data_source stringclasses 2
values | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict | level stringclasses 3
values | problem_id stringlengths 20 26 |
|---|---|---|---|---|---|---|
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"index": 0,
"split": "with-guidance"
} | hard-with-guidance | hard-0-with-guidance |
without-guidance | [
{
"content": "Let $ ABP, BCQ, CAR$ be three non-overlapping triangles erected outside of acute triangle $ ABC$. Let $ M$ be the midpoint of segment $ AP$. Given that $ \\angle PAB \\equal{} \\angle CQB \\equal{} 45^\\circ$, $ \\angle ABP \\equal{} \\angle QBC \\equal{} 75^\\circ$, $ \\angle RAC \\equal{} 105^\\... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"index": 0,
"split": "without-guidance"
} | hard-without-guidance | hard-0-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "2\\omega(m) + 1",
"style": "rule"
} | {
"index": 2,
"split": "with-guidance"
} | hard-with-guidance | hard-1-with-guidance |
without-guidance | [
{
"content": "Let $m>1$ be an integer. Find the smallest positive integer $n$, such that for any integers $a_1,a_2,\\ldots ,a_n; b_1,b_2,\\ldots ,b_n$ there exists integers $x_1,x_2,\\ldots ,x_n$ satisfying the following two conditions: \n\ni) There exists $i\\in \\{1,2,\\ldots ,n\\}$ such that $x_i$ and $m$ ar... | math | {
"ground_truth": "2\\omega(m) + 1",
"style": "rule"
} | {
"index": 2,
"split": "without-guidance"
} | hard-without-guidance | hard-1-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\frac{38}{7}",
"style": "rule"
} | {
"index": 3,
"split": "with-guidance"
} | hard-with-guidance | hard-2-with-guidance |
without-guidance | [
{
"content": "Convex quadrilateral $ ABCD$ is inscribed in a circle, $ \\angle{A}\\equal{}60^o$, $ BC\\equal{}CD\\equal{}1$, rays $ AB$ and $ DC$ intersect at point $ E$, rays $ BC$ and $ AD$ intersect each other at point $ F$. It is given that the perimeters of triangle $ BCE$ and triangle $ CDF$ are both inte... | math | {
"ground_truth": "\\frac{38}{7}",
"style": "rule"
} | {
"index": 3,
"split": "without-guidance"
} | hard-without-guidance | hard-2-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\min(m, n)^{\\frac{1}{r} - \\frac{1}{s}}",
"style": "rule"
} | {
"index": 4,
"split": "with-guidance"
} | hard-with-guidance | hard-3-with-guidance |
without-guidance | [
{
"content": "Given two integers $m,n$ which are greater than $1$. $r,s$ are two given positive real numbers such that $r<s$. For all $a_{ij}\\ge 0$ which are not all zeroes,find the maximal value of the expression\n\\[f=\\frac{(\\sum_{j=1}^{n}(\\sum_{i=1}^{m}a_{ij}^s)^{\\frac{r}{s}})^{\\frac{1}{r}}}{(\\sum_{i=... | math | {
"ground_truth": "\\min(m, n)^{\\frac{1}{r} - \\frac{1}{s}}",
"style": "rule"
} | {
"index": 4,
"split": "without-guidance"
} | hard-without-guidance | hard-3-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "n - k",
"style": "rule"
} | {
"index": 5,
"split": "with-guidance"
} | hard-with-guidance | hard-4-with-guidance |
without-guidance | [
{
"content": "Given positive integers $n, k$ such that $n\\ge 4k$, find the minimal value $\\lambda=\\lambda(n,k)$ such that for any positive reals $a_1,a_2,\\ldots,a_n$, we have\n\\[ \\sum\\limits_{i=1}^{n} {\\frac{{a}_{i}}{\\sqrt{{a}_{i}^{2}+{a}_{{i}+{1}}^{2}+{\\cdots}{{+}}{a}_{{i}{+}{k}}^{2}}}}\n\\le \\lambd... | math | {
"ground_truth": "n - k",
"style": "rule"
} | {
"index": 5,
"split": "without-guidance"
} | hard-without-guidance | hard-4-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "258",
"style": "rule"
} | {
"index": 6,
"split": "with-guidance"
} | hard-with-guidance | hard-5-with-guidance |
without-guidance | [
{
"content": "Let $P_1P_2\\ldots P_{24}$ be a regular $24$-sided polygon inscribed in a circle $\\omega$ with circumference $24$. Determine the number of ways to choose sets of eight distinct vertices from these $24$ such that none of the arcs has length $3$ or $8$.",
"role": "user"
}
] | math | {
"ground_truth": "258",
"style": "rule"
} | {
"index": 6,
"split": "without-guidance"
} | hard-without-guidance | hard-5-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\[\n\\left(\\frac{n+1}{2}\\right)^2\n\\]",
"style": "rule"
} | {
"index": 7,
"split": "with-guidance"
} | hard-with-guidance | hard-6-with-guidance |
without-guidance | [
{
"content": "Consider an $n$ -by- $n$ board of unit squares for some odd positive integer $n$ . We say that a collection $C$ of identical dominoes is a maximal grid-aligned configuration on the board if $C$ consists of $(n^2-1)/2$ dominoes where each domino covers exactly two neighboring squares and the domino... | math | {
"ground_truth": "\\[\n\\left(\\frac{n+1}{2}\\right)^2\n\\]",
"style": "rule"
} | {
"index": 7,
"split": "without-guidance"
} | hard-without-guidance | hard-6-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "3 L",
"style": "rule"
} | {
"index": 10,
"split": "with-guidance"
} | hard-with-guidance | hard-7-with-guidance |
without-guidance | [
{
"content": "Some people like to write with larger pencils than others. Ed, for instance, likes to write with the longest pencils he can find. However, the halls of MIT are of limited height $L$ and width $L$. What is the longest pencil Ed can bring through the halls so that he can negotiate a square turn?",
... | math | {
"ground_truth": "3 L",
"style": "rule"
} | {
"index": 10,
"split": "without-guidance"
} | hard-without-guidance | hard-7-without-guidance |
without-guidance | [
{
"content": "Human explorers discover a solar system with 15 planets, 7 of which are Earth-like, and 8 are Mars-like. Each Earth-like planet requires 2 units of colonization effort, while each Mars-like planet requires only 1 unit. If the expedition has a total of 16 units of colonization effort available, how... | math | {
"ground_truth": "1141",
"style": "rule"
} | {
"index": 0,
"split": "without-guidance"
} | easy-without-guidance | easy-256-without-guidance |
without-guidance | [
{
"content": "Let $a,$ $b,$ and $c$ be constants, and suppose the inequality \\[\\frac{(x-a)(x-b)}{x-c} \\geq 0\\] is true if and only if either $x < -6$ or $20 \\leq x \\leq 23.$ Given that $a < b,$ find the value of $a + 2b + 3c.$",
"role": "user"
}
] | math | {
"ground_truth": "48",
"style": "rule"
} | {
"index": 1,
"split": "without-guidance"
} | easy-without-guidance | easy-257-without-guidance |
without-guidance | [
{
"content": "Alex is an agricultural business owner who grows a single type of crop, corn, on a large farm. This season, Alex has planted corn on 150 acres of land. Each acre of Alex's farm typically produces about 120 bushels of corn. \n\nThis year, due to favorable weather conditions, the yield increased by ... | math | {
"ground_truth": "19536",
"style": "rule"
} | {
"index": 2,
"split": "without-guidance"
} | easy-without-guidance | easy-258-without-guidance |
without-guidance | [
{
"content": "Jenna, whose spouse was a miner who tragically lost their life in a mining accident, is now committed to advocating for stricter safety regulations in the mining industry. She decides to organize a community meeting to raise awareness and gather support. Jenna plans to invite 85 people to the meet... | math | {
"ground_truth": "247.50",
"style": "rule"
} | {
"index": 3,
"split": "without-guidance"
} | easy-without-guidance | easy-259-without-guidance |
without-guidance | [
{
"content": "Let $x$ and $y$ be positive integers such that $7x^5 = 11y^{13}.$ Find the prime factorization of the minimum possible value of $x$ and determine the sum of the exponents and the prime factors.",
"role": "user"
}
] | math | {
"ground_truth": "31",
"style": "rule"
} | {
"index": 4,
"split": "without-guidance"
} | easy-without-guidance | easy-260-without-guidance |
without-guidance | [
{
"content": "In a press conference before the All-Star Game, nine All-Stars are taking questions. Four are from the Cubs, three are from the Red Sox, and two are from the Yankees. Additionally, the coach of the Cubs insists on sitting with his team. If teammates and their coach insist on sitting together, how ... | math | {
"ground_truth": "8640",
"style": "rule"
} | {
"index": 5,
"split": "without-guidance"
} | easy-without-guidance | easy-261-without-guidance |
without-guidance | [
{
"content": "For which integer $a$ does $x^2 - x + a$ divide $x^{15} + x + 100$?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 6,
"split": "without-guidance"
} | easy-without-guidance | easy-262-without-guidance |
without-guidance | [
{
"content": "A wealthy philanthropist named Mr. Thompson donates $5,000 each month to three different organizations that promote digital privacy. In addition, he decides to give a one-time bonus donation of $2,500 to one of the organizations during the holiday season. \n\nIf Mr. Thompson continues his monthly ... | math | {
"ground_truth": "182500",
"style": "rule"
} | {
"index": 7,
"split": "without-guidance"
} | easy-without-guidance | easy-263-without-guidance |
without-guidance | [
{
"content": "Alex has a rare phobia of balloons popping, called globophobia. To overcome their fear, Alex decides to take small steps by gradually exposing themselves to balloons in a controlled setting. On the first day, Alex bravely handles 3 balloons. Each day, they increase the number of balloons by 2 more... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"index": 8,
"split": "without-guidance"
} | easy-without-guidance | easy-264-without-guidance |
without-guidance | [
{
"content": "Evaluate the expression $(2(2(2(2(2(2(3+2)+2)+2)+2)+2)+2)+2)$.",
"role": "user"
}
] | math | {
"ground_truth": "446",
"style": "rule"
} | {
"index": 9,
"split": "without-guidance"
} | easy-without-guidance | easy-265-without-guidance |
without-guidance | [
{
"content": "An ambitious young woman named Aisha grew up in the small town of Allipur and recently moved to a large city to attend university. In Allipur, Aisha used to walk 2 kilometers to her local library every week. Now, in the city, the university library is 5 kilometers from her apartment, but she can u... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"index": 10,
"split": "without-guidance"
} | easy-without-guidance | easy-266-without-guidance |
without-guidance | [
{
"content": "This was a highly dangerous car rally. It began with a small and very narrow bridge, where one out of five cars would fall into the water. Then followed a terrifying sharp turn, where three out of ten cars would go off the road. Next, there was a dark and winding tunnel where one out of ten cars w... | math | {
"ground_truth": "69.76",
"style": "rule"
} | {
"index": 11,
"split": "without-guidance"
} | easy-without-guidance | easy-267-without-guidance |
without-guidance | [
{
"content": "If rose bushes are spaced about 2 feet apart, calculate the number of bushes needed to surround a circular patio whose radius is 15 feet.",
"role": "user"
}
] | math | {
"ground_truth": "47",
"style": "rule"
} | {
"index": 12,
"split": "without-guidance"
} | easy-without-guidance | easy-268-without-guidance |
without-guidance | [
{
"content": "The owner of an art restoration studio, Ms. Lee, offers apprenticeships to recent art school graduates. Each apprentice works on restoring paintings under her guidance. The studio has received 15 paintings for restoration this month. Ms. Lee has 3 apprentices working in her studio. Each apprentice... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 13,
"split": "without-guidance"
} | easy-without-guidance | easy-269-without-guidance |
without-guidance | [
{
"content": "A sample is divided into 5 groups, with a total of 160 data points in the first, second, and third groups, and a total of 260 data points in the third, fourth, and fifth groups, and the frequency of the third group is 0.20. Calculate the frequency of the third group.",
"role": "user"
}
] | math | {
"ground_truth": "70",
"style": "rule"
} | {
"index": 14,
"split": "without-guidance"
} | easy-without-guidance | easy-270-without-guidance |
without-guidance | [
{
"content": "The graph below shows the number of home runs in April for the top hitters in the league. What is the mean (average) number of home runs hit by these players?\n\n[asy]\ndraw((0,0)--(0,7)--(24,7)--(24,0)--cycle);\nlabel(\"KEY:\",(3,5));\nfill((3,2.5)..(3.5,2)..(3,1.5)..(2.5,2)..cycle);\nlabel(\"- o... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 15,
"split": "without-guidance"
} | easy-without-guidance | easy-271-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "4041",
"style": "rule"
} | {
"index": 12,
"split": "with-guidance"
} | hard-with-guidance | hard-8-with-guidance |
without-guidance | [
{
"content": "Let $S$ be the set of $3^{4}$ points in four-dimensional space where each coordinate is in $\\{-1,0,1\\}$. Let $N$ be the number of sequences of points $P_{1}, P_{2}, \\ldots, P_{2020}$ in $S$ such that $P_{i} P_{i+1}=2$ for all $1 \\leq i \\leq 2020$ and $P_{1}=(0,0,0,0)$. (Here $P_{2021}=P_{1}$.... | math | {
"ground_truth": "4041",
"style": "rule"
} | {
"index": 12,
"split": "without-guidance"
} | hard-without-guidance | hard-8-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\frac{3-\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": 14,
"split": "with-guidance"
} | hard-with-guidance | hard-9-with-guidance |
without-guidance | [
{
"content": "Anastasia is taking a walk in the plane, starting from $(1,0)$. Each second, if she is at $(x, y)$, she moves to one of the points $(x-1, y),(x+1, y),(x, y-1)$, and $(x, y+1)$, each with $\\frac{1}{4}$ probability. She stops as soon as she hits a point of the form $(k, k)$. What is the probability... | math | {
"ground_truth": "\\frac{3-\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": 14,
"split": "without-guidance"
} | hard-without-guidance | hard-9-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 16,
"split": "with-guidance"
} | hard-with-guidance | hard-10-with-guidance |
without-guidance | [
{
"content": "Let $A$ be as in problem 33. Let $W$ be the sum of all positive integers that divide $A$. Find $W$.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 16,
"split": "without-guidance"
} | hard-without-guidance | hard-10-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 18,
"split": "with-guidance"
} | hard-with-guidance | hard-11-with-guidance |
without-guidance | [
{
"content": "For each prime $p$, a polynomial $P(x)$ with rational coefficients is called $p$-good if and only if there exist three integers $a, b$, and $c$ such that $0 \\leq a<b<c<\\frac{p}{3}$ and $p$ divides all the numerators of $P(a)$, $P(b)$, and $P(c)$, when written in simplest form. Compute the number... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 18,
"split": "without-guidance"
} | hard-without-guidance | hard-11-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "118",
"style": "rule"
} | {
"index": 19,
"split": "with-guidance"
} | hard-with-guidance | hard-12-with-guidance |
without-guidance | [
{
"content": "Consider the cube whose vertices are the eight points $(x, y, z)$ for which each of $x, y$, and $z$ is either 0 or 1 . How many ways are there to color its vertices black or white such that, for any vertex, if all of its neighbors are the same color then it is also that color? Two vertices are nei... | math | {
"ground_truth": "118",
"style": "rule"
} | {
"index": 19,
"split": "without-guidance"
} | hard-without-guidance | hard-12-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "477",
"style": "rule"
} | {
"index": 20,
"split": "with-guidance"
} | hard-with-guidance | hard-13-with-guidance |
without-guidance | [
{
"content": "How many elements are in the set obtained by transforming $\\{(0,0),(2,0)\\} 14$ times?",
"role": "user"
}
] | math | {
"ground_truth": "477",
"style": "rule"
} | {
"index": 20,
"split": "without-guidance"
} | hard-without-guidance | hard-13-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\frac{\\sqrt{6}+\\sqrt{2}}{2}",
"style": "rule"
} | {
"index": 22,
"split": "with-guidance"
} | hard-with-guidance | hard-14-with-guidance |
without-guidance | [
{
"content": "Points $X$ and $Y$ are inside a unit square. The score of a vertex of the square is the minimum distance from that vertex to $X$ or $Y$. What is the minimum possible sum of the scores of the vertices of the square?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{6}+\\sqrt{2}}{2}",
"style": "rule"
} | {
"index": 22,
"split": "without-guidance"
} | hard-without-guidance | hard-14-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\sqrt[3]{\\frac{1-\\sqrt{33}}{2}}",
"style": "rule"
} | {
"index": 23,
"split": "with-guidance"
} | hard-with-guidance | hard-15-with-guidance |
without-guidance | [
{
"content": "Over all pairs of complex numbers $(x, y)$ satisfying the equations $$x+2y^{2}=x^{4} \\quad \\text{and} \\quad y+2x^{2}=y^{4}$$ compute the minimum possible real part of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt[3]{\\frac{1-\\sqrt{33}}{2}}",
"style": "rule"
} | {
"index": 23,
"split": "without-guidance"
} | hard-without-guidance | hard-15-without-guidance |
without-guidance | [
{
"content": "At the rally commemorating the 60th anniversary of the Chinese people's victory in the War of Resistance against Japan, two schools each send 3 representatives to speak in turns, criticizing the heinous crimes committed by the Japanese aggressors and praising the heroic deeds of the Chinese people... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"index": 16,
"split": "without-guidance"
} | easy-without-guidance | easy-272-without-guidance |
without-guidance | [
{
"content": "In triangle \\(ABC\\), points \\(P\\) and \\(Q\\) are taken on the base \\(AC\\) such that \\(AP < AQ\\). The lines \\(BP\\) and \\(BQ\\) divide the median \\(AM\\) into three equal parts. It is known that \\(PQ = 3\\).\n\nFind \\(AC\\).",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 17,
"split": "without-guidance"
} | easy-without-guidance | easy-273-without-guidance |
without-guidance | [
{
"content": "Mary is preparing for a Sunday service at her Christian Science Church, where she plans to hand out special bookmarks with inspirational quotes. She has 120 bookmarks and wants to distribute them equally among the 8 Sunday school classes. Each class should also receive an extra bookmark for the te... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 18,
"split": "without-guidance"
} | easy-without-guidance | easy-274-without-guidance |
without-guidance | [
{
"content": "The line $y = b-x$ where $0 < b < 6$ intersects the $y$-axis at $P$ and the line $x=6$ at $S$. If the ratio of the area of triangle $QRS$ to the area of triangle $QOP$ is 4:9, what is the value of $b$? Express the answer as a decimal to the nearest tenth.",
"role": "user"
}
] | math | {
"ground_truth": "3.6",
"style": "rule"
} | {
"index": 19,
"split": "without-guidance"
} | easy-without-guidance | easy-275-without-guidance |
without-guidance | [
{
"content": "A can complete a piece of work in 12 days. B is 33% less efficient than A. Determine the number of days it takes B to do the same piece of work.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 20,
"split": "without-guidance"
} | easy-without-guidance | easy-276-without-guidance |
without-guidance | [
{
"content": "Xiao Wang left home at 8:30 to visit a housing exhibition and returned home at 12:00, while his alarm clock at home was showing 11:46 when he got back. Calculate the time in minutes until the alarm clock will point to 12:00 exactly.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 21,
"split": "without-guidance"
} | easy-without-guidance | easy-277-without-guidance |
without-guidance | [
{
"content": "The High School Ten basketball conference has 10 teams. Each team plays every other conference team twice and also plays 5 games against non-conference opponents. Calculate the total number of games in a season involving the High School Ten teams.",
"role": "user"
}
] | math | {
"ground_truth": "140",
"style": "rule"
} | {
"index": 22,
"split": "without-guidance"
} | easy-without-guidance | easy-278-without-guidance |
without-guidance | [
{
"content": "Determine the order of operations in the expression\n\n$$\n1891-(1600: a+8040: a) \\times c \n$$\n\nand calculate its value when \\( a = 40 \\) and \\( c = 4 \\). Show how the expression can be modified without changing its numerical value.",
"role": "user"
}
] | math | {
"ground_truth": "927",
"style": "rule"
} | {
"index": 23,
"split": "without-guidance"
} | easy-without-guidance | easy-279-without-guidance |
without-guidance | [
{
"content": "Tim is choosing between two internet plans for his new apartment. Plan X does not have a base charge but costs 25 cents per GB of data used. Plan Y has an initial setup fee of $15 and charges 15 cents per GB of data used. How many gigabytes of data must Tim use for Plan Y to become the more cost-e... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"index": 24,
"split": "without-guidance"
} | easy-without-guidance | easy-280-without-guidance |
without-guidance | [
{
"content": "The yearly changes in the population census of a town for four consecutive years are, respectively, 25% increase, 25% increase, 25% decrease, 25% decrease. The net change over the four years, to the nearest percent, is:",
"role": "user"
}
] | math | {
"ground_truth": "-12",
"style": "rule"
} | {
"index": 25,
"split": "without-guidance"
} | easy-without-guidance | easy-281-without-guidance |
without-guidance | [
{
"content": "The café has enough chairs to seat $310_5$ people. If $3$ people are supposed to sit at one table, how many tables does the café have?",
"role": "user"
}
] | math | {
"ground_truth": "26",
"style": "rule"
} | {
"index": 26,
"split": "without-guidance"
} | easy-without-guidance | easy-282-without-guidance |
without-guidance | [
{
"content": "Factorize the expression $27x^6 - 512y^6$ and find the sum of all integer coefficients in its factorized form.",
"role": "user"
}
] | math | {
"ground_truth": "92",
"style": "rule"
} | {
"index": 27,
"split": "without-guidance"
} | easy-without-guidance | easy-283-without-guidance |
without-guidance | [
{
"content": "Find the sum of $453_6$, $436_6$, and $42_6$ in base 6.",
"role": "user"
}
] | math | {
"ground_truth": "1415_6",
"style": "rule"
} | {
"index": 28,
"split": "without-guidance"
} | easy-without-guidance | easy-284-without-guidance |
without-guidance | [
{
"content": "A person is waiting at the $A$ HÉV station. They get bored of waiting and start moving towards the next $B$ HÉV station. When they have traveled $1 / 3$ of the distance between $A$ and $B$, they see a train approaching $A$ station at a speed of $30 \\mathrm{~km/h}$. If they run at full speed eithe... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 29,
"split": "without-guidance"
} | easy-without-guidance | easy-285-without-guidance |
without-guidance | [
{
"content": "Xiaopang, Xiaodingding, Xiaoya, and Xiaoqiao have a total of 8 parents and 4 children in their four families. They are going to an amusement park together. The ticket pricing is as follows: Adult tickets are 100 yuan per person, children's tickets are 50 yuan per person. If there are 10 or more pe... | math | {
"ground_truth": "800",
"style": "rule"
} | {
"index": 30,
"split": "without-guidance"
} | easy-without-guidance | easy-286-without-guidance |
without-guidance | [
{
"content": "Entrepreneurs Vasiliy Petrovich and Petr Gennadievich opened a clothing factory \"ViP.\" Vasiliy Petrovich invested 200 thousand rubles, while Petr Gennadievich invested 350 thousand rubles. The factory was successful, and after a year, Anastasia Alekseevna approached them with an offer to buy par... | math | {
"ground_truth": "1000000",
"style": "rule"
} | {
"index": 31,
"split": "without-guidance"
} | easy-without-guidance | easy-287-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 26,
"split": "with-guidance"
} | hard-with-guidance | hard-16-with-guidance |
without-guidance | [
{
"content": "Compute the number of complex numbers $z$ with $|z|=1$ that satisfy $$1+z^{5}+z^{10}+z^{15}+z^{18}+z^{21}+z^{24}+z^{27}=0$$",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 26,
"split": "without-guidance"
} | hard-without-guidance | hard-16-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "75",
"style": "rule"
} | {
"index": 28,
"split": "with-guidance"
} | hard-with-guidance | hard-17-with-guidance |
without-guidance | [
{
"content": "Let $E$ be a three-dimensional ellipsoid. For a plane $p$, let $E(p)$ be the projection of $E$ onto the plane $p$. The minimum and maximum areas of $E(p)$ are $9 \\pi$ and $25 \\pi$, and there exists a $p$ where $E(p)$ is a circle of area $16 \\pi$. If $V$ is the volume of $E$, compute $V / \\pi$.... | math | {
"ground_truth": "75",
"style": "rule"
} | {
"index": 28,
"split": "without-guidance"
} | hard-without-guidance | hard-17-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"index": 29,
"split": "with-guidance"
} | hard-with-guidance | hard-18-with-guidance |
without-guidance | [
{
"content": "Compute the number of labelings $f:\\{0,1\\}^{3} \\rightarrow\\{0,1, \\ldots, 7\\}$ of the vertices of the unit cube such that $$\\left|f\\left(v_{i}\\right)-f\\left(v_{j}\\right)\\right| \\geq d\\left(v_{i}, v_{j}\\right)^{2}$$ for all vertices $v_{i}, v_{j}$ of the unit cube, where $d\\left(v_{i... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"index": 29,
"split": "without-guidance"
} | hard-without-guidance | hard-18-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "436",
"style": "rule"
} | {
"index": 30,
"split": "with-guidance"
} | hard-with-guidance | hard-19-with-guidance |
without-guidance | [
{
"content": "Let $P$ be the set of points $$\\{(x, y) \\mid 0 \\leq x, y \\leq 25, x, y \\in \\mathbb{Z}\\}$$ and let $T$ be the set of triangles formed by picking three distinct points in $P$ (rotations, reflections, and translations count as distinct triangles). Compute the number of triangles in $T$ that ha... | math | {
"ground_truth": "436",
"style": "rule"
} | {
"index": 30,
"split": "without-guidance"
} | hard-without-guidance | hard-19-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 32,
"split": "with-guidance"
} | hard-with-guidance | hard-20-with-guidance |
without-guidance | [
{
"content": "Two vertices of a cube are given in space. The locus of points that could be a third vertex of the cube is the union of $n$ circles. Find $n$.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 32,
"split": "without-guidance"
} | hard-without-guidance | hard-20-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "\\frac{56 \\pi \\sqrt{3}}{9}",
"style": "rule"
} | {
"index": 33,
"split": "with-guidance"
} | hard-with-guidance | hard-21-with-guidance |
without-guidance | [
{
"content": "Find the smallest possible area of an ellipse passing through $(2,0),(0,3),(0,7)$, and $(6,0)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{56 \\pi \\sqrt{3}}{9}",
"style": "rule"
} | {
"index": 33,
"split": "without-guidance"
} | hard-without-guidance | hard-21-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "2448",
"style": "rule"
} | {
"index": 34,
"split": "with-guidance"
} | hard-with-guidance | hard-22-with-guidance |
without-guidance | [
{
"content": "The squares of a $3 \\times 3$ grid are filled with positive integers such that 1 is the label of the upperleftmost square, 2009 is the label of the lower-rightmost square, and the label of each square divides the one directly to the right of it and the one directly below it. How many such labelin... | math | {
"ground_truth": "2448",
"style": "rule"
} | {
"index": 34,
"split": "without-guidance"
} | hard-without-guidance | hard-22-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "4030",
"style": "rule"
} | {
"index": 37,
"split": "with-guidance"
} | hard-with-guidance | hard-23-with-guidance |
without-guidance | [
{
"content": "Let $\\Delta A_{1} B_{1} C$ be a triangle with $\\angle A_{1} B_{1} C=90^{\\circ}$ and $\\frac{C A_{1}}{C B_{1}}=\\sqrt{5}+2$. For any $i \\geq 2$, define $A_{i}$ to be the point on the line $A_{1} C$ such that $A_{i} B_{i-1} \\perp A_{1} C$ and define $B_{i}$ to be the point on the line $B_{1} C$... | math | {
"ground_truth": "4030",
"style": "rule"
} | {
"index": 37,
"split": "without-guidance"
} | hard-without-guidance | hard-23-without-guidance |
without-guidance | [
{
"content": "A pedestrian is moving in a straight line towards a crosswalk at a constant speed of 3.6 km/h. Initially, the distance from the pedestrian to the crosswalk is 40 meters. The length of the crosswalk is 6 meters. What distance from the crosswalk will the pedestrian be after two minutes?",
"role"... | math | {
"ground_truth": "74",
"style": "rule"
} | {
"index": 32,
"split": "without-guidance"
} | easy-without-guidance | easy-288-without-guidance |
without-guidance | [
{
"content": "The perimeter of a semicircle with an area of ______ square meters is 15.42 meters.",
"role": "user"
}
] | math | {
"ground_truth": "14.13",
"style": "rule"
} | {
"index": 33,
"split": "without-guidance"
} | easy-without-guidance | easy-289-without-guidance |
without-guidance | [
{
"content": "Define a new function $\\$N$ such that $\\$N = 0.75N + 2$. Calculate $\\$(\\$(\\$30))$.",
"role": "user"
}
] | math | {
"ground_truth": "17.28125",
"style": "rule"
} | {
"index": 34,
"split": "without-guidance"
} | easy-without-guidance | easy-290-without-guidance |
without-guidance | [
{
"content": "Eight students from Adams school worked for $4$ days, six students from Bentley school worked for $6$ days, and seven students from Carter school worked for $10$ days. If a total amount of $\\ 1020$ was paid for the students' work, with each student receiving the same amount for a day's work, dete... | math | {
"ground_truth": "517.39",
"style": "rule"
} | {
"index": 35,
"split": "without-guidance"
} | easy-without-guidance | easy-291-without-guidance |
without-guidance | [
{
"content": "Given that a new kitchen mixer is listed in a store for $\\textdollar 129.99$ and an online advertisement offers the same mixer for four easy payments of $\\textdollar 29.99$ and a one-time shipping and handling fee of $\\textdollar 19.99$, calculate how many cents are saved by purchasing the mixe... | math | {
"ground_truth": "996",
"style": "rule"
} | {
"index": 36,
"split": "without-guidance"
} | easy-without-guidance | easy-292-without-guidance |
without-guidance | [
{
"content": "$10 \\cdot 52 \\quad 1990-1980+1970-1960+\\cdots-20+10$ equals:",
"role": "user"
}
] | math | {
"ground_truth": "1000",
"style": "rule"
} | {
"index": 37,
"split": "without-guidance"
} | easy-without-guidance | easy-293-without-guidance |
without-guidance | [
{
"content": "How many ways are there to arrange the letters of the word $\\text{B}_1\\text{A}_1\\text{N}_1\\text{A}_2\\text{N}_2\\text{A}_3\\text{B}_2$, where three A's, two N's, and two B's are all considered different within each letter group but identical between groups?",
"role": "user"
}
] | math | {
"ground_truth": "210",
"style": "rule"
} | {
"index": 38,
"split": "without-guidance"
} | easy-without-guidance | easy-294-without-guidance |
without-guidance | [
{
"content": "Interior numbers begin in the third row of Pascal's Triangle. Calculate the sum of the squares of the interior numbers in the eighth row.",
"role": "user"
}
] | math | {
"ground_truth": "3430",
"style": "rule"
} | {
"index": 39,
"split": "without-guidance"
} | easy-without-guidance | easy-295-without-guidance |
without-guidance | [
{
"content": "If an irrational number $a$ multiplied by $\\sqrt{8}$ is a rational number, write down one possible value of $a$ as ____.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"index": 40,
"split": "without-guidance"
} | easy-without-guidance | easy-296-without-guidance |
without-guidance | [
{
"content": "What percent of square $ABCD$ is shaded? All angles in the diagram are right angles. [asy]\nimport graph;\ndefaultpen(linewidth(0.7));\n\nxaxis(0,5,Ticks(1.0,NoZero));\nyaxis(0,5,Ticks(1.0,NoZero));\n\nfill((0,0)--(1,0)--(1,1)--(0,1)--cycle);\nfill((2,0)--(3,0)--(3,3)--(0,3)--(0,2)--(2,2)--cycle)... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"index": 41,
"split": "without-guidance"
} | easy-without-guidance | easy-297-without-guidance |
without-guidance | [
{
"content": "Calculate the result of $655_6 - 222_6 + 111_6$ in base-6.",
"role": "user"
}
] | math | {
"ground_truth": "544_6",
"style": "rule"
} | {
"index": 42,
"split": "without-guidance"
} | easy-without-guidance | easy-298-without-guidance |
without-guidance | [
{
"content": "Using 4 different colors to paint the 4 faces of a regular tetrahedron (each face is an identical equilateral triangle) so that different faces have different colors, how many different ways are there to paint it? (Coloring methods that remain different even after any rotation of the tetrahedron a... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 43,
"split": "without-guidance"
} | easy-without-guidance | easy-299-without-guidance |
without-guidance | [
{
"content": "The numbers \\(2^{2000}\\) and \\(5^{2000}\\) are written consecutively. How many digits are written in total?",
"role": "user"
}
] | math | {
"ground_truth": "2001",
"style": "rule"
} | {
"index": 44,
"split": "without-guidance"
} | easy-without-guidance | easy-300-without-guidance |
without-guidance | [
{
"content": "Given the conditions in the diagram, what is the ratio of the angles \\(\\frac{\\alpha}{\\beta}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 45,
"split": "without-guidance"
} | easy-without-guidance | easy-301-without-guidance |
without-guidance | [
{
"content": "Given\n$$\nS_{n}=|n-1|+2|n-2|+\\cdots+10|n-10| \\text {, }\n$$\nwhere \\( n \\in \\mathbf{Z}_{4} \\). Find the minimum value of \\( S_{n} \\).",
"role": "user"
}
] | math | {
"ground_truth": "112",
"style": "rule"
} | {
"index": 46,
"split": "without-guidance"
} | easy-without-guidance | easy-302-without-guidance |
without-guidance | [
{
"content": "Dr. Emma, a marine biologist from New Zealand, is studying the population of shell creatures in a coastal area. She discovers that there are 120 hermit crabs, 75 sea snails, and 45 scallops living in the region. During her study, she finds that every week, the population of hermit crabs increases ... | math | {
"ground_truth": "248.25",
"style": "rule"
} | {
"index": 47,
"split": "without-guidance"
} | easy-without-guidance | easy-303-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "4 p(p-1)",
"style": "rule"
} | {
"index": 38,
"split": "with-guidance"
} | hard-with-guidance | hard-24-with-guidance |
without-guidance | [
{
"content": "Let $p>2$ be a prime number. $\\mathbb{F}_{p}[x]$ is defined as the set of all polynomials in $x$ with coefficients in $\\mathbb{F}_{p}$ (the integers modulo $p$ with usual addition and subtraction), so that two polynomials are equal if and only if the coefficients of $x^{k}$ are equal in $\\mathb... | math | {
"ground_truth": "4 p(p-1)",
"style": "rule"
} | {
"index": 38,
"split": "without-guidance"
} | hard-without-guidance | hard-24-without-guidance |
with-guidance | [
{
"content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc... | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 39,
"split": "with-guidance"
} | hard-with-guidance | hard-25-with-guidance |
without-guidance | [
{
"content": "It is known that exactly one of the three (distinguishable) musketeers stole the truffles. Each musketeer makes one statement, in which he either claims that one of the three is guilty, or claims that one of the three is innocent. It is possible for two or more of the musketeers to make the same s... | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 39,
"split": "without-guidance"
} | hard-without-guidance | hard-25-without-guidance |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 18