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 1 510k |
|---|---|---|---|---|---|---|
[
{
"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": 1,
"temperature": 0.7
} | 1 | 83 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's analyze each option in the context of converting a sequential algorithm into a parallel algorithm for solving higher-dimensional heat equations with matrix exponential approximations.
A) Existence of nonlocal boundary conditions: Nonlocal boundary conditions might complicate 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: Consider the following reactions (unbalanced)\n$\\mathrm{Zn}+$ hot con... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 224 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each given reaction step by step and determine the products based on the reactants and chemical principles. Let's start by balancing each equation and identifying the products.
### Reaction 1: Zn + hot conc. H₂SO₄ → G + R + X
Zinc (Zn) reacts with concentrated sulfuric acid (... |
[
{
"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 | 158 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if Vanya can transform the sequence \( s \) into \( t \) using XOR operations on contiguous subsequences. The key insight is to recognize that each XOR operation effectively cancels out the effect of previous operations if the same indices are chosen again. This leads us to c... |
[
{
"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 | 340 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of game configurations where Bob wins when the number of stones in each pile can vary between 1 and a given maximum, and both players play optimally. The solution involves understanding the game's rules and using dynamic programming to efficiently compute the winni... |
[
{
"content": "Problem: Let $f$ be the unique function defined on the positive integers such that \\[\\sum_{d\\mid n}d\\cdot f\\left(\\frac{n}{d}\\right)=1\\] for all positive integers $n$. What is $f(2023)$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 12 | AMC23 | {
"expected_answer": "96",
"problem_id": "14",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \( f(2023) \), we start by analyzing the given functional equation:
\[
\sum_{d \mid n} d \cdot f\left(\frac{n}{d}\right) = 1
\]
This equation holds for all positive integers \( n \). Our goal is to determine \( f(2023) \).
First, let's consider the case when \( n = 1 \). The divisors of 1 are only 1. So... |
[
{
"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 heavy nucleus $Q$ of half-life 20 minutes undergoes alpha-decay with pr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 312 | JEEBench | {
"expected_answer": "D",
"problem_id": "4",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the number of alpha-decays of the heavy nucleus \( Q \) in the first hour, given its half-life and the probabilities of alpha and beta decay.
### Step-by-Step Solution:
1. **Understand the Problem:**
- The half-life of \( Q \) is 20 minutes.
- The probabilities of alp... |
[
{
"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 | 53 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum number of starting cells from which Rostam will be trapped forever in the witch's maze. The key insight is that Rostam will be trapped if and only if the maze forms a cycle, meaning he keeps moving in a loop indefinitely. Therefore, our task is to maximize the num... |
[
{
"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 | 162 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find a cyclic route in Pelican Town that allows Farmer Buba to visit each road with an NPC exactly once. The route must start and end at the same house, and each road with an NPC must be traversed exactly once. The solution must handle multiple test cases efficiently.
### Approach
1. ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In the lab, a chemist discovers an unnamed bottle with a white solid inside. He gathers the following spectral information in order to identify the liquid. Make a reason... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 153 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to analyze the given spectral data (mass spectrometry, IR, and NMR) to determine the structure of the unidentified white solid. Let's break down each piece of information step by step.
1. **Mass Spectrometry (MS) Data:**
- The molecular ion peak is at m/z 156 (100%).
- Another peak... |
[
{
"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 | 80 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if two arrays \(a\) and \(b\) can be made identical by performing a specific set of swaps. The allowed swaps involve swapping elements in both arrays such that after all swaps, both arrays are the same.
### Approach
1. **Problem Analysis**: The problem allows swapping elemen... |
[
{
"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 | 433 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum possible rating of the last remaining fighter after a series of battles. The key insight is that each battle between two fighters results in the elimination of the first fighter and a reduction in the rating of the second fighter by the first's rating. The goal 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 272 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of bottle caps that need to be removed so that the front row of bottles can be arranged in a way that satisfies the owner's requirements. The requirements are that each bottle in the front row must be shorter than the corresponding bottle in the back row, 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.Takahashi has created a game where the player controls a dragon on a coordinate plane.\nThe dragon consists of N parts... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 358 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where a dragon is moving on a coordinate plane. Let's see what the problem is asking for.
So, there are N parts, numbered 1 to N, with part 1 being the head. Initially, each part i is at (i, 0). Then we have Q queries. The queries are either moving the head in a direction or ... |
[
{
"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 | 352 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine whether every pair of vertices in a cycle graph has a palindrome route. A palindrome route is defined as a path where the edge colors along the path form a palindrome sequence.
### Approach
1. **Understanding the Problem**: For each pair of vertices (i, j), there must exist... |
[
{
"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 the function $f:[0,1] \\rightarrow \\mathbb{R}$ be defined... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 309 | JEEBench | {
"expected_answer": "19",
"problem_id": "52",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the given problem, we need to evaluate the sum \( f\left(\frac{1}{40}\right) + f\left(\frac{2}{40}\right) + \cdots + f\left(\frac{39}{40}\right) - f\left(\frac{1}{2}\right) \) where the function \( f(x) = \frac{4^x}{4^x + 2} \).
First, let's analyze the function \( f(x) \). We can rewrite it as:
\[
f(x) = \fr... |
[
{
"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 | 76 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of groups such that Bob's score exceeds Alice's score by at least \( k \) points. Each group is a contiguous subsegment of fishes, and each fish in group \( i \) has a value of \( i-1 \). The goal is to split the fishes into groups optimally to maximize Bob... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: cyclohexanone was treated with bromine, forming product 1.\n1 was heated with sodium hydroxide, forming product 2.\n2 was treated with thionyl chloride and pyridine, for... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 47 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's work through the problem step by step to determine the number of chemically distinct hydrogen atoms on product 4.
Starting with cyclohexanone, which is the initial compound. When treated with bromine, it forms product 1. Cyclohexanone has a carbonyl group (C=O) attached to a carbon in the cyclohexane ring. Bromi... |
[
{
"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 | 192 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if Alex can find a time interval of at least \( s \) minutes during the day when he is not busy with any of his tasks. The tasks are represented by non-overlapping time intervals, and we need to check if there's a free period long enough for Alex to shower.
### Approach
1. *... |
[
{
"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.For positive integers x and y, define f(x, y) as follows:\n\n- Interpret the decimal representations of x and y as str... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 446 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compute the sum of the concatenation of every pair of distinct integers in a given list, modulo 998244353. The key insight is to recognize that the concatenation of two numbers can be broken down into contributions based on their digits, which allows us to compute the result efficientl... |
[
{
"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 correct sequence of reagents to synthesize 1-(cyclohexyl(hydroxy)methyl)cyclohexanecarbaldehyde from ethynylcyclohexane.\n\n\nOptions: A) 1. NaNH2, methyl c... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 61 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's work through the problem step by step to determine the correct sequence of reagents for synthesizing 1-(cyclohexyl(hydroxy)methyl)cyclohexanecarbaldehyde from ethynylcyclohexane.
First, let's analyze the target molecule. The structure is a cyclohexane ring with a methyl group attached to a carbon that also has 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 a 0-indexed integer array nums.\nYou can perform any number of operations, where each operation involves selecting a subarray of the array and re... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 139 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum length of a non-decreasing array that can be formed by replacing any subarray with the sum of its elements. The key is to efficiently find the longest possible non-decreasing subarray through optimal operations.
### Approach
1. **Dynamic Programming Insight**: We... |
[
{
"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 $a$ and $b$ be positive real numbers. Suppose $\\overrightarrow{P ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 304 | JEEBench | {
"expected_answer": "AC",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given conditions step by step. Let's start by understanding the problem statement and the vectors involved.
Given:
- \(\overrightarrow{PQ} = a\hat{i} + b\hat{j}\)
- \(\overrightarrow{PS} = a\hat{i} - b\hat{j}\)
- These are adjacent sides of a parallelogram \(PQRS\).
- \(\v... |
[
{
"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 | 185 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find a permutation \( q \) that minimizes the number of pairs \((i, j)\) where the sum of elements from \( p_i \) to \( p_j \) equals the sum of elements from \( q_i \) to \( q_j \).
### Approach
1. **Understanding the Problem**: The goal is to minimize the number of subarray sum pai... |
[
{
"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 a single integer N written on a blackboard.\r\nTakahashi will repeat the following series of operations until... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 381 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the total amount of money Takahashi will pay by performing a series of operations on the integers written on a blackboard until all integers not less than 2 are removed. The key insight is that the total payment is constant regardless of the order of operations, so we can fin... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 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 \(8 \cos^2 \alpha\) given the conditions on vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\).
### Step-by-Step Solution:
1. **Given Conditions:**
- \(\vec{a}\) and \(\vec{b}\) are unit vectors.
- \(\vec{a} \cdot \vec{b} = 0\) (they are orthogonal).
- \... |
[
{
"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 | 364 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if it's possible to form an isosceles trapezoid using four sticks from a given list of sticks. If possible, we need to return the lengths of the four sticks; otherwise, output -1.
### Approach
The key insight is based on the properties of an isosceles trapezoid. The necessa... |
[
{
"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 $a$ and $b$ be positive real numbers. Suppose $\\overrightarrow{P ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 304 | JEEBench | {
"expected_answer": "AC",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given vectors and conditions step by step. Let's start by understanding the problem thoroughly.
Given:
- Vectors \(\overrightarrow{PQ} = a\hat{i} + b\hat{j}\) and \(\overrightarrow{PS} = a\hat{i} - b\hat{j}\) are adjacent sides of a parallelogram \(PQRS\).
- \(\vec{u}\) an... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Let |alpha> be the state describing an electron, such that it is proportional to (1+i) |up> + (2-i) |down>, where |up> and |down> are the eigenstates of the z-projection... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 111 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the probabilities of measuring the electron in the eigenstates of the z-projection spin operator (which are |up> and |down>) and the average value of the operator given by the matrix A. The operator's matrix elements A_ij are defined as hbar/2 if i ≠ j and 0 otherwise.
Firs... |
[
{
"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 $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(1+x)^{2}+(... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 38 | JEEBench | {
"expected_answer": "5",
"problem_id": "51",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve for the smallest positive integer \( m \) such that the coefficient of \( x^2 \) in the expansion of \( (1+x)^2 + (1+x)^3 + \cdots + (1+x)^{49} + (1+mx)^{50} \) is \( (3n+1) \binom{51}{3} \) for some positive integer \( n \), we need to follow these steps:
### Step 1: Understand the Problem
The given expressi... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 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 tangent to each other and two of them 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 expressed a... |
[
{
"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 | 255 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum length of a good array that can be formed given two integers \( l \) and \( r \), where each element of the array must be within the range \([l, r]\). A good array is defined as an array that is strictly increasing and has the property that the differences between... |
[
{
"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 and a non-negative integer k. In one operation, you can increase or decrease any element by 1.\nReturn the minimum number o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 474 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of operations required to make the median of the array equal to a given non-negative integer \( k \). The operations allowed are increasing or decreasing any element by 1.
### Approach
1. **Understanding the Median**: The median of an array is the middle ... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 323 | 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 consecutive duplicate pairs in a substring for multiple queries. Let's think about how to approach this.
First, the input is a string S of length N, and Q queries. Each query is a range (l_i, r_i) where I have to check the substring from in... |
[
{
"content": "Problem: What is the value of\n\\[2^3 - 1^3 + 4^3 - 3^3 + 6^3 - 5^3 + \\dots + 18^3 - 17^3?\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 3 | AMC23 | {
"expected_answer": "3159",
"problem_id": "3",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the given problem, we need to evaluate the sum:
\[2^3 - 1^3 + 4^3 - 3^3 + 6^3 - 5^3 + \dots + 18^3 - 17^3.\]
First, observe the pattern in the terms. Each term is of the form \( (2n)^3 - (2n-1)^3 \) where \( n \) starts from 1. Let's check the first few terms:
- When \( n=1 \): \(2^3 - 1^3 = 8 - 1 = 7\)
- W... |
[
{
"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 | 224 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to efficiently manage a set of integers and perform operations to insert, remove, and compute the k-load of the set. The k-load is defined as the smallest positive integer d such that the integers d, d+1, ..., d+k-1 are not present in the set.
### Approach
The approach involves using a ... |
[
{
"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 | 448 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum value of k such that all given cells can be painted black using the fewest possible operations. Each operation allows painting two white cells i and j black as long as |i - j| ≤ k. Additionally, at most one cell not in the given list can be painted black.
### App... |
[
{
"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 | 359 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if QED can sort a given permutation using a series of allowed operations. The operations are based on a string \( s \) that guides the swaps. Each character in \( s \) determines whether we swap adjacent elements from the left or right. The challenge is to check after each qu... |
[
{
"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: A sample $(5.6 \\mathrm{~g})$ containing iron is completely di... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 358 | JEEBench | {
"expected_answer": "18.75",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the number of moles of Fe²⁺ in the 250 mL solution and then use that to find the percentage of iron by weight in the sample. Let's break it down step by step.
### Step 1: Determine the number of moles of MnO₄⁻ consumed in the titration
The titration involves using potassium ... |
[
{
"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 | 179 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of free cells in a 2xN grid such that blocking any of these cells results in exactly three connected regions. The grid is initially either connected as a single region or has no regions (all cells blocked). The key insight is to identify cells whose removal would s... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In gametogenesis, the germline undergoes two cycles of meiosis to give rise to haploid gametes. The goal of meiosis, unlike mitosis, is to separate not only the replicat... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 96 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's first understand the question. Klinefelter's syndrome is a condition in boys where there's an extra X chromosome (47,XXY), leading to various phenotypic effects. The question asks why Klinefelter's might have less prominent consequences compared to Down's syndrome (47,Trisomy 21),... |
[
{
"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 | 170 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if it's possible to transform a binary string `s` into another binary string `r` of length `n-1` through a series of operations. Each operation involves finding a pair of consecutive characters in `s` that are different, replacing them with the corresponding character from `r... |
[
{
"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 | 375 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if it's possible to transform a given number into another number divisible by 9 using the allowed operations. The allowed operation is to replace a digit with its square, but the square must result in a single-digit number (i.e., 0-9).
### Approach
1. **Understanding the Op... |
[
{
"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 permutation A=(A_1,\\ldots,A_N) of (1,2,\\ldots,N).\r\nTransform A into (1,2,\\ldots,N) by performing the following operation between 0 and N-1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 429 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to transform a permutation array A into the sorted array [1, 2, ..., N] using swaps between pairs. The output should show the number of operations and each step's swap. Hmm.
First, let's understand the problem. The allowed operation is swapping two elements in th... |
[
{
"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 Daily Planet's rate for one agate line of print is $4. It has a circulation of 2 million. What is themillinerate?\nOptions: A. $6.00, B. $1.50, C... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 120 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is asking about the millinerate for The Daily Planet's agate line print. Hmm, I need to figure out what that means. Wait, millinerate—maybe it's a typo? Or perhaps it's a term I'm not familiar with. Let me think.
Wait, the user mentioned that the rate for one agate line is $4. Agat... |
[
{
"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 | 181 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum possible value of the tree after performing operations to make all node values equal. The operations allow us to increase the values of all nodes in a subtree by 1, starting from a chosen root node. The goal is to find the smallest initial value that can be achiev... |
[
{
"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 | 161 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine for each query whether the Sheriff can prevent Robin Hood from winning when the game is played only on a subset of targets specified by the query. The solution involves understanding the optimal play strategy for both players and efficiently computing the results for each que... |
[
{
"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 | 64 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to handle two types of queries on a tree structure. The first type modifies the edge weights using XOR with a given integer, and the second type involves finding a specific cycle after adding a new edge and determining the maximum XOR of the edges in that cycle.
### Approach
1. **Tree Re... |
[
{
"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 nums consisting of positive integers.\nYou can do the following operation on the array any number of times:\n\nChoose an intege... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 57 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to maximize the largest element in the array by performing a series of operations. Each operation involves selecting an element that is less than or equal to the next element, replacing it with their sum, and removing the selected element. The goal is to determine the maximum possible val... |
[
{
"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: Use divergence therem to evaluate $\\iint_S \\vec{F} \\cdot d \\vec{S}$ where $\\vec{F} = sin(\\pi x) \\vec{i} + (z y^3)\\vec{j} + (z^2 + 4x)\\vec{k}... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 227 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the given problem using the divergence theorem, we need to evaluate the surface integral of the vector field \(\vec{F}\) over the closed surface \(S\) of a box. The divergence theorem states that the surface integral of a vector field over a closed surface is equal to the volume integral of the divergence of t... |
[
{
"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 | 178 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of operations required to change all characters in a given string of 0s and 1s to 0s. Each operation involves selecting a non-empty subsequence where any two adjacent characters are different, flipping each character in that subsequence (0 becomes 1 and vic... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We have a large ensemble of 10.000 (ten thousand) identical systems. Each system has a particle that are the same and under the same conditions. Each particle can move a... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 38 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the value of \( a \) such that the wave function \( \psi(x) = \frac{a}{\sqrt{1 + x}} - 0.5i \) is normalized between \( x = 1 \) and \( x = 3 \). Normalization means that the integral of the probability density over all space must equal 1. Since the particles are only found 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 202 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the latest time one can leave home to reach the event intersection (n) on time, considering the constraints of both walking and bus travel, as well as a mandatory phone call during the journey. The solution involves finding the shortest path using the bus and comparing it wit... |
[
{
"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 monopoly with a straight, downward-sloping demand curve has a marginal revenue curve that is\nOptions: A. initially upward sloping and then downwar... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 300 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the shape of the marginal revenue (MR) curve for a monopoly with a straight, downward-sloping demand curve, let's recall the relationship between demand and MR.
In a monopolistic market, the demand curve is downward sloping, meaning that as price decreases, quantity increases. The MR curve for a monopolis... |
[
{
"content": "Problem: A cylindrical beaker is 8 cm high and has a radius of 3 cm. How many such beakers of water will it take to fill a spherical tank of radius 6 cm?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 325 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | To determine how many cylindrical beakers are needed to fill a spherical tank, we need to calculate the volumes of both the beaker and the tank and then divide the tank's volume by the beaker's volume.
First, let's calculate the volume of the spherical tank. The formula for the volume of a sphere is:
\[
V_{\text{spher... |
[
{
"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 | 340 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of valid configurations of stone piles (each pile can have between 1 and a given maximum) where Bob wins the game. The game is played optimally by both players, so we need to model the game states and determine the winning positions for Bob.
### Approach
1. **Unde... |
[
{
"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 heavy nucleus $N$, at rest, undergoes fission $N \\rightarrow P+Q$, ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 344 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "5",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the fission process of a heavy nucleus \( N \) into two lighter nuclei \( P \) and \( Q \). We start by considering the conservation of energy and momentum, and the given definitions of the variables involved.
Given:
- \( N \) is at rest initially.
- After fission, \( N \) bec... |
[
{
"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 a non-zero complex number $z$, let $\\arg (z)$ denote the principa... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 137 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To determine which statement(s) are false, we need to analyze each option step by step.
**Option (A):** $\arg (-1 - i) = \frac{\pi}{4}$
First, compute the argument of the complex number $-1 - i$. The argument of a complex number $a + bi$ is given by $\tan^{-1}(b/a)$ adjusted for the correct quadrant.
Here, $a = -1$ ... |
[
{
"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 2D integer array nums representing the coordinates of the cars parking on a number line. For any index i, nums[i] = [start_i, end_i] ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 97 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of integer points on a number line that are covered by any part of a car. Each car is represented by a start and end coordinate on the line, and we need to count all unique points that are within or on the boundaries of any of these intervals.
### Approach
1. **Pr... |
[
{
"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: Two men are walking along a horizontal straight line in the sa... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 125 | JEEBench | {
"expected_answer": "5",
"problem_id": "8",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to determine the frequency of the beats heard by the stationary man when the two moving men are 10 meters apart. The key steps involve using the Doppler effect for each moving man and then finding the beat frequency between the two resulting frequencies.
### Step-by-Step Solution:
1. **... |
[
{
"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 | 114 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of operations required to make a given tree "wonderful". A tree is called wonderful if for every vertex with children, the value of the vertex is less than or equal to the sum of the values of its children. Each operation allows us to increment the value of... |
[
{
"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: Let $p, q, r$ be nonzero real numbers that are, respectively, the $10^{\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 391 | JEEBench | {
"expected_answer": "B",
"problem_id": "17",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to analyze the given system of linear equations and determine the conditions under which the system has different types of solutions (unique, infinitely many, or none) based on the relationships between \( p, q, \) and \( r \).
Given the system:
\[
\begin{cases}
x + y + z = 1 \\
10x + 10... |
[
{
"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: Which of the following liberates $\\mathrm{O}_{2}$ upon hydrolysis?\n(A) ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 250 | JEEBench | {
"expected_answer": "B",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To determine which of the given compounds liberates \(\mathrm{O}_2\) upon hydrolysis, we need to analyze each option and their respective reactions with water.
1. **Option (A): \(\mathrm{Pb}_3\mathrm{O}_4\)**
Lead(II,IV) oxide, \(\mathrm{Pb}_3\mathrm{O}_4\), when reacted with water, forms lead(II) hydroxide and ox... |
[
{
"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 | 64 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of ways to split an array into segments such that the bitwise OR of each segment is non-decreasing. The solution involves dynamic programming and a clever approach to track the minimum and maximum values that can form the required segments.
### Approach
1. **Dynam... |
[
{
"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 | 220 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum score achievable by performing operations on a strip of cells. Each operation involves selecting a segment from 'L' to 'R', adding the sum of the values in that segment to the score, and then removing those cells from the strip. The key is to find the optimal segm... |
[
{
"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 | 326 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum number of non-overlapping segments in an array such that each segment sums to zero. The solution involves dynamic programming and a clever approach to track the sum of segments efficiently.
### Approach
1. **Understanding the Problem**: We need to find the maximu... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 476 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the maximum distance between the indices of two prime numbers in a given integer array. The solution should efficiently determine the positions of the prime numbers and compute the maximum distance between them.
### Approach
1. **Prime Identification**: First, identify all prime ... |
[
{
"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 | 331 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if there exists a permutation of a given string such that certain conditions based on the characters in the string are met. The string consists of characters 'p', 's', and '.' (dot). Each character in the string imposes specific permutation constraints on the corresponding po... |
[
{
"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: In a triangle $X Y Z$, let $x, y, z$ be the lengths of sides opposite ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 32 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given conditions and use geometric properties to find the correct options. Let's start by understanding the problem step by step.
Given:
- In triangle XYZ, sides opposite angles X, Y, Z are x, y, z respectively.
- The semi-perimeter \( s = \frac{x + y + z}{2} \).
- The con... |
[
{
"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: Which of the following statement(s) is(are) true?\n(A) Monosaccharides... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 196 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "29",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate each statement individually to determine their accuracy based on our knowledge of organic chemistry and biochemistry. Let's go through each option step by step.
**Option (A): Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones.**
Monosaccharides ar... |
[
{
"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: One morning, an employee arrived at work and found his boss passed out on the floor of his office. The employee determined that his boss was not brea... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 289 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's analyze the situation step by step. The employee rendered CPR to the boss when he was unconscious and called paramedics. Two weeks later, the boss expressed gratitude by promising the employee a lifetime job. The question is about the legal relationship and whether the promise 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": 0,
"temperature": 0.7
} | 0 | 3 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of pieces a binary string can be divided into such that each piece can be rearranged to form a sorted binary string. A sorted binary string is one where all '0's come before any '1's.
### Approach
1. **Understanding the Problem**: The key insight is that a... |
[
{
"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 | 233 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum number of students that can be gathered around each coffee machine after the teachers turn off the lights in some rooms. The key insight is that the order in which the rooms are processed does not matter, and we can always maximize the number of students at a part... |
[
{
"content": "Problem: Let $N$ be the greatest four-digit positive integer with the property that whenever one of its digits is changed to $1$ , the resulting number is divisible by $7$ . Let $Q$ and $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$ . Find $Q+R$ .\nMark ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 6 | AIME24 | {
"expected_answer": "699",
"problem_id": "aime24-6",
"reference_solution": "We note that by changing a digit to $1$ for the number $\\overline{abcd}$ , we are subtracting the number by either $1000(a-1)$ , $100(b-1)$ , $10(c-1)$ , or $d-1$ . Thus, $1000a + 100b + 10c + d \\equiv 1000(a-1) \\equiv 100(b-1... | To solve this problem, we need to find the greatest four-digit number \( N \) such that when any one of its digits is changed to 1, the resulting number is divisible by 7. Then, we need to divide \( N \) by 1000 and find the quotient \( Q \) and remainder \( R \), summing them up to get \( Q + R \).
### Approach
1. **... |
[
{
"content": "Problem: In the sequence 0, 1, 1, 3, 6, 9, 27, ..., the first term is 0. Subsequent terms are produced by alternately adding and multiplying by each successive integer beginning with 1. For instance, the second term is produced by adding 1 to the first term; the third term is produced by mu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 282 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to understand the sequence generation rules and determine the first term greater than 125. Let's break down the steps.
1. **Sequence Definition**: The first term \( a_1 = 0 \). Subsequent terms alternate between adding and multiplying by the next integer starting from 1. Specifically:
... |
[
{
"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 and two positive integers m and k.\nReturn the maximum sum out of all almost unique subarrays of length k of nums. If no su... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 82 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the maximum sum of an almost unique subarray of length k. Let's think about how to approach this.
First, the problem says a subarray is almost unique if it has at least m distinct elements. So for each possible subarray of length k, I need to check if it ... |
[
{
"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 | 427 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum number of happy people in an optimal seating arrangement on a bus with given rows and family members. A person is happy if they are either in the same row as another family member or sitting alone with an empty seat next to them.
### Approach
1. **Understand the... |
[
{
"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 | 237 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of ways to fill in the gaps in the given list of launched paper airplanes such that the sequence is valid according to the rules provided. The solution involves dynamic programming to track the possible configurations of the launched planes.
### Approach
1. **Dyna... |
[
{
"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. A subarray of nums is called continuous if:\n\nLet i, i + 1, ..., j_ be the indices in the subarray. Then, for ea... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 54 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to count all continuous subarrays of the given array `nums` where the absolute difference between any two elements in the subarray is at most 2.
### Approach
The key insight is to efficiently determine the valid continuous subarrays. For each element in the array, we want to find the lo... |
[
{
"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 $f_1:(0, \\infty) \\rightarrow \\mathbb{R}$ and $f_2:(0, \... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 371 | JEEBench | {
"expected_answer": "6",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the given problem, we need to analyze the functions \( f_1 \) and \( f_2 \) defined on the interval \((0, \infty)\) and determine the number of local minima and maxima for each. Then, compute the value of \(6m_2 + 4n_2 + 8m_2n_2\) where \(m_2\) and \(n_2\) are the number of local minima and maxima of \(f_2\).
... |
[
{
"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: As of 2019, about what percentage of the world population lives in extreme poverty (less than $1.90 a day)?\nOptions: A. 35%, B. 10%, C. 50%, D. 45%,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 409 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, I need to recall or look up the percentage of the world population living in extreme poverty as of 2019. Extreme poverty is defined as living on less than $1.90 per day.
From recent data, the World Bank reported that the number of people living in extreme poverty decreased to 9.2% of ... |
[
{
"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 organic compound. The following 1H NMR data was obtained:\n1H NMR: chemical reference (ppm): 7.0 (1H, d, J = 16.0 Hz), 5.5 (1H, dq), 2.1 (3H... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 54 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to analyze the given 1H NMR data and match it with the possible structures of the unknown organic compounds. The options are cis-propenyl acetate, trans-propenyl acetate, cis-butenyl acetate, or trans-butenyl acetate. Let's break down the NMR data step by step.
The NMR spectrum provided ... |
[
{
"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 | 333 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum cost to move from cell (1,1) to (n,m) in a grid where each cell can be cyclically shifted in any row any number of times before moving. The cost is calculated based on the number of shifts (x) and the sum of the values of the visited cells (y), with the formula k*... |
[
{
"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 | 167 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to process a series of queries on an array of zeros such that after all queries are applied, the sum of the array elements is minimized. Each query allows us to choose between two elements and a direction (either positive or negative) to adjust the element. The challenge is to determine t... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Compounds that have the same molecular formula but are different in their structural arrangement are known as isomers. Isomers have two types, constitutional isomers and... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 20 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine two things based on the given compounds:
1. Which of the given compounds (benzoquinone or cyclohexane-1,3,5-trione) does not show tautomerism (A).
2. Between methyl 2-hydroxypropanoate and dimethyl fumarate, which one will show optical isomerism (B).
**Step 1: Understanding... |
[
{
"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 | 214 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if we can replace each '?' in the string 's' with a lowercase English letter such that the string 't' becomes a subsequence of 's'. If possible, we need to generate such a string; otherwise, output "NO".
### Approach
1. **Problem Analysis**: The task is to check if 't' can 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 64 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to handle two types of queries on a tree structure. The first type modifies the weights of all edges using a bitwise XOR operation with a given integer. The second type involves finding the maximum XOR of all edges in a unique cycle formed by adding a new edge from a specified vertex to 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 a string s and a positive integer k.\nLet vowels and consonants be the number of vowels and consonants in a string.\nA string is beautiful if:\n\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 138 | 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 beautiful substrings in a given string s with a positive integer k. Let me think about how to approach this.
First, let's understand the problem. A substring is considered beautiful if two conditions are met: the number of vowels equals the ... |
[
{
"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 | 100 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum possible size of the largest connected component of '#' cells that Alex can achieve after performing at most one operation. The operation involves selecting a row or a column and setting all cells in that row or column to '#'.
### Approach
The key insight is to ... |
[
{
"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 ideal solution is a\nOptions: A. mixture where the solvents cannot be dissolved in any ratio, B. mixture that reacts violently when combined, C. m... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 189 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let me think about this. The problem is asking for the definition of an ideal solution. From what I remember, an ideal solution is one where the interactions between the components are the same as those in the pure substances. So, the potential energy of the mixture should be the same as the sum of the individual compo... |
[
{
"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 | 188 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine for each impression whether it can be unique. An impression is unique if there exists a possible array where that impression's value is different from all others. The key insight is to check if the range of possible values for each impression (given by l_i and r_i) allows it ... |
[
{
"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: One mole of an ideal gas expands adiabatically from an initial state $\\l... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 468 | JEEBench | {
"expected_answer": "A",
"problem_id": "23",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the ratio \( T_A / T_B \) for two different processes involving an ideal gas: an adiabatic expansion and an isothermal expansion, both leading to the same final state. The key is to use the properties of these processes and the ideal gas law.
### Step-by-Step Solution:
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: For water, $\\Delta H_{\\text {vaporization }}$ is $40.656 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$, and the normal boiling point is $373.12 \\mathrm{~K}$.... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 402 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to calculate the boiling point of water at the top of Mount Everest, where the barometric pressure is 253 Torr. The given values are the normal boiling point of water (373.12 K) and the enthalpy of vaporization ($\Delta H_{\text{vaporization}} = 40.656 \text{ kJ mol}^{-1}$).
The key con... |
[
{
"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 | 363 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum number of points Kevin can earn by rearranging the given integers. The key insight is that the maximum points are achieved by strategically placing even numbers early in the sequence to maximize the number of points earned from subsequent odd numbers.
### Approac... |
[
{
"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 | 104 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum possible cost of a path from the cell (1,1) to the cell (2,n) in a 2xN matrix. The path can only move to adjacent cells (right or down), and the cost is the sum of the values along the path. We can modify the matrix by swapping columns any number of times before c... |
[
{
"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 heavy nucleus $Q$ of half-life 20 minutes undergoes alpha-decay with pr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 312 | JEEBench | {
"expected_answer": "D",
"problem_id": "4",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the number of alpha-decays of the heavy nucleus \( Q \) in the first hour. Let's break down the problem step by step.
### Step 1: Understand the given parameters
- Half-life of \( Q \) is 20 minutes.
- Probability of alpha-decay per nucleus is 60% (0.6).
- Probability of bet... |
[
{
"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 that consists of lowercase English letters.\nA string is called special if it is made up of only a single character. For example, the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 172 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the longest special substring of a given string `s` that occurs at least three times. A special substring is one that consists of only a single character. If no such substring exists, we return -1.
### Approach
1. **Identify All Possible Substrings**: Generate all possible substr... |
[
{
"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 | 263 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to find the fifth restaurant that the user hasn't visited yet. Let's see. The input is four distinct numbers between 1 and 5, each representing the restaurant visited from Monday to Thursday. The output should be the remaining restaurant number for Friday.
Hmm, so the ap... |
[
{
"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: Two fair dice, each with faces numbered 1,2,3,4,5 and 6, are r... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 308 | JEEBench | {
"expected_answer": "8",
"problem_id": "51",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the probability that the sum of the numbers on two fair dice is a perfect square before it becomes a prime number. Then, we need to find the value of \(14p\), where \(p\) is this probability.
### Step 1: Identify Possible Sums
First, list all possible sums when two dice are ... |
[
{
"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 integers num1 and num2.\nIn one operation, you can choose integer i in the range [0, 60] and subtract 2^i + num2 from num1.\nReturn the integ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 40 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of operations required to reduce a given integer `num1` to zero using a specific set of operations. Each operation involves choosing an integer `i` between 0 and 60 and subtracting `2^i + num2` from `num1`. If it's impossible to reduce `num1` to zero using ... |
[
{
"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\n\\[\nM=\\left[\\begin{array}{lll}\n0 & 1 & a \\\\\n1 & 2 & 3 \\\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 205 | 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 matrix \( M \) and its adjugate matrix \( \text{adj} M \) to determine which of the given options are correct. Let's proceed step by step.
First, let's recall some properties of matrices:
1. The determinant of the product of two matrices is the product of their deter... |
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