data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Ollie the Otter and Dana the Deer are climbing a staircase with a certain number of steps. Ollie jumps three steps at a time, and Dana jumps four steps at a time. However, if few... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 the arithmetic sequence $\\{{a_{n}}\\}$, ${a_{2}=9, a_{5}=33}$. Determine the common difference of the sequence $\\{{a_{n}}\\}$.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 diagram shows four identical white triangles symmetrically placed on a grey square. Each triangle is isosceles and right-angled. The total area of the visible grey regions is... | math | {
"ground_truth": "15^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $a$ is a real number such that $3a + 6$ is the greatest integer less than or equal to $a$ and $4a + 9$ is the least integer greater than or equal to $a$ . Comput... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x, y, z, w$ are nonnegative real numbers satisfying \\[\\left\\{ \\begin{array}{l}y = x - 2003 z = 2y - 2003 w = 3z - 2003 \n \\end{array} \\right.\n\\] find the small... | math | {
"ground_truth": "x = \\frac{10015}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $ABCD$ be a parallelogram such that $\\angle BAD = 60^{\\circ}.$ Let $K$ and $L$ be the midpoints of $BC$ and $CD,$ respectively. Assuming that $ABKL$ is a cycl... | math | {
"ground_truth": "75^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 intersection of the sets $A=\\{1,2, \\frac{1}{2}\\}$ and $B=\\{y \\mid y=x^{2}, x \\in A\\}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left\\{ 1 \\right\\}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A scalene triangle has side lengths which are consecutive odd prime numbers, and the perimeter of the triangle is also a prime number. What is the smallest possible perimeter of ... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 ways can the integers from -7 to 7 be arranged in a sequence such that the absolute value of the numbers in the sequence is nondecreasing?",
"role": "user"
}
] | math | {
"ground_truth": "128",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $|x+1|$ and $|y+2x|$ are opposites of each other, then $(x+y)^{2004}=$ .",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 integers 234 and 78 are expressed in base 4 and added. What is the resulting sum, expressed in base 4?",
"role": "user"
}
] | math | {
"ground_truth": "13020",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Patrick drives from $\\mathrm{P}$ to $\\mathrm{Q}$ at an average speed of $40 \\mathrm{mph}$. His drive back from $\\mathrm{Q}$ to $\\mathrm{P}$ is at an average speed of $45 \\m... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the polynomials $ f(x)$ having the following properties:\r\n\r\n(i) $ f(0) \\equal{} 1$ , $ f'(0) \\equal{} f''(0) \\equal{} \\cdots \\equal{} f^{(n)}(0) \\equal{} 0$ \r... | math | {
"ground_truth": "f(x) = x^n G(x) + x^n h(x) (x-1)^m + 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 smallest four-digit positive integer that is divisible by 37?",
"role": "user"
}
] | math | {
"ground_truth": "1036",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 permutation $a_1,a_2,\\cdots ,a_6$ of numbers $1,2,\\cdots ,6$ can be transformed to $1,2,\\cdots,6$ by transposing two numbers exactly four times. Find the number of suc... | math | {
"ground_truth": "360",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $|\\vec{a}|=2$, $\\vec{b}$ is a unit vector, and the angle between $\\vec{a}$ and $\\vec{b}$ is $60^{\\circ}$, then $\\vec{a}\\cdot(\\vec{a}-\\vec{b})$ equals \\_\\_\\... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the largest natural number $ n$ for which there exist different sets $ S_1,S_2,\\ldots,S_n$ such that:\r\n\r $ 1^\\circ$ $ |S_i\\cup S_j|\\leq 2004$ for each two $ 1... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define an even function $f(x)$ on **R** that satisfies: for any $x_1$, $x_2 \\in (-\\infty, 0)$ ($x_1 \\neq x_2$), it holds that $f(x_1) > f(x_2)$. Then, arrange $f(-2)$, $f(1)$,... | math | {
"ground_truth": "f(3) < f(-2) < f(1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "List the properties of a rhombus known to you. Among the listed properties, find groups of properties sufficient to define a rhombus.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{1 and 2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three geometric sequences have their first terms forming a geometric sequence with a common ratio of \\( q_3 = 2 \\). The common ratios of the three geometric sequences form an a... | math | {
"ground_truth": "1, 2, 4, \\dots; 2, 6, 18, \\dots; 4, 16, 64, \\dots; \\frac{192}{31}, -\\frac{168}{31}, \\frac{147}{31}, \\dots; \\frac{384}{31}, \\frac{48}{31}, \\frac{6}{31}, \\dots; \\frac{768}{31}, \\frac{684}{31}, \\frac{972}{31}, \\dots.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the radius of the inscribed circle of triangle \\( \\triangle ABC \\) is 2 and \\(\\tan A = -\\frac{4}{3}\\), find the minimum value of the area of triangle \\( \\tria... | math | {
"ground_truth": "18 + 8 \\sqrt{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are two tightly fitting transmission rollers. Each roller has a line passing through its center as a marker.\n\nThe radius of the driving roller is 105 cm, and the radius o... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At the beginning of the school year, $40\\%$ of all students in Ms. Lee's class answered \"Yes\" to the question \"Do you love science\", and $60\\%$ answered \"No.\" At the end ... | math | {
"ground_truth": "20\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 number $x$ is chosen at random from the set $\\{1,2,3,\\cdots,12\\}$, and then $y$ is chosen at random from the same set. The probability that the integer $4^x+5^y$ has units d... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 the quotient of the division \\((5z^4 - 3z^3 + 4z^2 - 8z + 3)/(z^2 + 2z + 1)\\).",
"role": "user"
}
] | math | {
"ground_truth": "5z^2 - 13z + 21",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $(3x + 25) + (150x - 5) + x^2$.",
"role": "user"
}
] | math | {
"ground_truth": "x^2 + 153x + 20",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 $ABCD$ be a convex quadrilateral with $AB=AD, m\\angle A = 40^{\\circ}, m\\angle C = 130^{\\circ},$ and $m\\angle ADC - m\\angle ABC = 20^{\\circ}.$ Find the measure of... | math | {
"ground_truth": "35^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 the function \\( f(x) = \\log_a x \\) where \\( a > 0 \\) and \\( a \\neq 1 \\). If \\( f(x_1 x_2 \\cdots x_{2003}) = 8 \\), determine the value of \\( f(x_1^2) + f(x_2^2) + ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the sequence $\\{a_n\\}$ satisfy: $a_1=5$, $a_{n+1}+4a_n=5$ $(n\\in\\mathbb{N}^*)$. \n(1) Is there a real number $t$ such that $\\{a_n+t\\}$ is a geometric sequence? \n(2) ... | math | {
"ground_truth": "\\dfrac{4^{2014}-1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\\heartsuit$ and $\\diamondsuit$, called `hearts' and `diamonds') are r... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 inequality $\\frac{1}{\\sqrt{20 a+23 b}}+\\frac{1}{\\sqrt{23 a+20 b}} \\geqslant \\frac{\\lambda}{\\sqrt{a+b}}$ holds for all positive real numbers $a, b$, find the maximu... | math | {
"ground_truth": "\\frac{2}{\\sqrt{43}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a round-robin tournament with 6 teams, each team plays one game against each other team, and each game results in one team winning and one team losing. Determine the maximum n... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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 eight cubes with volumes \\(1, 8, 27, 64, 125, 216, 343,\\) and \\(512\\) cubic units, and each cube having its volume decreasing upwards, determine the overall external su... | math | {
"ground_truth": "1021",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 function \\( y = f(t) \\) is such that the sum of the roots of the equation \\( f(\\sin x) = 0 \\) in the interval \\([3 \\pi / 2, 2 \\pi]\\) is \\( 33 \\pi \\), and the sum ... | math | {
"ground_truth": "17 \\pi",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How much money should I invest at an annually compounded interest rate of \\(7\\%\\) so that I have \\(\\$600,000\\) in fifteen years? Express your answer as a dollar value round... | math | {
"ground_truth": "\\$217,474.41",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are several red, yellow, and blue balls in a pocket. The probability of drawing a red ball is $0.45$, and the probability of drawing a red or yellow ball is $0.65$. What is... | math | {
"ground_truth": "0.80",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $x , y$ which are roots of the equation \r\n\r\n $2 x^y-y= 2005$ \r\n<u>Babis</u>",
"role": "... | math | {
"ground_truth": "(x, y) = (1003, 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 triangle $ABC,$ $AB = 7,$ $BC = 8,$ and $AC = 9.$ If $D$ and $E$ are chosen on $\\overline{AB}$ and $\\overline{AC}$ so that $AD = 3$ and $AE = 6,$ then find the area of trian... | math | {
"ground_truth": "\\frac{24\\sqrt{5}}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**p1.** Triangle $ABC$ has side lengths $AB = 3^2$ and $BC = 4^2$ . Given that $\\angle ABC$ is a right angle, determine the length of $AC$ .**p2.** Suppose $m$ and $n... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\[\n\\left\\{\n\\begin{array}{l}\n3^{1+2 \\log _{3}(y-x)}=48, \\\\\n2 \\log _{5}(2 y-x-12)-\\log _{5}(y-x)=\\log _{5}(y+x) .\n\\end{array}\n\\right.\n\\]",
"role": "user"
... | math | {
"ground_truth": "(16, 20)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathcal{F}$ be the set of all functions $f : (0,\\infty)\\to (0,\\infty)$ such that $f(3x) \\geq f( f(2x) )+x$ for all $x$ . Find the largest $A$ such that $f(x)... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 number of terms in the expansion of $[(a+3b)^{2}(a-3b)^{2}]^{2}$ when simplified is to be determined.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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 equation \\[(x^{2}-7)^{2}=25,\\] determine the number of different real numbers $x$ that satisfy the equation.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 values of \\( a \\) satisfy that the line \\( y = 3x + a \\) passes through the vertex of the parabola \\( y = x^3 + 3a^2 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow 0} \\frac{3^{5 x}-2^{x}}{x-\\sin 9 x}$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{8} \\ln \\frac{2}{243}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For $k\\ge 1$ , define $a_k=2^k$ . Let $$ S=\\sum_{k=1}^{\\infty}\\cos^{-1}\\left(\\frac{2a_k^2-6a_k+5}{\\sqrt{(a_k^2-4a_k+5)(4a_k^2-8a_k+5)}}\\right). $$ Compute $\\lfloo... | math | {
"ground_truth": "157",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Chuck and Huck were decorating the Christmas tree. To prevent them from arguing, their mom allocated the same number of branches and the same number of ornaments to each of them.... | math | {
"ground_truth": "\\text{The number of branches is 3 and the number of toys is 4.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all sequences of integer $x_1,x_2,..,x_n,...$ such that $ij$ divides $x_i+x_j$ for any distinct positive integer $i$ , $j$ .",
"role": "user"
}
] | math | {
"ground_truth": "x_i = 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 universal set $U=\\mathbb{R}$, the set $M=\\{x\\mid x^2 - 2x < 0\\}$, and $N=\\{x\\mid x \\geq 1\\}$, find the intersection of set $M$ and the complement of $N$ in $U$,... | math | {
"ground_truth": "D: \\{x \\mid 0 < x < 1\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 range of the function $\\mathrm{y}=\\frac{1}{2} \\sin 2 \\mathrm{x} \\tan \\mathrm{x}+2 \\sin \\mathrm{x} \\tan \\frac{\\mathrm{x}}{2}$ is $\\qquad$",
"role": "user"
}
... | math | {
"ground_truth": "[0, 3) \\cup (3, 4)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The solution to the equation $x^{2}=2x$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "x_{1} = 0, x_{2} = 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 \\(3 \\sin ^{3} x + \\cos ^{3} x = 3\\), what is the value of \\(\\sin ^{2018} x + \\cos ^{2018} x\\)?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow \\pi} \\frac{\\operatorname{tg}\\left(3^{\\pi / x}-3\\right)}{3^{\\cos (3 x / 2)}-1}$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-2}{\\pi}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A large ice cream cone has a radius of 2 inches and a height of 8 inches. What is the radius of a sphere of ice cream which has twice the volume of this cone?",
"role": "user... | math | {
"ground_truth": "2^{4/3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$2$ darts are thrown randomly at a circular board with center $O$ , such that each dart has an equal probability of hitting any point on the board. The points at which they lan... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $N$ of three positive integers is $6$ times their sum, and one of the integers is the sum of the other two. Find the sum of all possible values of $N.$",
"ro... | math | {
"ground_truth": "232128000",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the perimeter of an equilateral triangle $ABC$ is $24$ inches, calculate the altitude of the triangle.",
"role": "user"
}
] | math | {
"ground_truth": "4\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\[\n\\begin{cases}\nx + y = 10 \\\\\n\\frac{xy}{x^2} = -\\frac{3}{2}\n\\end{cases}\n\\]\n\n\\[\n\\begin{cases}\nx + y = 10 \\\\\n\\frac{x}{y} = 2 \\frac{1}{3}\n\\end{cases}\n\\]... | math | {
"ground_truth": "7, 3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function \\( g(x) \\) satisfies\n\\[ g(x - y) = g(x) g(y) \\]\nfor all real numbers \\( x \\) and \\( y \\), and \\( g(x) \\neq 0 \\) for all real numbers \\( x \\). Assume f... | math | {
"ground_truth": "e^5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the arithmetic sequence $\\{a_n\\}$, it is known that $a_1+a_3+a_5=9$, and $a_3 \\cdot a_4^2=27$. Find $a_{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "-39 \\text{ or } 30",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 month with $31$ days has the same number of Sundays and Tuesdays. How many of the seven days of the week could be the first day of this month?\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5",
... | math | {
"ground_truth": "\\textbf{(C)}\\ 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 group of $6$ friends are to be seated in the back row of an otherwise empty movie theater with $8$ seats in a row. Euler and Gauss are best friends and must sit next to eac... | math | {
"ground_truth": "3360",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 expression given by $$2 + \\cfrac{3}{4 + \\cfrac{5}{6 + \\frac{7}{8}}}.$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{137}{52}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "During a mathematics competition preparation period, John aims to score a perfect \"100\" on at least $85\\%$ of his $40$ practice tests. He has scored a \"100\" on $30$ of the f... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the greatest integer of $\\pi - 5$, expressed as $[\\pi - 5]$.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 permutation $(a_1, a_2, a_3, \\dots, a_{100})$ of $(1, 2, 3, \\dots, 100)$ is chosen at random. Denote by $p$ the probability that $a_{2i} > a_{2i - 1}$ for all $i \\i... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "No math tournament exam is complete without a self referencing question. What is the product of\nthe smallest prime factor of the number of words in this problem times the larges... | math | {
"ground_truth": "1681",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 the plane region determined by the inequality ${{x}^{2}}+{{y}^{2}}\\leqslant 4$ be $U$, and the plane region determined by $\\left| x \\right|+\\left| y \\right|\\leqslant 1$... | math | {
"ground_truth": "m=243, n=125",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 first digit (from left to right) of the base $9$ representation of $1024_{10}$?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 triples \\((a, b, n)\\) of positive integers such that \\(a\\) and \\(b\\) are both divisors of \\(n\\), and \\(a + b = \\frac{n}{2}\\).",
"role": "user"
}
] | math | {
"ground_truth": "(k, 2k, 6k), (2k, k, 6k), (k, k, 4k)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all triples of real numbers $(a, b, c)$ satisfying $$ a+b+c=14, \\quad a^2+b^2+c^2=84,\\quad a^3+b^3+c^3=584. $$",
"role": "user"
}
] | math | {
"ground_truth": "(4, 2, 8), (2, 4, 8), (8, 2, 4)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 functions \\( f \\) and \\( g \\) be defined such that \\( g(x) = 2f(200-x) \\) and the graph of \\( g \\) contains the vertex of \\( f \\). Assume the four \\( x \\)-interce... | math | {
"ground_truth": "D) \\( 600 \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a $12 \\times 12 \\times 12$ cube, which is constructed from sixty-four $3 \\times 3 \\times 3$ smaller cubes. In a new design, we remove the centre cube from each face ... | math | {
"ground_truth": "B) 3408 square units",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 the Cartesian coordinate system \\(xOy\\), given two points \\(M(-1,2)\\) and \\(N(1,4)\\), point \\(P\\) moves along the \\(x\\)-axis. When \\(\\angle MPN\\) reaches its maxi... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square with sides 8 inches is shown. If $Q$ is a point such that the segments $\\overline{QA}$, $\\overline{QB}$, and $\\overline{QC}$ are equal in length, and segment $\\overl... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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_1, a_2\\), and \\(a_3\\) be nonzero complex numbers with nonnegative real and imaginary parts. Find the minimum possible value of\n$$\n\\frac{\\left|a_1 + a_2 + a_3\\rig... | math | {
"ground_truth": "\\sqrt{3} \\sqrt[3]{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$, $b$, and $c$ be solutions of the equation $x^3 - 6x^2 + 11x = 12$.\n\nCompute $\\frac{ab}{c} + \\frac{bc}{a} + \\frac{ca}{b}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{23}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In how many ways can you pay 78 rubles, using tickets with denominations of 3 rubles and 5 rubles?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bag contains four balls of the same shape and size, numbered $1$, $2$, $3$, and $4$.\n$(1)$ Two balls are randomly drawn from the bag. Find the probability that the sum of the ... | math | {
"ground_truth": "\\frac{13}{16}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 triangle with side lengths $12$, $30$, and $x$, determine how many integers $x$ satisfy the condition that the triangle has one right angle.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 set of $n$ numbers has the sum $s$. Each number in the set is first increased by $15$, then multiplied by $3$, decreased by $10$, and finally divided by $2$. Find the sum of th... | math | {
"ground_truth": "\\frac{3s}{2} + \\frac{35n}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 that $a_n = \\dfrac{(n+9)!}{(n-1)!}$, find the smallest positive integer $k$ for which the rightmost nonzero digit of $a_k$ is odd.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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 angle formed by the hands of a clock at 2:15 is: Calculate the angle formed by the hands of a clock at 2:15.",
"role": "user"
}
] | math | {
"ground_truth": "22.5",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Convert the quadratic equation $2x^{2}=3x-1$ into general form and calculate the coefficient of the linear term.",
"role": "user"
}
] | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two railway tracks intersect at a right angle. Two trains are simultaneously speeding towards the intersection point from different tracks: one from a station located 40 km from ... | math | {
"ground_truth": "16 \\text{ km}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Susan has scored 87, 90, 95, 98, and 100 in her five math assignments. What is the arithmetic mean of these scores?",
"role": "user"
}
] | math | {
"ground_truth": "94",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 $n \\in \\{-2, -1, 0, 1, 2, 3\\}$, if $$(- \\frac {1}{2})^{n} > (- \\frac {1}{5})^{n}$$, then $n = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "-1 \\text{ or } 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 child's wading pool contains 200 gallons of water. Water evaporates at the rate of 0.5 gallons per day and no other water is added or removed. Determine the amount of water in ... | math | {
"ground_truth": "185",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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,b,c,d$ be positive integers such that the number of pairs $(x,y) \\in (0,1)^2$ such that both $ax+by$ and $cx+dy$ are integers is equal with 2004. If $\\gcd (a,c)... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alexio has 120 cards numbered 1-120, inclusive, and places them in a box. Alexio then chooses a card from the box at random. What is the probability that the number on the card h... | math | {
"ground_truth": "\\frac{11}{15}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 radii of five circles, calculate the points $(C,A)$ where $C$ represents the circumference and $A$ represents the area, multiplied by a factor of $2$, for each circle."... | math | {
"ground_truth": "\\{(2\\pi, 2\\pi), (6\\pi, 18\\pi), (10\\pi, 50\\pi), (14\\pi, 98\\pi), (18\\pi, 162\\pi)\\}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 a line \\( l \\) passing through point \\( P(0,1) \\) with slope \\( k \\), it intersects the hyperbola \\( C: x^{2}-\\frac{y^{2}}{3}=1 \\) at points \\( A \\) and \\( B \\... | math | {
"ground_truth": "1 \\text{ or } -1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\log_2(a) + \\log_2(b) + \\log_2(c) \\geq 9$, determine the minimum possible value of $a + b + c$ where $a, b, c$ are positive real numbers.",
"role": "user"
}... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 sequence of positive integers starts with one 1, followed by two 2's, three 3's, and so on. (Each positive integer \\( n \\) occurs \\( n \\) times.) How many of the first 105 ... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\sin^{2}\\left(\\frac{x}{2}+\\frac{\\pi}{12}\\right)+\\sqrt{3}\\sin\\left(\\frac{x}{2}+\\frac{\\pi}{12}\\right)\\cos\\left(\\frac{x}{2}+\\frac{\\pi}{12}... | math | {
"ground_truth": "(2n^{2}-n)\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It is given a 1001*1001 board divided in 1*1 squares. We want to amrk m squares in such a way that:\r\n1: if 2 squares are adjacent then one of them is marked.\r\n2: if 6 squares... | math | {
"ground_truth": "601200",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all integers $n$ for which there exist an integer $k\\geq 2$ and positive integers $x_1,x_2,\\hdots,x_k$ so that $$ x_1x_2+x_2x_3+\\hdots+x_{k-1}x_k=n\\text{ and... | math | {
"ground_truth": "[2018, 1009 \\cdot 1010]",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $a$, $b$, $c$, and $d$ be positive integers with $a < 3b$, $b < 2c$, and $c < 5d$. If $d < 150$, calculate the largest possible value for $a$.",
"role": "user"
}
] | math | {
"ground_truth": "4460",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three positive integers greater than 1000 satisfy the condition that the unit digit of the sum of any two of them is equal to the unit digit of the third number. What are the pos... | math | {
"ground_truth": "000, 250, 500, 750",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"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 coefficient of \\(x^3\\) in the expansion of \\((3x+2)^8\\)?",
"role": "user"
}
] | math | {
"ground_truth": "48384",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
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