\\overline{AD}$ so that $\\overline{BP}$ $\\perp$ $\\overline{AD}$, $AP = 3$, and $PD = 2$. What is the area of $ABCD$? (Note: The figure is not drawn to scale.)\n",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $P(x)$ be a polyno... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"index": 31,
"question": "Let $P(x)$ be a polynomial with rational coefficients such that when $P(x)$ is divided by the polynomial\n$x^2 + x + 1$, the remainder is $x+2$, and when $P(x)$ is divided by the polynomial $x^2+1$, the remainder\nis $2x+1$. There is a unique polynomial of least degree with these two pro... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $S$ be the set of ... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"index": 32,
"question": "Let $S$ be the set of circles in the coordinate plane that are tangent to each of the three circles with equations $x^{2}+y^{2}=4$, $x^{2}+y^{2}=64$, and $(x-5)^{2}+y^{2}=3$. What is the sum of the areas of all circles in $S$?Output the remainder when the answer is divided by 100.\n\n\n"... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Ant Amelia starts on t... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 33,
"question": "Ant Amelia starts on the number line at $0$ and crawls in the following manner. For $n=1,2,3,$ Amelia chooses a time duration $t_n$ and an increment $x_n$ independently and uniformly at random from the interval $(0,1).$ During the $n$th step of the process, Amelia moves $x_n$ units in th... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Let $x_0,x_1,x_2,\\dot... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 34,
"question": "Let $x_0,x_1,x_2,\\dotsc$ be a sequence of numbers, where each $x_k$ is either $0$ or $1$. For each positive integer $n$, define \n\\[S_n = \\sum_{k=0}^{n-1} x_k 2^k\\]\nSuppose $7S_n \\equiv 1 \\pmod{2^n}$ for all $n \\geq 1$. What is the value of the sum \n\\[x_{2019} + 2x_{2020} + 4x... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "The figure below depic... | math | {
"ground_truth": "47",
"style": "rule"
} | {
"index": 35,
"question": "The figure below depicts a regular $7$-gon inscribed in a unit circle.\n[asy] import geometry; unitsize(3cm); draw(circle((0,0),1),linewidth(1.5)); for (int i = 0; i < 7; ++i) { for (int j = 0; j < i; ++j) { draw(dir(i * 360/7) -- dir(j * 360/7),linewidth(1.5)); } } for(i... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "Four regular hexagons ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 36,
"question": "Four regular hexagons surround a square with side length 1, each one sharing an edge with the square,\nas shown in the figure below. The area of the resulting 12-sided outer nonconvex polygon can be\nwritten as $m \\sqrt{n} + p$, where $m$, $n$, and $p$ are integers and $n$ is not divisi... |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "How many of the first ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 37,
"question": "How many of the first ten numbers of the sequence $121, 11211, 1112111, \\ldots$ are prime numbers?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "For how many values of... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 38,
"question": "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?",
"split": "test"
} |
test-amc | [
{
"content": "You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Present your work in a well-organized manner and enclose your final answer in the box: \\boxed{Your Answer}.",
"role": "system"
},
{
"content": "What is the sum of the... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 39,
"question": "What is the sum of the x and y coordinates of the new position of the point $(-1, -2)$ after rotating $270^{\\circ}$ counterclockwise about the point $(3, 1)$?",
"split": "test"
} |
End of preview. Expand in Data Studio
RL-Forgetting math benchmarks
Train and test/benchmark sets used in the RL-Forgetting-Exp study of
replay-buffer freshness. All parquets share the verl RL schema
(data_source, prompt, ability, reward_model, extra_info).
Layout
polaris_full/
train.parquet # 52,309 prompts (Polaris-full training set)
test.parquet # 800 prompts (held-out test, 100/difficulty)
deepscaler/
train.parquet # 8,192 prompts (skywork_deepscaler_easy_8192, fixed ground_truth)
test/ # external math benchmarks used for pass@k eval
aime2024.parquet # 30
aime2025.parquet # 30
amc_test.parquet # 83
math500.parquet # 500
minerva_math.parquet # 272
Notes
polaris_fullis the Polaris-53k dataset;train.parquetis the RL training split andtest.parquetis the sampled held-out test set (100 prompts per difficulty bucket).deepscaler/train.parquetis the fixed-ground-truth variant ofskywork_deepscaler_easy_8192used for RL training.- The DeepScaleR "test set" is the standard suite of external math benchmarks (AIME 2024/2025, AMC, MATH-500, Minerva-Math) rendered in the same prompt template as training, used to measure pass@k.
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