context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 425 187k |
|---|---|---|---|---|---|---|
[
{
"content": "Problem: Let\n\\[f(x) = (\\arccos x)^2 + (\\arcsin x)^2.\\]Find the range of $f(x).$ All functions are in radians.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
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] | {
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} | 0 | 431 | MATH500 | {
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} | To find the range of the function \( f(x) = (\arccos x)^2 + (\arcsin x)^2 \), we start by using the identity that relates \(\arccos x\) and \(\arcsin x\). Specifically, for any \( x \in [-1, 1] \), we have \(\arccos x + \arcsin x = \frac{\pi}{2}\). Let's denote \(\theta = \arccos x\). Then \(\arcsin x = \frac{\pi}{2} -... |
[
{
"content": "Problem: In the $xy$-plane, a circle of radius $4$ with center on the positive $x$-axis is tangent to the $y$-axis at the origin, and a circle with radius $10$ with center on the positive $y$-axis is tangent to the $x$-axis at the origin. What is the slope of the line passing through the two point... | {
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"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 23 | AMC23 | {
"expected_answer": "7",
"problem_id": "26",
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"subject": null,
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} | To solve the problem, we need to determine the slope of the line passing through the two points of intersection of two circles. The first circle has a radius of 4 and is centered on the positive x-axis, tangent to the y-axis at the origin. The second circle has a radius of 10 and is centered on the positive y-axis, tan... |
[
{
"content": "Problem: How many ordered pairs of positive real numbers $(a,b)$ satisfy the equation\n\\[(1+2a)(2+2b)(2a+b) = 32ab?\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 13 | AMC23 | {
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"problem_id": "15",
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} | We start with the equation \((1 + 2a)(2 + 2b)(2a + b) = 32ab\). Let's introduce substitutions to simplify the variables. Let \(x = 2a\) and \(y = 2b\). Then the equation becomes \((1 + x)(2 + y)(x + \frac{y}{2}) = 32 \cdot \frac{x y}{4}\). Simplifying the right-hand side, we get \(32 \cdot \frac{xy}{4} = 8xy\). So 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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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 265 | CodeElo | {
"expected_answer": "",
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} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a game between Alice and Bob on a tree. The winner depends on their starting positions. The key here is to determine for each position in the path from u to v whether Alice can win when she starts at 1 and Bob starts at that position.
First, I need to ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A bus is in operation. The number of passengers on the bus is always a non-negative integer.\nAt some point in time, t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 377 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's see. The problem is about finding the minimum possible number of passengers currently on the bus based on the stops and the initial state. Hmm. So the bus starts with some number of passengers (could be zero or more), and then it stops N times. Each stop adds A_i to the passenger count. But after ea... |
[
{
"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 | 445 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's tackle this problem. Hmm, the task is to find the first year when the process becomes stable. So, the process is that each year, spiders exchange plushies based on some rules. The process is stable when each spider has the same number of plushies as the previous year before the exchange. And we need... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 384 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's try to tackle this problem. Hmm, the problem statement is a bit complex, so I need to break it down step by step.
So, the problem is about Alice and Jack playing a game with pockets of peanuts. The goal is to find the number of ways Alice can divide the pockets into boxes such that she wins when bo... |
[
{
"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: From this information compute: a) The current ratio. b) The quick asset ratio. c) The net working capital. 1. Current Assets: Current Liabilities Cas... | {
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} | 0 | 22 | MMLUPro | {
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} | To solve this problem, we need to compute three financial ratios: the current ratio, the quick asset ratio, and the net working capital. Let's break down each calculation step by step.
### Step 1: Compute Net Working Capital
Net working capital (NWC) is calculated as:
\[ \text{Net Working Capital} = \text{Current Asse... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A positive integer x is called a 321-like Number when it satisfies the following condition.\n\n- The digits of x are s... | {
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"seed": 1,
"temperature": 0.7
} | 1 | 284 | LiveCodeBench | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to write a Python function that checks if a number is a 321-like Number. Let's see the problem statement again. The digits have to be strictly decreasing from top to bottom. So for example, each digit in the number must be greater than the one following it. Oh right, and the input is N, which we ha... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 21 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's see. The problem is to find the maximum score by shuffling an array, where the score is the sum of (c_i - b_i) for each i. And b_i is the minimum up to i, c_i is the maximum up to i.
Hmm. So the challenge is to arrange the elements in such a way that when you compute these min and max arrays, the ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: α-β unsaturated carbonyls have a much more electrophilic carbon double bond. These double bonds act as a good Lewis acid and react with nucleophiles to produce enolate i... | {
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} | 0 | 152 | GPQADiamond | {
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} | Let's approach this step by step.
First, I need to understand what a Michael addition reaction is. The problem states that when a nucleophile attacks the β position of an α-β unsaturated carbonyl, it produces a resonance-stabilized intermediate. The key here is that the double bond is electrophilic due to the carbony... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 180 | CodeElo | {
"expected_answer": "",
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"subject": null,
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} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the minimum cost of a regular bracket sequence by placing brackets in the odd positions. The cost is calculated as the sum of distances between each pair of corresponding brackets.
First, I need to understand the problem thoroughly. So, the 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 348 | CodeForces | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a crow that needs to teleport ahead of scarecrows. The goal is to find the minimum time the crow needs to reach a position >= l by teleporting, considering the movements of the scarecrows. Oh right, and the output is twice the minimum time.
First, I n... |
[
{
"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,
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} | 1 | 172 | CodeForces | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to make a graph cool by performing certain operations. Let's understand what a cool graph is. The graph is cool if it's either a tree (which has no cycles) or has no edges. So the goal is to get rid of all edges either by making it a tree or by removing all edges.... |
[
{
"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,
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} | 1 | 190 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the maximum possible product of the min(a_i, b_i) after each modification. And we need to output the product before any modifications and after each of the q operations. The constraints are pretty tight—n and q can be up to 2e5 each, and t up 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: A previously healthy 27-year-old nulligravid woman comes to the emergency department because of a 2-day history of moderate-to-severe pain and swelli... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 246 | MMLUPro | {
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} | To determine the most appropriate next step in management for this patient, let's analyze the provided information step by step.
The patient is a 27-year-old nulligravid woman with a 2-day history of moderate-to-severe pain and swelling in the left labia. She is sexually active but uses condoms inconsistently, which s... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: The reaction of $\\mathrm{K}_3\\left[\\mathrm{Fe}(\\mathrm{CN})_6\\right]... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 360 | JEEBench | {
"expected_answer": "C",
"problem_id": "33",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's see. I need to figure out what precipitate X is in this problem. Let's read through the information given.
So, when K4[Fe(CN)6] reacts with FeSO4 solution in the absence of air, it forms a white precipitate X. Then, when this X is exposed to air, it turns blue. Hmm. So the X is white but reacts wit... |
[
{
"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 | 113 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the minimum number of button presses to get at least k cans of lemonade from a vending machine with n slots. Each slot has a certain number of cans, but the buttons are labeled randomly. So, when you press a button, if the corresponding slot has... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 257 | CodeForces | {
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"problem_id": "",
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} | <think>
Okay, let's tackle this problem. So the task is to find the minimum number of operations to make all elements in the array have the same parity. Each operation allows us to take two elements with different parities, replace the smaller one with their sum, and repeat this until all are the same parity.
Hmm. Le... |
[
{
"content": "Problem: Rows 1, 2, 3, 4, and 5 of a triangular array of integers are shown below.\n1\n1 1\n1 3 1\n1 5 5 1\n1 7 11 7 1\nEach row after the first row is formed by placing a 1 at each end of the row, and each interior entry is 1 greater than the sum of the two numbers diagonally above it in the prev... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 10 | AMC23 | {
"expected_answer": "5",
"problem_id": "12",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to solve this problem. So, we have a triangular array of integers, and we need to find the units digit of the sum of the 2023rd row. Hmm. Let's look at the example given here. The first five rows are shown, and each row after the first has 1s at the ends, and the interior numbers are the sum of ... |
[
{
"content": "Problem: How many positive whole-number divisors does 196 have?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 3 | MATH500 | {
"expected_answer": "",
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"subject": null,
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} | <think>
Okay, I need to find out how many positive whole-number divisors 196 has. Hmm, let's think. I remember that to find the number of divisors, I should start by finding the prime factorization of the number. Right, so first step is to break down 196 into its primes.
Let me see. 196 is even, so divide by 2. 196 di... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A compound with the molecular formula C8H9NO and the given NMR data is reacted with the following set of reagents:\n\n1. NaNO2 + HCl\n2. H2O\n3. aq. KOH, Heat \n\n1H-NMR... | {
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} | 2 | 149 | GPQADiamond | {
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} | Let’s think through the problem step by step. The goal is to identify the final product after a series of reactions on a C8H9NO compound based on the given NMR data.
First, let's analyze the NMR data provided:
1H-NMR (ppm) values are:
- 9.72 (t, 1H): This suggests a terminal aldehyde group (C=O) with a triplet. Aldeh... |
[
{
"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: Among $\\mathrm{B}_{2} \\mathrm{H}_{6}, \\mathrm{~B}_{3} \\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 197 | JEEBench | {
"expected_answer": "4",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's see. I need to find the total number of molecules in the given list that have at least one covalent bond between two atoms of the same kind. So I have to check each molecule's structure and count if there's any such bond.
First, I'll list all the options:
1. B2H6 (diborane)
2. B3N3H6 (triaboranetr... |
[
{
"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 pair of indices i, j where 0 <= i < j < nums.length is called beautiful if the first digit of nums[i] and the l... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 36 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to find the number of beautiful pairs in an array of integers. A beautiful pair is defined by the first digit of nums[i] and the last digit of nums[j] being coprime, with i < j.
Hmm, so the first thing I need to do is figure out how to get the first digit of a n... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Michael reaction is a chemical process in organic chemistry where a nucleophile adds to a molecule containing a specific carbon-carbon double bond (C=C) adjacent to ... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 18 | GPQADiamond | {
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} | To solve this problem, we need to determine the correct options for the products of the two given Michael reactions. Let's analyze each reaction step by step.
### First Reaction:
Reagents: NaOEt, THF, 2,4-dimethyl-1-(vinylsulfinyl)benzene.
Product: methyl 2-oxocyclohexane-1-carboxylate.
The Michael reaction involves ... |
[
{
"content": "Problem: How many ways are there to put 5 balls in 2 boxes if the balls are not distinguishable and neither are the boxes?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
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} | 0 | 226 | MATH500 | {
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} | <think>
Okay, let's see. The problem is to find the number of ways to put 5 indistinct balls into 2 indistinct boxes. Hmm, so since the balls are identical, the order in which we place them doesn't matter. And the boxes are also identical, so swapping the boxes doesn't create a new scenario.
First, I remember that wh... |
[
{
"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, an integer array queries, and an integer x.\nFor each queries[i], you need to find the index of the queries[i]^th occurren... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 510 | LiveCodeBench | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's see. I need to solve this problem where for each query, I have to find the index of the queries[i]-th occurrence of x in the nums array. If there are not enough occurrences, return -1. Hmm.
So the input is three arrays: nums, queries, and x. The output is an array of answers for each query.
Let me... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a string s, return the maximum length of a substring such that it contains at most two occurrences of each character.\n \nExample 1:\n\nInput: s = \"bcbb... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 465 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to find the maximum length of a substring in a given string such that it contains at most two occurrences of each character. Hmm, let's think about how to approach this.
First, the examples. For the first example, "bcbbbcba", the output is 4. Looking at that, may... |
[
{
"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: Calamine, malachite, magnetite and cryolite, respectively, are\n(A) $\\ma... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 189 | JEEBench | {
"expected_answer": "C",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's see. I need to figure out which of the given options correctly matches the four minerals: calamine, malachite, magnetite, and cryolite. Hmm, let's start by recalling what each of these minerals is made of.
First, calamine. Calamine is a mixture of zinc carbonate, ZnCO3. So that's straightforward. S... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: which of the following molecules has c3h symmetry?\ntriisopropyl borate\nquinuclidine\nbenzo[1,2-c:3,4-c':5,6-c'']trifuran-1,3,4,6,7,9-hexaone\ntriphenyleno[1,2-c:5,6-c'... | {
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} | 2 | 8 | GPQADiamond | {
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} | To determine which molecule has C3h symmetry, we need to analyze each option's structure and determine its point group. The C3h symmetry implies that the molecule has a threefold rotation axis (C3) and a horizontal plane of symmetry (h).
Let's break down each option:
**Option A: Quinuclidine**
Quinuclidine has a sev... |
[
{
"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": 2,
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} | 2 | 94 | CodeElo | {
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"type": null
} | <think>
Okay, let's see. The problem is to find the best x between 2 and n inclusive, such that the sum of all multiples of x up to n is maximized. Hmm. So for each n, I need to compute the maximum possible sum of x + 2x + 3x + ... + kx, where kx <=n. And then output that x.
First, I need to think about how to calcula... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 1-indexed integer array nums of length n.\nAn element nums[i] of nums is called special if i divides n, i.e. n % i == 0.\nReturn the sum of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 42 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes a list of integers called nums and returns the sum of the squares of all special elements. A special element is one where the index i (which is 1-based) divides the length of the array. Oh right, the array is 1-indexed, so the length is n, and i rang... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider a system with Hamiltonian operator $H = \\varepsilon \\vec{\\sigma}.\\vec{n}$. Here, $\\vec{n}$ is an arbitrary unit vector, $\\varepsilon $ is a constant of di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 184 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the eigenvalues of the Hamiltonian operator \( H = \varepsilon \vec{\sigma} \cdot \vec{n} \), we need to analyze the properties of the Pauli spin matrices and their dot product with the unit vector \(\vec{n}\).
The Pauli spin matrices \(\vec{\sigma}\) are given by:
\[
\sigma_1 = \begin{pmatrix} 0 & 1 \\ 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 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 388 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is a bit complex, but breaking it down step by step might help.
So, the problem asks for the sum of f(i) from i=0 to m, where f(i) is the maximum x obtained after performing any number of operations starting with x=i. Each operation allows choosing a sequence ... |
[
{
"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 | 432 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about finding the minimum time Zhan needs to blend all his fruits. Hmm. So the blender can process up to x fruits per second. But in each second, Zhan can put up to y fruits into the blender. So after putting the fruits, the blender blends the minimum of x and the current number ... |
[
{
"content": "Problem: The square root of $t$ is greater than $2$ and less than $3.5$. How many integer values of $t$ satisfy this condition?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 468 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem where the square root of \( t \) is greater than 2 and less than 3.5, we need to determine the integer values of \( t \) that satisfy this condition. Let's break this down step by step.
1. **Understanding the Inequality**: The problem states that \( \sqrt{t} > 2 \) and \( \sqrt{t} < 3.5 \). We can... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given an array of strings words and a string s, determine if s is an acronym of words.\nThe string s is considered an acronym of words if it can be formed by c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 84 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if a string s is the acronym of a given list of words. Let's see. The problem says that an acronym is formed by concatenating the first character of each string in the words list in order. So, for example, if the words are ["apple", "banana"], the acr... |
[
{
"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 | 14 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem says that we have n points on the x-axis at increasing coordinates. For each pair (i,j) where i < j, we draw a segment [x_i, x_j]. Then, for each query k_i, we need to find how many points are contained in exactly k_i segments.
First, I need to understand how ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array coins representing coins of different denominations and an integer k.\nYou have an infinite number of coins of each denomination... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 477 | 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 k-th smallest amount that can be made using the given coins, and I can use each coin any number of times but they have to be the same denomination each time. Hmm. Let's think about how to approach this.
First, the problem is about finding the k-th sma... |
[
{
"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 2D boolean matrix grid.\nReturn an integer that is the number of right triangles that can be made with the 3 elements of grid such that all of ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 497 | 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 right triangles in a 2D grid. Let's see the problem statement again. So a right triangle is formed when three elements are 1, and one of them is in the same row as another and same column as the third. Hmm. So the three points form a right-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 and an integer k.\nYou can perform the following operation on the array at most k times:\n\nChoose any index i fro... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 131 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to maximize the score by adjusting elements in the array up to k operations. The score is the frequency of the most frequent element. So, the goal is to make as many elements as possible the same (or as close as possible given the operations allowed) and then find the maximum pos... |
[
{
"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 | 19 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about maximizing the sum of two gcds after swapping elements in a way that costs us up to d coins. The swaps can be done for any i, and each swap costs c_i. So, the goal is to find, for each d in the q queries, the maximum possible value of gcd(a) + gcd(b) af... |
[
{
"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 grid with H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and the j-th column... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 367 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this programming problem. Let's read the problem carefully.
The problem is about a grid where each cell can be o, x, or .. We can change any .. to o any number of times. We need to check if it's possible to have a sequence of K consecutive cells (either horizontally or vertically) all o. ... |
[
{
"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 gas is enclosed in a cylinder with a movable frictionless piston. Its i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 44 | JEEBench | {
"expected_answer": "C",
"problem_id": "3",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the amount of heat supplied to the system in two different processes: the adiabatic process and the two-step process (isobaric followed by isochoric). The difference between the heat supplied in these two processes will give us the answer.
### Step 1: Calculate the Heat Supp... |
[
{
"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 | 0 | 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 number of minimal coprime segments within [l, r]. Minimal coprime segments are those that don't contain any other coprime segments besides themselves. And a coprime segment is one where the endpoints are coprime.
Hmm, the key note says tha... |
[
{
"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 | 251 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a tree with nodes numbered in a specific way, and after each update to the edge weights (t_i), we need to compute the sum of the maximum possible distances from each node i to i mod n +1. And the tree's structure is given as a depth-first traversal with... |
[
{
"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: An $\\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 317 | JEEBench | {
"expected_answer": "4",
"problem_id": "17",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the ratio of the radii of the circular orbits of a singly charged sulfur ion and an alpha-particle when they are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their velocities.
### Step 1: Understand the Accelerati... |
[
{
"content": "Problem: Positive real numbers $x$ and $y$ satisfy $y^3=x^2$ and $(y-x)^2=4y^2$. What is $x+y$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 1 | AMC23 | {
"expected_answer": "36",
"problem_id": "1",
"reference_solution": "",
"subject": null,
"type": null
} | We start with the given equations for positive real numbers \(x\) and \(y\):
1. \(y^3 = x^2\)
2. \((y - x)^2 = 4y^2\)
First, we expand the second equation:
\[
(y - x)^2 = y^2 - 2xy + x^2 = 4y^2
\]
Rearranging terms, we get:
\[
y^2 - 2xy + x^2 = 4y^2 \implies -2xy + x^2 = 3y^2 \implies x^2 - 2xy = 3y^2
\]
We can f... |
[
{
"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: Consider the following lists:\nList-I\n(I) $\\left\\{x \\in\\left[-\\frac... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 389 | JEEBench | {
"expected_answer": "B",
"problem_id": "15",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the number of solutions in each of the four lists (I, II, III, IV) and match them to the corresponding elements in List-II (P, Q, R, S, T). Let's analyze each list one by one.
### List-I: \(\cos x + \sin x = 1\) in \([- \frac{2\pi}{3}, \frac{2\pi}{3}]\)
1. **Rewrite the equ... |
[
{
"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 tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects vertices A_i and B_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 420 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have a tree with N vertices, each has a value C_i. The function f(x) is the sum over all i of C_i multiplied by the distance d(x, i). And I need to find the minimum f(v) over all v from 1 to N.
Hmm. So the problem is to find the vertex x that minimizes this... |
[
{
"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, num and t.\nAn integer x is called achievable if it can become equal to num after applying the following operation no more than t t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 28 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the maximum possible achievable number x by performing increase/decrease operations on num. The operations can be done up to t times. Each time, x and num are changed by 1 in the same direction. So, the problem is to maximize x after t steps.
Hmm. Let's think about the possible ... |
[
{
"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 | 47 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to tackle this problem. Hmm, the problem statement is a bit lengthy, so I need to read it carefully.
So, the problem is about Narek and ChatGPT creating problems. The main goal is to maximize the score difference score_n - score_c by selecting a subset of the strings and concatenating them.
L... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums and an integer k.\nIn one operation, you can pick any index i of nums such that 0 <= i < nums.length - 1 and repla... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 168 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum possible value of the bitwise OR of the remaining elements after applying at most k operations. Each operation allows replacing two adjacent elements with their bitwise AND. Hmm.
First, I need to understand what's the best way to combine these elements. Since the ope... |
[
{
"content": "Problem: The proper divisors of 12 are 1, 2, 3, 4 and 6. A proper divisor of an integer $N$ is a positive divisor of $N$ that is less than $N$. What is the sum of the proper divisors of the sum of the proper divisors of 284?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 12 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to find the sum of the proper divisors of the sum of the proper divisors of 284. Let's proceed step by step.
First, we need to determine the proper divisors of 284 and their sum.
### Step 1: Find the proper divisors of 284
Proper divisors of 284 are all positive divisors of 284 except 28... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A methanol solution of (R)-(+)-Limonene is stirred with Pd/C under a Hydrogen atmosphere. After 1 equivalent of hydrogen is consumed, product 1 is isolated as the major ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 12 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to follow the series of chemical transformations step by step and determine the possible structure of the final product 4. Let's break down each step:
1. **Hydrogenation of (R)-(+)-Limonene**:
- Limonene is a cyclic monoterpene with a specific configuration. When hydrogenated over Pd... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: 7-(tert-butoxy)bicyclo[2.2.1]hepta-2,5-diene is combined with 2 equivalents of 5,6-bis(dibromomethyl)cyclohexa-1,3-diene and sodium iodide at elevated temperature, formi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 71 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of chemically distinct hydrogen atoms in the final product (4) formed through a series of reactions starting from 7-(tert-butoxy)bicyclo[2.2.1]hepta-2,5-diene. Let's proceed step by step.
### Step 1: Understanding the Reactions
1. **First Reaction:** 7-(tert-butox... |
[
{
"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 $|M|$ denote the determinant of a square matrix $M$. Let $g:\\left... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 388 | JEEBench | {
"expected_answer": "AC",
"problem_id": "14",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the quadratic polynomial \( p(x) \) whose roots are the maximum and minimum values of the function \( g(\theta) \). Given that \( p(2) = 2 - \sqrt{2} \), we will evaluate the given options to determine which are true.
First, let's simplify the expressions for \( f(\theta) \)... |
[
{
"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": 5,
"temperature": 0.7
} | 5 | 22 | AIME24 | {
"expected_answer": "197",
"problem_id": "aime24-22",
"reference_solution": "Draw an altitude from both end circles of the diagram with the circles of radius one, and call the lengths you get drawing the altitudes of the circles down to $BC$ $a$ and $b$ . Now we have the length of side $BC$ of being $(2)... | We need to determine the inradius of triangle \(ABC\) given that eight circles of radius 34 are sequentially tangent, with two of them tangent to sides \(AB\) and \(BC\) respectively, and 2024 circles of radius 1 arranged in the same manner. The inradius can be expressed as \(\frac{m}{n}\) where \(m\) and \(n\) are rel... |
[
{
"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 furniture store had a truck that an employee of the store used to deliver furniture to the store's customers. One afternoon while the employee was ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 259 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the furniture store's recoverable amount from its employee after the employee caused an accident while delivering furniture. The key points to consider are the principles of contribution and indemnity, the employee's negligence, and the store's potential liability.
1. **Empl... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the total number of isomers, considering both structur... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 231 | JEEBench | {
"expected_answer": "10",
"problem_id": "32",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's see. I need to find the total number of isomers of cyclic ethers with the formula C4H8O. Both structural and stereoisomers. Hmm. Alright, let's break this down step by step.
First, I remember that a cyclic ether has a ring structure with an oxygen atom. So the molecule is a ring where one carbon 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": 2,
"temperature": 0.7
} | 2 | 422 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to solve this problem. Hmm, the problem is about painting a strip of zeros to all ones using the minimum number of operations. The operations are two types. The first type is flipping a zero to one. The second type is flipping a range of zeros to ones, but there's a condition based on the sum of... |
[
{
"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: Although corporate profit maximization is not directly prescribed by major normative theories to which normative theory is it most similar?\nOptions:... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 12 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine which normative theory is most similar to corporate profit maximization, even though profit maximization is not directly prescribed by any major normative theory. Normative theories provide principles for moral action, so we need to find the theory that aligns closest with th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence of positive integers of length N: A=(A_1,A_2,\\ldots,A_N). Find the number of triples of posi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 274 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of triples (i,j,k) where i<j<k, A_i = A_k, and A_i != A_j. Hmm. So the problem is about counting pairs of i and k where A_i equals A_k, and in between there's some j that's different from i and k.
Wait, the triple is (i,j,k). So for each pair (i,k), we need to check i... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: For how many values of $p$, the circle $x^{2}+y^{2}+2 x+4 y-p=0$ and the coordinate axes have exactly three co... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 89 | JEEBench | {
"expected_answer": "2",
"problem_id": "44",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve the problem, we need to determine the number of values of \( p \) such that the circle given by the equation \( x^2 + y^2 + 2x + 4y - p = 0 \) intersects the coordinate axes at exactly three distinct points.
First, we start by rewriting the equation of the circle in standard form. The given equation is:
\[
x... |
[
{
"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 | 225 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem. Let's read the problem statement carefully.
So, the problem is about finding the maximum number of inversions in an interesting permutation. An interesting permutation is one where, for each interval [l_i, r_i], there's a k_i in that interval such that the maximum of p_j fro... |
[
{
"content": "Problem: Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers are randomly chosen from $S.$ She wins a prize if at least two of her numbers were $2$ of the randomly chosen numbers, and wins the grand prize if all four of her numbers were the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 18 | AIME24 | {
"expected_answer": "116",
"problem_id": "aime24-18",
"reference_solution": "This is a conditional probability problem. Bayes' Theorem states that \n \\[P(A|B)=\\dfrac{P(B|A)\\cdot P(A)}{P(B)}\\] in other words, the probability of $A$ given $B$ is equal to the probability of $B$ given $A$ times the proba... | <think>
Okay, let's tackle this problem step by step. So, Jen picks 4 distinct numbers from the set S which has numbers 1 to 10. Then, 4 numbers are randomly chosen from S. We need to find the probability that she wins the grand prize given that she won a prize. The grand prize is when all four of her numbers are chose... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The treatment of galena with $\\mathrm{HNO}_{3}$ produces a gas that i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 408 | JEEBench | {
"expected_answer": "AD",
"problem_id": "48",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the gas produced when galena (PbS) reacts with nitric acid (HNO3). Let's analyze the reaction step by step.
First, galena (PbS) reacts with nitric acid. The reaction can be broken down into two parts: the oxidation of sulfur (S) to sulfuric acid (H2SO4) and the reduction of ... |
[
{
"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 pendulum consists of a bob of mass $m=0.1 \\mathrm{~kg}$ and... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 346 | JEEBench | {
"expected_answer": "0.16",
"problem_id": "10",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to determine the kinetic energy of the pendulum just after it lifts off the floor. Let's break down the problem step by step.
### Step 1: Understanding the Initial Conditions and Impulse
- The pendulum bob has a mass \( m = 0.1 \, \text{kg} \) and is initially at rest.
- The string lengt... |
[
{
"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 | 157 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding start days for Robin's brother and mother such that the brother's visit overlaps with the maximum number of jobs, the mother's with the minimum, and choosing the earliest possible days if there's a tie. Oh right, and the days have to be within 1... |
[
{
"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 the decay sequence,\n${ }_{92}^{238} \\mathrm{U} \\stackrel{-\\math... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 195 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each step of the given decay sequence and determine the type of particle or radiation emitted at each step. Let's break down each decay step by step.
The given decay sequence is:
\[ _{92}^{238}\text{U} \xrightarrow{-x_1} _{90}^{234}\text{Th} \xrightarrow{-x_2} _{91}^{234}\text... |
[
{
"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 | 359 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement is a bit complex, so I need to break it down step by step.
So, we have a permutation p and a string s of L and R. The operations allowed are swapping adjacent elements based on the s string's characters. The goal is, after each query that flips a char... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Dienes are organic compounds with two adjacent double bonds in their structure, and they exhibit unique reactivity due to their conjugated pi-electron system. They play ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's approach this problem step by step. The given reaction is between a diene (A) and cyclohexene to form 8,8-diiodobicyclo[4.2.0]octan-7-one. We need to determine which option for A (the reactant) would make this possible, and then arrange the dienes in order of their reactivity from most to least reactive.
First, ... |
[
{
"content": "Problem: Let $x,$ $y,$ and $z$ be positive real numbers such that $xyz(x + y + z) = 1.$ Find the minimum value of\n\\[(x + y)(y + z).\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 332 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the minimum value of \((x + y)(y + z)\) given that \(xyz(x + y + z) = 1\) with \(x, y, z > 0\), we start by introducing new variables to simplify the expression. Let \(a = x + y\), \(b = y + z\), and \(c = z + x\). Note that \(a + b + c = 2(x + y + z)\), so \(x + y + z = \frac{a + b + c}{2}\).
The given condit... |
[
{
"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 | 364 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm. So the task is to find four sticks from a given list that can form an isosceles trapezoid. The trapezoid must have a positive area, so the condition is that the absolute difference between the two bases is less than twice the length of the legs. Oh right, and rectangles and... |
[
{
"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 | 340 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about calculating the strength of a sequence described by pairs (a_i, b_i). The strength is the number of seconds it takes for the array to become empty when every second cosmic rays delete certain elements. Hmm.
So each second, all elements s_i that are in a position where i=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.The programming contest World Tour Finals is underway, where N players are participating, and half of the competition ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 296 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to generate a Python function that takes stdin and prints the required outputs. The problem is about players in a programming contest and how many more problems they need to solve to exceed all others' current scores. Hmm.
First, the function needs to read N and M from the input. Then t... |
[
{
"content": "Problem: A list of positive integers has the following properties: $\\bullet$ The sum of the items in the list is $30$ . $\\bullet$ The unique mode of the list is $9$ . $\\bullet$ The median of the list is a positive integer that does not appear in the list itself. Find the sum of the squares... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 1 | AIME24 | {
"expected_answer": "236",
"problem_id": "aime24-1",
"reference_solution": "The third condition implies that the list's size must be an even number, as if it were an odd number, the median of the list would surely appear in the list itself. Therefore, we can casework on what even numbers work. Say the size is 2.... | We need to find the sum of the squares of all items in a list of positive integers that meets the following conditions:
1. The sum of the items is 30.
2. The unique mode is 9.
3. The median is a positive integer that does not appear in the list.
Let's break down the problem step by step.
### Step 1: Understanding 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 an array nums consisting of positive integers where all integers have the same number of digits.\nThe digit difference between two integers is th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 502 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that calculates the sum of digit differences between all pairs of integers in an array. All numbers have the same number of digits. Hmm.
So, the digit difference between two numbers is the count of digits that are different in the same positions. Like for 13 v... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A positive integer x is called a 321-like Number when it satisfies the following condition.\n\n- The digits of x are s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 284 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that checks if a number is a 321-like Number. Let's see the problem statement again. The digits have to be strictly decreasing from top to bottom. So for example, each digit at position i (starting from the top) must be greater than the digit at position i+1.
The input ... |
[
{
"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: What is the sum of the number of lone pairs of electrons on each central atom in the following species?\n$\\le... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 81 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, let's see. I need to find the sum of the number of lone pairs on each central atom in these chemical species. Hmm. So first, I should figure out the central atom in each species and then determine how many lone pairs it has.
Let me start with the first species: [TeBr6]²-. The central atom here is tellur... |
[
{
"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: List-I shows different radioactive decay processes and List-II provides p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 474 | JEEBench | {
"expected_answer": "A",
"problem_id": "31",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | <think>
Okay, let's see. I need to match each nuclear decay reaction in List-I with the correct combination of emitted particles from List-II. Hmm. Let's start by analyzing each reaction one by one.
First, reaction P: ${ }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa}$. The atomic number decreases by 1, from 92 ... |
[
{
"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 | 130 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this programming problem. Let me read the problem statement carefully.
So the problem is about a matrix that can be colored with red (R) and blue (B) through certain actions. The actions are painting entire rows or columns. The cost is based on how many actions are done at 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": 0,
"temperature": 0.7
} | 0 | 25 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a game between Alice and Bob where they take turns cutting rows or columns from a grid and earning points based on the chips on those cuts. The challenge is to compute the scores after all moves are made.
First, I need to understand the problem thoroug... |
[
{
"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 current carrying wire heats a metal rod. The wire provides a constant p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 182 | JEEBench | {
"expected_answer": "A",
"problem_id": "3",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the heat capacity of the metal rod given the temperature-time relationship and the power provided by the current-carrying wire. Let's proceed step by step.
1. **Understanding the Problem:**
- The wire provides constant power \( P \) to the rod.
- The temperature of 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: The correct option(s) regarding the complex $\\left[\\mathrm{Co}(\\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 162 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given complex ion \([ \text{Co}(\text{en})(\text{NH}_3)_3(\text{H}_2\text{O}) ]^{3+}\) and determine which of the given options are correct. Let's break down each option step by step.
### Option (A): It has two geometrical isomers.
First, we need to determine the geometry... |
[
{
"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: Galena (an ore) is partially oxidized by passing air through i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 165 | JEEBench | {
"expected_answer": "6.47",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. The problem is about calculating the weight of lead (Pb) produced per kilogram of oxygen (O₂) consumed in a process where galena is partially oxidized and then undergoes self-reduction. Hmm, right. So first, I need to understand the chemical reactions involved here.... |
[
{
"content": "Problem: The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? [asy]\ndraw((-.3,-3)--(.1,1)--(-1,0)--(3,0)--cycle);\nlabel(\"$A$\",(.1,1),N);\nlabel(\"$B$\",(-1,0),W);\nlabel(\"$C... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the area of triangle CDE given that the area of triangle ABC is 6 square centimeters, and that AB is parallel to DE. Additionally, BD is four times the length of BC.
First, let's analyze the given information. Since AB is parallel to DE, triangles ABC and CDE are similar by ... |
[
{
"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 $X$ be the set consisting of the first 2018 terms of the a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 144 | JEEBench | {
"expected_answer": "3748",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the problem, we need to determine the number of elements in the union of two arithmetic sequences, \(X\) and \(Y\). Let's start by defining the sequences.
The first sequence \(X\) starts at 1 with a common difference of 5. The \(n\)-th term of \(X\) can be expressed as:
\[
a_n = 1 + (n-1) \cdot 5 = 5n -4
\]
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 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 346 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that we can perform an operation where we spend 1 unit of every other material to gain 1 unit of the selected material. And we need to determine if we can reach the required b_i for all materials.
So the key here is to figure out if after any 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 78 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the smallest cost connected subset of vertices in a tree, with the constraints that each value from 1 to n is present at least once. Each vertex has a cost of 2^i, so the minimal cost is crucial.
First, I need to understand the problem thoroug... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: toluene is treated with nitric acid and sulfuric acid, forming product 1.\n\n1 is treated with MnO2 and H2SO4, forming product 2.\n\n2 is treated with acetone and aqueou... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 30 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the molecular symmetry group of product 3, we need to follow the transformations step by step and analyze the symmetry of each intermediate product.
### Step 1: Toluene treated with nitric acid and sulfuric acid to form product 1.
Toluene (C7H8) has a planar structure with a benzene ring. When reacted wi... |
[
{
"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: Among the following, the correct statement(s) is(are)\n[A] $\\mathrm{A... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 106 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement regarding the chemical structures and bonding of the given compounds. Let's break down each option step by step.
### Option [A]: Al(CH₃)₃ has three-centre two-electron bonds in its dimeric structure.
1. **Structure of Al(CH₃)₃**: This compound is aluminum tris(... |
[
{
"content": "Problem: What is the degree measure of the acute angle formed by lines with slopes $2$ and $\\frac{1}{3}$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 2 | AMC23 | {
"expected_answer": "45",
"problem_id": "2",
"reference_solution": "",
"subject": null,
"type": null
} | To find the degree measure of the acute angle formed by lines with slopes 2 and \(\frac{1}{3}\), we can use the formula for the angle between two lines. The formula for the absolute value of the difference in their slopes gives the tangent of the angle between them. However, since we need the acute angle, we will compu... |
[
{
"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 | 208 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about arranging BBQ buns such that each filling is either not used at all or used at least twice, and for any two buns with the same filling, their distance must be a perfect square. And we need to output such an arrangement if possible, otherwise return -1.
... |
[
{
"content": "Problem: Find the largest possible real part of \\[(75+117i)z+\\frac{96+144i}{z}\\] where $z$ is a complex number with $|z|=4$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 21 | AIME24 | {
"expected_answer": "540",
"problem_id": "aime24-21",
"reference_solution": "Let $z=a+bi$ such that $a^2+b^2=4^2=16$ . The expression becomes: \\[(75+117i)(a+bi)+\\dfrac{96+144i}{a+bi}.\\] Call this complex number $w$ . We simplify this expression. \\begin{align*}\nw&=(75+117i)(a+bi)+\\dfrac{96+144i}{a+bi} \... | To find the largest possible real part of the expression \((75 + 117i)z + \frac{96 + 144i}{z}\) where \(z\) is a complex number with \(|z|=4\), we start by expressing \(z\) in terms of its polar form. Let \(z = 4e^{i\theta}\). Then, the expression becomes:
\[
(75 + 117i)4e^{i\theta} + \frac{96 + 144i}{4e^{i\theta}} = ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 372 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about Kevin and Nivek competing in n matches. Each match can be type 1 or 2. For type 1, Kevin needs to spend a certain amount of time to win. If he doesn't, Nivek wins. For type 2, the outcome depends on their historical records. The goal is to find the mini... |
[
{
"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 $\\alpha$ be a positive real number. Let $f: \\mathbb{R} \... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 377 | JEEBench | {
"expected_answer": "0.5",
"problem_id": "2",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To find the value of \(\lim_{x \to \alpha^+} f(g(x))\), we need to evaluate the limit of the composition of functions \(f\) and \(g\) as \(x\) approaches \(\alpha\) from the right. Let's proceed step by step.
First, recall the definitions of the functions \(f\) and \(g\):
\[
f(x) = \sin \left( \frac{\pi x}{12} \right)... |
[
{
"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: What happens to neurotransmitters once they have \"done their job?\"\nOptions: A. Neurotransmitters diffuse away and are exhaled, B. Neurotransmitter... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 219 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine what happens to neurotransmitters once they have "done their job," let's break down the process step by step.
1. **Understanding Neurotransmission**: Neurotransmitters are chemicals that transmit signals across a synapse from one neuron to another. When a neuron fires, it releases neurotransmitters into 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 291 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the smallest n such that after flipping bulbs in a certain way, exactly k bulbs are on.
Initially, all bulbs are on. Then, for each i from 1 to n, we flip all bulbs j that are divisible by i. So each bulb j is flipped once for each of its divi... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Sigmatropic rearrangement is a class of pericyclic reactions. In these reactions, the terminal pi bond migrates into the sigma bond. Cope and Claisen rearrangements are ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 48 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's tackle these sigmatropic rearrangement reactions step by step.
First, let's look at reaction 1: 1,1-dimethoxyethan-1-amine + but-3-en-2-ol → ?
This reaction involves a Cope rearrangement. The Cope rearrangement is a sigmatropic shift where the terminal π bond moves into a sigma bond. Let's break down the reacta... |
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