source stringclasses 10 values | domain listlengths 1 3 | llama8b_solve_rate float64 0 0.09 ⌀ | data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|---|---|
aops_forum | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A quadrilateral $ABCD$ has a right angle ... | math | {
"ground_truth": "769",
"style": "rule"
} | {
"answer": "769",
"index": 18600,
"question": "A quadrilateral $ABCD$ has a right angle at $\\angle ABC$ and satisfies $AB = 12$ , $BC = 9$ , $CD = 20$ , and $DA = 25$ . Determine $BD^2$ .\n.\n",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the rectangular coordinate system xOy, t... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 18601,
"question": "In the rectangular coordinate system xOy, the parametric equation of line l is $$\\begin{cases} x=1+t \\\\ y=t-3 \\end{cases}$$ (where t is the parameter). Establish a polar coordinate system with the origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of curve C is $$ρ= \\frac{2cosθ}{sin^{2}θ}$$. If line l intersects curve C at points A and B, find the area of triangle AOB.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $1 < m < 4$, $F\\_1$ and $F\\_2$... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18602,
"question": "Given that $1 < m < 4$, $F\\_1$ and $F\\_2$ are the left and right foci of the curve $C: \\frac{x^2}{4} + \\frac{y^2}{4-m} = 1$, and point $P$ is the intersection point of curve $C$ and curve $E: x^2 - \\frac{y^2}{m-1} = 1$ in the first quadrant. Line $l$ is the tangent line to curve $C$ at point $P$. If the incenter of triangle $F\\_1 P F\\_2$ is point $M$, and line $F\\_1 M$ intersects line $l$ at point $N$, then calculate the sum of the x-coordinates of points $M$ and $N$. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find a two-digit number such that the cube ... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 18603,
"question": "Find a two-digit number such that the cube of the sum of its digits is equal to the square of the number itself.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A jeweler can get an alloy that is $40\\%$... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"answer": "240",
"index": 18604,
"question": "A jeweler can get an alloy that is $40\\%$ gold for $200$ dollars per ounce, an alloy that is $60\\%$ gold for $300$ dollar per ounce, and an alloy that is $90\\%$ gold for $400$ dollars per ounce. The jeweler will purchase some of these gold alloy products, melt them down, and combine them to get an alloy that is $50\\%$ gold. Find the minimum number of dollars the jeweler will need to spend for each ounce of the alloy she makes.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Set Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sets \\( A = \\{2, 0, 1, 7\\} \\)... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18605,
"question": "Given the sets \\( A = \\{2, 0, 1, 7\\} \\) and \\( B = \\{ x \\mid x^2 - 2 \\in A, \\, x - 2 \\notin A \\} \\), calculate the product of all elements in set \\( B \\). Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are two concentric circles, with six ... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 18606,
"question": "There are two concentric circles, with six non-overlapping points on the circumference of the outer circle and three non-overlapping points on the circumference of the inner circle. Determine the minimum number of straight lines that can be formed using these nine points. Express your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The ancient Chinese calendrical system, \"H... | math | {
"ground_truth": "1950",
"style": "rule"
} | {
"answer": "1950",
"index": 18607,
"question": "The ancient Chinese calendrical system, \"Heavenly Stems and Earthly Branches\", also known as \"Ganzhi\", is used for years' notation. The ten Heavenly Stems are Jia (甲), Yi (乙), Bing (丙), Ding (丁), Wu (戊), Ji (已), Geng (庚), Xin (辛), Ren (壬), and Gui (癸). The twelve Earthly Branches are Zi (子), Chou (丑), Yin (寅), Mao (卯), Chen (辰), Si (巳), Wu (午), Wei (未), You (酉), Xu (戌), and Hai (亥). The combination of both Heavenly Stems and Earthly Branches constitutes the cycle by which years are denoted. If the year 2010 corresponds to the Geng-Yin year, calculate the previous Geng-Yin year. Express your answer as a year in the format YYYY.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A right triangle \\(ABC\\) is divided by th... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18608,
"question": "A right triangle \\(ABC\\) is divided by the altitude \\(CD\\), drawn to the hypotenuse, into two triangles: \\(BCD\\) and \\(ACD\\). The radii of the circles inscribed in these triangles are 4 and 3, respectively. Find the radius of the circle inscribed in triangle \\(ABC\\).",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a prime number p and an integer n, le... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 18609,
"question": "Given a prime number p and an integer n, let r be the product of the integers from 1 to n, inclusive. Find the greatest integer k for which p^k is a factor of r, where n is a much larger number.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The Gauss Candy Company has 8362 lollipops ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 18610,
"question": "The Gauss Candy Company has 8362 lollipops to package. They place exactly 12 lollipops in each package. Calculate the number of lollipops that remain after the maximum possible number of packages are filled. Provide your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n During the Tree Planting Festival, students... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 18611,
"question": "During the Tree Planting Festival, students from a class are planting trees. There are three different types of saplings, labeled as A, B, and C, available in the nursery, with an ample supply of each type. They need to plant 5 saplings in a row in 5 pits, with the condition that the same type of sapling cannot be adjacent, and only type A saplings can be planted in the first and the fifth pits. Calculate the total number of planting methods available.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Angles"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the diagram, \\(ABCD\\) and \\(DEFG\\) a... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"answer": "140",
"index": 18612,
"question": "In the diagram, \\(ABCD\\) and \\(DEFG\\) are squares with equal side lengths, and \\(\\angle DCE = 70^\\circ\\). Find the value of \\(y\\), the measure of the angle formed by the extension of segments \\(DC\\) and \\(DE\\). Express your answer in degrees as a whole number.",
"split": "train"
} |
math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Compute the sum of all possible values for ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 18613,
"question": "Compute the sum of all possible values for $x,$ where $(x, y)$ is a solution to the system of equations \\[\\begin{aligned} x &= y^2 - 6y + 5, \\\\ y &= |x|. \\end{aligned}\\]",
"split": "train"
} |
olympiads | [
"Mathematics -> Calculus -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Determine the smallest possible value of th... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18614,
"question": "Determine the smallest possible value of the expression\n\n$$\n4 + x^{2} y^{4} + x^{4} y^{2} - 3 x^{2} y^{2}\n$$\n\nfor real number pairs \\((x, y)\\).",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Mrs. Evans gave a test to her freshmen econ... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 18615,
"question": "Mrs. Evans gave a test to her freshmen economics class, which has 30 students enrolled. On this test, 25 of them answered question 1 correctly, 22 answered question 2 correctly, and 18 answered question 3 correctly. If 5 students did not take the test, how many students answered all three questions correctly?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the largest integer \\( A \\) such tha... | math | {
"ground_truth": "505",
"style": "rule"
} | {
"answer": "505",
"index": 18616,
"question": "Find the largest integer \\( A \\) such that for any permutation of natural numbers from 1 to 100, there always exists a sequence of 10 consecutive numbers whose sum is greater than or equal to \\( A \\).",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Solve in integers the equation: \\( 5x^{2} ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18617,
"question": "Solve in integers the equation: \\( 5x^{2} - 2xy + 2y^{2} - 2x - 2y = 3 \\). In the answer, write the sum of all solutions \\((x, y)\\).",
"split": "train"
} |
math | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the sum of all the positive two-dig... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"answer": "72",
"index": 18618,
"question": "What is the sum of all the positive two-digit integers divisible by both the sum and product of their digits?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Triangle $ABC$ is acute. Equilateral tria... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"answer": "26",
"index": 18619,
"question": "Triangle $ABC$ is acute. Equilateral triangles $ABC',AB'C,A'BC$ are constructed externally to $ABC$ . Let $BB'$ and $CC'$ intersect at $F$ . Let $CC'$ intersect $AB$ at $C_1$ and $AA'$ intersect $BC$ at $A_1$ , and let $A_1C_1$ intersect $AC$ at $D$ . If $A'F=23$ , $CF=13$ , and $DF=24$ , find $BD$ .",
"split": "train"
} |
olympiads | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the minimum possible value of \\((x^2 ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 18620,
"question": "Find the minimum possible value of \\((x^2 + 6x + 2)^2\\) over all real numbers \\( x \\).",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Triangulations"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the diagram, \\( P Q = 19 \\), \\( Q R =... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18621,
"question": "In the diagram, \\( P Q = 19 \\), \\( Q R = 18 \\), and \\( P R = 17 \\). Point \\( S \\) is on \\( P Q \\), point \\( T \\) is on \\( P R \\), and point \\( U \\) is on \\( S T \\) such that \\( Q S = S U \\) and \\( U T = T R \\). Find the perimeter of \\(\\triangle P S T\\). Express your answer as a whole number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Assuming we have four male students and thr... | math | {
"ground_truth": "3600",
"style": "rule"
} | {
"answer": "3600",
"index": 18622,
"question": "Assuming we have four male students and three female students who are to stand in a row for a photo, calculate the number of arrangements where exactly two female students are standing next to each other.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Calculus -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the Cartesian coordinate plane $(xOy)$, ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 18623,
"question": "In the Cartesian coordinate plane $(xOy)$, a point $P(a, b)$ lies in the first quadrant on the line $x + 2y - 1 = 0$. Find the minimum value of $\\frac{4}{a + b} + \\frac{1}{b}$.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a four-level symbol pyramid, the symbols... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 18624,
"question": "In a four-level symbol pyramid, the symbols in the two bottom cells determine the symbol above them. If the symbols are the same, the cell above will be \"+\", otherwise, it will be \"-\". How many possible ways are there to fill the bottom row of four cells such that the top of the pyramid results in a \"+\"? Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the inequality about $x$, $\\frac {1}... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18625,
"question": "Given the inequality about $x$, $\\frac {1}{a}x^{2}+bx+c < 0(ab > 1)$, its solution set is an empty set. Find the minimum value of $T= \\frac {1}{2(ab-1)}+ \\frac {a(b+2c)}{ab-1}$. Express your answer as a single number.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the line $3x-4y+5=0$ intersects the c... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 18626,
"question": "Given the line $3x-4y+5=0$ intersects the circle $x^{2}+y^{2}=r^{2}$ ($r > 0$) at points $A$ and $B$, and $\\angle AOB=120^{\\circ}$ ($O$ is the origin), calculate the radius $r$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( R \\) be a semicircle with diameter... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 18627,
"question": "Let \\( R \\) be a semicircle with diameter \\( XY \\). A trapezoid \\( ABCD \\) in which \\( AB \\) is parallel to \\( CD \\) is circumscribed about \\( R \\) such that \\( AB \\) contains \\( XY \\). If \\( AD = 4 \\), \\( CD = 5 \\), and \\( BC = 6 \\), determine \\( AB \\).",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In triangle $ABC$, the median from vertex $... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18628,
"question": "In triangle $ABC$, the median from vertex $A$ is perpendicular to the angle bisector of angle $B$, and the median from vertex $B$ is perpendicular to the angle bisector of angle $A$. It is known that side $AB = 1$. Find the perimeter of triangle $ABC$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a small village in Sri Lanka, 5% of the ... | math | {
"ground_truth": "5716",
"style": "rule"
} | {
"answer": "5716",
"index": 18629,
"question": "In a small village in Sri Lanka, 5% of the population left the village seeking better job opportunities. After a few weeks, a calamity struck and a tragic bombardment led to a loss of 8% of the population. This was followed by a mass departure, where an additional 15% of the remaining residents left out of fear. Within those who courageously stayed back, unfortunately 10% were seriously injured during the reconstruction activities and could not be considered as active members of the population. Another 12% of the still-existing population left due to insufficient resources. Now, the only active population is reduced to 3553. How many people were there in the village at the very beginning?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find \\( g(2022) \\) if for any real number... | math | {
"ground_truth": "4086462",
"style": "rule"
} | {
"answer": "4086462",
"index": 18630,
"question": "Find \\( g(2022) \\) if for any real numbers \\( x, y \\) the following equality holds:\n\n\\[ g(x-y) = g(x) + g(y) - 2021(x+y) \\]",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A great-grandfather banker left an inherita... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18631,
"question": "A great-grandfather banker left an inheritance to his newborn great-grandson. According to the bank agreement, the amount in the great-grandson's account increases. Each year, on the day after his birthday, the current amount increases by one million rubles more than the previous year. Thus, if the initial amount was zero rubles, after one year it will be +1 million rubles; after 2 years, $1+2$ million rubles; after 3 years, $1+2+3$; and so on. According to the agreement, the process will stop, and the great-grandson will receive the money when the amount in the account is a three-digit number consisting of three identical digits.\n\nHow old will the great-grandson be when the conditions of the agreement are fulfilled?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics",
"Mathematics -> Number Theory -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \nGiven the set \\( A = \\{1, 2, 3, \\ldots... | math | {
"ground_truth": "502",
"style": "rule"
} | {
"answer": "502",
"index": 18632,
"question": "\nGiven the set \\( A = \\{1, 2, 3, \\ldots, 1002\\} \\), Petya and Vasya play a game. Petya names a number \\( n \\), and Vasya then selects a subset of \\( A \\) consisting of \\( n \\) elements. Vasya wins if there are no two coprime numbers in the subset he selects; otherwise, Petya wins. What is the minimum \\( n \\) that Petya must name to guarantee a win?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given vectors $\\overrightarrow{a}$ and $\\... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 18633,
"question": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ that satisfy $|\\overrightarrow{a}| = 2$, $|\\overrightarrow{b}| = 3$, and $|2\\overrightarrow{a} - \\overrightarrow{b}| = \\sqrt{13}$, find the projection of vector $\\overrightarrow{a}$ onto vector $\\overrightarrow{b}$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n one day , raviraj left home and cycled 20 k... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 18634,
"question": "one day , raviraj left home and cycled 20 km southwards , turned right and cycled 10 km and turned right and cycled 20 km and turned left and cycled 20 km . how many kilometres will he have to cycle to reach his home straight ?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given two arithmetic sequences $\\{a_n\\}$ ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 18635,
"question": "Given two arithmetic sequences $\\{a_n\\}$ and $\\{b_n\\}$, with the sum of the first $n$ terms denoted as $S_n$ and $T_n$, respectively, and the ratio $\\frac{a_n}{b_n}$ equals $\\frac{3n+21}{n+1}$, find the value of $\\frac{S_{15}}{T_{15}}$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n CCTV Channel 1 is scheduled to broadcast 5 ... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18636,
"question": "CCTV Channel 1 is scheduled to broadcast 5 advertisements in a row, including 3 different commercial advertisements and 2 different public service announcements (PSAs). The requirement is that the last advertisement must be a PSA, and the two PSAs cannot be broadcast consecutively. How many different broadcasting sequences are there?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In each cell of a $10 \\times 10$ table, a ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18637,
"question": "In each cell of a $10 \\times 10$ table, a natural number is written. Then, each cell is painted if the number written in that cell is less than one of its neighbors but greater than another neighbor. (Two numbers are considered neighbors if they are in cells sharing a common side.) As a result, only two cells remain unpainted, and neither of these cells is in a corner. What is the minimum possible sum of the numbers in these two cells?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n How many subsets consisting of 5 elements c... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"answer": "32",
"index": 18638,
"question": "How many subsets consisting of 5 elements can be selected from the set $\\{1,2,3,4,\\ldots,10\\}$ such that the sum of any two numbers within these 5 elements is not equal to 11? Express your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combinations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n From a group of 8 students, consisting of 6... | math | {
"ground_truth": "720",
"style": "rule"
} | {
"answer": "720",
"index": 18639,
"question": "From a group of 8 students, consisting of 6 boys and 2 girls, select 4 students to participate in a relay race using stratified sampling by gender. If girls are not allowed to be the last runner, find the total number of different arrangements. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \nA company recorded its expenses in rubles... | math | {
"ground_truth": "51",
"style": "rule"
} | {
"answer": "51",
"index": 18640,
"question": "\nA company recorded its expenses in rubles for 100 budget items, resulting in a list of 100 numbers (each number has no more than two decimal places). Each accountant took a copy of the list and found an approximate total of the expenses by doing the following: Initially, they arbitrarily chose two numbers from the list, added them, discarded the decimal part of the sum (if any), and recorded the result instead of the two chosen numbers. They repeated this process with the resulting list of 99 numbers, and so on, until only one integer remained in the list. It turned out that ultimately all the accountants obtained different results. What is the maximum number of accountants that could have been working at the company?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If positive numbers $x$ and $y$ satisfy $x^... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 18641,
"question": "If positive numbers $x$ and $y$ satisfy $x^{2}-y^{2}=3xy$, the value of $\\frac{x^{2}}{y^{2}}+\\frac{y^{2}}{x^{2}}-2=$ \\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a function $y = f(x)$ defined on $\\m... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 18642,
"question": "Given a function $y = f(x)$ defined on $\\mathbb{R}$ that is an even function satisfying $f(2 + x) = f(2 - x)$, and given that the function $y = f(x)$ has at least one zero in the interval $(0, 4)$ and $f(0) = 0$, find the minimum number of zeros of the function $y = f(x)$ in the interval $(-8, 10]$. Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A shepherd uses 15 sections of 2-meter-long... | math | {
"ground_truth": "112",
"style": "rule"
} | {
"answer": "112",
"index": 18643,
"question": "A shepherd uses 15 sections of 2-meter-long fences to form a square or rectangular sheep pen against a wall. What is the maximum area of the sheep pen in square meters? Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a chess tournament, 12 participants play... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"answer": "54",
"index": 18644,
"question": "In a chess tournament, 12 participants played. After the tournament, each participant compiled 12 lists. The first list includes only the participant himself, the second list includes himself and those he won against, the third list includes everyone from the second list and those they won against, and so on. The twelfth list includes everyone from the eleventh list and those they won against. It is known that for any participant, there is a person in their twelfth list who was not in their eleventh list. How many drawn games were played in the tournament?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The coefficient of the $x^3$ term in the ex... | math | {
"ground_truth": "-112",
"style": "rule"
} | {
"answer": "-112",
"index": 18645,
"question": "The coefficient of the $x^3$ term in the expansion of $(x^2-1)(x-2)^7$ is ______.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In two weeks three cows eat all the grass o... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18646,
"question": "In two weeks three cows eat all the grass on two hectares of land, together with all the grass that regrows there during the two weeks. In four weeks, two cows eat all the grass on two hectares of land, together with all the grass that regrows there during the four weeks.\n How many cows will eat all the grass on six hectares of land in six weeks, together with all the grass that regrows there over the six weeks?\n\n (Assume: $\\bullet$ the quantity of grass on each hectare is the same when the cows begin to graze, $\\bullet$ the rate of growth of the grass is uniform during the time of grazing, $\\bullet$ the cows eat the same amount of grass each week.)",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If the graph of the function $f(x)=ax^{3}+b... | math | {
"ground_truth": "-8066",
"style": "rule"
} | {
"answer": "-8066",
"index": 18647,
"question": "If the graph of the function $f(x)=ax^{3}+bx^{2}+cx+d\\ (a\\neq 0)$ has a center of symmetry at $M(x_{0},f(x_{0}))$, and the derivative of the function $f(x)$ is denoted as $g(x)$, then we have $g'(x_{0})=0$. If the function $f(x)=x^{3}-3x^{2}$, then the value of $f\\left( \\frac {1}{2017}\\right)+f\\left( \\frac {2}{2017}\\right)+\\ldots+f\\left( \\frac {4032}{2017}\\right)+f\\left( \\frac {4033}{2017}\\right)=$ \\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n As shown in the figure, natural numbers sta... | math | {
"ground_truth": "113",
"style": "rule"
} | {
"answer": "113",
"index": 18648,
"question": "As shown in the figure, natural numbers starting from 1 are arranged according to a certain pattern. What is the number in the 3rd row and 51st column?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combinations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Calculate the value of $C_{2n}^{10-2n} + C_... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 18649,
"question": "Calculate the value of $C_{2n}^{10-2n} + C_{3+n}^{2n}$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The small animals in the forest are going o... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"answer": "25",
"index": 18650,
"question": "The small animals in the forest are going on an outing. They form a line 40 meters long and move forward at a speed of 3 meters per second. A little rabbit needs to run from the end of the line to the front and then immediately return to the end. The rabbit's speed is 5 meters per second. How many seconds will it take for the rabbit to return to the end of the line?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Use the Horner's Method to calculate the va... | math | {
"ground_truth": "30214",
"style": "rule"
} | {
"answer": "30214",
"index": 18651,
"question": "Use the Horner's Method to calculate the value of the polynomial $f(x) = 3x^4 + 2x^2 + x + 4$ when $x = 10$. During the process, the value of $V_1$ is equal to _______.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find all numbers \\( k \\) for which\n\n\\[... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 18652,
"question": "Find all numbers \\( k \\) for which\n\n\\[ \n\\left(\\frac{k}{2}\\right)!\\left(\\frac{k}{4}\\right) = 2016 + k^2 \n\\]\n\nThe symbol \\( n! \\) denotes the factorial of the number \\( n \\), that is, the product of all integers from 1 to \\( n \\) inclusive (defined only for non-negative integers; \\( 0! = 1 \\) ).",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Five people, numbered 1, 2, 3, 4, 5, are to... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 18653,
"question": "Five people, numbered 1, 2, 3, 4, 5, are to sit in five seats, also numbered 1, 2, 3, 4, 5. Calculate the number of ways in which exactly two people sit in seats that match their numbers. Express your answer as a single numerical value.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A group has 4 boys and 3 girls. If 2 boys a... | math | {
"ground_truth": "216",
"style": "rule"
} | {
"answer": "216",
"index": 18654,
"question": "A group has 4 boys and 3 girls. If 2 boys and 2 girls are selected to form a small choir, how many different arrangements are there if the 2 girls cannot stand next to each other?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the smallest positive integer $n$ fo... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18655,
"question": "Find the smallest positive integer $n$ for which the number \\[ A_n = \\prod_{k=1}^n \\binom{k^2}{k} = \\binom{1}{1} \\binom{4}{2} \\cdots \\binom{n^2}{n} \\] ends in the digit $0$ when written in base ten.",
"split": "train"
} |
math | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that\n$\\frac 1{2!17!}+\\frac 1{3!16!... | math | {
"ground_truth": "137",
"style": "rule"
} | {
"answer": "137",
"index": 18656,
"question": "Given that\n$\\frac 1{2!17!}+\\frac 1{3!16!}+\\frac 1{4!15!}+\\frac 1{5!14!}+\\frac 1{6!13!}+\\frac 1{7!12!}+\\frac 1{8!11!}+\\frac 1{9!10!}=\\frac N{1!18!}$\nfind the greatest integer that is less than $\\frac N{100}$.",
"split": "train"
} |
omnimath | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $N$ is a positive integer between 100000... | math | {
"ground_truth": "67",
"style": "rule"
} | {
"answer": "67",
"index": 18657,
"question": "If $N$ is a positive integer between 1000000 and 10000000, inclusive, what is the maximum possible value for the sum of the digits of $25 \\times N$?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a right triangle \\( \\triangle ABC \\),... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18658,
"question": "In a right triangle \\( \\triangle ABC \\), the lengths of the two legs are 5 and 12. Two arcs are drawn with centers at points \\( A \\) and \\( B \\) and radii 12 and 5, respectively. These arcs intersect the hypotenuse at points \\( M \\) and \\( N \\). Calculate the length of the segment \\( MN \\). Express your answer as a single numerical value.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 5 people numbered 1, 2, 3, 4, 5 s... | math | {
"ground_truth": "109",
"style": "rule"
} | {
"answer": "109",
"index": 18659,
"question": "There are 5 people numbered 1, 2, 3, 4, 5 sitting in seats also numbered 1, 2, 3, 4, 5. Find the number of different seating arrangements where at most two people are sitting in their corresponding numbered seats. Express your answer as a whole number.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $x^{2}-2x-1=0$, the value of $3x^{3}-... | math | {
"ground_truth": "2023",
"style": "rule"
} | {
"answer": "2023",
"index": 18660,
"question": "Given $x^{2}-2x-1=0$, the value of $3x^{3}-10x^{2}+5x+2027$ is ______.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Five students wrote a quiz with a maximum s... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18661,
"question": "Five students wrote a quiz with a maximum score of 50. The scores of four of the students were 42, 43, 46, and 49. The score of the fifth student was \\( N \\). The average (mean) of the five students' scores was the same as the median of the five students' scores. Find the number of possible values of \\( N \\). Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A square \\(ABCD\\) has a side length of 40... | math | {
"ground_truth": "320",
"style": "rule"
} | {
"answer": "320",
"index": 18662,
"question": "A square \\(ABCD\\) has a side length of 40 units. Point \\(F\\) is the midpoint of side \\(AD\\). Point \\(G\\) lies on \\(CF\\) such that \\(3CG = 2GF\\). What is the area of triangle \\(BCG\\)?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Polynomial Operations"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The product of two of the four roots of the... | math | {
"ground_truth": "86",
"style": "rule"
} | {
"answer": "86",
"index": 18663,
"question": "The product of two of the four roots of the quartic equation \\( x^4 - 18x^3 + kx^2 + 200x - 1984 = 0 \\) is -32. Determine the value of \\( k \\).",
"split": "train"
} |
math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n We can write\n\\[\\sum_{k = 1}^{100} (-1)^k... | math | {
"ground_truth": "202",
"style": "rule"
} | {
"answer": "202",
"index": 18664,
"question": "We can write\n\\[\\sum_{k = 1}^{100} (-1)^k \\cdot \\frac{k^2 + k + 1}{k!} = \\frac{a}{b!} - c,\\]where $a,$ $b,$ and $c$ are positive integers. Find the smallest possible value of $a + b + c.$",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The 5-digit number '$XX4XY$' is exactly div... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 18665,
"question": "The 5-digit number '$XX4XY$' is exactly divisible by 165. What is the value of $X+Y$?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n An integer is called \"octal\" if it is div... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"answer": "28",
"index": 18666,
"question": "An integer is called \"octal\" if it is divisible by 8 or if at least one of its digits is 8. How many integers between 1 and 100 are octal? Express your answer as a whole number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There is a six-digit number A15B94 that can... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18667,
"question": "There is a six-digit number A15B94 that can be made with the single-digit numbers A and B. When this number is divisible by 99, find the value that can be B.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a $7 \\times 7$ grid, some squares are p... | math | {
"ground_truth": "1022",
"style": "rule"
} | {
"answer": "1022",
"index": 18668,
"question": "In a $7 \\times 7$ grid, some squares are painted black and the rest are painted white, with at least one square of each color. A pattern is called \"symmetric\" if it looks the same when rotated $90^{\\circ}$ and if it can be folded along either diagonal such that the two halves match. Find the total number of symmetric patterns. Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a class of 100 students, 5 students did ... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"answer": "50",
"index": 18669,
"question": "In a class of 100 students, 5 students did not borrow any books from the library, 20 students each borrowed 1 book, 25 students each borrowed 2 books, 30 students each borrowed at least 3 books, and the remaining 20 students each borrowed at least 5 books. If the average number of books per student is 3, considering that there is a limited number of books in the library, what is the maximum number of books any single student could have borrowed?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n \nEgorov decided to open a savings account ... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"answer": "29",
"index": 18670,
"question": "\nEgorov decided to open a savings account to buy a car worth 900,000 rubles. The initial deposit is 300,000 rubles. Every month, Egorov plans to add 15,000 rubles to his account. The bank offers a monthly interest rate of $12\\%$ per annum. The interest earned each month is added to the account balance, and the interest for the following month is calculated on the new balance. After how many months will there be enough money in the account to buy the car?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What least number should be added to 1024, ... | math | {
"ground_truth": "10315",
"style": "rule"
} | {
"answer": "10315",
"index": 18671,
"question": "What least number should be added to 1024, so that the sum is completely divisible by the product of the following prime numbers: 17, 23, and 29?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Timmy plans to ride a skateboard ramp that ... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 18672,
"question": "Timmy plans to ride a skateboard ramp that is 50 feet high. He knows he needs to go 40 mph at the start to make it all the way to the top. He measures his speed on three trial runs. He has to go 4 mph faster than his average speed to make it up the ramp. What were the speeds of his three trial runs?",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the smallest three-digit number with t... | math | {
"ground_truth": "183",
"style": "rule"
} | {
"answer": "183",
"index": 18673,
"question": "Find the smallest three-digit number with the following property: if you append a number that is 1 greater to its right, the resulting six-digit number will be a perfect square.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $n\\in\\mathbb{N}^{*}$, if $C_{n}^{1}... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18674,
"question": "Given $n\\in\\mathbb{N}^{*}$, if $C_{n}^{1}+2C_{n}^{2}+2^{2}C_{n}^{3}+\\ldots+2^{n-2}C_{n}^{n-1}+2^{n-1}=40$, then $n=$ ______.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Algebra -> Exponential Functions"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the product of all real $x$ for whic... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 18675,
"question": "Find the product of all real $x$ for which \\[ 2^{3x+1} - 17 \\cdot 2^{2x} + 2^{x+3} = 0. \\]",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $(1+ax)^5 = 1 + 10x + bx^2 + \\ldots ... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 18676,
"question": "Given $(1+ax)^5 = 1 + 10x + bx^2 + \\ldots + a^5x^5$, find the value of $b$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Non-Euclidean Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the hyperbola $C: x^{2} - \\frac{y^{2... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 18677,
"question": "Given the hyperbola $C: x^{2} - \\frac{y^{2}}{3} = 1$ with left and right foci $F_1$ and $F_2$ respectively, a point $A$ lies on the hyperbola, and point $M$ has coordinates $(\\frac{2}{3}, 0)$. The distances from $M$ to lines $AF_1$ and $AF_2$ are equal. Find $|AF_1|$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There is a greatest number which, when divi... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 18678,
"question": "There is a greatest number which, when dividing 1642 and another number, leaves remainders 6 and 4 respectively. The greatest number is 4. What is the second number?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given positive integers \\( N \\) and \\( k... | math | {
"ground_truth": "2007",
"style": "rule"
} | {
"answer": "2007",
"index": 18679,
"question": "Given positive integers \\( N \\) and \\( k \\), we counted how many different ways the number \\( N \\) can be written in the form \\( a + b + c \\), where \\( 1 \\leq a, b, c \\leq k \\), and the order of the summands matters. Could the result be 2007?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n An 11-digit mobile phone number starts with... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"answer": "54",
"index": 18680,
"question": "An 11-digit mobile phone number starts with 1390931. Given that the remaining 4 digits can only be 1, 3, or 5, and each of these digits must appear at least once, how many such mobile phone numbers are there?",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Divisibility -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the least number that must be subtract... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 18681,
"question": "Find the least number that must be subtracted from 899830 so that the remaining number is divisible by a certain number. The least number is 6. What is the divisor?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The lines $l_1: x+3y-7=0$ and $l_2: kx-y-2=... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18682,
"question": "The lines $l_1: x+3y-7=0$ and $l_2: kx-y-2=0$ and the positive halves of the x-axis and y-axis enclose a quadrilateral that has a circumscribed circle. Find the value of $k$ that satisfies this condition.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The sequence $\\{{a_n}\\}$ is an arithmetic... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"answer": "60",
"index": 18683,
"question": "The sequence $\\{{a_n}\\}$ is an arithmetic sequence with a common difference of $\\frac{1}{2}$. The sum of its first $100$ terms is $145$. Find the value of $({a_1}+{a_3}+{a_5}+ \\cdots +{a_{99}})=$______.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Suppose two equally strong tennis players p... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 18684,
"question": "Suppose two equally strong tennis players play against each other until one player wins three games in a row. The results of each game are independent, and each player will win with probability $\\frac{1}{2}$ . What is the expected value of the number of games they will play?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 200 different cards on the table ... | math | {
"ground_truth": "437844",
"style": "rule"
} | {
"answer": "437844",
"index": 18685,
"question": "There are 200 different cards on the table with numbers $201, 203, 205, \\ldots, 597, 599$ (each card has exactly one number, and each number appears exactly once). In how many ways can you choose 3 cards such that the sum of the numbers on the chosen cards is divisible by 3?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If in triangle $ABC$, the sides opposite to... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 18686,
"question": "If in triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are respectively $a$, $b$, and $c$, and it is given that $2b\\sin 2A=a\\sin B$, and $c=2b$, then $\\dfrac{a}{b}=$_______.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Igor Gorshkov has all seven books about Har... | math | {
"ground_truth": "75600",
"style": "rule"
} | {
"answer": "75600",
"index": 18687,
"question": "Igor Gorshkov has all seven books about Harry Potter. In how many ways can Igor arrange these seven volumes on three different shelves, such that each shelf has at least one book? (Arrangements that differ in the order of books on a shelf are considered different).",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Petya and Vasya took a math test. Petya ans... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"answer": "60",
"index": 18688,
"question": "Petya and Vasya took a math test. Petya answered $80\\%$ of all the questions correctly, while Vasya answered exactly 35 questions correctly. The number of questions both answered correctly is exactly half the total number of questions. No one answered 7 questions. How many questions were on the test?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a sequence $\\{a_n\\}$ and its sum of... | math | {
"ground_truth": "189",
"style": "rule"
} | {
"answer": "189",
"index": 18689,
"question": "Given a sequence $\\{a_n\\}$ and its sum of the first $n$ terms $S_n$, satisfying $S_n=2a_n-3$ ($n\\in\\mathbb{N}^*$), find $S_6$.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> Least Common Multiples (LCM)"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n For some positive integers $m>n$ , the qua... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 18690,
"question": "For some positive integers $m>n$ , the quantities $a=\\text{lcm}(m,n)$ and $b=\\gcd(m,n)$ satisfy $a=30b$ . If $m-n$ divides $a$ , then what is the value of $\\frac{m+n}{b}$ ?",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Prealgebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the dividend when the divisor is (-... | math | {
"ground_truth": "269",
"style": "rule"
} | {
"answer": "269",
"index": 18691,
"question": "What is the dividend when the divisor is (-4 2/3), the quotient is (-57 1/5), and the remainder is (2 1/9)?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A line $l$ passing through the focus $F$ of... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 18692,
"question": "A line $l$ passing through the focus $F$ of the parabola $y^2=4x$ intersects the parabola at points $P(x_1, y_1)$ and $Q(x_2, y_2)$. If $x_1+x_2=9$, then the length $|PQ|$ is ____.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Some welders work at a constant rate and co... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 18693,
"question": "Some welders work at a constant rate and complete an order in 8 days. If after the first day, 9 welders start to work on the other project, the remaining welders will need 16 more days to complete the rest of the order. How many welders were initially working on the order?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the equations of two circles:\n- $x^{... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 18694,
"question": "Given the equations of two circles:\n- $x^{2}+y^{2}+2ax+a^{2}-4=0$\n- $x^{2}+y^{2}-4by-1+4b^{2}=0$\n\nThe circles have exactly three common tangents. If $a\\in R$, $b\\in R$, and $ab\\neq 0$, find the minimum value of $\\dfrac{1}{a^{2}}+\\dfrac{1}{b^{2}}$. Express your answer as a single numerical value.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence: $$( \\frac{1}{1}), ( \\... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 18695,
"question": "Given the sequence: $$( \\frac{1}{1}), ( \\frac{1}{2}, \\frac{2}{1}), ( \\frac{1}{3}, \\frac{2}{2}, \\frac{3}{1}), ( \\frac{1}{4}, \\frac{2}{3}, \\frac{3}{2}, \\frac{4}{1}), \\ldots, ( \\frac{1}{n}, \\frac{2}{n-1}, \\frac{3}{n-2}, \\ldots, \\frac{n-1}{2}, \\frac{n}{1})$$, denote the elements of the sequence as: $a_1, a_2, a_3, a_4, a_5, \\ldots$ then $a_{2009} = \\boxed{?}$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Calculus -> Integral Calculus -> Other",
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $m=3\\int_{0}^{{\\pi}}\\sin xdx$... | math | {
"ground_truth": "-6480",
"style": "rule"
} | {
"answer": "-6480",
"index": 18696,
"question": "Given that $m=3\\int_{0}^{{\\pi}}\\sin xdx$, find the coefficient of $ab^{2}c^{m-3}$ in the expansion of $(a+2b-3c)^{m}$.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What least number must be subtracted from 1... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 18697,
"question": "What least number must be subtracted from 157,632 so that the remaining number is simultaneously divisible by 12, 18, and 24?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a class of 36 students, everyone bought ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 18698,
"question": "In a class of 36 students, everyone bought pencils, totaling 50 pencils. Some students bought 1 pencil, some bought 2 pencils, and some bought 3 pencils. If the number of students who bought 1 pencil is twice the number of students who bought the other amounts, how many students bought 2 pencils?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the complex number \\( z \\) that sat... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 18699,
"question": "Given the complex number \\( z \\) that satisfies \\( z^2 + 2z = \\bar{z} \\neq z \\) (where \\( \\bar{z} \\) represents the conjugate of \\( z \\)), find the product of all possible values of \\( z \\).",
"split": "train"
} |
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