data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Through the point \\( M(-2, 0, 3) \\), draw a line that intersects the lines\n\n\\[ \n\\left\\{\n\\begin{array}{l}\nx = 2 - t \\\\\ny = 3 \\\\\nz = -2 + t\n\\end{array}\n\\right.... | math | {
"ground_truth": "x = -2 + 13t, \\, y = -3t, \\, z = 3 - 12t",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Students are to be assigned to three grades with 2 students per grade, with the additional constraints that student A must be in the first grade, and students B and C cannot be i... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many integers \\( n \\) between 1 and 100 make \\( x^{2}+x-n \\) factorable into the product of two linear factors with integer coefficients?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $m$ in the equation $(256)^{\\frac{1}{3}} = 2^m$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{8}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the ordinate of a point is three times its abscissa, then this point is called a \"three times point.\" For a quadratic function $y=-x^{2}-x+c$ in the range of $-3 \\lt x \\lt... | math | {
"ground_truth": "-4 \\leqslant c < 5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Square each integer $n$ in the range $1 \\leq n \\leq 15$ and find the remainders when the squares are divided by $16$. Add up all the distinct results and call it $m$. What is t... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A convex polyhedron $P$ has 26 vertices, 60 edges, and 36 faces, 24 of which are triangular, and 12 of which are quadrilaterals. A space diagonal is a line segment connecting t... | math | {
"ground_truth": "241",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the integer $n \\ge 48$ for which the number of trailing zeros in the decimal representation of $n!$ is exactly $n-48$ .\n\n*Proposed by Kevin Sun*",
"role": "user"... | math | {
"ground_truth": "62",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sasha chose five numbers from 1, 2, 3, 4, 5, 6, and 7 and informed Anya of their product. Based on this information, Anya realized that she could not uniquely determine the parit... | math | {
"ground_truth": "420",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each integer $1$ through $12$ is written on a separate slip of paper and all twelve slips are put into a hat. Alice picks one of these slips at random and puts it back. Then Bob ... | math | {
"ground_truth": "\\textbf{(D)}\\ \\frac{1}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In two places, A and B, the monthly telephone rental fee is $18. The monthly telephone fee $y (in dollars)$ varies with time $x (in minutes)$. Based on the data in the table belo... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the plane Cartesian coordinate system \\( xOy \\), the circle \\( \\Omega \\) intersects the parabola \\( \\Gamma: y^{2} = 4x \\) at exactly one point, and the circle \\( \\Om... | math | {
"ground_truth": "\\frac{4 \\sqrt{3}}{9}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest possible total number of measurements, $N$, for a frequency distribution given by:\n\\[\\begin{tabular}{c c}\n\\text{measured value}&\\text{percent frequen... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many integer triples $(x,y,z)$ are there such that $\\begin{array}{rcl} x - yz^2&\\equiv & 1 \\pmod {13} \\\\ xz+y&\\equiv& 4 \\pmod {13} \\end{array}$ where $0\\leq x < 13$... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system $xOy$, if the line $ax+y-2=0$ intersects with a circle centered at $C$ and defined by $(x-1)^{2}+(y-a)^{2}= \\frac {16}{3}$ at points $A$ and $... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For certain real numbers \\( p \\), \\( q \\), and \\( r \\), the polynomial \n\\[ h(x) = x^3 + px^2 + 2x + 20 \\] \nhas three distinct roots, and each root of \\( h(x) \\) is al... | math | {
"ground_truth": "-155",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define function $g$ on the set of integers such that: \n\\[g(n)= \\begin{cases} \nn-3 & \\mbox{if }n\\ge 1200 \\\\\ng(g(n+6)) & \\mbox{if }n<1200.\n\\end{cases}\\]\nFind $g(84)$... | math | {
"ground_truth": "g(84) = 1197",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Danica drove her new car on a trip for a whole number of hours, averaging $55$ miles per hour. At the beginning of the trip, $abc$ miles was displayed on the odometer, where $a\\... | math | {
"ground_truth": "37",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Thirty goblins and ten pixies are attending a Fantasy Creatures Ball. The pixies, due to a spell, can only shake hands with an even number of goblins. Goblins are friendly and sh... | math | {
"ground_truth": "735",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sets $A=[1,4)$ and $B=(-\\infty,a)$, if $A \\cap B = A$, then the range of the real number $a$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "a \\geq 4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A stone is dropped into a well, and it's observed that the noise of the stone hitting the bottom is heard 9.5 seconds later. Assume the stone descends according to the equation $... | math | {
"ground_truth": "1332",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circular wheel has 7 equal sections, and each of them will be painted with one of two colors. Two colorings are considered equivalent if one can be rotated to produce the other... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Harry has 3 sisters and 5 brothers. His sister Harriet has S sisters and B brothers. Calculate the product of S and B.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$ and $b$ be real numbers such that $a+b=\\log_2( \\log_2 3)$ . What is the minimum value of $2^a + 3^b$ ?",
"role": "user"
}
] | math | {
"ground_truth": "\\log_2 6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The line $\\begin{cases}x=-2-2t \\\\ y=3+ \\sqrt{2}t\\end{cases}$ (where $t$ is the parameter), corresponds to the standard equation of ______.",
"role": "user"
}
] | math | {
"ground_truth": "x+ \\sqrt{2}y+2-3\\sqrt{2}=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number $1540$ is expressed in the form $1540 = \\frac{a_1! a_2! \\cdots a_m!}{b_1! b_2! \\cdots b_n!}$, where $a_1 \\ge a_2 \\ge \\cdots \\ge a_m$ and $b_1 \\ge b_2 \\ge \\cd... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Eight straight lines are drawn in a plane with no two parallel and no three concurrent. Calculate the number of regions into which these lines divide the plane.\nA) 35\nB) 36\nC)... | math | {
"ground_truth": "C) 37",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A pair of standard $6$-sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. Find the probability that the numerical value of the area of ... | math | {
"ground_truth": "\\frac{1}{12}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of distinct points common to the circle described by the equation $x^2 + y^2 = 16$ and the vertical line defined by $x = 4$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $DEF$, $DE = 14$, $DF = 15$, and $EF = 21$. The medians $DG$, $EH$, and $FI$ of triangle $DEF$ intersect at the centroid $J$. Let $M$ be the foot of the altitude from... | math | {
"ground_truth": "\\frac{8}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $f(x) = x^3 + ax$ ($x \\in \\mathbb{R}$) has an extremum at $x = l$. Then, the equation of the tangent line to the curve $y = f(x)$ at the origin is ____.",
"rol... | math | {
"ground_truth": "3x + y = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify first, then evaluate: $(3x^{2}y-xy^{2})-2(-2xy^{2}+x^{2}y)$, where $x=2$, $y=-1$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the greatest common divisor of 15 and 70.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the algebraic expressions $3x^2 - 2x - 1$ and $-9x^2 + 6x - 1$, find the value of the expression $-9x^2 + 6x - 1$ when the value of the expression $3x^2 - 2x - 1$ is $2$.",... | math | {
"ground_truth": "-10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Carolyn and Paul are playing a game starting with a list of the integers $1$ to $10$. The rules of the game are:\n\n- Carolyn always has the first turn.\n- Carolyn and Paul alter... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$, $B$, $C$, and $D$ be the vertices of a regular tetrahedron each of whose edges measures 2 meters. A bug, starting from vertex $A$, observes the following rule: at each v... | math | {
"ground_truth": "1641",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the area of the triangle (see the diagram) on graph paper. (Each side of a square is 1 unit.)",
"role": "user"
}
] | math | {
"ground_truth": "1.5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Fill integers from $1$ to $10000$ in natural order into a $100 \\times 100$ table, with each row filling from left to right: the first row is $1$ to $100$, the second row is $101... | math | {
"ground_truth": "1950",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence of monomials, where each subsequent monomial is obtained by multiplying the previous one by $2$ and increasing the exponent of $x$ by $2$, find the general formu... | math | {
"ground_truth": "2^{n}x^{2n-1}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The two asymptotes of the hyperbola $$\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1 \\quad (a > 0, b > 0)$$ divide the plane into four regions – \"up\", \"down\", \"left\", \"right\" (... | math | {
"ground_truth": "(1, \\sqrt{5})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The median of the set $\\{m, m + 2, m + 7, m + 11, m + 18\\}$ is 16. What is the mean?",
"role": "user"
}
] | math | {
"ground_truth": "16.6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(\\left(\\frac{\\sqrt{3}}{2}+\\frac{x}{2} \\mathrm{i}\\right)^{2008}=f(x)+\\mathrm{i} g(x)\\), where \\(f(x)\\) and \\(g(x)\\) are polynomials with real coefficients. Find ... | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a moving circle M, which always passes through the point F(1, 0) and is always tangent to the line $l: x = -1$.\n(1) Find the equation of the trajectory C of the center M o... | math | {
"ground_truth": "(4, 0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Every time these two wheels are spun, two numbers are selected by the pointers. Calculate the probability that the sum of the two selected numbers is even.",
"role": "user"
... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Shanille O'Keal shoots free throws on a basketball court. She hits the first and misses the second, and thereafter the probability that she hits the next shot is equal to the pro... | math | {
"ground_truth": "\\frac{1}{99}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive real numbers \\( a, b, c \\) are in a geometric progression \\((q \\neq 1)\\), and \\( \\log _{a} b, \\log _{b} c, \\log _{c} a \\) are in an arithmetic progression. Fin... | math | {
"ground_truth": "-\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given three vertices of parallelogram $PQRS$ are $P = (4, -2, 3)$, $Q = (0, 3, -5)$, and $R = (-2, 2, 3)$. Find the coordinates of $S$.",
"role": "user"
}
] | math | {
"ground_truth": "S = (2, -3, 11)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $2^{\\left(0^{\\left(1^9\\right)}\\right)}+\\left(\\left(2^0\\right)^1\\right)^9$?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each side of a rhombus contains one vertex of a square whose sides are parallel to the diagonals of the rhombus.\n\nFind the side of the square if the diagonals of the rhombus ar... | math | {
"ground_truth": "4.8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Quantities \\( p \\) and \\( q \\) vary inversely. When \\( p \\) is \\( 1500, \\) \\( q \\) is \\( 0.25. \\) Determine the value of \\( q \\) when \\( p \\) is \\( 3000. \\) Pro... | math | {
"ground_truth": "0.125",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the mean of the data $x_1, x_2, \\ldots, x_n$ is 5 and the variance is 2, let the mean of the data $7x_1-2, 7x_2-2, 7x_3-2, \\ldots, 7x_n-2$ be $\\bar{x}$, and the var... | math | {
"ground_truth": "131",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The quadratic equation \\(ax^2 + bx + c\\) has exactly one root, and the real numbers \\(a, b, c\\) form an arithmetic sequence with \\( a \\leq b \\leq c \\leq 10 \\) and \\( c ... | math | {
"ground_truth": "-\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\bigtriangleup ABC$, $AB = 75$, and $AC = 100$. A circle with center $A$ and radius $75$ intersects $\\overline{BC}$ at points $B$ and $Y$ and also intersects $\\overline... | math | {
"ground_truth": "125",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Square $PQRS$ is constructed along diameter $PQ$ of a semicircle. The semicircle and square $PQRS$ are coplanar. Line segment $PQ$ has a length of 8 centimeters. If point $N$ is ... | math | {
"ground_truth": "4\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of the function $f\\left(x\\right)=\\sin (x-\\frac{π}{6})$ is shifted to the right by $\\frac{π}{6}$ units, and then all the x-coordinates of the points are halved whil... | math | {
"ground_truth": "\\left(\\frac{π}{3}, \\frac{π}{2}\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $[A]$ denote the largest integer not exceeding $A$. Solve the equation $[(5 + 6x) / 8] = (15x - 7) / 5$.",
"role": "user"
}
] | math | {
"ground_truth": "x = \\frac{7}{15} \\text{ or } x = \\frac{4}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of the expression $( \\frac {64}{27})\\,^{ \\frac {1}{2}}+\\log _{3} \\frac {10}{9}+\\log _{3} \\frac {9}{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {8 \\sqrt {3}}{9}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest number of queens that can be placed on an $8\\times8$ chess board so that every square is either occupied or can be reached in one move, assuming a queen c... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Lisa and her father observed a train passing by a crossing, with 10 train cars passing in 15 seconds at a constant speed. The entire train passed the crossing in 3 minutes and 30... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the sum of two numbers is $4$ and their product is $-5$, then the sum of their cubes is:\nA) 131\nB) 127\nC) 124\nD) 129",
"role": "user"
}
] | math | {
"ground_truth": "C) 124",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Twelve points are spaced around at intervals of one unit around a $3 \\times 3$ square, as shown. Two of the $12$ points are chosen at random. What is the probability that the tw... | math | {
"ground_truth": "\\textbf{(C)}\\ \\frac{2}{11}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four rectangular paper strips of varying lengths and widths are arranged perpendicularly on a table as shown: two strips are 12 units long and 1 unit wide, two strips are 8 units... | math | {
"ground_truth": "B) 48 square units",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a positive integer $n$ , we say an $n$ -*shuffling* is a bijection $\\sigma: \\{1,2, \\dots , n\\} \\rightarrow \\{1,2, \\dots , n\\}$ such that there exist exactly two e... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $\\sqrt{\\left(5-3\\sqrt{3}\\right)^2} - \\sqrt{\\left(5+3\\sqrt{3}\\right)^2}$?",
"role": "user"
}
] | math | {
"ground_truth": "-6\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a_1,a_2,\\ldots,a_n$ be a permutation of the numbers $1,2,\\ldots,n$ , with $n\\geq 2$ . Determine the largest possible value of the sum \\[ S(n)=|a_2-a_1|+ |a_3-a_2| + ... | math | {
"ground_truth": "\\left\\lfloor \\frac{n^2}{2} \\right\\rfloor - 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\frac{3}{5}$ of the marbles in a bag are blue and the rest are red, if the number of red marbles is doubled and the number of blue marbles stays the same, what fract... | math | {
"ground_truth": "\\frac{4}{7}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An urn contains 9 balls, numbered from 1 to 9. José and Maria each simultaneously draw one ball from the urn. They form a two-digit number, with the number on José's ball being t... | math | {
"ground_truth": "\\frac{4}{9}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The 21st question of the 2009 Jiangsu Province college entrance examination mathematics test paper was an optional question, requiring students to choose two questions from A, B,... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A particle moves such that its position at time $t$ is given by $(t^2 + 2t + 7, 4t - 13)$. Find the speed of the particle at time $t = 3$, measured in units of distance per unit ... | math | {
"ground_truth": "\\sqrt{97}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Construct the right triangle when its hypotenuse is given and the line bisecting the right angle divides the hypotenuse in a $4:1$ ratio. Calculate the legs of the triangle.",
... | math | {
"ground_truth": "BC = \\frac{AB}{\\sqrt{17}}, \\ AC = \\frac{4AB}{\\sqrt{17}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $t$ be positive number. Draw two tangent lines to the palabola $y=x^{2}$ from the point $(t,-1).$ Denote the area of the region bounded by these tangent lines and the p... | math | {
"ground_truth": "(\\frac{6}{5})^{\\frac{3}{2}}\\sqrt[4]{5}.\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation of the tangent line to the circle \\\\(x^{2}+y^{2}-4x+2y=0\\\\) at the point \\\\(P(1,1)\\\\) is: __________.",
"role": "user"
}
] | math | {
"ground_truth": "x-2y+1=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x = 3$ and $y = 2,$ what is the value of $3 \\times x - 4 \\times y?$",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive integers less than or equal to $1000$ are 7 times the sum of their digits?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular table of size \\(14 \\times n\\) is given. A piece is initially placed in the top-left cell. Sasha and Olya take turns moving the piece one cell to the right or dow... | math | {
"ground_truth": "13, 14, 15",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "<details><summary>B stands for Bernoulli, G stands for Germain</summary>they had two problem sets under those two names</details> **B1** What is the sum of the first $5$ positi... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A regular tetrahedron $SABC$ of volume $V$ is given. The midpoints $D$ and $E$ are taken on $SA$ and $SB$ respectively and the point $F$ is taken on the edge $SC$ ... | math | {
"ground_truth": "\\frac{15}{16}V",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three speed skaters have a friendly \"race\" on a skating oval. They all start from the same point and skate in the same direction, but with different speeds that they maintain t... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the following:\n1. Given $f(α)= \\frac {2sin(π+α)cos(π-α)-cos(π+α)}{1+sin^{2}α+cos( \\frac {3π}{2}+α)-sin^{2}( \\frac {π}{2}+α)}(1+2sinα≠0)$, find the value of $f(- \\fr... | math | {
"ground_truth": "- \\frac { \\sqrt {3}+2}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( a(x+1)=x^{3}+3x^{2}+3x+1 \\), find \\( a \\) in terms of \\( x \\).\n\nIf \\( a-1=0 \\), then the value of \\( x \\) is \\( 0 \\) or \\( b \\). What is \\( b \\) ?\n\nIf \... | math | {
"ground_truth": "1000",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the expression \\(\\left[(1+x)\\left(1+2 x^{3}\\right)\\left(1+4 x^{9}\\right)\\left(1+8 x^{27}\\right)\\left(1+16 x^{81}\\right)\\left(1+32 x^{243}\\right)\\left(1+64 x^{72... | math | {
"ground_truth": "2^{30}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all primes \\( p \\) and \\( q \\) such that \\( p(p+1) + q(q+1) = n(n+1) \\) for some positive integer \\( n \\).",
"role": "user"
}
] | math | {
"ground_truth": "(3,5,6), (5,3,6), (2,2,3)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A passenger train departs at 12 noon from $A$ to $B$ at a constant speed of $60 \\, \\mathrm{km/h}$. At the same time, a freight train is traveling from $B$ to $A$ on the same tr... | math | {
"ground_truth": "9:30 \\, \\text{AM}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression\n\n$$\n\\frac{3 a^{2} + 3 a b + 3 b^{2}}{4 a + 4 b} \\cdot \\frac{2 a^{2} - 2 b^{2}}{9 a^{3} - 9 b^{3}}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of ordered pairs $(m, n)$ such that $m$ and $n$ are positive integers in the set $\\{1, 2, ..., 30\\}$ and the greatest common divisor of $2^m + 1$ and $2^n - 1$ ... | math | {
"ground_truth": "295",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are two arithmetic sequences: $2$, $6$, $10$, $\\ldots$, $190$ and $2$, $8$, $14$, $\\ldots$, $200$. A new sequence is formed by the common terms of these two sequences in ... | math | {
"ground_truth": "1472",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1. If the acute angles $α$ and $β$ satisfy $(1+ \\sqrt{3} \\tan α)(1+ \\sqrt{3} \\tan β)=4$, find the value of $α+β$.\n\n2. Given that $2 \\overset{→}{a} - \\overset{→}{b} =(-1, ... | math | {
"ground_truth": "\\text{Conclusions (3) and (4) are correct}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the constant $c$ such that the minimum value of the expression\n\\[5x^2 - 8cxy + (4c^2 + 3) y^2 - 5x - 5y + 7\\]\nover all real numbers $x$ and $y$ is 0.",
"role": ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real values of the parameter $a$ for which the system\n\\begin{align*}\n&1+\\left(4x^2-12x+9\\right)^2+2^{y+2}=a\n&\\log_3\\left(x^2-3x+\\frac{117}4\\right)+32=a+\\log... | math | {
"ground_truth": "a = 33",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Grogg takes an a × b × c rectangular block (where a, b, c are positive integers), paints\nthe outside of it purple, and cuts it into abc small 1 × 1 × 1 cubes. He then places all... | math | {
"ground_truth": "120, 160, 240, 360",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence $\\{F_n\\}$, which satisfies: $F_1 = F_2 = 1$, $F_{n+2} = F_{n+1} + F_n$ ($n \\in \\mathbb{N}^*$), and $r_n$ is the remainder when $F_n$ is divided by 3, find ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Non-negative numbers \\( x, y, z \\) satisfy the inequalities \\( 5 \\leq x, y, z \\leq 8 \\).\n\nWhat is the maximum and minimum value that the quantity \\( S = 2x^2y^2 + 2x^2z^... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an equilateral triangle with side length 10, it is divided by lines parallel to its sides into several equilateral triangles with side length 1. There are \\( m \\) equilat... | math | {
"ground_truth": "\\text{The set of all possible \\(m\\) is } \\{5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25\\}.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The numbers \\( p, q, r, \\) and \\( t \\) satisfy \\( p < q < r < t \\). When these numbers are paired, each pair has a different sum and the four largest sums are 19, 22, 25, a... | math | {
"ground_truth": "\\frac{17}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Al steps onto the start of the walkway and stands. Bob steps onto the start of the walkway two sec... | math | {
"ground_truth": "52",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the following variables: ① Smoking, ② Gender, ③ Religious Belief, ④ Nationality \nAmong these, the categorical variables are __________.",
"role": "user"
}
] | math | {
"ground_truth": "②③④",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)$ be a function such that $f(x)+2f\\left(\\frac{x+2010}{x-1}\\right)=4020 - x$ for all $x \\ne 1$ . Find the value of $f(2012)$.",
"role": "user"
}
] | math | {
"ground_truth": "2010",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of the $12$ edges of a cube is labeled $0$ or $1$. Two labelings are considered different even if one can be obtained from the other by a sequence of one or more rotations a... | math | {
"ground_truth": "B) 8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an opaque bag, there are several red, yellow, and blue glass balls that are identical except for their color. There are 6 red balls and 9 yellow balls. It is known that the pr... | math | {
"ground_truth": "\\frac{6}{25}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following system of equations:\n(1) \\(x y = (z - a)^{2}\\),\n(2) \\(y z = (x - b)^{2}\\),\n(3) \\(z x = (y - c)^{2}\\).",
"role": "user"
}
] | math | {
"ground_truth": "x = \\frac{ (b^{2}-ac )^{2} }{D}, \\quad y = \\frac{(c^{2}-ab)^{2}}{D}, \\quad z = \\frac{(a^{2}-bc)^{2} }{D }",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.