context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 8
values | metadata dict | model_outputs stringlengths 1 186k |
|---|---|---|---|---|---|---|
[
{
"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 strings s and t of equal length n. You can perform the following operation on the string s:\n\nRemove a suffix of s of length l where 0 < l <... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 92 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of ways to transform string s into t using exactly k operations. Each operation is removing a suffix and appending it to the start. Hmm.
First, I need to understand when such a transformation is possible. Oh right, the two strings must be cyclically equivalent. Becaus... |
[
{
"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 have an empty sequence and N balls. The size of the i-th ball (1 \\leq i \\leq N) is 2^{A_i}.\nYou will perform N ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 435 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem. Let's read the problem carefully.
So, the task is to simulate a process where we add N balls to a sequence step by step, following certain rules. Each ball has a size which is 2^A_i, where A_i is given. For each operation (each ball addition), after adding the ball to the ri... |
[
{
"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 | 313 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where the sages have to select the minimum number of paths to block all magical resonance vibrations. Hmm. The problem statement says that for every pair of channels (edges) that diverge from a node, there must be a selected path that includes both. So, the goal is ... |
[
{
"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 $\\omega \\neq 1$ be a cube root of unity. Then what is th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 211 | JEEBench | {
"expected_answer": "3",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to find the minimum value of the expression \(\left|a + b\omega + c\omega^2\right|^2\) where \(\omega\) is a non-trivial cube root of unity, and \(a, b, c\) are distinct non-zero integers.
First, recall that the cube roots of unity are the solutions to the equation \(x^3 = 1\). These ro... |
[
{
"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.We have a grid with H rows and W columns.\r\nLet (i,j) denote the square at the i-th row from the top and j-th column ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 194 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Takahashi has to reach the goal square in at most T moves, and I have to find the maximum number of candy squares (o) he can visit on his way. Hmm. Let's think about the approach.
First, the problem seems to require checking all possible paths that Takahashi can take wi... |
[
{
"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: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belon... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 138 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to analyze two statements about finite groups and determine their validity. Let's tackle each statement one by one.
**Statement 1:** If a finite group has order n, then the group contains a subgroup of order d for every positive divisor d of n.
This statement is known as Lagrange's Theo... |
[
{
"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 initially have an empty string S.\r\nAdditionally, there are bags 1, 2, \\dots, N, each containing some strings.\r... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 400 | 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 minimum cost to build a string T by concatenating strings from bags, and each bag has multiple possible strings. The cost is the number of yen spent, which is equivalent to the number of times we choose to take a string from the bags. So the idea is to... |
[
{
"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 $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be given by $f(x)=(x-1)(... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 236 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the function \( F(x) = \int_{0}^{x} f(t) \, dt \) where \( f(x) = (x-1)(x-2)(x-5) \). We will determine which of the given options are correct by examining the properties of \( F(x) \) based on the behavior of \( f(x) \).
### Step-by-Step Solution:
1. **Understanding \( f(x) ... |
[
{
"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: Two identical moving coil galvanometers have $10 \\Omega$ resistance a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 186 | JEEBench | {
"expected_answer": "BC",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the correct statements regarding the conversion of galvanometers into voltmeters and ammeters, and their subsequent use to measure the resistance of a 1000 Ω resistor. Let's break down the problem step by step.
### Step 1: Convert Galvanometer to Voltmeter
The given galvanom... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In an experiment, compound X (C11H12O) was subjected to a reaction with 1,4-diazabicyclo[2.2.2]octane in nonpolar solvent at a temperature of 403 K for a duration of 1 d... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 78 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct compound X from the given options, let's analyze the NMR data provided.
First, let's look at the 1H-NMR signals:
- Two singlets at 2.28 and 2.31 ppm (3H each). These are likely from methylene groups (CH2) in a ring, possibly part of a cyclopropane or similar structure. The presence of two ide... |
[
{
"content": "Problem: Among the 900 residents of Aimeville, there are 195 who own a diamond ring, 367 who own a set of golf clubs, and 562 who own a garden spade. In addition, each of the 900 residents owns a bag of candy hearts. There are 437 residents who own exactly two of these things, and 234 residents wh... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 0 | AIME24 | {
"expected_answer": "73",
"problem_id": "aime24-0",
"reference_solution": "Let $w,x,y,z$ denote the number of residents who own 1,2,3 and 4 of these items, respectively. We know $w+x+y+z=900$ , since there are 900 residents in total. This simplifies to $w+z=229$ , since we know $x=437$ and $y=234$ . Now, w... | Let's denote the four sets as follows:
- \( D \) for diamond ring owners.
- \( G \) for golf club owners.
- \( S \) for garden spade owners.
- \( C \) for candy heart owners. Note that every resident owns a bag of candy hearts, so \( |C| = 900 \).
We need to find the number of residents who own all four things, i.e., ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Identify the EXO product of the following [4+2] cycloaddition reaction.\n2,5-dimethylthiophene + Furan-2,5-dione + Heat ---> ?\nOptions: A) (3aR,4S,7R,7aS)-4,7-dimethyl-... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 32 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the product of a [4+2] cycloaddition reaction between 2,5-dimethylthiophene and furan-2,5-dione under heat. Let's break down the process step by step.
First, understanding the reactants: 2,5-dimethylthiophene is a sulfur-containing aromatic compound, and furan-2,5-dione is a... |
[
{
"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.We have N cups of ice cream.\r\nThe flavor and deliciousness of the i-th cup are F_i and S_i, respectively (S_i is an ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 266 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to choose two ice cream cups to maximize my satisfaction. Let's see the problem statement again.
So, for each pair of cups, when I eat them, their deliciousness is s and t where s >= t. The satisfaction depends on whether their flavors are the same or different. ... |
[
{
"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 16 consisting of 0 and 1.\nIf the i-th character of S is 0 for every even number i ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 294 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that checks if certain characters in a string are 0. The problem says that for every even number i from 2 through 16, the i-th character must be 0. Wait, wait, the indexes here—like, in Python, strings are zero-based, but the problem is using i as the position starting fr... |
[
{
"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 $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be a differentia... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 310 | JEEBench | {
"expected_answer": "4",
"problem_id": "53",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve for \( f(0) \), we start by analyzing the given problem. We are given that \( F(x) = \int_0^x f(t) \, dt \) and the integral equation:
\[
\int_0^\pi \left( f'(x) + F(x) \right) \cos x \, dx = 2.
\]
First, let's expand the integrand. The integrand is \( f'(x) \cos x + F(x) \cos x \). So the integral becomes:
... |
[
{
"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: A rocket is launched normal to the surface of the Earth, away from the Su... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 96 | JEEBench | {
"expected_answer": "B",
"problem_id": "6",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the minimum initial velocity \( v_S \) required for a rocket to escape the Sun-Earth system. The rocket is launched normal to the Earth's surface away from the Sun along the line joining the Sun and Earth.
### Step-by-Step Solution:
1. **Understand the System:**
- The 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": 1,
"temperature": 0.7
} | 1 | 118 | 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 a permutation p, and a string s. The task is to build a graph by adding edges according to the rules given, and then find the maximum possible diameter of the connected graph. Hmm. Wait, the problem says that the graph must be connected, right? Or does ... |
[
{
"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 deficiency of which vitamin has been associated with enamel defects and increased risk of dental caries?\n \nOptions: A. Vitamin E, B. Vitamin C, C... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 375 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B |
[
{
"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 1-indexed integer array nums of length n.\nAn element nums[i] of nums is called special if i divides n, i.e. n % i == 0.\nReturn the sum of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 42 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that calculates the sum of the squares of the special elements in the array. Let's see. The problem says that an element is special if its index (which is 1-based) divides the length of the array. So for example, if the array has length 4, then indices 1, 2, and 4 are con... |
[
{
"content": "Problem: Find the number of rectangles that can be formed inside a fixed regular dodecagon ( $12$ -gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles. [asy] unitsize(0.6 inch); for(int i=0; i<360; i+=30) { d... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 14 | AIME24 | {
"expected_answer": "315",
"problem_id": "aime24-14",
"reference_solution": "By Furaken There are two kinds of such rectangles: those whose sides are parallel to some edges of the regular 12-gon (Case 1), and those whose sides are not (Case 2). For Case 1, WLOG assume that the rectangle's sides are horizontal an... | To solve this problem, we need to determine the number of rectangles that can be formed inside a regular dodecagon (12-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon.
### Approach
1. **Understanding the Dodecagon**: A regular dodecagon has 12 vertices. Each vertex can be co... |
[
{
"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: The least value of $\\alpha \\in \\mathbb{R}$ for which $4 \\alpha x^{2}+... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 28 | JEEBench | {
"expected_answer": "C",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve the problem of finding the least value of \(\alpha \in \mathbb{R}\) such that the inequality \(4 \alpha x^2 + \frac{1}{x} \geq 1\) holds for all \(x > 0\), we need to analyze the given inequality carefully.
First, let's rewrite the inequality:
\[4 \alpha x^2 + \frac{1}{x} \geq 1.\]
We need this inequality to... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A methanol solution of (R)-(+)-Limonene is stirred with Pd/C under a Hydrogen atmosphere. After 1 equivalent of hydrogen is consumed, product 1 is isolated as the major ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 12 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the structure of product 4 after a series of reactions starting from (R)-(+)-Limonene. Let's break down each step to understand the transformations and deduce the correct structure of product 4.
**Step 1: Hydrogenation with Pd/C on (R)-(+)-Limonene**
Limonene is a cyclic mo... |
[
{
"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 = S_1S_2\\ldots S_N of length N consisting of lowercase English letters.\nAdditionally, you a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 323 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each query, I have to count the number of positions p in the substring from l_i to r_i (inclusive) where S_p equals S_{p+1}. Let's think about how to approach this.
First, the input size can be up to 3e5, so O(1) per query is needed. If I precompute something for ea... |
[
{
"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 an unknown compound. To identify the product, you have used the following characterisation techniques: FTIR and 1H NMR. The FTIR spectrum shows a very ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 98 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to identify the unknown compound based on the given FTIR and 1H NMR spectroscopic data. Let's break down the information provided and analyze each piece step by step.
### FTIR Analysis
1. **Very broad absorption peak at 3000 wavenumbers**: This region corresponds to OH or NH groups. The ... |
[
{
"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 of integers nums, and an integer target.\nReturn the length of the longest subsequence of nums that sums up to target. If no su... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 109 | 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 longest subsequence in an array that sums up to a target. The subsequence doesn't have to be contiguous, right? And the answer should be the length of that longest subsequence, or -1 if it doesn't exist. Let's think about how to approach this.
First, ... |
[
{
"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 sales tax that you pay at the grocery store is commonly labeled a\nOptions: A. direct tax., B. indirect tax., C. flat tax., D. luxury tax., E. ad... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 272 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B |
[
{
"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 strings source and target, both of length n and consisting of lowercase English letters. You are also given two 0-indexed character... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 156 | 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 minimum cost to convert the source string into the target string using the given original and changed arrays along with their costs. Hmm. Let's think about how to approach this.
First, the problem says that in one operation, I can pick a character fro... |
[
{
"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: Fusion of $\\mathrm{MnO}_{2}$ with $\\mathrm{KOH}$ in presence of $\\m... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 191 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "24",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. First, I need to figure out what the salts W and X are, based on the given reactions. Let's start with the first part: when MnO2 is fused with KOH in the presence of O2, what product is formed?
Hmm, I remember that when manganese dioxide (MnO2) reacts with potassiu... |
[
{
"content": "Problem: Find the number of rectangles that can be formed inside a fixed regular dodecagon ( $12$ -gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles. [asy] unitsize(0.6 inch); for(int i=0; i<360; i+=30) { d... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 14 | AIME24 | {
"expected_answer": "315",
"problem_id": "aime24-14",
"reference_solution": "By Furaken There are two kinds of such rectangles: those whose sides are parallel to some edges of the regular 12-gon (Case 1), and those whose sides are not (Case 2). For Case 1, WLOG assume that the rectangle's sides are horizontal an... | To solve this problem, we need to determine the number of rectangles that can be formed inside a regular dodecagon (12-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon.
### Approach
1. **Understanding the Structure**: A regular dodecagon has 12 vertices. Each rectangle formed... |
[
{
"content": "Problem: The weight of $\\frac{1}{3}$ of a large pizza together with $3 \\frac{1}{2}$ cups of orange slices is the same as the weight of $\\frac{3}{4}$ of a large pizza together with $\\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\\frac{1}{4}$ of a pound. What is the weight, i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 9 | AMC23 | {
"expected_answer": "4",
"problem_id": "11",
"reference_solution": "",
"subject": null,
"type": null
} | Let's denote the weight of the large pizza as \( P \) pounds and the weight of a cup of orange slices as \( O \) pounds. According to the problem, we have the following equation based on the given conditions:
\[
\frac{1}{3}P + 3 \frac{1}{2}O = \frac{3}{4}P + \frac{1}{2}O
\]
First, convert the mixed number \( 3 \frac{... |
[
{
"content": "Problem: When converting $\\frac{31}{11111}$ to a decimal, the decimal turns out to be a repeating decimal. How many digits repeat in this repeating decimal?\n\nFor example, if you get the repeating decimal $0.\\overline{123},$ then your answer should be $3,$ and if you get $0.436\\overline{7},$ y... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 302 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the number of digits that repeat in the decimal expansion of \(\frac{31}{11111}\), we need to convert the fraction into a decimal and identify the repeating sequence.
First, let's perform the long division of 31 by 11111.
1. **Long Division Setup**:
- 31 divided by 11111. Since 11111 is larger than 31... |
[
{
"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: In a historical experiment to determine Planck's constant, a metal surfac... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 0 | JEEBench | {
"expected_answer": "B",
"problem_id": "1",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To determine Planck's constant from the given data, we need to use the photoelectric effect equation. The equation relates the energy of the incident photon to the stopping potential and the work function of the metal. The key relationship here is:
\[ E = h \nu = \phi + e V_0 \]
where:
- \( E \) is the energy of the ... |
[
{
"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: The value of $\\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\frac{x^{2} \\c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 59 | JEEBench | {
"expected_answer": "A",
"problem_id": "40",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^{2} \cos x}{1+e^{x}} \, dx\), we will use properties of definite integrals and symmetry. Let's proceed step by step.
First, observe that the integrand is \(\frac{x^2 \cos x}{1 + e^x}\). Let's consider the substitution \(u = -x\). Then, \(du = -dx\),... |
[
{
"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: For any $y \\in \\mathbb{R}$, let $\\cot ^{-1}(y) \\in(0, \\pi)$ and $\\t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 487 | JEEBench | {
"expected_answer": "C",
"problem_id": "3",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to find the sum of all solutions for the equation \(\tan^{-1}\left(\frac{6y}{9-y^2}\right) + \cot^{-1}\left(\frac{9-y^2}{6y}\right) = \frac{2\pi}{3}\) given the constraints \(0 < |y| < 3\).
First, recall the relationship between the inverse tangent and inverse cotangent functions. Specif... |
[
{
"content": "Problem: Let $ABC$ be a triangle inscribed in circle $\\omega$ . Let the tangents to $\\omega$ at $B$ and $C$ intersect at point $D$ , and let $\\overline{AD}$ intersect $\\omega$ at $P$ . If $AB=5$ , $BC=9$ , and $AC=10$ , $AP$ can be written as the form $\\frac{m}{n}$ , wher... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 24 | AIME24 | {
"expected_answer": "113",
"problem_id": "aime24-24",
"reference_solution": "From the tangency condition we have $\\let\\angle BCD = \\let\\angle CBD = \\let\\angle A$ . With LoC we have $\\cos(A) = \\frac{25+100-81}{2*5*10} = \\frac{11}{25}$ and $\\cos(B) = \\frac{81+25-100}{2*9*5} = \\frac{1}{15}$ . Then, ... | To solve this problem, we start by understanding the given configuration. We have a triangle \(ABC\) inscribed in a circle \(\omega\). The tangents to \(\omega\) at \(B\) and \(C\) intersect at point \(D\). The line \(AD\) intersects the circle again at point \(P\). We need to find the length \(AP\) given the side leng... |
[
{
"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 containing 8 carbon atoms in total. Peaks in the FTIR spectrum of this compound indicate the presenc... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 86 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the correct 1H NMR data for a di-substituted 6-membered aromatic ring compound with 8 carbon atoms. The compound has a carbonyl group and an aromatic-halogen bond, as indicated by the FTIR peaks.
First, let's analyze the structure of the compound. The aromatic ring is a 6-me... |
[
{
"content": "Problem: A rectangular box $P$ has distinct edge lengths $a$, $b$, and $c$. The sum of the lengths of all $12$ edges of $P$ is $13$, the areas of all $6$ faces of $P$ is $\\frac{11}{2}$, and the volume of $P$ is $\\frac{1}{2}$. Find the length of the longest interior diagonal connecting two vertic... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 26 | AMC23 | {
"expected_answer": "13",
"problem_id": "29",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the length of the longest interior diagonal of a rectangular box with edge lengths \(a\), \(b\), and \(c\), given specific conditions on the sum of the edges, the sum of the face areas, and the volume.
First, let's recall the formulas involved:
1. The sum of all 12 edges of a... |
[
{
"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 $\\boldsymbol{f}: \\mathbb{R} \\rightarrow \\mathbb{R}$ and $\\bol... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 302 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given functional equations and use the provided limit condition to determine which statements are true. Let's proceed step by step.
First, we have the functional equations:
1. \( f(x+y) = f(x) + f(y) + f(x) f(y) \)
2. \( f(x) = x g(x) \)
And the condition \( \lim_{x \to 0}... |
[
{
"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 | 361 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if a subarray is orangutan-approved. Let's see what the problem says.
So, the array is called orangutan-approved if we can empty it by repeatedly selecting a subarray where all elements are the same and that value is present in the set S. When we se... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Two quantum states with energies E1 and E2 have a lifetime of 10^-9 sec and 10^-8 sec, respectively. We want to clearly distinguish these two energy levels. Which one of... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 0 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine which energy difference allows distinguishing the two quantum states, we need to consider the resolution in energy. The lifetime of each state is given, and the energy difference must be sufficient to resolve the natural line width associated with each state's decay.
The natural line width (Γ) is related ... |
[
{
"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 is an ultramarathon course totaling 100\\;\\mathrm{km}.\r\nWater stations are set up every 5\\;\\mathrm{km} alon... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 212 | 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 an integer N (from stdin) and outputs the nearest water station's position. The course is 100 km long, and water stations are every 5 km, including start and goal. So there are 21 stations in total. The problem says that the nearest is uniquely deter... |
[
{
"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 one of following statements about nitrogen balance is correct?\n\nOptions: A. Positive nitrogen balance means that there is a net loss of prote... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 1 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct statement about nitrogen balance, let's first understand the concepts.
**Nitrogen Balance**: This is calculated as the difference between nitrogen intake and nitrogen output. It helps assess protein metabolism.
- **Positive Nitrogen Balance**: When the body's nitrogen intake exceeds its outpu... |
[
{
"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.\r\nFind the maximum length of a contiguous substring of S that is a palindrome.\r\nNote that... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 280 | 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 length of a contiguous palindromic substring in a given string. Hmm, let's think about how to approach this.
First, what's a palindrome here? Oh right, a substring that reads the same forwards and backwards. And contiguous means it's a sequenc... |
[
{
"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 rectangular sheets spread out on a coordinate plane.\nEach side of the rectangular region covered by each ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 271 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to calculate the area covered by one or more rectangular sheets. The sheets are on a coordinate plane, and their sides are parallel to the axes. The challenge is to find the union area of all these rectangles.
Hmm, the straightforward approach would be to comput... |
[
{
"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 | 42 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about determining if Nikita can end up with exactly m cubes after n moves. Each move is either adding 1 cube or removing 1 from the top. Hmm.
Wait, the key here is to model the net effect of the moves. Because each move is either +1 or -1. So the total number of cubes after n mo... |
[
{
"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, which is known to be a concatenation of anagrams of some string t.\nReturn the minimum possible length of the string t.\nAn anagram i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 494 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have a string s that's a concatenation of anagrams of some string t. My goal is to find the minimum possible length of t. Hmm. Let's think about how to approach this.
First, let's understand the problem. The string s is made by combining multiple anagrams of t. So eac... |
[
{
"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: An ideal gas is in thermodynamic equilibrium. The number of degrees of fr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 502 | JEEBench | {
"expected_answer": "C",
"problem_id": "21",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to understand the relationship between the number of degrees of freedom (n) of a gas molecule and the speed of sound (v) and internal energy (U) in thermodynamic equilibrium. Let's break down the problem step by step.
### Step 1: Understanding Degrees of Freedom
The number of degrees of ... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 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)... | To solve this problem, we need to determine the inradius of triangle \(ABC\) given that eight circles of radius 34 are sequentially tangent, and two of these circles are tangent to the sides \(AB\) and \(BC\) respectively. Additionally, 2024 circles of radius 1 can be arranged in the same manner. The inradius can be ex... |
[
{
"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: For any $3 \\times 3$ matrix $M$, let $|M|$ denote the determinant of ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 334 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement carefully based on the given matrices and properties of determinants and matrix operations.
### Statement (A)
Check if \( F = PEP \) and \( P^2 = I \).
First, compute \( PEP \). The matrix \( P \) is a permutation matrix that swaps the second and third rows and... |
[
{
"content": "Problem: There exist real numbers $x$ and $y$ , both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$ . Find $xy$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 16 | AIME24 | {
"expected_answer": "25",
"problem_id": "aime24-16",
"reference_solution": "By properties of logarithms, we can simplify the given equation to $x\\log_xy=4y\\log_yx=10$ . Let us break this into two separate equations: \\[x\\log_xy=10\\] \n \\[4y\\log_yx=10.\\] \nWe multiply the two equations to get: \n \\[4xy\\... | To solve the problem, we start by analyzing the given equations. We have two logarithmic equations:
1. \(\log_x(y^x) = 10\)
2. \(\log_y(x^{4y}) = 10\)
First, we can simplify each equation using logarithm properties.
For the first equation:
\[
\log_x(y^x) = 10 \implies x \log_x y = 10 \implies \log_x y = \frac{10}{x}... |
[
{
"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 N and strings R and C of length N consisting of A, B, and C. Solve the following problem.\nTh... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 314 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to fill an N x N grid with characters A, B, C such that each row and column has exactly one of each. Also, the leftmost character in each row must match the corresponding character in R, and the topmost in each column must match C's corresponding character. Hmm.
... |
[
{
"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 | 85 | 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 determine if a given integer x can be the sum of two large positive integers with the same number of digits. Hmm. Let's break this down.
First, what's a large integer here? Oh right, a large digit is between 5 and 9 inclusive. So a number is large i... |
[
{
"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 best conclusion that can be drawn about the four-day ( compressed) workweek is that it has:\nOptions: A. negative effects on productivity but lit... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 482 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the best conclusion about the four-day (compressed) workweek, we need to consider the effects on productivity and attitudes. Let's break down each option based on possible research findings.
First, compressed workweeks often involve working more hours in fewer days, typically four days instead of five. Th... |
[
{
"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 is an election to choose one winner from N candidates with candidate numbers 1, 2, \\ldots, N, and there have be... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 329 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where, given the votes for each candidate over time, I have to determine the current winner after each vote. Let's think about how to approach this.
The input is N (number of candidates) and M (number of votes). Then there's a list of A_i which are the candidates each vote is... |
[
{
"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 | 122 | 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 kill monsters on a tree such that in each round, I take the sum of all living monsters' attack points as damage, then kill some monsters but can't kill two connected ones in the same round. The goal is to minimize the total damage over all rounds (wh... |
[
{
"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: According to the Arrhenius equation,\n(A) a high activation energy usu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 16 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "24",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate each statement in the context of the Arrhenius equation and determine which ones are correct. The Arrhenius equation is given by \( k = A e^{-E_a/(RT)} \), where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is... |
[
{
"content": "Problem: Find the number of rectangles that can be formed inside a fixed regular dodecagon ( $12$ -gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles. [asy] unitsize(0.6 inch); for(int i=0; i<360; i+=30) { d... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 14 | AIME24 | {
"expected_answer": "315",
"problem_id": "aime24-14",
"reference_solution": "By Furaken There are two kinds of such rectangles: those whose sides are parallel to some edges of the regular 12-gon (Case 1), and those whose sides are not (Case 2). For Case 1, WLOG assume that the rectangle's sides are horizontal an... | To solve this problem, we need to determine the number of rectangles that can be formed inside a regular dodecagon (12-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon.
### Approach
1. **Understanding the Structure**: A regular dodecagon has 12 vertices. Each vertex can be co... |
[
{
"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 k and an integer x.\nConsider s is the 1-indexed binary representation of an integer num. The price of a number num is the number of i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 159 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the maximum number num such that the sum of the prices of all numbers from 1 to num is <= k. The price of a number is the count of positions i (starting from 0?) where i mod x equals 0 and the ith bit in the binary representation is set. Wait, wait. Wait, the problem statement sa... |
[
{
"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 $z$ be a complex number with non-zero imaginary part. If\n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 379 | JEEBench | {
"expected_answer": "0.5",
"problem_id": "4",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the value of \( |z|^2 \) given that the expression \(\frac{2+3z+4z^2}{2-3z+4z^2}\) is a real number. Let's proceed step by step.
### Step 1: Express the Condition for Real Number
Let \( z = x + yi \) where \( x \) and \( y \) are real numbers, and \( y \neq 0 \). We need the... |
[
{
"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: For any real numbers $\\alpha$ and $\\beta$, let $y_{\\alpha, \\beta}(... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 366 | JEEBench | {
"expected_answer": "AC",
"problem_id": "40",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which of the given functions belong to the set \( S \), which is defined as the set of solutions to the differential equation \(\frac{dy}{dx} + \alpha y = x e^{\beta x}\) with the initial condition \( y(1) = 1 \). Let's proceed step by step.
### Step 1: Solve the Differentia... |
[
{
"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 string s, a string a, a string b, and an integer k.\nAn index i is beautiful if:\n\n0 <= i <= s.length - a.length\ns[i..(i + a.length... | {
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} | <think>
Okay, I need to solve this problem where I have to find beautiful indices in a string. Let me read the problem carefully.
So, a beautiful index i is one where certain conditions are met. Let's break down the conditions.
First, the index i must be such that the substring of s starting at i with length equal to... |
[
{
"content": "Problem: Two sides of a triangle are each $8$ units long. If the third side has a whole number length, what is the greatest possible perimeter, in units, for the triangle?\nMark your solution with \\boxed\nAnswer:",
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] | {
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} | 0 | 368 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | To solve this problem, we need to determine the greatest possible perimeter of a triangle where two sides are each 8 units long, and the third side is a whole number. Let's denote the third side as \( x \).
First, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sid... |
[
{
"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... | {
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"seed": 1,
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} | 1 | 41 | 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 a rooted tree, and I have to add exactly k edges and find the minimum possible number of bridges after adding those edges. The constraints are n up to 3e5, which means I need an efficient approach.
First, let me understand the problem. A bridge is an e... |
[
{
"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... | {
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} | 0 | 187 | CodeElo | {
"expected_answer": "",
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} | <think>
Okay, I need to solve this problem where I have to determine for each starting island s (from 1 to n-1) whether Bessie can win when she starts there. The output is a binary string of length n-1 where each character is 1 if Bessie can win from that starting island, else 0.
Let me read the problem statement care... |
[
{
"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... | {
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} | 0 | 235 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where David is trying to avoid being caught by multiple teachers in a one-dimensional line. The goal is to find out how many moves it takes for the teachers to catch David, given that they act optimally.
Let me read the problem carefully. The problem states that all teachers... |
[
{
"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.A bus is in operation. The number of passengers on the bus is always a non-negative integer.\nAt some point in time, t... | {
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} | 0 | 377 | LiveCodeBench | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to find the minimum possible current number of passengers on a bus given some stops. Let's see the problem statement again.
The bus starts with zero or more passengers. Then, after the initial state, it stops N times. At each stop i, the number of passengers inc... |
[
{
"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... | {
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"seed": 1,
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} | 1 | 411 | JEEBench | {
"expected_answer": "D",
"problem_id": "54",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's tackle this problem. So, I need to match the compounds in LIST-I with the observations in LIST-II and figure out which option is correct. Let's go through each compound one by one and see what reactions they undergo.
Starting with Aniline (I). I remember that aniline is a phenol with an amino group... |
[
{
"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) (z = 11) 1s^2 2s^2 2p^6, (b) (z = 25) 1s^2 2s^2 2p^6 3s^2 3p^6 3d^5, and (c) (z = 29) 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10; provide the proper ionic sy... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 407 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to figure out the correct ionic symbols for each part (a), (b), and (c) based on their electron configurations. Let's start by understanding each case.
First, part (a) has z=11. The electron configuration given is 1s² 2s² 2p⁶. That's the electron configuration for sodium (Na), since the atomic num... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider an aperture, which shapes like a N-sided polygon. All the apothems are of the same length a. When a monochromatic light (of wavelength \\lambda), travelling alo... | {
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} | 2 | 159 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the angular distance between the first two minima when a monochromatic light falls on an infinitely large N-sided polygon aperture. The key is to understand the diffraction pattern produced by such an aperture and use the appropriate formula for the angular positions of the m... |
[
{
"content": "Problem: For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nMark your solution with \\boxed\nAnswer:",
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] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 37 | AMC23 | {
"expected_answer": "901",
"problem_id": "47",
"reference_solution": "",
"subject": null,
"type": null
} | To determine for how many integers \( n \) the expression
\[
\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}}
\]
represents a real number, we need to ensure that the argument of the square root is non-negative and that the denominator is not zero. Let's break this down step by step.
### Step 1: Simplify the Argume... |
[
{
"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... | {
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} | 2 | 212 | CodeElo | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to determine after each swap whether the permutation forms a valid DFS order for the given perfect binary tree.
First, I need to understand what makes a permutation a valid DFS order. A DFS order is built by starting at the root and visiting nodes in a certain... |
[
{
"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, cost and time, of size n representing the costs and the time taken to paint n different walls respectively. There a... | {
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} | 1 | 25 | LiveCodeBench | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's see. I need to find the minimum cost to paint all the walls using both the paid and free painters. The paid painter can work on any wall, taking the time specified, and costs the given amount. The free painter can work on any wall in 1 unit of time but doesn't cost anything. But the free painter can... |
[
{
"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) regarding the binary transition metal carbony... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 129 | JEEBench | {
"expected_answer": "BC",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement regarding the properties of binary transition metal carbonyl compounds, specifically for iron (Fe) and nickel (Ni). Let's go through each option step by step.
### Option (A): Total number of valence shell electrons at metal centre in Fe(CO)₅ or Ni(CO)₄ is 16
1.... |
[
{
"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 4-year-old boy is brought to the physician because of temperatures to 39.4°C (102.9°F) for 8 days. Examination shows anterior cervical lymphadenopa... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 310 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | To determine the most appropriate pharmacotherapy for this patient, let's first consider the clinical presentation. The child has a high fever for 8 days, anterior cervical lymphadenopathy, nonexudative conjunctivitis, a strawberry tongue, erythematous truncal rash, and hand-foot edema. This combination of symptoms is ... |
[
{
"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: If the foot is abducted, it is moved in which direction?\nOptions: A. Backward, B. Circular motion, C. No movement, it remains stationary, D. Toward ... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 108 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | To determine the correct direction when the foot is abducted, we need to understand the anatomical term "abduction."
Abduction generally refers to the movement of a limb away from the midline of the body. For example, when you move your arm out to the side, away from the center of your body, that's abduction. Applyin... |
[
{
"content": "Problem: For complex number $u = a+bi$ and $v = c+di$ (where $i=\\sqrt{-1}$), define the binary operation\n$u \\otimes v = ac + bdi$\nSuppose $z$ is a complex number such that $z\\otimes z = z^{2}+40$. What is $|z|^2$?\nMark your solution with \\boxed\nAnswer:",
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] | {
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"seed": 8,
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} | 8 | 25 | AMC23 | {
"expected_answer": "50",
"problem_id": "28",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the value of \( |z|^2 \) given that \( z \otimes z = z^2 + 40 \) for a complex number \( z = a + bi \).
First, let's understand the binary operation \( \otimes \). For complex numbers \( u = a + bi \) and \( v = c + di \), the operation is defined as:
\[ u \otimes v = ac + bd... |
[
{
"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: Why do economists stress the cross-elasticitiesbetween different factors of production?\nOptions: A. Cross-elasticity is used to calculate the gross ... | {
"do_sample": true,
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} | 0 | 47 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | I think the correct answer is I. Cross-elasticity between factors of production is important because factors often interact, complementing or substituting each other. This helps in understanding how changes in one factor affect others, which is crucial for economic analysis. Options like A to H seem to focus on specifi... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 186 | CodeElo | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to maximize the score by performing operations on the array a. Let me read the problem carefully.
So the problem says that for each test case, we have an array a and a binary array b. We can perform operations where we select an index i where b_i is 1, and increa... |
[
{
"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: Model studies of a sea wall are conducted at a scale of 1 : 25. If the wave period in the prototype is 10 sec, what should be the period of wave gene... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 413 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine two things: the wave period in the model and the corresponding prototype force per foot of wall given a model wave force. Let's break this down step by step.
### Step 1: Determine the Wave Period in the Model
The problem states that the model studies are conducted at a scale... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 83 | CodeElo | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each query, I have to compute the sum of a_i XOR i along the path from x to y. Hmm, let's think about how to approach this.
First, the input is a tree, and each query is a pair of nodes. The straightforward way would be to find the path between x and y for each quer... |
[
{
"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: A thin and uniform rod of mass $M$ and length $L$ is held vertical on ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 217 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "1",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the motion of a thin, uniform rod of mass \( M \) and length \( L \) as it falls from a vertical position to an angle of \( 60^\circ \) with the vertical, rotating about its contact point with the floor without slipping. We will determine which of the given statements are corre... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Your colleague has devised a new quantum field theory on four-dimensional spacetime, and is exploring the regularization of certain higher-order loop diagrams in that th... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 49 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | To determine the number of loops in the Feynman diagram based on the given expression, we need to analyze the factors provided in the problem. Let's break down each component of the expression:
The expression given is: \(\alpha^3 \cdot g^2 \sqrt{2} \cdot 8 \cdot \frac{1}{(4\pi)^6} \cdot (Q/M)^2\).
First, let's recall... |
[
{
"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 zero or more sensors placed on a grid of H rows and W columns. Let (i, j) denote the square in the i-th row ... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 307 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where sensors interact with their adjacent cells (including diagonally) and count them as one sensor if they are connected. Hmm. The problem is to find the number of distinct sensor regions after considering all interactions.
So the input is a grid where each cell ... |
[
{
"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 | 374 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to compute G(n, k), the index of the n-th Fibonacci number divisible by k. And since n can be up to 1e18 and k up to 1e5, a brute-force approach isn't going to work. So I need a smarter way.
First, let's think about the Fibonacci sequence modulo k. Since k is fix... |
[
{
"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: Two alternatives for interconnecting a set of processors with bidirectional links are (1) the fully interconnected network, in which each processor i... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 162 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compare the figure of merit for two types of network topologies: the fully interconnected network and the ring network. The figure of merit is calculated as the product of the number of links in the network and the worst-case path length. We need to find the ratio of this figure of mer... |
[
{
"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 and Aoki are playing a game using N cards. The front side of the i-th card has A_i written on it, and the ba... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 449 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Takahashi and Aoki are playing a game with cards, and I have to determine who wins if both play optimally. The input is N cards, each with A_i and B_i on their front and back. They take turns removing pairs where either the front numbers are the same or the ba... |
[
{
"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 option(s) about entropy (S) is(are)\n$[\\mathrm{R}=$ gas c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 443 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "46",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate each statement regarding entropy changes and determine which are correct based on the given conditions and principles.
### Analysis of Each Option:
**Option (A):**
The reaction is \( \text{M}(s) + 2 \text{H}^+(aq) \rightarrow \text{H}_2(g) + \text{M}^{2+}(aq) \).
Given that ... |
[
{
"content": "Problem: Consider the set of complex numbers $z$ satisfying $|1+z+z^{2}|=4$. The maximum value of the imaginary part of $z$ can be written in the form $\\tfrac{\\sqrt{m}}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\nMark your solution with \\boxed\nAnswer:",
"... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 6 | AMC23 | {
"expected_answer": "21",
"problem_id": "7",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the maximum value of the imaginary part of a complex number \( z \) that satisfies the equation \( |1 + z + z^2| = 4 \). Let's denote \( z \) as \( x + yi \), where \( x \) and \( y \) are real numbers, and \( i \) is the imaginary unit.
First, we express \( 1 + z + z^2 \) in 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": 2,
"temperature": 0.7
} | 2 | 357 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about finding a binary string s of length n such that the oneness is as small as possible. Oneness is defined as the absolute difference between f(t) and g(t), where f(t) is the count of non-empty subsequences with only 0s, and g(t) is the count of those with at least one 1. So, ... |
[
{
"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 of integers nums of length n, and a positive odd integer k.\nThe strength of x subarrays is defined as strength = sum[1] * x - ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 460 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to select k disjoint subarrays from the nums array such that their strength is maximized. The strength is calculated in a specific way. Let me try to understand the problem step by step.
First, the strength formula. The strength is the sum of sum[i] multiplied by... |
[
{
"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 | 383 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem. Let's read the description carefully.
The problem is about binary search correctness. Bessie's code is a binary search that finds the insertion point for k, but since the array is possibly unsorted, the code might not work correctly. The tests are such that each test (x_i, k... |
[
{
"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: Three numbers are chosen at random, one after another with rep... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 329 | JEEBench | {
"expected_answer": "24.5",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the probabilities \( p_1 \) and \( p_2 \) and then compute the value of \( \frac{125}{4} p_2 \).
### Step 1: Understanding \( p_1 \)
\( p_1 \) is the probability that the maximum of three chosen numbers is at least 81.
The maximum of three numbers is at least 81 if at leas... |
[
{
"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 | 13 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where given an array b and a number k, I need to find an array a such that applying the function f, k times, gives b. The function f is defined in terms of the Fenwick Tree, but maybe there's a way to reverse engineer this.
First, let me understand what the function f does. T... |
[
{
"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: S Select the best translation into predicate logic. Some kind people help some endangered species. (Ex: x is endangered; Kx: x is kind; Px: x is a p... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 203 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to translate the sentence "Some kind people help some endangered species." into predicate logic using the provided options. Let's break down the sentence and analyze each part step by step.
First, the sentence can be split into two main parts: "some kind people" and "some endangered spec... |
[
{
"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 arrays of strings wordsContainer and wordsQuery.\nFor each wordsQuery[i], you need to find a string from wordsContainer that has the longest ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 468 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each word in the query, I have to find the corresponding word in the container that has the longest common suffix. If there are multiple, choose the shortest length, and if there's a tie, the one that appears first in the container. Then return the indices of those w... |
[
{
"content": "Problem: There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of a $5\\times5$ grid such that: each cell contains at most one chip all chips in the same row and all ch... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 8 | AIME24 | {
"expected_answer": "902",
"problem_id": "aime24-8",
"reference_solution": "The problem says \"some\", so not all cells must be occupied.\nWe start by doing casework on the column on the left. There can be 5,4,3,2, or 1 black chip. The same goes for white chips, so we will multiply by 2 at the end. There is $1$... | To solve this problem, we need to determine the number of ways to place 25 indistinguishable white and 25 indistinguishable black chips on a 5x5 grid such that each cell contains at most one chip. Additionally, all chips in the same row and column must have the same color. Any additional chip would violate these condit... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 161 | 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 powerful integers between start and finish. A powerful integer is one that ends with the given string s and each of its digits is at most the limit. Hmm, let's think about how to approach this.
First, the problem is to count how many numbers... |
[
{
"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 sticks with several balls stuck onto them. Each ball has a lowercase English letter written on it.\nFor ea... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 240 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to count the number of distinct sticks based on the sequences of letters on them. Each stick's letters are given as a string, and two sticks are the same if their sequences are equal or their reversals. So the key is to check for each string whether its reverse is... |
[
{
"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 Shop has N products.\r\nThe price of the i-th product (1\\leq i\\leq N) is P _ i.\r\nThe i-th product (1\\leq ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 239 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that checks if there's a product i that is strictly superior to product j. The conditions are that i's price is greater than or equal to j's, j has all functions of i, and either i's price is strictly greater than j's, or j has some functions that i doesn't hav... |
[
{
"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 | 311 | 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 two strongly connected directed graphs, each with n vertices. The cycles in both have lengths divisible by k. And I need to connect them with exactly n new edges such that each outgoing vertex in the first graph has exactly one outgoing edge (so maybe e... |
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