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 147k |
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[
{
"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:",
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} | To find the range of the function \( f(x) = (\arccos x)^2 + (\arcsin x)^2 \), we start by noting the domain of the function. The domains of \(\arccos x\) and \(\arcsin x\) are \([-1, 1]\), and their ranges are \([0, \pi]\) and \([- \frac{\pi}{2}, \frac{\pi}{2}]\) respectively. Therefore, the domain of \( f(x) \) is \([... |
[
{
"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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} | 8 | 23 | AMC23 | {
"expected_answer": "7",
"problem_id": "26",
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} | To solve the problem, we need to determine the slope of the line passing through the intersection points 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, tangent to... |
[
{
"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"
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] | {
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"max_new_tokens": 32768,
"seed": 3,
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} | 3 | 13 | AMC23 | {
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} | To solve the problem of finding the number of ordered pairs \((a, b)\) of positive real numbers that satisfy the equation \((1 + 2a)(2 + 2b)(2a + b) = 32ab\), we will proceed with the following steps:
1. **Introduce substitutions to simplify the equation**:
Let’s set \( x = 2a \) and \( y = 2b \). This transforms 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... | {
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} | 1 | 265 | CodeElo | {
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} | <think>
Okay, I have this programming problem to solve. Let's read the problem statement carefully.
So the problem is about a game played on a tree by Alice and Bob. The rules are that they take turns moving to unvisited neighboring vertices. The player who can't move loses. We need to determine for each position alon... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A bus is in operation. The number of passengers on the bus is always a non-negative integer.\nAt some point in time, t... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 377 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, let's see. The problem is about a bus that stops N times. Each time, the number of passengers changes by A_i. The initial number of passengers was zero or more, and at all times after each stop, the passenger count was non-negative. We need to find the minimum possible current number of passengers that fi... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 445 | CodeForces | {
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to find the first year when the process becomes stable. Let's understand the problem again.
So each spider starts with 1 plushie. Every year, if a spider has at least one plushie, it gives exactly one to the spider named r_i. All transfers happen at the same time... |
[
{
"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,
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} | 2 | 384 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's try to understand this problem. So, the problem is about determining the number of ways Alice can divide the pockets into boxes such that she wins the resulting game, considering that both players play optimally. The game's rules are a bit tricky.
First, let's restate the game mechanics. The pocke... |
[
{
"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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} | Let's compute the required ratios step by step.
First, let's list out the given values:
Current Assets:
- Cash: $22,150
- Marketable Securities: $16,000
- Accounts Receivable: $30,450
- Inventories: $25,000
Total Current Assets: $22,150 + $16,000 = 38,150? Wait, wait. Wait, the total current assets sum provided is $9... |
[
{
"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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} | 1 | 284 | LiveCodeBench | {
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} | <think>
Okay, let's see. The problem is to determine if a given number N is a 321-like number. Hmm. So the definition says that the digits must be strictly decreasing from top to bottom. Oh right, that means each digit must be greater than the next one. So for example, 321 is 3>2>1, so yes. But 123 is 1<2, so no.
The... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
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"temperature": 0.7
} | 0 | 21 | CodeForces | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, so I need to solve this problem where we have to rearrange an array such that when we compute the min prefix array (b) and max prefix array (c), the sum of (c_i - b_i) is maximized. Hmm. Let's think about how to approach this.
First, let's understand what the problem is asking. For each i, b_i is the min... |
[
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"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 see. I need to figure out the products of the given Michael addition reactions. Let's start with each problem one by one.
First problem: dimethyl malonate + methyl (E)-3-(p-tolyl)acrylate + (NaOEt, EtOH) → ?
Dimethyl malonate is a diene, and when reacted with an α,β-unsaturated ketone like methyl (E)-3-(p-tolyl... |
[
{
"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 | {
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} | <think>
Okay, let's see. I have to find the minimum cost of a regular bracket sequence where some positions are already fixed (the even indices) and others (odd indices) are underscores that I can replace with either '(' or ')'. The cost is the sum of the distances between matching pairs. For example, each pair's contr... |
[
{
"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 | 348 | CodeForces | {
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"subject": null,
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} | <think>
Okay, let's tackle this problem. Hmm. So the problem is about Florida Man's crow that needs to teleport to a certain position while avoiding scarecrows that move towards it. We need to find the minimal time required for the crow to reach the target, considering the scarecrows can move optimally. Oh right, and t... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
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} | 1 | 172 | CodeForces | {
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} | <think>
Okay, let's see. So the problem is to transform a given undirected graph into a cool graph by performing certain operations. The cool graph is either empty or a tree. The allowed operation is to select three distinct vertices a, b, c and toggle the existence of the edges (a,b), (b,c), (c,a). Each operation can ... |
[
{
"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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} | 1 | 190 | CodeForces | {
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} | <think>
Okay, let's tackle this problem. Hmm. The task is to find the maximum possible product of the minimums of pairs between arrays a and b, after each modification. The modifications involve incrementing elements of a or b. We need to compute this maximum product modulo 998244353 for each test case, both before mod... |
[
{
"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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} | B |
[
{
"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]... | {
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"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 which compound X is formed when K4[Fe(CN)6] reacts with FeSO4 solution in the absence of air. The options are given, and I have to choose the correct one.
First, let's understand the reactions described. The problem says that when K3[Fe(CN)6] reacts with freshly prepared F... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 1 | 113 | CodeForces | {
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} | <think>
Okay, let's try to understand this problem. So, we have a vending machine with n slots, each containing a_i cans of lemonade. The catch is that the buttons are unlabeled, so each time we press a button, we might get a can from that slot, but we don't know which one we pressed. We need to find the minimum number... |
[
{
"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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} | 0 | 257 | CodeForces | {
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} | <think>
Okay, let's see. 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. The operation allows me to pick two elements with different parities, replace the smaller one with their sum. And each such operation counts as one step. Hmm... |
[
{
"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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} | 1 | 10 | AMC23 | {
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"problem_id": "12",
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"subject": null,
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} | <think>
Okay, let's tackle this problem. So, the problem is about a triangular array of integers, and we need to find the units digit of the sum of the 2023rd row. Hmm. Let's start by understanding the structure of the triangle.
The first few rows are given. Row 1 is 1. Row 2 is 1 1. Row 3 is 1 3 1. Row 4 is 1 5 5 1. ... |
[
{
"content": "Problem: How many positive whole-number divisors does 196 have?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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} | 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. Since 196 is even, we divide by 2:
\[ 196 \div 2 = 98 \]
So, we have one factor of 2. Again, 98 is even:
\[ 98 \div 2 = 49 \]
Now, 49 is not divis... |
[
{
"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 see. The original compound has the formula C8H9NO. Let's figure out its structure based on the NMR data given.
The 1H NMR data is:
- 9.72 (t, 1H): This is likely the aromatic proton of a phenol group. The multiplet here probably corresponds to the hydroxyl proton of a phenol, which is usually a singlet or a bro... |
[
{
"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... | {
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"max_new_tokens": 32768,
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} | 2 | 197 | JEEBench | {
"expected_answer": "4",
"problem_id": "31",
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"subject": "chem",
"type": "Numeric"
} | Okay, let's tackle this problem step by step. The task is to determine how many molecules from the given list contain a covalent bond between two atoms of the same kind. Let's break down each compound one by one.
First, let's list all the compounds provided:
1. B2H6 (Borane)
2. B3N3H6 (Triaminoborazine)
3. N2O (Dinit... |
[
{
"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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} | 1 | 36 | LiveCodeBench | {
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} | <think>
Okay, let's see. I need to solve this problem where I have to count the number of beautiful pairs in an array. The definition is a pair (i, j) where i < j, and the first digit of nums[i] is coprime with the last digit of nums[j]. Hmm. Right.
So, the first thing I need to do is, for each element in the array, g... |
[
{
"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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} | To solve this problem, we need to determine the correct products formed in each of the two Michael addition reactions described. Let's break down each reaction step by step.
### First Reaction
The first reaction involves the Michael addition of sodium ethoxide (NaOEt) to 2,4-dimethyl-1-(vinylsulfinyl)benzene (vinylsul... |
[
{
"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"
}
] | {
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} | To solve the problem of determining how many ways there are to put 5 indistinctive balls into 2 indistinctive boxes, we can approach it using combinatorics.
The key insight here is that since both the balls and the boxes are indistinctive, the problem reduces to finding the number of distinct distributions where 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 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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"seed": 2,
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} | 2 | 510 | LiveCodeBench | {
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"subject": null,
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} | <think>
Okay, 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 fewer occurrences than the query number, return -1. Hmm.
Let me think about the approach here. So, the straightforward way would be to first collect all the indi... |
[
{
"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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} | 1 | 465 | LiveCodeBench | {
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} | <think>
Okay, let's see. I need to find the maximum length of a substring in the given string where each character appears at most twice. Hmm. So the problem is similar to the classic sliding window problem where we track the frequency of characters and adjust the window's start and end to maintain the constraint. But ... |
[
{
"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... | {
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"seed": 1,
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} | 1 | 189 | JEEBench | {
"expected_answer": "C",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | Okay, let's see. I need to figure out which of these options correctly identifies the compounds for calamine, malachite, magnetite, and cryolite. Hmm.
First, let's think about each term one by one.
Calamine: I remember that calamine is zinc carbonate. So the formula should be ZnCO3. Right, because when you heat it, i... |
[
{
"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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} | Let me think. So the question is to find which of the given molecules has C3h symmetry. Hmm. Let's recall that C3h symmetry implies that there's a center of inversion (i) along with a 120-degree rotation (C3) and a mirror plane. So the molecule must be symmetric upon rotation by 120 degrees and inversion through the ce... |
[
{
"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 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where for a given n, I have to find the optimal x between 2 and n inclusive. The goal is to maximize the sum of all multiples of x that are ≤n. Let's think about how to approach this.
First, let's understand the problem. For each x, the sum is x*(1 + 2 + ... +k) where kx ≤n. ... |
[
{
"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 generate a Python function that calculates the sum of squares of special elements in an array. Let's think about the steps.
First, the problem says a special element is one where the index (1-based) divides the length of the array. So for example, if the array has 4 elements, the indices 1, 2, ... |
[
{
"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
} | \boxed{D} |
[
{
"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 try to understand this problem. So the task is to compute the sum of f(i) for all i from 0 to m, where f(i) is the maximum value attainable starting with x = i, through any number of operations. Each operation involves choosing a sequence and updating x to be the mex of x and the elements of the seq... |
[
{
"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. I need to find the minimum time required for Zhan to blend all the fruits. Hmm. Let me read the problem again carefully.
So, the blender can mix up to x fruits per second. Each second, Zhan can put up to y fruits into the blender. After putting them in, the blender takes min(x, c) where c is t... |
[
{
"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. **Understand the Inequality**: The problem states that \( 2 < \sqrt{t} < 3.5 \). We need to find all integers... |
[
{
"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, let's see. The problem is to check if a given string s is an acronym formed by taking the first character of each word in the list. So, the steps I need to take are:
First, for each word in the list, I need to get the first character. Then, I'll concatenate all those first characters into a string and co... |
[
{
"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 try to figure out this problem. So, the task is to determine, for each query k_i, how many points are covered by exactly k_i segments. Each segment is formed by choosing a pair of points (i,j) where i < j, and the segment is [x_i, x_j], which includes all integers from x_i to x_j.
First, let's und... |
[
{
"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, let's see. I need to find the k-th smallest amount that can be made using the given coins without combining different denominations. Hmm. So each amount is a multiple of exactly one coin. Wait, no, wait. Wait, the problem says you can't combine coins. So each amount is a multiple of a single coin. So for ... |
[
{
"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, let's see. I need to find the number of right triangles in a binary matrix where each triangle is formed by three elements that are all 1s. The triangle must satisfy that one element is in the same row as another and the same column as a third. So, like a right angle triangle with the right angle at one o... |
[
{
"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. I need to solve this problem where I have to maximize the frequency of the most frequent element in an array after performing at most k operations. Each operation allows me to increment or decrement an element by 1. The frequency is the count of the most occurrences in the array. Hmm.
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... | {
"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 to maximize the sum of two gcds from a and b arrays after swapping some elements, with each swap costing c_i coins. The total cost can't exceed d for each query d. The answer is this sum for each d in the list of queries.
Hmm, first, the problem seems ... |
[
{
"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, let's see. I need to solve this programming problem. Let's read the problem statement carefully.
The problem is about a grid with H rows and W columns. Each cell can be 'o', 'x', or '.' (initially empty). We can change '.' cells to 'o' by paying 1 operation each. We need to find the minimum number of ope... |
[
{
"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"
} | Okay, let's tackle this problem step by step. The problem is about comparing the heat supplied to a gas during two different processes: an adiabatic process and a two-step process (isobaric followed by isochoric). We need to find the difference in heat supplied between these two processes.
First, let's understand the ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 0 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to find the number of minimal coprime segments in [l, r]. Hmm. So, first I need to understand what a minimal coprime segment is. From the description, a minimal coprime segment is one that doesn't contain any other coprime segment. And the key example given is that two consecutiv... |
[
{
"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 try to understand this problem. So, we have a rooted tree where each node (except the root) has a parent, and each edge has a weight t_i. The nodes are numbered in a specific way: each subtree's nodes are consecutive. The example given shows that in the subtree of node 2, the nodes are 2,3,4,5. So t... |
[
{
"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"
} | $\textbf{Solution}$
Okay, let's tackle this problem step by step. So, we have an alpha particle and a sulfur ion that are accelerated through the same potential difference V. Then they enter a magnetic field, moving in circular orbits. We need to find the ratio of their radii.
First, let's think about the acceleratio... |
[
{
"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
} | Let's solve the problem step by step. We are given two equations involving positive real numbers \(x\) and \(y\):
1. \(y^3 = x^2\)
2. \((y - x)^2 = 4y^2\)
Our goal is to find \(x + y\).
First, let's expand the second equation:
\[
(y - x)^2 = 4y^2
\]
Expanding the left side:
\[
y^2 - 2xy + x^2 = 4y^2
\]
Rearrange... |
[
{
"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"
} | Okay, I need to solve this problem where I have to find out how many elements are in each of the lists I to IV. Then match them with options A to D. Let's tackle each list one by one.
First, let's work on List-I: Solve cos x + sin x = 1 for x in [-2π/3, 2π/3].
Hmm. Let's square both sides. (cos x + sin x)^2 = 1^2 → 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.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 programming problem. Let's read the problem carefully.
So, the problem is about a tree with N vertices. Each vertex has a value C_i. We need to compute for each vertex x, the sum of C_i multiplied by the distance from x to i (d(x, i)) for all i from 1 to N. Then, find the minimum of ... |
[
{
"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 about finding the maximum possible achievable number given a starting num and t steps. Each step allows me to adjust x and num by 1 either increasing or decreasing. But the key is that after t steps, x equals num. Wait, no, the problem says that after applying the operation no mo... |
[
{
"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
} | Okay, let's try to understand this problem. Hmm. So, the problem is about selecting some strings from a list to form a concatenated string. The goal is to maximize the score difference between Narek's score and ChatGPT's score.
First, let's break down how each score is calculated.
Narek's score (score_n): He looks fo... |
[
{
"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 after performing at most k operations. Each operation allows me to replace two adjacent elements with their bitwise AND, and I can do this up to k times. Hmm.
So the goal is to minimize the OR of the remaining elements. The OR of a co... |
[
{
"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
} | \documentclass{article}
\usepackage{amsmath}
\begin{document}
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, find the proper divisors of 284. Then sum them. Then find the proper divisors of that sum and sum them again.
Step 1: Find 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
} | A |
[
{
"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 problem step by step to determine the number of chemically distinct hydrogen atoms in the final product 4.
First, let's analyze the initial reactants and the reaction steps.
The problem states that the starting material is 7-(tert-butoxy)bicyclo[2.2.1]hepta-2,5-diene. When combined with 2 equi... |
[
{
"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 maximum and minimum values of the function \( g(\theta) \) defined on the interval \([0, \frac{\pi}{2}]\), then use these values to form a quadratic polynomial \( p(x) \) such that \( p(2) = 2 - \sqrt{2} \). Finally, we evaluate the given options to determine which are tr... |
[
{
"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)... | <think>
Okay, let's tackle this problem. Hmm. So, the problem says that there are eight circles arranged around triangle ABC. Two of them are tangent to AB and BC respectively. The rest are arranged in some way. Then, considering that the inradius is 2024 circles of radius 1 arranged in the same manner, we need to find... |
[
{
"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 scenario is: An employee of a furniture store was driving a truck to deliver furniture when he negligently ran a stop sign and hit a car. The driver of the car sued the furniture store and recovered $25,000. Now, the furniture store is seeking to recover from its employee.
... |
[
{
"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"
} | ## Solution
Okay, let's tackle this problem. So, we need to find the total number of isomers (including structural and stereoisomers) for cyclic ethers with the molecular formula C4H8O. Hmm. Right, cyclic ethers are compounds where there's a ring structure containing oxygen. And isomerism can arise from the arrangemen... |
[
{
"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 first-type operations needed to turn all elements of the array into 1s. The first-type operation is straightforward: you pick a zero and turn it into a one. The second-type operation is a bit more complex. It requires choo... |
[
{
"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
} | Let's think about this step by step. The question is asking which normative theory is most similar to corporate profit maximization. So, I need to compare each option to see which one aligns least with the idea of maximizing profit for a corporation.
First, let's understand what each option means:
A. Ethics of care: ... |
[
{
"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 solve this problem where I have to find the number of triples (i,j,k) with i<j<k such that A_i = A_k and A_i ≠ A_j. Hmm. So the conditions are, the first and third elements in the triple are equal, and the middle one is different.
First, let's think about the approach. The naive way... |
[
{
"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 the number of values of \( p \) for which the circle given by the equation \( x^2 + y^2 + 2x + 4y - p = 0 \) intersects the coordinate axes at exactly three distinct points.
### Step 1: Understanding the Circle Equation
The given equation is \( x^2 + y^2 + 2x + 4y - p = 0 \... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 225 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this hard version of the problem where Turtle gives some intervals and I have to find the maximum number of inversions in an interesting permutation. The permutation has to satisfy certain conditions based on these intervals. Let's try to understand the problem step by step.
First, what's... |
[
{
"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. Hmm. The problem is about calculating the probability that Jen wins the grand prize given that she already won a prize. So, the key here is to use conditional probability. The formula would be the probability of both winning a prize and the grand prize divided by the probability... |
[
{
"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)"
} | Okay, let's see. The problem is about galena treated with HNO3 producing a gas. Hmm, I need to figure out which of the given options (A-D) are correct. Let me approach this step by step.
First, the reaction between galena (PbS) and HNO3. Galena is lead(II) sulfide. When you react it with nitric acid, the products woul... |
[
{
"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"
} | ### Detailed Solution
Let's tackle the problem step by step.
1. **Initial Setup and Given Values**:
- Mass of the bob, \( m = 0.1 \, \text{kg} \)
- Length of the string, \( L = 1.0 \, \text{m} \)
- Height of the suspension point above the floor, \( H = 0.9 \, \text{m} \)
- Horizontal impulse, \( P = 0.2 \... |
[
{
"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, I need to solve this problem where Robin's brother and mother are visiting, and I have to choose their start days such that the brother's visit overlaps as many jobs as possible, the mother's as few as possible. And if there are multiple options, pick the earliest day for each.
Hmm, let's think about how... |
[
{
"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)"
} | Okay, let's tackle this problem step by step. The problem is about a decay sequence of uranium-238, and we need to determine which of the given options are correct. Let's go through each option one by one.
First, let's write down the decay sequence:
${ }_{92}^{238} \mathrm{U} \stackrel{-\mathrm{x}_{1}}{\longrightarro... |
[
{
"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 try to figure out this problem. So, the problem is about permutations and strings that dictate certain movement possibilities. The main question is, after each query that flips an 'L' to 'R' or vice versa, whether we can sort the permutation using the allowed swaps.
First, let's understand the allo... |
[
{
"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 think about this problem step by step.
First, the problem is about identifying the correct reactants and the order of dienes based on their reactivity. The given reaction is Cyclohexene + A → 8,8-diiodobicyclo[4.2.0]octan-7-one. We need to determine which option (A or B) is the correct reagent, and then arrange ... |
[
{
"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 analyzing the given condition and the expression we need to minimize.
First, let's denote \(a = x + y\), \(b = y + z\), and \(c = z + x\). However, this approach might complicate the problem. Alternatively, we can use substi... |
[
{
"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. The problem is to find four sticks to form an isosceles trapezoid. The key points are that two pairs of equal lengths form the bases and legs. But wait, according to the editorial, the condition is that the absolute difference between the bases is less than twice the leg length. So the approach... |
[
{
"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 try to figure out this problem. So, the task is to compute the strength of an array after each prefix of the given pairs. The strength is the number of seconds it takes for the array to become empty. Each second, the cosmic rays delete all elements that are either at the beginning (i=1) or different... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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 solves this problem. The function should take stdin as input and print each player's required number of problems to solve. Let's try to break this down.
First, the problem says that for each player, we have to find out how many of the remaining problem... |
[
{
"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 a list of positive integers that meets the given criteria and then compute the sum of their squares. Let's break down the problem step by step.
### Problem Analysis
1. **Sum of the list is 30**
The total sum of all elements must be 30.
2. **Unique mode is 9**
The n... |
[
{
"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 calculate the sum of digit differences between all pairs of numbers in the given array. Hmm. The digit difference is the count of different digits in the same positions. So for each pair, compare each digit from left to right until they differ, then count how many differences there ar... |
[
{
"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, let's see. The problem is to determine if a given number N is a 321-like number. Hmm. So the conditions are that the digits are strictly decreasing from top to bottom. Oh right, that means each digit must be greater than the next one. So for example, 321 is yes because 3>2>1. But 123 is no because 1 is no... |
[
{
"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"
} | Okay, I need to solve this problem where I have to calculate the sum of the number of lone pairs on each central atom in the given species. Let's break this down step by step.
First, let's list out all the species provided:
1. [TeBr6]^2-
2. [BrF2]+
3. SNF3 (assuming S is the central atom)
4. [XeF3]^-
I need to find ... |
[
{
"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"
} | $\boxed{D}$
Now, let's get into solving this problem. We need to match each radioactive decay process in List-I with the correct emitted particles from List-II. Let's break down each decay reaction step by step.
First, let's look at each decay reaction in List-I and determine the type of particles emitted.
Starting ... |
[
{
"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 tackle this problem. Hmm. So the problem is about coloring a matrix with row and column operations. The goal is to find the minimum cost after each query, where the cost depends on how many actions we take.
First, I need to understand the problem thoroughly. Let's read the description again. The 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 | 25 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem. So, the problem is about Alice and Bob playing a game where they take turns cutting parts of a grid. Each time they cut, they earn points equal to the number of chips on the cut part. The goal is to compute how many points each of them scores based on the sequence of ... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: 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"
} | Okay, let's tackle this problem step by step. The goal is to find the heat capacity of the metal rod based on the given temperature-time relationship.
First, let's understand the problem. The wire provides a constant power P, which means the rate at which energy is added to the rod is constant. The temperature change... |
[
{
"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)"
} | Okay, let's tackle this problem step by step. The problem is about the complex [Co(en)(NH3)3(H2O)]3+. We need to determine which options are correct regarding its properties.
First, let's parse the complex's structure. The central cobalt(3+) ion is surrounded by three NH3 molecules and one en (ethylenediamine) ligand.... |
[
{
"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"
} | ### Solution
Let's tackle this problem step by step. The problem involves the oxidation of galena (which is lead sulfide, $\mathrm{PbS}$) and then the self-reduction process. We need to determine the weight of lead ($\mathrm{Pb}$) produced per kilogram of oxygen ($\mathrm{O}_2$) consumed.
First, we need to write the ... |
[
{
"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 this 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. Let's proceed step by step.
1. **Understand the Given Information:**
- The area of triangle ABC is 6 square centimeters.
... |
[
{
"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 this problem, we need to determine the number of unique elements in the union of two arithmetic sequences, \(X\) and \(Y\). The sequences are defined as follows:
- Sequence \(X\) starts at 1 with a common difference of 5. Thus, the terms are \(1, 6, 11, \ldots\).
- Sequence \(Y\) starts at 9 with a common dif... |
[
{
"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 certain operations on materials. The operations allow us to increase a material by 1 and decrease all others by 1 each time. But we have to make sure that all materials reach or exceed their requir... |
[
{
"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 try to figure out this problem. So, we have a tree with 2n vertices, each labeled with a number from 1 to n, each appearing exactly twice. We need to select a connected subset that includes at least one vertex for each value from 1 to n, with the goal of minimizing the total cost, which is the sum o... |
[
{
"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
} | Let's see. Let's track the transformations step by step.
First reaction: toluene (C7H8) is treated with nitric acid and sulfuric acid to form product 1. Toluene is C6H5CH3. When nitrated, the typical product would be 2,4,6-trinitrotoluene (2,4,6-TNT), but depending on the conditions, maybe mononitro or other positions... |
[
{
"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)"
} | Okay, let's tackle this problem step by step. The problem is about understanding the bonding and acidity of certain compounds. Let's look at each option one by one.
First, the problem mentions dimeric structures and three-centre two-electron bonds. So, I need to recall what those are. Three-centre two-electron bonds i... |
[
{
"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 tangent of the angle \(\theta\) between two lines with slopes \(m_1\) and \(m_2\) is given by:
\[
\tan \theta = \left| \frac{m_1 - m_2}{1 + 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,
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} | 1 | 208 | CodeForces | {
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} | <think>
Okay, let's tackle this problem. Hmm, the problem is about assigning fillings to BBQ buns such that each filling appears at least twice, and any two occurrences of the same filling are exactly squared apart. Oh right, the distance |i-j| must be a perfect square.
First, let's understand the constraints. For an... |
[
{
"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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} | 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} \... | <think>
Okay, I need to find the largest possible real part of the expression (75+117i)z + (96+144i)/z, given that |z| = 4. Hmm. Let's see. Since z is a complex number with absolute value 4, maybe I can represent z in terms of its polar form. Like, z = 4 eiθ, where θ is some angle. Then maybe substituting that into the... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 1 | 372 | CodeForces | {
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} | <think>
Okay, let's see. I need to solve this problem where Kevin and Nivek are having matches, and I have to compute for each k (from 0 to n) the minimal time Kevin needs to spend so that he wins at least k matches. The matches can be type 1 or 2.
Hmm. Let's understand the problem again. For each match i:
- Type 1:... |
[
{
"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} \... | {
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"subject": "math",
"type": "Numeric"
} | To find the value of \(\lim_{x \to \alpha^+} f(g(x))\), 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, let's understand the functions involved:
- \(f(x) = \sin \left( \frac{\pi x}{12} \right)\)
- \(g(x) = \frac{2 \log_e... |
[
{
"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... | {
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} | 0 | 219 | MMLUPro | {
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} | I think the correct answer is I. Because once neurotransmitters have done their job, they need to be deactivated to prevent continuous signaling. So the options that make sense are either I or J. But J says they bond permanently, which isn't right. So I is the right choice.
Final answer: I. |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 291 | CodeElo | {
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} | <think>
Okay, so I have this programming problem to solve. Let's read the problem carefully.
The problem is about flipping light bulbs. We start with all bulbs on. Then for each i from 1 to n, we flip all bulbs j that are divisible by i. After doing this for all i, exactly k bulbs are on. We need to find the smallest ... |
[
{
"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 ... | {
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} | 1 | 48 | GPQADiamond | {
"expected_answer": "",
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} | Let's tackle each problem step by step.
First, let's look at the first reaction: 1,1-dimethoxyethan-1-amine + but-3-en-2-ol + (H+ + Heat) → ?
We need to determine what product forms when these reactants undergo a sigmatropic rearrangement. But-3-en-2-ol is a secondary alcohol with a conjugated system. The terminal p... |
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