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values | metadata dict | model_outputs stringlengths 8 169k |
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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 using a known trigonometric identity. Recall that for any \( x \) in the domain of \( \arccos x \) and \( \arcsin x \), the following holds:
\[
\arccos x + \arcsin x = \frac{\pi}{2}
\]
This identity can be derived from the fact ... |
[
{
"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 | {
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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:",
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} | To solve the equation \((1+2a)(2+2b)(2a+b) = 32ab\) for ordered pairs \((a, b)\) of positive real numbers, we start by simplifying and analyzing the equation.
First, let's expand the left-hand side (LHS) of the equation:
\[
(1+2a)(2+2b)(2a+b)
\]
Expand \((1+2a)(2+2b)\):
\[
(1+2a)(2+2b) = 1 \cdot 2 + 1 \cdot 2b + 2a \... |
[
{
"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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} | Okay, let's see. So the problem is about Alice and Bob playing a game on a tree. The goal is to determine the winner when Alice starts at vertex 1 and Bob starts at each vertex in the path from u to v. The catch is that u equals v, and the path from u to v doesn't go through vertex 1. Also, the tree is given, and we ne... |
[
{
"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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} | 1 | 377 | LiveCodeBench | {
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} | <think>
Okay, let's see. I need to find the minimum possible current number of passengers on the bus. The bus stops N times, and at each stop i, the number of passengers changes by A_i. The initial number of passengers was zero or more, and after all stops, the passengers should still be non-negative. So the problem is... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | Okay, I need to solve this problem where a group of spiders exchange plushies each year. The goal is to find the first year in which the distribution of plushies becomes stable. Let's think about how to approach this.
First, let's understand the problem. Each spider starts with 1 plushie. Each year, if a spider has at... |
[
{
"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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} | 2 | 384 | CodeForces | {
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} | Okay, I need to solve this problem where Alice divides the pockets into boxes, and then both players take turns removing peanuts from the leftmost non-empty box. The goal is to count the number of ways Alice can divide the pockets into boxes so that she wins, assuming optimal play from both.
First, let's understand th... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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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} | <think>
Okay, let's tackle this problem step by step. I need to calculate the current ratio, quick asset ratio, and net working capital based on the given financial data.
First, let's recall the formulas for each ratio.
**Current Ratio** is calculated as Current Assets divided by Current Liabilities. It's a liquidi... |
[
{
"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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} | <think>
Okay, I need to create a Python function that checks if a number is a 321-like number. Let me think about the problem again. So a 321-like number has digits that are strictly decreasing from left to right. So each digit is larger than the next one. Right, like 321 where 3>2>1. So the steps I need to take are:
... |
[
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | </html>
To solve this problem, we need to determine the maximum possible score that can be obtained by shuffling the elements of an array \(a\). The score is calculated as the sum of the differences between the maximum and minimum values of the first \(i\) elements of the array for each position \(i\).
### Approach
1.... |
[
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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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} | <think>
Okay, let's try to figure out the correct answer here. The question is about Michael addition reactions and the products formed. Let's start by recalling what a Michael reaction is. The Michael reaction involves the addition of a nucleophile to the β-position of an α-β unsaturated carbonyl compound. The key her... |
[
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 180 | CodeElo | {
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} | <think>
Okay, I need to solve this problem where Monocarp has a regular bracket sequence (RBS) but lost the odd-position characters. The task is to restore the RBS by placing brackets in the odd positions such that the cost is minimized. The cost is calculated as the sum of distances between pairs of corresponding brac... |
[
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | Okay, let's tackle this problem. The task is to determine the minimum time required for a crow to teleport to a position >= ℓ, given that it has to stay at least k units ahead of the nearest scarecrow. The input includes the number of scarecrows, their positions, k, and ℓ. The output is twice the minimum time needed.
... |
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | </html>
To solve this problem, we need to transform a given undirected graph into a cool graph by performing a specific operation a limited number of times. A graph is considered cool if it has no edges or is a tree. The operation allows us to add or remove edges between three chosen vertices a, b, and c for at most 2... |
[
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 1 | 190 | CodeForces | {
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} | Okay, let's tackle this problem. The task is to find the maximum product P = Π min(a_i, b_i) after each modification, where modifications can increase elements of a or b by 1. The answer needs to be modulo 998,244,353.
First, I need to understand how the product P is affected by changes to a and b. The key insight her... |
[
{
"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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} | 0 | 246 | MMLUPro | {
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} | The patient is a 27-year-old female with acute onset of pain and swelling in the left labia. The symptoms have been worsening over two days. She is sexually active but uses condoms inconsistently. The physical exam reveals a fluctuant mass, which is tender and measures 4x3 cm, located medial to the left labium majus, p... |
[
{
"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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} | 0 | 360 | JEEBench | {
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"problem_id": "33",
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"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's try to figure out what precipitate X is here. The problem gives us a few reactions and their outcomes, so I need to piece together the information step by step.
First, the reaction between K3[Fe(CN)6] and FeSO4 produces a dark blue precipitate, which is Turnbull's blue. I remember that Turnbull's 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 the ... | {
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} | 1 | 113 | CodeForces | {
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} | Okay, let's tackle this problem. The task is to determine the minimum number of button presses needed to get at least k cans of lemonade from a vending machine with n slots. The buttons are initially indistinguishable, but each press reveals if a can falls. The key insight is that the optimal strategy is to sort the in... |
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 0 | 257 | CodeForces | {
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} | <think>
Okay, I need to solve this parity and sum problem. Let me read the problem statement again carefully. So the task is to make all elements in an array have the same parity through the minimum number of operations. Each operation involves selecting a pair of indices where the elements have different parity and re... |
[
{
"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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} | To solve this problem, we need to determine the units digit of the sum of the 2023rd row in a triangular array where each row is formed by placing 1 at each end and each interior entry is 1 greater than the sum of the two diagonally above it from the previous row. Let's start by analyzing the given rows and identifying... |
[
{
"content": "Problem: How many positive whole-number divisors does 196 have?\nMark your solution with \\boxed\nAnswer:",
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] | {
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} | <think>
Okay, I need to find out how many positive whole-number divisors 196 has. Hmm, I remember that to figure out the number of divisors, you first have to find the prime factorization of the number. Let's start with 196.
I know that 196 is even, so divisible by 2. Let me divide 196 by 2: 196 ÷ 2 = 98. Then 98 ÷ 2... |
[
{
"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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} | \boxed{D} |
[
{
"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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"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. The question is asking for the total number of molecules among the given list that contain a covalent bond between two atoms of the same kind. So, I need to look at each molecule in the list and check if there's a bond between two identical atoms.
The given molecu... |
[
{
"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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} | <think>
Okay, I need to solve this problem where I have to find the number of beautiful pairs in the array. Let's read the problem again. A beautiful pair is when the first digit of nums[i] and the last digit of nums[j] are coprime. And coprime means their gcd is 1. So the task is to count all such pairs where i < j.
... |
[
{
"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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} | <think>
Okay, let's see. I need to figure out the correct products for these two Michael reactions. Hmm. The Michael reaction involves a nucleophile adding to a C=C double bond next to a carbonyl group. Let's look at each reaction step by step.
First reaction: methyl 2-oxocyclohexane-1-carboxylate reacts with (NaOEt, ... |
[
{
"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:",
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} | <think>
Okay, so I need to figure out how many ways there are to put 5 indistinguishable balls into 2 indistinguishable boxes. Hmm, this seems like a problem that's related to partitions, maybe? Because the boxes are the same, so I can't just use the usual combinations where boxes are distinct.
Let me think. If the bo... |
[
{
"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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} | <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 than that number of occurrences, return -1 for that query. Hmm.
Let's look at the examples. In the first example, nums is [1,3,1,7], queries are [1,3,2,4]... |
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{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.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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} | <think>
Okay, I need to solve this problem where I have to find the maximum length of a substring in a given string s, such that each character in the substring appears at most two times. Hmm. Let's think about how to approach this.
First, I remember that the problem is similar to the one where you find the longest su... |
[
{
"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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} | 1 | 189 | JEEBench | {
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} | To solve this problem, we need to identify the correct chemical formulas for calamine, malachite, magnetite, and cryolite from the given options. Let's analyze each compound one by one.
1. **Calamine**:
- Calamine is a zinc-containing mineral. The common formula for calamine is \(\mathrm{ZnCO}_3\), which is also kn... |
[
{
"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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} | \boxed{C} |
[
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} | Okay, I need to solve this Maximum Multiple Sum problem. Let's read the problem carefully. The task is to find an integer x between 2 and n inclusive such that the sum of all multiples of x that are less than or equal to n is maximized. Hmm.
So for each test case, given n, I have to find that x. The example given is w... |
[
{
"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... | {
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"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes a list of integers and returns the sum of the squares of the elements that are in special positions. A special position is one where the index (starting from 1) divides the length of the list. So first, I need to find all elements nums[i] where i (1-... |
[
{
"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
} | <think>
Okay, let's see. I need to find the eigenvalues of the Hamiltonian operator H = ε ⋅ σ ⋅ n. Hmm. The Hamiltonian here is a vector dot product with the Pauli spin matrices. Wait, the Pauli matrices are σx, σy, σz. So when we take the dot product with the unit vector n, which has components nx, ny, nz, the Hamilto... |
[
{
"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 Turtle has to maximize the value of x by performing operations on sequences. The problem is a bit complex, but let's break it down.
First, let's understand what the problem is asking. For each test case, there are n sequences. Each sequence has a certain length and elem... |
[
{
"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
} | Okay, I need to solve this problem where Zhan has to blend all his fruits using his blender. Let's see what the problem is asking.
So, the problem states that Zhan has n fruits. The blender can mix up to x fruits per second. But each second, Zhan can put up to y fruits into the blender. The question is, what's the mi... |
[
{
"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
} | <think>
Okay, let's see. The problem says that the square root of t is greater than 2 and less than 3.5. So I need to find all the integer values of t that satisfy this condition. Hmm.
First, I remember that if the square root of t is between 2 and 3.5, then t must be between 2² and 3.5². Let me calculate those square... |
[
{
"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 formed from an array of words. The acronym is created by taking the first character of each word in order. So, the first character of the first word, then the first of the second, and so on, until the length of s. I have to ret... |
[
{
"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 All Pairs Segments problem. Let's read the problem carefully. So, given n points on the x-axis at increasing coordinates, we draw segments between every pair (i, j) where i < j. Each segment is [x_i, x_j], which includes all integer points from x_i to x_j. Then, for each query with a ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array coins representing coins of different denominations and an integer k.\nYou have an infinite number of coins of each denomination... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 477 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the k-th smallest amount that can be made using given coins, with the condition that each coin can be used any number of times but no combination of different denominations. Hmm, let's think about this.
So the problem is similar to the coin change problem... |
[
{
"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 matrix. Let's think about how right triangles can be formed here.
Hmm, the problem says that a right triangle is made with three elements from the grid. The elements don't have to be next to each other, but on... |
[
{
"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 score of the array by modifying elements up to k times. The score is the frequency of the most frequent element. Hmm. Let's think about how to approach this.
First, the examples given. In the first example, after operations, the array becomes [2,2... |
[
{
"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 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 the GCDs of two arrays after swapping elements between them with certain costs. The catch is that the total cost of swaps can't exceed a given value d for each query. And there are multiple queries. Hmm.
First, let's understand t... |
[
{
"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 where we have a grid and we can change '.' cells to 'o' to form a consecutive sequence of 'o's in either rows or columns. The goal is to find the minimum number of changes required, or -1 if impossible.
First, let me understand the problem. We have H rows and W columns. Each ... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: A gas is enclosed in a cylinder with a movable frictionless piston. Its i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 44 | JEEBench | {
"expected_answer": "C",
"problem_id": "3",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the amount of heat supplied to the system during the two-step process (isobaric expansion followed by isochoric process) and compare it to the heat supplied during the adiabatic process. The key is to calculate the heat added in each step of the two-step process and then sum ... |
[
{
"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
} | </html>
To solve this problem, we need to determine the number of minimal coprime segments within a given range [l, r]. A minimal coprime segment is defined as a segment [l', r'] that does not contain any other coprime segment apart from itself.
### Key Insight
From the editorial, we learn that:
1. Two consecutive i... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 251 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Iris has a tree and edge weights are unknown except for some events where she learns specific weights. The goal is to compute the sum of maximum possible distances from each node to its modulo n+1 neighbor after each event. Let's break this down.
First, understanding th... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: An $\\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 317 | JEEBench | {
"expected_answer": "4",
"problem_id": "17",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the ratio of the radii of the circular orbits of an alpha-particle and a singly charged sulfur ion when they are accelerated through the same potential difference and then move in a uniform magnetic field.
### Step-by-Step Solution:
1. **Determine the Kinetic Energies:**
... |
[
{
"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
} | To solve for \(x + y\) given the equations \(y^3 = x^2\) and \((y - x)^2 = 4y^2\), we start by analyzing the second equation. Expanding the left side, we get:
\[
(y - x)^2 = y^2 - 2xy + x^2
\]
Setting this equal to \(4y^2\), we have:
\[
y^2 - 2xy + x^2 = 4y^2
\]
Rearranging terms to bring all to one side:
\[
x^2 -... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Consider the following lists:\nList-I\n(I) $\\left\\{x \\in\\left[-\\frac... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 389 | JEEBench | {
"expected_answer": "B",
"problem_id": "15",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the number of elements in each set defined in List-I and match them with the corresponding entries in List-II. Let's analyze each set one by one.
### List-I Analysis
**Set (I):**
\[ \left\{x \in \left[-\frac{2\pi}{3}, \frac{2\pi}{3}\right] : \cos x + \sin x = 1\right\} \]
... |
[
{
"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 a tree with N vertices and a sequence of integers C. The task is to find the vertex v that minimizes the sum f(v) = Σ (C_i * d(v, i)) for all i from 1 to N. Hmm, how do I approach this?
First, let's understand what d(v, i) represents. It's the number of edges bet... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given 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 x such that after at most t operations, x equals num. Each operation allows us to increase or decrease x and num by 1 together.
Hmm. So, the key here is to understand how x and num change with each operation. Let's think. If ... |
[
{
"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, I need to solve this problem where Narek and ChatGPT are scoring points based on some strings. Let's start by understanding the problem properly.
So, the problem states that Narek is too lazy to create a problem, so he uses ChatGPT. ChatGPT generates n strings, each of length m. Narek can select a subset of thes... |
[
{
"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 a way to minimize the bitwise OR of the remaining elements after performing at most k operations. Each operation allows me to pick an index i and replace nums[i] and nums[i+1] with their bitwise AND. Hmm.
Wait, the problem is about combining elements via AND and then finding 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
} | <think>
Okay, let's tackle this problem step by step. The question is asking for the sum of the proper divisors of the sum of the proper divisors of 284. Hmm. First, I need to understand what proper divisors are. Oh right, a proper divisor of a number \( N \) is a positive divisor that is less than \( N \) itself. So f... |
[
{
"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
} | \boxed{D} |
[
{
"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
} | \boxed{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: 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)"
} | <think>
Okay, let's start by trying to understand this problem. We need to find the maximum and minimum values of the function \( g(\theta) \), which is defined in terms of \( f(\theta) \). Then, we have a quadratic polynomial \( p(x) \) whose roots are these max and min values, and we have to check certain conditions ... |
[
{
"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 sequentially tangent, and two of these circles are tangent to the sides \(AB\) and \(BC\) respectively. Additionally, 2024 circles of radius 1 are arranged in the same manner. The goal is to express th... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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
} | \boxed{D} |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the total number of isomers, considering both structur... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 231 | JEEBench | {
"expected_answer": "10",
"problem_id": "32",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, I need to find the total number of isomers, including both structural and stereoisomers, for cyclic ethers with the molecular formula C4H8O. Let me start by recalling what cyclic ethers look like. A cyclic ether is a ring structure containing an oxygen atom. The general formula for a cyclic ether is (C4H8... |
[
{
"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
} | To solve this problem, we need to determine the minimum number of operations of the first type required to make all elements of the array equal to 1. The operations allowed are either setting a single element to 1 (operation 1) or setting all elements in a segment [l, r] to 1 (operation 2), provided certain conditions ... |
[
{
"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, let's see. The question is asking which normative theory is most similar to corporate profit maximization. Hmm, I need to think about what each of these options entails.
First, corporate profit maximization. That's all about making the most money, right? So it's a goal-oriented approach where the main dr... |
[
{
"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) in a sequence of positive integers such that i < j < k, A_i = A_k, and A_i ≠ A_j. Hmm. Let's think about how to approach this.
First, let's understand the problem better. The conditions are that i is less than j ... |
[
{
"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 determine the number of values of \( p \) for which the circle \( x^2 + y^2 + 2x + 4y - p = 0 \) intersects the coordinate axes exactly three times, we need to analyze the conditions under which the circle touches two axes and cuts the third.
First, we start by rewriting the equation of the circle in standard form... |
[
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | To solve this problem, we need to determine the maximum number of inversions in a permutation of length \( n \) that satisfies certain conditions defined by intervals. The key challenge is to efficiently process each test case and output the result within the given constraints.
### Approach
1. **Understanding the Prob... |
[
{
"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... | {
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"seed": 3,
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} | 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 won a prize. Let's break this down step by step.
First, define the events:
- \( W \): Jen wins a prize (at least two numbers match).
- \( G \): Jen wins the grand prize (all four numbers match).
We need to fin... |
[
{
"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... | {
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"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)"
} | <details><p>
Okay, let's try to figure out the correct answers here. The problem is about the treatment of galena with HNO3 producing a gas. I need to determine which of the given options describe that gas.
First, I remember that galena is the mineral form of lead sulfide, PbS. When it 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"
} | <think>
Okay, let's tackle this problem step by step. We need to find the kinetic energy \( K \) of the pendulum just after the bob lifts off the floor. Let's start by understanding the given information and the physical scenario.
First, the pendulum consists of a bob of mass \( m = 0.1 \, \text{kg} \) attached to a m... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 157 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Okay, I need to solve this problem where Robert's brother and mother are visiting, and we need to choose the start days for each to maximize the overlap with the most jobs for the brother and minimize the overlap for the mother. Hmm, let's think about how to approach this.
First, let's understand the problem. For each... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: In the decay sequence,\n${ }_{92}^{238} \\mathrm{U} \\stackrel{-\\math... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 195 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each step of the given decay sequence and determine the correct particles/radiation emitted at each step. Let's go through each decay step by step.
1. **First Decay: ${ }_{92}^{238} \mathrm{U} \stackrel{-\mathrm{x}_{1}}{\longrightarrow}{ }_{90}^{234} \mathrm{Th}**
- The a... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 1 | 359 | CodeElo | {
"expected_answer": "",
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"subject": null,
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} | Okay, let's try to figure out this problem. So, the problem is about a permutation p and a string s. The goal is to determine if we can sort the permutation in non-decreasing order using certain operations based on the string s. Also, there are queries that change the string s and we need to check after each query if s... |
[
{
"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 ... | {
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"seed": 0,
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} | 0 | 25 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem step by step. First, I need to understand what's being asked here. The question is about identifying the correct reactant (A) for a given reaction and the correct reactivity sequence (B) of the dienes from the provided options. The reaction in question is between cyclohexene and ... |
[
{
"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"
}
] | {
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} | 0 | 332 | MATH500 | {
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} | To find the minimum value of \((x + y)(y + z)\) given that \(xyz(x + y + z) = 1\) where \(x, y, z\) are positive real numbers, we start by expanding and analyzing the expression.
First, let's expand \((x + y)(y + z)\):
\[
(x + y)(y + z) = xy + xz + y^2 + yz.
\]
We need to express this in a form that allows us to use... |
[
{
"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 | 364 | CodeForces | {
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} | </div>
To solve this problem, we need to determine if it's possible to select four sticks from a given list to form an isosceles trapezoid. If possible, return the four lengths; otherwise, return -1.
### Approach
An isosceles trapezoid has two pairs of equal adjacent sides. The key condition for forming such a trape... |
[
{
"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 | 340 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | Okay, I need to solve this Cosmic Rays problem. Let me read the problem statement carefully.
The problem describes an array that gets modified every second. The modification rule is that any element that is different from the previous one or is the first element will be deleted. Then the remaining elements are concat... |
[
{
"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 ... | {
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} | 0 | 296 | LiveCodeBench | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to determine for each player how many problems they must solve from the ones they haven't yet solved to exceed all other players' current total scores. Let's think through the problem step by step.
First, let's understand the problem. Each player has a certain nu... |
[
{
"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... | {
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"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 conditions and then find the sum of their squares. Let's break down the problem step by step.
### Step 1: Understanding the Conditions
1. **Sum of the items is 30**: The total of all numbers in the list equals 30.
2. **Unique ... |
[
{
"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... | {
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} | 1 | 502 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the sum of digit differences between all pairs of integers in the array nums. Hmm. The digit difference between two numbers is the count of different digits in the same positions. So for example, 13 and 23: the first digit is different (1 vs 2), second is same (3 vs 3?), wait wai... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A positive integer x is called a 321-like Number when it satisfies the following condition.\n\n- The digits of x are s... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 284 | LiveCodeBench | {
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"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to create a Python function that checks if a number is a 321-like number. Let me think about how to approach this.
First, the problem says that a 321-like number has digits that are strictly decreasing from left to right. So each digit is bigger than the next one. For example, 321 is valid because... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 81 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, let's tackle this problem. We need to find the sum of the number of lone pairs on each central atom in the given species. The species are [TeBr6]²⁻, [BrF2]⁺, SNF3, and [XeF3]⁻.
First, I need to determine the Lewis structures for each of these compounds. The central atom's lone pairs will depend on the n... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: List-I shows different radioactive decay processes and List-II provides p... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 474 | JEEBench | {
"expected_answer": "A",
"problem_id": "31",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | <think>
Okay, I need to match each radioactive decay process in List-I with the correct emitted particles in List-II. Let's start by understanding each decay reaction.
First, let's look at each reaction in List-I:
P: ${ }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa}$
This looks like alpha decay. Alpha particle... |
[
{
"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 | 130 | CodeElo | {
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} | <think>
Okay, I need to solve this problem where we have a matrix and we can perform actions to color entire rows or columns. The goal is to handle queries where each query specifies a cell that must be colored a certain way. After each query, we have to find the minimum cost to satisfy all the color restrictions. Let'... |
[
{
"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,
"temperature": 0.7
} | 0 | 25 | CodeElo | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this Cutting Game problem. Let's start by understanding the problem description.
So, the game is played on an a x b grid. There are n chips placed in different cells, and each cell can have at most one chip. The players take turns, with Alice starting. Each move involves cutting some rows... |
[
{
"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... | {
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"seed": 1,
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} | 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. Let's start by analyzing the given information and the problem step by step.
The temperature of the rod is given by:
\[ T(t) = T_0 \left(1 + \beta t^{\frac{1}{4}}\right) \]
The power provided by the... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The correct option(s) regarding the complex $\\left[\\mathrm{Co}(\\mat... | {
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"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 162 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given complex \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3+}\) and determine which of the given statements are correct. Let's break down each part step by step.
### Step 1: Determine the Coordination Geome... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 165 | JEEBench | {
"expected_answer": "6.47",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem. So, we need to find out how much lead (Pb) is produced per kilogram of oxygen (O₂) consumed in this chemical process. The problem involves the oxidation of galena, which is lead sulfide (PbS), and then some reduction happening when the air supply is stopped but heating continues... |
[
{
"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... | {
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"max_new_tokens": 32768,
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} | 0 | 222 | MATH500 | {
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"problem_id": "",
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} | To solve the problem, we need to find the area of triangle \( \triangle CDE \) given that the area of \( \triangle ABC \) is 6 square centimeters, \( \overline{AB} \parallel \overline{DE} \), and \( BD = 4BC \).
First, let's analyze the given information. Since \( \overline{AB} \parallel \overline{DE} \), triangles \(... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 144 | JEEBench | {
"expected_answer": "3748",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, I need to find the number of elements in the union of sets X and Y. Let me start by understanding what these sets look like.
Set X is the first 2018 terms of the arithmetic progression starting at 1 with a common difference of 5. So the nth term of X can be found using the formula for the nth term of an... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 346 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | Okay, let's see. So the problem is about crafting an artifact by converting magical materials. The key operation is spending 1 unit of every other material to gain 1 unit of a chosen material. We need to determine if we can reach the required amounts for all materials.
Hmm. The example given makes me think that the so... |
[
{
"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
} | Okay, I need to solve this Vertex Pairs problem. Let's read through the problem statement carefully.
So, the problem gives a tree with 2n vertices. Each vertex has a value from 1 to n, with each value appearing exactly twice. The cost of a vertex is 2^i where i is its index. We need to find a connected subset of vert... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: toluene is treated with nitric acid and sulfuric acid, forming product 1.\n\n1 is treated with MnO2 and H2SO4, forming product 2.\n\n2 is treated with acetone and aqueou... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 30 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the molecular symmetry group of product 3, let's follow the synthesis step by step and deduce the structure of product 3.
**Step 1: Toluene (C7H8) is treated with nitric acid and sulfuric acid, forming product 1.**
This reaction is likely a nitration. Nitration of toluene typically occurs at the meta pos... |
[
{
"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,
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} | 1 | 106 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement regarding the bonding and Lewis acidity of the given compounds. Let's go through each option step by step.
**Option [A]: \(\mathrm{Al}(\mathrm{CH}_3)_3\) has three-centre two-electron bonds in its dimeric structure.**
First, consider the structure of \(\mathrm{... |
[
{
"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"
}
] | {
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} | 4 | 2 | AMC23 | {
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"subject": null,
"type": null
} | <think>
Okay, so I need to find the degree measure of the acute angle formed by two lines with slopes 2 and 1/3. Hmm, I remember that the formula for the angle between two lines involves their slopes. Let me think... The formula is arctangent of the absolute value of (m1 - m2) divided by (1 + m1*m2). Wait, but wait, do... |
[
{
"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 | 208 | CodeForces | {
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To solve this problem, we need to arrange BBQ buns such that each filling appears at least twice and the distance between any two buns with the same filling is a perfect square. If no valid arrangement exists, we should output -1.
### Key Insight
The problem requires that for any two positions i and j with t... |
[
{
"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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"seed": 9,
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} | 9 | 21 | AIME24 | {
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"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. Since \(|z|=4\), we can write \(z = 4e^{i\theta}\) for some real angle \(\theta\). Then, the expression becomes:
\[
(75+117i)4e^{i\thet... |
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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To solve this problem, we need to determine the minimum amount of time Kevin needs to spend on matches to ensure he wins at least \( k \) matches, for each \( k \) from 0 to \( n \). The matches can be of two types: Type 1 (fixed time cost) and Type 2 (dependent on historical wins).
### Approach
1. **Dynamic Prog... |
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"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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Okay, let's try to solve this problem step by step. We need to find the value of the limit \(\lim_{x \to \alpha^+} f(g(x))\) given the functions \(f(x) = \sin\left(\frac{\pi x}{12}\right)\) and \(g(x) = \frac{2 \log_e(\sqrt{x} - \sqrt{\alpha})}{\log_e(e^{\sqrt{x}} - e^{\sqrt{\alpha}})}\).
First, let's understa... |
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"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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[
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | Okay, let's tackle this problem. The task is to find the smallest number of light bulbs \( n \) such that after performing a series of flips based on divisors, exactly \( k \) bulbs remain on. Hmm. Let's understand the problem first.
So, initially, all bulbs are on. For each \( i \) from 1 to \( n \), we flip all bulb... |
[
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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: 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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Okay, let's see. I need to figure out the correct products for these sigmatropic rearrangements. Let me start by recalling what sigmatropic rearrangements are. Oh right, in these reactions, the terminal pi bond migrates into the sigma bond. So the key is to identify which atoms or groups are part of the pi bond... |
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