Datasets:
Tasks:
Text Generation
Modalities:
Text
Formats:
parquet
Languages:
English
Size:
10K - 100K
License:
prompt listlengths 2 2 | data_source stringclasses 2
values | ability stringclasses 1
value | reward_model dict | extra_info dict | system stringclasses 1
value |
|---|---|---|---|---|---|
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "gray"
} | {
"index": 46915,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Mitranov I.V.\n\nThe King decided to reward a group of $n$ sages. They will be placed in a row, all facing ... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "n - k - 1"
} | {
"index": 47440,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized logistics network, a cargo vessel travels between $n$ consecutive maritime waypoints, inde... | polymath | math | {
"style": "rule",
"ground_truth": "2012"
} | {
"index": 11062,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a remote high-tech logistics network, there are $n$ independent server nodes, where $n > 4$. The network... | polymath | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 12178,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Dima is driving on a straight highway from point A to point B. From point B, a traffic jam is extending tow... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 15806,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a remote digital architecture firm, a designer is tasked with creating \"Safety Tilesets\" for various r... | polymath | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 14020,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Triangle \\(ABC\\) has circumcenter \\(O\\) and circumcircle \\(\\omega\\). Let \\(A_{\\omega}\\) be the po... | polymath | math | {
"style": "rule",
"ground_truth": "44"
} | {
"index": 3479,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Geometry"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For a nonnegative integer $n$, let $r_7(n)$ represent the remainder when $n$ is divided by $7$. Determine t... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 23896,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "M2. The diagram shows a circle that has been divided into six sectors of different sizes.\nTwo of the secto... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 34832,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In the city of Autolândia, car license plates are numbered with three-digit numbers ranging from 000 to 999... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "255"
} | {
"index": 27683,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Pick \\(x, y, z\\) to be real numbers satisfying \\((-x+y+z)^{2}-\\frac{1}{3}=4(y-z)^{2}, (x-y+z)^{2}-\\fra... | polymath | math | {
"style": "rule",
"ground_truth": "1727"
} | {
"index": 4299,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "Algebra"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The base of a quadrilateral pyramid $S A B C D$ is a parallelogram $A B C D$. 1) Construct a cross-section ... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 20769,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a remote archipelago, a research council has identified 11 unique mineral deposits, known as \"Core Site... | polymath | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 10571,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A specialized chemical engineering firm is testing a new catalytic stabilizer. The stability profile of a r... | polymath | math | {
"style": "rule",
"ground_truth": "49/6"
} | {
"index": 13006,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A specialized digital archive contains a collection of exactly 1000 unique data packets, each assigned a di... | polymath | math | {
"style": "rule",
"ground_truth": "2^{14}"
} | {
"index": 11149,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Three. (50 points)\nBefore the World Cup, the coach of country $F$ plans to evaluate 7 players, $A_{1}, A_{... | polymath | math | {
"style": "rule",
"ground_truth": "42244"
} | {
"index": 2956,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A remote weather research station uses a digital atmospheric pressure gauge that tracks a variable integer ... | polymath | math | {
"style": "rule",
"ground_truth": "250997"
} | {
"index": 10245,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "4. (22 points) Suppose a set of planar points $S$ has the following properties:\n(1) No three points are co... | polymath | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 3074,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 5 yellow pegs, 4 red pegs, 3 green pegs, 2 blue pegs, and 1 orange peg to be placed on a triangul... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 31402,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "volleyball"
} | {
"index": 41915,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Compute the number of ways to color the vertices of a regular heptagon red, green, or blue (with rotations ... | polymath | math | {
"style": "rule",
"ground_truth": "294"
} | {
"index": 2451,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let \\(a_{0}, a_{1}, \\ldots, a_{n}\\) be such that \\(a_{n} \\neq 0\\) and\n\n\\[\n\\left(1+x+x^{3}\\right... | polymath | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 5133,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Number\\ Theory"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "On each of the $1 \\times 1$ squares of the top row of an $8 \\times 8$ chessboard, there is a black pawn, ... | polymath | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 5642,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "Logic and Puzzles"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "google pixel 6"
} | {
"index": 41932,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are several pairs of integers $ (a, b) $ satisfying $ a^2 - 4a + b^2 - 8b = 30 $. Find the sum of the... | polymath | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 2840,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Algebra"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Twenty seven unit cubes are painted orange on a set of four faces so that two non-painted faces share an ed... | polymath | math | {
"style": "rule",
"ground_truth": "160"
} | {
"index": 4010,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized laboratory, a cubic data-storage module is being prepared for a high-security network. The... | polymath | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 10777,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let a positive integer \\( M \\) in base \\( n \\) be represented such that all its digits are distinct, an... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "2^{n+1}-2n-2"
} | {
"index": 32196,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For each integer $n$ greater than 1, let $G(n)$ be the number of solutions of the equation $\\sin x = \\sin... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "10296"
} | {
"index": 34460,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a remote forest, a circular wildlife sanctuary has been established with a radius of exactly 1 kilometer... | polymath | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 14818,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "On the board, 100 different integers are written. Each number Vasya raised either to the square or to the c... | polymath | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 2947,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "Number\\ Theory"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the maximum value of real number $A$ such that $$ 3x^2 + y^2 + 1 \\geq A(x^2 + xy + x) $$ for al... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "\\frac{5}{3}"
} | {
"index": 20893,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized logistics hub, security codes are generated to manage automated drones. A systems architec... | polymath | math | {
"style": "rule",
"ground_truth": "190"
} | {
"index": 10688,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find all triples $(a, b, c)$ of positive integers such that the expression $\\frac{32a + 3b + 48c}{4abc}$ i... | polymath | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 4825,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Number Theory"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Given the function \\( f: \\mathbb{N} \\to \\mathbb{N} \\) that satisfies \\( f(f(n+1) + f(n + f(n))) = n +... | polymath | math | {
"style": "rule",
"ground_truth": "2584"
} | {
"index": 5176,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "Algebra"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "If $\\sum_{n = 0}^{\\infty}\\sin^{2n}\\theta = 4$, what is the value of $\\sin{2\\theta}$?"
}
] | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2}"
} | {
"index": 19167,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A polynomial $P(x)$ is a \\emph{base-$n$ polynomial} if it is of the form $a_dx^d+a_{d-1}x^{d-1}+\\cdots + ... | polymath | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 4789,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Algebra"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized logistics simulation, a network analyst is calculating the \"Interference Coefficient\" of... | polymath | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 10698,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Aybike places any odd number of boxes around a circle and distributes $2013$ beads among some of these boxe... | polymath | math | {
"style": "rule",
"ground_truth": "1342"
} | {
"index": 5369,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For a nonnegative integer $n$ and a strictly increasing sequence of real numbers $t_0,t_1,\\dots,t_n$, let ... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "29"
} | {
"index": 25596,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a remote industrial logistics hub, there are exactly 29 unique shipping containers (calculated as $5^2 +... | polymath | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 12896,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The electricity price in a certain region last year was 0.80 yuan per kilowatt-hour, with an annual electri... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "0.60"
} | {
"index": 32757,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In an acute-angled triangle \\( \\triangle ABC \\), \\( BE \\) and \\( CF \\) are the altitudes. A circle w... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "M,P,N,Q"
} | {
"index": 28139,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a remote industrial zone, a specialized parabolic pipeline $K$ is modeled by the equation $y = \\frac{1}... | polymath | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 14752,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A swimmer goes downstream in a river from point \\( P \\) to point \\( Q \\), and then crosses a still lake... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "\\frac{15}{2}"
} | {
"index": 27106,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Given a $6 \\times 6$ grid, fill each cell with an integer between 1 and 6 (inclusive). Denote by $i \\diam... | polymath | math | {
"style": "rule",
"ground_truth": "122"
} | {
"index": 2510,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Determine the maximum $n \\geq 3$ such that there exists any $n$-gon where each angle is an integer and the... | polymath | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 2458,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "Geometry"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized digital archive, a security researcher is analyzing a set of unique access codes. Every co... | polymath | math | {
"style": "rule",
"ground_truth": "2232"
} | {
"index": 12471,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a triangle $ABC$, $AM$ is a median, $BK$ is the angle bisector of $\\angle ABC$, and $L$ is the intersec... | polymath | math | {
"style": "rule",
"ground_truth": "76"
} | {
"index": 4340,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Geometry"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $n$ be a positive integer. The numbers $\\{1, 2, \\ldots, n^2\\}$ are placed in an $n \\times n$ grid, ... | polymath | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 3347,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "soccer"
} | {
"index": 50972,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "69. $N$ oligarchs built a country with $N$ cities, each oligarch owns exactly one city. In addition, each o... | polymath | math | {
"style": "rule",
"ground_truth": "\\frac{N(N-1)(N-2)}{6}"
} | {
"index": 1567,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let \\( a \\) be the answer to Problem 19, \\( b \\) be the answer to Problem 20, and \\( c \\) be the answ... | polymath | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 4634,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Geometry"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A parking lot consists of 2012 parking spots equally spaced in a line, numbered 1 through 2012. One by one,... | polymath | math | {
"style": "rule",
"ground_truth": "2062301"
} | {
"index": 4728,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A unit side regular hexagonal lattice point is reflected to the midpoint of the six sides. Calculate the ar... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "\\dfrac{9\\sqrt{3}}{2}"
} | {
"index": 40063,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a domino game with 45 tiles, we draw 3 tiles one after another. What is the probability that the second ... | polymath | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 5366,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 41336,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "red"
} | {
"index": 47019,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $N$ be a positive integer. Consider a $N \\times N$ array of square unit cells. Two corner cells that l... | polymath | math | {
"style": "rule",
"ground_truth": "2n - 4"
} | {
"index": 5025,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Logic and Puzzles"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In the isosceles triangle $ABC$, the vertex angle is $B A C = \\alpha$. The base $BC$ is divided into $n$ e... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "\\frac{\\alpha}{2}"
} | {
"index": 22448,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "If the graph of the linear function $y=(7-m)x-9$ does not pass through the second quadrant, and the fractio... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 20924,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Question 3 Given $a b c=-1, a^{2} b+b^{2} c+c^{2} a=t$, $\\frac{a^{2}}{c}+\\frac{b}{c^{2}}=1$. Try to find ... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 36876,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "Peter"
} | {
"index": 34733,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "34. [?] The Game. Eric and Greg are watching their new favorite TV show, The Price is Right. Bob Barker rec... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 40250,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "Samantha"
} | {
"index": 47142,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "oneplus 9"
} | {
"index": 47664,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $\\Gamma_1, \\Gamma_2, \\Gamma_3$ be three pairwise externally tangent circles with radii $1,2,3,$ ... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "\\frac{8}{15}"
} | {
"index": 24374,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find all positive integers $a$ such that there exist infinitely many prime numbers $p$ for which $p \\nmid ... | polymath | math | {
"style": "rule",
"ground_truth": "110"
} | {
"index": 5552,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "\\text{Number Theory}"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $[n] = \\{1, 2, \\dots, n\\}$. We consider functions $f: 2^{[n]} \\to 2^{[n]}$ which satisfy $|A \\cap ... | polymath | math | {
"style": "rule",
"ground_truth": "1088"
} | {
"index": 3637,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Two boys were given a sack of potatoes, with $150$ tubers in each sack. The boys take turns moving the pota... | polymath | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 278,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "For positive real numbers \\(a, b, c\\),\n\\[\n(\\sqrt{a b}-1)(\\sqrt{b c}-1)(\\sqrt{c a}-1)=1\n\\]\nis sat... | polymath | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 4123,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Algebra"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let \\( Oxyz \\) be a three-dimensional Cartesian coordinate system and \\( S \\) a finite set of points in... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "|S|^2\\le|S_x|\\cdot|S_y|\\cdot|S_z|"
} | {
"index": 33850,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A father drives Xiao Hong to a point 1000 meters away from the school and lets her walk the rest of the way... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "12000\\,"
} | {
"index": 18740,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized cyber-security facility, a high-security vault requires a sequence of seven unique biometr... | polymath | math | {
"style": "rule",
"ground_truth": "4876"
} | {
"index": 14742,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "ranch"
} | {
"index": 34620,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Find the number of functions \\( f : \\{1, 2, 3, \\ldots, n\\} \\to \\{1, 2, 3, 4, 5\\} \\) such that \\( |... | polymath | math | {
"style": "rule",
"ground_truth": "\\( 2F_{n+2} \\)"
} | {
"index": 1633,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In the remote logistics hub of Aetheria, three specialized transport drones—Alpha, Beta, and Gamma—operate ... | polymath | math | {
"style": "rule",
"ground_truth": "\\( 3\\sqrt{26} \\)"
} | {
"index": 13438,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Three numbers are chosen independently at random, one from each of the three intervals $[0, L_i](i=1, 2,3)$... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 43471,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "An architect is designing three custom ventilation shafts for a high-tech facility, each characterized by i... | polymath | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 10922,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Given two lines $l_1: ax+2y+6=0$, and $l_2: x+(a-1)y+a^2-1=0$.\n(1) If $l_1 \\perp l_2$, find the value of ... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 12216,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "How many positive integers $n$ less than $1000$ have the property that the number of positive integers less... | polymath | math | {
"style": "rule",
"ground_truth": "41"
} | {
"index": 5629,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Number Theory"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized network of 10 data processing hubs, every hub is required to perform exactly one bilateral... | polymath | math | {
"style": "rule",
"ground_truth": "0"
} | {
"index": 11160,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Several sets of prime numbers, such as $\\{7,83,421,659\\}$ use each of the nine nonzero digits exactly onc... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "207"
} | {
"index": 14386,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized logistics network, a \"secure hub system\" of $n$ nodes is established. A system is consid... | polymath | math | {
"style": "rule",
"ground_truth": "298"
} | {
"index": 13756,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A specialized digital forensics team is analyzing a corrupted 158-digit encrypted transmission representing... | polymath | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 10530,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a specialized digital archive, a compression algorithm processes a sequence of data packets labeled with... | polymath | math | {
"style": "rule",
"ground_truth": "92"
} | {
"index": 13936,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Let $ABCD$ be an isosceles trapezoid with $\\overline{AD}||\\overline{BC}$ whose angle at the longer base $... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "32"
} | {
"index": 15935,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A shipping logistics manager is organizing a transport hub. A client arrives with a manifest listing severa... | polymath | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 13474,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A team of civil engineers is designing a reinforced structural joint where three different force stresses—r... | polymath | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 14359,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Five robbers took a wallet filled with ducats from a passerby. The strongest among them took 81 ducats, and... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "160"
} | {
"index": 45453,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In the competitive world of high-tech manufacturing, two corporations, Arasaka and Biotech, are battling fo... | polymath | math | {
"style": "rule",
"ground_truth": "625"
} | {
"index": 12342,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "The point $(1,1,1)$ is first reflected through the $yz$-plane, then rotated $90^\\circ$ about the $y$-axis,... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "(1, -1, -1)"
} | {
"index": 47758,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A circular tower has 16 doors, each hiding Captain Flint's gold, numbered from 1 to 16 in a clockwise direc... | polymath | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 5147,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Alice, Bob, and Carol each independently roll a fair six-sided die and obtain the numbers $a, b, c$, respec... | polymath | math | {
"style": "rule",
"ground_truth": "551"
} | {
"index": 3703,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0.5,
"problem_type": "Algebra"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "Given \\( N \\) different numbers on a blackboard, one of which is \\( 0 \\), one may take any polynomial w... | polymath | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 2883,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Algebra"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In the right triangle \\(ABC\\), segment \\(BH\\) is the altitude dropped onto the hypotenuse, and \\(BL\\)... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "\\arccos(\\frac{23}{4\\sqrt{37}})"
} | {
"index": 25644,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occup... | Polaris-Dataset-53K | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 34654,
"difficulty": "0/8",
"split": "train",
"config": null,
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "A circular high-security server farm contains 24 server racks, arranged in a perfect ring. The racks are in... | polymath | math | {
"style": "rule",
"ground_truth": "258"
} | {
"index": 11533,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "On the Cartesian grid, Johnny wants to travel from \\((0,0)\\) to \\((5,1)\\), and he wants to pass through... | polymath | math | {
"style": "rule",
"ground_truth": "252"
} | {
"index": 2267,
"difficulty": null,
"split": "train",
"config": "normal",
"oss_20b_low_pass_rate": 0,
"oss_20b_medium_pass_rate": 0,
"problem_type": "Combinatorics"
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
[
{
"role": "system",
"content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}."
},
{
"role": "user",
"content": "In a remote industrial logistics hub, a quality control inspector is evaluating a specific type of \"bulk b... | polymath | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 14117,
"difficulty": null,
"split": "train",
"config": "revised",
"oss_20b_low_pass_rate": null,
"oss_20b_medium_pass_rate": null,
"problem_type": null
} | You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}. |
End of preview. Expand in Data Studio
recursive-rl-hard-mix
A training set of hard math problems with verifiable final answers, mixed so that Qwen3.5-4B starts near 30% accuracy. Built for RL experiments in which the model can call copies of itself as a tool.
Contents
| split | problems | by source |
|---|---|---|
| train | 17,058 | polymath: 10,090, Polaris-Dataset-53K: 6,968 |
| test | 510 | polymath: 340, Polaris-Dataset-53K: 170 |
Columns follow the verl RL layout: prompt (a system and a user message), data_source,
ability, reward_model (ground_truth is the final answer), extra_info (index in the
source set and its difficulty fields), system.
Sources
- AIMO-Corpus/PolyMath (CC-BY-4.0): olympiad-style problems gathered for the AI
Mathematical Olympiad, both configs:
revised(rewritten to have an integer answer) andnormal(answers in their original form). All problems with an answer of at most 60 characters.data_source = "polymath". - POLARIS-Project/Polaris-Dataset-53K (Apache-2.0): the hardest tier, difficulty
0/8(none of 8 samples of the set's reference model correct). 7,000 of its 15,250 problems.data_source = "Polaris-Dataset-53K".
Please cite the two source datasets when using this mix.
Difficulty for Qwen3.5-4B
Measured on 2026-10-03 with Qwen/Qwen3.5-4B (thinking off, 16k response budget, temperature
1.0, 128 held-out problems x 4 samples), an answer counted correct if the strict
\boxed{} match or math_verify accepts it:
| part | accuracy | truncated at 16k | problems solved 0/4, 1-3/4, 4/4 |
|---|---|---|---|
| PolyMath revised | 13.9% | 18% | 87, 37, 4 |
| PolyMath normal | 12.3% | 14% | 90, 35, 3 |
| Polaris 0/8 | 56.0% | 10% | 27, 50, 40 |
The mix is about 59% PolyMath and 41% Polaris by problem count, so about 31% expected. Many gold answers are expressions, not plain numbers; a string-match checker undercounts (by 10 points on Polaris here), so score with a symbolic verifier.
Splits
train is shuffled with a fixed seed. test holds 170 problems from each part's own
held-out split; none of them appears in train.
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