context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 425 187k |
|---|---|---|---|---|---|---|
[
{
"content": "Problem: Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ and $BC$ of triangle $ABC$ , respectively. $2024$ circles of radius $1$ can be arranged in the same manner. The inradius of triangle $ABC$ can be expressed as $\\frac{m}{n}$ , w... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 22 | AIME24 | {
"expected_answer": "197",
"problem_id": "aime24-22",
"reference_solution": "Draw an altitude from both end circles of the diagram with the circles of radius one, and call the lengths you get drawing the altitudes of the circles down to $BC$ $a$ and $b$ . Now we have the length of side $BC$ of being $(2)... | We are given that eight circles of radius 34 are sequentially tangent, with two of them tangent to the sides AB and BC of triangle ABC. The problem states that 2024 circles of radius 1 can be arranged in the same manner. We need to find the inradius of triangle ABC expressed as \(\frac{m}{n}\) where \(m\) and \(n\) are... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Consider an ionic solid $\\mathbf{M X}$ with $\\mathrm{NaCl}$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 133 | JEEBench | {
"expected_answer": "3",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the ratio of the number of anions to the number of cations in the modified structure Z, starting from the NaCl structure. Let's go through each step of the problem systematically.
### Step 1: Understanding the NaCl Structure
The NaCl structure is a face-centered cubic (FCC) ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given an integer sequence A=(A_1,A_2,\\ldots,A_N) of length N and integers L and R such that L\\leq R.\nFor ea... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 333 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to find for each element in the array A, the X_i that satisfies two conditions. X_i is between L and R, and for every Y in [L, R], the absolute difference between X_i and A_i is less than or equal to the absolute difference between Y and A_i. Hmm, so X_i is the value in [L, R] th... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: For $x \\in \\mathbb{R}$, let $\\tan ^{-1}(x) \\in\\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right)$. Then what... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 492 | JEEBench | {
"expected_answer": "0",
"problem_id": "8",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To find the minimum value of the function \( f(x) = \int_{0}^{x \tan^{-1} x} \frac{e^{(t - \cos t)}}{1 + t^{2023}} \, dt \), we need to analyze the behavior of the integrand and the limits of integration.
First, let's consider the integrand \( g(t) = \frac{e^{(t - \cos t)}}{1 + t^{2023}} \). We need to understand how ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a non-empty string S consisting of (, ), and ?.\r\nThere are 2^x ways to obtain a new string by replacin... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 252 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes a string S as input and returns the number of ways to replace the '?' with parentheses so that the resulting string is a valid parenthesis string. The answer should be modulo 998244353. Hmm.
First, I need to understand what makes a parenthesis strin... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 252 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the minimum number of operations to make all nodes in a tree have zero value. The operations are performed in a specific way: for the first n operations, each operation is on node i, and for operations beyond n, each is on the same node as the i... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 332 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to assign numbers to each dragon such that each dragon's number is the mex (minimum excluded value) of the numbers of its friends. And the friends are the usual next ones, plus x and y being friends.
So, the problem is to generate a sequence a_1 to a_n where ea... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The treatment of an aqueous solution of $3.74 \\mathrm{~g}$ of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 403 | JEEBench | {
"expected_answer": "0.32",
"problem_id": "40",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's see. I need to figure out the amount of product X formed when treating a solution of 3.74 g of Cu(NO3)2 with excess KI, leading to a precipitate X. Then passing H2S through the brown solution gives X. Hmm, so there are a few steps here. Let me break it down.
First, I should write the chemical equat... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 32 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to count the number of different deterministic max-heaps created by applying exactly k add operations. The answer should be modulo p. Hmm.
First, I need to understand the problem thoroughly. Let's go through the description again. The key points are th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array nums. The uniqueness array of nums is the sorted array that contains the number of distinct elements of all the subarrays of num... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 491 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to find the median of the uniqueness array of a given nums array. The uniqueness array is the sorted array of the number of distinct elements in all possible subarrays. Hmm. So the median is the middle element of this sorted array. If even length, take ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: An animal has adipoidnumber of 8. During meiosis, how many chromatids are present a)inthe tetrad stage? b) In latetelophaseof the first meiotic divis... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 173 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's think through this step by step. The problem is about meiosis and the number of chromatids at different stages. Let's start by understanding the given information and each stage.
First, the animal's adipoid number is 8. Adipoid number refers to the number of fat cells, but in the context of meiosis, perhaps it's... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums of non-negative integers and an integer k.\nAn array is called special if the bitwise OR of all of its elements is at least k.\nRet... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 483 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the shortest subarray whose bitwise OR is at least k. Hmm. The problem is similar to finding the minimum length subarray with a certain OR value. Hmm.
First, I remember that for maximum length subarray problems with OR, there's a sliding window approach. But here, we need the mi... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are at a fruit market with different types of exotic fruits on display.\nYou are given a 1-indexed array prices, where prices[i] denotes the number of coin... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 137 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum number of coins required to buy all the fruits. The market has this offer where if you buy the i-th fruit, you can get the next i fruits for free. But you can still buy those next i fruits if you want. So the decision to take the free fruits or buy them affects the to... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A hot air balloon is carrying some passengers, and a few sandbags of mass $1 \\mathrm{~kg}$ each so that its t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 278 | JEEBench | {
"expected_answer": "4",
"problem_id": "4",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the number of sandbags \( N \) that must be thrown out of the hot air balloon so that it rises to a new equilibrium height of 150 meters. The key here is to understand the principles of buoyancy and how the density of air changes with height.
### Step 1: Understanding Buoyan... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 414 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about minimizing the range of an array after performing certain operations. Each operation allows Dora to increase an element by a or b. The range is the max minus min, so our goal is to make all elements as close as possible in value.
First, I need to under... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S of length N consisting of lowercase English letters.\nFind the number of non-empty substrings... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 328 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of non-empty substrings of S that are repetitions of one character. Hmm. So the problem is asking for all possible substrings (contiguous characters) in the string S that consist of the same character repeated any number of times, and each such substring must be counte... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 334 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about using stamps (rectangles) to cover a grid and find the minimum possible sum of the perimeters of the connected black regions after all stamps are used. Each stamp can be placed anywhere, and overlapping is allowed. But the key is to arrange the stamps i... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N sellers and M buyers in an apple market.\nThe i-th seller may sell an apple for A_i yen or more (yen is th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 251 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum integer X such that the number of sellers who are willing to sell at X or more is greater than or equal to the number of buyers willing to buy at X or less. Hmm.
So the problem is about finding the smallest X where the count of sellers with A_i >= X is >= the count o... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 65 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have barrels connected by pipes, and by adding clay to them, I can affect the water distribution and the pipes' effectiveness. The goal is to maximize the water in the first barrel. Hmm.
First, I need to understand how the clay affects the system. Each time... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.In the Kingdom of AtCoder, a week consists of A+B days, with the first through A-th days being holidays and the (A+1)-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 412 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Takahashi has N plans scheduled D_i days later, and I have to determine if all of them can fall on holidays. The weeks here are A+B days long. The first A days are holidays, then the next B days are weekdays. So, the week repeats every A+B days.
The input giv... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 380 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm. So the problem is about a circuit with n lights and 2n switches. Each light is connected to two switches, and each switch connects to exactly one light. The initial state is all switches given. We need to find the min and max number of lights that can be on after optimally ... |
[
{
"content": "Problem: Below is a magic square, meaning that the sum of the numbers in each row, in each column, and in each of the $2$ main diagonals are equal. What is the value of $n$?\n\n[asy]size(125);\nfor(int i = 0; i<4; ++i)\n{\n\ndraw((0,i)--(3,i),linewidth(1));\n}\n\nfor(int j = 0; j<4; ++j)\n{\n\ndra... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 473 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \( n \) in the given magic square, we need to ensure that all rows, columns, and diagonals sum to the same value. Let's denote the magic sum by \( S \).
First, let's list all the elements in the magic square. The given elements are:
- Rows: \( n-3 \), 3, \( n+1 \)
- Middle row: \( n+2 \), \( 2n-9 \), 1
- ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $\\vec{a}$ and $\\vec{b}$ be two unit vectors such that $\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 147 | JEEBench | {
"expected_answer": "3",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the problem, we need to determine the value of \(8 \cos^2 \alpha\) where \(\alpha\) is the angle between the vector \(\vec{c}\) and both unit vectors \(\vec{a}\) and \(\vec{b}\). Given that \(\vec{a} \cdot \vec{b} = 0\), \(\vec{c} = x \vec{a} + y \vec{b} + (\vec{a} \times \vec{b})\), and \(|\vec{c}| = 2\), we ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string $s$ of length $n$, consisting of lowercase Latin letters, and an integer $k$.\n\nYou need to ch... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 3 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to determine if there's a way to remove exactly k characters from the string s such that the remaining characters can be rearranged into a palindrome. Hmm. So the problem is checking if after deleting k characters, the frequency counts of each character allow forming a palindrome.
For a... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: $R=\\left\\{\\left(\\begin{array}{lll}a & 3 & b \\\\ c & 2 & d \\\\ 0 & 5 & 0\\end{array}\\right): a, b, c, d ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 496 | JEEBench | {
"expected_answer": "3780",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To find the number of invertible matrices in the set \( R \), we need to determine for which matrices \( A \in R \) the determinant is non-zero. The set \( R \) consists of \( 3 \times 3 \) matrices where the entries are from the set \(\{0,3,5,7,11,13,17,19\}\). Let's denote this set as \( S = \{0,3,5,7,11,13,17,19\} \... |
[
{
"content": "Problem: What integer $n$ satisfies $0\\le n<18$ and $$n\\equiv -11213141\\pmod{18}~?$$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 130 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | We need to find an integer \( n \) such that \( 0 \leq n < 18 \) and \( n \equiv -11213141 \pmod{18} \). This means we need to find the remainder when \(-11213141\) is divided by \(18\). Let's compute this step by step.
First, we can simplify the problem by finding the remainder of \(11213141\) when divided by \(18\) ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 265 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a game played on a tree where Alice and Bob take turns moving along the path from u to v. The path is given as p_1 to p_m, where p_1 is u and p_m is v. The path is the shortest path between u and v. The game starts with Alice at vertex 1 and Bob at p_j ... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $\\alpha$ and $\\beta$ be real numbers such that $-\\frac{\\pi}{4}<\\beta<0<\\alpha<\\frac{\\pi}{4}$. If $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 412 | JEEBench | {
"expected_answer": "1",
"problem_id": "1",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve the given problem, we start by analyzing the given trigonometric equations and the expression we need to evaluate. The problem states that \(\sin (\alpha + \beta) = \frac{1}{3}\) and \(\cos (\alpha - \beta) = \frac{2}{3}\). We need to find the greatest integer less than or equal to the square of the expression... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 435 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to find the smallest possible value of the sum of GCDs from the prefix of a sorted array. Oh right, after rearranging the array elements in any order. So the key here is to arrange the numbers such that each step's GCD is as small as possible.
Let me think abo... |
[
{
"content": "Problem: Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take turns with Alice going first. On each turn, the player removes either $1$ token or $4$ tokens from the stack. Whoever removes the last token wins. Find the number of positive integers $n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 17 | AIME24 | {
"expected_answer": "809",
"problem_id": "aime24-17",
"reference_solution": "Let's first try some experimentation. Alice obviously wins if there is one coin. She will just take it and win. If there are 2 remaining, then Alice will take one and then Bob will take one, so Bob wins. If there are $3$ , Alice will t... | We need to determine the number of positive integers \( n \) less than or equal to 2024 for which Bob can guarantee a win regardless of Alice's choices. The game involves removing 1 or 4 tokens each turn, and the player who removes the last token wins.
First, we analyze the game using the concept of winning and losing... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal{P}$ we took crosses one of th... | To solve the problem, we need to determine the difference between the radius of the circle along which the torus is internally tangent to the sphere and the radius of the circle along which it is externally tangent. Let's break down the problem step by step.
### Step 1: Understanding the Torus and Sphere Configuration... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.An ant is on a boundary. It sometimes goes left and sometimes right.\nYou are given an array of non-zero integers nums. The ant starts reading nums from the fi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 182 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that counts how many times an ant returns to the boundary while moving according to the nums array. Hmm.
So the ant starts at the boundary. For each element in the array, it moves left or right based on the value. If the current element is negative, it moves l... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s representing a 12-hour format time where some of the digits (possibly none) are replaced with a \"?\".\n12-hour times are formatted as... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 475 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to replace all the '?' in a time string to get the latest possible valid time. Let's see. The input is a string in the format "HH:MM", but some digits are replaced with '?'. The output should be the latest valid time possible by replacing those '?'s.
First, let's... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You have prepared a di-substituted 6-membered aromatic ring compound. The FTIR spectrum of this compound shows absorption peaks indicating the presence of an ester group... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 52 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's break down the problem step by step.
First, the compound is a di-substituted 6-membered aromatic ring. This means the ring is benzene (since it's 6 members) with two substituents. The FTIR shows an ester group, which implies one of the substituents is an ester (like -COOR). The 1H NMR has six signals: two aromat... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 255 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that we have two permutations a and b, and we need to find a sequence of at most 2n operations to transform a into b. If it's not possible, output -1.
First, I need to understand the allowed operations. Each operation involves choosing an index ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: While solving higher dimensional heat equations subject to suitable initial and boundary conditions through higher order finite difference approximations and parallel sp... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 83 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the key factor that converts a sequential algorithm into a parallel algorithm when approximating the matrix exponential function in higher-dimensional heat equations, let's analyze each option step by step.
**Problem Analysis:**
The problem is about converting a sequential algorithm into a parallel one fo... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A uniform electric field exists in a region between two oppositely charged plates. An electron is released from rest at the surface of the negatively... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 424 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the speed of an electron as it strikes the opposite plate after being accelerated by a uniform electric field. Let's break down the problem step by step.
1. **Understanding the Problem:**
- The electron starts from rest at the negatively charged plate.
- It travels 2.0... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Discuss three indicators of emotion.\nOptions: A. Mood swings, depression, anxiety, B. Social media usage, internet browsing habits, television viewi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 30 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to identify three indicators of emotion from the given options. Let's analyze each option step by step:
Option A: Mood swings, depression, anxiety. These are all emotional states, but they are more specific conditions rather than general indicators. For example, mood swings indicate chan... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 172 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to reduce a grid by a factor of k. So the grid is n x n, and k is a divisor of n. The way to reduce it is by splitting into k x k blocks and replacing each block with the average (but since the blocks are all same value, it's just the value of any cell ... |
[
{
"content": "Problem: Solve for the positive value of $x$ such that $\\sqrt[3]{x^2 - 4x + 4} = 16$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 346 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | We start with the equation given:
\[
\sqrt[3]{x^2 - 4x + 4} = 16
\]
First, we eliminate the cube root by cubing both sides of the equation. This gives:
\[
x^2 - 4x + 4 = 16^3
\]
Next, we calculate \(16^3\):
\[
16^3 = (4^2)^3 = 4^6 = 4096
\]
So the equation becomes:
\[
x^2 - 4x + 4 = 4096
\]
We then move all ter... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 42 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about Nikita building a tower by adding or removing cubes one at a time. We need to determine if after exactly n moves, the tower can have m cubes. Hmm.
So each move, he either adds 1 or removes 1. The initial tower is empty. So after n moves, what's the possible range of cubes ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array coins representing coins of different denominations and an integer k.\nYou have an infinite number of coins of each denomination... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 477 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to find the k-th smallest amount that can be made using the given coins, where each coin can be used multiple times but not combined. Hmm. Let's think about this.
So the coins are like [3,6,9] in the first example. Each coin generates multiples of its value. The possible amounts are the union of a... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given 2 integer arrays nums1 and nums2 of lengths n and m respectively. You are also given a positive integer k.\nA pair (i, j) is called good if nums1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 504 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the number of good pairs between two arrays. A good pair (i,j) is one where nums1[i] is divisible by nums2[j] multiplied by k. Hmm. Let's see.
First, let's understand the problem. For each element in nums1 (i), I need to check how many elements in nums2 (... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 358 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, so the problem is about Alice and Bob playing a game with boolean values and operators. The goal is to determine who wins if both play optimally. Let's try to understand the problem step by step.
So, the initial setup is a string of n boolean values (0s and 1s). The player... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 148 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem says that Kmes needs to divide the cards into the minimum number of bad segments such that each segment is bad. A segment is bad if there's no subset of cards in it whose product equals x. So, the goal is to split the array into the least number of contiguous se... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A particle moves with $v=$ const. along the curve $r=k(1+\\cos \\theta)$ (a cardioid). Find $\\ddot{\\mathbf{r}} \\cdot \\mathbf{e}_r=\\mathbf{a} \\c... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 117 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the radial component of the particle's acceleration as it moves along a cardioid curve with constant speed. Let's break down the solution step by step.
First, recall that the particle's velocity is constant in magnitude, \( v \). The curve is given by \( r = k(1 + \cos \theta) \)... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 318 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem says that Monocarp receives one of m lists of questions, each with n-1 questions. For each list, we need to determine if he knows all the questions in that list. If he does, output 1, else 0.
So the key here is that each list i has exactly n-1 questions, and t... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N sports players.\nAmong them, there are M incompatible pairs. The i-th incompatible pair (1\\leq i\\leq M) ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 241 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that calculates the number of ways to divide N players into T teams such that no incompatible pairs are in the same team. The input is N, T, M, followed by M incompatible pairs. The output is the count of valid divisions.
Hmm. The problem seems combinatorial. ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 366 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about determining if we can transform sequence a into sequence b using some operations. The operation allows erasing two numbers that are within 1 of each other and replacing them with their sum. Hmm.
Wait, the key here is to figure out if the multiset of a and b are the same. B... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 268 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about folding segments and finding the number of folding sequences that result in the shortest possible interval. The key here is to understand the operations LTR and RTL and how they affect the possible folding sequences.
First, I need to figure out what th... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: With respect to hypochlorite, chlorate and perchlorate ions, choose th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 254 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "29",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement regarding the hypochlorite (ClO⁻), chlorate (ClO₃⁻), and perchlorate (ClO₄⁻) ions. Let's examine each option step by step.
**Option (A): The hypochlorite ion is the strongest conjugate base.**
Conjugate bases are formed when acids lose a proton. The strength of... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The circle $C_{1}: x^{2}+y^{2}=3$, with centre at $O$, intersects the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 35 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the correct options based on the given geometric configurations. Let's proceed step by step.
1. **Find the Intersection Point P:**
The circle \( C_1 \) is given by \( x^2 + y^2 = 3 \) and the parabola \( C \) by \( x^2 = 2y \). Substitute \( x^2 = 2y \) into the circle's ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi is initially at his house and is about to visit Aoki's house.\nThere are N bus stops numbered 1 to N between... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 278 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Takahashi is trying to get to Aoki's house as early as possible by taking buses and walking. The goal is to compute for each query time q_i, the earliest time he can arrive at Aoki's place.
Hmm. Let's break down the problem. First, the bus routes and schedule... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Your company has just written one million units of a one-year European asset-or-nothing put option on an equity index fund. The equity index fund is ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 363 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the price of a one-million unit European asset-or-nothing put option using the Black-Scholes model. Let's break down the problem step by step.
First, let's identify the given parameters:
- Current equity index fund price (S) = 1000
- Dividend yield (q) = 2% per year (contin... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a positive integer D.\nFind the minimum value of |x^2+y^2-D| for non-negative integers x and y.\n\nInput... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 334 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum value of the absolute difference between D and x squared plus y squared, where x and y are non-negative integers. Hmm. So the problem is to find the smallest possible |x² + y² - D|.
First, I should think about how to approach this. For small values of D, maybe a bru... |
[
{
"content": "Problem: Jackson's paintbrush makes a narrow strip with a width of $6.5$ millimeters. Jackson has enough paint to make a strip $25$ meters long. How many square centimeters of paper could Jackson cover with paint?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 34 | AMC23 | {
"expected_answer": "1625",
"problem_id": "44",
"reference_solution": "",
"subject": null,
"type": null
} | First, we need to determine the area that Jackson's paintbrush can cover. The paintbrush makes a narrow strip with a width of 6.5 millimeters, and the total length of the strip is 25 meters.
First, convert the length from meters to millimeters because the width is given in millimeters.
1 meter = 1000 millimeters. S... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 121 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to find the longest strictly increasing sequence of positive integers where each term after the first is greater than the previous, and each term after the first must have a bitwise OR equal to n. Oh right, and all terms must be <=n.
Wait, the third condition ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 451 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the maximum possible value of a subsequence's value, which is defined as the subsequence length minus the number of set bits in their bitwise OR.
Wait, so the goal is to select a subset of elements (subsequence) such that the size of that subs... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 309 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about finding the maximum Fibonacciness possible for an array of 5 integers, given a1, a2, a4, a5. The array is [a1, a2, a3, a4, a5]. The Fibonacciness is the number of indices i (1-based) where a[i+2] equals a[i] + a[i+1]. We can choose a3 freely, and we need to maximize this co... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 96 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So the task is to create a permutation of size n where every adjacent pair meets certain conditions. The conditions are: if one element divides the other, then the smaller one comes first. Otherwise, the larger one comes first. Hmm.
Wait, but how do we arrange the elements such... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider this density matrix\n\n$\\rho=\\frac{1}{2}\\left(\\left|0\\right\\rangle \\left\\langle 0\\right|+\\left|1\\right\\rangle \\left\\langle 1\\right|\\right)$\n\nW... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 141 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the geometrical position of the given density matrix in qubit space, we need to understand how density matrices are represented in such spaces. The density matrix for a qubit can be represented in terms of its eigenvalues and the Bloch vector. However, the given density matrix is already in a form that all... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N buildings aligned in a row. The i-th building from the left has a height of H_i.\nDetermine if there is a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 444 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the leftmost building that's taller than the first one. Let's see. The input is N buildings with their heights. The first building is at position 1. So I need to check from the second building onwards if any is taller than the first's height. Once found, r... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array usageLimits of length n.\nYour task is to create groups using numbers from 0 to n - 1, ensuring that each number, i, is used no... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 77 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes a list called usageLimits and returns the maximum number of groups possible under the given conditions. Hmm. Let me think through the problem carefully.
The conditions are:
1. Each group must have distinct numbers. So no duplicates within a group.
2... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two 0-indexed integer arrays nums1 and nums2, each of length n, and a 1-indexed 2D array queries where queries[i] = [x_i, y_i].\nFor the i^th que... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 41 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where for each query, I have to find the maximum sum of nums1[j] + nums2[j] where both are greater than or equal to x_i and y_i respectively. If there's no such j, return -1. And I have to do this for all queries efficiently because the constraints are up to 1e5 for... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 118 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that we need to find the lexicographically largest array a where each element is from a given set S, and for every pair of indices i < j, the element at the gcd of i and j is not equal to the gcd of elements a_i and a_j. Oh right, and if there's n... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N sleighs numbered 1,2,\\ldots, N.\nR_i reindeer are required to pull sleigh i.\nAdditionally, each reindeer... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 354 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where there are N sleighs, each requiring a certain number of reindeers. The sum of the required reindeers for any group of sleighs can't exceed the total reindeers available. But each reindeer can pull at most one sleigh. So for each query X, I need to find the max... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Determine the starting material needed to synthesize 5-isopropyl-3,4-dimethylcyclohex-1-ene via ring-closing metathesis.\nOptions: A) 5-isopropyl-3,4-dimethylocta-1,6-di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 53 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the starting material needed to synthesize 5-isopropyl-3,4-dimethylcyclohex-1-ene via ring-closing metathesis (RCM), we need to understand the process and the structure of the starting material.
Ring-closing metathesis is a reaction that forms a cyclic compound from a diene. The general structure of the d... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 307 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about Alice and Bob playing a game with piles of stones. Each pile has a certain number of stones and a value. The players take turns removing stones from a pile, but they can only remove a number of stones that satisfies two conditions: the number must be be... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the value of\n\\[\n\\left(\\left(\\log _{2} 9\\right)^... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 142 | JEEBench | {
"expected_answer": "8",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let's try to solve this problem step by step. The expression given is quite complex, so I need to break it down into manageable parts. Let's look at it again:
\[
\left(\left(\log _{2} 9\right)^{2}\right)^{\frac{1}{\log _{2}\left(\log _{2} 9\right)}} \times (\sqrt{7})^{\frac{1}{\log _{4} 7}}
\]
Hmm. Let'... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 91 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Magic Trick II problem. Let's read the problem carefully.
So the task is to find the maximum possible k such that we can sort the permutation by removing any k-length continuous subarray and inserting it back anywhere. Then, output the steps to sort it using such operations, with at ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 303 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is asking for, given a graph and p nodes that need internet, and for each k from 1 to n, the minimum possible total latency when choosing up to k servers. The latency for a node is the maximum edge weight on the path from the node to the server. So, for each k, ... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\\gamma=5 / 3)$ and... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 472 | JEEBench | {
"expected_answer": "121",
"problem_id": "28",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the change in internal energy of a gas mixture when it does work at constant pressure. The solution involves calculating the heat added to the system, then using the first law of thermodynamics to find the change in internal energy.
### Step 1: Understanding the Process
The ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Two stars are being studied. It has been observed that iron atoms in the photosphere of star_1 are twice as excited in a specific energy level when compared to the iron ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 171 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's think about this step by step. So, we have two stars, star_1 and star_2. The problem states that iron atoms in star_1's photosphere are twice as excited in a specific energy level compared to star_2. The energy difference between these levels is given as 1.38 x 10^-23 J. We need to find the correct equation relat... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Compound A shows two signals in the proton NMR, a triplet at 0.9 ppm for 6H and a quartet at 1.3 ppm for 4H. It undergoes monobromination to form compound B. B reacts wi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 115 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's break down the problem step by step to identify compound D.
### Step 1: Analyze Compound A
Compound A shows two signals in proton NMR:
- A triplet at 0.9 ppm for 6H (indicating 6 hydrogens in a triplet, which suggests a primary alkyl group with three substituents, like a methyl group attached to a secondary carb... |
[
{
"content": "Problem: Find the degree measure of the least positive angle $\\theta$ for which\n\\[\\tan \\theta = \\frac{\\cos 5^\\circ \\cos 20^\\circ + \\cos 35^\\circ \\cos 50^\\circ - \\sin 5^\\circ \\sin 20^\\circ - \\sin 35^\\circ \\sin 50^\\circ}{\\sin 5^\\circ \\cos 20^\\circ - \\sin 35^\\circ \\cos 50... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 109 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the given problem, we need to find the least positive angle \(\theta\) such that \(\tan \theta\) equals a specific trigonometric expression. Let's break down the problem step by step.
First, let's simplify the numerator and the denominator of the given fraction separately.
The given expression is:
\[
\tan \t... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $P$ be the plane $\\sqrt{3} x+2 y+3 z=16$ and let $S=\\left\\{\\alpha \\hat{i}+\\beta \\hat{j}+\\gamma \\h... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 461 | JEEBench | {
"expected_answer": "45",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve this problem, we need to determine the volume of a parallelepiped formed by three vectors \(\vec{u}, \vec{v}, \vec{w}\) that satisfy certain conditions. Let's break down the problem step by step.
### Step 1: Understanding the Plane and Vectors in \(S\)
The plane \(P\) is given by the equation \(\sqrt{3}x + 2y... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 403 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to convert a singular Amog'u noun into its plural form. The rules are that the singular form ends with "us", and the plural is formed by removing "us" and adding "i". But wait, the example given for "amogus" becomes "amogi". Let me check that. Oh right, because the singular form ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 279 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to tackle this problem. Hmm, the problem statement is a bit complex, so I need to break it down step by step.
So, the task is to determine whether we can draw exactly n edges between two strongly connected directed graphs such that certain conditions are met. The key points are:
1. Each added ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums and an integer threshold.\nFind the length of the longest subarray of nums starting at index l and ending at index... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 52 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the longest subarray that starts with an even number, then all consecutive elements alternate in parity (so after an even, the next is odd, then even, etc.), and all elements are <= threshold. Hmm.
So the problem is to look for the longest possible subarray where the first eleme... |
[
{
"content": "Problem: The volume of a cone is given by the formula $V = \\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. The area of the base of a cone is 30 square units, and its height is 6.5 units. What is the number of cubic units in its volume?\nMark your solution with \\boxed\nAn... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 167 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the volume of the cone, we start with the given formula:
\[ V = \frac{1}{3} B h \]
where \( B \) is the area of the base and \( h \) is the height. We are provided with \( B = 30 \) square units and \( h = 6.5 \) units.
First, substitute the given values into the formula:
\[ V = \frac{1}{3} \times 30 \time... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums and an integer k.\nIn one operation, you can pick any index i of nums such that 0 <= i < nums.length - 1 and repla... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 168 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum possible bitwise OR of the remaining elements after doing at most k operations. Each operation allows me to combine two adjacent elements with a bitwise AND and replace them with that result. The key is to figure out how to choose which pairs to combine so that the fi... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Match the compounds in LIST-I with the observations in LIST-II, and choos... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 411 | JEEBench | {
"expected_answer": "D",
"problem_id": "54",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's tackle this problem. I need to match each compound from LIST-I with the correct observations from LIST-II. The correct option is one of the given letters A, B, C, or D. Let's think through each compound and the tests described.
First, let's recall the chemical properties of each compound:
(I) Anil... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: MRI is preferred over CT (computed tomography) in all of the following scenarios, EXCEPT:\nOptions: A. The detection of spinal cord injuries, B. The ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 435 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine which scenario listed does not prefer MRI (Magnetic Resonance Imaging) over CT (Computed Tomography). Let's analyze each option step by step.
First, recall that MRI is particularly good at imaging soft tissues, whereas CT is better for detecting bone and acute injuries. So, ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 166 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement is a bit complex, but breaking it down step by step, maybe I can figure out the approach.
So, the problem is about distributing a deck of n×m cards between two players such that the first player can beat all of the second player's cards in a certain w... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The correct statement(s) related to processes involved in the extracti... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 477 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "35",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's see. I need to figure out which of these statements about metal extraction processes are correct. Let me tackle each one by one.
Starting with (A): Roasting of Malachite produces Cuprite. Hmm, malachite is a copper carbonate, right? So when you roast it, you heat it in the presence of oxygen. The r... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.AtCoder cafeteria sells meals consisting of a main dish and a side dish.\r\nThere are N types of main dishes, called m... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 341 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the most expensive set meal offered. The problem says that the set meals are all possible combinations of main and side dishes except for those L pairs that aren't allowed. So the maximum price would be the sum of the maximum a_i and maximum b_j, unless there's a pair that's excl... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $E$ denote the parabola $y^{2}=8 x$. Let $P=(-2,4)$, and let $Q$ a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 367 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given parabola \( E \) defined by \( y^2 = 8x \), the point \( P = (-2, 4) \), and the points \( Q \) and \( Q' \) on \( E \) such that \( PQ \) and \( PQ' \) are tangents to \( E \). We will check each statement to determine which are true.
First, recall that the focus \(... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: The net production of ATP via substrate-level phosphorylation in glycolysis is:\nOptions: A. 2 from glucose and 4 from glycogen., B. 2 from glucose a... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 376 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's analyze the process of glycolysis and substrate-level phosphorylation.
Glycolysis is the metabolic pathway that converts glucose into pyruvate. The process can be divided into two main stages: the energy investment phase and the energy payoff phase.
1. **Energy Investment Phase*... |
[
{
"content": "Problem: Given\n\\[\\mathbf{A} = \\begin{pmatrix} 3 & 7 \\\\ -1 & -2 \\end{pmatrix},\\]compute $\\mathbf{A}^{27} + \\mathbf{A}^{31} + \\mathbf{A}^{40}.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 248 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \(\mathbf{A}^{27} + \mathbf{A}^{31} + \mathbf{A}^{40}\) where \(\mathbf{A} = \begin{pmatrix} 3 & 7 \\ -1 & -2 \end{pmatrix}\), we first need to find the eigenvalues and eigenvectors of \(\mathbf{A}\) to diagonalize it. The sum of the matrices raised to these exponents can then be computed using the diagona... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given three integers start, finish, and limit. You are also given a 0-indexed string s representing a positive integer.\nA positive integer x is called... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 161 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of powerful integers between start and finish, inclusive. The criteria are that the number must end with the string s, and each digit must be at most the given limit.
Hmm. So the problem is to count all numbers in [start, finish] that have s as a suffix and all digit... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 269 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says we need to find the minimum value of x that the richest person must add to their wealth so that more than half of the population is unhappy. If it's impossible, return -1.
First, let's understand the problem. So, after adding x to the richest per... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Which of the following statements would \"supply-side\" economists disagree with?\nOptions: A. Tax changes cause shifts in aggregate supply that work... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 419 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to identify which statement supply-side economists would disagree with. Supply-side economics focuses on the supply side of the economy, emphasizing the role of production factors, incentives, and tax policies. Let's analyze each option:
A. Tax changes cause shifts in aggregate supply th... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 48 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about maximizing the sum of two GCDs after swapping elements in certain intervals. So, the task is to find the maximum possible value of GCD(a) + GCD(b) after performing exactly one swap operation where we swap a[i] and b[i] for all i in [l, r]. Also, we need... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 64 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about splitting an array into segments such that each segment's OR is in non-decreasing order. And we need to count the number of ways to do this modulo 998244353.
First, I need to understand the problem thoroughly. Let's look at the examples.
In the firs... |
[
{
"content": "Problem: Bob and Alice each have a bag that contains one ball of each of the colors, blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probabilit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 138 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's calculate the probability that after Alice and Bob exchange a ball each, their bags end up with the same contents.
First, let's understand the initial state. Each bag has 5 balls: blue, green, orange, red, violet. So, each bag starts with all colors.
Alice picks one ball from her bag and puts it into Bob's ba... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array nums.\nReturn an integer that is the maximum distance between the indices of two (not necessarily different) prime numbers in nu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 476 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the maximum distance between two primes in an array. Hmm. Let's think about how to approach this.
First, the problem says the maximum distance between two primes. So, primes can be the same element (like if there are duplicates). So even if the primes are... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 199 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that we need to find the maximum score by performing certain operations. Let's read carefully.
So, the operations are: choose two indices l and r where s_l is 'L' and s_r is 'R'. Then add the sum of a_l to a_r (the elements in between) to the sco... |
[
{
"content": "Problem: Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an $11$ on the next quiz, her mean will increase by $1$. If she scores an $11$ on each of the next three quizzes, her mean will increase by $2$. What is the mean of her quiz scores currently?\nMark yo... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 21 | AMC23 | {
"expected_answer": "7",
"problem_id": "23",
"reference_solution": "",
"subject": null,
"type": null
} | Let's denote Maureen's current total score as \( S \) and the number of quizzes she has taken so far as \( n \). The current mean is therefore \( \frac{S}{n} \).
If she scores 11 on the next quiz, her new total will be \( S + 11 \) and the number of quizzes becomes \( n + 1 \). The new mean is \( \frac{S + 11}{n + 1} ... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: If $y=y(x)$ satisfies the differential equation\n\\[\n8 \\sqrt{x}(\\sqrt{... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 110 | JEEBench | {
"expected_answer": "A",
"problem_id": "39",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve the given differential equation and find \( y(256) \) given \( y(0) = \sqrt{7} \), we will follow these steps:
1. **Rewrite the Differential Equation**:
The given equation is:
\[
8 \sqrt{x} (\sqrt{9 + \sqrt{x}}) \, dy = \left( \sqrt{4 + \sqrt{9 + \sqrt{x}}} \right)^{-1} \, dx
\]
We can rearran... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.N people numbered 1 through N tossed a coin several times. We know that person i's tosses resulted in A_i heads and B... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 229 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this programming problem. Let's read the problem statement carefully.
The problem is about sorting people based on their success rates from highest to lowest. The success rate is A_i divided by A_i plus B_i. But if two people have the same success rate, we sort them by their number in asc... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.