data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "The image of the point with coordinates $(1,1)$ under the reflection across the line $y=mx+b$ is the point with coordinates $(9,5)$. Find $m+b$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 28949,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many triples \\((a, b, c)\\) of positive integers satisfy the conditions \\( 6ab = c^2 \\) and \\( a < b < c \\leq 35 \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 28950,
"solution": "There are 8 such triplets: \\((2,3,6), (3,8,12), (4,6,12), (6,9,18), (6,16,24), (8,12,24), (6,25,30), (10,15,30)\\)."
} |
deepscaler | [
{
"role": "user",
"content": "The equation $x^2 - kx - 24 = 0$ has only integer solutions for certain positive integers $k$. What is the sum of all such values of $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 28951,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)$ is a monotonic function on the real numbers $\\mathbb{R}$, and for any real number $x$, it satisfies the equation $f\\left[f(x)+ \\frac{2}{2^{x}+1}\\right]= \\frac{1}{3}$, find the value of $f(\\log_23)$. Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 28952,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=(\\sin x+\\cos x)^{2}+2\\cos ^{2}x$,\n(1) Find the smallest positive period and the monotonically decreasing interval of the function $f(x)$;\n(2) When $x\\in[0, \\frac{\\pi}{2}]$, find the maximum and minimum values of $f(x)$. Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "2+\\sqrt{2}"
} | {
"split": "train",
"index": 28953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the integers $1,2, \\ldots, 2004$ can be represented as $(m n+1) /(m+n)$ for positive integers $m$ and $n$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2004"
} | {
"split": "train",
"index": 28954,
"solution": "For any positive integer $a$, we can let $m=a^{2}+a-1, n=a+1$ to see that every positive integer has this property, so the answer is 2004."
} |
deepscaler | [
{
"role": "user",
"content": "Huanhuan and Lele are playing a game together. In the first round, they both gain the same amount of gold coins, and in the second round, they again gain the same amount of gold coins. \n\nAt the beginning, Huanhuan says: \"The number of my gold coins is 7 times the number of y... | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 28955,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the vertices of a pyramid with a square base, and two vertices connected by an edge are called adjacent vertices, with the rule that adjacent vertices cannot be colored the same color, and there are 4 colors to choose from, calculate the total number of different coloring... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 28956,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four identical squares and one rectangle are placed together to form one large square as shown. The length of the rectangle is how many times as large as its width?\n\n[asy]\nunitsize(8mm); defaultpen(linewidth(.8pt));\ndraw((0,0)--(4,0)--(4,4)--(0,4)--cycle);\ndraw((0,3)--(0,4... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 28957,
"solution": "1. **Identify the dimensions of the small squares and the large square**: Let the side length of each small square be $x$. Since there are four small squares placed side by side along one side of the large square, the side length of the large square is $4x$.\n\n2. ... |
deepscaler | [
{
"role": "user",
"content": "Javier is going to Disneyland during spring break. He plans on visiting four particular attractions all before lunch. In how many orders could he visit all four attractions once? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 28958,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify $\\left(\\frac{a^2}{a+1}-a+1\\right) \\div \\frac{a^2-1}{a^2+2a+1}$, then choose a suitable integer from the inequality $-2 \\lt a \\lt 3$ to substitute and evaluate. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 28959,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a rectangular sheet of paper, a picture in the shape of a \"cross\" made of two rectangles $ABCD$ and $EFGH$ was drawn, with sides parallel to the edges of the sheet. It is known that $AB = 9$, $BC = 5$, $EF = 3$, $FG = 10$. Find the area of the quadrilateral $AFCH$. Let's t... | math | {
"style": "rule",
"ground_truth": "52.5"
} | {
"split": "train",
"index": 28960,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $R, S$ and $T$ are digits and that $N$ is the four-digit positive integer $8 R S T$. That is, $N$ has thousands digit 8, hundreds digit $R$, tens digits $S$, and ones (units) digit $T$, which means that $N=8000+100 R+10 S+T$. Suppose that the following conditions a... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 28961,
"solution": "We make a chart of the possible integers, building their digits from left to right. In each case, we could determine the required divisibility by actually performing the division, or by using the following tests for divisibility: - An integer is divisible by 3 when... |
deepscaler | [
{
"role": "user",
"content": "Given sets $A=\\{1, 2, 3, 4\\}$, $B=\\{5, 6, 7\\}$, and $C=\\{8, 9\\}$. Now, take any two sets from these three sets, and then pick one element from each of the two selected sets to form a new set with two elements. The total number of distinct sets that can be formed is $\\_\\... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 28962,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The smaller square in the figure below has a perimeter of $4$ cm, and the larger square has an area of $16$ $\\text{cm}^2$. What is the distance from point $A$ to point $B$? Express your answer as a decimal to the nearest tenth.\n\n[asy]\ndraw((0,0)--(12,0));\ndraw((2,0)--(2,1... | math | {
"style": "rule",
"ground_truth": "5.8"
} | {
"split": "train",
"index": 28963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five points, no three of which are collinear, are given. Calculate the least possible value of the number of convex polygons whose some corners are formed by these five points. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 28964,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\alpha$ be a root of $x^6-x-1$ , and call two polynomials $p$ and $q$ with integer coefficients $\\textit{equivalent}$ if $p(\\alpha)\\equiv q(\\alpha)\\pmod3$ . It is known that every such polynomial is equivalent to exactly one of $0,1,x,x^2,\\ldots,x^{727}$... | math | {
"style": "rule",
"ground_truth": "727"
} | {
"split": "train",
"index": 28965,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence $(x_n)$ is defined by $x_1 = 25$ and $x_k = x_{k - 1}^2 + x_{k - 1}$ for all $k \\ge 2.$ Compute\n\\[\\frac{1}{x_1 + 1} + \\frac{1}{x_2 + 1} + \\frac{1}{x_3 + 1} + \\dotsb.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{25}"
} | {
"split": "train",
"index": 28966,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest four-digit number which is a multiple of 17? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9996"
} | {
"split": "train",
"index": 28967,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A tetrahedron has a triangular base with sides all equal to 2, and each of its three lateral faces are squares. A smaller tetrahedron is placed within the larger one so that its base is parallel to the base of the larger tetrahedron and its vertices touch the midpoints of the l... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{12}"
} | {
"split": "train",
"index": 28968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\(5^p + 5^3 = 140\\), \\(3^r + 21 = 48\\), and \\(4^s + 4^3 = 280\\), find the product of \\(p\\), \\(r\\), and \\(s\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 28969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A buyer took goods worth 10 rubles from a seller and gave 25 rubles. The seller did not have change, so he exchanged money with a neighbor. After they finished the transaction and the buyer left, the neighbor discovered that the 25 rubles were counterfeit. The seller returned 2... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 28970,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of solutions to the equation\n\\[\\tan (5 \\pi \\cos \\theta) = \\cot (5 \\pi \\sin \\theta)\\]where $\\theta \\in (0, 2 \\pi).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 28971,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "One dimension of a cube is increased by $2$, another is decreased by $2$, and the third is increased by $3$. The volume of the new rectangular solid is $7$ less than the volume of the cube. Find the original volume of the cube. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 28972,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $BCD$, $\\angle C = 90^\\circ$, $CD = 3$, and $BD = \\sqrt{13}$. What is $\\tan B$? 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": 28973,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Kyle knows that $4 = 2^{5r+1}$. What is the value of $r$? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 28974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f: \\mathbb{N} \\rightarrow \\mathbb{N}$ be a strictly increasing function such that $f(1)=1$ and $f(2n)f(2n+1)=9f(n)^{2}+3f(n)$ for all $n \\in \\mathbb{N}$. Compute $f(137)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2215"
} | {
"split": "train",
"index": 28975,
"solution": "Plugging in $n=1$ gives $f(2)f(3)=12$, therefore $(f(2), f(3))=(2,6)$ or $(3,4)$. However, the former implies $$f(4)f(5) \\geq (6+1)(6+2)>42=9 \\cdot 2^{2}+3 \\cdot 2$$ which is impossible; therefore $f(2)=3$ and $f(3)=4$. We now show by induction with step size 2 ... |
deepscaler | [
{
"role": "user",
"content": "There are five concentric circles \\(\\Gamma_{0}, \\Gamma_{1}, \\Gamma_{2}, \\Gamma_{3}, \\Gamma_{4}\\) whose radii form a geometric sequence with a common ratio \\(q\\). Find the maximum value of \\(q\\) such that a closed polyline \\(A_{0} A_{1} A_{2} A_{3} A_{4}\\) can be dr... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5} + 1}{2}"
} | {
"split": "train",
"index": 28976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\tau (n)$ denote the number of positive integer divisors of $n$ (including $1$ and $n$). Find the sum of the six least positive integers $n$ that are solutions to $\\tau (n) + \\tau (n+1) = 7$.\n Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "540"
} | {
"split": "train",
"index": 28977,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of $x$ such that $\\sqrt{x+ 7} = 9$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "74"
} | {
"split": "train",
"index": 28978,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are six empty slots corresponding to the digits of a six-digit number. Claire and William take turns rolling a standard six-sided die, with Claire going first. They alternate with each roll until they have each rolled three times. After a player rolls, they place the numb... | math | {
"style": "rule",
"ground_truth": "\\frac{43}{192}"
} | {
"split": "train",
"index": 28979,
"solution": "A number being divisible by 6 is equivalent to the following two conditions: - the sum of the digits is divisible by 3 - the last digit is even Regardless of Claire and William's strategies, the first condition is satisfied with probability $\\frac{1}{3}$. So Clair... |
deepscaler | [
{
"role": "user",
"content": "If $m>0$ and the points $(m,3)$ and $(1,m)$ lie on a line with slope $m$, then $m=$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 28980,
"solution": "1. **Identify the slope formula**: Given two points $(x_1, y_1)$ and $(x_2, y_2)$, the slope $m$ of the line passing through these points is given by:\n \\[\n m = \\frac{y_2 - y_1}{x_2 - x_1}\n \\]\n For the points $(m, 3)$ and $(1, m)$, substituting into t... |
deepscaler | [
{
"role": "user",
"content": "If $|x-2|=p$, where $x<2$, then what is $x-p$ in terms of $p$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2-2p"
} | {
"split": "train",
"index": 28981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a round glass, the axial cross-section of which is the graph of the function \\( y = x^4 \\), a cherry (a sphere with radius \\( r \\)) is placed. For which maximum \\( r \\) will the sphere touch the bottom point of the glass? (In other words, what is the maximum radius \\(... | math | {
"style": "rule",
"ground_truth": "\\frac{3 \\cdot 2^{1/3}}{4}"
} | {
"split": "train",
"index": 28982,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Ponde family's Powerjet pumps 420 gallons of water per hour. At this rate, how many gallons of water will it pump in 45 minutes? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "315"
} | {
"split": "train",
"index": 28983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and it is given that $\\sqrt{3}b\\cos A=a\\cos B$.\n\n$(1)$ Find the angle $A$;\n\n$(2)$ If $a= \\sqrt{2}$ and $\\frac{c}{a}= \\frac{\\sin A}{\\sin B}$, find the p... | math | {
"style": "rule",
"ground_truth": "3 \\sqrt{2}"
} | {
"split": "train",
"index": 28984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\{a_{n}\\}$ be a sequence with the sum of its first $n$ terms denoted as $S_{n}$, and ${S}_{n}=2{a}_{n}-{2}^{n+1}$. The sequence $\\{b_{n}\\}$ satisfies ${b}_{n}=log_{2}\\frac{{a}_{n}}{n+1}$, where $n\\in N^{*}$. Find the maximum real number $m$ such that the inequality $... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 28985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the product of $10101_2$ and $101_2$. Express your answer in base $2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1101001_2"
} | {
"split": "train",
"index": 28986,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( n \\) be an integer between 1 and 1990, and let \\( x^2 + x - 3n \\) be factored into the product of two linear factors with integer coefficients. Determine the number of integers \\( n \\) that satisfy this condition. Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 28987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|= \\sqrt {2}$, and $\\overrightarrow{a}\\perp (\\overrightarrow{a}- \\overrightarrow{b})$, then the angle between vector $\\overrightarrow{a}$ and vector $\\ov... | math | {
"style": "rule",
"ground_truth": "\\dfrac {\\pi}{4}"
} | {
"split": "train",
"index": 28988,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all monic polynomials $f$ with integer coefficients satisfying the following condition: there exists a positive integer $N$ such that $p$ divides $2(f(p)!)+1$ for every prime $p>N$ for which $f(p)$ is a positive integer. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "x - 3"
} | {
"split": "train",
"index": 28989,
"solution": "\nThe problem requires finding all monic polynomials \\( f \\) with integer coefficients such that there exists a positive integer \\( N \\) where, for every prime \\( p > N \\) for which \\( f(p) \\) is a positive integer, \\( p \\mid 2(f(p)!)+1 \\).\n\nGiven:\n- ... |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a convex quadrilateral with $AB = CD = 10$, $BC = 14$, and $AD = 2\\sqrt{65}$. Assume that the diagonals of $ABCD$ intersect at point $P$, and that the sum of the areas of triangles $APB$ and $CPD$ equals the sum of the areas of triangles $BPC$ and $APD$. Find the... | math | {
"style": "rule",
"ground_truth": "112"
} | {
"split": "train",
"index": 28990,
"solution": "Either $PA=PC$ or $PD=PB$. Let $PD=PB=s$. Applying Stewart's Theorem on $\\triangle ABD$ and $\\triangle BCD$, dividing by $2s$ and rearranging, \\[\\tag{1}CP^2+s^2=148\\] \\[\\tag{2}AP^2+s^2=180\\] Applying Stewart on $\\triangle CAB$ and $\\triangle CAD$, \\[\\ta... |
deepscaler | [
{
"role": "user",
"content": "Let $a, b \\in \\mathbb{R}^+$, and $a+b=1$. Find the minimum value of $\\sqrt{a^2+1} + \\sqrt{b^2+4}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{10}"
} | {
"split": "train",
"index": 28991,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The school organized a picnic with several attendees. The school prepared many empty plates. Each attendee who arrives will count the empty plates and then take one plate for food (no one can take more than one plate). The first attendee will count all the empty plates, the sec... | math | {
"style": "rule",
"ground_truth": "1006"
} | {
"split": "train",
"index": 28992,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A component is made up of 3 identical electronic components in parallel. The component works normally if at least one of the electronic components works normally. It is known that the service life $\\xi$ (in years) of this type of electronic component follows a normal distribut... | math | {
"style": "rule",
"ground_truth": "0.488"
} | {
"split": "train",
"index": 28993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the square one of whose diagonals has endpoints $(1/10,7/10)$ and $(-1/10,-7/10)$. A point $v=(x,y)$ is chosen uniformly at random over all pairs of real numbers $x$ and $y$ such that $0 \\le x \\le 2012$ and $0\\le y\\le 2012$. Let $T(v)$ be a translated copy of $S$... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{25}"
} | {
"split": "train",
"index": 28994,
"solution": "1. **Identify the Length of the Diagonal of Square $S$:**\n The endpoints of one diagonal of square $S$ are given as $(\\frac{1}{10}, \\frac{7}{10})$ and $(-\\frac{1}{10}, -\\frac{7}{10})$. The length of the diagonal can be calculated using the distance formula:\... |
deepscaler | [
{
"role": "user",
"content": "Given the function \\( f(x) \\) such that \\( f(x+4) + f(x-4) = f(x) \\) for all \\( x \\in \\mathbb{R} \\), determine the common minimum period of such functions. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 28995,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The set $S=\\{1,2,3, \\ldots, 49,50\\}$ contains the first 50 positive integers. After the multiples of 2 and the multiples of 3 are removed, how many integers remain in the set $S$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 28996,
"solution": "The set $S$ contains 25 multiples of 2 (that is, even numbers). When these are removed, the set $S$ is left with only the odd integers from 1 to 49. At this point, there are $50-25=25$ integers in $S$. We still need to remove the multiples of 3 from $S$. Since $S$ ... |
deepscaler | [
{
"role": "user",
"content": "Jenna is at a fair with four friends. They all want to ride the roller coaster, but only three people can fit in a car. How many different groups of three can the five of them make? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 28997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $A(11, 9)$ and $B(2, -3)$ are vertices of $\triangle ABC$ with $AB=AC$. The altitude from $A$ meets the opposite side at $D(-1, 3)$. What are the coordinates of point $C$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left( -4, 9 \\right)"
} | {
"split": "train",
"index": 28998,
"solution": "1. **Identify the properties of the triangle**: Given that $\\triangle ABC$ is isosceles with $AB = AC$, and the altitude from $A$ meets the opposite side at $D$.\n\n2. **Use the midpoint property**: Since $D$ is the point where the altitude from $A$ meets $BC$, an... |
deepscaler | [
{
"role": "user",
"content": "How many three-digit whole numbers contain at least one 6 or at least one 8? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "452"
} | {
"split": "train",
"index": 28999,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nHow many employees of the enterprise can be insured by the given insurance company if the enterprise is willing to pay an insurance premium of 5,000,000 rubles? \n\nThe cost of service for one person in the clinic (without hospitalization), with which the insurance company ha... | math | {
"style": "rule",
"ground_truth": "121"
} | {
"split": "train",
"index": 29000,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph of the function $y=f(x)$ is shown below. For all $x > 4$, it is true that $f(x) > 0.4$. If $f(x) = \\frac{x^2}{Ax^2 + Bx + C}$, where $A,B,$ and $C$ are integers, then find $A+B+C$. [asy]\nimport graph; size(10.9cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); ... | math | {
"style": "rule",
"ground_truth": "-12"
} | {
"split": "train",
"index": 29001,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two cylindrical cans have the same volume. The height of one can is triple the height of the other. If the radius of the narrower can is 12 units, how many units are in the length of the radius of the wider can? Express your answer in simplest radical form. Let's think step by ... | math | {
"style": "rule",
"ground_truth": "12\\sqrt{3}"
} | {
"split": "train",
"index": 29002,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area of the region bounded by the graph of $r = \\sec \\theta,$ the graph of $r = \\csc \\theta,$ the $x$-axis, and the $y$-axis. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 29003,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three squares, $ABCD$, $EFGH$, and $GHIJ$, each have side length $s$. Point $C$ is located at the midpoint of side $HG$, and point $D$ is located at the midpoint of side $EF$. The line segment $AJ$ intersects the line segment $GH$ at point $X$. Determine the ratio of the area o... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 29004,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A box contains 4 labels marked with the numbers $1$, $2$, $3$, and $4$. Two labels are randomly selected according to the following conditions. Find the probability that the numbers on the two labels are consecutive integers:\n1. The selection is made without replacement;\n2. T... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{16}"
} | {
"split": "train",
"index": 29005,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $α$ is an angle in the first quadrant, it satisfies $\\sin α - \\cos α = \\frac{\\sqrt{10}}{5}$. Find $\\cos 2α$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "- \\frac{4}{5}"
} | {
"split": "train",
"index": 29006,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If for any real number $x$, the equation $(1-2x)^{10} = a_0 + a_1x + a_2x^2 + a_3x^3 + \\ldots + a_{10}x^{10}$ holds, then the value of $(a_0 + a_1) + (a_0 + a_2) + (a_0 + a_3) + \\ldots + (a_0 + a_{10})$ is _____. (Answer with a number) Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 29007,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find \\( k \\) such that for all real numbers \\( a, b, \\) and \\( c \\):\n\n\\[ \n(a+b)(b+c)(c+a) = (a+b+c)(ab + bc + ca) + k \\, abc \n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 29008,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distance from the intersection point of the diameter of a circle with a chord of length 18 cm to the center of the circle is 7 cm. This point divides the chord in the ratio 2:1. Find the radius of the circle.\n\n$$\nAB = 18, EO = 7, AE = 2 BE, R = ?\n$$ Let's think step by ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 29009,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number $0.428125$ can be written as a fraction $\\frac{a}{b}$ for positive integers $a$ and $b$. When this fraction is in simplest terms, what is $a+b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "457"
} | {
"split": "train",
"index": 29010,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( x, y, z \\in [0, 1] \\). The maximum value of \\( M = \\sqrt{|x-y|} + \\sqrt{|y-z|} + \\sqrt{|z-x|} \\) is ______ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} + 1"
} | {
"split": "train",
"index": 29011,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and it is given that $a\\sin C= \\sqrt{3}c\\cos A$.\n\n$(1)$ Find the measure of angle $A$;\n\n$(2)$ If $a= \\sqrt{13}$ and $c=3$, find the area of triangle $ABC$. Let's think step by ... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 29012,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be a positive integer and $d$ be a digit such that the value of the numeral $32d$ in base $n$ equals $263$, and the value of the numeral $324$ in base $n$ equals the value of the numeral $11d1$ in base six. What is $n + d$? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 29013,
"solution": "1. **Convert $\\underline{32d}$ in base $n$ to decimal:** \n The numeral $\\underline{32d}$ in base $n$ can be expressed in decimal as:\n \\[\n 3n^2 + 2n + d\n \\]\n Given that this equals 263, we have the equation:\n \\[\n 3n^2 + 2n + d = 263\n \\... |
deepscaler | [
{
"role": "user",
"content": "A rectangular grid is given. Let's call two cells neighboring if they share a common side. Count the number of cells that have exactly four neighboring cells. There are 23 such cells. How many cells have three neighboring cells? Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 29014,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that Asha's study times were 40, 60, 50, 70, 30, 55, 45 minutes each day of the week and Sasha's study times were 50, 70, 40, 100, 10, 55, 0 minutes each day, find the average number of additional minutes per day Sasha studied compared to Asha. Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "-3.57"
} | {
"split": "train",
"index": 29015,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that a hyperbola $mx^{2}+ny^{2}=1$ has a focus that is the same as the focus of the parabola $y=\\frac{1}{8}{x^2}$ and an eccentricity of $2$, calculate the distance from the focus of the parabola to one of the asymptotes of the hyperbola. Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 29016,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A stacking of circles in the plane consists of a base, or some number of unit circles centered on the $x$-axis in a row without overlap or gaps, and circles above the $x$-axis that must be tangent to two circles below them (so that if the ends of the base were secured and gravi... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 29017,
"solution": "$C(4)=14$."
} |
deepscaler | [
{
"role": "user",
"content": "Is there a triangle with $12 \\, cm^2$ area and $12$ cm perimeter? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\text{No}"
} | {
"split": "train",
"index": 29018,
"solution": "\nTo determine whether a triangle can exist with a given area of \\( 12 \\, \\text{cm}^2 \\) and a perimeter of \\( 12 \\, \\text{cm} \\), we employ the following steps:\n\nThe area \\( A \\) of a triangle with sides \\( a, b, c \\) can be calculated using Heron's ... |
deepscaler | [
{
"role": "user",
"content": "What is the average of five-digit palindromic numbers? (A whole number is a palindrome if it reads the same backward as forward.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "55000"
} | {
"split": "train",
"index": 29019,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all positive integers $n \\leq 2015$ that can be expressed in the form $\\left\\lceil\\frac{x}{2}\\right\\rceil+y+x y$, where $x$ and $y$ are positive integers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2029906"
} | {
"split": "train",
"index": 29020,
"solution": "Lemma: $n$ is expressible as $\\left\\lceil\\frac{x}{2}\\right\\rceil+y+x y$ iff $2 n+1$ is not a Fermat Prime. Proof: Suppose $n$ is expressible. If $x=2 k$, then $2 n+1=(2 k+1)(2 y+1)$, and if $x=2 k-1$, then $n=k(2 y+1)$. Thus, if $2 n+1$ isn't prime, we can fac... |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathcal{T}$ be the set of ordered triples $(x,y,z)$ of nonnegative real numbers that lie in the plane $x+y+z=1.$ Let us say that $(x,y,z)$ supports $(a,b,c)$ when exactly two of the following are true: $x\\ge a, y\\ge b, z\\ge c.$ Let $\\mathcal{S}$ consist of those trip... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{18}"
} | {
"split": "train",
"index": 29021,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many 7-digit numbers divisible by 9 are there, where the second to last digit is 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100000"
} | {
"split": "train",
"index": 29022,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\\( x_{1} = 2001 \\). When \\( n > 1, x_{n} = \\frac{n}{x_{n-1}} \\). Given that \\( x_{1} x_{2} x_{3} \\ldots x_{10} = a \\), find the value of \\( a \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3840"
} | {
"split": "train",
"index": 29023,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven dwarfs stood at the corners of their garden, each at one corner, and stretched a rope around the entire garden. Snow White started from Doc and walked along the rope. First, she walked four meters to the east where she met Prof. From there, she continued two meters north ... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 29024,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x)=x^{3}+ax^{2}+bx+a^{2}$, the extreme value at $x=1$ is $10$. Find the value of $a+b$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 29025,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A stick 5 cm long, a stick 9 cm long, and a third stick $n$ cm long form a triangle. What is the sum of all possible whole number values of $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 29026,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For $-1<s<1$, let $T(s)$ denote the sum of the geometric series \\[20 + 20s + 20s^2 + 20s^3+\\cdots .\\] Let $b$ between $-1$ and $1$ satisfy $T(b)T(-b) = 4800$. Find $T(b) + T(-b)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "480"
} | {
"split": "train",
"index": 29027,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the following value when expressed as a common fraction: $$\\frac{1}{3^{1}}+\\frac{1}{3^{2}}+\\frac{1}{3^{3}}+\\frac{1}{3^{4}}+\\frac{1}{3^{5}}+\\frac{1}{3^{6}}?$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{364}{729}"
} | {
"split": "train",
"index": 29028,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and it satisfies $(2a-c)\\cos B = b\\cos C$; \n(1) Find the magnitude of angle $B$; \n(2) Let $\\overrightarrow{m}=(\\sin A, \\cos 2A), \\overrightarrow{n}=(4k,1... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 29029,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many possible distinct arrangements are there of the letters in the word SUCCESS? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "420"
} | {
"split": "train",
"index": 29030,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An electrician was called to repair a garland of four light bulbs connected in series, one of which has burned out. It takes 10 seconds to unscrew any bulb from the garland and 10 seconds to screw it back in. The time spent on other actions is negligible. What is the minimum ti... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 29031,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\frac{x^2-bx}{ax-c}=\\frac{m-1}{m+1}$ has roots which are numerically equal but of opposite signs, the value of $m$ must be: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{a-b}{a+b}"
} | {
"split": "train",
"index": 29032,
"solution": "1. **Cross-multiplying the given equation:**\n \\[\n \\frac{x^2 - bx}{ax - c} = \\frac{m-1}{m+1}\n \\]\n Cross-multiplying gives:\n \\[\n (m+1)(x^2 - bx) = (m-1)(ax - c)\n \\]\n Expanding both sides:\n \\[\n (m+1)x^2 - (m+1)bx = (m-1)ax - (m-1)c... |
deepscaler | [
{
"role": "user",
"content": "\nIn the parallelepiped $ABCD A_1B_1C_1D_1$, the face $ABCD$ is a square with side length 5, the edge $AA_1$ is also equal to 5, and this edge forms angles of $60^\\circ$ with the edges $AB$ and $AD$. Find the length of the diagonal $BD_1$. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "5\\sqrt{3}"
} | {
"split": "train",
"index": 29033,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $a$ is three times $b$, $b$ is twice $c$, and $c$ is four times $d$, what is the value of $\\frac{a\\cdot c}{b\\cdot d}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 29034,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The military kitchen needs 1000 jin of rice and 200 jin of millet for dinner. Upon arriving at the rice store, the quartermaster finds a promotion: \"Rice is 1 yuan per jin, with 1 jin of millet given for every 10 jin purchased (fractions of 10 jins do not count); Millet is 2 y... | math | {
"style": "rule",
"ground_truth": "1200"
} | {
"split": "train",
"index": 29035,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the \\(1005\\) roots of the polynomial \\((x-1)^{1005} + 2(x-2)^{1004} + 3(x-3)^{1003} + \\cdots + 1004(x-1004)^2 + 1005(x-1005)\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1003"
} | {
"split": "train",
"index": 29036,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers in the sequence $101$, $104$, $109$, $116$,$\\ldots$ are of the form $a_n=100+n^2$, where $n=1,2,3,\\ldots$ For each $n$, let $d_n$ be the greatest common divisor of $a_n$ and $a_{n+1}$. Find the maximum value of $d_n$ as $n$ ranges through the positive integers. Le... | math | {
"style": "rule",
"ground_truth": "401"
} | {
"split": "train",
"index": 29037,
"solution": "We know that $a_n = 100+n^2$ and $a_{n+1} = 100+(n+1)^2 = 100+ n^2+2n+1$. Since we want to find the GCD of $a_n$ and $a_{n+1}$, we can use the Euclidean algorithm:\n$a_{n+1}-a_n = 2n+1$\n Now, the question is to find the GCD of $2n+1$ and $100+n^2$. We subtract $2n... |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the sum of all positive integers $n$ such that $n^2+12n-2007$ is a perfect square. Find the remainder when $S$ is divided by $1000.$\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "464"
} | {
"split": "train",
"index": 29038,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the following value expressed as a common fraction: $$\\frac{1}{4^{1}}+\\frac{1}{4^{2}}+\\frac{1}{4^{3}}+\\frac{1}{4^{4}}+\\frac{1}{4^{5}}+\\frac{1}{4^{6}}+\\frac{1}{4^{7}}.$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{16383}{49152}"
} | {
"split": "train",
"index": 29039,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the function $f(x)$ is an odd function defined on $\\mathbb{R}$, and $f(x) = \\begin{cases} \\log_{2}(x+1), & x \\geqslant 0 \\\\ g(x), & x < 0 \\end{cases}$, find $g[f(-7)]$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 29040,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If\n\\[\\tan x = \\frac{2ab}{a^2 - b^2},\\]where $a > b > 0$ and $0^\\circ < x < 90^\\circ,$ then find $\\sin x$ in terms of $a$ and $b.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2ab}{a^2 + b^2}"
} | {
"split": "train",
"index": 29041,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Subtract $123.45$ from $567.89.$ Express the result as a decimal to the nearest hundredth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "444.44"
} | {
"split": "train",
"index": 29042,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the decimal function denoted by $\\{ x \\} = x - \\lfloor x \\rfloor$ which represents the decimal part of a number $x$. Find the sum of the five smallest positive solutions to the equation $\\{x\\} = \\frac{1}{\\lfloor x \\rfloor}$. Express your answer as a mixed numb... | math | {
"style": "rule",
"ground_truth": "21\\frac{9}{20}"
} | {
"split": "train",
"index": 29043,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\frac {35x - 29}{x^2 - 3x + 2} = \\frac {N_1}{x - 1} + \\frac {N_2}{x - 2}$ be an identity in $x$. The numerical value of $N_1N_2$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-246"
} | {
"split": "train",
"index": 29044,
"solution": "1. **Expression Setup**: Given the identity\n \\[\n \\frac {35x - 29}{x^2 - 3x + 2} = \\frac {N_1}{x - 1} + \\frac {N_2}{x - 2}\n \\]\n we start by expressing the right-hand side over a common denominator:\n \\[\n \\frac {N_1}{x - 1} + \\frac {N_2}{x - ... |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to color the vertices of a triangle red, green, blue, or yellow such that no two vertices have the same color? Rotations and reflections are considered distinct. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 29045,
"solution": "There are 4 ways to color the first vertex, then 3 ways to color the second vertex to be distinct from the first, and finally 2 ways to color the third vertex to be distinct from the earlier two vertices. Multiplying gives 24 ways."
} |
deepscaler | [
{
"role": "user",
"content": "Let \\((a,b,c,d)\\) be an ordered quadruple of integers, each in the set \\(\\{-2, -1, 0, 1, 2\\}\\). Determine the count of such quadruples for which \\(a\\cdot d - b\\cdot c\\) is divisible by 4. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 29046,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A clock currently shows the time $10:10$ . The obtuse angle between the hands measures $x$ degrees. What is the next time that the angle between the hands will be $x$ degrees? Round your answer to the nearest minute. Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "11:15"
} | {
"split": "train",
"index": 29047,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A mathematical organization is producing a set of commemorative license plates. Each plate contains a sequence of five characters chosen from the four letters in AIME and the four digits in 2007. No character may appear in a sequence more times than it appears among the four le... | math | {
"style": "rule",
"ground_truth": "372"
} | {
"split": "train",
"index": 29048,
"solution": ""
} |
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