data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Determine the minimum possible value of the sum\n\\[\n\\frac{a}{3b} + \\frac{b}{6c} + \\frac{c}{9a},\n\\]\nwhere \\( a, b, \\) and \\( c \\) are positive real numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3\\sqrt[3]{2}}"
} | {
"split": "train",
"index": 31949,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( x = \\sqrt{1 + \\frac{1}{1^{2}} + \\frac{1}{2^{2}}} + \\sqrt{1 + \\frac{1}{2^{2}} + \\frac{1}{3^{2}}} + \\cdots + \\sqrt{1 + \\frac{1}{2012^{2}} + \\frac{1}{2013^{2}}} \\). Find the value of \\( x - [x] \\), where \\( [x] \\) denotes the greatest integer not exceeding \... | math | {
"style": "rule",
"ground_truth": "\\frac{2012}{2013}"
} | {
"split": "train",
"index": 31950,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $10 \\cdot \\left(\\frac{1}{2} + \\frac{1}{5} + \\frac{1}{10}\\right)^{-1}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{25}{2}"
} | {
"split": "train",
"index": 31951,
"solution": "1. **Simplify the expression inside the parentheses**: \n We start by simplifying the sum inside the parentheses:\n \\[\n \\frac{1}{2} + \\frac{1}{5} + \\frac{1}{10}\n \\]\n To add these fractions, we need a common denominator. The least common multiple (... |
deepscaler | [
{
"role": "user",
"content": "Suppose F_1 and F_2 are the two foci of a hyperbola C, and there exists a point P on the curve C that is symmetric to F_1 with respect to an asymptote of C. Calculate the eccentricity of the hyperbola C. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 31952,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest solution to the equation \\[\\lfloor x^2 \\rfloor - \\lfloor x \\rfloor^2 = 19.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{109}"
} | {
"split": "train",
"index": 31953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the matrix $\\mathbf{M}$ that triples the second row of a matrix. In other words,\n\\[\\mathbf{M} \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix} = \\begin{pmatrix} a & b \\\\ 3c & 3d \\end{pmatrix}.\\]If no such matrix $\\mathbf{M}$ exists, then enter the zero matrix. L... | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 1 & 0 \\\\ 0 & 3 \\end{pmatrix}"
} | {
"split": "train",
"index": 31954,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest negative integer $x$ which satisfies the congruence $34x+6\\equiv 2\\pmod {20}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 31955,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$f : \\mathbb{Z} \\rightarrow \\mathbb{Z}$ satisfies $m+f(m+f(n+f(m))) = n + f(m)$ for every integers $m,n$. Given that $f(6) = 6$, determine $f(2012)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2000"
} | {
"split": "train",
"index": 31956,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Initially, the fairy tale island was divided into three counties: in the first county lived only elves, in the second - only dwarves, and in the third - only centaurs.\n\n- During the first year, each county where there were no elves was divided into three counties.\n- During t... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 31957,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many even divisors does \\(10!\\) have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "240"
} | {
"split": "train",
"index": 31958,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$A$ is located 60 kilometers west of $B$. Individuals A and B depart from location $A$ while individuals C and D depart from location $B$ at the same time. A, B, and D all travel east, while C travels west. It is known that the speeds of A, B, C, and D form an arithmetic sequen... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 31959,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest natural number that can be represented in exactly two ways as \\(3x + 4y\\), where \\(x\\) and \\(y\\) are natural numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 31960,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five packages are delivered to five houses, one to each house. If these packages are randomly delivered, what is the probability that exactly three of them are delivered to the correct houses? Express your answer as a common fraction. Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{12}"
} | {
"split": "train",
"index": 31961,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the numbers $1, 2, \\cdots, 2005$, choose $n$ different numbers. If it is always possible to find three numbers among these $n$ numbers that can form the side lengths of a triangle, determine the minimum value of $n$. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 31962,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $p(x) = x^{2008} + x^{2007} + x^{2006} + \\cdots + x + 1,$\nand let $r(x)$ be the polynomial remainder when $p(x)$ is divided by $x^4+x^3+2x^2+x+1$. Find the remainder when $|r(2008)|$ is divided by $1000$.\n Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 31963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\) be the number of six-digit numbers divisible by 13 but not divisible by 17, and \\( b \\) be the number of six-digit numbers divisible by 17 but not divisible by 13.\n\nFind \\( a - b \\). Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "16290"
} | {
"split": "train",
"index": 31964,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a tram with a starting station A and an ending station B. A tram departs from station A every 5 minutes towards station B, completing the journey in 15 minutes. A person starts cycling along the tram route from station B towards station A just as a tram arrives at stat... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 31965,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 2.$ Find the maximum value of\n\\[(x^2 - xy + y^2)(x^2 - xz + z^2)(y^2 - yz + z^2).\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{256}{243}"
} | {
"split": "train",
"index": 31966,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the largest four-digit number $M$ has digits with a product of $72$, find the sum of its digits. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 31967,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find four consecutive odd numbers, none of which are divisible by 3, such that their sum is divisible by 5. What is the smallest possible value of this sum? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 31968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 31969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $xOy$, the parametric equations of line $l$ are $$\\begin{cases} x=2 \\sqrt {3}+at \\\\ y=4+ \\sqrt {3}t\\end{cases}$$ (where $t$ is the parameter), and in the polar coordinate system with the coordinate origin $O$ as the pole and the positi... | math | {
"style": "rule",
"ground_truth": "\\frac {1}{2}"
} | {
"split": "train",
"index": 31970,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of $3x + 15$ is one third of the value of $6x + 45$. After finding $x$, subtract 5 from the result. What is the final value? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-5"
} | {
"split": "train",
"index": 31971,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two hundred people were surveyed. Of these, 150 indicated they liked Beethoven, and 120 indicated they liked Chopin. Additionally, it is known that of those who liked both Beethoven and Chopin, 80 people also indicated they liked Vivaldi. What is the minimum number of people su... | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 31972,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations\n\\begin{align*}\nx &= at + b, \\\\\ny &= ct + d,\n\\end{align*}where $0 \\le t \\le 1,$ and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2.$ Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "94"
} | {
"split": "train",
"index": 31973,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many perfect squares less than 1000 have a ones digit of 2, 3 or 4? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 31974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Divide the product of the first six positive composite integers by the product of the next six composite integers. Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{49}"
} | {
"split": "train",
"index": 31975,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify first, then evaluate: $({1-\\frac{2}{{x+1}}})÷\\frac{{{x^2}-1}}{{3x+3}}$, where $x=\\sqrt{3}-1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 31976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive four-digit integer equivalent to 6 mod 7? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"split": "train",
"index": 31977,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\triangle PQR$ be a triangle in the plane, and let $S$ be a point outside the plane of $\\triangle PQR$, so that $SPQR$ is a pyramid whose faces are all triangles.\n\nSuppose that every edge of $SPQR$ has length $18$ or $41$, but no face of $SPQR$ is equilateral. Then wha... | math | {
"style": "rule",
"ground_truth": "1440"
} | {
"split": "train",
"index": 31978,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $0 < \\alpha < \\pi$ and $\\cos{\\alpha} = -\\frac{3}{5}$, find the value of $\\tan{\\alpha}$ and the value of $\\cos{2\\alpha} - \\cos{(\\frac{\\pi}{2} + \\alpha)}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{25}"
} | {
"split": "train",
"index": 31979,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When $x=$____, the expressions $\\frac{x-1}{2}$ and $\\frac{x-2}{3}$ are opposite in sign. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{5}"
} | {
"split": "train",
"index": 31980,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The school plans to organize a movie viewing for the students either on January 4th or January 10th. After finalizing the date, the teacher informs the class leader. However, due to the similarity in pronunciation between \"four\" and \"ten,\" there is a 10% chance that the cla... | math | {
"style": "rule",
"ground_truth": "0.82"
} | {
"split": "train",
"index": 31981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The average (arithmetic mean) age of a group consisting of doctors and lawyers in 40. If the doctors average 35 and the lawyers 50 years old, then the ratio of the numbers of doctors to the number of lawyers is Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "2: 1"
} | {
"split": "train",
"index": 31982,
"solution": "1. **Define Variables:**\n Let $d$ be the number of doctors and $l$ be the number of lawyers.\n\n2. **Set Up Equations for Total Ages:**\n - The average age of the doctors is 35, so the total age of the doctors is $35d$.\n - The average age of the lawyers is ... |
deepscaler | [
{
"role": "user",
"content": "Given that α is an acute angle, cos(α+π/6) = 2/3, find the value of sinα. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\sqrt{15} - 2}{6}"
} | {
"split": "train",
"index": 31983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the terminal side of angle $\\alpha$ passes through point $P\\left(\\sin \\frac{7\\pi }{6},\\cos \\frac{11\\pi }{6}\\right)$, find the value of $\\frac{1}{3\\sin ^{2}\\alpha -\\cos ^{2}\\alpha }=\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.$ Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 31984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let\n\\[z = \\frac{(-11 + 13i)^3 \\cdot (24 - 7i)^4}{3 + 4i},\\]and let $w = \\frac{\\overline{z}}{z}.$ Compute $|w|.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 31985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 31986,
"solution": "To solve this problem, we can use the \"stars and bars\" theorem, which is a common combinatorial method to determine the number of ways to distribute $n$ identical items into $k$ distinct groups.\n\nIn this problem, Pat wants to buy four donuts (identical items) f... |
deepscaler | [
{
"role": "user",
"content": "What is the base $2$ representation of $125_{10}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1111101_2"
} | {
"split": "train",
"index": 31987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of all 3-tuples $(a, b, c)$ of positive integers such that $a + b + c = 2013$ . Find $$ \\sum_{(a,b,c)\\in S} abc. $$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\binom{2015}{5}"
} | {
"split": "train",
"index": 31988,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many positive integers $n$ less than $2013$, does $p^2+p+1$ divide $n$ where $p$ is the least prime divisor of $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "212"
} | {
"split": "train",
"index": 31989,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For $1 \\leq i \\leq 215$ let $a_i = \\dfrac{1}{2^{i}}$ and $a_{216} = \\dfrac{1}{2^{215}}$. Let $x_1, x_2, ..., x_{216}$ be positive real numbers such that $\\sum_{i=1}^{216} x_i=1$ and $\\sum_{1 \\leq i < j \\leq 216} x_ix_j = \\dfrac{107}{215} + \\sum_{i=1}^{216} \\dfrac{a_i... | math | {
"style": "rule",
"ground_truth": "863"
} | {
"split": "train",
"index": 31990,
"solution": "Note that \\begin{align*}\\sum_{1 \\leq i < j \\leq 216} x_ix_j &= \\frac12\\left(\\left(\\sum_{i=1}^{216} x_i\\right)^2-\\sum_{i=1}^{216} x_i^2\\right)\\\\&=\\frac12\\left(1-\\sum x_i^2\\right).\\end{align*} Substituting this into the second equation and collectin... |
deepscaler | [
{
"role": "user",
"content": "Find the least common multiple of 8 and 15. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 31991,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A ball with a diameter of 6 inches rolls along a complex track from start point A to endpoint B. The track comprises four semicircular arcs with radii $R_1 = 120$ inches, $R_2 = 50$ inches, $R_3 = 90$ inches, and $R_4 = 70$ inches respectively. The ball always stays in contact ... | math | {
"style": "rule",
"ground_truth": "330\\pi"
} | {
"split": "train",
"index": 31992,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Translate the graph of $y= \\sqrt{2}\\sin(2x+ \\frac{\\pi}{3})$ to the right by $\\varphi$ ($0<\\varphi<\\pi$) units to obtain the graph of the function $y=2\\sin x(\\sin x-\\cos x)-1$. Find the value of $\\varphi$. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "\\frac{13\\pi}{24}"
} | {
"split": "train",
"index": 31993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Gavrila found that the front tires of the car last for 21,000 km, and the rear tires last for 28,000 km. Therefore, he decided to swap them at some point so that the car would travel the maximum possible distance. Find this maximum distance (in km). Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "24000"
} | {
"split": "train",
"index": 31994,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Bao was given $\\$1,\\!000$ for his birthday. He decided to invest the money in a bank account that earns $10\\%$ interest, compounded annually. In dollars, how much total interest will Bao have earned 3 years later? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "331"
} | {
"split": "train",
"index": 31995,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the production of a certain item, its weight \\( X \\) is subject to random fluctuations. The standard weight of the item is 30 g, its standard deviation is 0.7, and the random variable \\( X \\) follows a normal distribution. Find the probability that the weight of a random... | math | {
"style": "rule",
"ground_truth": "0.9215"
} | {
"split": "train",
"index": 31996,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c,$ $d$ be real numbers such that\n\\[a^2 + b^2 + c^2 + d^2 = 4.\\]Find the maximum value of $a^3 + b^3 + c^3 + d^3.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 31997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two connected rooms have different sizes and temperatures. One room has a length of $5 \\,\\mathrm{m}$, a width of $3 \\,\\mathrm{m}$, a height of $4 \\,\\mathrm{m}$, and a temperature of $22 \\,^{\\circ}\\mathrm{C}$; the other room has a length of $6 \\,\\mathrm{m}$, a width o... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 31998,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the puzzle:\n\n$$\n\\text { SI } \\cdot \\text { SI } = \\text { SALT. }\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "98"
} | {
"split": "train",
"index": 31999,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer $n$ for which $$1!2!\\cdots(n-1)!>n!^{2}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 32000,
"solution": "Dividing both sides by $n!^{2}$, we obtain $$\\begin{aligned} \\frac{1!2!\\ldots(n-3)!(n-2)!(n-1)!}{[n(n-1)!][n(n-1)(n-2)!]} & >1 \\\\ \\frac{1!2!\\ldots(n-3)!}{n^{2}(n-1)} & >1 \\\\ 1!2!\\ldots(n-3)! & >n^{2}(n-1) \\end{aligned}$$ Factorials are small at first, so... |
deepscaler | [
{
"role": "user",
"content": "Let $g$ be a function taking the positive integers to the positive integers, such that:\n\n(i) $g$ is increasing (i.e. $g(n + 1) > g(n)$ for all positive integers $n$),\n(ii) $g(mn) = g(m) g(n)$ for all positive integers $m$ and $n,$ and\n(iii) if $m \\neq n$ and $m^n = n^m,$ t... | math | {
"style": "rule",
"ground_truth": "104976"
} | {
"split": "train",
"index": 32001,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\(a\\), \\(b\\), \\(c\\), \\(d\\), \\(e\\), and \\(f\\) are integers for which \\(729x^3+64 = (ax^2 + bx + c)(dx^2 + ex + f)\\) for all \\(x\\), then what is \\(a^2+b^2+c^2+d^2+e^2+f^2\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8210"
} | {
"split": "train",
"index": 32002,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is equal to $\\frac{\\frac{1}{3}-\\frac{1}{4}}{\\frac{1}{2}-\\frac{1}{3}}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 32003,
"solution": "1. **Identify the Least Common Multiple (LCM):** \n The denominators in the fractions are 3, 4, 2, and 3. The LCM of these numbers is the smallest number that each of these numbers can divide without leaving a remainder. The LCM of 2, 3, and 4 is $12$ (since $12... |
deepscaler | [
{
"role": "user",
"content": "A certain brand of computers has a warranty period of $1$ year. Based on a large amount of repair record data, the maximum number of repairs for this brand of computers within one year is $3$ times, with $15\\%$ needing $1$ repair, $6\\%$ needing $2$ repairs, and $4\\%$ needing... | math | {
"style": "rule",
"ground_truth": "0.9"
} | {
"split": "train",
"index": 32004,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many two-digit numbers have digits whose sum is a prime number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 32005,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain senior high school has a total of 3200 students, with 1000 students each in the second and third grades. A stratified sampling method is used to draw a sample of size 160. The number of first-grade students that should be drawn is ______ . Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 32006,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An integer between $1000$ and $9999$, inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "615"
} | {
"split": "train",
"index": 32007,
"solution": "If the common sum of the first two and last two digits is $n$, such that $1 \\leq n \\leq 9$, there are $n$ choices for the first two digits and $n + 1$ choices for the second two digits (since zero may not be the first digit). This gives $\\sum_{n = 1}^9 n(n + 1) ... |
deepscaler | [
{
"role": "user",
"content": "The diagonal of an isosceles trapezoid bisects its obtuse angle. The shorter base of the trapezoid is 3 cm, and the perimeter is 42 cm. Find the area of the trapezoid. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 32008,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": " $1.$ A bottle in the shape of a cone lies on its base. Water is poured into the bottle until its level reaches a distance of 8 centimeters from the vertex of the cone (measured vertically). We now turn the bottle upside down without changing the amount of water it contains; Th... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 32009,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alex sent 150 text messages and talked for 28 hours, given a cell phone plan that costs $25 each month, $0.10 per text message, $0.15 per minute used over 25 hours, and $0.05 per minute within the first 25 hours. Calculate the total amount Alex had to pay in February. Let's thi... | math | {
"style": "rule",
"ground_truth": "142.00"
} | {
"split": "train",
"index": 32010,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Multiply the sum of $158.23$ and $47.869$ by $2$, then round your answer to the nearest tenth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "412.2"
} | {
"split": "train",
"index": 32011,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The car engine operates with a power of \\( P = 60 \\text{ kW} \\). Determine the car's speed \\( v_0 \\) if, after turning off the engine, it stops after traveling a distance of \\( s = 450 \\text{ m} \\). The force resisting the car's motion is proportional to its speed. The ... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 32012,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The curve parameterized by $(x,y) = (2t + 4, 4t - 5)$ is a line, where $t$ is a real number. Find the equation of the line. Enter the equation in the form \"$y = mx + b$\". Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y = 2x - 13"
} | {
"split": "train",
"index": 32013,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the first 1000 positive integers can be written as the sum of finitely many distinct numbers from the sequence $3^{0}, 3^{1}, 3^{2}, \\ldots$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 32014,
"solution": "We want to find which integers have only 0 's and 1 's in their base 3 representation. Note that $1000_{10}=1101001_{3}$. We can construct a bijection from all such numbers to the binary strings, by mapping $x_{3} \\leftrightarrow x_{2}$. Since $1101001_{2}=105_{10... |
deepscaler | [
{
"role": "user",
"content": "In triangle $A.\\sqrt{21}$, $2\\sin 2A\\cos A-\\sin 3A+\\sqrt{3}\\cos A=\\sqrt{3}$\n\n$(1)$ Find the size of angle $A$;\n\n$(2)$ Given that $a,b,c$ are the sides opposite to angles $A,B,C$ respectively, and $a=1$ and $\\sin A+\\sin (B-C)=2\\sin 2C$, find the area of triangle $A... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{6}"
} | {
"split": "train",
"index": 32015,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\((1+x-x^2)^{10} = a_0 + a_1 x + a_2 x^2 + \\cdots + a_{20} x^{20}\\), find \\( a_0 + a_1 + 2a_2 + 3a_3 + \\cdots + 20a_{20} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-9"
} | {
"split": "train",
"index": 32016,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What two digits should be added to the right of the number 2013, so that the resulting six-digit number is divisible by 101? Find all possible solutions. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "94"
} | {
"split": "train",
"index": 32017,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In square $ABCD$ with side length $2$ , let $M$ be the midpoint of $AB$ . Let $N$ be a point on $AD$ such that $AN = 2ND$ . Let point $P$ be the intersection of segment $MN$ and diagonal $AC$ . Find the area of triangle $BPM$ .\n\n*Proposed by Jacob Xu* Let's t... | math | {
"style": "rule",
"ground_truth": "2/7"
} | {
"split": "train",
"index": 32018,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many natural numbers between 200 and 400 are divisible by 8? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 32019,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of ways to arrange the letters of the word PERSEVERANCE. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9,979,200"
} | {
"split": "train",
"index": 32020,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A license plate in a certain state consists of 5 digits, not necessarily distinct, and 3 letters, with the condition that at least one of the letters must be a vowel (A, E, I, O, U). These letters do not need to be next to each other but must be in a sequence. How many distinct... | math | {
"style": "rule",
"ground_truth": "4,989,000,000"
} | {
"split": "train",
"index": 32021,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nA group of schoolchildren, heading to a school camp, was planned to be seated in buses so that there would be an equal number of passengers in each bus. Initially, 22 people were seated in each bus, but it turned out that three schoolchildren could not be seated. However, whe... | math | {
"style": "rule",
"ground_truth": "135"
} | {
"split": "train",
"index": 32022,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\binom{18}{8}=31824$, $\\binom{18}{9}=48620$, and $\\binom{18}{10}=43758$, calculate $\\binom{20}{10}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "172822"
} | {
"split": "train",
"index": 32023,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has $AC = 450$ and $BC = 300$ . Points $K$ and $L$ are located on $\\overline{AC}$ and $\\overline{AB}$ respectively so that $AK = CK$ , and $\\overline{CL}$ is the angle bisector of angle $C$ . Let $P$ be the point of intersection of $\\overline{BK}$ and $\\over... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 32024,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We define \\( a \\star b = a \\times a - b \\times b \\). Find the value of \\( 3 \\star 2 + 4 \\star 3 + 5 \\star 4 + \\cdots + 20 \\star 19 \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "396"
} | {
"split": "train",
"index": 32025,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The degree measures of the angles in a convex 18-sided polygon form an increasing arithmetic sequence with integer values. Find the degree measure of the smallest angle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "143"
} | {
"split": "train",
"index": 32026,
"solution": "Each individual angle in a $18$-gon is $\\frac {(18-2) \\cdot 180^\\circ}{18} = 160^\\circ$. Since no angle in a convex polygon can be larger than $180^\\circ$, the smallest angle possible is in the set $159, 161, 157, 163, 155, 165, 153, 167, 151, 169, 149, 171, 1... |
deepscaler | [
{
"role": "user",
"content": "In how many ways can 5 people be seated around a round table? (Two seatings are considered the same if one is a rotation of the other.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 32027,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven distinct integers are picked at random from $\\{1,2,3,\\ldots,12\\}$. What is the probability that, among those selected, the third smallest is $4$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{35}{132}"
} | {
"split": "train",
"index": 32028,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Lee can make 18 cookies with two cups of flour. How many cookies can he make with three cups of flour? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 32029,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of increasing sequences of positive integers $a_1 \\le a_2 \\le a_3 \\le \\cdots \\le a_{10} \\le 2007$ such that $a_i-i$ is even for $1\\le i \\le 10$ can be expressed as ${m \\choose n}$ for some positive integers $m > n$. Compute the remainder when $m$ is divided ... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 32030,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of th... | math | {
"style": "rule",
"ground_truth": "64,\\!328"
} | {
"split": "train",
"index": 32031,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A paper equilateral triangle of side length 2 on a table has vertices labeled \\(A\\), \\(B\\), and \\(C\\). Let \\(M\\) be the point on the sheet of paper halfway between \\(A\\) and \\(C\\). Over time, point \\(M\\) is lifted upwards, folding the triangle along segment \\(BM\... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{6}"
} | {
"split": "train",
"index": 32032,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Samson derives utility according the relation $$\\text{Utility} = \\text{hours of math done} \\times \\text{hours of frisbee played}.$$On Monday he plays $t$ hours of frisbee and spends $8 - t$ hours doing math. On Tuesday, he ends up getting the same amount of utility as Mon... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 32033,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to choose 4 cards from a standard deck of 52 cards, where two cards come from one suit and the other two each come from different suits? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "158184"
} | {
"split": "train",
"index": 32034,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the 6-digit repetend in the decimal representation of $\\frac{7}{29}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "241379"
} | {
"split": "train",
"index": 32035,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(1) Use the Euclidean algorithm to find the greatest common divisor of 117 and 182, and verify it using the subtraction method. \n(2) Use the Horner's method to evaluate the polynomial $f(x) = 1 - 9x + 8x^2 - 4x^4 + 5x^5 + 3x^6$ at $x = -1$. Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 32036,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the heights on the two equal sides of an isosceles triangle is equal to the height on the base. Find the sine of the base angle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{15}}{4}"
} | {
"split": "train",
"index": 32037,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In right triangle $DEF$, we have $\\sin D = \\frac{5}{13}$ and $\\sin E = 1$. Find $\\sin F$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12}{13}"
} | {
"split": "train",
"index": 32038,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A 5-dimensional ant starts at one vertex of a 5-dimensional hypercube of side length 1. A move is when the ant travels from one vertex to another vertex at a distance of $\\sqrt{2}$ away. How many ways can the ant make 5 moves and end up on the same vertex it started at? Let's ... | math | {
"style": "rule",
"ground_truth": "6240"
} | {
"split": "train",
"index": 32039,
"solution": "We let the cube lie in $\\mathbb{R}^{5}$ with each corner with coordinates 1 or 0. Assume the ant starts at $(0,0,0,0,0)$. Every move the ant adds or subtracts 1 to two of the places. Note that this means the ant can only land on a vertex with the sum of its coordi... |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, $c$ represent the lengths of the sides of a triangle, and they are all natural numbers, where $a \\leq b \\leq c$. If $b = 2008$, then the total number of triangles that satisfy this condition is . Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "2017036"
} | {
"split": "train",
"index": 32040,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What integer $n$ satisfies $0\\le n<{101}$ and $$100n\\equiv 72\\pmod {101}~?$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 32041,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The diagonal of a square is $\\sqrt{2}$ inches long. How many inches long is the side of the square? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 32042,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In right triangle $DEF$, $DE=15$, $DF=9$, and $EF=12$ units. What is the distance from $F$ to the midpoint of segment $DE$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7.5"
} | {
"split": "train",
"index": 32043,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If two different properties are randomly selected from the five types of properties (metal, wood, water, fire, and earth) where metal overcomes wood, wood overcomes earth, earth overcomes water, water overcomes fire, and fire overcomes metal, determine the probability that the ... | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{2}"
} | {
"split": "train",
"index": 32044,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many multiples of 15 are between 15 and 305? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 32045,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers 60, 221, and 229 are the legs and hypotenuse of a right triangle. Find the multiplicative inverse to 450 modulo 3599. (Express your answer as an integer $n$ with $0\\leq n<3599$.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 32046,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $n$: $0.03n + 0.08(20 + n) = 12.6$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 32047,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $n$ is an integer, what is the remainder when the sum of $7 - n$ and $n + 3$ is divided by $7$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 32048,
"solution": ""
} |
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