Datasets:
Tasks:
Text Generation
Modalities:
Text
Formats:
parquet
Languages:
English
Size:
10K - 100K
License:
data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The orchestra has more than 150 members but fewer than 250 members. When they line up in rows of 4, there are 2 extra members; when lined up in rows of 5, there are 3 extra; when... | math | {
"ground_truth": "58",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\\\(\\{a_n\\}\\\\) be a positive geometric sequence with \\\\(a_4=81\\\\), and the arithmetic mean of \\\\(a_2\\\\) and \\\\(a_3\\\\) is \\\\(\\dfrac{3}{2}(a_1+a_2)\\\\).\n\... | math | {
"ground_truth": "T_n= \\dfrac{n}{2n+1}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The vertices of a cube ABCD-A1B1C1D1 with edge length $a$ are all on the surface of a sphere $O$. $E$ and $F$ are the midpoints of edges $AA1$ and $DD1$, respectively. The length... | math | {
"ground_truth": "a\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $n$ is an integer such that $n \\ge 2^k$ and $n < 2^{k+1}$ , where $k = 1000$ , compute the following: $$ n - \\left( \\lfloor \\frac{n -2^0}{2^1} \\rfloor + \\lfloor ... | math | {
"ground_truth": "n - \\sum_{i=0}^{k-1} \\left\\lfloor \\frac{n}{2^{i+1}} \\right\\rfloor + k",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given real numbers $a, b,$ and $c$, such that $a^3 + b^3 + c^3 = 3abc$, consider the matrix\n\\[\n\\begin{pmatrix} a & b & c \\\\ c & a & b \\\\ b & c & a \\end{pmatrix}\n\\]\nis... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Together, the two positive integers $a$ and $b$ have $9$ digits and contain each of the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ exactly once. For which possible values of $a$... | math | {
"ground_truth": "\\frac{9876}{12345}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\\\(\\alpha \\in (0, 2\\pi)\\\\) and \\\\(\\sin \\alpha < 0\\\\), \\\\(\\cos \\alpha > 0\\\\), determine the range of angle \\\\(\\alpha\\\\).",
"role": "user"
}
] | math | {
"ground_truth": "(\\frac{3\\pi}{2}, 2\\pi)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A pipe with an inside diameter of 12 inches is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the in... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the center of the hyperbola \\(9x^2 - 54x - 36y^2 + 288y - 576 = 0.\\)",
"role": "user"
}
] | math | {
"ground_truth": "(3, 4)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A heavy concrete platform anchored to the seabed in the North Sea supported an oil rig that stood 40 m above the calm water surface. During a severe storm, the rig toppled over. ... | math | {
"ground_truth": "68.2 \\text{ meters}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the area, in square units, of a triangle whose vertices are at $(2, 2)$, $(2, -3)$, and $(7, 2)$?",
"role": "user"
}
] | math | {
"ground_truth": "12.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Six children take turns playing a game of doubles for 120 minutes, with only two children playing at a time. The number of minutes each child plays is\nA) 30 minutes\nB) 35 minut... | math | {
"ground_truth": "C) 40 minutes",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the cube \\( ABCD - A_1B_1C_1D_1 \\) with a side length of 2, \\( M \\) and \\( N \\) are the midpoints of edges \\( BB_1 \\) and \\( B_1C_1 \\) respectively. If \\( P \\) is ... | math | {
"ground_truth": "\\frac{2 \\sqrt{34}}{17}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider integers \\( S_k \\) analogously defined like \\( R_k \\) such that \\( S_k \\) represents \\( k \\)-length sequence of twos in its decimal presentation (for instance, \... | math | {
"ground_truth": "C) 20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $x$ in the equation $\\frac{45}{75} = \\sqrt{\\frac{x}{75}} + \\frac{1}{5}$?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. It is kno... | math | {
"ground_truth": "\\frac {8 \\sqrt {5}}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose S cans of soda are bought for Q quarters at a vending machine. A tax rate of t applies to every quarter spent (where t represents the tax as a fraction of 1, so a 10% tax... | math | {
"ground_truth": "\\frac{4DS(1 + t)}{Q}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a scale inaccurately measures weights below 50 pounds or over 200 pounds, and the weights of three parcels, obtained by weighing them in pairs, are 132 pounds, 145 pou... | math | {
"ground_truth": "213.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of $x$ such that $\\sqrt{x - 6} = 10$.",
"role": "user"
}
] | math | {
"ground_truth": "106",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $10 - 9^2 + 8 \\times 7 + 6^2 - 5 \\times 4 + 3 - 2^3$.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the greatest common divisor of the numbers $p^6-7p^2+6$ where $p$ runs through the prime numbers $p \\ge 11$ .",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If a class of 30 students is seated in a movie theater, then in any case, at least two classmates will be in the same row. If the same is done with a class of 26 students, then a... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the expression $\\frac{(2525 - 2424)^2 + 100}{225}$, calculate its value.",
"role": "user"
}
] | math | {
"ground_truth": "46",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The figure on the right shows the ellipse $\\frac{(x-19)^2}{19}+\\frac{(x-98)^2}{98}=1998$ .\nLet $R_1,R_2,R_3,$ and $R_4$ denote those areas within the ellipse that are in t... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Andrea has finished the third day of a six day canoe trip, having completed \\(\\frac{3}{7}\\) of the trip's total distance of 168 km. Calculate the distance Andrea must average ... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the probability of a contestant winning the quiz given that they answer at least 3 out of 4 questions correctly, assuming random guesses for each question with 3 possib... | math | {
"ground_truth": "\\frac{1}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $s (n)$ denote the sum of digits of a positive integer $n$ . Using six different digits, we formed three 2-digits $p, q, r$ such that $$ p \\cdot q \\cdot s(r) = p\\c... | math | {
"ground_truth": "(12, 36, 48)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Distribute 5 different books to 4 students, with each student receiving at least one book. There are $\\_ \\triangle \\_$ different distribution schemes.",
"role": "user"
}... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the repeating decimal $0.363636\\ldots$ is written in simplest fractional form, find the sum of the numerator and denominator.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given positive real numbers \\( x \\) and \\( y \\), let \\( a=x+y \\) and \\( b=\\sqrt{x^{2}+7xy+y^{2}} \\).\n\n(1) When \\( y=1 \\), find the range of values for \\( \\frac{b}{... | math | {
"ground_truth": "(1, 25)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the equation of the oblique asymptote of the graph of \\(\\frac{3x^2 + 8x + 12}{3x + 4}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "y = x + \\frac{4}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a cube with 4-inch edges constructed from 64 smaller cubes, each with 1-inch edges, find the fraction of the surface area that is green.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{24}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In parallelogram $ABCD$, angle $B$ measures $135^\\circ$. What is the number of degrees in the measure of angles $C$ and $A$?",
"role": "user"
}
] | math | {
"ground_truth": "45^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all the numbers formed by three different and non-zero digits, such that the six numbers obtained by\npermuting these digits leaves the same remainder after the divisio... | math | {
"ground_truth": "159",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given point F is the focus of the parabola $y^2=4x$, and M, N are two points on the parabola, with $|MF|+|NF|=6$, determine the x-coordinate of the midpoint of MN.",
"role": ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many $y$-intercepts does the graph of the parabola $x = 3y^2 - 5y + 9$ have?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any numbers \\( x \\) and \\( y \\), let \\( a = \\cos^2 x + \\cos^2 y - \\cos(xy) \\). Determine the range of values for \\( a \\).",
"role": "user"
}
] | math | {
"ground_truth": "(-3, 3)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A right pyramid has a rectangular base with length 12 cm and width 8 cm. Its peak is 15 cm directly above the center of its base. Calculate the total surface area of the pyramid,... | math | {
"ground_truth": "428.16 \\text{ cm}^2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\left(\\frac{1-i}{\\sqrt{2}}\\right)^{48}$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the remainder when $x^5 - 3x^3 + x + 5$ is divided by $(x - 3)^2.$",
"role": "user"
}
] | math | {
"ground_truth": "65",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point is chosen at random within the square in the coordinate plane whose vertices are (0, 0), (2020, 0), (2020, 2020), and (0, 2020). The probability that the point is within ... | math | {
"ground_truth": "0.4",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Add $1100_2$, $101_2$, $11_2$, $11011_2$, and $100_2$. Express your answer in base 2.",
"role": "user"
}
] | math | {
"ground_truth": "1000101_2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the inequality $x_1+x_2+\\dots + x_{13}\\leq 2006$, determine the number of positive integer tuples $(x_1,x_2,\\dots, x_{13})$ satisfying the inequality.",
"role": "use... | math | {
"ground_truth": "\\frac{2006!}{13!1993!}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the time it takes to send $100$ blocks of data over a communication channel if each block consists of $256$ chunks and the channel can transmit $150$ chunks per second,... | math | {
"ground_truth": "3.7222 \\text{ minutes}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "To create a civilized city, a patrol officer patrols on a motorcycle on an east-west avenue. One day, he departed from the guard post and stayed at point $A$ in the evening. The ... | math | {
"ground_truth": "3.1 \\text{ liters}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an integer $n\\geq 3$ . For each $3\\times3$ squares on the grid, call this $3\\times3$ square isolated if the center unit square is white and other 8 squares are blac... | math | {
"ground_truth": "4n",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The \fgure below shows a large square divided into $9$ congruent smaller squares. A shaded square bounded by some of the diagonals of those smaller squares has area $14$ . Fin... | math | {
"ground_truth": "63",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bricklayer Beth can build a wall in 8 hours, and bricklayer Ben can build it in 12 hours. When they work together, their chatting reduces their combined output by 8 bricks per ho... | math | {
"ground_truth": "C) 192",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the expansion of \\((x + 2)^n\\) where three consecutive terms have coefficients in the ratio \\(1:3:5\\). These can be expressed as \\[{n\\choose k} : {n\\choose k+1} :... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let Akbar and Birbal together have $n$ marbles, where $n > 0$ .\nAkbar says to Birbal, “ If I give you some marbles then you will have twice as many marbles as I will have.” \... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all real numbers $x$ for which the median of the numbers $3, 5, 7, 10,$ and $x$ is equal to the mean of those five numbers.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given tetrahedron $PQRS$ has $PQ=6$, $PR=4$, $PS=5$, $QR=5$, $QS=4$, and $RS=\\frac{7}{5}\\sqrt{11}$. Calculate the volume of the tetrahedron.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{2} \\sqrt{22}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the domain of the real-valued function $$f(x) = \\sqrt{-15x^2 + 13x + 8}.$$ Give the endpoints in your answer as common fractions, not mixed numbers or decimals.",
"role... | math | {
"ground_truth": "\\left[\\frac{13 - \\sqrt{649}}{30}, \\frac{13 + \\sqrt{649}}{30}\\right]",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a two-digit number, where the tens digit is $x$ and the units digit is $y$, find the difference between the number formed by swapping the tens and units digits and the orig... | math | {
"ground_truth": "-9x+9y",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that for a set of five distinct lines in a plane, there are exactly N distinct points that lie on two or more of these lines, find the sum of all possible values of N.",
... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a cone with a base area of $2\\pi$ and a lateral area of $4\\pi$, the volume of the cone is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {2 \\sqrt {6}}{3}\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the difference between the sum of the integers from 3001 to 3100 and the sum of the integers from 201 to 300.",
"role": "user"
}
] | math | {
"ground_truth": "280000",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a grid with 150 rows and 150 columns, numbered from 1 to 150, the shading pattern is as follows: In row 1, every box is shaded; in row 2, every second box is shaded; in row 3,... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that there are 100 seats in a saloon for 100 students. All students except one know their seat. First student (which is the one who doesn't know his seat) comes to the sa... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a rectangle where the perimeter is $p$ and the diagonal is $d$, calculate the area of the rectangle.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{p^2 - 4d^2}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If Art uses 120 sq inches of dough to make his cookies, and each cookie is an equilateral triangle with side length 4 inches, calculate the number of cookies Trisha can make from... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a semipro baseball league with 21 players on each team, where each player must be paid at least $15,000 and the total of all players' salaries for each team cannot exceed $... | math | {
"ground_truth": "400,000",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $2012$ distinct points in the plane, each of which is to be coloured using one of $n$ colours, so that the numbers of points of each colour are distinct. A set of ... | math | {
"ground_truth": "n = 61",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $\\frac{3a^{-1} + \\frac{2a^{-1}}{3}}{2a}$ when $a = 3$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{11}{54}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an isosceles triangle ABC, the base angles are \\(a^{\\circ}\\) and \\(b^{\\circ}\\) where \\(a = b\\) and \\(a + b\\) must sum to less than \\(180^{\\circ}\\) due to a small ... | math | {
"ground_truth": "\\textbf{(D)}\\ 59",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two concentric circles have radii in the ratio $2:5$. If $\\overline{AC}$ is a diameter of the larger circle, $\\overline{BC}$ is a chord of the larger circle that is tangent to ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of $a - b$ if the equation\n\\[\n\\frac{a}{2^x-2} + \\frac{b}{2^x+3} = \\frac{5 \\cdot 2^x + 4}{(2^x-2)(2^x+3)}\n\\]\nis an identity for positive rational val... | math | {
"ground_truth": "\\text{C) }\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ d_n$ be the determinant of the $ n\\times n$ matrix whose entries, from left to right and then from top to bottom, are $ \\cos 1,\\cos 2,\\dots,\\cos n^2.$ (For examp... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, where $\\angle A = 90^\\circ$, $BC = 15$, and $\\tan C = 3\\sin C$. What is $AB$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5\\sqrt{6}}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let point $O$ be the origin, and the coordinates of points $A$ and $B$ be $(a, 0)$ and $(0, a)$ respectively, where $a$ is a positive constant. Point $P$ lies on segment $AB$, an... | math | {
"ground_truth": "a^2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integer pairs \\((x, y)\\) that satisfy the equation \\(2x^2 + 5y^2 = 11(xy - 11)\\).",
"role": "user"
}
] | math | {
"ground_truth": "(14, 27)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The points $(x, y)$ represented in this table lie on a straight line. Determine the value of $y$ when $x = 50$ on the same line.\n\n\\[\n\\begin{tabular}{c|c}\n$x$ & $y$ \\\\ \\h... | math | {
"ground_truth": "155",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consecutive odd numbers are grouped as follows: $1 ;(3,5) ;(7,9,11) ;(13, 15, 17, 19) ; \\ldots$. Find the sum of the numbers in the $n$-th group.",
"role": "user"
}
] | math | {
"ground_truth": "n^3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the set of all ordered $6$ -tuples of nonnegative integers $(a,b,c,d,e,f)$ such that \\[a+2b+6c+30d+210e+2310f=2^{15}.\\] In the tuple with the property that $a+b+c+... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $x$, $y$, and $z$ are positive numbers satisfying:\n\\begin{align*}\nx^4/y &= 2, \\\\\ny^3/z &= 6, \\text{ and}\\\\\nz^2/x &= 8.\n\\end{align*}\nFind $x$.",
"role": "... | math | {
"ground_truth": "1/23",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive real solutions are there to $x^8 + 5x^7 + 10x^6 + 1728x^5 - 1380x^4 = 0$?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Out of three hundred eleventh-grade students, 77% received excellent and good grades on the first exam, 71% on the second exam, and 61% on the third exam. What is the minimum num... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $F\\_1$ and $F\\_2$ are the left and right foci of the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{2^2} = 1 (a > 0)$, and $P$ is a point on the hyperbola such that $\\an... | math | {
"ground_truth": "4\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The domain of the function $y= \\frac{ \\sqrt{x+4}}{x+2} $ is .",
"role": "user"
}
] | math | {
"ground_truth": "\\{x\\geqslant -4 \\text{ and } x\\neq -2\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let points $A = (0, 0)$, $B = (2, 3)$, $C = (5, 4)$, and $D = (6, 1)$. A quadrilateral $ABCD$ is divided by a line passing through $A$, which bisects its area. This line intersec... | math | {
"ground_truth": "C) 176",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The line $(1-2a)x-2y+3=0$ is perpendicular to the line $3x+y+2a=0$. Determine the value of the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{1}{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( S \\) be the set of points \\((x, y, z)\\) in \\(\\mathbb{R}^{3}\\) such that \\( x \\), \\( y \\), and \\( z \\) are positive integers less than or equal to 100. Let \\(... | math | {
"ground_truth": "30604",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the triangular park XYZ, where the distance from X to Y along the river is 4 miles, the distance from Y to Z along the river is 2 miles, and Z is directly south of X, separ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An object moves $10$ cm in a straight line from point $A$ to point $B$, then turns at an angle $\\alpha$ (measured in radians and randomly chosen from the interval $(0, \\pi)$), ... | math | {
"ground_truth": "\\textbf{(B) } \\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the rectangular coordinate system $(Oxyz)$, it is known that a normal vector of plane $(\\alpha)$ is $\\overrightarrow{n}=(1,-1,2)$, and plane $(\\alpha)$ passes through point... | math | {
"ground_truth": "x - y + 2z + 1 = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many non-congruent squares can be drawn such that their vertices are lattice points on a 6 by 6 grid of lattice points?",
"role": "user"
}
] | math | {
"ground_truth": "128",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $$(1 + i)z = 2i,$$ find the complex number $z$.",
"role": "user"
}
] | math | {
"ground_truth": "i + 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Concept learning \nDefinition: Several divisions of the same rational number (all not equal to $0$) are called division powers, such as $2\\div 2\\div 2$, $\\left(-3\\right)\\di... | math | {
"ground_truth": "-\\frac{31}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Parallelogram $ABCD$ is given such that $\\angle ABC$ equals $30^o$ . Let $X$ be the foot of the perpendicular from $A$ onto $BC$ , and $Y$ the foot of the perpendic... | math | {
"ground_truth": "880",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the base- $17$ integer $\\overline{8323a02421_{17}}$ (where a is a base- $17$ digit) is divisible by $\\overline{16_{10}}$ , find $a$ . Express your answer in ba... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Isosceles triangle $T$ has side lengths 7, 7, and 10. Calculate the inradius of the triangle. Which of the following is closest to the inradius?\nA) 1.9\nB) 2.0\nC) 2.1\nD) 2.2",... | math | {
"ground_truth": "\\textbf{C) 2.1}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Fix an integer $n\\geq4$ . Let $C_n$ be the collection of all $n$ –point configurations in the plane, every three points of which span a triangle of area strictly greater tha... | math | {
"ground_truth": "\\lceil n/3 \\rceil",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $PQR$, the medians $\\overline{PM}$ and $\\overline{QN}$ have lengths $15$ and $20$, respectively, and $PQ=30$. Extend $\\overline{QN}$ to intersect the circumcircle ... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n\\ge3$ be a positive integer. Find the real numbers $x_1\\ge0,\\ldots,x_n\\ge 0$ , with $x_1+x_2+\\ldots +x_n=n$ , for which the expression \\[(n-1)(x_1^2+x_2^2+\\ldots... | math | {
"ground_truth": "n^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A boy, standing on a horizontal surface of the ground at a distance $L=5$ m from a vertical wall of a house, kicked a ball lying in front of him on the ground. The ball flew at a... | math | {
"ground_truth": "2.5 \\text{ m}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the digits of an even ten-digit integer is 89. What is the last digit?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Convert the point \\((7, \\frac{\\pi}{4}, 8)\\) in cylindrical coordinates to rectangular coordinates.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{7\\sqrt{2}}{2}, \\frac{7\\sqrt{2}}{2}, 8\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many integers \\(n\\) between \\(1\\) and \\(100\\), inclusive, is \\[\\frac{(2n^2-1)!}{(2n!)^n}\\] an integer?\nA) 48\nB) 49\nC) 50\nD) 51\nE) 52",
"role": "user"
... | math | {
"ground_truth": "D) 51",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A recent poll showed that 55% of men and 80% of women are in favor of a new education policy. The study surveyed 200 men and 800 women. What was the overall percentage of the peo... | math | {
"ground_truth": "75\\%",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A ferry boat starts shuttling tourists to an island at 9 AM and continues every hour until its last trip at 3 PM. On the initial 9 AM trip, the ferry had 120 tourists, and on eac... | math | {
"ground_truth": "777",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
End of preview. Expand in Data Studio
rl-value-confidence-train-math
Math-domain training set (~10K) for a confidence / correctness estimator, sampled from the
numina portion of PRIME-RL/Eurus-2-RL-Data.
Pairs with YangyiYY/rl-value-eval-math
(eval) and a 50K RL-training split from the same pool (disjoint).
Sampled ~uniformly across the 6 numina sub-sources (cn_k12, synthetic_math, olympiads, synthetic_amc, aops_forum, amc_aime), deduplicated by problem text, and disjoint from the RL-train and eval splits (0 problem-text overlap).
Schema (our recipe)
data_source="math_box" · prompt=[{system: "Please reason step by step, and put your final answer within \boxed{}."}, {user: <problem>}] · ability="math" · reward_model.ground_truth (numina
answer) · sub_source (numina origin: cn_k12/synthetic_math/olympiads/synthetic_amc/aops_forum/amc_aime)
· extra_info (id, sub_source, split).
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