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 |
|---|---|---|---|---|---|---|---|
orca_math | [
"Mathematics -> Number Theory -> 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 The eight-digit number 757AB384 is divisibl... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 1600,
"question": "The eight-digit number 757AB384 is divisible by 357. Get B.",
"split": "train"
} |
omnimath | [
"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 Define $\\phi^{!}(n)$ as the product of all... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 1601,
"question": "Define $\\phi^{!}(n)$ as the product of all positive integers less than or equal to $n$ and relatively prime to $n$. Compute the remainder when $$ \\sum_{\\substack{2 \\leq n \\leq 50 \\\\ \\operatorname{gcd}(n, 50)=1}} \\phi^{!}(n) $$ is divided by 50 .",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 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 The organizing committee plans to allocate ... | math | {
"ground_truth": "22",
"style": "rule"
} | {
"answer": "22",
"index": 1602,
"question": "The organizing committee plans to allocate six staff members, named A, B, C, D, E, and F, to two different locations for reception work during the meeting. If A and B must be in the same group and each group must have at least two people, calculate the number of different distribution methods.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Other",
"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 Determine the number of lattice points on t... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 1603,
"question": "Determine the number of lattice points on the line segment with endpoints (3, 17) and (48, 281), including the endpoints. Express your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 sequence {a_n} satisfies 3a_{n+1}... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 1604,
"question": "Given the sequence {a_n} satisfies 3a_{n+1} + a_n = 4 (n ≥ 1), with a_1 = 9, and the sum of its first n terms is S_n, find the smallest integer n that meets the inequality |S_n - n - 6| < 1/125. Express your answer as a single integer.",
"split": "train"
} |
omnimath | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 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 Find the number of quadruples $(a, b, c, d)... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"answer": "49",
"index": 1605,
"question": "Find the number of quadruples $(a, b, c, d)$ of integers with absolute value at most 5 such that $\\left(a^{2}+b^{2}+c^{2}+d^{2}\\right)^{2}=(a+b+c+d)(a-b+c-d)\\left((a-c)^{2}+(b-d)^{2}\\right)$",
"split": "train"
} |
aops_forum | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 Consider a $25 \\times 25$ grid of unit s... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"answer": "48",
"index": 1606,
"question": "Consider a $25 \\times 25$ grid of unit squares. Draw with a red pen contours of squares of any size on the grid. What is the minimal number of squares we must draw in order to colour all the lines of the grid?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Solid 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 Find the area of the triangle $\\triangle P... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 1607,
"question": "Find the area of the triangle $\\triangle PMF$ formed by drawing a perpendicular line from point $P$ on the parabola $y^{2}=4x$ to its directrix, with $M$ being the foot of the perpendicular and $|PM|=5$. Let $F$ be the focus of the parabola.",
"split": "train"
} |
orca_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 The average weight of 25 people increases b... | math | {
"ground_truth": "310",
"style": "rule"
} | {
"answer": "310",
"index": 1608,
"question": "The average weight of 25 people increases by 4 kg when three new people come in place of three of them weighing 65 kg, 70 kg, and 75 kg respectively. What might be the weights of the new people?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 How many functions \\( f: \\{0,1\\}^{3} \\r... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 1609,
"question": "How many functions \\( f: \\{0,1\\}^{3} \\rightarrow \\{0,1\\} \\) satisfy the property that, for all ordered triples \\(\\left(a_{1}, a_{2}, a_{3}\\right)\\) and \\(\\left(b_{1}, b_{2}, b_{3}\\right)\\) such that \\( a_{i} \\geq b_{i} \\) for all \\( i \\), \\( f\\left(a_{1}, a_{2}, a_{3}\\right) \\geq f\\left(b_{1}, b_{2}, b_{3}\\right) \\)?",
"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 a can complete a project in 20 days, b can ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 1610,
"question": "a can complete a project in 20 days, b can complete the same project in 30 days, and c can complete the project in 40 days. If a, b, and c start working on the project together, and a quits 10 days before the project is completed while b quits 5 days before the project is completed, in how many days will the project be completed?",
"split": "train"
} |
olympiads | [
"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 As shown in the figure, the area of the rig... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 1611,
"question": "As shown in the figure, the area of the right trapezoid $\\mathrm{ABCD}$ is $52$. Given that $D E = F C$ and $\\mathrm{AF}$ intersects $\\mathrm{BE}$ at $\\mathrm{O}$, the area of triangle $\\mathrm{AOB}$ is 17. Determine the sum of the areas of triangles $\\mathrm{AOE}$ and $\\mathrm{BOF}$.",
"split": "train"
} |
math | [
"Mathematics -> Algebra -> Linear Algebra -> Matrices"
] | 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 For some matrix $\\mathbf{P} = \\begin{pmat... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 1612,
"question": "For some matrix $\\mathbf{P} = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ with nonzero integer entries,\n\\[\\begin{pmatrix} 4 & 3 \\\\ -1 & 0 \\end{pmatrix} = \\mathbf{P}^{-1} \\begin{pmatrix} 1 & 0 \\\\ 0 & 3 \\end{pmatrix} \\mathbf{P}.\\]Find the smallest possible value of $|a| + |b| + |c| + |d|.$",
"split": "train"
} |
big_math | [
"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 There are 7 balls of each of the three colo... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"answer": "60",
"index": 1613,
"question": "There are 7 balls of each of the three colors: red, blue, and yellow. Each set of 7 balls of the same color is numbered from 1 to 7. If we randomly pick 3 balls with different numbers, and these 3 balls are of different colors and their numbers are not consecutive, find the number of ways to do this. Express your answer as a single integer.",
"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 You have a \\(2 \\times 3\\) grid filled wi... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"answer": "49",
"index": 1614,
"question": "You have a \\(2 \\times 3\\) grid filled with integers between 1 and 9. The numbers in each row and column are distinct. The first row sums to 23, and the columns sum to 14, 16, and 17 respectively.\n\nGiven the following grid:\n\\[\n\\begin{array}{c|c|c|c|}\n & 14 & 16 & 17 \\\\\n\\hline \n23 & a & b & c \\\\\n\\hline \n & x & y & z \\\\\n\\hline\n\\end{array}\n\\]\n\nWhat is \\(x + 2y + 3z\\)?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Combinations"
] | 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 Distribute 2 identical novels and 2 identic... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 1615,
"question": "Distribute 2 identical novels and 2 identical picture albums among 3 students, with each student receiving at least 1 book. Find the total number of different distribution methods. Express your answer as a whole number.",
"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 What is the 20 - fifth decimal to the right... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 1616,
"question": "What is the 20 - fifth decimal to the right in the fraction 10 / n, if the answer is 9?",
"split": "train"
} |
cn_k12 | [
"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 Let $a > 0$, $b > 0$, and $a + 4b + ab = 3$... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 1617,
"question": "Let $a > 0$, $b > 0$, and $a + 4b + ab = 3$. Find the maximum value of $ab$.",
"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 A person moves $100\\sqrt{5}$ meters along ... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 1618,
"question": "A person moves $100\\sqrt{5}$ meters along a slope with a ratio of $1:2$. Calculate the increase in the person's position. Express your answer in meters.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Solid 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 circles \\\\(C_{1}: x^{2}+y^{2}-2x+4y... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 1619,
"question": "Given circles \\\\(C_{1}: x^{2}+y^{2}-2x+4y-4=0\\\\), \\\\(C_{2}: x^{2}+y^{2}+2x+2y-2=0\\\\), and \\\\(C_{3}: x^{2}+y^{2}-2x-2y- \\frac {14}{5}=0\\\\), find the length of the chord cut by circle \\\\(C_{3}\\\\) on the common chord of circles \\\\(C_{1}\\\\) and \\\\(C_{2}\\\\).",
"split": "train"
} |
big_math | [
"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 point is chosen inside an equilateral tri... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"answer": "33",
"index": 1620,
"question": "A point is chosen inside an equilateral triangle. From this point, three segments are drawn parallel to the sides of the triangle, with lengths 2 m, 3 m, and 6 m. Find the perimeter of the equilateral triangle. Express your answer in meters as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 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 Using Horner's Rule, calculate the value of... | math | {
"ground_truth": "-80",
"style": "rule"
} | {
"answer": "-80",
"index": 1621,
"question": "Using Horner's Rule, calculate the value of $v_3$ for the polynomial $f(x) = x^6 - 12x^5 + 60x^4 - 160x^3 + 240x^2 - 192x + 64$ when $x = 2$. Express your answer as an integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 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 Danka and Janka received two identical whit... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 1622,
"question": "Danka and Janka received two identical white cubes for their birthdays, with each cube composed of 125 small unit cubes as shown in the picture. To distinguish the cubes, they decided to paint them. Danka took a brush and painted three of the six faces of her cube red. Janka painted three of the six faces of her cube green. After some time, both cubes were cut into the individual unit cubes from which they were originally assembled. To their surprise, they found that the number of unit cubes with at least one red face differed from the number of unit cubes with at least one green face. Determine this difference.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series -> 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 For an arithmetic sequence $\\{a_n\\}$, the... | math | {
"ground_truth": "-49",
"style": "rule"
} | {
"answer": "-49",
"index": 1623,
"question": "For an arithmetic sequence $\\{a_n\\}$, the sum of the first $n$ terms is denoted as $S_n$. Given that $S_{10} = 0$ and $S_{15} = 25$, the minimum value of $nS_n$ is \\_\\_\\_\\_\\_\\_\\_\\_.",
"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 A luxury liner, Queen Mary II, is transport... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 1624,
"question": "A luxury liner, Queen Mary II, is transporting several cats, parrots, dogs, as well as the crew (sailors, a cook, and a one-legged captain) to a nearby port. Altogether, these passengers have 38 heads and 103 legs. How many cats, parrots, dogs, sailors, a cook, and a one-legged captain does the ship host?",
"split": "train"
} |
big_math | [
"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 a finite arithmetic sequence \\( a_{1... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 1625,
"question": "Given a finite arithmetic sequence \\( a_{1}, a_{2}, \\cdots a_{k} \\), and the conditions: $$ \\begin{array}{c} a_{4}+a_{7}+a_{10}=17, \\\\ a_{4}+a_{5}+a_{6}+a_{7}+a_{8}+a_{9}+a_{10}+a_{11}+a_{12}+a_{13}+a_{14}=77. \\end{array} $$ If \\( a_{k}=13 \\), calculate the value of \\( k \\). Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> 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 There are 16 distinct points on a circle. D... | math | {
"ground_truth": "1430",
"style": "rule"
} | {
"answer": "1430",
"index": 1626,
"question": "There are 16 distinct points on a circle. Determine the number of different ways to draw 8 nonintersecting line segments connecting pairs of points so that each of the 16 points is connected to exactly one other point.",
"split": "train"
} |
orca_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 Jeffrey owns a poultry farm with various ty... | math | {
"ground_truth": "236",
"style": "rule"
} | {
"answer": "236",
"index": 1627,
"question": "Jeffrey owns a poultry farm with various types of birds. There are 25 hens, 10 ducks, and 5 geese. The ratio of male to female birds for each type is 1:4. Each hen has 6 chicks, each duck has 8 ducklings, and each goose has 3 goslings. Calculate the total number of poultry on the farm, including all adult birds and their offspring.",
"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 a \\(7 \\times 7\\) table, some cells ar... | math | {
"ground_truth": "168",
"style": "rule"
} | {
"answer": "168",
"index": 1628,
"question": "In a \\(7 \\times 7\\) table, some cells are black while the remaining ones are white. In each white cell, the total number of black cells located with it in the same row or column is written; nothing is written in the black cells. What is the maximum possible sum of the numbers in the entire table?",
"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 A high school offers three separate electiv... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"answer": "54",
"index": 1629,
"question": "A high school offers three separate elective classes for the senior two-grade mathematics course. After the selection process, four students request to change their math class. However, each class can accept at most two more students. Determine the number of different ways the students can be redistributed among the classes.",
"split": "train"
} |
big_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 What is the minimum number of operations re... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 1630,
"question": "What is the minimum number of operations required to transform 2014 into 1, where an operation is defined as adding, subtracting, multiplying, or dividing by a single-digit number (1-9)?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> 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 Given the real numbers \\( x, y, \\) and \\... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 1631,
"question": "Given the real numbers \\( x, y, \\) and \\( z \\) that satisfy \\( xy \\neq 0 \\) and \\( x+y \\neq 0 \\), find the minimum value of the expression\n$$\n\\left(\\frac{y+z}{x}+2\\right)^{2}+\\left(\\frac{z}{y}+2\\right)^{2}+\\left(\\frac{z}{x+y}-1\\right)^{2}.\n$$",
"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 a 100 meter long train crosses a man standi... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 1632,
"question": "a 100 meter long train crosses a man standing on the platform in 5 sec . what is the speed of the train ?",
"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 Find the number of elements in the set $\\{... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 1633,
"question": "Find the number of elements in the set $\\{x|C_{10}^{x} \\leq 20\\}$. Express your answer as a whole number.",
"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 Among all proper fractions where both the n... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"answer": "81",
"index": 1634,
"question": "Among all proper fractions where both the numerator and the denominator are two-digit numbers, find the smallest fraction that is greater than $\\frac{5}{6}$. Provide the numerator of this fraction in your answer.",
"split": "train"
} |
orca_math | [
"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 If 2 ^ 2n + 2 ^ 2n + 2 ^ 2n + 2 ^ 2n = 4 ^ ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 1635,
"question": "If 2 ^ 2n + 2 ^ 2n + 2 ^ 2n + 2 ^ 2n = 4 ^ 18, what is the value of n?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 minimum number of cells that ne... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 1636,
"question": "What is the minimum number of cells that need to be marked in a $15 \\times 15$ grid so that in each vertical or horizontal $1 \\times 10$ strip, there is at least one marked cell?",
"split": "train"
} |
cn_k12 | [
"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 If set $A=\\{x\\in N\\left|\\right.-1 \\lt ... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 1637,
"question": "If set $A=\\{x\\in N\\left|\\right.-1 \\lt x\\leqslant 2\\}$, $B=\\{x\\left|\\right.x=ab,a,b\\in A\\}$, then the number of non-empty proper subsets of set $B$ is ______.",
"split": "train"
} |
orca_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 Tina is working on her homework when she re... | math | {
"ground_truth": "541",
"style": "rule"
} | {
"answer": "541",
"index": 1638,
"question": "Tina is working on her homework when she realizes she's having a hard time typing out her answers on her laptop because a lot of the keys are sticky. She is trying to get her homework done before dinner, though, so she needs to decide if she has time to clean her keyboard first. Tina knows her assignment will only take 20 minutes to complete. Dinner will be ready at 5:30 p.m. Tina decides to time how long it takes to remove and clean one key and will then multiply that time by how many keys she needs to fix. She counts 30 keys that are sticky and times it to take 7 minutes to clean one. After Tina has cleaned one key, there are 29 left to clean. Additionally, she'll need to wait 10 minutes for each key to dry before they can be used again. Tina also plans to take breaks between cleaning keys, and for every 5 keys she cleans, she takes a 3-minute break. How many minutes total will it take for Tina to both clean the remaining keys, wait for them to dry, take planned breaks, and finish her assignment?",
"split": "train"
} |
big_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 Let \\(a\\) be a positive integer less than... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 1639,
"question": "Let \\(a\\) be a positive integer less than 100. If \\(a^{3}+23\\) is divisible by 24, how many such values of \\(a\\) are there? Express your answer as a whole number.",
"split": "train"
} |
cn_k12 | [
"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 The sum of the first $n$ terms of an infini... | math | {
"ground_truth": "91",
"style": "rule"
} | {
"answer": "91",
"index": 1640,
"question": "The sum of the first $n$ terms of an infinite sequence $\\{a_n\\}$ is $S_n$. If for any positive integer $n$, $S_n$ belongs to $\\{k_1,k_2,k_3,…,k_{10}\\}$, then the maximum number of possible values for $a_{10}$ is __________.",
"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 Sally picked 7 lemons, Mary picked 9 lemons... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 1641,
"question": "Sally picked 7 lemons, Mary picked 9 lemons, and Tom picked 12 lemons from the lemon tree. However, 2 lemons fell on the ground and were eaten by animals, and the total number of lemons originally on the tree is unknown. How many lemons were remaining on the lemon tree after Sally, Mary, and Tom picked the lemons and the animals ate the fallen ones?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 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 What is the maximum number of diagonals of ... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 1642,
"question": "What is the maximum number of diagonals of a regular $12$ -gon which can be selected such that no two of the chosen diagonals are perpendicular?\n\nNote: sides are not diagonals and diagonals which intersect outside the $12$ -gon at right angles are still considered perpendicular.",
"split": "train"
} |
big_math | [
"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 The sum of the first n terms of a geometric... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 1643,
"question": "The sum of the first n terms of a geometric sequence is 24, and the sum of the first 3n terms is 42. Find the sum of the first 2n terms.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Applied Mathematics -> 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 Let $S$ be the set of positive integer di... | math | {
"ground_truth": "77",
"style": "rule"
} | {
"answer": "77",
"index": 1644,
"question": "Let $S$ be the set of positive integer divisors of $20^9.$ Three numbers are chosen independently and at random from the set $S$ and labeled $a_1,a_2,$ and $a_3$ in the order they are chosen. The probability that both $a_1$ divides $a_2$ and $a_2$ divides $a_3$ is $\\frac mn,$ where $m$ and $n$ are relatively prime positive integers. Find $m.$ ",
"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 In Yacleyland, the unit of money used is ca... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 1645,
"question": "In Yacleyland, the unit of money used is called the Yacley. There are only two denominations of paper money: the 17 Yacley bill and the 5 Yacley bill. How many different combinations of these bills total 453 Yacley? Express your answer as a whole number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> 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 On dividing 14698 by 164.98876404494382, we... | math | {
"ground_truth": "88",
"style": "rule"
} | {
"answer": "88",
"index": 1646,
"question": "On dividing 14698 by 164.98876404494382, we get a certain quotient and 14 as remainder. What is the quotient?",
"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 Two circles with radii 13 and 5 intersect, ... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 1647,
"question": "Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Find the length of the common chord of these two circles. Express your answer as a single numerical value.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 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 \nA $3 \\times 3 \\times 3$ cube is made ou... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 1648,
"question": "\nA $3 \\times 3 \\times 3$ cube is made out of $1 \\times 1 \\times 1$ smaller cubes. What is the maximum number of smaller cubes that can be removed while ensuring that the remaining structure satisfies the following two properties:\n\n- Looking at any face of the original cube, the structure appears as a $3 \\times 3$ square (there are no gaps, and all 9 cubes on each face are visible when looking perpendicularly at that face);\n- It is possible to travel from any cube to any other cube within the structure by moving through the shared faces of adjacent cubes.",
"split": "train"
} |
big_math | [
"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 The interior angles of a convex hexagon for... | math | {
"ground_truth": "175",
"style": "rule"
} | {
"answer": "175",
"index": 1649,
"question": "The interior angles of a convex hexagon form an arithmetic sequence of positive integers. Calculate the largest possible measure of the largest interior angle of the hexagon. Express your answer in degrees as a whole number.",
"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 The sum of two numbers is \\( t \\) and the... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"answer": "53",
"index": 1650,
"question": "The sum of two numbers is \\( t \\) and the positive difference between the squares of these two numbers is 208. What is the larger of the two numbers?",
"split": "train"
} |
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 In triangle $ABC$ , side $AB$ has length... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"answer": "72",
"index": 1651,
"question": "In triangle $ABC$ , side $AB$ has length $10$ , and the $A$ - and $B$ -medians have length $9$ and $12$ , respectively. Compute the area of the triangle.",
"split": "train"
} |
olympiads | [
"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 The lines tangent to a circle with center $... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 1652,
"question": "The lines tangent to a circle with center $O$ at points $A$ and $B$ intersect at point $M$. Find the chord $AB$ if the segment $MO$ is divided by it into segments equal to 2 and 18.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 smallest $k$ such that $k$ cell... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"answer": "50",
"index": 1653,
"question": "What is the smallest $k$ such that $k$ cells can be marked on a $10 \\times 11$ board so that any placement of a three-cell L-shaped piece will touch at least one marked cell?",
"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 What is the total time in hours, minutes, a... | math | {
"ground_truth": "59",
"style": "rule"
} | {
"answer": "59",
"index": 1654,
"question": "What is the total time in hours, minutes, and seconds when given 3450 minutes and 7523 seconds?",
"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 There are 28 students in a class. On March ... | math | {
"ground_truth": "44",
"style": "rule"
} | {
"answer": "44",
"index": 1655,
"question": "There are 28 students in a class. On March 8th, each boy gave each girl one flower - a tulip, a rose, or a daffodil. How many roses were given if it is known that the number of roses is 4 times the number of daffodils, but 3 times less than the number of tulips?",
"split": "train"
} |
aops_forum | [
"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 Kayla draws three triangles on a sheet of p... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 1656,
"question": "Kayla draws three triangles on a sheet of paper. What is the maximum possible number of regions, including the exterior region, that the paper can be divided into by the sides of the triangles?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> 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 Given that \\(a, b, c\\) are distinct real ... | math | {
"ground_truth": "186",
"style": "rule"
} | {
"answer": "186",
"index": 1657,
"question": "Given that \\(a, b, c\\) are distinct real roots of the polynomial equation \\(x^3 - 3x + 1 = 0\\), find the value of \\(a^8 + b^8 + c^8\\). Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 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 the tetrahedron \\(ABCD\\), \\(AB = 2\\)... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 1658,
"question": "In the tetrahedron \\(ABCD\\), \\(AB = 2\\), \\(AC = 3\\), \\(AD = 4\\), \\(BC = \\sqrt{13}\\), \\(BD = 2\\sqrt{5}\\), and \\(CD = 5\\). Calculate the volume of the tetrahedron \\(ABCD\\). Express your answer as a single number.",
"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 The sum of certain positive integers (not n... | math | {
"ground_truth": "133",
"style": "rule"
} | {
"answer": "133",
"index": 1659,
"question": "The sum of certain positive integers (not necessarily distinct) less than or equal to 10 is $S$. Find all values of $S$ such that, regardless of these integers, they can always be partitioned into two groups, each with a sum less than or equal to 70.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> 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 natural number \\( A \\) is written twice... | math | {
"ground_truth": "288",
"style": "rule"
} | {
"answer": "288",
"index": 1660,
"question": "A natural number \\( A \\) is written twice consecutively (for example, writing 12 as 1212) to obtain a new number \\( B \\). If \\( B \\) is a multiple of 2016, then the smallest value of \\( A \\) is ______.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Permutations"
] | 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 order of the letters in the English ... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 1661,
"question": "If the order of the letters in the English word \"good\" is written incorrectly, there are a total of $\\_\\_\\_\\_\\_$ possible errors.",
"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 What is the smallest number of sides that a... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 1662,
"question": "What is the smallest number of sides that a polygon (not necessarily convex) with an odd number of sides can have, if it can be divided into parallelograms?",
"split": "train"
} |
big_math | [
"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 Given the ellipse $\\frac {x^{2}}{25}+ \\fr... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 1663,
"question": "Given the ellipse $\\frac {x^{2}}{25}+ \\frac {y^{2}}{9}=1$, a line passing through one of its foci intersects the ellipse at points $A$ and $B$. If the sum of the distances from the other focus to points $A$ and $B$ is 12, calculate the length of segment $|AB|$.",
"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 Christian's father, the senior ranger, and ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 1664,
"question": "Christian's father, the senior ranger, and two other volunteers went to gather firewood at different locations in the park and brought with them various sized sacks. If Christian's father's sack can hold 20 pieces of wood, the senior ranger's sack can hold 30 pieces, and each volunteer's sack can hold 25 pieces, they were able to fill _____ sacks in total if they gathered 200 pieces of wood.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 André is hiking on the paths shown in the m... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 1665,
"question": "André is hiking on the paths shown in the map. He is planning to visit sites A to M in alphabetical order. He can never retrace his steps and he must proceed directly from one site to the next. What is the largest number of labelled points he can visit before going out of alphabetical order? Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"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 Given \\( a \\in \\mathbf{R} \\) and \\( b ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 1666,
"question": "Given \\( a \\in \\mathbf{R} \\) and \\( b \\in \\mathbf{R}_{+} \\), where \\( \\mathrm{e} \\) is the base of the natural logarithm, find the minimum value of \\( \\left( \\mathrm{e}^{a} - \\ln b \\right)^{2} + (a - b)^{2} \\).",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 an arithmetic sequence, the sum of th... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 1667,
"question": "Given an arithmetic sequence, the sum of the first four terms is 26, the sum of the last four terms is 110, and the sum of all terms in the sequence is 187. Determine the total number of terms in the sequence. Express your answer as a whole number.",
"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 The length of the bridge, which a train 200... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"answer": "200",
"index": 1668,
"question": "The length of the bridge, which a train 200 m long and traveling at 32 km/hr can cross in 20 seconds is?",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> 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 a sequence of positive integers \\(\\... | math | {
"ground_truth": "94",
"style": "rule"
} | {
"answer": "94",
"index": 1669,
"question": "Given a sequence of positive integers \\(\\{y_{n}\\}\\) satisfying\n\\[\ny_{n+2} = \\frac{y_{n} + 2013}{1 + y_{n+1}} \\quad (n \\geq 1),\n\\]\nfind the minimum value of \\(y_{1} + y_{2}\\).",
"split": "train"
} |
orca_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 the digits of integer k,... | math | {
"ground_truth": "362",
"style": "rule"
} | {
"answer": "362",
"index": 1670,
"question": "What is the sum of the digits of integer k, if k = (some number - 46) and the sum of the digits is 352?",
"split": "train"
} |
olympiads | [
"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 Find the smallest natural number that has e... | math | {
"ground_truth": "25920",
"style": "rule"
} | {
"answer": "25920",
"index": 1671,
"question": "Find the smallest natural number that has exactly 70 natural divisors (including 1 and the number itself).",
"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 the average ( arithmetic mean ) of the 5 po... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"answer": "23",
"index": 1672,
"question": "the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 18 , and k < m < r < s < t . if t is 40 , what is the greatest possible value of the median of the 5 integers ?",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 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 There are 39 ones written on the board. Eve... | math | {
"ground_truth": "741",
"style": "rule"
} | {
"answer": "741",
"index": 1673,
"question": "There are 39 ones written on the board. Every minute, Karlson erases two arbitrary numbers and writes their sum on the board, then eats a number of candies equal to the product of the two erased numbers. What is the maximum number of candies he could have eaten in 39 minutes?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Permutations"
] | 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 Calculate the number of arrangements of 6 i... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 1674,
"question": "Calculate the number of arrangements of 6 items taken 2 at a time, denoted as ${A}_{6}^{2}$. Express your answer as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combinations"
] | 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 a certain sports competition, the scorin... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 1675,
"question": "In a certain sports competition, the scoring rules are: winning a match gives 3 points, drawing a match gives 1 point, and losing a match gives 0 points. If a particular athlete plays 15 matches and scores a total of 22 points, how many possible scenarios are there? Express your answer as a single integer.",
"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 The manager of a store checked the sales pr... | math | {
"ground_truth": "511",
"style": "rule"
} | {
"answer": "511",
"index": 1676,
"question": "The manager of a store checked the sales price in 2006 of a television from the brand VejoTudo. He found a partially faded invoice that read: \"lot of 72 VejoTudo TVs sold for R$ \\ldots 679 \\ldots reais,\" where the digits of the unit and the ten thousand place were illegible. What was the sales price in 2006 of each of those televisions?",
"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 One hour after Yolanda started walking from... | math | {
"ground_truth": "38",
"style": "rule"
} | {
"answer": "38",
"index": 1677,
"question": "One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. Yolanda's walking rate was 8 miles per hour and Bob's was 9 miles per hour. How many miles had Bob walked when they met?",
"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 Nine integers from 1 to 5 are written on a ... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"answer": "26",
"index": 1678,
"question": "Nine integers from 1 to 5 are written on a board. It is known that seven of them are at least 2, six are greater than 2, three are at least 4, and one is at least 5. Find the sum of all the numbers.",
"split": "train"
} |
cn_k12 | [
"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 The function $\\[x\\]$ represents the large... | math | {
"ground_truth": "210",
"style": "rule"
} | {
"answer": "210",
"index": 1679,
"question": "The function $\\[x\\]$ represents the largest integer not greater than $x$. For example, $\\[π\\]=3$. Let $S\\_1=\\[√1\\}+\\[√2\\}+\\[√3\\}=3$, $S\\_2=\\[√4\\}+\\[√5\\}+\\[√6\\}+\\[√7\\}+\\[√8\\}=10$, and $S\\_3=\\[√9\\}+\\[√10\\}+\\[√11\\}+\\[√12\\}+\\[√13\\}+\\[√14\\}+\\[√15\\}=21$. Following this pattern, find $S\\_{10}=$\\_\\_\\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
big_math | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 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 x and y are positive numbers, an... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 1680,
"question": "Given that x and y are positive numbers, and 1/x + 4/y = 1, find the minimum value of x+y. Express your answer as a single numerical value.",
"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 how many different positive integers exist ... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"answer": "28",
"index": 1681,
"question": "how many different positive integers exist between 10 ^ 7 and 10 ^ 8 , the sum of whose digits is equal to 2 ?",
"split": "train"
} |
cn_k12 | [
"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 During the Spring Festival, a unit arranged... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 1682,
"question": "During the Spring Festival, a unit arranged for three people, A, B, and C, to be on duty from the first to the fifth day of the first lunar month. Each person must be on duty at least one day, and no one can be on duty for two consecutive days. A is not scheduled for duty on the second day. There are a total of _______ different scheduling arrangements.",
"split": "train"
} |
orca_math | [
"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 Alex is stacking his books in a pyramid. Ea... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"answer": "64",
"index": 1683,
"question": "Alex is stacking his books in a pyramid. Each level of the pyramid has 80% as many books as the number of books in the previous level. He makes four levels and the top level has a certain number of books. There are 369 books in the pyramid in total. How many books are in the top level of the pyramid?",
"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 school, there are 3 classrooms. Classr... | math | {
"ground_truth": "933",
"style": "rule"
} | {
"answer": "933",
"index": 1684,
"question": "In a school, there are 3 classrooms. Classroom A has 750 tables and 3/5 times as many books as the number of tables are on top of each table. Classroom B has 500 tables with 2/5 times as many books as the number of tables on top of each table. Classroom C has 850 tables with 1/3 times as many books as the number of tables on top of each table. What's the total number of books in the school across all classrooms?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 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 an arithmetic sequence $\\{a_n\\}$ wi... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 1685,
"question": "Given an arithmetic sequence $\\{a_n\\}$ with the sum of its first $n$ terms denoted as $S_n$, if $2\\vec{OC} = a_4\\vec{OA} + a_8\\vec{OB}$, and points A, B, C are not collinear (the line does not pass through point O), find $S_{11}$.",
"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 The line $l$ is the tangent to the circle $... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 1686,
"question": "The line $l$ is the tangent to the circle $x^2+y^2=4$ at the point $(-1, \\sqrt {3})$, and the point $P$ is a moving point on the circle $x^2-4x+y^2+3=0$. Calculate the minimum distance from the point $P$ to the line $l$. Express your answer as a single number.",
"split": "train"
} |
big_math | [
"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 Find the constant term in the expansion of ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 1687,
"question": "Find the constant term in the expansion of the algebraic expression $( \\sqrt {x}+2)( \\frac {1}{ \\sqrt {x}}-1)^{5}$. Express your answer as a single integer.",
"split": "train"
} |
math | [
"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 Let $S_n$ be the sum of the reciprocals of ... | math | {
"ground_truth": "63",
"style": "rule"
} | {
"answer": "63",
"index": 1688,
"question": "Let $S_n$ be the sum of the reciprocals of the non-zero digits of the integers from $1$ to $10^n$ inclusive. Find the smallest positive integer $n$ for which $S_n$ is an integer.",
"split": "train"
} |
big_math | [
"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 Find the total number of four-digit integer... | math | {
"ground_truth": "840",
"style": "rule"
} | {
"answer": "840",
"index": 1689,
"question": "Find the total number of four-digit integers between 1000 and 9999 with distinct digits where the absolute difference between the first and last digit is 2. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 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 the real numbers \\( a, b, c \\) sati... | math | {
"ground_truth": "38",
"style": "rule"
} | {
"answer": "38",
"index": 1690,
"question": "Given the real numbers \\( a, b, c \\) satisfy \\( a + b + c = 6 \\), \\( ab + bc + ca = 5 \\), and \\( abc = 1 \\), determine the value of \\( \\frac{1}{a^3} + \\frac{1}{b^3} + \\frac{1}{c^3} \\).",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Congruences"
] | 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 number of natural numbers \\( k \\... | math | {
"ground_truth": "4000",
"style": "rule"
} | {
"answer": "4000",
"index": 1691,
"question": "Find the number of natural numbers \\( k \\) not exceeding 267000 such that \\( k^{2} -1 \\) is divisible by 267.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 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 box contains three balls labeled with the... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"answer": "19",
"index": 1692,
"question": "A box contains three balls labeled with the numbers 1, 2, and 3, respectively. Each time a ball is drawn, its number is recorded and then the ball is returned to the box. If one draws balls three times, how many ways are there to obtain a maximum ball number of 3? Express your answer as a whole number.",
"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 In the expansion of $(x-3)(x-3^{2})(x-3^{3}... | math | {
"ground_truth": "-120",
"style": "rule"
} | {
"answer": "-120",
"index": 1693,
"question": "In the expansion of $(x-3)(x-3^{2})(x-3^{3})(x-3^{4})$, the coefficient of $x^{3}$ is _____. (Provide your answer as a number)",
"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 All possible three-digit natural numbers we... | math | {
"ground_truth": "298",
"style": "rule"
} | {
"answer": "298",
"index": 1694,
"question": "All possible three-digit natural numbers were made by picking three out of the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 and arranging them in a row. Among these, find the largest even number of no more than 300. ",
"split": "train"
} |
olympiads | [
"Mathematics -> Algebra -> 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 Let \\( Q(x) = x^2 + 2x + 3 \\), and suppos... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 1695,
"question": "Let \\( Q(x) = x^2 + 2x + 3 \\), and suppose that \\( P(x) \\) is a polynomial such that\n\\[ P(Q(x)) = x^6 + 6x^5 + 18x^4 + 32x^3 + 35x^2 + 22x + 8. \\]\n\nCompute \\( P(2) \\).",
"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 In the coordinate plane, we consider the fi... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 1696,
"question": "In the coordinate plane, we consider the figure \\( M \\), which consists of all points whose coordinates \\((x ; y)\\) satisfy the system of inequalities\n\n\\[\n\\left\\{\\begin{array}{l}\ny - x \\geqslant |x + y| \\\\\n\\frac{x^{2} + 8x + y^{2} + 6y}{2y - x - 8} \\leqslant 0\n\\end{array}\\right.\n\\]\n\nDepict the figure \\( M \\) and find its area.",
"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 Two trains of equal length are running on p... | math | {
"ground_truth": "86",
"style": "rule"
} | {
"answer": "86",
"index": 1697,
"question": "Two trains of equal length are running on parallel lines in the same direction at some speed and 36 km/hr. The faster train catches and completely passes the slower train in 72 seconds. The length of each train is 100 meters. What is the speed of the faster train in km/hr?",
"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 What is the largest integer for which each ... | math | {
"ground_truth": "81649",
"style": "rule"
} | {
"answer": "81649",
"index": 1698,
"question": "What is the largest integer for which each pair of consecutive digits is a square?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Probability -> 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 A foreign investor plans to invest in 3 dif... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"answer": "60",
"index": 1699,
"question": "A foreign investor plans to invest in 3 different projects across 4 candidate cities, with no more than 2 projects in the same city. Calculate the total number of different investment plans the investor can have.",
"split": "train"
} |
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