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": "A motorcycle and an ATV are traveling on a circular road, a quarter of which goes through a forest, while the remaining part goes through a field. The speed of the motorcycle is ... | math | {
"ground_truth": "\"After \\(11th\\) lap\"",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a regular triangular prism $ABC-A_{1}B_{1}C_{1}$ with a height of 2 and a base edge length of 1, the center of the top face regular triangle $A_{1}B_{1}C_{1}$ is $P$. A pla... | math | {
"ground_truth": "\\frac{\\sqrt{13}}{8}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$ represent the acceleration of an object, where $V = at + V_0$ and $S = \\frac{1}{3}at^3 + V_0t$. Find the expression for $t$ in terms of $a$, $V_0$, $V$, and $S$.",
"... | math | {
"ground_truth": "\\frac{V-V_0}{a}",
"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 ordered pairs of integers \\((x, y)\\) such that \\( x^4 + y^2 = 4y \\).",
"role": "user"
}
] | math | {
"ground_truth": "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": "A fancy bed and breakfast inn has $5$ rooms, each with a distinctive color-coded decor. One day $5$ friends arrive to spend the night. The friends can room in any combination the... | math | {
"ground_truth": "1620",
"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": "It is known that the equation $ |x - 1| + |x - 2| +... + |x - 2001| = a$ has exactly one solution. Find $a$ .",
"role": "user"
}
] | math | {
"ground_truth": "1001000",
"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 an arithmetic sequence $\\{a_n\\}$ with a common difference $d \\neq 0$ and the sum of the first $n$ terms denoted as $S_n$, determine the statement that must be true.",
... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(x = 3\\) and \\(y = 4\\), what is the value of \\(\\frac{x^4 \\cdot y^2}{8}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "162",
"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": "Suppose that $(u_n)$ is a sequence of real numbers satisfying\n\\[u_{n+2} = 3u_{n+1} - 2u_n\\]\nand that $u_3=15$ and $u_6=43$. What is $u_5$?",
"role": "user"
}
] | math | {
"ground_truth": "27",
"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 first term of a sequence is 2, and each successive term is the sum of all the previous terms of the sequence. What is the value of the first term which exceeds 10000?",
"... | math | {
"ground_truth": "16384",
"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 length of Pine Road is 3 miles, the length of Maple Road is 4 miles, and the length of the railway is 5 miles. What is the area of the triangular plot of land PQR?",
"rol... | 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": "For a sequence $x_1,x_2,\\ldots,x_n$ of real numbers, we define its $\\textit{price}$ as \\[\\max_{1\\le i\\le n}|x_1+\\cdots +x_i|.\\] Given $n$ real numbers, Dave and Geo... | math | {
"ground_truth": "c = 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": "A right triangle with perpendicular sides $a$ and $b$ and hypotenuse $c$ has the following properties: $a = p^m$ and $b = q^n$ with $p$ and $q$ prime numbers and $m... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, find the number of people added to the p... | math | {
"ground_truth": "700",
"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 altitude \\(AH\\) and the angle bisector \\(CL\\) of triangle \\(ABC\\) intersect at point \\(O\\). Find the angle \\(BAC\\) if it is known that the difference between the an... | math | {
"ground_truth": "92^\\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": "Given real numbers \\( x \\) and \\( y \\) satisfying \\( 3x^2 + 4y^2 = 1 \\). If the value of \\( |3x + 4y - \\lambda| + |\\lambda + 7 - 3x - 4y| \\) is independent of \\( x \\)... | math | {
"ground_truth": "[\\sqrt{7} - 7, -\\sqrt{7}]",
"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 $\\triangle DEF$, right-angled at $E$, $\\tan F = \\frac{4}{3}$. If $DE = 3$, find the length of side $DF$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a 2014 x 2014 grid board, several cells (at least one) are colored in such a way that in each 3 x 3 square on the board, the number of colored cells is even. What is the minim... | math | {
"ground_truth": "1342",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle such that $|BC|=7$ and $|AB|=9$. If $m(\\widehat{ABC}) = 2m(\\widehat{BCA})$, calculate the area of the triangle.",
"role": "user"
}
] | math | {
"ground_truth": "14\\sqrt{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": "Compute $1 - 2 + 3 - 4 + \\cdots + 97 - 98$.\nA) -49\nB) -50\nC) 0\nD) 49\nE) 50",
"role": "user"
}
] | math | {
"ground_truth": "A) -49",
"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 graph of the power function $f(x)$ passes through the point $\\left( \\frac{1}{2}, \\frac{ \\sqrt{2}}{2}\\right)$, calculate the value of $\\log _{4}f(2)$.",
"role"... | math | {
"ground_truth": "\\frac{1}{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": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow 0} \\frac{e^{2 x}-e^{x}}{\\sin 2 x-\\sin x}$$",
"role": "user"
}
] | 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": "Consider the function $f(x) = -x^2 + ax + 2(x^2 - x)\\ln x$.\n(Ⅰ) When $a=2$, determine the intervals on which $f(x)$ is monotonic.\n(Ⅱ) Assume that for $x\\in(0, +\\infty)$, the... | 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": "You can determine all 4-ples $(a,b, c,d)$ of real numbers, which solve the following equation system $\\begin{cases} ab + ac = 3b + 3c \nbc + bd = 5c + 5d \nac + cd = 7a + 7d ... | math | {
"ground_truth": "(3, 5, 7, 9)",
"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": "Some language has only three letters - $A, B$ and $C$ . A sequence of letters is called a word iff it contains exactly 100 letters such that exactly 40 of them are consonants ... | math | {
"ground_truth": "2^{40}",
"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": "Palindromes are numbers that read the same backwards and forwards, like 2112. What is the least possible four-digit palindrome that is divisible by 5?",
"role": "user"
}
] | math | {
"ground_truth": "1551",
"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 $I$ be the incenter of a triangle $ABC$ with $AB = 20$ , $BC = 15$ , and $BI = 12$ . Let $CI$ intersect the circumcircle $\\omega_1$ of $ABC$ at $D \\neq C $ . ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Twelve toddlers went outside to play in the sandbox. Each toddler who brought a bucket also brought a shovel. Nine toddlers forgot to bring a bucket, and two toddlers forgot to b... | 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": "$(1)$ Calculate: $3\\tan 45^{\\circ}-\\left(\\frac{1}{3}\\right)^{-1}+\\left(\\sin 30^{\\circ}-2022\\right)^{0}+|\\cos 30^{\\circ}-\\frac{\\sqrt{3}}{2}|$. \n$(2)$ Solve the equa... | math | {
"ground_truth": "x_{2}=-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three automated production lines produce identical products but have different productivity rates. The combined productivity of all three lines working simultaneously is 1.5 time... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the seven-digit number $746m813$ is divisible by 9, what is $m$?",
"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": "I have 7 red plates and 5 blue plates. If I randomly select three plates to serve dinner on, what is the probability that they're all the same color?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{44}",
"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 smallest natural number $n$ which has the following properties:\r\n\r\na) Its decimal representation has a 6 as the last digit.\r\n\r\nb) If the last digit 6 is erased... | math | {
"ground_truth": "153846",
"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 sum \\(1+3+9+27+81+243+729 \\), one can strike out any terms and change some signs in front of the remaining numbers from \"+\" to \"-\". Masha wants to get an expression ... | math | {
"ground_truth": "1093",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all the integer pairs $ (x,y)$ such that:\n \\[ x^2\\minus{}y^4\\equal{}2009\\]",
"role": "user"
}
] | math | {
"ground_truth": "(\\pm 45, \\pm 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": "How many terms will there be after expanding the expression: \\((a+1)(b+1)(c+1)(d+1)(e+1)(f+1)(g+1)\\)?",
"role": "user"
}
] | math | {
"ground_truth": "128",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find a positive integer $n$ such that there is a polygon with $n$ sides where each of its interior angles measures $177^o$",
"role": "user"
}
] | math | {
"ground_truth": "120",
"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 sum of the first hundred positive odd integers subtracted from the sum of the first hundred positive even integers.",
"role": "user"
}
] | math | {
"ground_truth": "100",
"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 the arithmetic sequence $\\{a_{n}\\}$, $a_{n} > 0$ and $a_{1} + a_{3} + a_{8} = a_{4}^{2}$, find the maximum value of $a_{3} \\cdot S_{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{375}{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 a population that decreased by $k\\%$ from $t=0$ to $t=1$ and increased by $m\\%$ from $t=1$ to $t=2$, calculate the net percentage change in the population from $t=0$ to $... | math | {
"ground_truth": "m - k - \\frac{km}{100}\\%",
"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 equation $x(x-1)=x$ has two solutions $x_1$ and $x_2$, find the value of these two solutions.",
"role": "user"
}
] | math | {
"ground_truth": "x_{1}=0, x_{2}=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 a hyperbola $\\dfrac {x^{2}}{a^{2}}- \\dfrac {y^{2}}{b^{2}}=1$ ($a > 0$, $b > 0$), if the distance from one of its foci to an asymptote equals $\\dfrac {1}{4}$ of the focal... | math | {
"ground_truth": "x± \\sqrt {3}y=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\{a_n\\}_{n\\geq 1}$ be a sequence defined by $a_n=\\int_0^1 x^2(1-x)^ndx$ .\nFind the real value of $c$ such that $\\sum_{n=1}^{\\infty} (n+c)(a_n-a_{n+1})=2.$",
... | math | {
"ground_truth": "22",
"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 school held a jumping competition. Within 5 minutes, Liu Li jumped a total of 480 times, while Zhang Hua jumped 420 times. On average, how many more jumps per minute did Liu Li... | math | {
"ground_truth": "12",
"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": "Cara and Dana each roll a sheet of 7-inch by 10-inch paper to form a cylindrical tube. Cara tapes the two 10-inch sides together without overlap. Dana tapes the two 7-inch sides ... | math | {
"ground_truth": "26.25",
"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 a number twelve times as large as $x$ is increased by three, then half of the result equals $3x + 2$, solve for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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 points $P(-1,-2)$ and $Q(4,2)$ in the $xy$-plane; point $R(1,m)$ is taken so that $PR+RQ$ is a minimum. Determine the value of $m$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{2}{5}",
"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": "Indonesia Regional <details><summary>MO</summary>also know as provincial level, is a qualifying round for National Math Olympiad</details> \nYear 2005 <details><summary>Part A<... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $\\lg \\left(x^{3}+\\frac{1}{3} y^{3}+\\frac{1}{9}\\right)=\\lg x+\\lg y$, solve for the number of elements in the set.",
"role": "user"
}
] | 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": "A segment of length $1$ is drawn such that its endpoints lie on a unit circle, dividing the circle into two parts. Compute the area of the larger region.",
"role": "user"
... | math | {
"ground_truth": "\\frac{5\\pi}{6} + \\frac{\\sqrt{3}}{4}",
"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 an integer \\( n > 1 \\), for a positive integer \\( m \\), let \\( S_{m} = \\{1, 2, \\cdots, mn\\} \\). Suppose there exists a collection \\( \\mathscr{F} \\) with \\( |\\... | math | {
"ground_truth": "2n - 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": "Seven boxes are arranged in a circle, each containing a certain number of coins. The picture shows how many coins are in each box.\n\nOne move allows you to transfer one coin to ... | math | {
"ground_truth": "22",
"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 vectors $\\overrightarrow{m}=( \\sqrt {2}\\cos \\frac {x}{4},2\\cos \\frac {x}{4})$ and $\\overrightarrow{n}=( \\sqrt {2}\\cos \\frac {x}{4}, \\sqrt {3}\\sin \\frac {x}{4})... | math | {
"ground_truth": "(2,3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of distinct solutions to the equation $|x-|2x+1||=3$, satisfy.",
"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 the universal set $U=\\mathbb{R}$, the set $A=\\{x|x<0\\}$, and $B=\\{x|x\\leq-1\\}$, determine the set $A\\cap(\\complement_{U}B)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x|-1<x<0\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the value of $x$ such that\n\n$$\\left(1+\\frac{1}{3}+\\frac{1}{9}+\\frac{1}{27}+\\cdots\\right)\\left(1-\\frac{1}{3}+\\frac{1}{9}-\\frac{1}{27}+\\cdots\\right)=1+\\frac{... | math | {
"ground_truth": "9",
"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 car company purchased 4 buses, each costing 2 million yuan, for long-distance passenger transport. It is estimated that each bus will earn about 1 million yuan per year, and th... | math | {
"ground_truth": "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": "An inverted cone with a base radius of $15 \\mathrm{cm}$ and a height of $20 \\mathrm{cm}$ is full of water. This water is then poured into a tall cylinder with a horizontal base... | math | {
"ground_truth": "1.7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a = \\log 8$ and $b = \\log 27,$ compute\n\\[5^{a/b} + 2^{b/a}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many lattice points $(v, w, x, y, z)$ does a $5$ -sphere centered on the origin, with radius $3$ , contain on its surface or in its interior?",
"role": "user"
}
] | math | {
"ground_truth": "1343",
"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 $a, b \\in \\mathbb{R}$, $a \\neq 0$, and the curves $y = \\frac{a + 2}{x}$ and $y = ax + 2b + 1$, if the two curves have at least one common point in the interval $[3... | math | {
"ground_truth": "\\frac{1}{100}",
"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 given arithmetic sequence, the first term is $3$, the last term is $48$, and the sum of all the terms is $255$. Find the common difference.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"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 a sequence $\\{a\\_n\\}$ where all terms are positive numbers, the sum of the first $n$ terms is $S\\_n$, and it satisfies $4S\\_n = a\\_n^2 + 2a\\_n (n \\in \\mathbb{N}^*)... | math | {
"ground_truth": "a\\_n = 2n",
"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": "Write the decomposition of the vector \\(\\vec{a}\\) in terms of the vectors\n\n\\[\n\\vec{p}=\\{1,2,4\\}, \\quad \\vec{q}=\\{1,-1,1\\}, \\quad \\vec{r}=\\{2,2,4\\}, \\quad \\vec... | math | {
"ground_truth": "\\vec{a} = \\vec{p} + 2 \\vec{q} - 2 \\vec{r}",
"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": "On the Cartesian plane, the midpoint between two points $A(a,b)$ and $B(c,d)$ is $M(m,n)$. If $A$ is moved vertically upwards 5 units and horizontally to the right 3 units, and $... | math | {
"ground_truth": "\\sqrt{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": "Twenty-five percent less than 80 is twenty-five percent more than what number?",
"role": "user"
}
] | math | {
"ground_truth": "48",
"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 positive integer $n>1$ is called beautiful if $n$ can be written in one and only one way as $n=a_1+a_2+\\cdots+a_k=a_1 \\cdot a_2 \\cdots a_k$ for some positive integers ... | math | {
"ground_truth": "95",
"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 value of $\\log_{10}{157489}$ is between which two consecutive integers $c$ and $d$? Find $c+d$.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f$ be a function defined by $f\\left(\\dfrac{x}{4}\\right) = 2x^2 - 3x + 5$. Find the sum of all values of $z$ for which $f(4z) = 9$.\nA) $\\frac{3}{32}$ \nB) $\\frac{3}{64... | math | {
"ground_truth": "\\frac{3}{32}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a_1 = 12, b_1 = 48$, and both are arithmetic sequences such that $a_{100} + b_{100} = 200$. Calculate the sum of the first one hundred terms of the sequence $a_1 + b_1, a_2 ... | math | {
"ground_truth": "13000",
"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": "Point \\(M(4, 6)\\) is the midpoint of \\(\\overline{CD}\\). If point \\(C\\) has coordinates \\( (10, 2)\\), what is the sum of the coordinates of point \\(D\\)?",
"role": "... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of the sum $-1 + 2 - 3 + 4 - 5 + 6 - 7 + \\dots + 12,000$?",
"role": "user"
}
] | math | {
"ground_truth": "6000",
"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": "In the fictional country of Mahishmati, there are $50$ cities, including a capital city. Some pairs of cities are connected by two-way flights. Given a city $A$ , an ordered l... | math | {
"ground_truth": "(25!)^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": "For how many values of the digit $A$ is it true that $45$ is divisible by $A$ and $273{,}1A6$ is divisible by $8$?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the least common multiple (LCM) of 150 and 456?",
"role": "user"
}
] | math | {
"ground_truth": "11400",
"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 $x$ be the original number of cherry jelly beans.",
"role": "user"
}
] | math | {
"ground_truth": "105",
"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": "Calculate the following indefinite integrals.\r\n\r\n[1] $\\int (2x+1)\\sqrt{x+2}\\ dx$ \r\n\r\n[2] $\\int \\frac{1+\\cos x}{x+\\sin x}\\ dx$ \r\n\r\n[3] $\\int \\sin ^ 5 x \\... | math | {
"ground_truth": "\\frac{2}{5} (x+2) (2x-1) \\sqrt{x+2} + C",
"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 a function $f(x)$ and its derivative $f'(x)$, if there exists $x_0$ such that $f(x_0) = f'(x_0)$, then $x_0$ is called a \"clever value point\" of $f(x)$. Among the followi... | math | {
"ground_truth": "\\text{①③⑤}",
"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 $A=\\{x|x^{2}-5x+4\\leqslant 0\\}$, set $B=\\{x|(x-a)(x-a^{2}-1) \\lt 0\\}$. \n$(1)$ When $a=\\sqrt{2}$, find $A$⋂$(\\complement _{R}B)$; \n$(2)$ If $B\\subseteq A$, ... | math | {
"ground_truth": "[1,\\sqrt{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": "Let $w$, $x$, $y$, $z$, and $k$ be whole numbers. Given that $2^w \\cdot 3^x \\cdot 5^y \\cdot 7^z \\cdot 11^k = 900$, calculate the value of $2w + 3x + 5y + 7z + 11k$.",
"ro... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many numbers between $1$ and $3000$ are integer multiples of $4$ or $5$ but not $20$ or $25$?\nA) 1300\nB) 1080\nC) 950\nD) 875",
"role": "user"
}
] | math | {
"ground_truth": "B) 1080",
"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 triangular array of numbers has a first row consisting of the odd integers $1, 3, 5, \\ldots, 199$ in increasing order. Each row below the first has one fewer entry than the ro... | math | {
"ground_truth": "65",
"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 basketball team has 12 members. I need to select a lineup consisting of 5 players, one of whom will be the team captain (the other four players are interchangeable in their pos... | math | {
"ground_truth": "3960",
"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": "Neznayka, Doctor Pilyulkin, Knopochka, Vintik, and Znayka participated in a math contest. Exactly four out of them solved each problem. Znayka solved more problems than each of t... | math | {
"ground_truth": "10",
"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 the polar coordinate system, the distance from point $P(4,\\frac{\\pi }{4})$ to line $l:\\rho \\sin \\theta =4\\sqrt{2}$ is equal to ___.",
"role": "user"
}
] | math | {
"ground_truth": "2 \\sqrt{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": "The function $g(x)$ satisfies\n\\[g(x + y) = g(x) + g(y)\\]for all real numbers $x$ and $y,$ and $g(3) = 4.$ Find $g(6).$",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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 $2-1.\\overline{8}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{9}",
"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 shorter side of a rectangle is equal to 1, and the acute angle between the diagonals is $60^\\circ$. Find the radius of the circle circumscribed around the rectangle.",
"... | 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": "Calculate (4!)!, then divide the result by 4!.",
"role": "user"
}
] | math | {
"ground_truth": "23!",
"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 $p=4k+3$ be a prime number. Find the number of different residues mod p of $(x^{2}+y^{2})^{2}$ where $(x,p)=(y,p)=1.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{p-1}{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": "Determine the smallest positive real $K$ such that the inequality\n\\[ K + \\frac{a + b + c}{3} \\ge (K + 1) \\sqrt{\\frac{a^2 + b^2 + c^2}{3}} \\]holds for any real numbers $... | math | {
"ground_truth": "\\frac{\\sqrt{6}}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Ten office employees attend a conference. If each employee shakes hands exactly once with everyone else, except for their direct manager and someone they directly manage (assume ... | math | {
"ground_truth": "35",
"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 function $f(x) = \\sin^2 x + \\sqrt{3}\\tan\\theta \\cdot \\cos x + \\frac{\\sqrt{3}}{8}\\tan\\theta - \\frac{3}{2}$, where $x \\in [0, \\frac{\\pi}{2}]$, $\\theta \\in... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the range of negative values for \\( a \\) such that the inequality \\( \\sin^2 x + a \\cdot \\cos x + a^2 > 1 + \\cos x \\) is true for all \\( x \\in \\mathbb{R} \\).",
... | math | {
"ground_truth": "a \\leq -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": "What is the value of\\[\\frac{\\log_2 64}{\\log_{32}2}-\\frac{\\log_2 256}{\\log_{16}2}?\\]\nA) -2\nB) 0\nC) 1\nD) 2\nE) 4",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A function \\( f: \\{1,2,3,4,5\\} \\rightarrow \\{1,2,3,4,5\\} \\) is said to be nasty if there do not exist distinct \\( a, b \\in \\{1,2,3,4,5\\} \\) satisfying \\( f(a) = b \\... | math | {
"ground_truth": "1950",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sherlock and Mycroft are playing Battleship on a $4\\times4$ grid. Mycroft hides a single $3\\times1$ cruiser somewhere on the board. Sherlock can pick squares on the grid an... | math | {
"ground_truth": "4",
"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": "There are $2017$ turtles in a room. Every second, two turtles are chosen uniformly at random and combined to form one super-turtle. (Super-turtles are still turtles.) The proba... | math | {
"ground_truth": "1009",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the shortest distance from the line \\(3x + 4y = 25\\) to the circle \\(x^2 + y^2 = 6x - 8y\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $M_1, M_2, . . ., M_{11}$ be $5-$ element sets such that $M_i \\cap M_j \\neq {\\O}$ for all $i, j \\in \\{1, . . ., 11\\}$ . Determine the minimum possible value of th... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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