data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "The average age of 8 people in Room C is 35. The average age of 6 people in Room D is 30. Calculate the average age of all people when the two groups are combined. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{460}{14}"
} | {
"split": "train",
"index": 8100,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\omega$ be a circle of radius 1 centered at $O$. Let $B$ be a point on $\\omega$, and let $l$ be the line tangent to $\\omega$ at $B$. Let $A$ be on $l$ such that $\\angle A O B=60^{\\circ}$. Let $C$ be the foot of the perpendicular from $B$ to $O A$. Find the length of l... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 8101,
"solution": "We have $O C / O B=\\cos \\left(60^{\\circ}\\right)$. Since $O B=1, O C=\\frac{1}{2}$."
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integers less than 1998 are relatively prime to 1547 ? (Two integers are relatively prime if they have no common factors besides 1.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1487"
} | {
"split": "train",
"index": 8102,
"solution": "The factorization of 1547 is \\(7 \\cdot 13 \\cdot 17\\), so we wish to find the number of positive integers less than 1998 that are not divisible by 7, 13, or 17. By the Principle of Inclusion-Exclusion, we first subtract the numbers that are divisible by one of 7,... |
deepscaler | [
{
"role": "user",
"content": "What is the area of the smallest square that can contain a circle of radius 6? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 8103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve in the set of real numbers the equation \\[ 3x^3 \\minus{} [x] \\equal{} 3,\\] where $ [x]$ denotes the integer part of $ x.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x = \\sqrt [3]{\\frac {4}{3}}"
} | {
"split": "train",
"index": 8104,
"solution": "To solve the equation \\( 3x^3 - [x] = 3 \\), where \\([x]\\) represents the integer part of \\(x\\), let's outline the steps systematically.\n\n### Step 1: Analyze the Equation\nGiven the equation \n\\[\n3x^3 - [x] = 3,\n\\]\nwe need to analyze how \\([x]\\) (the g... |
deepscaler | [
{
"role": "user",
"content": "Toner Drum and Celery Hilton are both running for president. A total of $129$ million people cast their vote in a random order, with exactly $63$ million and $66$ million voting for Toner Drum and Celery Hilton, respectively. The Combinatorial News Network displays the fa... | math | {
"style": "rule",
"ground_truth": "1/43"
} | {
"split": "train",
"index": 8105,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For each real number $x$, let $\\lfloor x \\rfloor$ denote the greatest integer that does not exceed x. For how many positive integers $n$ is it true that $n<1000$ and that $\\lfloor \\log_{2} n \\rfloor$ is a positive even integer? Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "340"
} | {
"split": "train",
"index": 8106,
"solution": "For integers $k$, we want $\\lfloor \\log_2 n\\rfloor = 2k$, or $2k \\le \\log_2 n < 2k+1 \\Longrightarrow 2^{2k} \\le n < 2^{2k+1}$. Thus, $n$ must satisfy these inequalities (since $n < 1000$):\n$4\\leq n <8$\n$16\\leq n<32$\n$64\\leq n<128$\n$256\\leq n<512$\n Th... |
deepscaler | [
{
"role": "user",
"content": "The value of $\\sqrt{73}$ is between two positive, consecutive integers. What is the product of these two integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 8107,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a $24$-inch by $30$-inch pan of brownies, cut into pieces that measure $3$ inches by $4$ inches. Calculate the number of pieces of brownie the pan contains. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 8108,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest natural number whose all digits in its decimal representation are different and which decreases 5 times if you cross out the first digit. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3750"
} | {
"split": "train",
"index": 8109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P(x)$ be the monic polynomial with rational coefficients of minimal degree such that $\\frac{1}{\\sqrt{2}}$, $\\frac{1}{\\sqrt{3}}, \\frac{1}{\\sqrt{4}}, \\ldots, \\frac{1}{\\sqrt{1000}}$ are roots of $P$. What is the sum of the coefficients of $P$? Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16000}"
} | {
"split": "train",
"index": 8110,
"solution": "For irrational $\\frac{1}{\\sqrt{r}},-\\frac{1}{\\sqrt{r}}$ must also be a root of $P$. Therefore $P(x)=\\frac{\\left(x^{2}-\\frac{1}{2}\\right)\\left(x^{2}-\\frac{1}{3}\\right) \\cdots\\left(x^{2}-\\frac{1}{1000}\\right)}{\\left(x+\\frac{1}{2}\\right)\\left(x+\\fra... |
deepscaler | [
{
"role": "user",
"content": "One of the mascots for the 2012 Olympic Games is called 'Wenlock' because the town of Wenlock in Shropshire first held the Wenlock Olympian Games in 1850. How many years ago was that?\n\nA) 62\n\nB) 152\n\nC) 158\n\nD) 162\n\nE) 172 Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "162"
} | {
"split": "train",
"index": 8111,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five standard six-sided dice are rolled. We are told there is no three-of-a-kind, but there is a pair of dice that show the same number. These two dice are set aside, and the other three dice are re-rolled. What is the probability that after re-rolling these three dice, at l... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{9}"
} | {
"split": "train",
"index": 8112,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integers (positive and negative) are divisors of 20? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 8113,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In which numeral system is 792 divisible by 297? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 8114,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Which of the following fractions has the greatest value: $\\frac{3}{10}$, $\\frac{4}{7}$, $\\frac{5}{23}$, $\\frac{2}{3}$, $\\frac{1}{2}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 8115,
"solution": "The fractions $\\frac{3}{10}$ and $\\frac{5}{23}$ are each less than $\\frac{1}{2}$ (which is choice $(E)$) so cannot be the greatest among the choices. The fractions $\\frac{4}{7}$ and $\\frac{2}{3}$ are each greater than $\\frac{1}{2}$, so $\\frac{1}{2}$ cannot be... |
deepscaler | [
{
"role": "user",
"content": "Compute $\\dbinom{15}{3}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "455"
} | {
"split": "train",
"index": 8116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $a-1=b+2=c-3=d+4$, which of the four quantities $a,b,c,d$ is the largest? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "c"
} | {
"split": "train",
"index": 8117,
"solution": "Given the equation $a-1=b+2=c-3=d+4$, we can express each variable in terms of $a$:\n\n1. From $a-1 = b+2$, solve for $b$:\n \\[\n b = a - 1 - 2 = a - 3\n \\]\n\n2. From $a-1 = c-3$, solve for $c$:\n \\[\n c = a - 1 + 3 = a + 2\n \\]\n\n3. From $a-1 = d+... |
deepscaler | [
{
"role": "user",
"content": "Given that the probability that a ball is tossed into bin k is 3^(-k) for k = 1,2,3,..., find the probability that the blue ball is tossed into a higher-numbered bin than the yellow ball. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{16}"
} | {
"split": "train",
"index": 8118,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of all positive integers which cannot be written in the form $80k + 3m$ , where $k,m \\in N = \\{0,1,2,...,\\}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "79"
} | {
"split": "train",
"index": 8119,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $G$ be the centroid of triangle $ABC.$ If $GA^2 + GB^2 + GC^2 = 58,$ then find $AB^2 + AC^2 + BC^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "174"
} | {
"split": "train",
"index": 8120,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the exact value of\n\\[\\sqrt{\\left( 2 - \\sin^2 \\frac{\\pi}{7} \\right) \\left( 2 - \\sin^2 \\frac{2 \\pi}{7} \\right) \\left( 2 - \\sin^2 \\frac{3 \\pi}{7} \\right)}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{8}"
} | {
"split": "train",
"index": 8121,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Teacher Shi distributed cards with the numbers 1, 2, 3, and 4 written on them to four people: Jia, Yi, Bing, and Ding. Then the following conversation occurred:\n\nJia said to Yi: \"The number on your card is 4.\"\nYi said to Bing: \"The number on your card is 3.\"\nBing said t... | math | {
"style": "rule",
"ground_truth": "2341"
} | {
"split": "train",
"index": 8122,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A straight line passing through the point $(0,4)$ is perpendicular to the line $x-3y-7=0$. Its equation is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y+3x-4=0"
} | {
"split": "train",
"index": 8123,
"solution": "1. **Identify the slope of the given line**: The equation of the given line is $x - 3y - 7 = 0$. We can rewrite this equation in slope-intercept form, $y = mx + c$, where $m$ is the slope. First, solve for $y$:\n \\[\n x - 3y - 7 = 0 \\implies 3y = x - 7 \\impli... |
deepscaler | [
{
"role": "user",
"content": "A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the diameter of the semicircle is contained in the base of the triangle. What is the radius of the semicircle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{120}{17}"
} | {
"split": "train",
"index": 8124,
"solution": "1. **Identify the Triangle and its Properties**: \n Let's denote the isosceles triangle as $\\triangle ABD$ where $AB = AD$ and $BD = 16$. The height from $A$ to $BD$ is given as $15$. Let $M$ be the midpoint of $BD$. \n\n2. **Divide the Triangle**:\n Draw a lin... |
deepscaler | [
{
"role": "user",
"content": "If the sum of the first $10$ terms and the sum of the first $100$ terms of a given arithmetic progression are $100$ and $10$, respectively, then the sum of first $110$ terms is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-110"
} | {
"split": "train",
"index": 8125,
"solution": "1. **Identify the formula for the sum of an arithmetic progression (AP)**:\n The sum of the first $n$ terms of an AP where $a$ is the first term and $d$ is the common difference is given by:\n \\[\n S_n = \\frac{n}{2} (2a + (n-1)d)\n \\]\n\n2. **Set up equat... |
deepscaler | [
{
"role": "user",
"content": "The expression $\\frac{x-3}{4x}$ is equal to zero for what value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 8126,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the following diagram showing a rectangular grid of dots consisting of 3 rows and 4 columns. How many rectangles can be formed in this grid? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 8127,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A $9\\times 7$ rectangle is tiled with tiles of the two types: L-shaped tiles composed by three unit squares (can be rotated repeatedly with $90^\\circ$) and square tiles composed by four unit squares.\nLet $n\\ge 0$ be the number of the $2 \\times 2 $ tiles which can be used i... | math | {
"style": "rule",
"ground_truth": "0 \\text{ and } 3"
} | {
"split": "train",
"index": 8128,
"solution": "\nConsider a \\(9 \\times 7\\) rectangle that needs to be tiled using two types of tiles: L-shaped tiles, which cover three unit squares, and \\(2 \\times 2\\) square tiles, which cover four unit squares. We need to find all possible values of \\(n\\), the number of... |
deepscaler | [
{
"role": "user",
"content": "I have two 20-sided dice that each have 4 maroon sides, 7 teal sides, 8 cyan sides, and one sparkly side. If I roll both dice, what is the probability they come up the same? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{13}{40}"
} | {
"split": "train",
"index": 8129,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let\n\\[x^5 + x^3 - x^2 - 1 = q_1(x) q_2(x) \\dotsm q_m(x),\\]\nwhere each non-constant polynomial $q_i(x)$ is monic with integer coefficients, and cannot be factored further over the integers. Compute $q_1(2) + q_2(2) + \\dots + q_m(2).$ Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 8130,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of the numbers \\(1, 2, 3, 4, 5, 6\\) is to be placed in the cells of a \\(2 \\times 3\\) table, with one number in each cell. In how many ways can this be done so that in each row and in each column the sum of the numbers is divisible by 3? Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 8131,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integers between 100 and 10,000 contain exactly 3 identical digits in their representation? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "324"
} | {
"split": "train",
"index": 8132,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mohan is selling cookies at the economics fair. As he decides how to package the cookies, he finds that when he bags them in groups of 4, he has 3 left over. When he bags them in groups of 5, he has 2 left over. When he bags them in groups of 7, he has 4 left over. What is the ... | math | {
"style": "rule",
"ground_truth": "67"
} | {
"split": "train",
"index": 8133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify first, then evaluate: $(1- \\frac {2}{x+1})÷ \\frac {x^{2}-x}{x^{2}-1}$, where $x=-2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {3}{2}"
} | {
"split": "train",
"index": 8134,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the sequence \\( 5, 55, 555, 5555, 55555, \\ldots \\). Are any of the numbers in this sequence divisible by 495; if so, what is the smallest such number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "555555555555555555"
} | {
"split": "train",
"index": 8135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": " $21$ Savage has a $12$ car garage, with a row of spaces numbered $1,2,3,\\ldots,12$ . How many ways can he choose $6$ of them to park his $6$ identical cars in, if no $3$ spaces with consecutive numbers may be all occupied?\n\n*2018 CCA Math Bonanza Team Round #9* Le... | math | {
"style": "rule",
"ground_truth": "357"
} | {
"split": "train",
"index": 8136,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle ABC, the lengths of the sides opposite to angles A, B, and C are a, b, and c, respectively. The area of triangle ABC is given by $\\frac{\\sqrt{3}}{6}b(b + c - a\\cos C)$.\n\n1. Find angle A.\n2. If b = 1 and c = 3, find the value of $\\cos(2C - \\frac{\\pi}{6})$. L... | math | {
"style": "rule",
"ground_truth": "-\\frac{4\\sqrt{3}}{7}"
} | {
"split": "train",
"index": 8137,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two regular polygons have the same perimeter. If the first has 38 sides and a side length twice as long as the second, how many sides does the second have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 8138,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of real solutions to the equation\n\\[\n\\frac{1}{x - 1} + \\frac{2}{x - 2} + \\frac{3}{x - 3} + \\dots + \\frac{10}{x - 10} = 2x.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 8139,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many numbers between 10 and 13000, when read from left to right, are formed by consecutive digits in ascending order? For example, 456 is one of these numbers, but 7890 is not.\n(a) 10\n(b) 13\n(c) 18\n(d) 22\n(e) 25 Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 8140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point is randomly dropped onto the interval $[8, 13]$ and let $k$ be the resulting value. Find the probability that the roots of the equation $\\left(k^{2}-2k-35\\right)x^{2}+(3k-9)x+2=0$ satisfy the condition $x_{1} \\leq 2x_{2}$. Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "0.6"
} | {
"split": "train",
"index": 8141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What must be the value of the coefficient $c$ in $P(x)=x^3+2x^2+cx+10$, in order for $x-5$ to be a factor of $P$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-37"
} | {
"split": "train",
"index": 8142,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For certain ordered pairs $(a,b)\\,$ of real numbers, the system of equations\n\\[\\begin{aligned} ax+by&=1 \\\\ x^2 + y^2 &= 50 \\end{aligned}\\]has at least one solution, and each solution is an ordered pair $(x,y)\\,$ of integers. How many such ordered pairs $(a,b)\\,$ are ... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 8143,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the binomial coefficient and the coefficient of the 4th term in the expansion of $\\left( \\left. x^{2}- \\frac{1}{2x} \\right. \\right)^{9}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "- \\frac{21}{2}"
} | {
"split": "train",
"index": 8144,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $a \\in \\{0,1,2\\}, b \\in \\{-1,1,3,5\\}$, determine the probability that the function $f(x)=ax^{2}-2bx$ is increasing in the interval $(1,+\\infty)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{5}{12}"
} | {
"split": "train",
"index": 8145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A math competition consists of three problems, each of which receives an integer score from 0 to 7. For any two competitors, it is known that there is at most one problem in which they received the same score. Find the maximum number of competitors in this competition. Let's th... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 8146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Line segment $\\overline{AB}$ is a diameter of a circle with $AB = 24$. Point $C$, not equal to $A$ or $B$, lies on the circle. As point $C$ moves around the circle, the centroid (center of mass) of $\\triangle ABC$ traces out a closed curve missing two points. To the nearest p... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 8147,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Yannick picks a number $N$ randomly from the set of positive integers such that the probability that $n$ is selected is $2^{-n}$ for each positive integer $n$. He then puts $N$ identical slips of paper numbered 1 through $N$ into a hat and gives the hat to Annie. Annie does not... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2 \\ln 2-1}"
} | {
"split": "train",
"index": 8148,
"solution": "Let $S$ denote the value drawn from the hat. The probability that 2 is picked is $\\frac{1}{n}$ if $n \\geq 2$ and 0 if $n=1$. Thus, the total probability $X$ that 2 is picked is $$P(S=2)=\\sum_{k=2}^{\\infty} \\frac{2^{-k}}{k}$$ By the definition of conditional pro... |
deepscaler | [
{
"role": "user",
"content": "Select 3 distinct numbers from the set {1, 2, ..., 10} such that they do not form an arithmetic sequence. How many such selections are possible? (Answer with a number). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 8149,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Greenhill Soccer Club has 25 players, including 4 goalies. During an upcoming practice, the team plans to have a competition in which each goalie will try to stop penalty kicks from every other player, including the other goalies. How many penalty kicks are required for eve... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 8150,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Chewbacca has 20 pieces of cherry gum and 30 pieces of grape gum. Some of the pieces are in complete packs, while others are loose. Each complete pack has exactly $x$ pieces of gum. If Chewbacca loses one pack of cherry gum, then the ratio of the number of pieces of cherry gu... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 8151,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "I won a trip for four to the Super Bowl. I can bring three of my friends. I have 8 friends. In how many ways can I form my Super Bowl party? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "56"
} | {
"split": "train",
"index": 8152,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine $\\sqrt[5]{102030201}$ without a calculator. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "101"
} | {
"split": "train",
"index": 8153,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the heights of the first ten students formed a geometric sequence, with the fourth student 1.5 meters tall and the tenth student 1.62 meters tall, determine the height of the seventh student. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2.43}"
} | {
"split": "train",
"index": 8154,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the numbers from the set $\\{1,\\ 2,\\ 3,\\ldots,\\ 100\\}$ have a perfect square factor other than one? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 8155,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Use the digits from $0$ to $9$ to form three-digit numbers that are divisible by $5$ and do not have repeating digits. How many such numbers are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "136"
} | {
"split": "train",
"index": 8156,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of ordered quadruples of positive integers $(a, b, c, d)$ such that $a, b, c$, and $d$ are all (not necessarily distinct) factors of 30 and $abcd>900$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1940"
} | {
"split": "train",
"index": 8157,
"solution": "Since $abcd>900 \\Longleftrightarrow \\frac{30}{a} \\frac{30}{b} \\frac{30}{c} \\frac{30}{d}<900$, and there are $\\binom{4}{2}^{3}$ solutions to $abcd=2^{2} 3^{2} 5^{2}$, the answer is $\\frac{1}{2}\\left(8^{4}-\\binom{4}{2}^{3}\\right)=1940$ by symmetry."
} |
deepscaler | [
{
"role": "user",
"content": "Two distinct numbers are selected simultaneously and at random from the set $\\{1, 2, 3, 4, 5\\}$. What is the probability that their product is an even number? 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{7}{10}"
} | {
"split": "train",
"index": 8158,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\left\\lceil\\sqrt{\\frac{9}{4}}\\right\\rceil+\\left\\lceil\\frac{9}{4}\\right\\rceil+\\left\\lceil\\left(\\frac{9}{4}\\right)^2\\right\\rceil$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 8159,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the sum of all numbers of the form $a/b,$ where $a$ and $b$ are relatively prime positive divisors of $1000.$ What is the greatest integer that does not exceed $S/10$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "248"
} | {
"split": "train",
"index": 8160,
"solution": "The sum is equivalent to $\\sum_{i | 10^6}^{} \\frac{i}{1000}$ Therefore, it's the sum of the factors of $10^6$ divided by $1000$. The sum is $\\frac{127 \\times 19531}{1000}$ by the sum of factors formula. The answer is therefore $\\boxed{248}$ after some computati... |
deepscaler | [
{
"role": "user",
"content": "The equation\n$$(x-1)(x-2)\\cdots(x-2016)=(x-1)(x-2)\\cdots (x-2016)$$\nis written on the board, with $2016$ linear factors on each side. What is the least possible value of $k$ for which it is possible to erase exactly $k$ of these $4032$ linear factors so that at least one fa... | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 8161,
"solution": "\nGiven the equation:\n\n\\[\n(x-1)(x-2)\\cdots(x-2016) = (x-1)(x-2)\\cdots(x-2016)\n\\]\n\nThis equation has 2016 linear factors on each side of the equation. Our goal is to find the smallest number \\( k \\) such that removing \\( k \\) factors from these \\( 4032... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sin(\\alpha + \\frac{\\pi}{5}) = \\frac{1}{3}$ and $\\alpha$ is an obtuse angle, find the value of $\\cos(\\alpha + \\frac{9\\pi}{20})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{2} + 4}{6}"
} | {
"split": "train",
"index": 8162,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the equation about $x$, $2x^{2}-( \\sqrt {3}+1)x+m=0$, its two roots are $\\sin θ$ and $\\cos θ$, where $θ∈(0,π)$. Find:\n$(1)$ the value of $m$;\n$(2)$ the value of $\\frac {\\tan θ\\sin θ}{\\tan θ-1}+ \\frac {\\cos θ}{1-\\tan θ}$;\n$(3)$ the two roots of the equation an... | math | {
"style": "rule",
"ground_truth": "\\frac {1}{2}"
} | {
"split": "train",
"index": 8163,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For each positive integer \\( n \\), let \\( \\varphi(n) \\) be the number of positive integers from 1 to \\( n \\) that are relatively prime to \\( n \\). Evaluate:\n$$\n\\sum_{n=1}^{\\infty} \\frac{\\varphi(n) 4^{n}}{7^{n}-4^{n}}\n$$ Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "28/9"
} | {
"split": "train",
"index": 8164,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the internal angles $A$ and $B$ of $\\triangle ABC$ satisfy $\\frac{\\sin B}{\\sin A} = \\cos(A+B)$, find the maximum value of $\\tan B$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 8165,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given $a(4-2 \\sqrt {7}\\cos B)=b(2 \\sqrt {7}\\cos A-5)$, find the minimum value of $\\cos C$. 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": 8166,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "1. Calculate the value of the following expression:\n$(1)(2\\frac{7}{9})^{\\frac{1}{2}} - (2\\sqrt{3} - \\pi)^{0} - (2\\frac{10}{27})^{-\\frac{2}{3}} + 0.25^{-\\frac{3}{2}}$\n2. Given that $x + x^{-1} = 4 (0 < x < 1)$, find the value of ${x^{\\frac{1}{2}}} + {x^{-\\frac{1}{2}}}... | math | {
"style": "rule",
"ground_truth": "\\frac{389}{48}"
} | {
"split": "train",
"index": 8167,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangle has an area of $A$. The midpoints of each side of the rectangle are connected to form a new, smaller rectangle inside the original. What is the ratio of the area of the smaller rectangle to the area of the original rectangle? Express your answer as a common fraction... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 8168,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the expression: $\\left( \\pi - 1 \\right)^{0} + \\left( \\frac{1}{2} \\right)^{-1} + \\left| 5 - \\sqrt{27} \\right| - 2 \\sqrt{3}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8 - 5 \\sqrt{3}"
} | {
"split": "train",
"index": 8169,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many functions $f:\\{1,2,3,4,5\\} \\rightarrow\\{1,2,3,4,5\\}$ have the property that $f(\\{1,2,3\\})$ and $f(f(\\{1,2,3\\}))$ are disjoint? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "94"
} | {
"split": "train",
"index": 8170,
"solution": "Let $f(\\{1,2,3\\})$ be $A$. Then $A \\cap f(A)=\\emptyset$, so $A$ must be a subset of $\\{4,5\\}$. If $B=\\{4,5\\}$, there are $2^{3}-2$ ways to assign each element in $\\{1,2,3\\}$ to a value in $\\{4,5\\}$, and 9 ways to assign each element of $\\{4,5\\}$ to a v... |
deepscaler | [
{
"role": "user",
"content": "Elmer the emu takes $44$ equal strides to walk between consecutive telephone poles on a rural road. Oscar the ostrich can cover the same distance in $12$ equal leaps. The telephone poles are evenly spaced, and the $41$st pole along this road is exactly one mile ($5280$ feet) fr... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 8171,
"solution": "1. **Calculate the number of gaps between the poles**: \n There are 41 poles, so there are \\(41 - 1 = 40\\) gaps between the poles.\n\n2. **Calculate the total number of strides and leaps**:\n - Elmer takes 44 strides per gap, so for 40 gaps, he takes \\(44 \\t... |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $E$: $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1(a > b > 0)$ with an eccentricity of $\\frac{\\sqrt{3}}{2}$ and a minor axis length of $2$.\n1. Find the equation of the ellipse $E$;\n2. A line $l$ is tangent to a circle $C$: $x^{2}+y^{2}=r^{2}(0 < r < b)$ at ... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 8172,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vasya and Petya live in the mountains and like to visit each other. They ascend the mountain at a speed of 3 km/h and descend at a speed of 6 km/h (there are no flat sections of the road). Vasya calculated that it takes him 2 hours and 30 minutes to go to Petya, and 3 hours and... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 8173,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all $y \\in [0,\\pi]$ for which \\[\\sin(x+y)\\leq \\sin(x)+\\sin(y)\\]for every $x$ between $0$ and $\\pi$, inclusive. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "[0,\\pi]"
} | {
"split": "train",
"index": 8174,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nA group of one hundred friends, including Petya and Vasya, live in several cities. Petya found the distance from his city to the city of each of the other 99 friends and summed these 99 distances, obtaining a total of 1000 km. What is the maximum possible total distance that ... | math | {
"style": "rule",
"ground_truth": "99000"
} | {
"split": "train",
"index": 8175,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Chords \\(AB\\) and \\(CD\\) of a circle with center \\(O\\) both have a length of 5. The extensions of segments \\(BA\\) and \\(CD\\) beyond points \\(A\\) and \\(D\\) intersect at point \\(P\\), where \\(DP=13\\). The line \\(PO\\) intersects segment \\(AC\\) at point \\(L\\)... | math | {
"style": "rule",
"ground_truth": "13/18"
} | {
"split": "train",
"index": 8176,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a triangular pyramid \\( S-ABC \\) whose base \\( ABC \\) is an isosceles right triangle with \\( AB \\) as the hypotenuse, and satisfying \\( SA = SB = SC = 2 \\) and \\( AB = 2 \\), assume that the four points \\( S, A, B, C \\) are all on the surface of a sphere center... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 8177,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For some positive integers $a$ and $b$, the product \\[\\log_a(a+1) \\cdot \\log_{a+1} (a+2) \\dotsm \\log_{b-2} (b-1) \\cdot\\log_{b-1} b\\]contains exactly $1000$ terms, and its value is $3.$ Compute $a+b.$ Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "1010"
} | {
"split": "train",
"index": 8178,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $s(n)$ denote the sum of the digits (in base ten) of a positive integer $n$. Compute the number of positive integers $n$ at most $10^{4}$ that satisfy $$s(11 n)=2 s(n)$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2530"
} | {
"split": "train",
"index": 8179,
"solution": "Note $2 s(n)=s(10 n)+s(n)=s(11 n)$, so there cannot be any carries when adding $n$ and $10 n$. This is equivalent to saying no two consecutive digits of $n$ sum to greater than 9 . We change the problem to nonnegative integers less than $10^{4}$ (as both 0 and $10^{... |
deepscaler | [
{
"role": "user",
"content": "What is the 200th term of the increasing sequence of positive integers formed by omitting only the perfect squares? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "214"
} | {
"split": "train",
"index": 8180,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number $2.29^{\\star \\star} N$ is an integer. Its representation in base $b$ is 777. Find the smallest positive integer $b$ such that $N$ is a perfect fourth power. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 8181,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Six students taking a test sit in a row of seats with aisles only on the two sides of the row. If they finish the test at random times, what is the probability that some student will have to pass by another student to get to an aisle? Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\frac{43}{45}"
} | {
"split": "train",
"index": 8182,
"solution": "The probability $p$ that no student will have to pass by another student to get to an aisle is the probability that the first student to leave is one of the students on the end, the next student to leave is on one of the ends of the remaining students, etc.: $p=\\fr... |
deepscaler | [
{
"role": "user",
"content": " $(MON 1)$ Find the number of five-digit numbers with the following properties: there are two pairs of digits such that digits from each pair are equal and are next to each other, digits from different pairs are different, and the remaining digit (which does not belong to any ... | math | {
"style": "rule",
"ground_truth": "1944"
} | {
"split": "train",
"index": 8183,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At Wednesday's basketball game, the Cayley Comets scored 90 points. At Friday's game, they scored $80\\%$ as many points as they scored on Wednesday. How many points did they score on Friday? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 8184,
"solution": "On Friday, the Cayley Comets scored $80\\%$ of 90 points. This is equal to $\\frac{80}{100} \\times 90 = \\frac{8}{10} \\times 90 = 8 \\times 9 = 72$ points. Alternatively, since $80\\%$ is equivalent to 0.8, then $80\\%$ of 90 is equal to $0.8 \\times 90 = 72$."
} |
deepscaler | [
{
"role": "user",
"content": "Two friends are playing tic-tac-toe. If Amy wins $\\frac{3}{8}$ of the time, Lily wins $\\frac{3}{10}$ of the time, and they tie the rest of the time, then what fraction of the time do they tie? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{40}"
} | {
"split": "train",
"index": 8185,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the smallest positive real $K$ such that the inequality\n\\[ K + \\frac{a + b + c}{3} \\ge (K + 1) \\sqrt{\\frac{a^2 + b^2 + c^2}{3}} \\]holds for any real numbers $0 \\le a,b,c \\le 1$ .\n\n*Proposed by Fajar Yuliawan, Indonesia* Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6}}{3}"
} | {
"split": "train",
"index": 8186,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an isosceles triangle \\(ABC\\), the angle at the vertex \\(B\\) is \\(20^\\circ\\). Points \\(D\\) and \\(K\\) are taken on the sides \\(AB\\) and \\(BC\\) respectively such that \\(\\angle KAC = 50^\\circ\\) and \\(\\angle DCA = 60^\\circ\\). Calculate \\(\\angle CDK\\). L... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 8187,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Charles has $5q + 1$ quarters and Richard has $q + 5$ quarters. The difference in their money in dimes is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10(q - 1)"
} | {
"split": "train",
"index": 8188,
"solution": "1. **Identify the number of quarters each person has:**\n - Charles has $5q + 1$ quarters.\n - Richard has $q + 5$ quarters.\n\n2. **Calculate the difference in the number of quarters between Charles and Richard:**\n \\[\n (5q + 1) - (q + 5) = 5q + 1 - q - 5... |
deepscaler | [
{
"role": "user",
"content": "What is the sum of the values of $x$ that satisfy the equation $x^2-5x+5=9$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 8189,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Call a positive integer strictly monotonous if it is a one-digit number or its digits, read from left to right, form a strictly increasing or a strictly decreasing sequence, and no digits are repeated. Determine the total number of strictly monotonous positive integers. Let's t... | math | {
"style": "rule",
"ground_truth": "1013"
} | {
"split": "train",
"index": 8190,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric sequence $\\{a_n\\}$, the sum of the first $n$ terms is $S_n$. Given that $a_1 + a_2 + a_3 = 3$ and $a_4 + a_5 + a_6 = 6$, calculate the value of $S_{12}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 8191,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\( A B C \\) with side \\( A C = 8 \\), a bisector \\( B L \\) is drawn. It is known that the areas of triangles \\( A B L \\) and \\( B L C \\) are in the ratio \\( 3: 1 \\). Find the bisector \\( B L \\), for which the height dropped from vertex \\( B \\) to the ... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2}"
} | {
"split": "train",
"index": 8192,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A standard $n$-sided die has $n$ sides labeled 1 to $n$. Luis, Luke, and Sean play a game in which they roll a fair standard 4-sided die, a fair standard 6-sided die, and a fair standard 8-sided die, respectively. They lose the game if Luis's roll is less than Luke's roll, and ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 8193,
"solution": "We perform casework on Luke's roll. If Luke rolls $n$, with $2 \\leq n \\leq 5$, then the probability Luis rolls less than Luke is $\\frac{n-1}{4}$, and the probability Sean rolls more than Luke is $\\frac{8-n}{8}$. If Luke rolls 6 then Luis will definitely roll les... |
deepscaler | [
{
"role": "user",
"content": "Given a runner who is 30 years old, and the maximum heart rate is found by subtracting the runner's age from 220, determine the adjusted target heart rate by calculating 70% of the maximum heart rate and then applying a 10% increase. Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "146"
} | {
"split": "train",
"index": 8194,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate: $9-8+7\\times6+5-4\\times3+2-1$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 8195,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $0.18\\div0.003.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 8196,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric sequence $\\{a_n\\}$ whose sum of the first $n$ terms is $S_n$, and $a_1=2$, if $\\frac {S_{6}}{S_{2}}=21$, then the sum of the first five terms of the sequence $\\{\\frac {1}{a_n}\\}$ is \n\nA) $\\frac {1}{2}$ or $\\frac {11}{32}$\n\nB) $\\frac {1}{2}$ or $\\... | math | {
"style": "rule",
"ground_truth": "\\frac {31}{32}"
} | {
"split": "train",
"index": 8197,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the tetrahedron P-ABC, $PC \\perpendicular$ plane ABC, $\\angle CAB=90^\\circ$, $PC=3$, $AC=4$, $AB=5$, then the surface area of the circumscribed sphere of this tetrahedron is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
... | math | {
"style": "rule",
"ground_truth": "50\\pi"
} | {
"split": "train",
"index": 8198,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "**Q13.** Determine the greatest value of the sum $M=11xy+3x+2012yz$ , where $x,y,z$ are non negative integers satisfying condition $x+y+z=1000.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "503000000"
} | {
"split": "train",
"index": 8199,
"solution": ""
} |
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