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": "The right vertex is \\(A\\), \\(P\\) is any point on the ellipse \\(C_{1}\\), and \\(\\overrightarrow{P F_{1}} \\cdot \\overrightarrow{P F_{2}}\\) attains its maximum value withi... | math | {
"ground_truth": "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": "The sequence $\\left\\{a_{n}\\right\\}$ is defined by $a_{1}=1$ and $a_{n+1}=\\sqrt{a_{n}^{2}-2a_{n}+3}+c$ for $n \\in \\mathbf{N}^{*}$, where $c$ is a constant greater than 0.\n... | math | {
"ground_truth": "(0, 1)",
"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": "It is known that the sum of two three-digit numbers, in which there are no repeating digits, equals a three-digit number with the following properties: the number of hundreds is ... | math | {
"ground_truth": "480 + 291 = 771",
"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": "Several stones are arranged in 5 piles. It is known that:\n\n- The number of stones in the fifth pile is six times the number of stones in the third pile.\n- The number of stones... | math | {
"ground_truth": "60",
"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": "In triangle $ABC$, the sides opposite angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and it is given that $\\frac{2a}{\\cos A} = \\frac{3c-2b}{\\cos B}$.\n(1) If $b = \\sqr... | math | {
"ground_truth": "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": "Given that three consecutive terms of a geometric sequence are $x$, $2x+2$, and $3x+3$, find the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "-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": "In a redesigned model, Doug constructs a square window using $8$ equal-size panes of glass, arranged in 2 rows and 4 columns. The ratio of the height to width for each pane is no... | math | {
"ground_truth": "\\textbf{(B)}\\ 27 \\text{ inches}",
"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": "The perimeter of a right triangle is 90 cm. The squares of the lengths of its sides sum up to 3362 cm². What is the area of the triangle?",
"role": "user"
}
] | math | {
"ground_truth": "180 \\, \\text{cm}^{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": "Determine the amount of water that remains in the pool after 45 days of evaporation at a rate of 1 gallon per day, starting with an initial amount of 400 gallons.",
"role": "... | math | {
"ground_truth": "355",
"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 box contains 3 red marbles, 3 green marbles, 3 yellow marbles, and 3 blue marbles. Carol takes 3 marbles from the box at random; then Claudia takes 3 marbles from the remaining... | math | {
"ground_truth": "\\frac{55}{1540}",
"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": "Find all natural numbers $n$ such that there exist $ x_1,x_2,\\ldots,x_n,y\\in\\mathbb{Z}$ where $x_1,x_2,\\ldots,x_n,y\\neq 0$ satisfying: \n\\[x_1 \\plus{} x_2 \\plus{} \... | math | {
"ground_truth": "n \\geq 2",
"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": "Let $\\mathbf{P}$ be the matrix for projecting onto the vector $\\begin{pmatrix} 3 \\\\ 1 \\\\ -4 \\end{pmatrix}$ in $\\mathbb{R}^3$. Find $\\det \\mathbf{P}$.",
"role": "use... | 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 sofa is initially priced at $450. It is offered at successive discounts of 25%, 10%, and 5%. What is the sale price of the sofa?\n**A)** $300.00 \n**B)** $325.00 \n**C)** $28... | math | {
"ground_truth": "288.56",
"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": "The children went to the forest to pick mushrooms. If Anya gives half of her mushrooms to Vitya, all the children will have the same number of mushrooms. However, if instead, Any... | math | {
"ground_truth": "6 \\;детей ⊤ children\\)",
"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 ball with diameter 5 inches starts at point A to roll along a racetrack shaped in five consecutive semicircular arcs until it reaches point B. The radii of these arcs are $R_1 ... | math | {
"ground_truth": "467.5\\pi",
"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": "Find all integer solutions to the system of equations\n\n$$\n\\left\\{\\begin{aligned}\nx+y+z & =2 \\\\\nx^{3}+y^{3}+z^{3} & =-10\n\\end{aligned}\\right.\n$$",
"role": "user"... | math | {
"ground_truth": "(3, 3, -4), (3, -4, 3), (-4, 3, 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": "For how many integers \\( n \\) is \\( \\frac{n}{15-n} \\) the square of an integer?\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5",
"role": "user"
}
] | math | {
"ground_truth": "B) 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": "Determine the area enclosed by the graph of the equation $x^2 + y^2 = 2|x| + 2|y|$.\nA) $4\\pi$\nB) $2\\pi + 8$\nC) $8$\nD) $2\\pi + 4$\nE) $2\\pi + 2\\sqrt{2}$",
"role": "us... | math | {
"ground_truth": "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": "A function is given by $f(x)=3\\sin (\\omega x+\\varphi)$. For any real number, it is always true that $f(\\frac{\\pi }{3}+x)=f(\\frac{\\pi }{3}-x)$. Let $g(x)=3\\cos (\\omega x+... | math | {
"ground_truth": "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": "Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, and let $a_{1}=-1, \\frac {a_{n+1}}{S_{n+1}}=S_{n}$. Find $S_{n}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac {1}{n}",
"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": "Given set $M=\\{2,4,6,8,10\\}$ and $N=\\{x\\left|\\right.-1 \\lt x \\lt 6\\}$, find $M\\cap N$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{2,4\\}",
"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 square dartboard is enclosed within a larger square with a side length of 4 units. The dartboard itself has been divided using the \"hour positions\" forming lines at every $45... | math | {
"ground_truth": "D) 12",
"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 $x-y=-2$ and $xy=3$, calculate the value of $x^{2}y-xy^{2}$.",
"role": "user"
}
] | 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": "Does there exist a surjective function $f:\\mathbb{R} \\rightarrow \\mathbb{R}$ for which $f(x+y)-f(x)-f(y)$ takes only 0 and 1 for values for random $x$ and $y$ ?",
"ro... | math | {
"ground_truth": "f(x) = \\begin{cases} x & \\text{if } x < 0 \\\\ x - 1 & \\text{if } x \\geq 0 \\end{cases}",
"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": "Suppose positive numbers $a$, $b$, and $c$ satisfy:\n\\begin{align*}\na^2/b &= 2, \\\\\nb^2/c &= 3, \\text{ and}\\\\\nc^2/a &= 4.\n\\end{align*}\nFind $a$.",
"role": "user"
... | math | {
"ground_truth": "576^{1/7}",
"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": "Point \\(Q\\) is on a line segment between \\(P\\) and \\(R\\). If \\(PR = 12\\) and \\(PQ = 3\\), calculate the length of \\(QR\\).",
"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": "While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in ... | math | {
"ground_truth": "8",
"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": "When further simplified and using negative exponents, what is the expression $(x + y)^{ - 2}(x^{ - 1} + y^{ - 1})^2$ equal to?\n**A)** $\\frac{x^{-2} + 2x^{-1}y^{-1} + y^{-2}}{x^... | math | {
"ground_truth": "\\frac{x^{-2} + 2x^{-1}y^{-1} + y^{-2}}{x^{2} + 2xy + y^{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": "The number of solutions in positive integers of \\( 3x + 4y = 1024 \\) is to be determined.",
"role": "user"
}
] | math | {
"ground_truth": "85",
"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 \\( P \\) be an odd prime. Consider the set \\(\\{1,2, \\cdots, 2p\\}\\) and its subset \\(A\\) satisfying the following two conditions:\n1. \\(|A|=p\\);\n2. The sum of all e... | math | {
"ground_truth": "\\frac{1}{p} \\left( \\binom{2p}{p} - 2 \\right) + 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": "Calculate the value of $5^5 + 5^5 + 5^5 + 5^5$.",
"role": "user"
}
] | math | {
"ground_truth": "5^6",
"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 the function $f(x)=e^{x}+x^{3}$, if $f(x^{2}) < f(3x-2)$, then the range of the real number $x$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "(1,2)",
"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": "Given the sets $S=\\{x|(x-1)(x-3)\\geqslant 0\\}$ and $T=\\{x|x > 0\\}$, determine the intersection $S\\cap T$.",
"role": "user"
}
] | math | {
"ground_truth": "[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": "The graph of the equation $18x + 450y = 4050$ is drawn on graph paper with each square representing one unit in each direction. How many of the $1$ by $1$ graph paper squares hav... | math | {
"ground_truth": "896",
"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": "Two circles touch internally. A line passing through the center of the larger circle intersects it at points \\( A \\) and \\( D \\), and intersects the smaller circle at points ... | 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": "Consider a rectangular block with dimensions 2 cm by 1 cm by 1 cm. A dot is marked at the center of one of the longer faces (2 cm by 1 cm), and the block is resting with another ... | math | {
"ground_truth": "k = 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": "Randomly select a number for $a$ from the set $\\{1,2,3,4,5\\}$, and randomly select a number for $b$ from the set $\\{1,2,3\\}$. Calculate the probability that $b > a$.",
"r... | math | {
"ground_truth": "\\frac{1}{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": "Vasya and Petya, who are participating in a school sports-entertainment game, need to cover a distance of 3 km as quickly as possible, having only one pair of roller skates betwe... | math | {
"ground_truth": "0.5 \\ \\text{hours}",
"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": "In rectangle ABCD, AB=30 and BC=15. Let F be a point on AB such that ∠BCF=30°. Find CF.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"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 a regular tetrahedron positioned in 3-space, the vertices are $(0, 0, 0)$, $(1, 0, 0)$, $(0, 1, 0)$, and $(0, 0, 1)$. The centers of the four faces form a smaller tetrahedron.... | math | {
"ground_truth": "m+n = 29",
"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": "Our school's girls volleyball team has 16 players, including a set of 4 quadruplets: Amy, Beth, Ciara, and Dana. In how many ways can we choose 7 starters if the only restriction... | math | {
"ground_truth": "11220",
"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 Emily rides her bicycle at a constant rate of 12 miles per hour and Emerson skates at a constant rate of 8 miles per hour, and the initial distance between Emily and E... | math | {
"ground_truth": "15",
"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 that $S_{n}$ is the sum of the first $n$ terms of the sequence $\\{a_{n}\\}$, $a_{1}=1$, and $2S_{n}=(n+1)a_{n}$, if there exists a unique positive integer $n$ such that th... | math | {
"ground_truth": "-2 < t\\leqslant -1 \\text{ or } \\dfrac {1}{2}\\leqslant t < 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": "Our club has 24 members, consisting of 14 boys and 10 girls, who are also part of two teams, Team A and Team B. Team A consists of 8 boys and 6 girls, and Team B consists of 6 bo... | math | {
"ground_truth": "136",
"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": "Ms. Hamilton now coaches two eighth-grade classes and both classes want to participate together in a similar annual three-person-team basketball tournament. This year, thirty-two... | math | {
"ground_truth": "31",
"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 regular hexagon $ABCDEF$ has a perimeter of $1$, calculate the perimeter of the six-pointed star formed by extending each side of the hexagon to meet the extension... | math | {
"ground_truth": "4",
"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": "After $\\frac{1}{3}$ of the water is removed, the remaining water is $\\frac{2}{3}$ of the original amount.",
"role": "user"
}
] | math | {
"ground_truth": "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": "A square grid of 16 dots contains the corners of nine \\( 1 \\times 1 \\) squares, four \\( 2 \\times 2 \\) squares, and one \\( 3 \\times 3 \\) square, for a total of 14 squares... | math | {
"ground_truth": "4",
"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 rectangular table with dimensions 9' by 12' sits in the corner of a square room. The owners plan to move the table to another position in the room as depicted in a similar scen... | math | {
"ground_truth": "B) 15",
"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": "What is the greatest integer less than 50 for which the greatest common divisor of that integer and 18 is 6?",
"role": "user"
}
] | math | {
"ground_truth": "42",
"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": "On the side \\(AB\\) of an equilateral triangle \\(\\mathrm{ABC}\\), a right triangle \\(\\mathrm{AHB}\\) is constructed (\\(\\mathrm{H}\\) is the vertex of the right angle) such... | math | {
"ground_truth": "15^\\circ",
"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": "Alexie and Baptiste each own a building. Each floor of Alexie's building has 3 bathrooms and 2 bedrooms. Each floor of Baptiste's building has 4 bathrooms and 3 bedrooms. There a... | math | {
"ground_truth": "3 \\text{ et } 4",
"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": "Five horizontal lines and five vertical lines are drawn in a plane. In how many ways can four lines be chosen such that a rectangular region is enclosed?",
"role": "user"
}... | math | {
"ground_truth": "100",
"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 expression $(x^2 - 3xy + 2y^2)^7$, find the sum of the numerical coefficients in the complete expansion of this expression.",
"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": "At Math Master School, to pass a geometry test you must score at least $75\\%$. If there are 50 problems on the test, what is the greatest number you can miss and still pass?",
... | math | {
"ground_truth": "12",
"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 an arithmetic sequence $\\{a_n\\}$ whose sum of the first $n$ terms is $S_n$, and a non-constant geometric sequence $\\{b_n\\}$ with a common ratio of $q$, satisfying: $a_1... | math | {
"ground_truth": "\\left(\\frac{1}{3}, +\\infty\\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": "Determine the value of the product $\\left(1-\\frac{1}{3^{2}}\\right)\\left(1-\\frac{1}{4^{2}}\\right)...\\left(1-\\frac{1}{12^{2}}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{18}",
"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": "Find all positive functions defined on \\((0,+\\infty)\\) that satisfy\n\\[ a b \\leqslant \\frac{1}{2}\\left\\{a f(a)+b f^{-1}(b)\\right\\} \\]\nwhere \\(a, b \\in (0,+\\infty)\... | math | {
"ground_truth": "f(x) = Cx, \\quad \\text{where} \\ C > 0 \\ \\text{is a constant}",
"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": "In triangle $ABC$, the medians $\\overline{AD}$ and $\\overline{CE}$ have lengths $15$ and $24$, respectively, and $AB=30$. Extend $\\overline{AD}$ to intersect the circumcircle ... | math | {
"ground_truth": "30\\sqrt{21}",
"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 $ABCDEFGHIJ$ be a regular $10$ -sided polygon that has all its vertices in one circle with center $O$ and radius $5$ . The diagonals $AD$ and $BE$ intersect at $P$... | math | {
"ground_truth": "PQ = 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": "Given that $\\log_{10}\\sin x + \\log_{10}\\cos x = -1$ and $\\log_{10}(\\sin x+\\cos x)=\\frac{1}{2}(\\log_{10}n-2)$, find $n$.",
"role": "user"
}
] | math | {
"ground_truth": "120",
"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": "Ike and Mike visit a café with $40 to spend. Sandwiches cost $5 each and soft drinks cost $1.25 each. They plan to buy at least 2 soft drinks, spending the rest on as many sandwi... | math | {
"ground_truth": "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": "The graph of the linear function $y=kx+2$ intersects the $x$-axis at a point that is $2$ units away from the origin. The value of $k$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
... | math | {
"ground_truth": "\\pm1",
"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 $\\#$ be the relation defined by $A \\# B = A^2 + B^2$. If $A \\# 7 = 194$, what is the positive value of A?",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{145}",
"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 $S = \\{1, \\cdots, 6\\}$ and $\\mathcal{P}$ be the set of all nonempty subsets of $S$ . Let $N$ equal the number of functions $f:\\mathcal P \\to S$ such that if $... | math | {
"ground_truth": "13872",
"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 product of $\\sqrt[5]{16}$ and $\\sqrt[6]{64}$ equals?\nA) $2\\sqrt[11]{16}$\nB) $2\\sqrt[5]{16}$\nC) $\\sqrt[5]{64}$\nD) $2\\sqrt[5]{64}$\nE) $\\sqrt[11]{32}$",
"role": ... | math | {
"ground_truth": "\\textbf{(B) } 2\\sqrt[5]{16}",
"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": "The base of a prism is a square with a side length of \\( a \\). One of the lateral faces is also a square, and another is a rhombus with an angle of \\( 60^{\\circ} \\). Determi... | math | {
"ground_truth": "a^2 (4 + \\sqrt{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": "Assume that x is a positive real number. Simplify the expression \\( \\sqrt[5]{x\\sqrt[4]{x}} \\).",
"role": "user"
}
] | math | {
"ground_truth": "x^{1/4}",
"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 $S$ be the set of the reciprocals of the first $2016$ positive integers and $T$ the set of all subsets of $S$ that form arithmetic progressions. What is the largest p... | math | {
"ground_truth": "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": "Masha tightly packed 165 identical balls into a regular triangular pyramid. How many balls are in the base?",
"role": "user"
}
] | math | {
"ground_truth": "45",
"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": "Evaluate the expression $\\frac{1-\\frac{1}{4}}{1-\\frac{1}{3}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{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": "The expression $\\frac{x^2 - 4}{4x - 8}$ is equal to zero for what value of $x$?",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"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 \\( f(x)=3^{x}+3x-8 \\). Use the bisection method to find an approximate solution of the equation \\( 3^{x}+3x-8=0 \\) in the interval \\( x∈(1,2) \\). During the process, it... | math | {
"ground_truth": "(1.25,1.5)",
"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": "A triangle has vertices at coordinates (1,3), (7,9), and (8,3). What is the number of units in the length of the longest side of the triangle?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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 if it is at least $75^{\\circ} F$ and sunny, and the wind speed is less than 10 mph, then the beach will be crowded, determine the weather conditions that could exist ... | math | {
"ground_truth": "\\textbf{(B)}\\ \\text{The temperature was cooler than } 75^{\\circ} \\text{F or it was not sunny or the wind was at least 10 mph.}",
"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": "The positions of cyclists in the race are determined by the total time across all stages: the first place goes to the cyclist with the shortest total time, and the last place goe... | math | {
"ground_truth": "91",
"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 that $\\frac{y}{x-z}=\\frac{x+y}{z}=\\frac{x}{y}$ for three positive numbers $x,y$ and $z$, all different, find the value of $\\frac{x}{y}$.",
"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": "Given a trapezoid with side lengths 3, 5, 7, and 11, determine the sum of all the possible areas of the trapezoid.",
"role": "user"
}
] | math | {
"ground_truth": "63",
"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": "The triangles are formed by midpoints of the previous triangle's sides, with the first three iterations shown. If the dividing and shading process is done 100 times, with AC=CG=6... | math | {
"ground_truth": "6",
"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 that $\\log _{2}(x+y)=\\log _{2} x+\\log _{2} y$, determine the range of values for $x + y$.",
"role": "user"
}
] | math | {
"ground_truth": "[4, \\infty)",
"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": "What is the value of the sum $S=\\sum_{k=0}^{74}(-1)^k\\binom{149}{2k}=\\binom{149}{0}-\\binom{149}{2}+\\binom{149}{4}-\\cdots -\\binom{149}{148}$?",
"role": "user"
}
] | math | {
"ground_truth": "-2^{74}",
"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 slope of the tangent line to the curve at $x = 1$ for the equation $2x^2 + 4x + 6y = 24$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{4}{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": "Positive integers $a$, $b$, and $c$ are such that $a \\leq 7$, $b \\leq 6$, and $c \\leq 4$. What is the largest possible value for $2ac - abc$?\nA) 12\nB) 24 \nC) 28\nD) 32\nE) ... | math | {
"ground_truth": "C) 28",
"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 $S$ be the set of all real numbers $x$ such that $0 \\le x \\le 2016 \\pi$ and $\\sin x < 3 \\sin(x/3)$ . The set $S$ is the union of a finite number of disjoint in... | math | {
"ground_truth": "1008\\pi",
"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": "Let $n$ be a positive integer. We call a $n$ -tuple $(a_1, . . . , a_n)$ of positive integers *nice* if $\\bullet$ $gcd (a_1, . . . , a_n) = 1$ , and $\\bullet$ $a_i|a_{... | math | {
"ground_truth": "F_{n+2} - 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate:<br/>$(1)-1^{2023}+(2023-π)^{0}+(-\\frac{1}{2})^{-2}$;<br/>$(2)(-\\frac{1}{2}xy)^{3}•2x(2{x}^{3}{y}^{2})÷(x{y}^{2})^{2}$;<br/>$(3)\\left(x-y\\right)\\left(x+y\\right)(x... | math | {
"ground_truth": "20x + 8y",
"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 least positive multiple of 75 for which the product of its digits is also a positive multiple of 75?",
"role": "user"
}
] | math | {
"ground_truth": "75375",
"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 equation $\\frac{{x}^{2}}{9-k}+\\frac{{y}^{2}}{k-1}=1$ represents an ellipse with its foci on the $y$-axis, then the range of values for the real number $k$ is .",... | math | {
"ground_truth": "(5,9)",
"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": "In the unit cube \\( A B C D - A' B' C' D' \\), place an inscribed sphere \\( O \\). Then, place a small sphere at each of the eight corners of the cube such that each small sphe... | math | {
"ground_truth": "\\frac{1}{2}(2 \\sqrt{3} - 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": "For positive integers $n$, let $h(n)$ return the smallest positive integer $k$ such that $\\frac{1}{k}$ has exactly $n$ digits after the decimal point, and $k$ is divisible by 3.... | math | {
"ground_truth": "4022",
"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": "It is known that on Monday, the painter painted half as fast as he did on Tuesday, Wednesday, and Thursday, while on Friday, he painted twice as fast as on these three days but w... | math | {
"ground_truth": "1500",
"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 \\( n \\) is a positive integer, the function \\( f \\) satisfies\n\\[ f(n+3) = \\frac{f(n) - 1}{f(n) + 1}, \\]\nwith \\( f(1) \\neq 0 \\), and \\( f(1) \\neq \\pm 1 \\).\n\... | math | {
"ground_truth": "-1",
"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": "How many four-digit numbers greater than 4999 can be formed such that the product of the middle two digits is an odd number?",
"role": "user"
}
] | math | {
"ground_truth": "1250",
"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": "When a polynomial is divided by \\(3x^2 - 7x + 5\\), what are the possible degrees of the remainder? Enter all possible values, separated by commas.",
"role": "user"
}
] | math | {
"ground_truth": "0, 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": "The trinomial $f(x)$ is such that $(f(x))^3-f(x)=0$ has three real roots. Find the y-coordinate of the vertex of $f(x)$ .",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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 geometric sequence $\\{a_n\\}$, $S_3 = \\frac{13}{9}$, $S_6 = \\frac{364}{9}$, find $a_n$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{6} \\cdot 3^{n-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": "Let $a, b, c$ be the side lengths of an non-degenerate triangle with $a \\le b \\le c$ . With $t (a, b, c)$ denote the minimum of the quotients $\\frac{b}{a}$ and $\\fra... | math | {
"ground_truth": "\\left[1, \\frac{1 + \\sqrt{5}}{2}\\right)",
"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 configuration of $4027$ points in the plane is called Colombian if it consists of $2013$ red points and $2014$ blue points, and no three of the points of the configuratio... | math | {
"ground_truth": "2013",
"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": "Alice's age is 20 more than the sum of Ben's age and Cindy's age. Additionally, the square of Alice's age is 2050 more than the square of the sum of Ben's and Cindy's age. Determ... | math | {
"ground_truth": "80",
"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 any two numbers \\( x \\) and \\( y \\), the operation \"*\" is defined as:\n\\[ x * y = \\frac{4 \\times x \\times y}{m \\times x + 3 \\times y} \\]\n(where \\( m \\) is a c... | math | {
"ground_truth": "m=2 \\quad 3 * 12 = \\frac{24}{7}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
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