data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "The first $30$ numbers of a similar arrangement are shown below. What would be the value of the $50^{\\mathrm{th}}$ number if the arrangement were continued?\n\n$\\bullet$ Row 1: $3,$ $3$\n\n$\\bullet$ Row 2: $6,$ $6,$ $6,$ $6$\n\n$\\bullet$ Row 3: $9,$ $9,$ $9,$ $9,$ $9,$ $9$\... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 25349,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $p(x)$ be a polynomial of degree 6 such that\n\\[p(2^n) = \\frac{1}{2^n}\\]for $n = 0,$ 1, 2, $\\dots,$ 6. Find $p(0).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{127}{64}"
} | {
"split": "train",
"index": 25350,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $k>0$ and that the line with equation $y=3kx+4k^{2}$ intersects the parabola with equation $y=x^{2}$ at points $P$ and $Q$. If $O$ is the origin and the area of $\triangle OPQ$ is 80, then what is the slope of the line? Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 25351,
"solution": "First, we find the coordinates of the points $P$ and $Q$ in terms of $k$ by finding the points of intersection of the graphs with equations $y=x^{2}$ and $y=3kx+4k^{2}$. Equating values of $y$, we obtain $x^{2}=3kx+4k^{2}$ or $x^{2}-3kx-4k^{2}=0$. We rewrite the le... |
deepscaler | [
{
"role": "user",
"content": "Given the graph of $y=\\sqrt{2}\\sin 3x$, calculate the horizontal shift required to obtain the graph of $y=\\sin 3x+\\cos 3x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\pi}{12}"
} | {
"split": "train",
"index": 25352,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The squares of a chessboard are labelled with numbers, as shown below.\n\n[asy]\nunitsize(0.8 cm);\n\nint i, j;\n\nfor (i = 0; i <= 8; ++i) {\n draw((i,0)--(i,8));\n draw((0,i)--(8,i));\n}\n\nfor (i = 0; i <= 7; ++i) {\nfor (j = 0; j <= 7; ++j) {\n label(\"$\\frac{1}{\" + st... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 25353,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest number $n \\geq 5$ for which there can exist a set of $n$ people, such that any two people who are acquainted have no common acquaintances, and any two people who are not acquainted have exactly two common acquaintances.\n\n*Bulgaria* Let's think step by s... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 25354,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Denote by $\\mathbb{Q}^+$ the set of all positive rational numbers. Determine all functions $f : \\mathbb{Q}^+ \\mapsto \\mathbb{Q}^+$ which satisfy the following equation for all $x, y \\in \\mathbb{Q}^+:$ \\[f\\left( f(x)^2y \\right) = x^3 f(xy).\\]\n\n[i] Let's think step by... | math | {
"style": "rule",
"ground_truth": "{f(x) = \\frac{1}{x}}"
} | {
"split": "train",
"index": 25355,
"solution": "\nTo solve the functional equation for all functions \\( f : \\mathbb{Q}^+ \\to \\mathbb{Q}^+ \\) such that for all \\( x, y \\in \\mathbb{Q}^+ \\),\n\n\\[\nf(f(x)^2 y) = x^3 f(xy),\n\\]\n\nwe proceed with the following steps:\n\n**Step 1: Simplify the equation usi... |
deepscaler | [
{
"role": "user",
"content": "In a right triangle, one of the acute angles $\\alpha$ satisfies\n\\[\\tan \\frac{\\alpha}{2} = \\frac{1}{\\sqrt[3]{2}}.\\]Let $\\theta$ be the angle between the median and the angle bisector drawn from this acute angle. Find $\\tan \\theta.$ Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 25356,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\tan (\\alpha+ \\frac {π}{3})=2$, find the value of $\\frac {\\sin (\\alpha+ \\frac {4π}{3})+\\cos ( \\frac {2π}{3}-\\alpha)}{\\cos ( \\frac {π}{6}-\\alpha )-\\sin (\\alpha + \\frac {5π}{6})}$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 25357,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For an arithmetic sequence $b_1,$ $b_2,$ $b_3,$ $\\dots,$ let\n\\[P_n = b_1 + b_2 + b_3 + \\dots + b_n,\\]and let\n\\[Q_n = P_1 + P_2 + P_3 + \\dots + P_n.\\]If you are told the value of $P_{2023},$ then you can uniquely determine the value of $Q_n$ for some integer $n.$ What ... | math | {
"style": "rule",
"ground_truth": "3034"
} | {
"split": "train",
"index": 25358,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $x$ in the equation $9^4+9^4+9^4=3^x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 25359,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 25360,
"solution": "1. **Calculate the number of small red faces:**\n The original cube has $6$ faces, and each face is $n \\times n$, so there are $n^2$ small faces per face of the cube. Since all faces are painted red, the total number of small red faces is $6n^2$.\n\n2. **Calcula... |
deepscaler | [
{
"role": "user",
"content": "Determine the number of ways to arrange the letters of the word RADII. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 25361,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the remainder when $109876543210$ is divided by $180$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 25362,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line \\( l \\) passes through the focus \\( F \\) of the parabola \\( y^2 = 4x \\) and intersects the parabola at points \\( A \\) and \\( B \\). Point \\( M \\) is given as \\( (4,0) \\). Extending \\( AM \\) and \\( BM \\) intersects the parabola again at points \\( C \\) a... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 25363,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, $c$, and $d$ be positive integers with $a < 2b$, $b < 3c$, and $c<4d$. If $d<100$, the largest possible value for $a$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2367"
} | {
"split": "train",
"index": 25364,
"solution": "1. **Understanding the inequalities**:\n Given are the inequalities $a < 2b$, $b < 3c$, and $c < 4d$. We also know that $d < 100$.\n\n2. **Finding the upper bound for $d$**:\n Since $d$ is a positive integer and $d < 100$, the maximum possible value for $d$ is ... |
deepscaler | [
{
"role": "user",
"content": "For a math tournament, each person is assigned an ID which consists of two uppercase letters followed by two digits. All IDs have the property that either the letters are the same, the digits are the same, or both the letters are the same and the digits are the same. Compute th... | math | {
"style": "rule",
"ground_truth": "9100"
} | {
"split": "train",
"index": 25365,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the best approximation of $\\sqrt{3}$ by a rational number with denominator less than or equal to $15$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{26}{15}"
} | {
"split": "train",
"index": 25366,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate:\n\n1. $(2\\frac{3}{5})^{0} + 2^{-2}\\cdot(2\\frac{1}{4})^{-\\frac{1}{2}} + (\\frac{25}{36})^{0.5} + \\sqrt{(-2)^{2}}$;\n2. $\\frac{1}{2}\\log\\frac{32}{49} - \\frac{4}{3}\\log\\sqrt{8} + \\log\\sqrt{245}$. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 25367,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a set of data: $a_{1}=\\frac{3}{1×2×3}$, $a_{2}=\\frac{5}{2×3×4}$, $a_{3}=\\frac{7}{3×4×5}$, $\\ldots $, $a_{n}=\\frac{2n+1}{n(n+1)(n+2)}$. Let $S_{n}=a_{1}+a_{2}+a_{3}+\\ldots +a_{n}$. Find the value of $S_{12}$. To solve this problem, Xiao Ming first simplified $a_{n... | math | {
"style": "rule",
"ground_truth": "\\frac{201}{182}"
} | {
"split": "train",
"index": 25368,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rich emir was admiring a new jewel, a small golden plate in the shape of an equilateral triangle, decorated with diamonds. He noticed that the shadow of the plate forms a right triangle, with the hypotenuse being the true length of each side of the plate. \n\nWhat is the angl... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 25369,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer that has exactly eight distinct positive factors? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 25370,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the plane rectangular coordinate system $xOy$, the parametric equations of the line $l$ are $\\left\\{\\begin{array}{l}x=1+\\frac{1}{2}t\\\\ y=\\frac{\\sqrt{3}}{2}t\\end{array}\\right.$ (where $t$ is a parameter). Taking $O$ as the pole and the positive half-axis of the $x$-... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{7}}{4}"
} | {
"split": "train",
"index": 25371,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $EFGH$, $EFDC$, and $EHBC$ be three adjacent square faces of a cube, for which $EC = 8$, and let $A$ be the eighth vertex of the cube. Let $I$, $J$, and $K$, be the points on $\\overline{EF}$, $\\overline{EH}$, and $\\overline{EC}$, respectively, so that $EI = EJ = EK = 2$.... | math | {
"style": "rule",
"ground_truth": "417"
} | {
"split": "train",
"index": 25372,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest $2$-digit prime factor of the integer $n = {300\\choose 150}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "97"
} | {
"split": "train",
"index": 25373,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the arithmetic sequence $\\{a_{n}\\}$, $\\frac{a_{1010}}{a_{1009}} < -1$. If its first $n$ terms' sum $S_{n}$ has a maximum value, then the maximum positive integer value of $n$ that makes $S_{n} > 0$ is $\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.$ Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "2018"
} | {
"split": "train",
"index": 25374,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Shauna takes five tests, each worth a maximum of $100$ points. Her scores on the first three tests are $76$, $94$, and $87$. In order to average $81$ for all five tests, what is the lowest score she could earn on one of the other two tests? Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 25375,
"solution": "1. **Calculate the total points Shauna has scored on the first three tests:**\n \\[\n 76 + 94 + 87 = 257 \\text{ points}\n \\]\n\n2. **Determine the total points needed for an average of 81 over five tests:**\n \\[\n 81 \\times 5 = 405 \\text{ points}\n ... |
deepscaler | [
{
"role": "user",
"content": "Two individuals undertake a certain task and work for an equal amount of time. $A$ misses 2 days and earns 80 forints in total, while $B$ misses 5 days and earns 63 forints. If $A$ had missed 5 days and $B$ had missed 2 days, then $A$ would earn 2 forints more than $B$. How man... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 25376,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square with side length 8 is cut in half, creating two congruent rectangles. What are the dimensions of one of these rectangles? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4 \\times 8"
} | {
"split": "train",
"index": 25377,
"solution": "1. **Identify the original dimensions of the square**: The square has a side length of 8 units. Therefore, each side of the square is 8 units long.\n\n2. **Understand the effect of cutting the square in half**: When the square is cut in half, one dimension is halve... |
deepscaler | [
{
"role": "user",
"content": "The check for a luncheon of 3 sandwiches, 7 cups of coffee and one piece of pie came to $3.15$. The check for a luncheon consisting of 4 sandwiches, 10 cups of coffee and one piece of pie came to $4.20$ at the same place. The cost of a luncheon consisting of one sandwich, one c... | math | {
"style": "rule",
"ground_truth": "$1.05"
} | {
"split": "train",
"index": 25378,
"solution": "1. **Define Variables:**\n Let $s$ be the cost of one sandwich, $c$ be the cost of one cup of coffee, and $p$ be the price of one piece of pie.\n\n2. **Set Up Equations:**\n From the problem, we have the following equations based on the given checks:\n \\[\n ... |
deepscaler | [
{
"role": "user",
"content": "Math City plans to add more streets and now has 10 streets, but two pairs of these streets are parallel to each other. No other streets are parallel, and no street is parallel to more than one other street. What is the greatest number of police officers needed at intersections,... | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 25379,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If four people, A, B, C, and D, line up in a row, calculate the number of arrangements in which B and C are on the same side of A. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 25380,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the smallest natural number written in the decimal system with the product of the digits equal to $10! = 1 \\cdot 2 \\cdot 3\\cdot ... \\cdot9\\cdot10$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45578899"
} | {
"split": "train",
"index": 25381,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x_{1}$ be a positive real number and for every integer $n \\geq 1$ let $x_{n+1} = 1 + x_{1}x_{2}\\ldots x_{n-1}x_{n}$ . \nIf $x_{5} = 43$ , what is the sum of digits of the largest prime factors of $x_{6}$ ? Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 25382,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In \\(\\triangle ABC\\), the external angle bisector of \\(\\angle BAC\\) intersects line \\(BC\\) at \\(D\\). \\(E\\) is a point on ray \\(\\overrightarrow{AC}\\) such that \\(\\angle BDE=2 \\angle ADB\\). If \\(AB=10, AC=12\\), and \\(CE=33\\), compute \\(\\frac{DB}{DE}\\). L... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 25383,
"solution": "Let \\(F\\) be a point on ray \\(\\overrightarrow{CA}\\) such that \\(\\angle ADF=\\angle ADB\\). \\(\\triangle ADF\\) and \\(\\triangle ADB\\) are congruent, so \\(AF=10\\) and \\(DF=DB\\). So, \\(CF=CA+AF=22\\). Since \\(\\angle FDC=2 \\angle ADB=\\angle EDC\\), ... |
deepscaler | [
{
"role": "user",
"content": "(1) If the terminal side of angle $\\theta$ passes through $P(-4t, 3t)$ ($t>0$), find the value of $2\\sin\\theta + \\cos\\theta$. \n(2) Given that a point $P$ on the terminal side of angle $\\alpha$ has coordinates $(x, -\\sqrt{3})$ ($x\\neq 0$), and $\\cos\\alpha = \\frac{\\... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"split": "train",
"index": 25384,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Continue the problem statement \"Petya and Kolya went to the forest to pick mushrooms. In the first hour, Petya collected twice as many mushrooms as Kolya...\" so that its solution is determined by the expression $30: 3+4$. Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 25385,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a box contains a total of 180 marbles, 25% are silver, 20% are gold, 15% are bronze, 10% are sapphire, and 10% are ruby, and the remainder are diamond marbles. If 10% of the gold marbles are removed, calculate the number of marbles left in the box. Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "176"
} | {
"split": "train",
"index": 25386,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C$ be a triangle with $A B=23, B C=24$, and $C A=27$. Let $D$ be the point on segment $A C$ such that the incircles of triangles $B A D$ and $B C D$ are tangent. Determine the ratio $C D / D A$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\frac{14}{13}"
} | {
"split": "train",
"index": 25387,
"solution": "Let $X, Z, E$ be the points of tangency of the incircle of $A B D$ to $A B, B D, D A$ respectively. Let $Y, Z, F$ be the points of tangency of the incircle of $C B D$ to $C B, B D, D C$ respectively. We note that $$C B+B D+D C=C Y+Y B+B Z+Z D+D F+F C=2(C Y)+2(B Y)+... |
deepscaler | [
{
"role": "user",
"content": "One piece of string is 1.5 inches long and another piece of string is 4.5 inches long. What is the average length, in inches, of these two pieces of string? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 25388,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $y^2=2px$ ($p>0$) with focus $F(1,0)$, and the line $l: y=x+m$ intersects the parabola at two distinct points $A$ and $B$. If $0\\leq m<1$, determine the maximum area of $\\triangle FAB$. Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "\\frac{8\\sqrt{6}}{9}"
} | {
"split": "train",
"index": 25389,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f$ is linear and satisfies $f(d+1)-f(d) = 3$ for all real numbers $d$. What is $f(3)-f(5)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 25390,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vasya is creating a 4-digit password for a combination lock. He dislikes the digit 2 and does not use it. Additionally, he does not like having two identical digits adjacent to each other. Moreover, he wants the first digit to be the same as the last digit. How many possible co... | math | {
"style": "rule",
"ground_truth": "576"
} | {
"split": "train",
"index": 25391,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The polynomial $(x+y)^{10}$ is expanded in decreasing powers of $x$. The second and third terms have equal values when evaluated at $x=p$ and $y=q$, where $p$ and $q$ are positive numbers whose sum of $p$ plus twice $q$ equals one. Determine the value of $p$. Let's think step b... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{13}"
} | {
"split": "train",
"index": 25392,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Positive integers \\(a\\), \\(b\\), \\(c\\), and \\(d\\) satisfy \\(a > b > c > d\\), \\(a + b + c + d = 2200\\), and \\(a^2 - b^2 + c^2 - d^2 = 2200\\). Find the number of possible values of \\(a\\). Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "548"
} | {
"split": "train",
"index": 25393,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Isabella writes the expression $\\sqrt{d}$ for each positive integer $d$ not exceeding 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Vidur simplifies each expression to the form $a \\sqrt{b}$, where $a$ and $b$ are integers such that $b$ is ... | math | {
"style": "rule",
"ground_truth": "534810086"
} | {
"split": "train",
"index": 25394,
"solution": "Let $\\sqrt{n}$ simplifies to $a_{n} \\sqrt{b_{n}}$, and replace 8 ! by $x$. First, notice that $\\sum_{n \\leq x} a_{n}$ is small $\\left(O\\left(x^{3 / 2}\\right)\\right.$ in particular) because each term cannot exceed $\\sqrt{x}$. On the other hand, $\\sum_{n \\... |
deepscaler | [
{
"role": "user",
"content": "A line segment starts at $(2, 4)$ and ends at the point $(7, y)$ with $y > 0$. The segment is 6 units long. Find the value of $y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4 + \\sqrt{11}"
} | {
"split": "train",
"index": 25395,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In Papa Carlo's room, there is a clock on each wall, and they all show incorrect times: the first clock is off by 2 minutes, the second by 3 minutes, the third by 4 minutes, and the fourth by 5 minutes. One day, Papa Carlo decided to find out the exact time before leaving the h... | math | {
"style": "rule",
"ground_truth": "14:58"
} | {
"split": "train",
"index": 25396,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A club has 10 members, 5 boys and 5 girls. Two of the members are chosen at random. What is the probability that they are both girls? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{2}{9}"
} | {
"split": "train",
"index": 25397,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of solutions to \\{1,~2\\} \\subseteq~X~\\subseteq~\\{1,~2,~3,~4,~5\\}, where $X$ is a subset of \\{1,~2,~3,~4,~5\\} is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 25398,
"solution": "1. **Identify the Problem Requirements:**\n The problem requires us to find the number of subsets $X$ of the set $\\{1, 2, 3, 4, 5\\}$ such that $\\{1, 2\\} \\subseteq X$. This means every subset $X$ must include both elements 1 and 2.\n\n2. **Determine the Remai... |
deepscaler | [
{
"role": "user",
"content": "The line $l: x - 2y + 2 = 0$ passes through the left focus F<sub>1</sub> and a vertex B of an ellipse. Find the eccentricity of the ellipse. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 25399,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the arithmetic sequence $\\{a_{n}\\}$, $d=-2$, $a_{1}+a_{4}+a_{7}+…+a_{31}=50$. Find the value of $a_{2}+a_{6}+a_{10}+…+a_{42}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-82"
} | {
"split": "train",
"index": 25400,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sin \\alpha - \\cos \\alpha = \\frac{1}{5}$, and $0 \\leqslant \\alpha \\leqslant \\pi$, find the value of $\\sin (2\\alpha - \\frac{\\pi}{4})$ = $\\_\\_\\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{31\\sqrt{2}}{50}"
} | {
"split": "train",
"index": 25401,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a square \\( PQRS \\) with an area of \\( 120 \\, \\text{cm}^2 \\). Point \\( T \\) is the midpoint of \\( PQ \\). The ratios are given as \\( QU: UR = 2:1 \\), \\( RV: VS = 3:1 \\), and \\( SW: WP = 4:1 \\).\n\nFind the area, in \\(\\text{cm}^2\\), of quadrilateral \\( T... | math | {
"style": "rule",
"ground_truth": "67"
} | {
"split": "train",
"index": 25402,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Inside a cube \\( C \\) with side length 1, an inscribed sphere \\( O_{1} \\) is placed. Another sphere \\( O_{2} \\) is also placed inside \\( C \\) such that it is tangent to the inscribed sphere \\( O_{1} \\) and also tangent to three faces of the cube. What is the surface a... | math | {
"style": "rule",
"ground_truth": "(7 - 4\\sqrt{3})\\pi"
} | {
"split": "train",
"index": 25403,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, if $a^{2} + b^{2} - 6c^{2}$, then the value of $(\\cot A + \\cot B) \\tan C$ is equal to: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"split": "train",
"index": 25404,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A geometric progression with 10 terms starts with the first term as 2 and has a common ratio of 3. Calculate the sum of the new geometric progression formed by taking the reciprocal of each term in the original progression.\nA) $\\frac{29523}{59049}$\nB) $\\frac{29524}{59049}$\... | math | {
"style": "rule",
"ground_truth": "\\frac{29524}{59049}"
} | {
"split": "train",
"index": 25405,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\\\(\\alpha \\in \\left( 0, \\frac{\\pi}{2} \\right)\\\\), and \\\\(\\cos \\left( \\frac{\\pi}{4} - \\alpha \\right) = 2 \\sqrt{2} \\cos 2\\alpha\\\\), then \\\\(\\sin 2\\alpha = \\)_______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{15}{16}"
} | {
"split": "train",
"index": 25406,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four steel balls, each with a radius of 1, are completely packed into a container in the shape of a regular tetrahedron. Find the minimum height of this regular tetrahedron. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2+\\frac{2 \\sqrt{6}}{3}"
} | {
"split": "train",
"index": 25407,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that point $O$ is the origin of coordinates, point $A$ in the first quadrant lies on the graph of the inverse proportional function $y=\\frac{1}{x}$ for $x>0$, and point $B$ in the second quadrant lies on the graph of the inverse proportional function $y=-\\frac{4}{x}$ fo... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 25408,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distance between locations A and B is 291 kilometers. Persons A and B depart simultaneously from location A and travel to location B at a constant speed, while person C departs from location B and heads towards location A at a constant speed. When person B has traveled \\( ... | math | {
"style": "rule",
"ground_truth": "221"
} | {
"split": "train",
"index": 25409,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = e^{x} \\cos x - x$.\n(I) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(0, f(0))$;\n(II) Find the maximum and minimum values of the function $f(x)$ on the interval $[0, \\frac{\\pi}{2}]$. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\pi}{2}"
} | {
"split": "train",
"index": 25410,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many odd numbers between $100$ and $999$ have distinct digits? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "320"
} | {
"split": "train",
"index": 25411,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many integers $a(1 \\leq a \\leq 200)$ is the number $a^{a}$ a square? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "107"
} | {
"split": "train",
"index": 25412,
"solution": "107 If $a$ is even, we have $a^{a}=\\left(a^{a / 2}\\right)^{2}$. If $a$ is odd, $a^{a}=\\left(a^{(a-1) / 2}\\right)^{2} \\cdot a$, which is a square precisely when $a$ is. Thus we have 100 even values of $a$ and 7 odd square values $\\left(1^{2}, 3^{2}, \\ldots, 1... |
deepscaler | [
{
"role": "user",
"content": "Shown below is a clock face with no hands. What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock? [asy]\n/* AMC8 1999 #2 Problem*/\ndraw(circle((0,0),10),linewidth(1));\n\n/* Hands\ndraw((25,0)--8dir(-18)+(25,0),linewidth(2));\ndraw((25,0... | math | {
"style": "rule",
"ground_truth": "60^\\circ"
} | {
"split": "train",
"index": 25413,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( I \\) is the incenter of \\( \\triangle ABC \\) and \\( 5 \\overrightarrow{IA} = 4(\\overrightarrow{BI} + \\overrightarrow{CI}) \\). Let \\( R \\) and \\( r \\) be the radii of the circumcircle and the incircle of \\( \\triangle ABC \\) respectively. If \\( r = 1... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 25414,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What is the area of the triangle?\n$\\mathrm{(A) \\ 6 } \\qquad \\mathrm{(B) \\frac{18}{\\pi^2} } \\qquad \\mathrm{(C) \\frac{9}{\\pi^2}(\\sqrt{3}-1) } \\... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{\\pi^2}(\\sqrt{3}+3)"
} | {
"split": "train",
"index": 25415,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( p(x) \\) be a polynomial with integer coefficients such that \\( p(m) - p(n) \\) divides \\( m^2 - n^2 \\) for all integers \\( m \\) and \\( n \\). If \\( p(0) = 1 \\) and \\( p(1) = 2 \\), find the largest possible value of \\( p(100) \\). Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "10001"
} | {
"split": "train",
"index": 25416,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a plane, there is a point set \\( M \\) and seven distinct circles \\( C_{1}, C_{2}, \\ldots, C_{7} \\). Circle \\( C_{7} \\) passes through exactly 7 points in \\( M \\), circle \\( C_{6} \\) passes through exactly 6 points in \\( M \\), and so on, until circle \\( C_{1} \\... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 25417,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify the expression: $({1-\\frac{1}{{x+3}}})÷\\frac{{{x^2}-9}}{{{x^2}+6x+9}}$, then choose a suitable number from $-3$, $2$, $3$ to substitute and evaluate. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 25418,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Henry walks $\\tfrac{3}{4}$ of the way from his home to his gym, which is $2$ kilometers away from Henry's home, and then walks $\\tfrac{3}{4}$ of the way from where he is back toward home. Determine the difference in distance between the points toward which Henry oscillates fr... | math | {
"style": "rule",
"ground_truth": "\\frac{6}{5}"
} | {
"split": "train",
"index": 25419,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four siblings inherited a plot of land shaped like a convex quadrilateral. By connecting the midpoints of the opposite sides of the plot, they divided the inheritance into four quadrilaterals. The first three siblings received plots of $360 \\, \\mathrm{m}^{2}$, $720 \\, \\math... | math | {
"style": "rule",
"ground_truth": "540"
} | {
"split": "train",
"index": 25420,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jia draws five lines in a plane without any three lines intersecting at one point. For each pair of intersecting lines, Jia gets a candy. If there is a set of parallel lines, Jia also gets a candy. For example, in a diagram with seven intersection points and one set of parallel... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 25421,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sin\\theta= \\frac {m-3}{m+5}$ and $\\cos\\theta= \\frac {4-2m}{m+5}$ ($\\frac {\\pi}{2} < \\theta < \\pi$), calculate $\\tan\\theta$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "- \\frac {5}{12}"
} | {
"split": "train",
"index": 25422,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, angle $A$ is $90^\\circ$, $BC = 10$ and $\\tan C = 3\\cos B$. What is $AB$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{20\\sqrt{2}}{3}"
} | {
"split": "train",
"index": 25423,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Circle $O$ is located on the coordinate plane with center at $(2,3)$. One endpoint of a diameter is at $(-1,-1)$. What are the coordinates of the other endpoint of this diameter? Express your answer as an ordered pair. Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "(5,7)"
} | {
"split": "train",
"index": 25424,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four mice: White, Gray, Fat, and Thin were dividing a cheese wheel. They cut it into 4 apparently identical slices. Some slices had more holes, so Thin's slice weighed 20 grams less than Fat's slice, and White's slice weighed 8 grams less than Gray's slice. However, White wasn'... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 25425,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If set $A=\\{-4, 2a-1, a^2\\}$, $B=\\{a-5, 1-a, 9\\}$, and $A \\cap B = \\{9\\}$, then the value of $a$ is. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 25426,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c$ be nonzero real numbers. Find the number of real roots of the equation\n\\[\\begin{vmatrix} x & c & -b \\\\ -c & x & a \\\\ b & -a & x \\end{vmatrix} = 0.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 25427,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $a$ is a multiple of 4 and $b$ is a multiple of 8. Which of the following statements are true?\n\nA. $a+b$ must be even.\nB. $a+b$ must be a multiple of 4.\nC. $a+b$ must be a multiple of 8.\nD. $a+b$ cannot be a multiple of 8.\n\nAnswer by listing your choices in ... | math | {
"style": "rule",
"ground_truth": "\\text{A,B}"
} | {
"split": "train",
"index": 25428,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let's call a number palindromic if it reads the same left to right as it does right to left. For example, the number 12321 is palindromic.\n\na) Write down any five-digit palindromic number that is divisible by 5.\n\nb) How many five-digit palindromic numbers are there that are... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 25429,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a random variable $\\xi \\sim N(1, \\sigma ^{2})$, $a \\gt 0$, $b \\gt 0$, if $P(\\xi \\leq a) = P(\\xi \\geq b)$, then the minimum value of $\\frac{{4a+b}}{{ab}}$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{2}"
} | {
"split": "train",
"index": 25430,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A large supermarket has recorded the number of customers during eight holidays (unit: hundreds of people) as $29$, $30$, $38$, $25$, $37$, $40$, $42$, $32$. What is the $75$th percentile of this data set? Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 25431,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a round table with 9 chairs, and 4 people are seated randomly. What is the probability that no two people are sitting next to each other? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1/14"
} | {
"split": "train",
"index": 25432,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ such that $\\frac{n}{n+110}$ is equal to a terminating decimal? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 25433,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many paths are there from the starting point $C$ to the end point $D$, if every step must be up or to the right in a grid of 8 columns and 7 rows? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6435"
} | {
"split": "train",
"index": 25434,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the sum of the series:\n\\[ 2(1 + 2(1 + 2(1 + 2(1 + 2(1 + 2(1 + 2(1 + 2))))))) \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "510"
} | {
"split": "train",
"index": 25435,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x)$ be a function defined on $R$ such that $f(x+3) + f(x+1) = f(2) = 1$. Find $\\sum_{k=1}^{2023} f(k) =$ ____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1012"
} | {
"split": "train",
"index": 25436,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integer quadruples $a,b,c,d$ are there such that $7$ divides $ab-cd$ where $0\\leq a,b,c,d < 7$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "385"
} | {
"split": "train",
"index": 25437,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the roots of $\\tan^2x-9\\tan x+1=0$ that are between $x=0$ and $x=2\\pi$ radians. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3 \\pi"
} | {
"split": "train",
"index": 25438,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Choose one digit from 0, 2, 4, and two digits from 1, 3, 5 to form a three-digit number without repeating digits. The total number of different three-digit numbers that can be formed is ( )\n\nA 36 B 48 C 52 D 54 Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 25439,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a moving circle $E$ that passes through the point $F(1,0)$, and is tangent to the line $l: x=-1$.\n(Ⅰ) Find the equation of the trajectory $G$ for the center $E$ of the moving circle.\n(Ⅱ) Given the point $A(3,0)$, if a line with a slope of $1$ intersects with the line se... | math | {
"style": "rule",
"ground_truth": "\\frac{32 \\sqrt{3}}{9}"
} | {
"split": "train",
"index": 25440,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a machine with 8 toys in it that each cost between 25 cents and 2 dollars, with each toy being 25 cents more expensive than the next most expensive one. Each time Sam presses the big red button on the machine, the machine randomly selects one of the remaining toys and ... | math | {
"style": "rule",
"ground_truth": "\\dfrac{6}{7}"
} | {
"split": "train",
"index": 25441,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangles $ABC$ and $ADC$ are isosceles with $AB=BC$ and $AD=DC$. Point $D$ is inside $\\triangle ABC$, $\\angle ABC = 40^\\circ$, and $\\angle ADC = 140^\\circ$. What is the degree measure of $\\angle\nBAD$? Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "50^{\\circ}"
} | {
"split": "train",
"index": 25442,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\alpha \\in \\left(0, \\frac{\\pi}{2}\\right)$, $\\beta \\in \\left(\\frac{\\pi}{2}, \\pi\\right)$, $\\cos\\beta = -\\frac{1}{3}$, $\\sin(\\alpha + \\beta) = \\frac{7}{9}$. \n(1) Find the value of $\\tan \\frac{\\beta}{2}$. \n(2) Find the value of $\\sin\\alpha$. Let'... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 25443,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of ordered pairs of positive integers \\((a, b)\\) satisfying the equation\n\\[ 100(a + b) = ab - 100. \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 25444,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On square $ABCD$, point $E$ lies on side $AD$ and point $F$ lies on side $BC$, so that $BE=EF=FD=30$. Find the area of the square $ABCD$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "810"
} | {
"split": "train",
"index": 25445,
"solution": "Drawing the square and examining the given lengths, [asy] size(2inch, 2inch); currentpen = fontsize(8pt); pair A = (0, 0); dot(A); label(\"$A$\", A, plain.SW); pair B = (3, 0); dot(B); label(\"$B$\", B, plain.SE); pair C = (3, 3); dot(C); label(\"$C$\", C, plain.NE... |
deepscaler | [
{
"role": "user",
"content": "Two circles, each with a radius of 12 cm, overlap such that each circle passes through the center of the other. Determine the length, in cm, of the common chord formed by these circles. Express your answer in simplest radical form. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "12\\sqrt{3}"
} | {
"split": "train",
"index": 25446,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Square A has side lengths each measuring $x$ inches. Square B has side lengths each measuring $5x$ inches. Square C has side lengths each measuring $2x$ inches. What is the ratio of the area of Square A to the area of Square B, and what is the ratio of the area of Square C to t... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{25}"
} | {
"split": "train",
"index": 25447,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A digital clock shows the time 4:56. How many minutes will pass until the clock next shows a time in which all of the digits are consecutive and are in increasing order? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "458"
} | {
"split": "train",
"index": 25448,
"solution": "We would like to find the first time after 4:56 where the digits are consecutive digits in increasing order. It would make sense to try 5:67, but this is not a valid time. Similarly, the time cannot start with 6, 7, 8, or 9. No time starting with 10 or 11 starts wi... |
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