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 158k |
|---|---|---|---|---|---|---|
[
{
"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
} | Let me think about this problem. The question is asking about the key factor that converts a sequential algorithm into a parallel algorithm when solving higher-dimensional heat equations using finite difference approximations and parallel splitting. The options given are A) existence of nonlocal boundary conditions, B)... |
[
{
"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)"
} | <think>
Okay, let's see. I need to figure out the correct options based on the given reactions. Hmm, let's start by balancing each of these reactions and identifying the products.
First reaction: Zn + hot conc. H2SO4 → G + R + X. Hot concentrated sulfuric acid. When Zn reacts with concentrated H2SO4 under heat, the pr... |
[
{
"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
} | <think>
Okay, let's try to figure out this problem. So the problem is about determining whether Vanya can transform the sequence s into t using the given XOR operations. Hmm. Let's read the problem again carefully.
The allowed operation is choosing an interval [l, r] and for each position i in [l, r], replace s_i with... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have to count the number of game configurations where Bob wins, given the constraints on the number of stones each pile can have. Let's try to break this down.
First, the problem is about Alice and Bob taking turns removing stones from piles. The key here is that each... |
[
{
"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 \( f(2023) \) given the functional equation \(\sum_{d \mid n} d \cdot f\left(\frac{n}{d}\right) = 1\) for all positive integers \( n \), we need to understand the properties of the function \( f \).
First, let's analyze the given equation. For each \( n \), the sum is over all divisors \( d \) of \( n \),... |
[
{
"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"
} | $\boxed{C}$
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 decay probabilities. Let's break down the problem step by step.
First, understand the decay process. The nucleus \( Q \) can decay either through alpha-decay (60% p... |
[
{
"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
} | <think>
Okay, let's see. I need to solve this problem where we have to find the maximum number of starting cells that will trap Rostam forever, given that the unspecified cells can be assigned directions optimally. Hmm.
So the problem is about determining for each test case the maximum number of starting cells that, 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 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
} | <think>
Okay, let's see. So the problem is to find a route that starts and ends at the same house, uses every road with an NPC exactly once, and doesn't use any road (in either direction) more than once. Hmm. So the main challenge is to model the graph and find such a cycle that covers all the NPC roads exactly once, a... |
[
{
"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
} | <think>
Okay, let's see. The problem is to identify an unknown compound based on the given spectral data. Let me start by breaking down the information provided.
First, the molecular ion peak is at m/z 156. The molecular ion is the highest mass in the mass spectrum and gives the formula's molecular weight. So the comp... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have two arrays a and b, and I can perform some swaps as per the rules to make them the same. Let's think about how to approach this.
First, the problem says that in one move, I can swap two elements in array a (from indices l to r) and two elements in array b, but th... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 433 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about maximizing the rating of the last remaining fighter after a series of battles. Each time two fighters are chosen, the smaller one is eliminated, and the larger one's rating is reduced by the smaller one's rating. Wait, no, wait. Wait, the problem says that in each battle, 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": 1,
"temperature": 0.7
} | 1 | 272 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to find the minimum number of caps to remove so that the front row bottles can be placed in such a way that they are all visible from the back row and form a mountain-like shape. Hmm. Let me break this down.
First, the problem states that each bottle i... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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 there's a dragon made of N parts, each moving based on the head's direction. The challenge is to process Q queries and output the coordinates of part p when queried. Let's think about how to approach this.
First, the initial positions. The head is part 1 at (1,0). Each ... |
[
{
"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
} | <think>
Okay, let's see. The problem is about determining for each test case whether every pair of vertices (i, j) in a cycle has a palindrome route. The cycle is such that each vertex is connected to its next and previous vertices with colors given by the string c.
First, I need to understand what a palindrome route... |
[
{
"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 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 \( f(x) = \frac{4^x}{4^x + 2} \).
### Step 1: Analyze the function \( f(x) \)
First, let's understand the behavior of 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": 0,
"temperature": 0.7
} | 0 | 76 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this competitive fishing problem. Let's read the problem carefully.
So, the problem is about splitting the fish into m groups such that Bob's score is at least k more than Alice's. And we need to find the minimal m possible. If it's impossible, return -1.
Hmm. Let's understand the setup.... |
[
{
"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.
1. **Cyclohexanone (Product 1 after Bromination):**
- Cyclohexanone reacts with bromine to form product 1. The likely product is 1-bromocyclohexane. However, the position of the bromine on the cyclohexane ring could be either axial or equatorial. But since the question i... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print 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
} | <think>
Okay, I need to solve this problem where Alex has to find a free interval of at least s minutes to shower. Let's see. The problem says that the tasks are non-overlapping and sorted. So, the input gives n intervals that don't overlap, and they are given in order. So, the first thought is to check the gaps betwee... |
[
{
"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
} | <think>
Okay, I need to solve this problem. Let's read the problem carefully.
So, the task is to compute the sum of f(A_i, A_j) for all pairs i < j, then take that sum modulo 998244353. The function f concatenates the decimal representations of x and y in that order. For example, f(3,14) is 314, which is 3 followed by... |
[
{
"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
} | <think>
Okay, I need to figure out the correct sequence of reagents to convert ethynylcyclohexane into 1-(cyclohexyl(hydroxy)methyl)cyclohexanecarbaldehyde. Let's break down the problem step by step.
First, let's look at the target molecule. It's a cyclohexane with a methyl group attached to the ring via a hydroxyl gr... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have to find the maximum length of a non-decreasing array that can be made after applying some operations. The operations allow selecting a subarray and replacing it with the sum of its elements. So, the goal is to maximize the length of the resulting non-decreasing ar... |
[
{
"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 and determine which statements are true based on the given information.
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... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have to find a permutation q that minimizes the number of equal sum subarrays compared to the original permutation p. Hmm. Let's think about how to approach this.
First, the problem is asking for any permutation q that gives the minimal possible number of such equal s... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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
} | <think>
Okay, I need to solve this problem where Takahashi is erasing numbers and writing their halves, and paying the erased number each time. The total amount he pays is the sum of all the numbers he erases. The question is to find that total sum efficiently, especially since N can be up to 10^17, which is way too bi... |
[
{
"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 this problem, we need to determine the value of \(8 \cos^2 \alpha\) given the conditions on vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\). Let's proceed step by step.
### Step 1: Understanding the Given Conditions
1. \(\vec{a}\) and \(\vec{b}\) are unit vectors with \(\vec{a} \cdot \vec{b} = 0\). This mea... |
[
{
"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
} | <think>
Okay, I need to solve this problem where Kevin has to select four sticks to form an isosceles trapezoid. Let's see the problem statement again. The key is that we have to find four sticks such that they can form such a trapezoid, and if possible, output any of them. If not, output -1.
First, I remember from th... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: 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)"
} | $\boxed{\text{A, C, D}}$
To solve this problem, we need to analyze the given vectors and their projections, then use the conditions provided to determine the correct statements.
**Step 1: Understanding the vectors and the parallelogram**
Given:
- \(\overrightarrow{PQ} = a\hat{i} + b\hat{j}\)
- \(\overrightarrow{PS} ... |
[
{
"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
} | <think>
Okay, let's see. I need to solve this problem step by step. The problem is about quantum mechanics, specifically dealing with the probabilities of measuring certain states and calculating the average value of an operator.
First, let's parse the problem statement. We have an electron in a state |α⟩ that's prop... |
[
{
"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 this problem, we need to determine the smallest positive integer \( m \) such that the coefficient of \( x^2 \) in the expansion of \( (1+x)^2 + (1+x)^3 + \cdots + (1+x)^{49} + (1 + m x)^{50} \) is equal to \( (3n + 1) \binom{51}{3} \) for some positive integer \( n \). Then, we need to find the value of \( n ... |
[
{
"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 sequentially tangent and two of these circles are tangent to sides \(AB\) and \(BC\) respectively. Additionally, 2024 circles of radius 1 are arranged in the same manner. The inradius can be expressed ... |
[
{
"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
} | <think>
Okay, I need to solve this problem where given l and r, I have to find the maximum possible length of a good array. Let's understand the problem first.
A good array is one that is strictly increasing, and the differences between adjacent elements are also strictly increasing. So, for example, the array [1,2,5]... |
[
{
"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... | {
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"subject": null,
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Okay, I need to solve this problem where I have to find the minimum number of operations to make the median of the array equal to k. Let's think about how to approach this.
First, let's understand the problem. The median is the middle element when the array is sorted. For an odd-length array, it's the exact mi... |
[
{
"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... | {
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"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 find the number of consecutive duplicate pairs in a substring for multiple queries. Let's see.
The input is a string S of length N and Q queries. Each query gives l_i and r_i, and I have to find how many times two consecutive same characters appear in the subs... |
[
{
"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 problem, we need to evaluate the sum \(2^3 - 1^3 + 4^3 - 3^3 + 6^3 - 5^3 + \dots + 18^3 - 17^3\). Let's break this down step by step.
First, observe the pattern in the terms. The sequence alternates between adding the cube of an even number and subtracting the cube of the preceding odd number. For example... |
[
{
"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,
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"seed": 2,
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} | 2 | 224 | CodeForces | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where we have a set that supports insert, remove, and query operations. The query is for the k-load, which is the smallest d such that there's a sequence of k consecutive numbers starting at d that are all not in the set.
Hmm, let's think about how to model this efficiently.... |
[
{
"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 ... | {
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"problem_id": "",
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Okay, I need to solve this problem where I have to find the minimum k such that all the given cells can be painted black, with at most one extra cell. Let me read the problem statement again carefully.
So the problem is about a strip of cells, all initially white. We can paint pairs of white cells (i and j) wh... |
[
{
"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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"temperature": 0.7
} | 0 | 359 | CodeElo | {
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} | <think>
Okay, I need to solve this problem where after each query, I have to determine if the permutation can be sorted using the allowed operations. Let's read the problem carefully.
So, the problem is about permutations and a string s that dictates how we can move elements. The allowed operations are swapping adjace... |
[
{
"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... | {
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"seed": 2,
"temperature": 0.7
} | 2 | 358 | JEEBench | {
"expected_answer": "18.75",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | **Step 1: Understanding the problem**
We need to determine the percentage by weight of iron (Fe) in the sample. The sample is dissolved in HCl to form a 250 mL solution. Titration of 25.0 mL of this solution with 0.03 M KMnO4 requires 12.5 mL to reach the endpoint. The key is to find the number of moles of Fe²+ in 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... | {
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"seed": 0,
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} | 0 | 179 | CodeElo | {
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"problem_id": "",
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} | <think>
Okay, I need to solve this problem where I have to find the number of cells in a 2-row by n-column grid that, when blocked, result in exactly 3 connected regions. Let's think about how to approach this.
First, the problem states that the original grid has at most one connected region. So, the original grid is ... |
[
{
"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... | {
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} | 2 | 96 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Let me think about this problem step by step. The question is asking about the molecular mechanism responsible for less prominent phenotypic consequences of Klinefelter's syndrome compared to Down's syndrome. The options are A to D.
First, I need to recall what Klinefelter's syndrome is. It's a condition in males wher... |
[
{
"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 ... | {
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"seed": 2,
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} | 2 | 170 | CodeForces | {
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} | <think>
Okay, let's see. So the problem is about determining whether it's possible to replace adjacent pairs in a binary string with another binary string such that each replacement reduces the length by one, and after n-1 operations, the string is down to one character. Hmm.
First, I need to model the process. Let'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 the ... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 375 | CodeForces | {
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"problem_id": "",
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} | <think>
Okay, let's see. The problem is to determine if we can transform a given number into one divisible by 9 by replacing digits with their squares. The allowed operations are choosing a digit, squaring it, and replacing the original digit with the result. But wait, the square must be a single digit. So, for example... |
[
{
"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... | {
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"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 generate a sequence of swaps to sort a permutation array. Let's see. The problem says that we can perform swaps between any two elements (i and j) any number of times between 0 and N-1, inclusive. And the output should be the steps taken to sort the array.
Hmm... |
[
{
"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 | {
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"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. The rate is $4 per one agate line, and the circulation is 2 million. Wait, the question says "themillinerate"—I think that's a typo and should be "milline rate" or maybe "milli rate"? Hmm.
Wait, the term "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 | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to find the minimum possible value of the balanced tree after performing some operations. The problem seems a bit complex, so I'll try to break it down step by step.
First, the problem statement says that the tree can be balanced by performing operatio... |
[
{
"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
} | <think>
Okay, let's try to figure out this problem. So, the problem is about determining for each query [l, r] whether the Sheriff can ensure he doesn't lose the game when considering only those targets. The game is that players take turns shooting targets, and each target gives a certain score. The key is that both pl... |
[
{
"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
} | <think>
Okay, let's try to figure out how to solve this problem. So the problem is about a tree with some queries. The queries can be of two types: XOR all edges with y, or for a vertex v and x, find the maximum XOR cycle when adding a virtual edge from v to u with weight x, and then choose u optimally to maximize 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 nums consisting of positive integers.\nYou can do the following operation on the array any number of times:\n\nChoose an intege... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 57 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to maximize the largest element in the array by performing certain operations. Let me try to understand the problem again.
So the operation allowed is: choose an index i (where i is less than the length minus one) and nums[i] is less than or equal to nums[i+1]. 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: 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
} | <think>
Okay, I need to evaluate the surface integral of the vector field F over the surface S of the box. The problem says to use the Divergence Theorem, which relates the flux through a closed surface to the divergence of the vector field integrated over the volume enclosed by the surface.
First, let's recall the Di... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have to find the minimum number of operations to turn all characters in a binary string to 0. Let's see the problem statement again.
So, each operation allows selecting a non-empty subsequence t of the string where any two adjacent characters are different. Then, flip... |
[
{
"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": "",
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"subject": null,
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} | To determine the value of 'a' in the given wave function, we need to ensure that the wave function is properly normalized. Normalization means that the total probability of finding the particle in the entire space must equal 1. The wave function is given as:
ψ(x) = (a / sqrt(1 + x)) - 0.5i
However, the problem states... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 202 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out how to solve this problem. So the problem is about finding the latest time I can leave home (intersection 1) to attend the event at intersection n by time t0, while also having a phone call from t1 to t2 where I can't take the bus. Hmm.
First, I need to model the city's transporta... |
[
{
"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... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 300 | MMLUPro | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what the shape of the marginal revenue (MR) curve is for a monopoly with a straight downward-sloping demand curve. Let me start by recalling some basic microeconomics principles.
First, in a perfectly competitive market, the demand curve is horizontal because each firm is a price ... |
[
{
"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"
}
] | {
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} | 0 | 325 | MATH500 | {
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} | To solve this problem, we need to determine how many cylindrical beakers filled with water are required to fill a spherical tank. The key steps involve calculating the volumes of both the cylindrical beaker and the spherical tank, then dividing the volume of the tank by the volume of one beaker.
First, let's recall th... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 340 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to count the number of x configurations such that Bob wins the game. Let's start by understanding the problem thoroughly.
So, the game is between Alice and Bob. They take turns removing stones from piles. Each pile has an a_i value, which determines how much they... |
[
{
"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 $N \\rightarrow P+Q$, ... | {
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"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)"
} | $\boxed{\text{A, B, D}}$
To solve this problem, we need to analyze the fission reaction \( N \rightarrow P + Q \) and determine which of the given statements are correct. Let's break down the problem step by step.
### Step 1: Conservation of Energy and Momentum
In any nuclear reaction, both energy and momentum are co... |
[
{
"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... | {
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"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 of the statements (A) to (D) are FALSE, we need to analyze each statement carefully based on complex analysis principles.
**Statement (A):**
\[
\arg (-1 - i) = \frac{\pi}{4}
\]
First, compute the argument of \(-1 - i\). The complex number \(-1 - i\) lies in the third quadrant. The principal argumen... |
[
{
"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] ... | {
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} | 1 | 97 | LiveCodeBench | {
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"problem_id": "",
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} | <think>
Okay, I need to solve this problem where I have to find the number of integer points on a number line that are covered by any car. The input is a list of intervals, each representing the start and end of a car's position. The output is the count of all unique points covered by these intervals.
Hmm, let's think... |
[
{
"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... | {
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"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 due to the sound waves emitted by the two moving men. The key steps involve calculating the apparent frequencies of the sounds from each moving man as perceived by the stationary observer, then finding the beat frequency ... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have to find the minimum number of operations to make a tree wonderful. Let me try to understand the problem first.
So the tree is rooted at vertex 1. For each vertex v, if it has children, then a_v must be less than or equal to the sum of its children's a values. If ... |
[
{
"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"
} | $\boxed{B}$
**Solution Breakdown:**
First, let's analyze the problem step by step.
Given that \(p, q, r\) are the 10th, 100th, and 1000th terms of a harmonic progression (HP). In an HP, the reciprocals form an arithmetic progression (AP). So, let’s denote the reciprocals as \(a, a+d, a+2d\). Therefore, the terms are... |
[
{
"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"
} | $\boxed{B}$
**Step-by-Step Explanation:**
To determine which compound liberates oxygen gas (\(\mathrm{O}_2\)) upon hydrolysis, we need to analyze each option's reactivity with water and identify if the reaction produces \(\mathrm{O}_2\).
1. **Hydrolysis Reaction**: Hydrolysis involves reacting a compound with water,... |
[
{
"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 ... | {
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} | <think>
Okay, I need to solve this problem where I have to split an array into segments such that the bitwise ORs of each segment are non-decreasing. And then count the number of valid ways to split the array modulo 998244353. Hmm, let's think about how to approach this.
First, let's understand the problem. The array ... |
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{
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} | <think>
Okay, let's see. I need to solve this problem where we have a strip of cells with numbers and directions. The goal is to maximize the score by selecting certain segments according to the rules. Hmm.
So the problem says that each operation allows choosing a segment l to r where s_l is 'L' and s_r is 'R'. When y... |
[
{
"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 ... | {
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} | <think>
Okay, I need to solve this problem where I have to find the maximum number of non-overlapping segments in an array such that each segment's sum is zero. Let's think through this step by step.
First, the problem says that a segment [l, r] is beautiful if the sum of elements from a_l to a_r is zero. And I need t... |
[
{
"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... | {
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Okay, I need to solve this problem where I have to find the maximum distance between indices of prime numbers in a given array. Let's think about how to approach this.
First, I remember that the primes in the range 1-100 are: 2, 3, 5, 7, 11, etc. So I can create a set of primes for quick look-up. Wait, but che... |
[
{
"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 ... | {
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Okay, I need to solve this problem where given a string s consisting of p, s, and dots, I have to determine if there's a permutation of length n that satisfies certain conditions for each position i. Let's try to understand the problem step by step.
So, for each character in the string s at position i (from 1 ... |
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{
"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 ... | {
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"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 trigonometric identities and formulas related to triangles to find the correct answer(s).
First, let's parse the given conditions:
1. \(2s = x + y + z\), where \(s\) is the semi-perimeter of the triangle.
2. \(\frac{s - x}{4} = \frac{s - y}{3} = \... |
[
{
"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... | {
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"type": "MCQ(multiple)"
} | $\boxed{C, D}$
To determine which statements are true, let's analyze each option step by step.
**Option (A): Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones.**
Monosaccharides are the simplest form of carbohydrates. They are polyhydroxy aldehydes or ketones. For example, glucose is a po... |
[
{
"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... | {
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} | Let's analyze the problem step by step.
The scenario is as follows: An employee saved the boss's life by performing CPR. The boss then promised to give the employee a job for life. We need to determine the legal relationship between them regarding this promise.
First, let's recall the key principles related to contra... |
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{
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Okay, I need to solve this Binary Cut problem. Let's see what the problem is asking. So, given a binary string, we have to split it into the minimum number of contiguous pieces such that when all the pieces are rearranged (in any order), they form a sorted binary string. The sorted string here means all 0s come... |
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{
"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 ... | {
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Okay, let's see. I need to solve this problem where there are n coffee machines arranged in a corridor. Each has some students. The teachers can turn off the lights in any room (except the ends, maybe?), which causes half the students to move left and half right. But if the number is odd, one stays. The goal is... |
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{
"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 ... | {
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} | 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 changing any one digit to 1 results in a number divisible by 7. We then need to determine \( Q + R \) where \( Q \) and \( R \) are the quotient and remainder when \( N \) is divided by 1000.
### Approach
1. **Understanding the Pro... |
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{
"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... | {
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} | To solve the problem, we need to determine the first term in the sequence that is greater than 125. The sequence starts with 0, and each subsequent term alternates between adding and multiplying by successive integers. Let's break down the sequence generation step by step.
The sequence given is: 0, 1, 1, 3, 6, 9, 27, ... |
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{
"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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Okay, I need to solve this problem where I have to find the maximum sum of almost unique subarrays of length k. The almost unique subarray must have at least m distinct elements. If there's no such subarray, return 0.
Let me think about how to approach this. So, the problem is similar to sliding window but wi... |
[
{
"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 ... | {
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Okay, let's see. I need to solve this problem where I have to find the maximum number of happy people in a bus seating arrangement. Hmm. Let's read the problem statement again carefully.
So, the problem is about families traveling to Pénjamo. The bus has r rows, each with 2 seats. A person is happy if either 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 ... | {
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Okay, I need to solve this problem where we have to fill in the missing values in the array such that the launches follow certain rules. Let me try to understand the problem first.
So, the problem is about people on different floors launching paper airplanes. The key points are:
1. Each person can see airplan... |
[
{
"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... | {
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Okay, I need to solve this problem where I have to find the total number of continuous subarrays in a given array of integers. The subarrays are called continuous if the absolute difference between any two elements in the subarray is at most 2. Hmm, the examples make sense. For instance, in the first example, [... |
[
{
"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, \... | {
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} | 0 | 371 | JEEBench | {
"expected_answer": "6",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to analyze the functions \( f_1 \) and \( f_2 \) to determine the number of local minima and maxima for each, then compute the required expression based on these counts.
### Step 1: Analyze \( f_1(x) \)
The function \( f_1(x) \) is defined as an integral:
\[ f_1(x) = \int_0^x \prod_{j=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: 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%,... | {
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Okay, I need to figure out what percentage of the world population lived in extreme poverty in 2019. Let me start by recalling some data I've come across before. I remember that extreme poverty, defined as living on less than $1.90 a day, was a major focus of the Millennium Development Goals.
In recent years,... |
[
{
"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... | {
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Okay, let's see. I need to figure out which of these compounds matches the given 1H NMR data. The data provided is:
- 7.0 ppm, 1H, d with J=16.0 Hz
- 5.5 ppm, 1H, dq
- 2.1 ppm, 3H, s
- 1.6 ppm, 3H, d
Hmm. Let me start by recalling what each of these peaks might indicate.
The 2.1 ppm, 3H, s is likely from a m... |
[
{
"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 ... | {
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Okay, let's try to figure out how to solve this problem. So the problem is about finding the minimum cost to move from (1,1) to (n,m) in a grid, where we can perform cyclic shifts on rows any number of times before moving. The cost depends on the number of shifts (k*x) plus the sum of the cells visited (y).
F... |
[
{
"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 ... | {
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Okay, let's see. So the problem is about processing q queries on an array of n elements, all starting at 0. For each query, we can choose between x_i or y_i as the p, and then add either +1 or -1 to a_p. After each query, all elements must be non-negative. The goal is to choose the operations such that the sum ... |
[
{
"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... | {
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} | Let's approach this step by step.
First, the question is divided into two parts. For part A, we need to determine which of the given compounds (benzoquinone & cyclohexane-1,3,5-trione) does not show tautomerism. For part B, we need to identify between methyl 2-hydroxypropanoate and dimethyl fumarate which one shows op... |
[
{
"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 ... | {
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Okay, I need to solve this problem where Slavic has to replace the '?'s in the string s such that the string t becomes a subsequence of s. Hmm. Let's think about how to approach this.
First, the problem says that t must be a subsequence of the modified s. A subsequence means that the characters of t appear in ... |
[
{
"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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Okay, let's see. I need to solve this problem where there's a tree and some queries. The queries can be two types: XOR all edges with y, or for a vertex v and x, find the maximum XOR cycle when adding a mental edge from v to u with weight x. Hmm.
First, I need to understand how the queries work. For the first ... |
[
{
"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\... | {
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Okay, I need to solve this problem where I have to find the number of beautiful substrings in a given string s and integer k. Let's understand the problem first.
A substring is beautiful if two conditions are met:
1. The number of vowels (v) equals the number of consonants (c). So v == c.
2. The product v * 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... | {
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} | <think>
Okay, I need to solve this problem where Alex can perform an operation of turning an entire row or column into '#' and wants to maximize the largest connected component of '#' cells. Let's think about how to approach this.
First, the problem requires considering each possible row or column as a candidate for 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: 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... | {
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"seed": 0,
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} | \boxed{D} |
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{
"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 ... | {
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"seed": 1,
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} | 1 | 188 | CodeForces | {
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} | <think>
Okay, let's see. I need to solve this problem where each impression can have a range [l_i, r_i], and I have to determine if each one can be unique. The uniqueness means that for impression i, there exists a possible array where all other elements are different from i's value.
Hmm. So the key here is to check ... |
[
{
"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... | {
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"seed": 1,
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} | 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 \( T_{\text{A}} / T_{\text{B}} \) for two different processes: an adiabatic expansion and an isothermal expansion of an ideal gas, both leading to the same final state. The key is to use the equations governing each process and relate the initial and final states.
... |
[
{
"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 $373.12 \\mathrm{~K}$.... | {
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Okay, I need to calculate the boiling point of water at 253 Torr. Let's think about how to approach this.
First, I remember that the normal boiling point is the temperature where the vapor pressure equals the atmospheric pressure. So here, the barometric pressure is 253 Torr, which is lower than the normal 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 the ... | {
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Okay, let's see. The problem is about maximizing the number of points Kevin can earn by rearranging the array of numbers. The rules are that each time he adds a number to s, if the resulting s is even, he divides it by 2 until it's odd. And each operation can give at most one point. The goal is to find the maxi... |
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"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 ... | {
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"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem. So the problem is about swapping columns and finding the path with the maximum possible cost. Hmm. Let's read the description carefully.
So, the matrix has 2 rows and n columns. We can swap any two columns any number of times. Then, we have to find a path from (1,1) ... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: 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"
} | $\boxed{C}$
Solution:
To solve this problem, we need to determine the number of alpha-decays of nucleus Q in the first one hour, given its half-life and the probabilities of alpha and beta decay.
First, let's understand the parameters provided:
- Half-life of nucleus Q: 20 minutes.
- Probability of alpha-decay: 60% (0... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have to find the longest special substring that occurs at least three times. Hmm, let's think about what a special substring is. Oh right, it's made up of only a single character. So like "aaa" is special, but "aab" isn't.
The task is to find the maximum length of suc... |
[
{
"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
} | <think>
Okay, let's see. The problem is to find the restaurant that hasn't been visited yet from Monday to Friday. So, given four distinct numbers (since each day is a different restaurant), we need to output the remaining one.
Hmm. So the input is four integers, each from 1 to 5, all unique. The output is the one tha... |
[
{
"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 perfect square obtained before a prime number is odd. We will then compute \(14p\) where \(p\) is this probability.
### Step 1: Identify Possible Sums
When rolling two fair dice, the possible sums range from 2 to 12. Each sum can be obtained with cer... |
[
{
"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
} | <think>
Okay, I need to solve this problem where given two integers num1 and num2, I have to find the minimum number of operations to make num1 zero. Each operation allows choosing an integer i between 0 and 60, then subtracting (2^i + num2) from num1. If it's impossible, return -1.
Hmm, let's think about the approach... |
[
{
"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)"
} | $\boxed{\text{A, B, C, D}}$
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 adjugate matrix \( \text{adj} M \) is the t... |
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