data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Let $m, n \\in \\mathbb{N}$, and $f(x) = (1+x)^m + (1+x)^n$.\n1. When $m=n=7$, $f(x) = a_7x^7 + a_6x^6 + \\ldots + a_1x + a_0$, find $a_0 + a_2 + a_4 + a_6$.\n2. If the coefficient of the expanded form of $f(x)$ is 19 when $m, n$ vary, find the minimum value of the coefficient ... | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 38949,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hemisphere-shaped bowl with radius 1 foot is filled full with chocolate. All of the chocolate is then evenly distributed between 36 cylindrical molds, each having a height equal to their diameter. What is the diameter of each cylinder? Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\frac{2^{1/3}}{3}"
} | {
"split": "train",
"index": 38950,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each vertex of a cube is to be labeled with an integer 1 through 8, with each integer being used once, in such a way that the sum of the four numbers on the vertices of a face is the same for each face. Arrangements that can be obtained from each other through rotations of the ... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 38951,
"solution": "To solve this problem, we need to label each vertex of a cube with integers from $1$ to $8$ such that the sum of the numbers on the vertices of each face is the same. Additionally, we consider two arrangements the same if one can be obtained from the other by rotat... |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $\\frac{17!}{7!10!}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "408408"
} | {
"split": "train",
"index": 38952,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $XYZ$, $\\cos(2X - Y) + \\sin(X + Y) = 2$ and $XY = 6$. What is $YZ$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 38953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S_n$ be the sum of the first $n$ terms of a geometric sequence $\\{a_n\\}$, where $a_n > 0$. If $S_6 - 2S_3 = 5$, then the minimum value of $S_9 - S_6$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 38954,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can four black balls, four white balls, and four blue balls be distributed into six different boxes? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2000376"
} | {
"split": "train",
"index": 38955,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There was a bonus fund in a certain institution. It was planned to distribute the fund such that each employee of the institution would receive $50. However, it turned out that the last employee on the list would receive only $45. Then, in order to ensure fairness, it was decid... | math | {
"style": "rule",
"ground_truth": "950"
} | {
"split": "train",
"index": 38956,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A noodle shop offers classic specialty noodles to customers, who can either dine in at the shop (referred to as \"dine-in\" noodles) or purchase packaged fresh noodles with condiments (referred to as \"fresh\" noodles). It is known that the total price of 3 portions of \"dine-i... | math | {
"style": "rule",
"ground_truth": "\\frac{40}{9}"
} | {
"split": "train",
"index": 38957,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\alpha, \\beta, \\gamma$ are all acute angles and $\\cos^{2} \\alpha + \\cos^{2} \\beta + \\cos^{2} \\gamma = 1$, find the minimum value of $\\tan \\alpha \\cdot \\tan \\beta \\cdot \\tan \\gamma$. Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 38958,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum number of cells on an $8 \\times 8$ chessboard that can be cut by a single straight line? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 38959,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We say that a number of 20 digits is *special* if its impossible to represent it as an product of a number of 10 digits by a number of 11 digits. Find the maximum quantity of consecutive numbers that are specials. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "10^9 - 1"
} | {
"split": "train",
"index": 38960,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lateral edges of a triangular pyramid are mutually perpendicular, and the sides of the base are $\\sqrt{85}$, $\\sqrt{58}$, and $\\sqrt{45}$. The center of the sphere, which touches all the lateral faces, lies on the base of the pyramid. Find the radius of this sphere. Let'... | math | {
"style": "rule",
"ground_truth": "14/9"
} | {
"split": "train",
"index": 38961,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a\\_n\\}$ with its sum of the first $n$ terms denoted as $S\\_n$. For any $n ∈ ℕ^∗$, it is known that $S\\_n = 2(a\\_n - 1)$.\n\n1. Find the general term formula for the sequence $\\{a\\_n\\}$.\n2. Insert $k$ numbers between $a\\_k$ and $a_{k+1}$ to form an... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 38962,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain high school has 1000 students in the first year. Their choices of elective subjects are shown in the table below:\n\n| Subject | Physics | Chemistry | Biology | Politics | History | Geography |\n|---------|---------|-----------|---------|----------|---------|---------... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"split": "train",
"index": 38963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many $6$ -tuples $(a, b, c, d, e, f)$ of natural numbers are there for which $a>b>c>d>e>f$ and $a+f=b+e=c+d=30$ are simultaneously true? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "364"
} | {
"split": "train",
"index": 38964,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The roots of $z^{6}+z^{4}+z^{2}+1=0$ are the vertices of a convex polygon in the complex plane. Find the sum of the squares of the side lengths of the polygon. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12-4 \\sqrt{2}"
} | {
"split": "train",
"index": 38965,
"solution": "Factoring the polynomial as $(z^{4}+1)(z^{2}+1)=0$, we find that the 6 roots are $e^{ \\pm i \\pi / 4}$, $e^{ \\pm i \\pi / 2}, e^{ \\pm i 3 \\pi / 4}$. The calculation then follows from the Law of Cosines or the distance formula."
} |
deepscaler | [
{
"role": "user",
"content": "Compute $\\sum_{n=2009}^{\\infty} \\frac{1}{\\binom{n}{2009}}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2009}{2008}"
} | {
"split": "train",
"index": 38966,
"solution": "Observe that $$\\frac{k+1}{k}\\left(\\frac{1}{\\binom{n-1}{k}}-\\frac{1}{\\binom{n}{k}}\\right) =\\frac{k+1}{k} \\frac{\\binom{n}{k}-\\binom{n-1}{k}}{\\binom{n}{k}\\binom{n-1}{k}} =\\frac{k+1}{k} \\frac{\\binom{n-1}{k-1}}{\\binom{n}{k}\\binom{n-1}{k}} =\\frac{k+1}{... |
deepscaler | [
{
"role": "user",
"content": "Given that there are 10 light bulbs in a box, with 8 of good quality and 2 defective, calculate P(ξ=4), where ξ is the number of draws to draw 2 good quality bulbs, drawing one at a time without replacement. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{15}"
} | {
"split": "train",
"index": 38967,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nIn a quadrilateral pyramid \\(S A B C D\\):\n\n- The areas of the lateral faces \\(S A B, S B C, S C D, S D A\\) are 9, 9, 27, 27 respectively.\n- The dihedral angles at the edges \\(A B, B C, C D, D A\\) are equal.\n- The quadrilateral \\(A B C D\\) is inscribed in a circle,... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 38968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\mathbf{A}^{-1} = \\begin{pmatrix} 2 & 5 \\\\ -1 & -3 \\end{pmatrix},$ then find the inverse of $\\mathbf{A}^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} -1 & -5 \\\\ 1 & 4 \\end{pmatrix}"
} | {
"split": "train",
"index": 38969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer $ K$ such that every $ K$-element subset of $ \\{1,2,...,50 \\}$ contains two distinct elements $ a,b$ such that $ a\\plus{}b$ divides $ ab$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 38970,
"solution": "\nTo find the smallest positive integer \\( K \\) such that every \\( K \\)-element subset of \\( \\{1, 2, \\ldots, 50\\} \\) contains two distinct elements \\( a \\) and \\( b \\) such that \\( a + b \\) divides \\( ab \\), we need to analyze the properties of the... |
deepscaler | [
{
"role": "user",
"content": "$S$ is a subset of the set $\\{1, 2, \\cdots, 2023\\}$, such that the sum of the squares of any two elements is not a multiple of 9. What is the maximum value of $|S|$? (Here, $|S|$ represents the number of elements in $S$.) Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "1350"
} | {
"split": "train",
"index": 38971,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together? Let's think step by st... | math | {
"style": "rule",
"ground_truth": "5760"
} | {
"split": "train",
"index": 38972,
"solution": "1. **Grouping Books**: Since the Arabic books must stay together and the Spanish books must stay together, we can treat each group as a single unit. Thus, we have:\n - One unit of Arabic books (consisting of 2 books)\n - One unit of Spanish books (consisting of... |
deepscaler | [
{
"role": "user",
"content": "Suppose that $m$ and $n$ are positive integers with $m<n$ such that the interval $[m, n)$ contains more multiples of 2021 than multiples of 2000. Compute the maximum possible value of $n-m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "191999"
} | {
"split": "train",
"index": 38973,
"solution": "Let $a=2021$ and $b=2000$. It is clear that we may increase $y-x$ unless both $x-1$ and $y+1$ are multiples of $b$, so we may assume that our interval is of length $b(k+1)-1$, where there are $k$ multiples of $b$ in our interval. There are at least $k+1$ multiples ... |
deepscaler | [
{
"role": "user",
"content": "Given the parametric equation of curve $C\\_1$ is $\\begin{cases} x=3\\cos \\alpha \\ y=\\sin \\alpha \\end{cases} (\\alpha \\text{ is the parameter})$, and the polar coordinate equation of curve $C\\_2$ is $\\rho \\cos \\left( \\theta +\\frac{\\pi }{4} \\right)=\\sqrt{2}$.\n\n... | math | {
"style": "rule",
"ground_truth": "\\frac{6 \\sqrt{3}}{5}"
} | {
"split": "train",
"index": 38974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $z$ be a complex number satisfying $12|z|^2=2|z+2|^2+|z^2+1|^2+31.$ What is the value of $z+\\frac 6z?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 38975,
"solution": "1. **Rewrite the given equation using $w \\overline{w} = |w|^2$:**\n \\[\n 12|z|^2 = 2|z+2|^2 + |z^2+1|^2 + 31\n \\]\n Expressing in terms of $z$ and $\\overline{z}$:\n \\[\n 12z\\overline{z} = 2(z+2)(\\overline{z}+2) + (z^2+1)(\\overline{z}^2+1) + 31\n... |
deepscaler | [
{
"role": "user",
"content": "The real value of $x$ such that $\\frac{81^{x-2}}{9^{x-2}} = 27^{3x+2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{10}{7}"
} | {
"split": "train",
"index": 38976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $A_{1}$ and $C_{1}$ are located on the sides $BC$ and $AB$ of triangle $ABC$. Segments $AA_{1}$ and $CC_{1}$ intersect at point $M$.\n\nIn what ratio does line $BM$ divide side $AC$, if $AC_{1}: C_{1}B = 2: 3$ and $BA_{1}: A_{1}C = 1: 2$? Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "1:3"
} | {
"split": "train",
"index": 38977,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Real numbers $a, b, c$ satisfy the equations $a+b+c=26,1 / a+1 / b+1 / c=28$. Find the value of $$\\frac{a}{b}+\\frac{b}{c}+\\frac{c}{a}+\\frac{a}{c}+\\frac{c}{b}+\\frac{b}{a}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "725"
} | {
"split": "train",
"index": 38978,
"solution": "Multiplying the two given equations gives $$\\frac{a}{a}+\\frac{a}{b}+\\frac{a}{c}+\\frac{b}{a}+\\frac{b}{b}+\\frac{b}{c}+\\frac{c}{a}+\\frac{c}{b}+\\frac{c}{c}=26 \\cdot 28=728$$ and subtracting 3 from both sides gives the answer, 725."
} |
deepscaler | [
{
"role": "user",
"content": "On the refrigerator, MATHCOUNTS is spelled out with 10 magnets, one letter per magnet. Two vowels and three consonants fall off and are put away in a bag. If the Ts are indistinguishable, how many distinct possible collections of letters could be put in the bag? Let's think ste... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 38979,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ such that $2n$ is a perfect square and $3n$ is a perfect cube? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 38980,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An experimenter selects 4 out of 8 different chemical substances to place in 4 distinct bottles. If substances A and B should not be placed in bottle 1, the number of different ways of arranging them is ____. Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "1260"
} | {
"split": "train",
"index": 38981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any real number a and positive integer k, define\n$\\binom{a}{k} = \\frac{a(a-1)(a-2)\\cdots(a-(k-1))}{k(k-1)(k-2)\\cdots(2)(1)}$\nWhat is\n$\\binom{-\\frac{1}{2}}{100} \\div \\binom{\\frac{1}{2}}{100}$? Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "-199"
} | {
"split": "train",
"index": 38982,
"solution": "1. **Define the binomial coefficient for non-integer upper index**:\n \\[\n {a \\choose k} = \\frac{a(a-1)(a-2)\\cdots(a-(k-1))}{k(k-1)(k-2)\\cdots(2)(1)}\n \\]\n This definition extends the binomial coefficient to cases where $a$ is not necessarily a non-n... |
deepscaler | [
{
"role": "user",
"content": "Sets $A, B$ , and $C$ satisfy $|A| = 92$ , $|B| = 35$ , $|C| = 63$ , $|A\\cap B| = 16$ , $|A\\cap C| = 51$ , $|B\\cap C| = 19$ . Compute the number of possible values of $ |A \\cap B \\cap C|$ . Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 38983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $|a|=1$, $|b|=2$, and $a+b=(1, \\sqrt{2})$, the angle between vectors $a$ and $b$ is _______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\pi}{3}"
} | {
"split": "train",
"index": 38984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the expression $10 \\square 10 \\square 10 \\square 10 \\square 10$, fill in the four spaces with each of the operators \"+\", \"-\", \"×\", and \"÷\" exactly once. The maximum possible value of the resulting expression is: Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "109"
} | {
"split": "train",
"index": 38985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the exponential function y=f(x) whose graph passes through the point $\\left( \\frac{1}{2}, \\frac{\\sqrt{2}}{2} \\right)$, find the value of $\\log_2 f(2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 38986,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If an internal point of an $n$-sided prism is connected to all its vertices, $n$ quadrangular pyramids with a common vertex at this point will be formed, with their bases being the lateral faces of the prism. Find the ratio of the sum of the volumes of these pyramids to the vol... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 38987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain department store sells a batch of shirts. The cost price of each shirt is $80. On average, 30 shirts can be sold per day, with a profit of $50 per shirt. In order to increase sales and profits, the store decides to take appropriate price reduction measures. After inve... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 38988,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the geometric series $6 - \\frac{12}{5} + \\frac{36}{25} - \\dots$, calculate the limiting sum of this series as the number of terms increases without bound. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{30}{7}"
} | {
"split": "train",
"index": 38989,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The circumference of a circle has 50 numbers written on it, each of which is either +1 or -1. We want to find the product of these numbers. What is the minimum number of questions needed to determine this product if we can ask about the product of three consecutive numbers at a... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 38990,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular prism has dimensions 10 inches by 3 inches by 30 inches. If a cube has the same volume as this prism, what is the surface area of the cube, in square inches? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6 \\times 900^{2/3}"
} | {
"split": "train",
"index": 38991,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the sixth, seventh, eighth, and ninth basketball games of the season, a player scored $23$, $14$, $11$, and $20$ points, respectively. Her points-per-game average was higher after nine games than it was after the first five games. If her average after ten games was greater t... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 38992,
"solution": "1. **Calculate the sum of the scores for games 6 through 9**: \n The scores are $23$, $14$, $11$, and $20$. Therefore, the sum is:\n \\[\n 23 + 14 + 11 + 20 = 68\n \\]\n\n2. **Calculate the average score for games 6 through 9**:\n The average is:\n \\[\... |
deepscaler | [
{
"role": "user",
"content": "In a box, 10 smaller boxes are placed. Some of the boxes are empty, and some contain another 10 smaller boxes each. Out of all the boxes, exactly 6 contain smaller boxes. How many empty boxes are there? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 38993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be a set of intervals defined recursively as follows: Initially, $[1,1000]$ is the only interval in $S$. If $l \\neq r$ and $[l, r] \\in S$, then both $\\left[l,\\left\\lfloor\\frac{l+r}{2}\\right\\rfloor\\right],\\left[\\left\\lfloor\\frac{l+r}{2}\\right\\rfloor+1, r\\... | math | {
"style": "rule",
"ground_truth": "10.976"
} | {
"split": "train",
"index": 38994,
"solution": "The answer is given by computing the sum of the lengths of all intervals in $S$ and dividing this value by 1000, where the length of an interval $[i, j]$ is given by $j-i+1$. An interval may be categorized based on how many times $[1,1000]$ must be split to attain ... |
deepscaler | [
{
"role": "user",
"content": "For positive integers $N$ and $k$ define $N$ to be $k$-nice if there exists a positive integer $a$ such that $a^k$ has exactly $N$ positive divisors. Determine the quantity of positive integers smaller than $1500$ that are neither $9$-nice nor $10$-nice. Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "1199"
} | {
"split": "train",
"index": 38995,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A particle starts from the origin on the number line, and at each step, it can move either 1 unit in the positive direction or 1 unit in the negative direction. After 10 steps, if the distance between the particle and the origin is 4, then the total number of distinct ways the ... | math | {
"style": "rule",
"ground_truth": "240"
} | {
"split": "train",
"index": 38996,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sled loaded with children starts from rest and slides down a snowy $25^\\circ$ (with respect to the horizontal) incline traveling $85$ meters in $17$ seconds. Ignore air resistance. What is the coefficient of kinetic friction between the sled and the slope? Let's think step b... | math | {
"style": "rule",
"ground_truth": "0.40"
} | {
"split": "train",
"index": 38997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify\n\\[\\cos \\frac{2 \\pi}{13} + \\cos \\frac{6 \\pi}{13} + \\cos \\frac{8 \\pi}{13}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{13} - 1}{4}"
} | {
"split": "train",
"index": 38998,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nThrough points \\( A(0, 14) \\) and \\( B(0, 4) \\), two parallel lines are drawn. The first line, passing through point \\( A \\), intersects the hyperbola \\( y = \\frac{1}{x} \\) at points \\( K \\) and \\( L \\). The second line, passing through point \\( B \\), intersect... | math | {
"style": "rule",
"ground_truth": "3.5"
} | {
"split": "train",
"index": 38999,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base of a pyramid is a square with side length \\( a = \\sqrt{21} \\). The height of the pyramid passes through the midpoint of one of the edges of the base and is equal to \\( \\frac{a \\sqrt{3}}{2} \\). Find the radius of the sphere circumscribed around the pyramid. Let's... | math | {
"style": "rule",
"ground_truth": "3.5"
} | {
"split": "train",
"index": 39000,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_{n}\\}$ such that $a_{2}=2a_{1}=4$, and $a_{n+1}-b_{n}=2a_{n}$, where $\\{b_{n}\\}$ is an arithmetic sequence with a common difference of $-1$. \n$(1)$ Investigation: Determine whether the sequence $\\{a_{n}-n\\}$ is an arithmetic sequence or a geometric... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 39001,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the minimum positive integer $k$ such that $f(n+k) \\equiv f(n)(\\bmod 23)$ for all integers $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2530"
} | {
"split": "train",
"index": 39002,
"solution": "Note that $\\phi(23)=22$ and $\\phi(22)=10$, so if $\\operatorname{lcm}(23,22,10)=2530 \\mid k$ then $f(n+k) \\equiv f(n)(\\bmod 23)$ is always true. We show that this is necessary as well. Choosing $n \\equiv 0(\\bmod 23)$, we see that $k \\equiv 0(\\bmod 23)$. Th... |
deepscaler | [
{
"role": "user",
"content": "A sports lottery stipulates that 7 numbers are drawn from a total of 36 numbers, ranging from 01 to 36, for a single entry, which costs 2 yuan. A person wants to select the lucky number 18 first, then choose 3 consecutive numbers from 01 to 17, 2 consecutive numbers from 19 to ... | math | {
"style": "rule",
"ground_truth": "2100"
} | {
"split": "train",
"index": 39003,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $C_1$ and $C_2$ be circles defined by $$\n(x-10)^2+y^2=36\n$$and $$\n(x+15)^2+y^2=81,\n$$respectively. What is the length of the shortest line segment $\\overline{PQ}$ that is tangent to $C_1$ at $P$ and to $C_2$ at $Q$? Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 39004,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A solid cube of side length $2$ is removed from each corner of a larger solid cube of side length $4$. Find the number of edges of the remaining solid. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 39005,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A clothing retailer offered a discount of $\\frac{1}{4}$ on all jackets tagged at a specific price. If the cost of the jackets was $\\frac{2}{3}$ of the price they were actually sold for and considering this price included a sales tax of $\\frac{1}{10}$, what would be the ratio... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{30}"
} | {
"split": "train",
"index": 39006,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A lady made 3 round doilies with radii of 2, 3, and 10 inches, respectively. She placed them on a round table so that each doily touches the two others and the edge of the table. What is the radius of the table? Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 39007,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the monic quadratic polynomial, in $x,$ with real coefficients, which has $-2 - i \\sqrt{5}$ as a root. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^2 + 4x + 9"
} | {
"split": "train",
"index": 39008,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest number of integers that we can choose from the set $\\{1, 2, 3, \\ldots, 2017\\}$ such that the difference between any two of them is not a prime number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "505"
} | {
"split": "train",
"index": 39009,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The data set $[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]$ has median $Q_2 = 40$, first quartile $Q_1 = 33$, and third quartile $Q_3 = 43$. An outlier in a data set is a value that is more than $1.5$ times the interquartile range below the first quartle ($Q_1$) or more than $1.5$ t... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 39010,
"solution": "1. **Identify the Interquartile Range (IQR):**\n The interquartile range (IQR) is calculated as $Q_3 - Q_1$. Given $Q_1 = 33$ and $Q_3 = 43$, we have:\n \\[\n \\text{IQR} = Q_3 - Q_1 = 43 - 33 = 10.\n \\]\n\n2. **Calculate the Outlier Thresholds:**\n Outl... |
deepscaler | [
{
"role": "user",
"content": "Let $f(n)$ denote the product of all non-zero digits of $n$. For example, $f(5) = 5$; $f(29) = 18$; $f(207) = 14$. Calculate the sum $f(1) + f(2) + f(3) + \\ldots + f(99) + f(100)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2116"
} | {
"split": "train",
"index": 39011,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Six people are arranged in a row. In how many ways can the three people A, B, and C be arranged such that they are not adjacent to each other? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 39012,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A quadrilateral connecting the midpoints of the sides of trapezoid $\\mathrm{ABCD}$ is a rhombus. Find its area if the height of the trapezoid $\\mathrm{BH}=5 \\mathrm{c}$, the smaller base $\\mathrm{BC}=6 \\mathrm{~cm}$, and the angle $\\mathrm{ABC}$ is $120^{\\circ}$. Let's t... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 39013,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the probability of having $2$ adjacent white balls or $2$ adjacent blue balls in a random arrangement of $3$ red, $2$ white and $2$ blue balls? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{10}{21}"
} | {
"split": "train",
"index": 39014,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Lucy has $19$ dollars and $23$ cents. She wants to buy as many popsicles as she can with her money. The popsicles are priced at $1$ dollar and $60$ cents each. How many popsicles can she buy? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 39015,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\lfloor17.2\\rfloor+\\lfloor-17.2\\rfloor$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 39016,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 39017,
"solution": "\n#### Solution 1 - Detailed Analysis\n\n1. **Represent the number and its reverse:** \n Let the two-digit number be represented as $10a + b$, where $a$ is the tens digit and $b$ is the units digit. The reverse of this number would be $10b + a$.\n\n2. **Formulat... |
deepscaler | [
{
"role": "user",
"content": "A $7\\times 1$ board is completely covered by $m\\times 1$ tiles without overlap; each tile may cover any number of consecutive squares, and each tile lies completely on the board. Each tile is either red, blue, or green. Let $N$ be the number of tilings of the $7\\times 1$ boa... | math | {
"style": "rule",
"ground_truth": "106"
} | {
"split": "train",
"index": 39018,
"solution": "This solution is basically solution 1 with more things done at once. The game plan:\n$\\sum_{i=0}^{7} ($the amount of ways to divide the board into $i$ pieces$) \\cdot ($the amount of ways to color the respective divisions)\n The amount of ways to divide the board ... |
deepscaler | [
{
"role": "user",
"content": "Let \\( a, b, c, d \\) be 4 distinct nonzero integers such that \\( a + b + c + d = 0 \\) and the number \\( M = (bc - ad)(ac - bd)(ab - cd) \\) lies strictly between 96100 and 98000. Determine the value of \\( M \\). Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "97344"
} | {
"split": "train",
"index": 39019,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rectangle \\(PQRS\\) is divided into 60 identical squares, as shown. The length of the diagonal of each of these squares is 2. The length of \\(QS\\) is closest to Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 39020,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Carolyn and Paul are playing a game starting with a list of the integers $1$ to $n.$ The rules of the game are:\n\n$\\bullet$ Carolyn always has the first turn.\n\n$\\bullet$ Carolyn and Paul alternate turns.\n\n$\\bullet$ On each of her turns, Carolyn must remove one number... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 39021,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Squares $JKLM$ and $NOPQ$ are congruent, $JM=20$, and $P$ is the midpoint of side $JM$ of square $JKLM$. Calculate the area of the region covered by these two squares in the plane.\nA) $500$\nB) $600$\nC) $700$\nD) $800$\nE) $900$ Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "600"
} | {
"split": "train",
"index": 39022,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AX = XY = YB = \\frac{1}{2}BC$ and $AB = 2BC$. If the measure of angle $ABC$ is 90 degrees, what is the measure of angle $BAC$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22.5"
} | {
"split": "train",
"index": 39023,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\(x\\) and \\(y\\) are real numbers, and:\n\\[\nz_1 = x + (y + 2)i,\n\\]\n\\[\nz_2 = (x - 2) + yi,\n\\]\nwith the condition \\(\\left|z_1\\right| + \\left|z_2\\right| = 4\\),\n\nFind the maximum value of \\(|x + y|\\). Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 39024,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a random variable $X \\sim B(10, 0.6)$, calculate the values of $E(X)$ and $D(X)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2.4"
} | {
"split": "train",
"index": 39025,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For positive integer \\( n \\), let \\( f(n) \\) denote the unit digit of \\( 1+2+3+\\cdots+n \\). Find the value of \\( f(1)+f(2)+\\cdots+f(2011) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7046"
} | {
"split": "train",
"index": 39026,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $AB$ and $CD$ are straight lines. What is the value of $x?$ [asy]\ndraw((0,0)--(12,0));\ndraw((0,5)--(12,5));\ndraw((3,0)--(5,5)--(9,0));\nlabel(\"$60^\\circ$\",(5,4.5),W);\nlabel(\"$50^\\circ$\",(5.5,4.5),E);\nlabel(\"$A$\",(0,5),W);\nlabel(\"$C$\",(0,0),W);\nl... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 39027,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the exact value of the series\n\\[\\frac{1}{5 + 1} + \\frac{2}{5^2 + 1} + \\frac{4}{5^4 + 1} + \\frac{8}{5^8 + 1} + \\frac{16}{5^{16} + 1} + \\dotsb.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 39028,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ be $S_n$, and it satisfies $S_{2014} > 0$, $S_{2015} < 0$. For any positive integer $n$, it holds that $|a_n| \\geqslant |a_k|$, determine the value of $k$. Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "1008"
} | {
"split": "train",
"index": 39029,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of integer points that satisfy the system of inequalities:\n\\[\n\\begin{cases}\ny \\leqslant 3x \\\\\ny \\geqslant \\frac{1}{3}x \\\\\nx + y \\leqslant 100\n\\end{cases}\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2551"
} | {
"split": "train",
"index": 39030,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When \\( n \\) is a positive integer, the function \\( f \\) satisfies\n\\[ f(n+3) = \\frac{f(n) - 1}{f(n) + 1}, \\]\nwith \\( f(1) \\neq 0 \\), and \\( f(1) \\neq \\pm 1 \\).\n\nCompute \\( f(1) f(2023) \\). Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 39031,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three distinct vertices of a regular 2020-gon are chosen uniformly at random. The probability that the triangle they form is isosceles can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100a+b$. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "773"
} | {
"split": "train",
"index": 39032,
"solution": "The number of isosceles triangles that share vertices with the 2020-gon is $2020 \\cdot 1009$, since there are 2020 ways to choose the apex of the triangle and then 1009 ways to choose the other two vertices. (Since 2020 is not divisible by 3, there are no equilate... |
deepscaler | [
{
"role": "user",
"content": "What is the minimum value of $y$ if $y=3x^2+6x+9?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 39033,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the polar equation of curve $C_{1}$ is $\\rho=2\\sin \\theta$, and the polar equation of curve $C_{2}$ is $\\theta= \\frac {\\pi}{3}$ ($\\rho\\in\\mathbb{R}$), curves $C_{1}$ and $C_{2}$ intersect at points $M$ and $N$, then the length of chord $MN$ is ______. Let's think... | math | {
"style": "rule",
"ground_truth": "\\sqrt {3}"
} | {
"split": "train",
"index": 39034,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is one-third times one-half times three-fourths times five-sixths? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{48}"
} | {
"split": "train",
"index": 39035,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\lceil{\\sqrt{x}}\\rceil=12$, how many possible integer values of $x$ are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 39036,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,b,c$ be three distinct positive integers such that the sum of any two of them is a perfect square and having minimal sum $a + b + c$ . Find this sum. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 39037,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If 554 is the base $b$ representation of the square of the number whose base $b$ representation is 24, then $b$, when written in base 10, equals Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 39038,
"solution": "1. **Convert the base $b$ representations to base 10 expressions:**\n - The number $24_b$ in base $b$ is represented as $2b + 4$.\n - The number $554_b$ in base $b$ is represented as $5b^2 + 5b + 4$.\n\n2. **Set up the equation based on the given condition:**\n... |
deepscaler | [
{
"role": "user",
"content": "The four consecutive digits $a$, $b$, $c$ and $d$ are used to form the four-digit numbers $abcd$ and $dcba$. What is the greatest common divisor of all numbers of the form $abcd+dcba$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1111"
} | {
"split": "train",
"index": 39039,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the maximum value of\n\\[\\frac{2x + 3y + 4}{\\sqrt{x^2 + 4y^2 + 2}}\\]\nover all real numbers \\( x \\) and \\( y \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{29}"
} | {
"split": "train",
"index": 39040,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Translate the function $y=\\sqrt{3}\\cos x+\\sin x$ $(x\\in\\mathbb{R})$ to the left by $m$ $(m > 0)$ units, and the resulting graph is symmetric about the $y$-axis. Find the minimum value of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{6}"
} | {
"split": "train",
"index": 39041,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the range of $y=|x+7|-|x-2|$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "[-9, 9]"
} | {
"split": "train",
"index": 39042,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Medians $\\overline{DP}$ and $\\overline{EQ}$ of $\\triangle DEF$ are perpendicular. If $DP= 18$ and $EQ = 24$, then what is ${DF}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8\\sqrt{13}"
} | {
"split": "train",
"index": 39043,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The ratio of the length to the width of a rectangle is $4:3$. If the rectangle has diagonal of length $d$, then the area may be expressed as $kd^2$ for some constant $k$. What is $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12}{25}"
} | {
"split": "train",
"index": 39044,
"solution": "1. **Assign Variables to Dimensions**:\n Let the length of the rectangle be $4x$ and the width be $3x$. This assignment is based on the given ratio of length to width, which is $4:3$.\n\n2. **Use the Pythagorean Theorem**:\n The diagonal $d$ of the rectangle fo... |
deepscaler | [
{
"role": "user",
"content": "A point A is a fixed point on the circumference of a circle with a perimeter of 3. If a point B is randomly selected on the circumference, the probability that the length of the minor arc is less than 1 is ______. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 39045,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The height of a trapezoid, whose diagonals are mutually perpendicular, is 4. Find the area of the trapezoid if one of its diagonals is 5. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{50}{3}"
} | {
"split": "train",
"index": 39046,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three clever monkeys divide a pile of bananas. The first monkey takes some bananas from the pile, keeps three-fourths of them, and divides the rest equally between the other two. The second monkey takes some bananas from the pile, keeps one-fourth of them, and divides the rest ... | math | {
"style": "rule",
"ground_truth": "408"
} | {
"split": "train",
"index": 39047,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)= \\begin{cases}x-1,0 < x\\leqslant 2 \\\\ -1,-2\\leqslant x\\leqslant 0 \\end{cases}$, and $g(x)=f(x)+ax$, where $x\\in[-2,2]$, if $g(x)$ is an even function, find the value of the real number $a$. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "-\\dfrac{1}{2}"
} | {
"split": "train",
"index": 39048,
"solution": ""
} |
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