data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Three distinct integers, $x$, $y$, and $z$, are randomly chosen from the set $\\{1,2,3,4,5,6,7,8,9,10,11,12\\}$. What is the probability that $xyz-xy-xz-yz$ is even? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{10}{11}"
} | {
"split": "train",
"index": 1100,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find whole numbers $\\heartsuit$ and $\\clubsuit$ such that $\\heartsuit \\cdot \\clubsuit = 48$ and $\\heartsuit$ is even, then determine the largest possible value of $\\heartsuit + \\clubsuit$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 1101,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An archipelago consists of \\( N \\geq 7 \\) islands. Any two islands are connected by at most one bridge. It is known that no more than 5 bridges lead from each island, and among any 7 islands, there are always two that are connected by a bridge. What is the largest possible v... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 1102,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, the opposite sides of angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\\tan A = 2\\tan B$, $b = \\sqrt{2}$, and the area of $\\triangle ABC$ is at its maximum value, find $a$. Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 1103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest integer $n$ satisfying the following conditions:\n (i) $n^2$ can be expressed as the difference of two consecutive cubes;\n (ii) $2n + 79$ is a perfect square. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "181"
} | {
"split": "train",
"index": 1104,
"solution": "Let us generate numbers $1$ to $1000$ for the second condition, for squares. We know for $N$ to be integer, the squares must be odd. So we generate $N = 1, 21, 45, 73, 105, 141, 181, 381, 441, 721, 801$. $N$ cannot exceed $1000$ since it is AIME problem. Now take th... |
deepscaler | [
{
"role": "user",
"content": "What common fraction (that is, a fraction reduced to its lowest terms) is equivalent to $0.1\\overline{35}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{67}{495}"
} | {
"split": "train",
"index": 1105,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The wheel shown below consists of two circles and five spokes, with a label at each point where a spoke meets a circle. A bug walks along the wheel, starting at point $A$. At every step of the process, the bug walks from one labeled point to an adjacent labeled point. Along the... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 1106,
"solution": "Let an $O$ signal a move that ends in the outer circle and $I$ signal a move that ends in the inner circle. Now notice that for a string of $15$ moves to end at $A$, the difference between $O$'s and $I$'s in the string must be a multiple of $5$.\n$15$ $I$'s: Trivial... |
deepscaler | [
{
"role": "user",
"content": "One angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. What is the area of the parallelogram? Express your answer in simplest radical form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60\\sqrt{3}"
} | {
"split": "train",
"index": 1107,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\tan (\\alpha+\\beta)= \\frac {3}{4}$ and $\\tan (\\alpha- \\frac {\\pi}{4})= \\frac {1}{2}$, find the value of $\\tan (\\beta+ \\frac {\\pi}{4})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {2}{11}"
} | {
"split": "train",
"index": 1108,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Luna writes down all the five-digit numbers that contain each of the digits 1, 2, 3, 4 and 5 exactly once. What is the smallest number in Luna's list that is divisible by 6? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12354"
} | {
"split": "train",
"index": 1109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rectangle $EFGH$ has area $2016$. An ellipse with area $2016\\pi$ passes through $E$ and $G$ and has foci at $F$ and $H$. What is the perimeter of the rectangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8\\sqrt{1008}"
} | {
"split": "train",
"index": 1110,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a set of data is multiplied by 2 and then reduced by 80 for each data point, resulting in a new set of data with an average of 1.2 and a variance of 4.4, determine the average and variance of the original data. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "1.1"
} | {
"split": "train",
"index": 1111,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least positive integer that satisfies the following conditions?\n\na) When divided by 2, the remainder is 1.\n\nb) When divided by 3, the remainder is 2.\n\nc) When divided by 4, the remainder is 3.\n\nd) When divided by 5, the remainder is 4. Let's think step by st... | math | {
"style": "rule",
"ground_truth": "59"
} | {
"split": "train",
"index": 1112,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(ABCD\\) be a quadrilateral inscribed in a circle with center \\(O\\). Let \\(P\\) denote the intersection of \\(AC\\) and \\(BD\\). Let \\(M\\) and \\(N\\) denote the midpoints of \\(AD\\) and \\(BC\\). If \\(AP=1\\), \\(BP=3\\), \\(DP=\\sqrt{3}\\), and \\(AC\\) is perpe... | math | {
"style": "rule",
"ground_truth": "3/4"
} | {
"split": "train",
"index": 1113,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph of $y = \\frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic. (Assume that the grid lines are at integers.)\n\n[asy]\nunitsize(0.6 cm);\n\nreal func (real x) {\n return (2*(x - 1)/(x + 2));\n}\n\nint i;\n\nfor (i = -8; i <= 8; ++i) {\n draw((i,... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"split": "train",
"index": 1114,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Losyash is walking to Sovunya's house along the river at a speed of 4 km/h. Every half hour, he launches paper boats that travel towards Sovunya at a speed of 10 km/h. At what time intervals do the boats arrive at Sovunya's house? (Provide a complete solution, not just the answ... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 1115,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two noncongruent integer-sided isosceles triangles have the same perimeter and the same area. The ratio of the lengths of the bases of the two triangles is $8: 7$. Find the minimum possible value of their common perimeter.\n Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "676"
} | {
"split": "train",
"index": 1116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle is circumscribed around an isosceles triangle whose two congruent angles have degree measure $x$. Two points are chosen independently and uniformly at random on the circle, and a chord is drawn between them. The probability that the chord intersects the triangle is $\\... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 1117,
"solution": "Because we know that we have an isosceles triangle with angles of $x$ (and we know that x is an inscribed angle), that means that the arc that is intercepted by this angle is $2x$. We form this same conclusion for the other angle $x$, and $180-2x$. Therefore we get ... |
deepscaler | [
{
"role": "user",
"content": "Compute $\\left\\lceil\\displaystyle\\sum_{k=2018}^{\\infty}\\frac{2019!-2018!}{k!}\\right\\rceil$ . (The notation $\\left\\lceil x\\right\\rceil$ denotes the least integer $n$ such that $n\\geq x$ .)\n\n*Proposed by Tristan Shin* Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "2019"
} | {
"split": "train",
"index": 1118,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two boards, one four inches wide and the other six inches wide, are nailed together to form an X. The angle at which they cross is 60 degrees. If this structure is painted and the boards are separated what is the area of the unpainted region on the four-inch board? (The holes c... | math | {
"style": "rule",
"ground_truth": "16\\sqrt{3}"
} | {
"split": "train",
"index": 1119,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sqrt{3}\\sin\\left(x+\\frac{\\pi}{4}\\right)\\sin\\left(x-\\frac{\\pi}{4}\\right)+\\sin x\\cos x$. \n$(Ⅰ)$ Find the smallest positive period and the center of symmetry of $f(x)$; \n$(Ⅱ)$ Given an acute triangle $\\triangle ABC$ with sides $a$, $b$, ... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 1120,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mark has a cursed six-sided die that never rolls the same number twice in a row, and all other outcomes are equally likely. Compute the expected number of rolls it takes for Mark to roll every number at least once. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "\\frac{149}{12}"
} | {
"split": "train",
"index": 1121,
"solution": "Suppose Mark has already rolled $n$ unique numbers, where $1 \\leq n \\leq 5$. On the next roll, there are 5 possible numbers he could get, with $6-n$ of them being new. Therefore, the probability of getting another unique number is $\\frac{6-n}{5}$, so the expected... |
deepscaler | [
{
"role": "user",
"content": "Consider the line parameterized by\n\\begin{align*} \nx&= 4t + 2,\\\\ \ny& = t+2.\n\\end{align*}Find a vector $\\begin{pmatrix}a \\\\ b \\end{pmatrix}$ pointing from the origin to this line that is parallel to $\\begin{pmatrix}2 \\\\1 \\end{pmatrix}$. Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix}6\\\\3\\end{pmatrix}"
} | {
"split": "train",
"index": 1122,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$ and $b$ be the real roots of\n\\[x^4 - 4x - 1 = 0.\\]Find $ab + a + b.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 1123,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three of the four vertices of a rectangle are $(3, 7)$, $(12, 7)$, and $(12, -4)$. What is the area of the intersection of this rectangular region and the region inside the graph of the equation $(x - 3)^2 + (y + 4)^2 = 16$? Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "4\\pi"
} | {
"split": "train",
"index": 1124,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Xiaoming's home is 30 minutes away from school by subway and 50 minutes by bus. One day, due to some reasons, Xiaoming first took the subway and then transferred to the bus, taking 40 minutes to reach the school. The transfer process took 6 minutes. How many minutes did Xiaomin... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 1125,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 soc... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 1126,
"solution": "\nLet $x$ be the number of $1$ pairs of socks, $y$ be the number of $3$ pairs of socks, and $z$ be the number of $4$ pairs of socks that Ralph bought. We are given the following system of equations based on the problem statement:\n\n1. **Total number of pairs**: $x ... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer \\( n \\) such that the mean of the squares of the first \\( n \\) natural numbers (\\( n > 1 \\)) is an integer.\n\n(Note: The mean of the squares of \\( n \\) numbers \\( a_1, a_2, \\cdots, a_n \\) is given by \\( \\sqrt{\\frac{a_{1}^2 + a_{... | math | {
"style": "rule",
"ground_truth": "337"
} | {
"split": "train",
"index": 1127,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least value of $y$ such that $3y^2 + 5y + 2 = 4$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 1128,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the set of three-digit numbers that do not contain the digits $0,1,2,3,4,5$, several numbers were written down in such a way that no two numbers could be obtained from each other by swapping two adjacent digits. What is the maximum number of such numbers that could have be... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 1129,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hexagon is obtained by joining, in order, the points $(0,1)$, $(1,2)$, $(2,2)$, $(2,1)$, $(3,1)$, $(2,0)$, and $(0,1)$. The perimeter of the hexagon can be written in the form $a+b\\sqrt{2}+c\\sqrt{5}$, where $a$, $b$ and $c$ are whole numbers. Find $a+b+c$. Let's think step... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 1130,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The fraction $\\frac{\\sqrt{a^2+x^2}-\\frac{x^2-a^2}{\\sqrt{a^2+x^2}}}{a^2+x^2}$ reduces to: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2a^2}{(a^2+x^2)^{\\frac{3}{2}}}"
} | {
"split": "train",
"index": 1131,
"solution": "1. **Simplify the Numerator**: Start by simplifying the numerator of the given fraction:\n \\[\n \\sqrt{a^2+x^2} - \\frac{x^2-a^2}{\\sqrt{a^2+x^2}}\n \\]\n Multiply the second term by $\\frac{\\sqrt{a^2+x^2}}{\\sqrt{a^2+x^2}}$ to get a common denominator:\n ... |
deepscaler | [
{
"role": "user",
"content": "Given that $a$, $b$, and $c$ are the roots of the equation $x^3-3x^2+mx+24=0$, and that $-a$ and $-b$ are the roots of the equation $x^2+nx-6=0$, then the value of $n$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 1132,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given three points $A$, $B$, $C$ on a straight line in the Cartesian coordinate system, satisfying $\\overrightarrow{OA}=(-3,m+1)$, $\\overrightarrow{OB}=(n,3)$, $\\overrightarrow{OC}=(7,4)$, and $\\overrightarrow{OA} \\perp \\overrightarrow{OB}$, where $O$ is the origin.\n$(1)... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 1133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two distinct integers, $x$ and $y$, are randomly chosen from the set $\\{1,2,3,4,5,6,7,8,9,10\\}$. What is the probability that $xy-x-y$ is even? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{9}"
} | {
"split": "train",
"index": 1134,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The radian measure of 300° is $$\\frac {5π}{3}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{3}"
} | {
"split": "train",
"index": 1135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all real numbers \\( x \\) such that\n\\[\n\\frac{16^x + 25^x}{20^x + 32^x} = \\frac{9}{8}.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x = 0"
} | {
"split": "train",
"index": 1136,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A spherical soap bubble lands on a horizontal wet surface and forms a hemisphere of the same volume. Given the radius of the hemisphere is $3\\sqrt[3]{2}$ cm, find the radius of the original bubble. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 1137,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When Lisa squares her favorite $2$ -digit number, she gets the same result as when she cubes the sum of the digits of her favorite $2$ -digit number. What is Lisa's favorite $2$ -digit number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 1138,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest possible value for $n$ if the average of the two positive integers $m$ and $n$ is 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 1139,
"solution": "Since the average of $m$ and $n$ is 5, then $\\frac{m+n}{2}=5$ which means that $m+n=10$. In order for $n$ to be as large as possible, we need to make $m$ as small as possible. Since $m$ and $n$ are positive integers, then the smallest possible value of $m$ is 1, wh... |
deepscaler | [
{
"role": "user",
"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 such permutations. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "360"
} | {
"split": "train",
"index": 1140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $T$ be the set of all rational numbers $r$, $0<r<1$, that have a repeating decimal expansion in the form $0.efghefgh\\ldots=0.\\overline{efgh}$, where the digits $e$, $f$, $g$, and $h$ are not necessarily distinct. To write the elements of $T$ as fractions in lowest terms, ... | math | {
"style": "rule",
"ground_truth": "6000"
} | {
"split": "train",
"index": 1141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are four positive integers that are divisors of each number in the list $$20, 40, 100, 80, 180.$$ Find the sum of these four positive integers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 1142,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $AB = 6$, $BC = 10$, $CA = 8$, and side $BC$ is extended to a point $P$ such that $\\triangle PAB$ is similar to $\\triangle PCA$. Calculate the length of $PC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 1143,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Veronica has 6 marks on her report card.\n\nThe mean of the 6 marks is 74.\n\nThe mode of the 6 marks is 76.\n\nThe median of the 6 marks is 76.\n\nThe lowest mark is 50.\n\nThe highest mark is 94.\n\nOnly one mark appears twice, and no mark appears more than twice.\n\nAssuming... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 1144,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle PQR$, we have $PQ = QR = 46$ and $PR = 40$. Point $M$ is the midpoint of $\\overline{QR}$. Find the length of segment $PM$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{1587}"
} | {
"split": "train",
"index": 1145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The largest and smallest possible three-digit numbers that can be formed using the digits 5, 1, and 9 are found by maximizing and minimizing the order of the digits, respectively. Calculate the difference between these two numbers. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "792"
} | {
"split": "train",
"index": 1146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A club is creating a special series of membership cards that includes a code consisting of five characters selected from the letters B, E, T, A and the digits in 2023. No character should appear in a code more often than it appears in \"BETA\" or \"2023\" (B, E, T, A appear onc... | math | {
"style": "rule",
"ground_truth": "312"
} | {
"split": "train",
"index": 1147,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $\\sum_{i=1}^{\\infty} \\frac{a i}{a^{i}}$ for $a>1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left(\\frac{a}{1-a}\\right)^{2}"
} | {
"split": "train",
"index": 1148,
"solution": "The sum $S=a+a x+a x^{2}+a x^{3}+\\cdots$ for $x<1$ can be determined by realizing that $x S=a x+a x^{2}+a x^{3}+\\cdots$ and $(1-x) S=a$, so $S=\\frac{a}{1-x}$. Using this, we have $\\sum_{i=1}^{\\infty} \\frac{a i}{a^{i}}=$ $a \\sum_{i=1}^{\\infty} \\frac{i}{a^{i}... |
deepscaler | [
{
"role": "user",
"content": "What is the maximum number of colors that can be used to color the cells of an 8x8 chessboard such that each cell shares a side with at least two cells of the same color? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1149,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( n \\) be a fixed integer, \\( n \\geqslant 2 \\).\n\n(a) Determine the minimal constant \\( c \\) such that the inequality\n$$\n\\sum_{1 \\leqslant i < j \\leqslant n} x_i x_j \\left(x_i^2 + x_j^2\\right) \\leqslant c \\left( \\sum_{1 \\leqslant i \\leqslant n} x_i \\ri... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"split": "train",
"index": 1150,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be a positive integer. Initially, a $2n \\times 2n$ grid has $k$ black cells and the rest white cells. The following two operations are allowed :\n(1) If a $2\\times 2$ square has exactly three black cells, the fourth is changed to a black cell; \n(2) If there are exact... | math | {
"style": "rule",
"ground_truth": "n^2 + n + 1"
} | {
"split": "train",
"index": 1151,
"solution": "\nLet \\( n \\) be a positive integer. Initially, a \\( 2n \\times 2n \\) grid has \\( k \\) black cells and the rest white cells. The following two operations are allowed:\n1. If a \\( 2 \\times 2 \\) square has exactly three black cells, the fourth is changed to a... |
deepscaler | [
{
"role": "user",
"content": "A particle is located on the coordinate plane at $(5,0)$. Define a move for the particle as a counterclockwise rotation of $\\pi/4$ radians about the origin followed by a translation of $10$ units in the positive $x$-direction. Given that the particle's position after $150$ mov... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 1152,
"solution": "Let $T:\\begin{pmatrix}x\\\\y\\end{pmatrix}\\rightarrow R(\\frac{\\pi}{4})\\begin{pmatrix}x\\\\y\\end{pmatrix}+\\begin{pmatrix}10\\\\0\\end{pmatrix}$. We assume that the rotation matrix $R(\\frac{\\pi}{4}) = R$ here. Then we have\n$T^{150}\\begin{pmatrix}5\\\\0\\end... |
deepscaler | [
{
"role": "user",
"content": "Find the number of positive integers that are divisors of at least one of $10^{10},15^7,18^{11}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "435"
} | {
"split": "train",
"index": 1153,
"solution": "$10^{10} = 2^{10}\\cdot 5^{10}$ so $10^{10}$ has $11\\cdot11 = 121$ divisors.\n$15^7 = 3^7\\cdot5^7$ so $15^7$ has $8\\cdot8 = 64$ divisors.\n$18^{11} = 2^{11}\\cdot3^{22}$ so $18^{11}$ has $12\\cdot23 = 276$ divisors.\n Now, we use the Principle of Inclusion-Exclus... |
deepscaler | [
{
"role": "user",
"content": "The escalator of the department store, which at any given time can be seen at $75$ steps section, moves up one step in $2$ seconds. At time $0$ , Juku is standing on an escalator step equidistant from each end, facing the direction of travel. He goes by a certain rule: one... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 1154,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the polynomial $x^2 - kx + 24$ has only positive integer roots, find the average of all distinct possible values for $k$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 1155,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The fraction halfway between $\\frac{1}{5}$ and $\\frac{1}{3}$ (on the number line) is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{15}"
} | {
"split": "train",
"index": 1156,
"solution": "To find the fraction halfway between $\\frac{1}{5}$ and $\\frac{1}{3}$, we calculate their average. The average of two numbers $a$ and $b$ is given by $\\frac{a+b}{2}$.\n\n1. **Convert fractions to a common denominator**:\n \\[\n \\frac{1}{5} = \\frac{3}{15} \\q... |
deepscaler | [
{
"role": "user",
"content": "A solid rectangular block is created using $N$ congruent 1-cm cubes adhered face-to-face. When observing the block to maximize visibility of its surfaces, exactly $252$ of the 1-cm cubes remain hidden from view. Determine the smallest possible value of $N.$ Let's think step by ... | math | {
"style": "rule",
"ground_truth": "392"
} | {
"split": "train",
"index": 1157,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum number of numbers we can choose from the first 1983 positive integers such that the product of any two chosen numbers is not among the chosen numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1939"
} | {
"split": "train",
"index": 1158,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of the $2005$ smallest positive multiples of $4$, and let $T$ be the set of the $2005$ smallest positive multiples of $6$. How many elements are common to $S$ and $T$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "668"
} | {
"split": "train",
"index": 1159,
"solution": "1. **Identify the common multiples in sets $S$ and $T$:**\n - Set $S$ consists of the first $2005$ smallest positive multiples of $4$. Thus, $S = \\{4, 8, 12, 16, \\ldots, 4 \\times 2005\\}$.\n - Set $T$ consists of the first $2005$ smallest positive multiples o... |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given vectors $\\overrightarrow{m} = (b+c, a^2 + bc)$ and $\\overrightarrow{n} = (b+c, -1)$ with $\\overrightarrow{m} \\cdot \\overrightarrow{n} = 0$.\n\n(1) Find the size o... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 1160,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Brent rolls a fair dodecahedral die with numbers $1,2,3,...,12$ on its faces. What is the expected number of digits in the number he obtains? Express your answer in a decimal. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1.25"
} | {
"split": "train",
"index": 1161,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of ordered pairs of integers $(a, b)$ such that the sequence\\[3, 4, 5, a, b, 30, 40, 50\\]is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "228"
} | {
"split": "train",
"index": 1162,
"solution": "divide cases into $7\\leq a<20; 21\\leq a\\leq28$.(Notice that $a$ can't be equal to $6,20$, that's why I divide them into two parts. There are three cases that arithmetic sequence forms: $3,12,21,30;4,16,28,40;3,5,7,9$.(NOTICE that $5,20,35,50$ IS NOT A VALID SEQUE... |
deepscaler | [
{
"role": "user",
"content": "Given that $α$ and $β$ belong to the interval $(0, \\frac{π}{2})$, and they satisfy the equation $\\tan(α + β) = 9\\tan(β)$, find the maximum value of $\\tan(α)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{3}"
} | {
"split": "train",
"index": 1163,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The least common multiple of $x$, $10$ and $14$ is $70$. What is the greatest possible value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 1164,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has side lengths $AB=7, BC=8,$ and $CA=9.$ Circle $\\omega_1$ passes through $B$ and is tangent to line $AC$ at $A.$ Circle $\\omega_2$ passes through $C$ and is tangent to line $AB$ at $A.$ Let $K$ be the intersection of circles $\\omega_1$ and $\\omega_2$ not e... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 1165,
"solution": "By the definition of $K$, it is the spiral center mapping $BA\\to AC$, which means that it is the midpoint of the $A$-symmedian chord. In particular, if $M$ is the midpoint of $BC$ and $M'$ is the reflection of $A$ across $K$, we have $\\triangle ABM'\\sim\\triangle... |
deepscaler | [
{
"role": "user",
"content": "Medians $\\overline{DP}$ and $\\overline{EQ}$ of isosceles $\\triangle DEF$, where $DE=EF$, are perpendicular. If $DP= 21$ and $EQ = 28$, then what is ${DE}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{70}{3}"
} | {
"split": "train",
"index": 1166,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points \\( M, N, P, Q \\) are taken on the diagonals \\( D_1A, A_1B, B_1C, C_1D \\) of the faces of cube \\( ABCD A_1B_1C_1D_1 \\) respectively, such that:\n\n\\[ D_1M: D_1A = BA_1: BN = B_1P: B_1C = DQ: DC_1 = \\mu, \\]\n\nand the lines \\( MN \\) and \\( PQ \\) are mutually p... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{\\sqrt{2}}"
} | {
"split": "train",
"index": 1167,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given in parallelogram $ABCD$, point $E$ is the midpoint of side $BC$. A point $F$ is arbitrarily chosen on side $AB$. The probability that the area ratio of $\\triangle ADF$ to $\\triangle BFE$ is not less than $1$ is ______. Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 1168,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest natural number that has exactly 70 natural divisors (including 1 and the number itself). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25920"
} | {
"split": "train",
"index": 1169,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Numbers from 1 to 6 are written on the faces of a gaming die. However, the weight of the die is distributed unevenly, and the probability of landing on number $k$ is directly proportional to $k$. The die is rolled two times in a row. What is the probability that the sum of the ... | math | {
"style": "rule",
"ground_truth": "0.13"
} | {
"split": "train",
"index": 1170,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A soccer team has $22$ available players. A fixed set of $11$ players starts the game, while the other $11$ are available as substitutes. During the game, the coach may make as many as $3$ substitutions, where any one of the $11$ players in the game is replaced by one of the su... | math | {
"style": "rule",
"ground_truth": "122"
} | {
"split": "train",
"index": 1171,
"solution": "There are $0-3$ substitutions. The number of ways to sub any number of times must be multiplied by the previous number. This is defined recursively. The case for $0$ subs is $1$, and the ways to reorganize after $n$ subs is the product of the number of new subs ($12... |
deepscaler | [
{
"role": "user",
"content": "The line $y=-\\frac{3}{4}x+9$ crosses the $x$-axis at $P$ and the $y$-axis at $Q$. Point $T(r,s)$ is on line segment $PQ$. If the area of $\\triangle POQ$ is three times the area of $\\triangle TOP$, then what is the value of $r+s$? [asy]\n\n// draw axes\ndraw((-3, 0)--(15, 0... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 1172,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An odd six-digit number is called \"just cool\" if it consists of digits that are prime numbers, and no two identical digits are adjacent. How many \"just cool\" numbers exist? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "729"
} | {
"split": "train",
"index": 1173,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nCalculate the limit of the function:\n\n$\\lim _{x \\rightarrow \\frac{1}{4}} \\frac{\\sqrt[3]{\\frac{x}{16}}-\\frac{1}{4}}{\\sqrt{\\frac{1}{4}+x}-\\sqrt{2x}}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{2\\sqrt{2}}{6}"
} | {
"split": "train",
"index": 1174,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In cube \\( ABCD A_{1} B_{1} C_{1} D_{1} \\), with an edge length of 6, points \\( M \\) and \\( N \\) are the midpoints of edges \\( AB \\) and \\( B_{1} C_{1} \\) respectively. Point \\( K \\) is located on edge \\( DC \\) such that \\( D K = 2 K C \\). Find:\n\na) The distan... | math | {
"style": "rule",
"ground_truth": "\\frac{66}{\\sqrt{173}}"
} | {
"split": "train",
"index": 1175,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the system of equations:\n$$\n\\begin{cases}\nx - 2y = z - 2u \\\\\n2yz = ux\n\\end{cases}\n$$\nfor each set of positive real number solutions \\{x, y, z, u\\}, where $z \\geq y$, there exists a positive real number $M$ such that $M \\leq \\frac{z}{y}$. Find the maximum v... | math | {
"style": "rule",
"ground_truth": "6 + 4\\sqrt{2}"
} | {
"split": "train",
"index": 1176,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An acute isosceles triangle, $ABC$, is inscribed in a circle. Through $B$ and $C$, tangents to the circle are drawn, meeting at point $D$. If $\\angle ABC = \\angle ACB = 3 \\angle D$ and $\\angle BAC = k \\pi$ in radians, then find $k$. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{13}"
} | {
"split": "train",
"index": 1177,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two parabolas have equations $y= x^2 + ax +b$ and $y= x^2 + cx +d$, where $a, b, c,$ and $d$ are integers, each chosen independently by rolling a fair six-sided die. What is the probability that the parabolas will have at least one point in common? Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "\\frac{31}{36}"
} | {
"split": "train",
"index": 1178,
"solution": "\n1. **Set the equations equal**: Given the equations of the parabolas $y = x^2 + ax + b$ and $y = x^2 + cx + d$, set them equal to find the condition for intersection:\n \\[\n x^2 + ax + b = x^2 + cx + d.\n \\]\n Simplifying this, we get:\n \\[\n ax + b... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sin \\alpha = \\frac{\\sqrt{5}}{5}$ and $\\sin (\\alpha - \\beta) = -\\frac{\\sqrt{10}}{10}$, where both $\\alpha$ and $\\beta$ are acute angles, find the value of $\\beta$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 1179,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The pages of a book are numbered $1_{}^{}$ through $n_{}^{}$. When the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of $1986_{}^{}$. What was the number of the page that was added twice? Let's think step ... | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 1180,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are integers $x$ that satisfy the inequality $|x-2000|+|x| \\leq 9999$. Find the number of such integers $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9999"
} | {
"split": "train",
"index": 1181,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the product of all real numbers that are tripled when added to their reciprocals? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 1182,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin x+a\\cos x(x∈R)$ whose one symmetric axis is $x=- \\frac {π}{4}$.\n(I) Find the value of $a$ and the monotonically increasing interval of the function $f(x)$;\n(II) If $α$, $β∈(0, \\frac {π}{2})$, and $f(α+ \\frac {π}{4})= \\frac { \\sqrt {10}}{5}... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {2}}{2}"
} | {
"split": "train",
"index": 1183,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $n$ is an integer between $1$ and $60$, inclusive, determine for how many values of $n$ the expression $\\frac{((n+1)^2 - 1)!}{(n!)^{n+1}}$ is an integer. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "59"
} | {
"split": "train",
"index": 1184,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For real numbers \\(x\\), \\(y\\), and \\(z\\), consider the matrix\n\\[\n\\begin{pmatrix} x+y & x & y \\\\ x & y+z & y \\\\ y & x & x+z \\end{pmatrix}\n\\]\nDetermine whether this matrix is invertible. If not, list all possible values of\n\\[\n\\frac{x}{y + z} + \\frac{y}{x + ... | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 1185,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a plane, there are 10 lines, among which 4 lines are parallel to each other. Then, these 10 lines can divide the plane into at most how many parts? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 1186,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the area of the triangle bounded by the axes and the curve $y = (x-5)^2 (x+3)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"split": "train",
"index": 1187,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $9^{2048}$ is divided by $50$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 1188,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the function $f(x)=a- \\frac {2}{2^{x}+1}(a\\in\\mathbb{R})$\n\n$(1)$ Determine the monotonicity of the function $f(x)$ and provide a proof;\n\n$(2)$ If there exists a real number $a$ such that the function $f(x)$ is an odd function, find $a$;\n\n$(3)$ For the $a$ found in ... | math | {
"style": "rule",
"ground_truth": "\\frac {12}{5}"
} | {
"split": "train",
"index": 1189,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of six-digit palindromes. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9000"
} | {
"split": "train",
"index": 1190,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What fraction of the volume of a parallelepiped is the volume of a tetrahedron whose vertices are the centroids of the tetrahedra cut off by the planes of a tetrahedron inscribed in the parallelepiped? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "1/24"
} | {
"split": "train",
"index": 1191,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P$ be the set of points $$\\{(x, y) \\mid 0 \\leq x, y \\leq 25, x, y \\in \\mathbb{Z}\\}$$ and let $T$ be the set of triangles formed by picking three distinct points in $P$ (rotations, reflections, and translations count as distinct triangles). Compute the number of tria... | math | {
"style": "rule",
"ground_truth": "436"
} | {
"split": "train",
"index": 1192,
"solution": "Lemma: The area of any triangle inscribed in an $a$ by $b$ rectangle is at most $\\frac{ab}{2}$. (Any triangle's area can be increased by moving one of its sides to a side of the rectangle). Given this, because any triangle in $T$ is inscribed in a $25 \\times 25$ s... |
deepscaler | [
{
"role": "user",
"content": "Expand the following expression: $(9x+4)\\cdot 2x^2$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18x^3+8x^2"
} | {
"split": "train",
"index": 1193,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a tetrahedron \\( P-ABC \\) with its four vertices on the surface of sphere \\( O \\), where \\( PA = PB = PC \\) and \\( \\triangle ABC \\) is an equilateral triangle with side length 2. \\( E \\) and \\( F \\) are the midpoints of \\( AC \\) and \\( BC \\) respectively,... | math | {
"style": "rule",
"ground_truth": "6\\pi"
} | {
"split": "train",
"index": 1194,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f$ is not defined for $x = 0,$ but for all non-zero real numbers $x,$\n\\[f(x) + 2f \\left( \\frac{1}{x} \\right) = 3x.\\]Find the real solutions to $f(x) = f(-x).$ Enter the real solutions, separated by commas. Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2},-\\sqrt{2}"
} | {
"split": "train",
"index": 1195,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the complex plane, consider the parallelogram formed by the points 0, $z,$ $\\frac{1}{z},$ and $z + \\frac{1}{z}$ where the area of the parallelogram is $\\frac{24}{25}.$ If the real part of $z$ is positive, determine the smallest possible value of $\\left| z + \\frac{1}{z} ... | math | {
"style": "rule",
"ground_truth": "\\frac{36}{25}"
} | {
"split": "train",
"index": 1196,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line $l$ does not pass through the origin $O$ and intersects an ellipse $\\frac{x^{2}}{2}+y^{2}=1$ at points $A$ and $B$. $M$ is the midpoint of segment $AB$. Determine the product of the slopes of line $AB$ and line $OM$. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 1197,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select three different numbers from the set {-8, -6, -4, 0, 3, 5, 7} to form a product and determine the smallest possible value. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-280"
} | {
"split": "train",
"index": 1198,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In regular hexagon $ABCDEF$, diagonal $AD$ is drawn. Given that each interior angle of a regular hexagon measures 120 degrees, calculate the measure of angle $DAB$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 1199,
"solution": ""
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.