data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Compute the number of ways to tile a $3 \\times 5$ rectangle with one $1 \\times 1$ tile, one $1 \\times 2$ tile, one $1 \\times 3$ tile, one $1 \\times 4$ tile, and one $1 \\times 5$ tile. (The tiles can be rotated, and tilings that differ by rotation or reflection are conside... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 35549,
"solution": "Our strategy is to first place the $1 \\times 5$ and the $1 \\times 4$ tiles since their size restricts their location. We have three cases: - Case 1: first row. There are 4 ways to place the $1 \\times 4$ tile. There is an empty cell next to the $1 \\times 4$ tile... |
deepscaler | [
{
"role": "user",
"content": "A math test consists of 12 multiple-choice questions, each worth 5 points. It is known that a student is confident in correctly answering 6 of these questions. For another three questions, the student can eliminate one incorrect option. For two questions, the student can elimin... | math | {
"style": "rule",
"ground_truth": "41.25"
} | {
"split": "train",
"index": 35550,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the plane vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, where $|\\overrightarrow{a}| = 1$, $|\\overrightarrow{b}| = \\sqrt{2}$, and $\\overrightarrow{a} \\cdot \\overrightarrow{b} = 1$, calculate the angle between vectors $\\overrightarrow{a}$ and $\\overrighta... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 35551,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all numbers $q$ which can be written in the form $q=\\frac{a}{b}$ where $a$ and $b$ are positive integers with $b \\leq 10$ and for which there are exactly 19 integers $n$ that satisfy $\\sqrt{q}<n<q$? Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "777.5"
} | {
"split": "train",
"index": 35552,
"solution": "Suppose that a number $q$ has the property that there are exactly 19 integers $n$ with $\\sqrt{q}<n<q$. Suppose that these 19 integers are $m, m+1, m+2, \\ldots, m+17, m+18$. Then $\\sqrt{q}<m<m+1<m+2<\\cdots<m+17<m+18<q$. This tells us that $q-\\sqrt{q}>(m+18)-m=1... |
deepscaler | [
{
"role": "user",
"content": "Let $m$ be the smallest integer whose cube root is of the form $n+s$, where $n$ is a positive integer and $s$ is a positive real number less than $1/2000$. Find $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 35553,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Grandma has two balls of yarn: one large and one small. From the large ball, she can either knit a sweater and three socks, or five identical hats. From the small ball, she can either knit half a sweater or two hats. (In both cases, all the yarn will be used up.) What is the ma... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 35554,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a positive integer $n$ , define $n?=1^n\\cdot2^{n-1}\\cdot3^{n-2}\\cdots\\left(n-1\\right)^2\\cdot n^1$ . Find the positive integer $k$ for which $7?9?=5?k?$ .\n\n*Proposed by Tristan Shin* Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35555,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the pattern in the diagram continues, what fraction of eighth triangle would be shaded?\n[asy] unitsize(10); draw((0,0)--(12,0)--(6,6sqrt(3))--cycle); draw((15,0)--(27,0)--(21,6sqrt(3))--cycle); fill((21,0)--(18,3sqrt(3))--(24,3sqrt(3))--cycle,black); draw((30,0)--(42,0)--... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{16}"
} | {
"split": "train",
"index": 35556,
"solution": "1. **Identify the pattern of shaded triangles**: Observing the given sequence of diagrams, we notice that the number of shaded triangles in each subsequent diagram follows the sequence of triangular numbers. The sequence of triangular numbers is defined by the form... |
deepscaler | [
{
"role": "user",
"content": "In the process of making a steel cable, it was determined that the length of the cable is the same as the curve given by the system of equations:\n\n$$\n\\left\\{\\begin{array}{l}\nx+y+z=10 \\\\\nx y+y z+x z=18\n\\end{array}\\right.\n$$\n\nFind the length of the cable. Let's th... | math | {
"style": "rule",
"ground_truth": "4 \\pi \\sqrt{\\frac{23}{3}}"
} | {
"split": "train",
"index": 35557,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "All of the triangles in the diagram below are similar to isosceles triangle $ABC$, in which $AB=AC$. Each of the $7$ smallest triangles has area $1,$ and $\\triangle ABC$ has area $40$. What is the area of trapezoid $DBCE$? Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 35558,
"solution": "1. **Identify the relationship between the triangles**: All of the triangles in the diagram are similar to isosceles triangle $ABC$, where $AB = AC$. Each of the 7 smallest triangles has an area of 1, and $\\triangle ABC$ has an area of 40.\n\n2. **Express the area... |
deepscaler | [
{
"role": "user",
"content": "During the November monthly exam at our school, approximately 1,000 science students participated, with mathematics scores distributed normally as $\\xi \\sim N(100, a^2), (a > 0)$, and a full score of 150. The statistics showed that about 60% of the students scored between 80 ... | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 35559,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f\\left( \\alpha \\right)=\\frac{\\cos \\left( \\frac{\\pi }{2}+\\alpha \\right)\\cdot \\cos \\left( 2\\pi -\\alpha \\right)\\cdot \\sin \\left( -\\alpha +\\frac{3}{2}\\pi \\right)}{\\sin \\left( -\\pi -\\alpha \\right)\\sin \\left( \\frac{3}{2}\\pi +\\alpha \\right)}$.\... | math | {
"style": "rule",
"ground_truth": "\\frac{2 \\sqrt{6}}{5}"
} | {
"split": "train",
"index": 35560,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $2468 + 8642 + 6824 + 4286$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22220"
} | {
"split": "train",
"index": 35561,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The partial fraction decomposition of\n\\[\\frac{x^2 - 19}{x^3 - 2x^2 - 5x + 6}\\]is\n\\[\\frac{A}{x - 1} + \\frac{B}{x + 2} + \\frac{C}{x - 3}.\\]Find the product $ABC.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 35562,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points \\(P, Q, R,\\) and \\(S\\) lie in the plane of the square \\(EFGH\\) such that \\(EPF\\), \\(FQG\\), \\(GRH\\), and \\(HSE\\) are equilateral triangles. If \\(EFGH\\) has an area of 25, find the area of quadrilateral \\(PQRS\\). Express your answer in simplest radical fo... | math | {
"style": "rule",
"ground_truth": "100 + 50\\sqrt{3}"
} | {
"split": "train",
"index": 35563,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\overrightarrow{a}$ and $\\overrightarrow{b}$ are unit vectors, and the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $90^{\\circ}$, if vector $\\overrightarrow{c}$ satisfies $|\\overrightarrow{c}- \\overrightarrow{a} \\overrightarrow{b}|=2$, cal... | math | {
"style": "rule",
"ground_truth": "2 + \\sqrt{2}"
} | {
"split": "train",
"index": 35564,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "35 times 61,000 unit cubes are combined to form a large cube with an edge length of 10 units. After being painted, the large cube is then separated back into the original unit cubes. How many of these unit cubes have at least one face painted? Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "488"
} | {
"split": "train",
"index": 35565,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=x^{3}+ax^{2}+bx+a^{2}-1$ has an extremum of $9$ at $x=1$, find the value of $f(2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 35566,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select two different digits from 0, 1, 2, 3, 4 to form a two-digit number and determine the number of even numbers among these. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35567,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vinny wrote down all the single-digit base-$b$ numbers and added them in base $b$, getting $34_b$.\n\nWhat is $b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 35568,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the product of the real parts of the solutions to the equation \\(2x^2 + 4x = 1 + i\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1 - 3}{4}"
} | {
"split": "train",
"index": 35569,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the isosceles trapezoid \\(ABCD\\), the bases \\(AD\\) and \\(BC\\) are related by the equation \\(AD = (1 + \\sqrt{15}) BC\\). A circle is constructed with its center at point \\(C\\) and radius \\(\\frac{2}{3} BC\\), which cuts a chord \\(EF\\) on the base \\(AD\\) of leng... | math | {
"style": "rule",
"ground_truth": "2:1"
} | {
"split": "train",
"index": 35570,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if exactly one of the triplets is in the starting lineup? Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "1386"
} | {
"split": "train",
"index": 35571,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many integers $x$ is the point $(x, -x)$ inside or on the circle of radius $10$ centered at $(5, 5)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 35572,
"solution": "1. **Identify the equation of the circle**: The circle is centered at $(5, 5)$ with a radius of $10$. The equation of a circle with center $(h, k)$ and radius $r$ is given by:\n \\[\n (x-h)^2 + (y-k)^2 = r^2\n \\]\n Substituting $h = 5$, $k = 5$, and $r = 1... |
deepscaler | [
{
"role": "user",
"content": "Each of the points $A,B,C,D,E,$ and $F$ in the figure below represents a different digit from $1$ to $6.$ Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums i... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 35573,
"solution": "1. **Identify the sums along each line**: Given the points $A, B, C, D, E, F$, each representing a unique digit from 1 to 6, and the lines connecting them, we can write the sums for each line as:\n - Line through $A, B, C$: $A + B + C$\n - Line through $A, E, F... |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\in \\mathbf{R}_{+} \\). If the function\n\\[ \nf(x)=\\frac{a}{x-1}+\\frac{1}{x-2}+\\frac{1}{x-6} \\quad (3 < x < 5) \n\\]\nachieves its maximum value at \\( x=4 \\), find the value of \\( a \\). 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": 35574,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the ellipse $C:\\dfrac{x^2}{b^2}+\\dfrac{y^2}{a^2}=1 \\left( a > b > 0 \\right)$ has an eccentricity of $\\dfrac{\\sqrt{2}}{2}$, and point $A(1,\\sqrt{2})$ is on the ellipse.\n\n$(1)$ Find the equation of ellipse $C$;\n\n$(2)$ If a line $l$ with a slope of $\\sqrt{2}$ int... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 35575,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given points $F_{1}$, $F_{2}$ are the foci of the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0$, $b > 0$), and point $M(x_{0},y_{0})$ ($x_{0} > 0$, $y_{0} > 0$) lies on the asymptote of the hyperbola such that $MF_{1} \\perp MF_{2}$. If there is a parabola with f... | math | {
"style": "rule",
"ground_truth": "2 + \\sqrt{5}"
} | {
"split": "train",
"index": 35576,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alfred and Bonnie play a game in which they take turns tossing a fair coin. The winner of a game is the first person to obtain a head. Alfred and Bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. Suppose that Alfred g... | math | {
"style": "rule",
"ground_truth": "93"
} | {
"split": "train",
"index": 35577,
"solution": "The probability that the $n$th flip in each game occurs and is a head is $\\frac{1}{2^n}$. The first person wins if the coin lands heads on an odd numbered flip. So, the probability of the first person winning the game is $\\frac{1}{2}+\\frac{1}{8}+\\frac{1}{32}+\\... |
deepscaler | [
{
"role": "user",
"content": "Eight celebrities meet at a party. It so happens that each celebrity shakes hands with exactly two others. A fan makes a list of all unordered pairs of celebrities who shook hands with each other. If order does not matter, how many different lists are possible? Let's think step... | math | {
"style": "rule",
"ground_truth": "3507"
} | {
"split": "train",
"index": 35578,
"solution": "Let the celebrities get into one or more circles so that each circle has at least three celebrities, and each celebrity shook hands precisely with his or her neighbors in the circle. Let's consider the possible circle sizes: - There's one big circle with all 8 cele... |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to paint each of the integers $2, 3, \\cdots , 9$ either red, green, or blue so that each number has a different color from each of its proper divisors? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "432"
} | {
"split": "train",
"index": 35579,
"solution": "To solve this problem, we need to consider the constraints imposed by the requirement that each number must have a different color from each of its proper divisors. We start by identifying the divisors of each number from $2$ to $9$:\n\n- $2$: No proper divisors in... |
deepscaler | [
{
"role": "user",
"content": "For what smallest natural $k$ is the number \\( 2016 \\cdot 20162016 \\cdot 201620162016 \\cdot \\ldots \\cdot 20162016\\ldots2016 \\) (with $k$ factors) divisible by \\(3^{67}\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 35580,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A and B play a game with the following rules: In the odd-numbered rounds, A has a winning probability of $\\frac{3}{4}$, and in the even-numbered rounds, B has a winning probability of $\\frac{3}{4}$. There are no ties in any round, and the game ends when one person has won 2 m... | math | {
"style": "rule",
"ground_truth": "16/3"
} | {
"split": "train",
"index": 35581,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given points P(0, -3) and Q(5, 3) in the xy-plane; point R(x, m) is taken so that PR + RQ is a minimum where x is fixed to 3, determine the value of m. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 35582,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the circumferences of the two bases of a cylinder lie on the surface of a sphere with an area of $20\\pi$, the maximum value of the lateral surface area of the cylinder is ____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10\\pi"
} | {
"split": "train",
"index": 35583,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AB=13$, $BC=14$, and $CA=15$. Distinct points $D$, $E$, and $F$ lie on segments $\\overline{BC}$, $\\overline{CA}$, and $\\overline{DE}$, respectively, such that $\\overline{AD}\\perp\\overline{BC}$, $\\overline{DE}\\perp\\overline{AC}$, and $\\overline{AF}\... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 35584,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $DEF$ is isosceles with angle $E$ congruent to angle $F$. The measure of angle $F$ is three times the measure of angle $D$. What is the number of degrees in the measure of angle $E$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{540}{7}"
} | {
"split": "train",
"index": 35585,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can $345$ be written as the sum of an increasing sequence of two or more consecutive positive integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 35586,
"solution": "To solve the problem, we need to find the number of ways $345$ can be expressed as the sum of two or more consecutive positive integers.\n\n1. **Represent the sum of consecutive integers:**\n Let's consider a sequence of $n$ consecutive integers starting from $k$... |
deepscaler | [
{
"role": "user",
"content": "A $\\emph{convex}$ polygon is a polygon in which every interior angle is less than 180 degrees. A $\\emph{diagonal}$ of a convex polygon is a line segment that connects two non-adjacent vertices. How many diagonals does a convex polygon with 20 sides have? Let's think step by... | math | {
"style": "rule",
"ground_truth": "170"
} | {
"split": "train",
"index": 35587,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = \\sin\\left(\\frac{5\\pi}{3}x + \\frac{\\pi}{6}\\right) + \\frac{3x}{2x-1}$, then the value of $f\\left(\\frac{1}{2016}\\right) + f\\left(\\frac{3}{2016}\\right) + f\\left(\\frac{5}{2016}\\right) + f\\left(\\frac{7}{2016}\\right) + \\ldots + f\\left(\... | math | {
"style": "rule",
"ground_truth": "1512"
} | {
"split": "train",
"index": 35588,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain product costs $6$ per unit, sells for $x$ per unit $(x > 6)$, and has an annual sales volume of $u$ ten thousand units. It is known that $\\frac{585}{8} - u$ is directly proportional to $(x - \\frac{21}{4})^2$, and when the selling price is $10$ dollars, the annual sa... | math | {
"style": "rule",
"ground_truth": "135"
} | {
"split": "train",
"index": 35589,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A solid box is 15 cm by 10 cm by 8 cm. A new solid is formed by removing a cube 3 cm on a side from each corner of this box. What percent of the original volume is removed? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18\\%"
} | {
"split": "train",
"index": 35590,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $T$ denote the sum of all three-digit positive integers where each digit is different and none of the digits are 5. Calculate the remainder when $T$ is divided by $1000$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "840"
} | {
"split": "train",
"index": 35591,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From 50 products, 10 are selected for inspection. The total number of items is \\_\\_\\_\\_\\_\\_\\_, and the sample size is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35592,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a certain weekend, the weatherman predicts that it will rain with a $40\\%$ probability on Saturday and a $50\\%$ probability on Sunday. Assuming these probabilities are independent, what is the probability that it rains over the weekend (that is, on at least one of the day... | math | {
"style": "rule",
"ground_truth": "70\\%"
} | {
"split": "train",
"index": 35593,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the figure below, $ABCD$ is a square piece of paper 6 cm on each side. Corner $C$ is folded over so that it coincides with $E$, the midpoint of $\\overline{AD}$. If $\\overline{GF}$ represents the crease created by the fold such that $F$ is on $CD,$ what is the length of $\\... | math | {
"style": "rule",
"ground_truth": "\\frac94"
} | {
"split": "train",
"index": 35594,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The segments connecting the feet of the altitudes of an acute-angled triangle form a right triangle with a hypotenuse of 10. Find the radius of the circumcircle of the original triangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35595,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $10\\times 10$ square we choose $n$ cells. In every chosen cell we draw one arrow from the angle to opposite angle. It is known, that for any two arrows, or the end of one of them coincides with the beginning of the other, or\nthe distance between their ends is at least... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 35596,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine how many solutions the following equation has:\n\\[\n\\frac{(x-1)(x-2)(x-3)\\dotsm(x-50)}{(x-2^2)(x-4^2)(x-6^2)\\dotsm(x-24^2)} = 0\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "47"
} | {
"split": "train",
"index": 35597,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "My three-digit code is 023. Reckha can't choose a code that is the same as mine in two or more of the three digit-positions, nor that is the same as mine except for switching the positions of two digits (so 320 and 203, for example, are forbidden, but 302 is fine). Reckha can o... | math | {
"style": "rule",
"ground_truth": "969"
} | {
"split": "train",
"index": 35598,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The polynomial $f(x) = x^3 + x^2 + 2x + 3$ has three distinct roots. Let $g(x) = x^3+bx^2+cx+d$ be a cubic polynomial with leading coefficient $1$ such that the roots of $g(x)$ are the squares of the roots of $f(x)$. Find the ordered triple $(b,c,d)$. Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "(3,-2,-9)"
} | {
"split": "train",
"index": 35599,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let's call a natural number \"remarkable\" if it is the smallest among natural numbers with the same sum of digits. What is the sum of the digits of the two-thousand-and-first remarkable number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2001"
} | {
"split": "train",
"index": 35600,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, and $c$ be solutions of the equation $x^3 - 6x^2 + 11x - 6 = 0$. Compute $ \\frac{ab}{c} + \\frac{bc}{a} + \\frac{ca}{b}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{49}{6}"
} | {
"split": "train",
"index": 35601,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A four-digit palindrome between $1000$ and $10,000$ is chosen at random. What is the probability that it is divisible by $9$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{10}"
} | {
"split": "train",
"index": 35602,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Expand the product ${4(x-5)(x+8)}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4x^2 + 12x - 160"
} | {
"split": "train",
"index": 35603,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A telephone number has the form \\text{ABC-DEF-GHIJ}, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, $A > B > C$, $D > E > F$, and $G > H > I > J$. Furthermore, $D$, $E$, and $F$ are consecutive even digit... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 35604,
"solution": "1. **Identify the constraints**: The telephone number is in the form $\\text{ABC-DEF-GHIJ}$, where each segment has digits in decreasing order. Additionally, $D$, $E$, and $F$ are consecutive even digits; $G$, $H$, $I$, and $J$ are consecutive odd digits; and $A + ... |
deepscaler | [
{
"role": "user",
"content": "In a box, there are two red balls, two yellow balls, and two blue balls. If a ball is randomly drawn from the box, at least how many balls need to be drawn to ensure getting balls of the same color? If one ball is drawn at a time without replacement until balls of the same colo... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{5}"
} | {
"split": "train",
"index": 35605,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are $n$ mathematicians attending a conference. Each mathematician has exactly 3 friends (friendship is mutual). If they are seated around a circular table such that each person has their friends sitting next to them on both sides, the number of people at the table is at l... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 35606,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the expression $\\frac{x + 1}{x - 1}$ each $x$ is replaced by $\\frac{x + 1}{x - 1}$. The resulting expression, evaluated for $x = \\frac{1}{2}$, equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 35607,
"solution": "1. **Substitute $x$ with $\\frac{x+1}{x-1}$ in the expression:**\n \\[\n \\frac{\\left(\\frac{x+1}{x-1}\\right) + 1}{\\left(\\frac{x+1}{x-1}\\right) - 1}\n \\]\n\n2. **Simplify the expression:**\n - For the numerator:\n \\[\n \\frac{x+1}{x-1} + 1 = ... |
deepscaler | [
{
"role": "user",
"content": "One root of the equation $5x^2+kx=4$ is 2. What is the other? 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": 35608,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$, $B$, $C$, and $D$ be vertices of a regular tetrahedron where each edge is 1 meter. A bug starts at vertex $A$ and at each vertex chooses randomly among the three incident edges to move along. Compute the probability $p$ that the bug returns to vertex $A$ after exactly ... | math | {
"style": "rule",
"ground_truth": "4921"
} | {
"split": "train",
"index": 35609,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Private Petrov took a bucket of unpeeled potatoes and peeled them in 1 hour. During this process, 25% of the potatoes went to peels. How long did it take him to collect half a bucket of peeled potatoes? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 35610,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of four positive integers that form an arithmetic sequence is 46. Of all such possible sequences, what is the greatest possible third term? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 35611,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two concentric circles have radii $r$ and $R>r$. Three new circles are drawn so that they are each tangent to the big two circles and tangent to the other two new circles. Find $\\frac{R}{r}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 35612,
"solution": "The centers of the three new circles form a triangle. The diameter of the new circles is $R-r$, so the side length of the triangle is $R-r$. Call the center of the concentric circle $O$, two vertices of the triangle $A$ and $B$, and $A B$ 's midpoint $D$. $O A$ is ... |
deepscaler | [
{
"role": "user",
"content": "In a round-robin hockey tournament, 2016 teams participated. According to the tournament rules, 3 points are awarded for a win. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6093360"
} | {
"split": "train",
"index": 35613,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The probability that the random variable $X$ follows a normal distribution $N\\left( 3,{{\\sigma }^{2}} \\right)$ and $P\\left( X\\leqslant 4 \\right)=0.84$ can be expressed in terms of the standard normal distribution $Z$ as $P(Z\\leqslant z)=0.84$, where $z$ is the z-score co... | math | {
"style": "rule",
"ground_truth": "0.68"
} | {
"split": "train",
"index": 35614,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $α∈[\\dfrac{π}{2}, \\dfrac{3π}{2}]$, $β∈[-\\dfrac{π}{2}, 0]$, and the equations $(α-\\dfrac{π}{2})^{3}-\\sin α-2=0$ and $8β^{3}+2\\cos^{2}β+1=0$ hold, find the value of $\\sin(\\dfrac{α}{2}+β)$. Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 35615,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $x= \\frac {\\pi}{12}$ is a symmetry axis of the function $f(x)= \\sqrt {3}\\sin(2x+\\varphi)+\\cos(2x+\\varphi)$ $(0<\\varphi<\\pi)$, after shifting the graph of function $f(x)$ to the right by $\\frac {3\\pi}{4}$ units, find the minimum value of the resulting function $... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 35616,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given complex numbers $z_1 = \\cos\\theta - i$ and $z_2 = \\sin\\theta + i$, the maximum value of the real part of $z_1 \\cdot z_2$ is \\_\\_\\_\\_\\_\\_, and the maximum value of the imaginary part is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 35617,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct arrangements of the letters in the word \"balloon\" are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1260"
} | {
"split": "train",
"index": 35618,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the ages of everyone who wrote a problem for this year's HMMT November contest. If your answer is $X$ and the actual value is $Y$, your score will be $\\max (0,20-|X-Y|)$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "258"
} | {
"split": "train",
"index": 35619,
"solution": "There was one problem for which I could not determine author information, so I set the author as one of the problem czars at random. Then, I ran the following command on a folder containing TeX solutions files to all four contests: ``` evan@ArchMega ~/Downloads/Nov... |
deepscaler | [
{
"role": "user",
"content": "Calculate: $|\\sqrt{8}-2|+(\\pi -2023)^{0}+(-\\frac{1}{2})^{-2}-2\\cos 60^{\\circ}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}+2"
} | {
"split": "train",
"index": 35620,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $A$ and $B$ are on parabola $y=4x^2+7x-1$, and the origin is the midpoint of $\\overline{AB}$. Find the square of the length of $\\overline{AB}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 35621,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The diagram shows three touching semicircles with radius 1 inside an equilateral triangle, with each semicircle also touching the triangle. The diameter of each semicircle lies along a side of the triangle. What is the length of each side of the equilateral triangle? Let's thin... | math | {
"style": "rule",
"ground_truth": "2 \\sqrt{3}"
} | {
"split": "train",
"index": 35622,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the difference between 12.358 and 7.2943, keeping the answer in decimal form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5.0637"
} | {
"split": "train",
"index": 35623,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The average of the five numbers in a list is 54. The average of the first two numbers is 48. What is the average of the last three numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "58"
} | {
"split": "train",
"index": 35624,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S=\\{-100,-99,-98, \\ldots, 99,100\\}$. Choose a 50-element subset $T$ of $S$ at random. Find the expected number of elements of the set $\\{|x|: x \\in T\\}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8825}{201}"
} | {
"split": "train",
"index": 35625,
"solution": "Let us solve a more generalized version of the problem: Let $S$ be a set with $2n+1$ elements, and partition $S$ into sets $A_{0}, A_{1}, \\ldots, A_{n}$ such that $|A_{0}|=1$ and $|A_{1}|=|A_{2}|=\\cdots=|A_{n}|=2$. (In this problem, we have $A_{0}=\\{0\\}$ and $A... |
deepscaler | [
{
"role": "user",
"content": "There are four different passwords, $A$, $B$, $C$, and $D$, used by an intelligence station. Each week, one of the passwords is used, and each week it is randomly chosen with equal probability from the three passwords not used in the previous week. Given that the password used ... | math | {
"style": "rule",
"ground_truth": "61/243"
} | {
"split": "train",
"index": 35626,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lengths of the sides of a triangle with positive area are $\\log_{10} 12$, $\\log_{10} 75$, and $\\log_{10} n$, where $n$ is a positive integer. Find the number of possible values for $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "893"
} | {
"split": "train",
"index": 35627,
"solution": "By the Triangle Inequality and applying the well-known logarithmic property $\\log_{c} a + \\log_{c} b = \\log_{c} ab$, we have that\n$\\log_{10} 12 + \\log_{10} n > \\log_{10} 75$\n$\\log_{10} 12n > \\log_{10} 75$\n$12n > 75$\n$n > \\frac{75}{12} = \\frac{25}{4} =... |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, the ellipse $C: \\frac{x^2}{2} + \\frac{y^2}{3} = 1$ has a focus on the positive y-axis denoted as $F$. A line $l$ passing through $F$ with a slope angle of $\\frac{3\\pi}{4}$ intersects $C$ at points $M$ and $N$. The quadrilateral $OMP... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}\\sqrt{6}"
} | {
"split": "train",
"index": 35628,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right triangle has side lengths $a, b$, and $\\sqrt{2016}$ in some order, where $a$ and $b$ are positive integers. Determine the smallest possible perimeter of the triangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48+\\sqrt{2016}"
} | {
"split": "train",
"index": 35629,
"solution": "There are no integer solutions to $a^{2}+b^{2}=2016$ due to the presence of the prime 7 on the right-hand side (by Fermat's Christmas Theorem). Assuming $a<b$, the minimal solution $(a, b)=(3,45)$ which gives the answer above."
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = \\sin x + \\cos x$.\n\n(1) If $f(x) = 2f(-x)$, find the value of $\\frac{\\cos^2x - \\sin x\\cos x}{1 + \\sin^2x}$;\n\n(2) Find the maximum value and the intervals of monotonic increase for the function $F(x) = f(x) \\cdot f(-x) + f^2(x)$. Let's think... | math | {
"style": "rule",
"ground_truth": "\\frac{6}{11}"
} | {
"split": "train",
"index": 35630,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The solutions to the system of equations\n$\\log_{225}x+\\log_{64}y=4$\n$\\log_{x}225-\\log_{y}64=1$\n are $(x_1,y_1)$ and $(x_2,y_2)$. Find $\\log_{30}\\left(x_1y_1x_2y_2\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 35631,
"solution": "Let $A=\\log_{225}x$ and let $B=\\log_{64}y$.\n From the first equation: $A+B=4 \\Rightarrow B = 4-A$.\n Plugging this into the second equation yields $\\frac{1}{A}-\\frac{1}{B}=\\frac{1}{A}-\\frac{1}{4-A}=1 \\Rightarrow A = 3\\pm\\sqrt{5}$ and thus, $B=1\\pm\\sqrt... |
deepscaler | [
{
"role": "user",
"content": "Point $A$ , $B$ , $C$ , and $D$ form a rectangle in that order. Point $X$ lies on $CD$ , and segments $\\overline{BX}$ and $\\overline{AC}$ intersect at $P$ . If the area of triangle $BCP$ is 3 and the area of triangle $PXC$ is 2, what is the area of the entire... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 35632,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Every day, the ram learns the same number of languages. By the evening of his birthday, he knew 1000 languages. On the first day of the same month, he knew 820 languages by evening, and on the last day of that month, he knew 1100 languages. When is the ram's birthday? Let's thi... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 35633,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that (1+ex)<sup>2019</sup>=a<sub>0</sub>+a<sub>1</sub>x+a<sub>2</sub>x<sup>2</sup>+……+a<sub>2019</sub>x<sup>2019</sup>, find the value of:\n- $$\\frac {a_{1}}{e}$$+ $$\\frac {a_{2}}{e^{2}}$$\\- $$\\frac {a_{3}}{e^{3}}$$+ $$\\frac {a_{4}}{e^{4}}$$\\-……- $$\\frac {a_{2019}}... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 35634,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $Q$ be the product of the first $50$ positive even integers. Find the largest integer $l$ such that $Q$ is divisible by $2^l$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "97"
} | {
"split": "train",
"index": 35635,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When the two diagonals of an $8 \\times 10$ grid are drawn, calculate the number of the $1 \\times 1$ squares that are not intersected by either diagonal. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 35636,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many different four-digit numbers can be formed by rearranging the four digits in $2004$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 35637,
"solution": "To find the number of different four-digit numbers that can be formed by rearranging the digits in $2004$, we need to consider the repetitions of the digits and the restrictions on the arrangement.\n\n1. **Identify the digits and their repetitions**: The digits in ... |
deepscaler | [
{
"role": "user",
"content": "Crystal has a running course marked out for her daily run. She starts this run by heading due north for one mile. She then runs northeast for one mile, then southeast for one mile. The last portion of her run takes her on a straight line back to where she started. How far, in m... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 35638,
"solution": "1. **Understanding the Path**: Crystal's path consists of four segments:\n - North for 1 mile.\n - Northeast for 1 mile.\n - Southeast for 1 mile.\n - A straight line back to the starting point.\n\n2. **Breaking Down the Northeast and Southeast Runs**:\n ... |
deepscaler | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, $\\angle BAC = \\frac{π}{3}$, $D$ is the midpoint of $AB$, $P$ is a point on segment $CD$, and satisfies $\\overrightarrow{AP} = t\\overrightarrow{AC} + \\frac{1}{3}\\overrightarrow{AB}$. If $|\\overrightarrow{BC}| = \\sqrt{6}$, then the maximum va... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 35639,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S=(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1$. Then $S$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^4"
} | {
"split": "train",
"index": 35640,
"solution": "1. **Substitute $y = x - 1$ into $S$:**\n \\[\n S = (x-1)^4 + 4(x-1)^3 + 6(x-1)^2 + 4(x-1) + 1\n \\]\n Replace $x-1$ with $y$:\n \\[\n S = y^4 + 4y^3 + 6y^2 + 4y + 1\n \\]\n\n2. **Recognize the pattern in $S$:**\n The expression $S = y^4 + 4y^3 + 6y... |
deepscaler | [
{
"role": "user",
"content": "Find the remainder when $x^3 - 3x + 5$ is divided by $x + 2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 35641,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular tetrahedron has two spheres, one inscribed within it and the other circumscribed around it. Between each face of the tetrahedron and the circumscribed sphere, there are four smaller spheres centered on each face. Given a point \\( P \\) within the circumscribed sphere... | math | {
"style": "rule",
"ground_truth": "0.2"
} | {
"split": "train",
"index": 35642,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Starting from which number $n$ of independent trials does the inequality $p\\left(\\left|\\frac{m}{n}-p\\right|<0.1\\right)>0.97$ hold, if in a single trial $p=0.8$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "534"
} | {
"split": "train",
"index": 35643,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The cafeteria in a certain laboratory is open from noon until 2 in the afternoon every Monday for lunch. Two professors eat 15 minute lunches sometime between noon and 2. What is the probability that they are in the cafeteria simultaneously on any given Monday? Let's think step... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 35644,
"solution": "15."
} |
deepscaler | [
{
"role": "user",
"content": "Given the parametric equation of line $l$ as $$\\begin{cases} x=t \\\\ y= \\frac { \\sqrt {2}}{2}+ \\sqrt {3}t \\end{cases}$$ (where $t$ is the parameter), if the origin $O$ of the Cartesian coordinate system $xOy$ is taken as the pole and the direction of $Ox$ as the polar ax... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {10}}{2}"
} | {
"split": "train",
"index": 35645,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In quadrilateral \\(ABCD\\), \\(\\angle ABD = 70^\\circ\\), \\(\\angle CAD = 20^\\circ\\), \\(\\angle BAC = 48^\\circ\\), \\(\\angle CBD = 40^\\circ\\). Find \\(\\angle ACD\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 35646,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Randomly split 2.5 into the sum of two non-negative numbers, and round each number to its nearest integer. What is the probability that the sum of the two resulting integers is 3? 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": 35647,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain year, a specific date was never a Sunday in any month. Determine this date. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 35648,
"solution": ""
} |
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