data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Let $N$ be the number of ways to write $2010$ in the form $2010 = a_3 \\cdot 10^3 + a_2 \\cdot 10^2 + a_1 \\cdot 10 + a_0$, where the $a_i$'s are integers, and $0 \\le a_i \\le 99$. An example of such a representation is $1\\cdot 10^3 + 3\\cdot 10^2 + 67\\cdot 10^1 + 40\\cdot 1... | math | {
"style": "rule",
"ground_truth": "202"
} | {
"split": "train",
"index": 30849,
"solution": "If we choose $a_3$ and $a_1$ such that $(10^3)(a_3) + (10)(a_1) \\leq 2010$ there is a unique choice of $a_2$ and $a_0$ that makes the equality hold. So $N$ is just the number of combinations of $a_3$ and $a_1$ we can pick. If $a_3 = 0$ or $a_3 = 1$ we can let $a_1... |
deepscaler | [
{
"role": "user",
"content": "For natural numbers $m$ greater than or equal to 2, the decomposition of their cube powers can be represented as follows: $2^3 = 3 + 5$, $3^3 = 7 + 9 + 11$, $4^3 = 13 + 15 + 17 + 19$. Then, \n(1) The smallest number in the decomposition of $8^3$ is; \n(2) Following the above ... | math | {
"style": "rule",
"ground_truth": "57"
} | {
"split": "train",
"index": 30850,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle with a radius of 3 units has its center at $(0, 0)$. A circle with a radius of 5 units has its center at $(12, 0)$. A line tangent to both circles intersects the $x$-axis at $(x, 0)$ to the right of the origin. What is the value of $x$? Express your answer as a common ... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{2}"
} | {
"split": "train",
"index": 30851,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Farmer James invents a new currency, such that for every positive integer $n \\leq 6$, there exists an $n$-coin worth $n$ ! cents. Furthermore, he has exactly $n$ copies of each $n$-coin. An integer $k$ is said to be nice if Farmer James can make $k$ cents using at least one co... | math | {
"style": "rule",
"ground_truth": "210"
} | {
"split": "train",
"index": 30852,
"solution": "We use the factorial base, where we denote $$ \\left(d_{n} \\ldots d_{1}\\right)_{*}=d_{n} \\times n!+\\cdots+d_{1} \\times 1! $$ The representation of $2018_{10}$ is $244002_{*}$ and the representation of $720_{10}$ is $100000_{*}$. The largest nice number less th... |
deepscaler | [
{
"role": "user",
"content": "Find the probability that a monkey typing randomly on a typewriter will type the string 'abc' before 'aaa'. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{7}"
} | {
"split": "train",
"index": 30853,
"solution": "It suffices to assume that the monkey starts all over as soon as he has typed a string that ends in no prefix of either $abc$ or $aaa$. For instance, if the monkey gets to $abb$ we can throw these out because there's no way to finish one of those strings from this ... |
deepscaler | [
{
"role": "user",
"content": "What is the greatest integer value of $b$ such that $-4$ is not in the range of $y=x^2+bx+12$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 30854,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Arthur walks six blocks east and then 12 blocks north. If each block is one-third of a mile, how many miles did he walk? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 30855,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the remainder when \\( 8x^4 - 18x^3 - 6x^2 + 4x - 30 \\) is divided by \\( 2x - 8 \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "786"
} | {
"split": "train",
"index": 30856,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the angle \\(\\theta\\) for the expression \\[ e^{11\\pi i/60} + e^{23\\pi i/60} + e^{35\\pi i/60} + e^{47\\pi i/60} + e^{59\\pi i/60} \\] in the form \\( r e^{i \\theta} \\), where \\( 0 \\leq \\theta < 2\\pi \\). Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "\\frac{7\\pi}{12}"
} | {
"split": "train",
"index": 30857,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AB = 10$, $BC = 14$, and $CA = 16$. Let $D$ be a point in the interior of $\\overline{BC}$. Let points $I_B$ and $I_C$ denote the incenters of triangles $ABD$ and $ACD$, respectively. The circumcircles of triangles $BI_BD$ and $CI_CD$ meet at distinct points... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 30858,
"solution": "Proceed as in Solution 2 until you find $\\angle CPB = 150$. The locus of points $P$ that give $\\angle CPB = 150$ is a fixed arc from $B$ to $C$ ($P$ will move along this arc as $D$ moves along $BC$) and we want to maximise the area of [$\\triangle BPC$]. This mea... |
deepscaler | [
{
"role": "user",
"content": "Let $a, b, c$, and $d$ be positive real numbers such that\n\\[\n\\begin{array}{c@{\\hspace{3pt}}c@{\\hspace{3pt}}c@{\\hspace{3pt}}c@{\\hspace{3pt}}c}\na^2+b^2 &=& c^2+d^2 &=& 2016, \\\\\nac &=& bd &=& 1024.\n\\end{array}\n\\]\nIf $S = a + b + c + d$, compute the value of $\\lfl... | math | {
"style": "rule",
"ground_truth": "127"
} | {
"split": "train",
"index": 30859,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $y= |x-1|+|2x-1|+|3x-1|+ |4x-1|+|5x-1|$ achieves its minimum value when the variable $x$ equals what value? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 30860,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An isosceles trapezoid has sides labeled as follows: \\(AB = 25\\) units, \\(BC = 12\\) units, \\(CD = 11\\) units, and \\(DA = 12\\) units. Compute the length of the diagonal \\( AC \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{419}"
} | {
"split": "train",
"index": 30861,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ava's machine takes four-digit positive integers as input. When the four-digit integer $ABCD$ is input, the machine outputs the integer $A \times B + C \times D$. What is the output when the input is 2023? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 30862,
"solution": "Using the given rule, the output of the machine is $2 \times 0 + 2 \times 3 = 0 + 6 = 6$."
} |
deepscaler | [
{
"role": "user",
"content": "We roll a fair 6-sided die 5 times. What is the probability that we get an odd number in exactly 4 of the 5 rolls? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{5}{32}"
} | {
"split": "train",
"index": 30863,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five packages are delivered to five houses, one to each house. If the packages are randomly delivered, what is the probability that exactly three of them are delivered to their correct houses? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 30864,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest positive integer with only even digits that is less than $10,000$ and is a multiple of $9$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8820"
} | {
"split": "train",
"index": 30865,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\frac{x}{x-1} = \\frac{y^2 + 2y - 1}{y^2 + 2y - 2},$ then $x$ equals Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y^2 + 2y - 1"
} | {
"split": "train",
"index": 30866,
"solution": "1. Start with the given equation:\n \\[\n \\frac{x}{x-1} = \\frac{y^2 + 2y - 1}{y^2 + 2y - 2}\n \\]\n\n2. Cross multiply to eliminate the fractions:\n \\[\n x(y^2 + 2y - 2) = (x-1)(y^2 + 2y - 1)\n \\]\n\n3. Expand both sides of the equation:\n \\[\n ... |
deepscaler | [
{
"role": "user",
"content": "The greatest prime number that is a divisor of $16{,}384$ is $2$ because $16{,}384 = 2^{14}$. What is the sum of the digits of the greatest prime number that is a divisor of $16{,}383$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 30867,
"solution": "1. **Identify the number to factorize**: We start with the number $16{,}383$. We note that $16{,}384 = 2^{14}$, so $16{,}383 = 2^{14} - 1$.\n\n2. **Factorize $16{,}383$**: We use the difference of squares to factorize $16{,}383$:\n \\[\n 16{,}383 = 2^{14} - 1 =... |
deepscaler | [
{
"role": "user",
"content": "Given the arithmetic sequence $\\{a_n\\}$ that satisfies the recursive relation $a_{n+1} = -a_n + n$, calculate the value of $a_5$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{4}"
} | {
"split": "train",
"index": 30868,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many times does 24 divide into 100! (factorial)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 30869,
"solution": "We first determine the number of times 2 and 3 divide into $100!=1 \\cdot 2 \\cdot 3 \\cdots 100$. Let \\langle N\\rangle_{n}$ be the number of times $n$ divides into $N$ (i.e. we want to find \\langle 100!\\rangle_{24}$). Since 2 only divides into even integers, \... |
deepscaler | [
{
"role": "user",
"content": "The increasing [sequence](https://artofproblemsolving.com/wiki/index.php/Sequence) $3, 15, 24, 48, \\ldots\\,$ consists of those [positive](https://artofproblemsolving.com/wiki/index.php/Positive) multiples of 3 that are one less than a [perfect square](https://artofproblemsolv... | math | {
"style": "rule",
"ground_truth": "063"
} | {
"split": "train",
"index": 30870,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A designer has 3 fabric colors he may use for a dress: red, green, and blue. Four different patterns are available for the dress. If each dress design requires exactly one color and one pattern, how many different dress designs are possible? Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 30871,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The left and right foci of the ellipse $\\dfrac{x^{2}}{16} + \\dfrac{y^{2}}{9} = 1$ are $F_{1}$ and $F_{2}$, respectively. There is a point $P$ on the ellipse such that $\\angle F_{1}PF_{2} = 30^{\\circ}$. Find the area of triangle $F_{1}PF_{2}$. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "18 - 9\\sqrt{3}"
} | {
"split": "train",
"index": 30872,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The four positive integers $a,$ $b,$ $c,$ $d$ satisfy\n\\[a \\times b \\times c \\times d = 10!.\\]Find the smallest possible value of $a + b + c + d.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "175"
} | {
"split": "train",
"index": 30873,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the one-variable quadratic equation $x^{2}+3x+m=0$ with two real roots for $x$, determine the range of values for $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{4}"
} | {
"split": "train",
"index": 30874,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of the first $150$ positive integers is painted on a different marble, and the $150$ marbles are placed in a bag. If $n$ marbles are chosen (without replacement) from the bag, what is the smallest value of $n$ such that we are guaranteed to choose three marbles wit... | math | {
"style": "rule",
"ground_truth": "101"
} | {
"split": "train",
"index": 30875,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Kelvin the Frog and 10 of his relatives are at a party. Every pair of frogs is either friendly or unfriendly. When 3 pairwise friendly frogs meet up, they will gossip about one another and end up in a fight (but stay friendly anyway). When 3 pairwise unfriendly frogs meet up, t... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 30876,
"solution": "Consider a graph $G$ with 11 vertices - one for each of the frogs at the party - where two vertices are connected by an edge if and only if they are friendly. Denote by $d(v)$ the number of edges emanating from $v$; i.e. the number of friends frog $v$ has. Note tha... |
deepscaler | [
{
"role": "user",
"content": "Given a harmonic progression with the first three terms 3, 4, 6, find the value of $S_4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 30877,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the equation of the directrix of the parabola \\( y = \\frac{x^2 - 8x + 12}{16} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y = -\\frac{1}{2}"
} | {
"split": "train",
"index": 30878,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any three real numbers $a$, $b$, and $c$, with $b\\neq c$, the operation $\\otimes$ is defined by:\n\\[\\otimes(a,b,c)=\\frac{a}{b-c}\\]\nWhat is $\\otimes(\\otimes(1,2,3),\\otimes(2,3,1),\\otimes(3,1,2))$? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{4}"
} | {
"split": "train",
"index": 30879,
"solution": "1. **Calculate each $\\otimes$ operation inside the main operation**:\n - $\\otimes(1,2,3) = \\frac{1}{2-3} = \\frac{1}{-1} = -1$\n - $\\otimes(2,3,1) = \\frac{2}{3-1} = \\frac{2}{2} = 1$\n - $\\otimes(3,1,2) = \\frac{3}{1-2} = \\frac{3}{-1} = -3$\n\n2. **Sub... |
deepscaler | [
{
"role": "user",
"content": "Equilateral triangle $\\triangle ABC$ is inscribed in circle $\\omega$ with radius $18.$ Circle $\\omega_A$ is tangent to sides $\\overline{AB}$ and $\\overline{AC}$ and is internally tangent to $\\omega.$ Circles $\\omega_B$ and $\\omega_C$ are defined analogously. Circles $\\... | math | {
"style": "rule",
"ground_truth": "378"
} | {
"split": "train",
"index": 30880,
"solution": "Let $O$ be the center, $R = 18$ be the radius, and $CC'$ be the diameter of $\\omega.$ Let $r$ be the radius, $E,D,F$ are the centers of $\\omega_A, \\omega_B,\\omega_C.$ Let $KGH$ be the desired triangle with side $x.$ We find $r$ using \\[CC' = 2R = C'K + KC = r ... |
deepscaler | [
{
"role": "user",
"content": "There is a stack of 200 cards, numbered from 1 to 200 from top to bottom. Starting with the top card, the following operations are performed in sequence: remove the top card, then place the next card at the bottom of the stack; remove the new top card, then place the next card ... | math | {
"style": "rule",
"ground_truth": "145"
} | {
"split": "train",
"index": 30881,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Harriet lives in a large family with 4 sisters and 6 brothers, and she has a cousin Jerry who lives with them. Determine the product of the number of sisters and brothers Jerry has in the house. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 30882,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The fourth power of $\\sqrt{1+\\sqrt{1+\\sqrt{1}}}$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3+2\\sqrt{2}"
} | {
"split": "train",
"index": 30883,
"solution": "Let's denote the expression $\\sqrt{1+\\sqrt{1+\\sqrt{1}}}$ as $x$. Thus, we have:\n\\[ x = \\sqrt{1+\\sqrt{1+\\sqrt{1}}} \\]\n\n1. **Simplify the innermost square root:**\n \\[ \\sqrt{1} = 1 \\]\n So, the expression becomes:\n \\[ x = \\sqrt{1+\\sqrt{1+1}} =... |
deepscaler | [
{
"role": "user",
"content": "Given complex numbers $u$ and $v$ such that $|u+v| = 3$ and $|u^2 + v^2| = 10,$ determine the largest possible value of $|u^3 + v^3|.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31.5"
} | {
"split": "train",
"index": 30884,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nOver two days, 100 bankers collected funds to fight a new virus. Each banker contributed a whole number of thousands of rubles, not exceeding 200. Contributions on the first day did not exceed 100 thousand, and contributions on the second day were greater than this amount. Ad... | math | {
"style": "rule",
"ground_truth": "10050"
} | {
"split": "train",
"index": 30885,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface area in square units?\n[asy] import three; defaultpen(linewidth(0.8)); real r=0.5; currentprojection=orthographic(1,1/2,1/4); draw(unitcube, white, thick(), n... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{30}"
} | {
"split": "train",
"index": 30886,
"solution": "1. **Calculate the Volume:**\n Each unit cube has a volume of $1$ cubic unit. Since there are seven unit cubes joined together, the total volume \\( V \\) is:\n \\[\n V = 7 \\times 1 = 7 \\text{ cubic units}\n \\]\n\n2. **Calculate the Surface Area:**\n T... |
deepscaler | [
{
"role": "user",
"content": "In the parallelepiped $ABCD-A_{1}B_{1}C_{1}D_{1}$, where $AB=4$, $AD=3$, $AA_{1}=3$, $\\angle BAD=90^{\\circ}$, $\\angle BAA_{1}=60^{\\circ}$, $\\angle DAA_{1}=60^{\\circ}$, find the length of $AC_{1}$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\sqrt{55}"
} | {
"split": "train",
"index": 30887,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least common multiple of 135 and 468? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7020"
} | {
"split": "train",
"index": 30888,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To protect the ecological environment, a mountainous area in our city has started to implement the policy of returning farmland to forest since 2005. It is known that at the end of 2004, the forest coverage area of this mountainous area was $a$ acres. \n(1) Assuming the annual... | math | {
"style": "rule",
"ground_truth": "7.2\\%"
} | {
"split": "train",
"index": 30889,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The positive integers $m$ and $n$ satisfy $8m + 9n = mn + 6$. Find the maximum value of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 30890,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a right triangular prism $ABC-A_{1}B_{1}C_{1}$, where $\\angle BAC=90^{\\circ}$, the area of the side face $BCC_{1}B_{1}$ is $16$. Find the minimum value of the radius of the circumscribed sphere of the right triangular prism $ABC-A_{1}B_{1}C_{1}$. Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "2 \\sqrt {2}"
} | {
"split": "train",
"index": 30891,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle has side lengths of 8, 15 and 17 units. What is the area of the triangle, in square units? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 30892,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the integral \\(\\int_{0}^{2}\\left(x^{2}+x-1\\right) e^{x / 2} \\, d x\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2 (3e - 5)"
} | {
"split": "train",
"index": 30893,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $\\angle C = 90^\\circ$ and $AB = 12$. Squares $ABXY$ and $CBWZ$ are constructed outside of the triangle. The points $X$, $Y$, $Z$, and $W$ lie on a circle. What is the perimeter of the triangle? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "12 + 12\\sqrt{2}"
} | {
"split": "train",
"index": 30894,
"solution": "1. **Identify the Problem Setup**: We are given a right triangle $\\triangle ABC$ with $\\angle C = 90^\\circ$ and hypotenuse $AB = 12$. Squares $ABXY$ and $CBWZ$ are constructed outside the triangle, and points $X$, $Y$, $Z$, and $W$ lie on a circle.\n\n2. **Under... |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $PQR$ is a straight line. What is the value of $x$?\n\n[asy]\ndraw((-2,0)--(8,0),linewidth(0.7)); draw((8,0)--(5,-5.5)--(0,0),linewidth(0.7));\nlabel(\"$P$\",(-2,0),W); label(\"$Q$\",(0,0),N); label(\"$R$\",(8,0),E); label(\"$S$\",(5,-5.5),S);\n\nlabel(\"$136^\... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 30895,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number 2017 has 7 ones and 4 zeros in binary representation. When will the nearest year come where the binary representation of the year has no more ones than zeros? (Enter the year.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2048"
} | {
"split": "train",
"index": 30896,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any set $S$ of five points in the plane, no three of which are collinear, let $M(S)$ and $m(S)$ denote the greatest and smallest areas, respectively, of triangles determined by three points from $S$. What is the minimum possible value of $M(S)/m(S)$ ? Let's think step by s... | math | {
"style": "rule",
"ground_truth": "\\phi=\\frac{1+\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 30897,
"solution": "\nLet \\( S \\) be a set of five points in the plane, no three of which are collinear. We need to determine the minimum possible value of \\( \\frac{M(S)}{m(S)} \\) where \\( M(S) \\) and \\( m(S) \\) are the maximum and minimum areas of triangles that can be forme... |
deepscaler | [
{
"role": "user",
"content": "When the mean, median, and mode of the list\n\\[10,2,5,2,4,2,x\\]\nare arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of $x$? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 30898,
"solution": "1. **Calculate the Mean**: \n The mean of the list $10, 2, 5, 2, 4, 2, x$ is calculated as follows:\n \\[\n \\text{Mean} = \\frac{10 + 2 + 5 + 2 + 4 + 2 + x}{7} = \\frac{25 + x}{7}.\n \\]\n\n2. **Determine the Mode**: \n The mode is the number that appear... |
deepscaler | [
{
"role": "user",
"content": "A positive integer n is called *primary divisor* if for every positive divisor $d$ of $n$ at least one of the numbers $d - 1$ and $d + 1$ is prime. For example, $8$ is divisor primary, because its positive divisors $1$ , $2$ , $4$ , and $8$ each differ by $1$ f... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 30899,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(ABCD\\) be a square of side length 13. Let \\(E\\) and \\(F\\) be points on rays \\(AB\\) and \\(AD\\), respectively, so that the area of square \\(ABCD\\) equals the area of triangle \\(AEF\\). If \\(EF\\) intersects \\(BC\\) at \\(X\\) and \\(BX=6\\), determine \\(DF\\... | math | {
"style": "rule",
"ground_truth": "\\sqrt{13}"
} | {
"split": "train",
"index": 30900,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define $a@b = ab - b^{2}$ and $a\\#b = a + b - ab^{2}$. What is $\\frac {6@2}{6\\#2}$? 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": 30901,
"solution": "1. **Calculate $6@2$:**\n Using the operation defined as $a@b = ab - b^2$, we substitute $a = 6$ and $b = 2$:\n \\[\n 6@2 = 6 \\cdot 2 - 2^2 = 12 - 4 = 8.\n \\]\n\n2. **Calculate $6\\#2$:**\n Using the operation defined as $a\\#b = a + b - ab^2$, we subst... |
deepscaler | [
{
"role": "user",
"content": "A given integer Fahrenheit temperature $F$ is first converted to Kelvin using the formula $K = \\frac{5}{9}(F - 32) + 273.15$, rounded to the nearest integer, then converted back to Fahrenheit using the inverse formula $F' = \\frac{9}{5}(K - 273.15) + 32$, and rounded to the ne... | math | {
"style": "rule",
"ground_truth": "401"
} | {
"split": "train",
"index": 30902,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bag has 4 red marbles and 6 white marbles. Three marbles are drawn from the bag without replacement. What is the probability that the sequence of marbles drawn is red, white, red? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{10}"
} | {
"split": "train",
"index": 30903,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and satisfy the vectors $\\overrightarrow{m}=(\\cos A,\\cos B)$, $\\overrightarrow{n}=(a,2c-b)$, and $\\overrightarrow{m} \\parallel \\overrightarrow{n}$.\n(I) Find the measure of an... | math | {
"style": "rule",
"ground_truth": "5 \\sqrt {3}"
} | {
"split": "train",
"index": 30904,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The expression $\\cos 2x + \\cos 6x + \\cos 10x + \\cos 14x$ can be written in the equivalent form\n\\[a \\cos bx \\cos cx \\cos dx\\] for some positive integers $a,$ $b,$ $c,$ and $d.$ Find $a + b + c + d.$ Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 30905,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain kingdom, the workforce consists only of a clan of dwarves and a clan of elves. Historically, in this kingdom, dwarves and elves have always worked separately, and no enterprise has ever allowed itself to hire both at the same time. The aggregate labor supply of dwa... | math | {
"style": "rule",
"ground_truth": "1.25"
} | {
"split": "train",
"index": 30906,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Due to the increasing personnel exchanges between Hefei and Nanjing as a result of urban development, there is a plan to build a dedicated railway to alleviate traffic pressure, using a train as a shuttle service. It is known that the daily round-trip frequency $y$ of the train... | math | {
"style": "rule",
"ground_truth": "7920"
} | {
"split": "train",
"index": 30907,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of permutations of the letters $ABCDE$ where the letters $A$ and $B$ are not adjacent and the letters $C$ and $D$ are not adjacent. For example, count the permutations $ACBDE$ and $DEBCA$ but not $ABCED$ or $EDCBA$ . Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 30908,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest divisor by which $29 \\cdot 14$ leaves the same remainder when divided by $13511, 13903,$ and $14589$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "98"
} | {
"split": "train",
"index": 30909,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Harry and Terry are each told to calculate $8-(2+5)$. Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$. If Harry's answer is $H$ and Terry's answer is $T$, what is $H-T$? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "-10"
} | {
"split": "train",
"index": 30910,
"solution": "1. **Calculate Harry's Answer ($H$):**\n Harry follows the correct order of operations (PEMDAS/BODMAS), which prioritizes parentheses first. Thus, he calculates:\n \\[\n H = 8 - (2 + 5) = 8 - 7 = 1\n \\]\n\n2. **Calculate Terry's Answer ($T$):**\n Terry i... |
deepscaler | [
{
"role": "user",
"content": "Find all values of $k$ for which the positive difference between the solutions of\n\\[5x^2 + 4x + k = 0\\]equals the sum of the squares of these solutions. Enter all possible values of $k,$ separated by commas. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}, -\\frac{12}{5}"
} | {
"split": "train",
"index": 30911,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\[P(x) = (3x^4 - 39x^3 + ax^2 + bx + c)(4x^4 - 96x^3 + dx^2 + ex + f),\\] where $a, b, c, d, e, f$ are real numbers. Suppose that the set of all complex roots of $P(x)$ is $\\{1, 2, 2, 3, 3, 4, 6\\}.$ Find $P(7).$ Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "86400"
} | {
"split": "train",
"index": 30912,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The pan containing 24-inch by 15-inch brownies is cut into pieces that measure 3 inches by 2 inches. Calculate the total number of pieces of brownies 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": 30913,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The hyperbola given by the equation \\[\\frac{x^2}{100} - \\frac{y^2}{64} = 1\\]has asymptotes $y = \\pm mx,$ where $m$ is positive. Find $m.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac45"
} | {
"split": "train",
"index": 30914,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are ten numbers \\( x_1, x_2, \\cdots, x_{10} \\), where the maximum number is 10 and the minimum number is 2. Given that \\( \\sum_{i=1}^{10} x_i = 70 \\), find the maximum value of \\( \\sum_{i=1}^{10} x_i^2 \\). Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "628"
} | {
"split": "train",
"index": 30915,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the linear function y=kx+b, where k and b are constants, and the table of function values, determine the incorrect function value. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 30916,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the number $2016^{* * * *} 02 * *$, each of the six asterisks must be replaced with any of the digits $0, 2, 4, 5, 7, 9$ (digits may be repeated) so that the resulting 12-digit number is divisible by 15. How many ways can this be done? Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "5184"
} | {
"split": "train",
"index": 30917,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $4a = \\sqrt{5}c$ and $\\cos C = \\frac{3}{5}$. \n$(Ⅰ)$ Find the value of $\\sin A$. \n$(Ⅱ)$ If $b = 11$, find the area of $\\triangle ABC$. Let's... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 30918,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let n rational numbers $x_{1}$, $x_{2}$, $\\ldots$, $x_{n}$ satisfy $|x_{i}| \\lt 1$ for $i=1,2,\\ldots,n$, and $|x_{1}|+|x_{2}|+\\ldots+|x_{n}|=19+|x_{1}+x_{2}+\\ldots+x_{n}|$. Calculate the minimum value of $n$. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 30919,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x) = \\frac{x^2 + 33}{x}, (x \\in \\mathbb{N}^*)$, find the minimum value of $f(x)$ in its domain. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{23}{2}"
} | {
"split": "train",
"index": 30920,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The workers laid a floor of size $n\\times n$ ($10 <n <20$) with two types of tiles: $2 \\times 2$ and $5\\times 1$. It turned out that they were able to completely lay the floor so that the same number of tiles of each type was used. For which $n$ could this happen? (You can’... | math | {
"style": "rule",
"ground_truth": "12, 15, 18"
} | {
"split": "train",
"index": 30921,
"solution": "\nTo solve this problem, we aim to find all integer values of \\( n \\) (where \\( 10 < n < 20 \\)) for which an \\( n \\times n \\) floor can be completely covered using the same number of \\( 2 \\times 2 \\) and \\( 5 \\times 1 \\) tiles. We cannot cut the tiles ... |
deepscaler | [
{
"role": "user",
"content": "We define the polynomial $$ P (x) = 2014x^{2013} + 2013x^{2012} +... + 4x^3 + 3x^2 + 2x. $$ Find the largest prime divisor of $P (2)$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "61"
} | {
"split": "train",
"index": 30922,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the following two equations, the same Chinese character represents the same digit, and different Chinese characters represent different digits:\n数字花园 + 探秘 = 2015,\n探秘 + 1 + 2 + 3 + ... + 10 = 花园\nSo the four-digit 数字花园 = ______ Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "1985"
} | {
"split": "train",
"index": 30923,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all ordered pairs $(a,b)$ of positive integers for which the numbers $\\dfrac{a^3b-1}{a+1}$ and $\\dfrac{b^3a+1}{b-1}$ are both positive integers Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\{(2,2), (1,3), (3,3)\\}"
} | {
"split": "train",
"index": 30924,
"solution": "Adding $1$ to both the given numbers we get:\n$\\dfrac{a^3b-1}{a+1} + 1$ is also a positive integer so we have:\n$\\dfrac{a^3b+a}{a+1}$ = $\\dfrac{a(a^2b+1)}{a+1}$ is a positive integer\n$\\implies (a+1) \\mid (a^2b+1)$ $\\implies (a+1) \\mid (((a+1) - 1)^2b+1)$ ... |
deepscaler | [
{
"role": "user",
"content": "Parallelogram $PQRS$ has vertices $P(4,4)$, $Q(-2,-2)$, $R(-8,-2)$, and $S(-2,4)$. If a point is selected at random from the region determined by the parallelogram, what is the probability that the point is not below the $x$-axis? Express your answer as a common fraction. Let's... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 30925,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle has an area of $16\\pi$ square units. What are the lengths of the circle's diameter and circumference, in units? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8\\pi"
} | {
"split": "train",
"index": 30926,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what value of $x$ does $3^{3x^{2} - 8x + 5} = 3^{3x^{2} + 5x - 6}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{13}"
} | {
"split": "train",
"index": 30927,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate: $\\frac{10^{-2}5^0}{10^{-3}}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 30928,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A function $f:\\{1,2,3,4,5\\} \\rightarrow\\{1,2,3,4,5\\}$ is said to be nasty if there do not exist distinct $a, b \\in\\{1,2,3,4,5\\}$ satisfying $f(a)=b$ and $f(b)=a$. How many nasty functions are there? Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "1950"
} | {
"split": "train",
"index": 30929,
"solution": "We use complementary counting. There are $5^{5}=3125$ total functions. If there is at least one pair of numbers which map to each other, there are \\binom{5}{2}=10$ ways to choose the pair and $5^{3}=125$ ways to assign the other values of the function for a total ... |
deepscaler | [
{
"role": "user",
"content": "Let $\\alpha$ be a real number. Determine all polynomials $P$ with real coefficients such that $$P(2x+\\alpha)\\leq (x^{20}+x^{19})P(x)$$ holds for all real numbers $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "P(x)\\equiv 0"
} | {
"split": "train",
"index": 30930,
"solution": "\nLet \\(\\alpha\\) be a real number. We need to determine all polynomials \\(P(x)\\) with real coefficients satisfying:\n\n\\[\nP(2x + \\alpha) \\leq (x^{20} + x^{19})P(x)\n\\]\n\nfor all real numbers \\(x\\).\n\n### Step-by-Step Solution\n\n1. **Analyzing the ine... |
deepscaler | [
{
"role": "user",
"content": "What is the coefficient of $x^5$ in the expansion of $(2x+3)^7$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6048"
} | {
"split": "train",
"index": 30931,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Six chairs are placed in a row. Find the number of ways 3 people can sit randomly in these chairs such that no two people sit next to each other. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 30932,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\omega$ be a fixed circle with radius 1, and let $B C$ be a fixed chord of $\\omega$ such that $B C=1$. The locus of the incenter of $A B C$ as $A$ varies along the circumference of $\\omega$ bounds a region $\\mathcal{R}$ in the plane. Find the area of $\\mathcal{R}$. Le... | math | {
"style": "rule",
"ground_truth": "\\pi\\left(\\frac{3-\\sqrt{3}}{3}\\right)-1"
} | {
"split": "train",
"index": 30933,
"solution": "We will make use of the following lemmas. Lemma 1: If $A B C$ is a triangle with incenter $I$, then $\\angle B I C=90+\\frac{A}{2}$. Proof: Consider triangle $B I C$. Since $I$ is the intersection of the angle bisectors, $\\angle I B C=\\frac{B}{2}$ and $\\angle I ... |
deepscaler | [
{
"role": "user",
"content": "Given a right prism with all vertices on the same sphere, with a height of $4$ and a volume of $32$, the surface area of this sphere is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32\\pi"
} | {
"split": "train",
"index": 30934,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right triangle when rotating around a large leg forms a cone with a volume of $100\\pi$ . Calculate the length of the path that passes through each vertex of the triangle at rotation of $180^o$ around the point of intersection of its bisectors, if the sum of the diameters ... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 30935,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a magic square, the numbers in each row, the numbers in each column, and the numbers on each diagonal have the same sum. In the magic square shown, what is the value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2.2"
} | {
"split": "train",
"index": 30936,
"solution": "Using the second row, we see that the sum of the numbers in each row, column and diagonal must be $3.6 + 3 + 2.4 = 9$. Since the sum of the numbers in the first column must be 9, then the bottom left number must be $9 - 2.3 - 3.6 = 9 - 5.9 = 3.1$. Since the sum of ... |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression\n\\[\n \\frac{121 \\left( \\frac{1}{13} - \\frac{1}{17} \\right) \n + 169 \\left( \\frac{1}{17} - \\frac{1}{11} \\right) + 289 \\left( \\frac{1}{11} - \\frac{1}{13} \\right)}{\n 11 \\left( \\frac{1}{13} - \\frac{1}{17} \\right) \n ... | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 30937,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\(ABC\\), the sides opposite to angles \\(A, B,\\) and \\(C\\) are denoted by \\(a, b,\\) and \\(c\\) respectively. Given that \\(c = 10\\) and \\(\\frac{\\cos A}{\\cos B} = \\frac{b}{a} = \\frac{4}{3}\\). Point \\(P\\) is a moving point on the incircle of triangle... | math | {
"style": "rule",
"ground_truth": "160"
} | {
"split": "train",
"index": 30938,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nAt the moment when Pierrot left the \"Commercial\" bar, heading to the \"Theatrical\" bar, Jeannot was leaving the \"Theatrical\" bar on his way to the \"Commercial\" bar. They were walking at constant (but different) speeds. When the vagabonds met, Pierrot proudly noted that... | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"split": "train",
"index": 30939,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $p$ denote the proportion of teams, out of all participating teams, who submitted a negative response to problem 5 of the Team round (e.g. \"there are no such integers\"). Estimate $P=\\lfloor 10000p\\rfloor$. An estimate of $E$ earns $\\max (0,\\lfloor 20-|P-E|/20\\rfloor)... | math | {
"style": "rule",
"ground_truth": "5568"
} | {
"split": "train",
"index": 30940,
"solution": "Of the 88 teams competing in this year's Team round, 49 of them answered negatively, 9 (correctly) provided a construction, 16 answered ambiguously or did not provide a construction, and the remaining 14 teams did not submit to problem 5. Thus $p=\\frac{49}{88} \\a... |
deepscaler | [
{
"role": "user",
"content": "Alice and the White Rabbit left the Rabbit's house together at noon to go to the Duchess's reception. Halfway through, the Rabbit remembered that he forgot his gloves and fan, and ran back home at twice the speed he had been walking with Alice. Grabbing the gloves and fan, he t... | math | {
"style": "rule",
"ground_truth": "12:40"
} | {
"split": "train",
"index": 30941,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $2000^3-1999\\cdot 2000^2-1999^2\\cdot 2000+1999^3$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3999"
} | {
"split": "train",
"index": 30942,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the arithmetic sequence $\\{a_n\\}$, it is given that $a_2+a_8-a_{12}=0$ and $a_{14}-a_4=2$. Let $s_n=a_1+a_2+\\ldots+a_n$, then determine the value of $s_{15}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 30943,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Is it possible to append two digits to the right of the number 277 so that the resulting number is divisible by any number from 2 to 12? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27720"
} | {
"split": "train",
"index": 30944,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a beach soccer tournament with 17 teams, where each team plays against every other team exactly once. A team earns 3 points for a win in regular time, 2 points for a win in extra time, and 1 point for a win in a penalty shootout. The losing team earns no points. What i... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 30945,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The curve $y=\\frac{1}{2}{x^2}-2$ has a slope of $\\frac{1}{2}$ at the point $(1$,$-\\frac{3}{2})$. Find the angle of inclination of the tangent line at this point. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 30946,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the hyperbola $\\frac{x^{2}}{4} - \\frac{y^{2}}{12} = 1$ with eccentricity $e$, and the parabola $x=2py^{2}$ with focus at $(e,0)$, find the value of the real number $p$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"split": "train",
"index": 30947,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given eight students, including Abby and Bridget, are randomly assigned to the 12 spots arranged in three rows of four as shown, calculate the probability that Abby and Bridget are seated directly adjacent to each other (in the same row or same column). Let's think step by step... | math | {
"style": "rule",
"ground_truth": "\\frac{17}{66}"
} | {
"split": "train",
"index": 30948,
"solution": ""
} |
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