data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Let \\( S \\) be the set comprising all sides and diagonals of a regular hexagon. A pair of elements from \\( S \\) are selected randomly without replacement. What is the probability that the two chosen segments have the same length? Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{35}"
} | {
"split": "train",
"index": 25449,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( M \\) and \\( m \\) be the maximum and minimum elements, respectively, of the set \\( \\left\\{\\left.\\frac{3}{a}+b \\right\\rvert\\, 1 \\leq a \\leq b \\leq 2\\right\\} \\). Find the value of \\( M - m \\). Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "5 - 2\\sqrt{3}"
} | {
"split": "train",
"index": 25450,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an experiment, a scientific constant $C$ is determined to be $2.43865$ with an error of at most $\\pm 0.00312$. \nThe experimenter wishes to announce a value for $C$ in which every digit is significant. \nThat is, whatever $C$ is, the announced value must be the correct resu... | math | {
"style": "rule",
"ground_truth": "2.44"
} | {
"split": "train",
"index": 25451,
"solution": "1. **Determine the range of possible values for $C$:**\n Given that $C = 2.43865$ with an error of $\\pm 0.00312$, we calculate the upper and lower bounds of $C$:\n \\[\n C_{\\text{upper}} = 2.43865 + 0.00312 = 2.44177\n \\]\n \\[\n C_{\\text{lower}} = ... |
deepscaler | [
{
"role": "user",
"content": "Find the set of solutions for $x$ in the inequality $\\frac{x+1}{x+2} > \\frac{3x+4}{2x+9}$ when $x \\neq -2, x \\neq \\frac{9}{2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{-9}{2} \\leq x \\leq -2 \\cup \\frac{1-\\sqrt{5}}{2} < x < \\frac{1+\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 25452,
"solution": "There are 3 possible cases of $x$: 1) $-\\frac{9}{2} < x$, 2) $\\frac{9}{2} \\leq x \\leq -2$, 3) $-2 < x$. For the cases (1) and (3), $x+2$ and $2x+9$ are both positive or negative, so the following operation can be carried out without changing the inequality sign... |
deepscaler | [
{
"role": "user",
"content": "Two right triangles, $ABC$ and $ACD$, are joined as shown. Squares are drawn on four of the sides. The areas of three of the squares are 9, 16 and 36 square units. What is the number of square units in the area of the fourth square?\n\nNote that the diagram is not drawn to scal... | math | {
"style": "rule",
"ground_truth": "61"
} | {
"split": "train",
"index": 25453,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify completely: $$\\sqrt[3]{30^3+40^3+50^3}$$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 25454,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the game of Frood, dropping $n$ froods gives a score of the sum of the first $n$ positive integers. For example, dropping five froods scores $1 + 2 + 3 + 4 + 5 = 15$ points. Eating $n$ froods earns $10n$ points. For example, eating five froods earns $10(5) = 50$ points. What... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 25455,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that we have an 8-sided die with 4 red faces, 3 yellow faces, and a blue face. What is the probability of rolling a yellow face? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac38"
} | {
"split": "train",
"index": 25456,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cuckoo clock produces a number of \"cuckoo\" sounds equal to the hour it indicates (for example, at 19:00, it sounds \"cuckoo\" 7 times). One morning, Maxim approaches the clock at 9:05 and starts turning the minute hand forward until the clock shows 7 hours later. How many \... | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 25457,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If a number is selected at random from the set of all five-digit numbers in which the sum of the digits is equal to 35, what is the probability that this number will be divisible by 11?\nA) $\\frac{1}{4}$\nB) $\\frac{1}{8}$\nC) $\\frac{1}{5}$\nD) $\\frac{1}{10}$\nE) $\\frac{1}{... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"split": "train",
"index": 25458,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all positive integers $a=2^n3^m$ where $n$ and $m$ are non-negative integers, for which $a^6$ is not a divisor of $6^a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 25459,
"solution": "Notice that the condition is equivalent to saying\n\\[v_2(a^6) \\geq v_2(6^a) \\implies 6n \\geq a\\] \\[v_3(a^6) \\geq v_3(6^a) \\implies 6m \\geq a.\\]\n Notice that we cannot have both expressions to be equality state, as that would result in $a^6 = 6^a.$ Testin... |
deepscaler | [
{
"role": "user",
"content": "Given that the price of a gallon of gasoline initially increased by $30\\%$ in January, then decreased by $10\\%$ in February, increased by $15\\%$ in March, and returned to its original value at the end of April, find the value of $x\\%$ that represents the percentage decrease... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 25460,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $(625^{\\log_2 250})^{\\frac{1}{4}}$, find the value of the expression. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "250"
} | {
"split": "train",
"index": 25461,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line segment begins at $(2, 5)$. It is 10 units long and ends at the point $(-6, y)$ where $y > 0$. What is the value of $y$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 25462,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A grocer sets up a pyramid display for a store promotion, where the topmost row has three cans and each succeeding row below has three more cans than the row immediately above it. If the grocer uses 225 cans in total for this display, how many rows are there in the display? Let... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 25463,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the volume of the solid generated by a rotation of the region enclosed by the curve $y=x^3-x$ and the line $y=x$ about the line $y=x$ as the axis of rotation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{64\\pi}{105}"
} | {
"split": "train",
"index": 25464,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For distinct complex numbers $z_1,z_2,\\dots,z_{673}$, the polynomial \\[(x-z_1)^3(x-z_2)^3 \\cdots (x-z_{673})^3\\]can be expressed as $x^{2019} + 20x^{2018} + 19x^{2017}+g(x)$, where $g(x)$ is a polynomial with complex coefficients and with degree at most $2016$. The sum $\\l... | math | {
"style": "rule",
"ground_truth": "352"
} | {
"split": "train",
"index": 25465,
"solution": "This is a quick fake solve using $z_i = 0$ where $3 \\le i \\le 673$ and only $z_1,z_2 \\neq 0$ .\n By Vieta's, \\[3z_1+3z_2=-20\\] and \\[3z_1^2+3z_2^2+9z_1z_2 = 19.\\] Rearranging gives $z_1 + z_2 = \\dfrac{-20}{3}$ and $3(z_1^2 + 2z_1z_2 + z_2^2) + 3z_1z_2 = 19$... |
deepscaler | [
{
"role": "user",
"content": "In a geometric progression with a common ratio of 4, denoted as $\\{b_n\\}$, where $T_n$ represents the product of the first $n$ terms of $\\{b_n\\}$, the fractions $\\frac{T_{20}}{T_{10}}$, $\\frac{T_{30}}{T_{20}}$, and $\\frac{T_{40}}{T_{30}}$ form another geometric sequence ... | math | {
"style": "rule",
"ground_truth": "300"
} | {
"split": "train",
"index": 25466,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a sphere, there are four points A, B, C, and D satisfying $AB=1$, $BC=\\sqrt{3}$, $AC=2$. If the maximum volume of tetrahedron D-ABC is $\\frac{\\sqrt{3}}{2}$, then the surface area of this sphere is _______. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "\\frac{100\\pi}{9}"
} | {
"split": "train",
"index": 25467,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a$, $b$, and $c$ represent the sides opposite to angles $A$, $B$, and $C$ respectively in $\\triangle ABC$, and the altitude on side $BC$ is $\\frac{a}{2}$. Determine the maximum value of $\\frac{c}{b}$. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} + 1"
} | {
"split": "train",
"index": 25468,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A quadrilateral is inscribed in a circle of radius $200\\sqrt{2}$. Three of the sides of this quadrilateral have length $200$. What is the length of the fourth side? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "500"
} | {
"split": "train",
"index": 25469,
"solution": "1. **Setup and Diagram**: Let quadrilateral $ABCD$ be inscribed in a circle $O$ with radius $200\\sqrt{2}$. Assume $AD$ is the side of unknown length, and $AB = BC = CD = 200$. Draw radii $OA$, $OB$, $OC$, and $OD$.\n\n2. **Using the Pythagorean Theorem in $\\trian... |
deepscaler | [
{
"role": "user",
"content": "A cylinder has a radius of 5 cm and a height of 12 cm. What is the longest segment, in centimeters, that would fit inside the cylinder? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{244}"
} | {
"split": "train",
"index": 25470,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Eight students participate in a pie-eating contest. The graph shows the number of pies eaten by each participating student. Sarah ate the most pies and Tom ate the fewest. Calculate how many more pies than Tom did Sarah eat and find the average number of pies eaten by all the s... | math | {
"style": "rule",
"ground_truth": "4.5"
} | {
"split": "train",
"index": 25471,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Quadrilateral $EFGH$ has right angles at $F$ and $H$, and $EG = 5$. If $EFGH$ has two sides with distinct integer lengths, and each side length is greater than 1, what is the area of $EFGH$? Express your answer in simplest radical form. Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 25472,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $QRS$ is a straight line. What is the measure of $\\angle RPS,$ in degrees? [asy]\npair Q=(0,0);\npair R=(1.3,0);\npair SS=(2.3,0);\npair P=(.8,1);\n\ndraw(P--Q--R--SS--P--R);\n\nlabel(\"$Q$\",Q,S);\nlabel(\"$R$\",R,S);\nlabel(\"$S$\",SS,S);\nlabel(\"$P$\",P,N);... | math | {
"style": "rule",
"ground_truth": "27^\\circ"
} | {
"split": "train",
"index": 25473,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P(x) = x^3 + ax^2 + bx + 1$ be a polynomial with real coefficients and three real roots $\\rho_1$ , $\\rho_2$ , $\\rho_3$ such that $|\\rho_1| < |\\rho_2| < |\\rho_3|$ . Let $A$ be the point where the graph of $P(x)$ intersects $yy'$ and the point $B(\\rho_1,... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 25474,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base-10 numbers 217 and 45 are multiplied. The product is then written in base-6. What is the units digit of the base-6 representation? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 25475,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The integer parts of two finite decimals are 7 and 10, respectively. How many possible values are there for the integer part of the product of these two finite decimals? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 25476,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the numerical value of $k$ such that\n\\[\\frac{12}{x + z} = \\frac{k}{z - y} = \\frac{5}{y - x}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 25477,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( n = 1990 \\), then what is \\( \\frac{1}{2^{n}}\\left(1-3 \\mathrm{C}_{n}^{2}+3^{2} \\mathrm{C}_{n}^{4}-3^{3} \\mathrm{C}_{n}^{6}+\\cdots+3^{994} \\mathrm{C}_{n}^{1988}-3^{9995} \\mathrm{C}_{n}^{1990}\\right) \\)? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 25478,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer $n$ such that there exists a sequence of $n+1$ terms $a_{0}, a_{1}, \\cdots, a_{n}$ satisfying $a_{0}=0, a_{n}=2008$, and $\\left|a_{i}-a_{i-1}\\right|=i^{2}$ for $i=1,2, \\cdots, n$. Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 25479,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a>0, b>0$) with a point C on it, a line passing through the center of the hyperbola intersects the hyperbola at points A and B. Let the slopes of the lines AC and BC be $k_1$ and $k_2$ respectively. Find the eccentri... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 25480,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many three-digit numbers are there in which each digit is greater than the digit to its right? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "84"
} | {
"split": "train",
"index": 25481,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the coefficient of $x^8$ in the expansion of $(x-1)^9$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-9"
} | {
"split": "train",
"index": 25482,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function \\[f(x) = \\left\\{ \\begin{aligned} x-3 & \\quad \\text{ if } x < 5 \\\\ \\sqrt{x} & \\quad \\text{ if } x \\ge 5 \\end{aligned} \\right.\\] has an inverse $f^{-1}.$ Find the value of $f^{-1}(0) + f^{-1}(1) + \\dots + f^{-1}(9).$ Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "291"
} | {
"split": "train",
"index": 25483,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alli rolls a standard $8$-sided die twice. What is the probability of rolling integers that differ by $3$ on her first two rolls? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"split": "train",
"index": 25484,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $A$ is at $(0, 0)$ and point $B$ is on the line $y = 4$. The slope of segment $AB$ is $\\frac{2}{3}$. What is the sum of the $x$- and $y$-coordinates of point $B$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 25485,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We are given a triangle $ABC$ . Points $D$ and $E$ on the line $AB$ are such that $AD=AC$ and $BE=BC$ , with the arrangment of points $D - A - B - E$ . The circumscribed circles of the triangles $DBC$ and $EAC$ meet again at the point $X\\neq C$ , and the circum... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 25486,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The integer numbers from $1$ to $2002$ are written in a blackboard in increasing order $1,2,\\ldots, 2001,2002$. After that, somebody erases the numbers in the $ (3k+1)-th$ places i.e. $(1,4,7,\\dots)$. After that, the same person erases the numbers in the $(3k+1)-th$ positions... | math | {
"style": "rule",
"ground_truth": "2,6,10"
} | {
"split": "train",
"index": 25487,
"solution": "\nLet's analyze the process of elimination step by step, starting from the list of integers from 1 to 2002:\n\n### Step 1:\nInitially, the numbers \\(1, 2, \\ldots, 2002\\) are written on the board. In this first step, numbers at positions \\(1, 4, 7, \\ldots\\) (i... |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $3^0 + 3^1 + 3^2 + \\cdots + 3^{2009}$ is divided by 8? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 25488,
"solution": "\n#### Step-by-step Analysis:\n\n**Solution 1:**\n1. **Observation of Pattern:** Notice that $3^0 + 3^1 + 3^2 + 3^3 = 1 + 3 + 9 + 27 = 40$, which is divisible by 8. This implies that any sum of four consecutive powers of 3 starting from a power of 0 modulo 4 is div... |
deepscaler | [
{
"role": "user",
"content": "In a Cartesian coordinate plane, the \"rectilinear distance\" between points $P\\left(x_{1}, y_{1}\\right)$ and $Q\\left(x_{2}, y_{2}\\right)$ is defined as $d(P, Q) = \\left|x_{1} - x_{2}\\right| + \\left|y_{1} - y_{2}\\right|$. If point $C(x, y)$ has an equal \"rectilinear di... | math | {
"style": "rule",
"ground_truth": "5(\\sqrt{2} + 1)"
} | {
"split": "train",
"index": 25489,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The isosceles right triangle $ABC$ has right angle at $C$ and area $12.5$. The rays trisecting $\\angle ACB$ intersect $AB$ at $D$ and $E$. What is the area of $\\triangle CDE$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{50-25\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 25490,
"solution": "1. **Identify the properties of triangle $ABC$:**\n Given that $ABC$ is an isosceles right triangle with a right angle at $C$ and an area of $12.5$, we can find the lengths of the legs. The area of a triangle is given by:\n \\[\n \\text{Area} = \\frac{1}{2} \... |
deepscaler | [
{
"role": "user",
"content": "Given that $a$ and $b$ are positive integers and that $a+b=24$, what is the value of $ab$ if $2ab + 10a = 3b + 222$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "108"
} | {
"split": "train",
"index": 25491,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $a$ if $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^{17} + bx^{16} + 1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "987"
} | {
"split": "train",
"index": 25492,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to put 7 balls into 4 boxes if the balls are indistinguishable and the boxes are also indistinguishable? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 25493,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When the vectors $\\begin{pmatrix} 4 \\\\ 1 \\end{pmatrix}$ and $\\begin{pmatrix} -1 \\\\ 3 \\end{pmatrix}$ are both projected onto the same vector $\\mathbf{v},$ the result is $\\mathbf{p}$ in both cases. Find $\\mathbf{p}.$ Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 26/29 \\\\ 65/29 \\end{pmatrix}"
} | {
"split": "train",
"index": 25494,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A heavy concrete platform anchored to the seabed in the North Sea supported an oil rig that stood 40 m above the calm water surface. During a severe storm, the rig toppled over. The catastrophe was captured from a nearby platform, and it was observed that the top of the rig dis... | math | {
"style": "rule",
"ground_truth": "68.2"
} | {
"split": "train",
"index": 25495,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $y = x^2 - 8x + 12$, find the vertex of the parabola and calculate the value of $y$ when $x = 3$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 25496,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(f_{0}(x)=\\frac{1}{c-x}\\) and \\(f_{n}(x)=f_{0}\\left(f_{n-1}(x)\\right)\\), \\(n=1,2,3, \\ldots\\). If \\(f_{2000}(2000)=d\\), find the value of \\(d\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2000"
} | {
"split": "train",
"index": 25497,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle is made of wood sticks of lengths 8, 15 and 17 inches joined end-to-end. Pieces of the same integral length are cut from each of the sticks so that the three remaining pieces can no longer form a triangle. How many inches are in the length of the smallest piece that ... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 25498,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $2^3\\times3\\times5^3\\times7$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21,\\!000"
} | {
"split": "train",
"index": 25499,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A town's reservoir has a usable water volume of 120 million cubic meters. Assuming the annual precipitation remains unchanged, it can sustain a water supply for 160,000 people for 20 years. After urbanization and the migration of 40,000 new residents, the reservoir will only be... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 25500,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If two 4'' by 4'' squares are added at each successive stage, what will be the area of the rectangle at Stage 4, in square inches? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "128"
} | {
"split": "train",
"index": 25501,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$D$ is a point on side $AB$ of triangle $ABC$, satisfying $AD=2$ and $DB=8$. Let $\\angle ABC=\\alpha$ and $\\angle CAB=\\beta$. <br/>$(1)$ When $CD\\perp AB$ and $\\beta =2\\alpha$, find the value of $CD$; <br/>$(2)$ If $α+\\beta=\\frac{π}{4}$, find the maximum area of triangl... | math | {
"style": "rule",
"ground_truth": "5(\\sqrt{2} - 1)"
} | {
"split": "train",
"index": 25502,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the pyramid \\(ABCD\\), points \\(M\\), \\(F\\), and \\(K\\) are the midpoints of edges \\(BC\\), \\(AD\\), and \\(CD\\) respectively. Points \\(P\\) and \\(Q\\) are chosen on lines \\(AM\\) and \\(CF\\) respectively such that \\(PQ \\parallel BK\\). Find the ratio \\(PQ : B... | math | {
"style": "rule",
"ground_truth": "2:5"
} | {
"split": "train",
"index": 25503,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the volume of the region in space defined by\n\\[|x + y + z| + |x + y - z| \\le 12\\]\nand \\(x, y, z \\ge 0.\\) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "108"
} | {
"split": "train",
"index": 25504,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Inside a circle \\(\\omega\\) there is a circle \\(\\omega_{1}\\) touching \\(\\omega\\) at point \\(K\\). Circle \\(\\omega_{2}\\) touches circle \\(\\omega_{1}\\) at point \\(L\\) and intersects circle \\(\\omega\\) at points \\(M\\) and \\(N\\). It turns out that the points ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 25505,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At 7:10 in the morning, Xiao Ming's mother wakes him up and asks him to get up. However, Xiao Ming sees the time in the mirror and thinks that it is not yet time to get up. He tells his mother, \"It's still early!\" Xiao Ming mistakenly believes that the time is $\\qquad$ hours... | math | {
"style": "rule",
"ground_truth": "4:50"
} | {
"split": "train",
"index": 25506,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Susie pays for $4$ muffins and $3$ bananas. Calvin spends twice as much paying for $2$ muffins and $16$ bananas. A muffin is how many times as expensive as a banana? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{3}"
} | {
"split": "train",
"index": 25507,
"solution": "1. **Define Variables:**\n Let $m$ represent the cost of one muffin and $b$ represent the cost of one banana.\n\n2. **Set Up Equations:**\n According to the problem, Susie's total cost for $4$ muffins and $3$ bananas is given by:\n \\[ 4m + 3b \\]\n Calvin ... |
deepscaler | [
{
"role": "user",
"content": "Given that 3 females and 2 males participate in a performance sequence, and the 2 males cannot appear consecutively, and female A cannot be the first to appear, determine the total number of different performance sequences. Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 25508,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The area of the smallest square that will contain a circle of radius 4 is what? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 25509,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle $X Y Z$ and a circle $\\omega$ of radius 2 are given in a plane, such that $\\omega$ intersects segment $\\overline{X Y}$ at the points $A, B$, segment $\\overline{Y Z}$ at the points $C, D$, and segment $\\overline{Z X}$ at the points $E, F$. Suppose that $X B>X A, ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{10}-1"
} | {
"split": "train",
"index": 25510,
"solution": "Let $d=A B$ and $x=d / 2$ for ease of notation. Let the center of $(A B C D E F)$ be $I$. Because $A B=C D=E F$, the distance from $I$ to $A B, C D$, and $E F$ are the same, so $I$ is the incenter of $\\triangle X Y Z$. Let $\\triangle X Y Z$ have inradius $r$. By ... |
deepscaler | [
{
"role": "user",
"content": "Given the function \\( f(x)=\\cos x + m \\left(x+\\frac{\\pi}{2}\\right) \\sin x \\) where \\( m \\leqslant 1 \\):\n\n(1) Discuss the number of zeros of \\( f(x) \\) in the interval \\( (-\\pi, 0) \\).\n\n(2) If there exists \\( t > 0 \\) such that \\( |f(x)| < -2x - \\pi \\) h... | math | {
"style": "rule",
"ground_truth": "m = -1"
} | {
"split": "train",
"index": 25511,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the vision data recorded by the five-point recording method satisfies the equation $L=5+\\lg V$, and a student's vision test data using the decimal recording method is $0.8$, calculate the student's vision data using the five-point recording method. Let's think step ... | math | {
"style": "rule",
"ground_truth": "4.9"
} | {
"split": "train",
"index": 25512,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The nonzero roots of the equation $x^2 + 6x + k = 0$ are in the ratio $2:1$. What is the value of $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 25513,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A ball is dropped from a height of 150 feet and rebounds to three-fourths of the distance it fell on each bounce. How many feet will the ball have traveled when it hits the ground the fifth time? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "765.234375"
} | {
"split": "train",
"index": 25514,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If Ella rolls a standard six-sided die until she rolls the same number on consecutive rolls, what is the probability that her 10th roll is her last roll? Express your answer as a decimal to the nearest thousandth. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": ".039"
} | {
"split": "train",
"index": 25515,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $F_m$ be the $m$th Fibonacci number, defined by $F_1 = F_2 = 1$ and $F_m = F_{m-1} + F_{m-2}$ for all $m \\geq 3$. Let $p(x)$ be the polynomial of degree $1008$ such that $p(2n+1) = F_{2n+1}$ for $n=0,1,2,\\dots,1008$. Find integers $j$ and $k$ such that $p(2019) = F_j - F_... | math | {
"style": "rule",
"ground_truth": "(j,k) = (2019, 1010)"
} | {
"split": "train",
"index": 25516,
"solution": "We prove that $(j,k) = (2019, 1010)$ is a valid solution. More generally, let $p(x)$ be the polynomial of degree $N$ such that $p(2n+1) = F_{2n+1}$ for $0 \\leq n \\leq N$. We will show that $p(2N+3) = F_{2N+3}-F_{N+2}$.\n\nDefine a sequence of polynomials $p_0(x),... |
deepscaler | [
{
"role": "user",
"content": "In acute triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $a\\sin B = \\frac{1}{2}b$. \n$(1)$ Find angle $A$; \n$(2)$ If $b+c=4\\sqrt{2}$ and the area of $\\triangle ABC$ is $2$, find $a$. Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}-2"
} | {
"split": "train",
"index": 25517,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a corridor 100 meters long, 20 carpet strips with a total length of 1000 meters are laid down. What could be the maximum number of uncovered sections (the width of the carpet strip is equal to the width of the corridor)? Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 25518,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A self-employed individual plans to distribute two types of products, A and B. According to a survey, when the investment amount is $x$ (where $x \\geq 0$) in ten thousand yuan, the profits obtained from distributing products A and B are $f(x)$ and $g(x)$ in ten thousand yuan, ... | math | {
"style": "rule",
"ground_truth": "12.6"
} | {
"split": "train",
"index": 25519,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C$ be a triangle and $D$ a point on $B C$ such that $A B=\\sqrt{2}, A C=\\sqrt{3}, \\angle B A D=30^{\\circ}$, and $\\angle C A D=45^{\\circ}$. Find $A D$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6}}{2}"
} | {
"split": "train",
"index": 25520,
"solution": "Note that $[B A D]+[C A D]=[A B C]$. If $\\alpha_{1}=\\angle B A D, \\alpha_{2}=\\angle C A D$, then we deduce $\\frac{\\sin \\left(\\alpha_{1}+\\alpha_{2}\\right)}{A D}=\\frac{\\sin \\alpha_{1}}{A C}+\\frac{\\sin \\alpha_{2}}{A B}$ upon division by $A B \\cdot A C... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the infinite series $\\frac{1}{3^{2}-1^{2}}\\left(\\frac{1}{1^{2}}-\\frac{1}{3^{2}}\\right)+\\frac{1}{5^{2}-3^{2}}\\left(\\frac{1}{3^{2}}-\\frac{1}{5^{2}}\\right)+\\frac{1}{7^{2}-5^{2}}\\left(\\frac{1}{5^{2}}-\\frac{1}{7^{2}}\\right)+$ Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 25521,
"solution": "$1-\\frac{1}{3}+\\frac{1}{3}-\\frac{1}{5}+\\cdots=1$."
} |
deepscaler | [
{
"role": "user",
"content": "Regular polygons with $5, 6, 7,$ and $8$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect? Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "68"
} | {
"split": "train",
"index": 25522,
"solution": "To solve this problem, we need to calculate the number of intersection points inside the circle where two sides from different polygons intersect. We consider pairs of polygons and count the intersections for each pair.\n\n1. **Understanding the Intersection Rule**... |
deepscaler | [
{
"role": "user",
"content": "A circle is tangent to both branches of the hyperbola $x^{2}-20y^{2}=24$ as well as the $x$-axis. Compute the area of this circle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "504\\pi"
} | {
"split": "train",
"index": 25523,
"solution": "Invert about the unit circle centered at the origin. $\\omega$ turns into a horizontal line, and the hyperbola turns into the following: $$\\begin{aligned} \\frac{x^{2}}{\\left(x^{2}+y^{2}\\right)^{2}}-\\frac{20y^{2}}{\\left(x^{2}+y^{2}\\right)^{2}}=24 & \\Longrigh... |
deepscaler | [
{
"role": "user",
"content": "Line $l$ in the coordinate plane has equation $3x-5y+40=0$. This line is rotated $45^{\\circ}$ counterclockwise about the point $(20,20)$ to obtain line $k$. What is the $x$-coordinate of the $x$-intercept of line $k?$ Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 25524,
"solution": "1. **Find the slope of line $l$:**\n The equation of line $l$ is given by $3x - 5y + 40 = 0$. We can rearrange this to slope-intercept form $y = mx + c$:\n \\[\n 5y = 3x + 40 \\implies y = \\frac{3}{5}x + 8\n \\]\n Thus, the slope $m$ of line $l$ is $\\fr... |
deepscaler | [
{
"role": "user",
"content": "Given that point M $(3n-2, 2n+7)$ is on the angle bisector of the second and fourth quadrants, then $n=$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 25525,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest quotient that can be formed using two numbers chosen from the set $\\{ -24, -3, -2, 1, 2, 8 \\}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 25526,
"solution": "To find the largest quotient formed using two numbers from the set $\\{-24, -3, -2, 1, 2, 8\\}$, we need to consider the absolute values of the numbers and the signs to maximize the quotient $\\frac{a}{b}$.\n\n1. **Maximizing the Quotient**:\n - The quotient $\\f... |
deepscaler | [
{
"role": "user",
"content": "It is known that there are four different venues $A$, $B$, $C$, $D$ at the Flower Expo. Person A and person B each choose 2 venues to visit. The probability that exactly one venue is the same in their choices is ____. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 25527,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the digits \\( a_{i} (i=1,2, \\cdots, 9) \\) satisfy\n$$\na_{9} < a_{8} < \\cdots < a_{5} \\text{ and } a_{5} > a_{4} > \\cdots > a_{1} \\text{, }\n$$\n\nthen the nine-digit positive integer \\(\\bar{a}_{9} a_{8} \\cdots a_{1}\\) is called a “nine-digit peak number”, for exa... | math | {
"style": "rule",
"ground_truth": "11875"
} | {
"split": "train",
"index": 25528,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $2^{1998} - 2^{1997} - 2^{1996} + 2^{1995} = k \\cdot 2^{1995},$ what is the value of $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 25529,
"solution": "1. **Rewrite the equation with a common factor:** \n Start by factoring out the smallest power of 2 from each term in the equation:\n \\[\n 2^{1998} - 2^{1997} - 2^{1996} + 2^{1995} = k \\cdot 2^{1995}\n \\]\n Factor out $2^{1995}$:\n \\[\n 2^{1995}(... |
deepscaler | [
{
"role": "user",
"content": "Please write down an irrational number whose absolute value is less than $3: \\_\\_\\_\\_\\_\\_.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 25530,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In circle $O$, $\\overline{EB}$ is a diameter and the line $\\overline{DC}$ is parallel to $\\overline{EB}$. The line $\\overline{AB}$ intersects the circle again at point $F$ such that $\\overline{AB}$ is parallel to $\\overline{ED}$. If angles $AFB$ and $ABF$ are in the ratio... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 25531,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of the first term in the geometric sequence $a,b,c,32,64$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 25532,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the constant term of the expansion of $\\left(5x + \\dfrac{1}{3x}\\right)^8$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{43750}{81}"
} | {
"split": "train",
"index": 25533,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of positive integers $a$ less than $12$ such that the congruence $ax\\equiv 1\\pmod{12}$ has a solution in $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 25534,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of different complex numbers $z$ such that $|z|=1$ and $z^{7!}-z^{6!}$ is a real number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7200"
} | {
"split": "train",
"index": 25535,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What real number is equal to the expression $2 + \\frac{4}{1 + \\frac{4}{2 + \\frac{4}{1 + \\cdots}}}$, where the $1$s and the $2$s alternate? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 25536,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right triangle $\\triangle ABC$ has sides $AC=3$, $BC=4$, and $AB=5$. When this triangle is rotated around the right-angle side $BC$, the surface area of the resulting solid is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24\\pi"
} | {
"split": "train",
"index": 25537,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let's modify the problem slightly. Sara writes down four integers $a > b > c > d$ whose sum is $52$. The pairwise positive differences of these numbers are $2, 3, 5, 6, 8,$ and $11$. What is the sum of the possible values for $a$? Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 25538,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define the sequence $a_1, a_2, a_3, \\ldots$ by $a_n = \\sum\\limits_{k=1}^n \\sin{k}$, where $k$ represents radian measure. Find the index of the 100th term for which $a_n < 0$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "628"
} | {
"split": "train",
"index": 25539,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the area bounded by the graph of $y = \\arcsin(\\cos x)$ and the $x$-axis over the interval $0 \\leq x \\leq 2\\pi$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\pi^2"
} | {
"split": "train",
"index": 25540,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is $\\frac{1}{2}$ foot from the top face. The second cut is $\\frac{1}{3}$ foot below the first cut, and the third cut is $\\frac{1}{17}$ foot below the second cut. F... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 25541,
"solution": "1. **Understanding the Problem**: We have a cube with a volume of 1 cubic foot, and it is cut into four pieces by three cuts parallel to the top face. The cuts are made at $\\frac{1}{2}$ foot, $\\frac{1}{3}$ foot, and $\\frac{1}{17}$ foot below each preceding cut. ... |
deepscaler | [
{
"role": "user",
"content": "The condition for three line segments to form a triangle is: the sum of the lengths of any two line segments is greater than the length of the third line segment. Now, there is a wire 144cm long, and it needs to be cut into $n$ small segments ($n>2$), each segment being no less... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 25542,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mark rolls 5 fair 8-sided dice. What is the probability that at least three of the dice show the same number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1052}{8192}"
} | {
"split": "train",
"index": 25543,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest six-digit number that can be obtained by removing nine digits from the number 778157260669103, without changing the order of its digits?\n(a) 778152\n(b) 781569\n(c) 879103\n(d) 986103\n(e) 987776 Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "879103"
} | {
"split": "train",
"index": 25544,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three aluminum cans can be recycled to make a new can. How many new cans can eventually be made from 243 aluminum cans? (Remember that the first new cans that are made can then be recycled into even newer cans!) Do not include the original 243 cans in your count. Let's think s... | math | {
"style": "rule",
"ground_truth": "121"
} | {
"split": "train",
"index": 25545,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x)={x}^{2023}+a{x}^{3}-\\frac{b}{x}-8$, $f\\left(-2\\right)=10$, find $f\\left(2\\right)=\\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-26"
} | {
"split": "train",
"index": 25546,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 7 students standing in a row. How many different arrangements are there in the following situations? \n(1) A and B must stand together; \n(2) A is not at the head of the line, and B is not at the end of the line; \n(3) There must be exactly one person between A and... | math | {
"style": "rule",
"ground_truth": "1200"
} | {
"split": "train",
"index": 25547,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $T$ be a subset of $\\{1,2,3,...,60\\}$ such that no pair of distinct elements in $T$ has a sum divisible by $5$. What is the maximum number of elements in $T$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 25548,
"solution": ""
} |
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