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": "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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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 431 | MATH500 | {
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"subject": null,
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} | To find the range of the function \( f(x) = (\arccos x)^2 + (\arcsin x)^2 \), we start by recalling the relationship between the inverse trigonometric functions. Specifically, for any \( x \) in the domain \([-1, 1]\), we have:
\[
\arccos x + \arcsin x = \frac{\pi}{2}
\]
This identity will be crucial in simplifying o... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 23 | AMC23 | {
"expected_answer": "7",
"problem_id": "26",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the slope of the line passing through the two intersection points of two circles. The circles are defined as follows: one has a radius of 4, centered on the positive x-axis, tangent to the y-axis at the origin. The other has a radius of 10, 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 | {
"expected_answer": "1",
"problem_id": "15",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the equation \((1+2a)(2+2b)(2a+b) = 32ab\) for positive real numbers \(a\) and \(b\), we will proceed step by step.
First, let's expand the left-hand side and simplify the equation.
The given equation is:
\[
(1 + 2a)(2 + 2b)(2a + b) = 32ab
\]
Let's denote \(x = 2a\) and \(y = 2b\). This substitution simplif... |
[
{
"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 | 265 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Alice and Bob are playing a game on a tree. The problem is a bit tricky, but let's break it down.
First, the problem says that for each test case, there's a path from u to v. But since u and v are the same, the path is just a single vertex. Wait, no. Wait, 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.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": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum possible current number of passengers on the bus based on the given stops and the initial state. The initial number of passengers could be zero or more, and then each stop adds or subtracts some passengers. Also, after each stop, the passenger count must remain non-ne... |
[
{
"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": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the first year when the spider's plushie exchange becomes stable. Let me read the problem carefully again.
So, each spider starts with 1 plushie. Every year, if a spider has at least one, it gives one to its recipient. All transfers happen simultaneously.... |
[
{
"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": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out how to solve this problem. So the problem is about counting the number of ways Alice can split the pockets into boxes such that she wins when both play optimally. Hmm.
First, I need to understand the game rules properly. The key points are:
- The game is taken turns: Alice first,... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: From this information compute: a) The current ratio. b) The quick asset ratio. c) The net working capital. 1. Current Assets: Current Liabilities Cas... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to calculate the current ratio, quick asset ratio, and net working capital based on the given financial data. Let me start by understanding what each of these ratios and metrics entails.
First, the current ratio. The formula for current ratio is Current Assets divided by Current Liabili... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 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 says that the digits must be strictly decreasing from left to right. So for each consecutive pair of digits, the first must be larger than the second.
Wait, right. So for example, 321: 3>2, 2>1. So yes... |
[
{
"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 | 21 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to maximize the score by rearranging the array. Let me read the problem again carefully.
The problem says that after rearranging the array a, we create two arrays b and c. b_i is the minimum of the first i elements of a, and c_i is the maximum of the first i elem... |
[
{
"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... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 152 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem step by step. So, the question is about Michael addition reactions and their products. The problem gives three reactions and asks which options correctly match the reactants and products. The options are labeled A, B, C, and D, and we need to pick the correct one.
Fir... |
[
{
"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 | 180 | 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 cost of a regular bracket sequence given that the even positions are known and the odd positions are missing. The cost is calculated as the sum of the distances between each pair of corresponding brackets. Hmm.
Let me start by understanding 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 | 348 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where the crow has to teleport past the scarecrows. The goal is to find the minimum time required for the crow to reach or exceed position ℓ, and output twice that time. Hmm.
First, let me understand the problem again. The crow starts at 0. The scarecrows are movin... |
[
{
"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 | 172 | 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 make a graph cool by performing certain operations. The operations involve choosing three distinct vertices a, b, c and toggling the edges between them (if an edge exists, remove it; if not, add it). The goal is to end up with either no edges or a tr... |
[
{
"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 | 190 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where after each modification, I have to find the maximum possible product of min(a_i, b_i) after rearranging b. And the product has to be computed modulo 998244353. Hmm.
First, I need to understand how to approach the maximum product problem. The key here is that ... |
[
{
"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... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 246 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Let's analyze the case step by step.
The patient is a 27-year-old woman with no prior health issues, not pregnant, sexually active with inconsistent condom use. She has had two days of moderate-to-severe pain and swelling in the left labia. On examination, there's a 4x3-cm, tender, fluctuant mass medial to the labium ... |
[
{
"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,
"temperature": 0.7
} | 0 | 360 | JEEBench | {
"expected_answer": "C",
"problem_id": "33",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | $\boxed{D}$
**Solution:**
To solve this problem, we need to determine the correct formula for precipitate X formed when $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ reacts with $\mathrm{FeSO}_4$ in the complete absence of air. Let's break down the information given and analyze each step systematically.
Firs... |
[
{
"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 | 113 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where there's a vending machine with n slots, each having some cans of lemonade. The buttons are labeled but the labels are worn off. Each time I press a button, if there's a can in that slot, I get it and the count decreases by 1. But I can't see the slots, so I 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,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 257 | 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 make all elements in an array have the same parity. Let's see. The operations allow swapping elements by summing them with the smaller one. Hmm.
First, let's understand the operation. When you pick two elements with dif... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 10 | AMC23 | {
"expected_answer": "5",
"problem_id": "12",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the units digit of the sum of the 2023rd row in a triangular array of integers. The triangular array is constructed such that each row after the first is formed by placing a 1 at each end and each interior entry is 1 greater than the sum of the two numbers diagonally above it... |
[
{
"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,
"temperature": 0.7
} | 0 | 3 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | To determine the number of positive whole-number divisors of 196, we start by finding its prime factorization.
First, we check if 196 is divisible by the smallest prime, 2. Dividing 196 by 2 gives 98. Dividing 98 by 2 gives 49. Since 49 is 7 squared, we stop here. So, the prime factorization is:
\[ 196 = 2^2 \times ... |
[
{
"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... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 149 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Let me try to figure out the correct answer step by step.
First, the problem states that the compound with the molecular formula C8H9NO is being reacted with a series of reagents. The NMR data given is for 1H-NMR, which can help determine the structure of the final product.
The reagents are:
1. NaNO2 + HCl
2. H2O
3.... |
[
{
"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,
"temperature": 0.7
} | 2 | 197 | JEEBench | {
"expected_answer": "4",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | **Step 1: Understanding the problem**
We need to determine how many molecules in the given list contain a covalent bond between two atoms of the same kind. The list includes:
1. B₂H₆
2. B₃N₃H₆
3. N₂O
4. N₂O₄
5. H₂S₂O₃
6. H₂S₂O₈
**Step 2: Identifying covalent bonds between same atoms in each molecule**
For each mole... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 36 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the number of beautiful pairs in the given array. Let me read the problem statement again carefully.
So, a beautiful pair is defined as a pair of indices i and j where i < j, such that the first digit of nums[i] and the last digit of nums[j] are coprime. ... |
[
{
"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 ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 18 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let me try to figure out the correct answer. The problem is asking about the products of two Michael reactions. Let's break down each reaction step by step.
First, looking at the first reaction:
methyl 2-oxocyclohexane-1-carboxylate + (NaOEt, THF, 2,4-dimethyl-1-(vinylsulfinyl)benzene) → A
The Michael reaction invol... |
[
{
"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,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 226 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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} | To solve the problem of determining how many ways there are to put 5 indistinguishable balls into 2 indistinguishable boxes, we need to consider the concept of combinations with repetition. However, since both the balls and the boxes are indistinguishable, we have to avoid overcounting equivalent distributions.
### St... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 510 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each query, I have to find the k-th occurrence of x in the nums array. If there aren't enough occurrences, return -1. The challenge is that the arrays can be up to 100,000 elements each, so efficiency is key here.
First, let's understand the problem. For each query ... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 465 | 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 substring in a given string s that contains at most two occurrences of each character. Hmm. Let's think about how to approach this.
So the problem is similar to the sliding window technique that's used in the "longest substring wit... |
[
{
"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"
} | $\boxed{D}$
To determine the correct answer, we need to analyze each of the given options and match the minerals listed with their respective chemical formulas. Let's go through each mineral one by one and verify their formulas.
**Step 1: Calamine**
Calamine is a mixture of zinc compounds, primarily zinc carbonate (... |
[
{
"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'... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 8 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | \boxed{B} |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 94 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where, given a number n, I have to find the x between 2 and n that maximizes the sum of multiples of x up to n. Let's think about how to approach this.
First, the sum of multiples of x up to n. Oh right, that's an arithmetic series. Like, for x=2 and n=15, the multiples are 2... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given 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, I need to write a Python function that calculates the sum of the squares of the special elements in the given array. Let's see. The problem says a special element is one where its index (1-based) divides the length of the array. So for example, if the array has length 4, the indices 1, 2, 4 are special be... |
[
{
"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 \( H = \varepsilon \vec{\sigma} \cdot \vec{n} \), where \(\vec{\sigma}\) are the Pauli matrices and \(\vec{n}\) is a unit vector, we need to analyze the properties of the Pauli matrices and their dot product with \(\vec{n}\).
First, recall that the Pauli matrice... |
[
{
"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, I need to solve this problem where I have to compute the sum of f(i) from i=0 to m, where f(i) is the maximum possible x after some operations starting from x=i. The operations involve choosing a sequence and setting x to the mex of x and the elements of the sequence.
Hmm. Let's start by understanding 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 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. So the problem is to find the minimum time required for Zhan to blend all his fruits. Hmm. The input is the number of test cases, each with n, x, y. And we need to output the time for each.
Let me think about the approach. Let's look at the editorial. Oh right, the key idea is to split into tw... |
[
{
"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 down the problem step by step.
First, we translate the given inequality into mathematical terms. The problem states:
\[ 2 < \sqrt{t} < 3... |
[
{
"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 check if a string s is an acronym of a list of words. The acronym is formed by taking the first character of each word in order. So, the approach here is straightforward: collect the first letters of each word in words and see if that concatenated string matche... |
[
{
"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, I need to solve this problem where given n points on the x-axis, I have to find for each query k, how many points are contained in exactly k segments. The segments are all pairs [x_i, x_j] where i < j. So first, let's understand the problem.
Each point x is part of some segments. For example, a point x i... |
[
{
"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 given some coins and a target k, I have to find the k-th smallest amount that can be formed using those coins, but without combining different denominations. Hmm, let's think about how to approach this.
So the coins are all distinct, and each can be used infinitely. But... |
[
{
"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 find the number of right triangles in a 2D boolean grid. The right triangle is defined such that one of the elements is in the same row as another, and the third is in the same column as the first. Wait, no, the problem says: a right triangle is formed if one e... |
[
{
"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, I need to solve this problem where I have to maximize the frequency of the most frequent element in an array after performing up to k increments or decrements on the elements. Let me think about how to approach this.
So the problem is, given nums and k, find the maximum possible frequency after at most k... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print 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 see. I need to solve this problem where I have two arrays a and b, and for each position i, I can swap a[i] and b[i] paying c[i] coins. The goal is to maximize the sum of the gcd of the a array and the gcd of the b array after swapping some elements, with the total cost not exceeding d. And for each... |
[
{
"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 problem. Let's read the problem carefully.
So the problem is about a grid where each cell can be 'o', 'x', or '.'. We can change '.' to 'o' with each operation. We need to find the minimum number of operations to make sure that there's either a horizontal or vertical line of K consec... |
[
{
"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"
} | $\boxed{D}$
**Step-by-Step Solution:**
1. **Understanding the Processes:**
- **Adiabatic Process:** The given process is adiabatic and follows \( P^3 V^5 = \text{constant} \). Since it's adiabatic and quasi-static, we can use the relation \( P^3 V^5 = \text{constant} \) to find the work done.
- **Two-Step Proce... |
[
{
"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 in a given interval [l, r]. Hmm. Let's start by understanding the problem properly.
So, a minimal coprime segment is a segment [a, b] such that it's coprime (gcd(a, b) == 1) and it doesn't contain any othe... |
[
{
"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, I need to solve this problem. Let's read through the description carefully.
So the problem is about a rooted tree where each edge has a weight t_i, which is a non-negative integer. The sum of all t_i from 2 to n is given as w. The tree is structured such that the vertex numbers are assigned in a depth-fi... |
[
{
"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"
} | **Step 1: Understanding the problem**
We need to find the ratio of the radii of the circular orbits of an α-particle and a singly charged sulfur ion after they are accelerated through the same potential difference V. Both particles are then subjected to a uniform magnetic field perpendicular to their velocities. The k... |
[
{
"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:
\[
(y - x)^2 = y^2 - 2xy + x^2 = 4y^2
\]
Subtract \(y^2\) from both sides:
\[
-2xy + x^2 = 3y^2
\]
Rearrange the equation to bring all terms to one side:
\[
... |
[
{
"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"
} | $\boxed{A}$
To solve this problem, we need to analyze each of the given trigonometric equations within their respective intervals and determine how many solutions each equation has. The goal is to match each list (I to IV) with the corresponding number of elements in List-II (P to T), where each letter represents a di... |
[
{
"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, I need to solve this problem where I have to find the minimum value of f(v) for any vertex v in a tree. The function f(v) is the sum over all i of C_i multiplied by the distance from v to i. Hmm, the distance here is the number of edges between v and i. So for each vertex v, I calculate the sum of C_i mul... |
[
{
"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. The problem is to find the maximum possible achievable number x given num and t. The operation allows us to increase or decrease x by 1 and simultaneously do the same to num. We can perform this operation up to t times.
Hmm. So each operation changes both x and num by ±1. But since we can choo... |
[
{
"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 figure out how to solve this problem. So the problem is about selecting some strings to concatenate and then calculate the maximum possible score_n minus score_c. Hmm. Let's break down the problem step by step.
First, the description says that Narek's score (score_n) is calculated by looking... |
[
{
"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, I need to solve this problem where I have to find the minimum possible bitwise OR of the remaining elements after performing at most k operations. Each operation allows me to pick an index i (not the last one) and replace nums[i] and nums[i+1] with their bitwise AND. The goal is to minimize the OR of the ... |
[
{
"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 break this down step by step.
First, let's understand what a proper divisor is. A proper divisor of an integer \( N \) is a positive divisor of \( N \) that is less than \( N \). For example, the proper... |
[
{
"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
} | <think>
Okay, let's try to figure out the structure of product 4 step by step. The problem starts with (R)-(+)-Limonene being hydrogenated with Pd/C and hydrogen. After 1 equivalent of H2 is consumed, product 1 is isolated. Then product 1 is treated with 3-chloroperbenzoic acid (CPB) to form product 2. Then product 2 i... |
[
{
"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
} | Let's work through this step by step.
First, I need to determine the structure of each intermediate and final product based on the given reactions.
Starting with product 1: The initial compound is 7-(tert-butoxy)bicyclo[2.2.1]hepta-2,5-diene. When combined with 2 equivalents of 5,6-bis(dibromomethyl)cyclohexa-1,3-die... |
[
{
"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)"
} | $\boxed{\text{B}}$
To solve this problem, we need to analyze the function \( g(\theta) \) and determine its maximum and minimum values over the interval \([0, \frac{\pi}{2}]\). Then, we will use these values to construct a quadratic polynomial \( p(x) \) and evaluate given expressions to determine which options are co... |
[
{
"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)... | To solve this problem, we need to determine the inradius of triangle \(ABC\) given that eight circles of radius 34 are arranged such that two are tangent to sides \(AB\) and \(BC\) respectively, and 2024 circles of radius 1 are arranged in the same manner. The inradius can be expressed as \(\frac{m}{n}\) in simplest fo... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A 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
} | Let's analyze the problem step by step.
The key points from the problem are:
- The furniture store's employee was driving a truck when they ran a stop sign, causing an accident.
- The employee was negligent.
- The car's driver was injured and received $25,000 from the furniture store.
- Now, the furniture store is con... |
[
{
"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"
} | $\boxed{11}$
**Step-by-Step Explanation:**
To determine the total number of isomers (both structural and stereoisomers) of cyclic ethers with the molecular formula $\mathrm{C}_4\mathrm{H}_8\mathrm{O}$, we need to follow a systematic approach. Let's break down the problem step by step.
### Step 1: Understand the Mole... |
[
{
"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 figure out this problem. So the task is to find the minimum number of operations of the first type (assigning 1s) needed to make all elements of the array equal to 1. The operations are either turning a single 0 into 1, or selecting a segment of 1s and setting all elements in between to 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: 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
} | <think>
Okay, so the question is asking which normative theory is most similar to corporate profit maximization, even though profit maximization isn't directly prescribed by any of the major theories. Hmm, let me think about each option.
First, normative theories are ethical theories that prescribe how people should a... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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... | {
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} | 1 | 274 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the number of triples (i, j, k) such that i < j < k, A[i] = A[k], and A[i] != A[j]. Let's think about how to approach this efficiently.
First, the constraints are big. N can be up to 3e5, so a brute force approach checking all possible triples would be O(... |
[
{
"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 this problem, we need to determine how many values of \( p \) result in the circle \( x^2 + y^2 + 2x + 4y - p = 0 \) intersecting the coordinate axes exactly three times. Let's break this down step by step.
### Step 1: Understand the Circle Equation
The given equation is:
\[ x^2 + y^2 + 2x + 4y - p = 0 \]
We... |
[
{
"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 where I have to find the maximum number of inversions in an interesting permutation. Let's start by understanding the problem statement thoroughly.
So, the problem is about permutations of length n. A permutation is considered interesting if for each interval [l_i, r_i], ther... |
[
{
"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... | To solve this problem, we need to determine the probability that Jen wins the grand prize given that she has already won a prize. This requires understanding conditional probability, where the probability of the grand prize (event A) given that she won a prize (event B) is calculated using the formula \( P(A \mid 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: 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)"
} | $\boxed{\text{A, C, D}}$
To solve this problem, we need to determine the properties of the gas produced when galena is treated with HNO₃. Let's break down the problem step by step.
First, identify the reactants and the chemical reaction involved. Galena, which is lead(II) sulfide (PbS), reacts with nitric acid (HNO₃)... |
[
{
"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 \( K \) of the pendulum just after the bob lifts off the floor. Let's break down the problem step by step.
### Step 1: Understanding the Initial Conditions
- The pendulum bob has a mass \( m = 0.1 \, \text{kg} \).
- The string length \( L = 1.0 \, \text{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 ... | {
"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 see. So the problem is about scheduling the visits of Robin's brother and mother such that the brother's visit overlaps as many jobs as possible, and the mother's as few as possible. And we have to choose the earliest possible start days for each. Hmm.
First, I need to process each test case. For e... |
[
{
"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)"
} | $\boxed{\text{B, C}}$
**Step-by-Step Explanation:**
**Problem:** Determine the correct particles/radiation emitted in the given decay sequence. The options are (A) to (D), and the correct answers are to be selected with justification.
**Given Decay Sequence:**
$${ }_{92}^{238} \mathrm{U} \stackrel{-\mathrm{x}_{1}}{\... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 359 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where after each query, I have to determine if the permutation can be sorted using the given operations. Hmm. Let's try to understand the problem step by step.
So, the problem is about checking whether a permutation can be sorted by swapping adjacent elements accor... |
[
{
"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
} | <think>
Okay, let's tackle this problem step by step. The question is about Dienes and their reactivity in a specific reaction. The reaction given is Cyclohexene + A → 8,8-diiodobicyclo[4.2.0]octan-7-one. We need to determine which option for A is correct and then list the dienes in order of reactivity from most to lea... |
[
{
"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 \(xyz(x + y + z) = 1\), we start by introducing substitutions and applying inequalities to find the minimum.
First, let's denote \(a = x + y\), \(b = y + z\), and \(c = z + x\). Note that \(a, b, c\) are all positive since \(x, y, z\) are positive. However, 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 | 364 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Kevin has to select four sticks to form an isosceles trapezoid. If it's impossible, output -1. Hmm. Let's think about the conditions for forming such a trapezoid.
From the problem's note, the necessary and sufficient condition is that the longest edge must be... |
[
{
"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, I need to solve this problem where given a sequence of pairs (a_i, b_i) that represent a_i copies of b_i, I have to compute the strength of the array after considering the first i pairs for each i from 1 to n. The strength is the number of seconds it takes for the array to become empty based on the deleti... |
[
{
"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, I need to solve this programming problem. Let's read the problem carefully and understand what's required.
So the problem is about a programming contest where N players are participating, and M problems. Each problem has a score A_i which is a multiple of 100 between 500 and 2500. Each player has a strin... |
[
{
"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.... | To solve this problem, we need to determine the sum of the squares of all items in a list of positive integers that meets specific criteria. Let's break down the problem step by step.
### Step 1: Understanding the Properties
1. **Sum of the list**: The total sum of all items is 30.
2. **Unique mode**: The number 9 app... |
[
{
"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, I need to solve this problem where I have to calculate the sum of digit differences between all pairs of integers in an array. Let's think about how to approach this.
First, the problem says that all numbers have the same number of digits. That's helpful because each number has the same length, so when c... |
[
{
"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 says that a 321-like number has its digits strictly decreasing from left to right. So each digit must be larger than the one to its right. Like, for example, 321: 3>2>1. 96410: 9>6>4>1>0. And single-digi... |
[
{
"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"
} | To solve this problem, we need to determine the number of lone pairs of electrons on each central atom in the given species and then sum them up. Let's break down each species step by step.
### Step 1: Understanding the Species
The species given are:
1. \([ \text{TeBr}_6 ]^{2-}\)
2. \([ \text{BrF}_2 ]^{+}\)
3. \(\text... |
[
{
"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"
} | $\boxed{B}$
**Solution:**
To solve this problem, we need to determine the correct emitted particles for each radioactive decay process listed in List-I by analyzing the changes in the atomic numbers and mass numbers of the parent and daughter nuclei. Let's go through each decay reaction step by step.
### Step 1: Ana... |
[
{
"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, I need to solve this problem where after each query, there are multiple color constraints on certain cells. The goal is to find the minimum cost to paint the matrix according to these constraints. The operations allowed are painting entire rows red or columns blue, and the cost depends on how many actions... |
[
{
"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, I need to solve this problem where Alice and Bob are cutting a grid and earning points based on the chips they cut. Let's think through the problem step by step.
First, the input gives multiple test cases. For each test case, the initial grid is a x b. There are n chips and m moves. The moves can be U, D... |
[
{
"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 break down the problem step by step.
First, the temperature of the rod as a function of time is given by:
\[ T(t) = T_0 \left(1 + \beta t^{\f... |
[
{
"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)"
} | $\boxed{\text{A, C, D}}$
**Step-by-Step Explanation:**
**Problem:** Determine the correct options regarding the complex $\left[\text{Co(en}(\text{NH}_3)_3\text{H}_2\text{O}\right]^{3+}$.
**Given:**
- The ligand en is bidentate, meaning each en donates two ligating sites (ammonium-like).
- The complex has a charge 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: 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"
} | To solve this problem, we need to determine the amount of lead (Pb) produced per kilogram of oxygen (O₂) consumed during the partial oxidation of galena (PbS) followed by self-reduction. Let's break down the problem step by step.
### Step 1: Understanding the Reaction Pathways
1. **Partial Oxidation of Galena (PbS):**... |
[
{
"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 4 times BC.
First, let's analyze the given information and the geometric properties involved. Since AB is parallel to DE, triangles ABC an... |
[
{
"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 of finding the number of elements in the union of sets \(X\) and \(Y\), we need to first understand the structure of each set and then apply the principle of inclusion-exclusion. Let's proceed step by step.
### Step 1: Define the Arithmetic Progressions
Set \(X\) is the first 2018 terms of the ari... |
[
{
"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 see. I need to solve this problem where we have to determine if we can craft an artifact by performing some operations on the materials. The operations allow us to convert all other materials into one type, but we have to make sure that after all operations, each material's count meets or exceeds 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": 2,
"temperature": 0.7
} | 2 | 78 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find a subset of vertices in a tree that meets certain conditions. Let me try to understand the problem step by step.
So, the problem says that the tree has 2n vertices, each labeled with a number from 1 to n, each exactly twice. The subset I choose must be co... |
[
{
"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
} | <think>
Okay, let's try to figure out the problem step by step. So, the problem is about determining the molecular symmetry group of product 3 after three chemical transformations. Let me break down each step to see how the molecule changes and what its symmetry might be.
First, the initial reactant is toluene. Toluen... |
[
{
"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)"
} | $\boxed{\text{A, B, D}}$
To determine the correct statements among the options provided, we need to analyze each compound's structure and bonding in detail. Let's examine each option step by step.
**Option [A]: $\mathrm{Al}\left(\mathrm{CH}_{3}\right)_{3}$ has the three-centre two-electron bonds in its dimeric struct... |
[
{
"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 \( m_1 = 2 \) and \( m_2 = \frac{1}{3} \), we can use the formula for the angle between two lines. The formula for the tangent of the angle \( \theta \) between two lines is given by:
\[
\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|... |
[
{
"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 see. I need to solve this problem where Penchick wants his BBQ buns to have fillings that meet certain conditions. The problem is, for each test case given n, output a sequence of fillings that are either all the same or arranged such that any duplicates are spaced by a square distance, and no filli... |
[
{
"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"
}
] | {
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"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 polar form. Let \(z = 4e^{i\theta}\), where \(\theta\) is a real number. This allows us to write the expression in terms of \(\theta\).
First, ... |
[
{
"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 see. I need to solve this problem where Kevin and Nivek are competing, and I have to find the minimum time Kevin needs to spend to win at least k matches for each k from 0 to n. Hmm.
First, let's understand the problem. Each match can be type 1 or 2. For type 1, Kevin can pay a_i time to win. For t... |
[
{
"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 limit \(\lim_{x \to \alpha^+} f(g(x))\), we need to evaluate 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:
- \(f(x) = \sin\left(\frac{\pi x}{12}\right)\)
- \(g(x) = \frac{2 \log_e(\sqrt... |
[
{
"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
} | I'll start by recalling what I know about neurotransmitters. They transmit signals across a synapse. Once they've done their job, which is binding to receptors, they need to be removed or deactivated to prevent continuous signaling. Let's go through the options.
Option A says they diffuse away and are exhaled. While s... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 291 | 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 smallest n such that after flipping the bulbs in the described way, exactly k bulbs are left on. Let's think through this step by step.
First, let's understand the process. All bulbs start as on (1). For each i from 1 to n, we flip all bulbs j divisib... |
[
{
"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 me tackle these one by one.
Starting with reaction 1: 1,1-dimethoxyethan-1-amine + but-3-en-2-ol + (H+ + Heat) → A.
Hmm. The reactants are an amine and an alcohol. The presence of H+ and heat suggests a sigmatropic rearrangement. Let's think about the possible mechanisms.
The first reactant is 1,1-dimethoxyethan... |
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