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 8 169k |
|---|---|---|---|---|---|---|
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array nums of length n.\nThe distinct difference array of nums is an array diff of length n such that diff[i] is equal to the number ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to generate a distinct difference array based on the given nums array. Let me think about how to approach this.
The problem says that for each index i, the diff[i] is the number of distinct elements in the prefix (elements from 0 to i inclusive) minus the number ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A particle of mass $m$ moves in circular orbits with potential energy ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 243 | JEEBench | {
"expected_answer": "BC",
"problem_id": "7",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given potential energy function and apply the Bohr model to determine the relationships for the radius, speed, and energy of the particle's orbit. Let's proceed step by step.
### Step 1: Understanding the Potential Energy
The potential energy is given by \( V(r) = F r \), ... |
[
{
"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 horizontal rows and W vertical columns. Each cell has a lowercase English letter written on it... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 197 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find a sequence of five cells in a grid that spell "snuke" (s, n, u, k, e) and are contiguous. The grid is given as H rows of strings, each of length W. The cells must form a connected path either vertically, horizontally, or diagonally. Also, the centers of th... |
[
{
"content": "Problem: A regular octagon has the same perimeter as the regular hexagon shown here with side length 16 cm. How long is each side of the octagon? [asy]size(80); pair A = dir(120); pair B=dir(60); pair M=(A+B)/2; draw(dir(360)--B--A--dir(180)--dir(240)--dir(300)--cycle); label(\"16 cm\", M, N);[/a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 40 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to find the side length of a regular octagon that has the same perimeter as a regular hexagon with side length 16 cm. Let's start by recalling the formula for the perimeter of a regular polygon. The perimeter is the number of sides multiplied by the length of each side.
First, the hexagon. It has ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 352 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. The task is to determine if for every pair of vertices in a cycle, there exists a palindrome route. A palindrome route here is a path that allows movement forward or backward along edges, and the color of the edges in the first half must match the colors in the reverse order of the seco... |
[
{
"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: If $I=\\sum_{k=1}^{98} \\int_{k}^{k+1} \\frac{k+1}{x(x+1)} d x$, then\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 119 | JEEBench | {
"expected_answer": "BD",
"problem_id": "50",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve the given problem, we need to evaluate the sum \( I = \sum_{k=1}^{98} \int_{k}^{k+1} \frac{k+1}{x(x+1)} \, dx \) and determine which of the provided inequalities hold.
First, let's simplify the integrand. The integrand is \(\frac{k+1}{x(x+1)}\). We can use partial fraction decomposition to break this down. Le... |
[
{
"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 | 285 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out how to approach this problem. The task is to determine the maximum MEX value that Nikyr can achieve by choosing the order in which he serves the queues. The MEX is the smallest non-negative integer not present in the final counts of customers in each queue.
First, let's understand the pro... |
[
{
"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 n that consists of exactly 3 digits.\nWe call the number n fascinating if, after the following modification, the resulting number cont... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 32 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function to check if a given 3-digit number is fascinating. The problem says that the number is fascinating if when you concatenate it with its double and triple, the result has all digits 1-9 exactly once and no zeros.
Hmm. So first, the function will take n as input.... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s. The score of a string is defined as the sum of the absolute difference between the ASCII values of adjacent characters.\nReturn the s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 486 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to create a Python function that calculates the score of a string. The score is the sum of the absolute differences between adjacent ASCII values. Let's think about how to approach this.
First, the function will take a string s as input. For each character in the string except the last one, I need... |
[
{
"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 contains metal species and LIST-II contains their properties.\nLIS... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 410 | JEEBench | {
"expected_answer": "A",
"problem_id": "53",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, I need to match each metal species in LIST-I with their corresponding properties in LIST-II. Let me start by understanding what each species is and what properties they would have.
First, looking at the metal species in LIST-I:
I. \([ \text{Cr}(\text{CN})_6 ]^{4-}\)
II. \([ \text{RuCl}_6 ]^{2-}\)
III. \... |
[
{
"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 | 116 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to count the number of integers \( y \) (where \( 1 \leq y \leq m \)) such that \( x \neq y \) and the bitwise XOR of \( x \) and \( y \) (i.e., \( x \oplus y \)) is a divisor of either \( x \), \( y \), or both.
### Approach
1. **Understanding XOR and Divisors**: The XOR operation betw... |
[
{
"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 value of\n\\[\n\\sec ^{-1}\\left(\\frac{1}{4} \\su... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 241 | JEEBench | {
"expected_answer": "0",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. We need to find the value of the given expression and then round it to the second decimal digit. The expression is the inverse secant of a sum involving secants. Hmm, first, let's break down the components.
The main part is the sum inside the sec^{-1} function. The... |
[
{
"content": "Problem: Suppose $a$ and $b$ are different prime numbers greater than 2. How many whole-number divisors are there for the integer $a(2a+b)-2a^{2}+ab$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 280 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we first need to simplify the given expression and then determine its divisors. The expression is \(a(2a + b) - 2a^2 + ab\).
Let's start by expanding and simplifying the expression step by step.
First, expand \(a(2a + b)\):
\[
a(2a + b) = 2a^2 + ab
\]
Now substitute this back into the original ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let\n\\[\n\\begin{aligned}\n& P_{1}=I=\\left[\\begin{array}{lll}\n1 & ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 232 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given matrices and the expression for \(X\). Let's start by understanding the structure of the matrices \(P_k\) and how they transform the matrix \(A = \left[\begin{array}{lll}2 & 1 & 3 \\1 & 0 & 2 \\3 & 2 & 1\end{array}\right]\) when multiplied by \(P_k\) and \(P_k^T\).
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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 93 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to swap the first characters of two strings a and b. Let's see. The problem says that for each test case, given two strings a and b of length 3, swap their first characters. Then output the new strings. And do this for all test cases.
First, let me understand the... |
[
{
"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 kind of angle is formed where two perpendicular lines meet?\nOptions: A. reflex, B. complementary, C. supplementary, D. zero, E. right, F. invis... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 459 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so the question is about what kind of angle is formed where two perpendicular lines meet. Let me think. Perpendicular lines, right, they intersect each other at a certain angle. I remember from geometry that when two lines are perpendicular, the angle between them is a right angle. That's 90 degrees. So 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 0-indexed integer array batteryPercentages having length n, denoting the battery percentages of n 0-indexed devices.\nYour task is to test each... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 143 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to create a Python function that solves this problem. The problem is about testing devices based on their battery percentages. The key points are:
So the function will take the batteryPercentages array as input and return the number of tested devices. The testing process goes through ea... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S consisting of A, B, and C. S is guaranteed to contain all of A, B, and C.\nIf the characters ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 244 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have a string S made up of A, B, and C. The task is to find out how many characters I need to check from the left until all three characters have appeared at least once. The catch is to find the first time all three are found when checking up to that position. Let me t... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a 0-indexed string s, repeatedly perform the following operation any number of times:\n\nChoose an index i in the string, and let c be the character in p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 33 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to minimize the length of a string by repeatedly deleting the closest occurrences of a character to the left and right of a chosen index. Hmm. The examples show that after some operations, the string becomes such that no such deletions can be made anymore. The minimized length is... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 197 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. The task is to determine the maximum possible size of a deck after buying up to k new cards and partitioning all the cards (original plus bought) into decks of equal size, with no two cards of the same value in a deck.
First, I need to understand the constraints and the optimal strateg... |
[
{
"content": "Problem: Let $\\mathcal{B}$ be the set of rectangular boxes with surface area $54$ and volume $23$ . Let $r$ be the radius of the smallest sphere that can contain each of the rectangular boxes that are elements of $\\mathcal{B}$ . The value of $r^2$ can be written as $\\frac{p}{q}$ , wh... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 29 | AIME24 | {
"expected_answer": "721",
"problem_id": "aime24-29",
"reference_solution": "Observe that the \"worst\" possible box is one of the maximum possible length. \nBy symmetry, the height and the width are the same in this antioptimal box. (If the height and width weren't the same, the extra difference between them co... | To solve this problem, we need to determine the smallest sphere that can contain all rectangular boxes in the set \(\mathcal{B}\), which have a surface area of 54 and a volume of 23. The radius squared of this sphere, \(r^2\), should be expressed as \(\frac{p}{q}\) in simplest form, and we need to find \(p + q\).
### ... |
[
{
"content": "Problem: When $n$ standard six-sided dice are rolled, the product of the numbers rolled can be any of $936$ possible values. What is $n$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 31 | AMC23 | {
"expected_answer": "11",
"problem_id": "40",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the number of standard six-sided dice \( n \) such that the product of the numbers rolled can be any of 936 possible values.
First, let's analyze the possible outcomes. Each die has faces with numbers 1 through 6. The product of the numbers rolled will be the product of \( n... |
[
{
"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 number of 5 digit numbers which are divisible by 4... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 143 | JEEBench | {
"expected_answer": "625",
"problem_id": "44",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, I need to find the number of 5-digit numbers divisible by 4, using digits from the set {1,2,3,4,5} with repetition allowed. Let's think about how to approach this.
First, a number is divisible by 4 if its last two digits form a number that's divisible by 4. So the key here is to look at the last two digi... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Michael reaction is a chemical process in organic chemistry where a nucleophile adds to a molecule containing a specific carbon-carbon double bond (C=C) adjacent to ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 18 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to figure out the correct products for these two Michael reactions. Let's start by recalling how the Michael reaction works. The nucleophile adds to the carbon adjacent to the carbonyl group, which is the beta position. The nucleophile in the first reaction is NaOEt (ethoxide) in THF. The 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 226 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out how to approach this problem. So, the problem is about a gorilla who needs to take an exam. The task is to make an array empty by performing operations, and we can modify some elements up to k times. We need to minimize the number of distinct elements in the array after all modifications.
... |
[
{
"content": "Problem: Simplify\n\\[\\cos \\left( \\frac{2 \\pi}{15} \\right) \\cos \\left (\\frac {4 \\pi}{15} \\right) \\cos \\left( \\frac{8 \\pi}{15} \\right) \\cos \\left( \\frac {16 \\pi}{15} \\right).\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 351 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To simplify the given product of cosines, we can use properties of complex numbers and roots of unity. Let's start by considering the complex exponential form of cosine. Recall that \(\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}\). However, another approach involves using the fact that the cosine function at spec... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A disk of radius $\\mathrm{R}$ with uniform positive charge density $\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 435 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "30",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the motion of a charged particle under the influence of both the Coulomb potential and an external vertical force. Let's break down the problem step by step.
### Step 1: Understanding the Forces
The particle is subject to two forces:
1. **Coulomb Force**: The electric field du... |
[
{
"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 non-negative integer k. There exists a staircase with an infinite number of stairs, with the lowest stair numbered 0.\nAlice has an integer jum... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 503 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Alice has to reach stair k using certain operations. Let's think about the possible moves she can make.
So, the problem says that from stair i, Alice can either go down to i-1 (but not consecutively or from 0) or go up to i + 2^jump, which increases the jump by 1 each ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Astronomers are studying two binary star systems: system_1 and system_2. Observations reveal that both systems exhibit eclipses with periods of 2 years and 1 year, respe... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 163 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{D} |
[
{
"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 $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be given by $f(x)=(x-1)(... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 236 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the function \( F(x) = \int_0^x f(t) \, dt \) where \( f(x) = (x-1)(x-2)(x-5) \). We need to determine the correct options regarding the critical points and the behavior of \( F(x) \).
### Step 1: Find the critical points of \( F(x) \)
The critical points of \( F(x) \) occur w... |
[
{
"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: Highly excited states for hydrogen-like atoms (also called Rydberg sta... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 2 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "6",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the properties of highly excited states (Rydberg states) for hydrogen-like atoms. These states are characterized by a principal quantum number \( n \gg 1 \). Let's consider the given statements one by one.
### Statement (A): Relative change in the radii of two consecutive orbi... |
[
{
"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 are N roulette wheels.\nThe i-th (1\\leq i\\leq N) wheel has P _ i integers S _ {i,1},S _ {i,2},\\ldots,S _ {i,P... | {
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} | 2 | 262 | LiveCodeBench | {
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} | <think>
Okay, I need to solve this problem where Takahashi wants to minimize the expected amount of money he spends to earn at least M points. The problem has N roulette wheels, each with a set of possible points and a cost to play. The key is to find the optimal strategy and compute the expected cost.
First, let me u... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | Okay, I need to solve this problem where flowers in a row lose height over time due to wind. The goal is to find out how many seconds it takes until all flowers are gone (height 0). Let's think about the process.
First, let's understand the problem. Each second, the wind blows from the left. For each flower from left ... |
[
{
"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: Two possible metabolic fates of \\alpha-D-glucose are given below. Compare the standard free energy changes at 25°C for these processes. Which proces... | {
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"seed": 0,
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} | 0 | 153 | MMLUPro | {
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Okay, I need to determine which of the two metabolic processes is more efficient for utilizing alpha-D-glucose. The problem gives me the standard free energy changes (ΔG°) for each reaction. Let me recall that a more negative ΔG° means the reaction is more spontaneous and efficient.
First, let's look at react... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 183 | CodeElo | {
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} | <think>
Okay, let's try to figure out how to approach this problem. So the task is to place n chips into x points (numbered 1 to x) and then perform operations to minimize the number of chips, with the cost being that minimum number. We need to count the number of initial placements that result in a cost of m, modulo 9... |
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{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed sorted array of integers nums.\nYou can perform the following operation any number of times:\n\nChoose two indices, i and j, where i ... | {
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} | 0 | 104 | LiveCodeBench | {
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"subject": null,
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} | <think>
Okay, I need to solve this problem where we have a sorted array and we can perform an operation any number of times. The operation is to choose two indices i and j (i < j) where nums[i] < nums[j], then remove those elements. The goal is to find the minimum possible length of the array after performing these ope... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Which of the following statement(s) is(are) correct about the spectrum... | {
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"seed": 1,
"temperature": 0.7
} | 1 | 316 | JEEBench | {
"expected_answer": "AD",
"problem_id": "14",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement regarding the spectrum of the hydrogen atom. Let's go through each option step by step.
**Option (A): The ratio of the longest wavelength to the shortest wavelength in Balmer series is \(9/5\).**
The Balmer series corresponds to transitions ending at the \(n=2\... |
[
{
"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 physical theories never requires regularization at high energies?\nOptions: A) Quantum Electrodynamics, B) Classical Electrodynamics, C) Quantum C... | {
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} | 0 | 57 | GPQADiamond | {
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} | <think>
Okay, so I need to figure out which of these physical theories doesn't require regularization at high energies. Let me start by recalling what regularization is. From what I remember, in quantum field theories, especially when dealing with high energies or short distances, there are divergences in calculations.... |
[
{
"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 \"strictly binary tree\" is a binary tree in which every node that is not a leaf has two children. Suppose that for a class of strictly binary tree... | {
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} | 0 | 26 | MMLUPro | {
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} | <think>
Okay, let's try to figure out this problem. So, we have a strictly binary tree, which means every non-leaf node has exactly two children. The problem mentions that for any tree in the class, the ratio of the lengths of any two root-to-leaf paths is bounded above by some constant c. We need to determine how the ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 140 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Triangle Formation problem. Let's see what the problem is asking. So, given a list of sticks numbered from 1 to n, each with a length, we have to answer q queries. Each query gives a range [l, r] (where r - l + 1 >=6) and we need to determine if we can choose 6 distinct sticks from th... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Two planets have been detected orbiting a star using both the transit and radial velocity (RV) methods. The star has a mass of 1.5 times that of the Sun, a radius 1.2 ti... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 84 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | \boxed{C} |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 204 | CodeElo | {
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"subject": null,
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} | <think>
Okay, I need to solve this problem where we have a cyclic array and we can perform operations to make all elements equal. The operation is to delete one of two adjacent elements where the previous is not greater than the next. The goal is to find the minimum number of operations needed.
First, let me understan... |
[
{
"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 | 349 | CodeForces | {
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"subject": null,
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} | To solve this problem, we need to determine the minimum number of moves required to ensure each of the \( n \) haystacks is emptied at least once, given their initial haybale counts and height limits after being emptied. If it's impossible, we should return -1. The key insight is to model the problem using graph theory... |
[
{
"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 | 166 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this bouquet problem where the girl wants to maximize the number of petals in her bouquet given the constraints. Let me read through the problem again to make sure I understand everything.
So, the problem says that the girl can choose flowers from n different types. Each type has a certai... |
[
{
"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: The reaction of $\\mathrm{Xe}$ and $\\mathrm{O}_{2} \\mathrm{~F}_{2}$ gives a Xe compound $\\mathbf{P}$. What ... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 440 | JEEBench | {
"expected_answer": "4",
"problem_id": "40",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, let's see. The problem is about a reaction between xenon (Xe) and oxygen difluoride (O₂F₂) that produces a compound P. Then, when 1 mole of P is completely hydrolyzed, we need to find out how many moles of HF are produced. Hmm.
First, I need to figure out what the reaction between Xe and O₂F₂ is. Let me ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: acetic acid is treated with bromine, pyridine, and acetic anhydride with heating, forming product 1.\n\n1 is heated with ethanol and a small amount of sulfuric acid, for... | {
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} | \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: What is the energy of the Relativistic Heavy Ion Collider (RHIC) so that the speed of the nucleus X is equal to 0.96c?\n\nKnowing that X is defined as Li with 3 neutrons... | {
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"seed": 2,
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} | \boxed{A} |
[
{
"content": "Problem: Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and\n \\[a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 10 | AIME24 | {
"expected_answer": "601",
"problem_id": "aime24-10",
"reference_solution": "$ab(a+b)+bc(b+c)+ac(a+c)=300(ab+bc+ac)-3abc=6000000, 100(ab+bc+ac)-abc=2000000$ Note that \n $(100-a)(100-b)(100-c)=1000000-10000(a+b+c)+100(ab+bc+ac)-abc=0$ . Thus, $a/b/c=100$ . There are $201$ cases for each but we need to subtrac... | To solve the problem of finding the number of triples of nonnegative integers \((a, b, c)\) that satisfy \(a + b + c = 300\) and \(a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000\), we start by analyzing the given equations.
First, observe that the second equation can be rewritten using symmetry. Notice that 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: The correct statement(s) regarding the binary transition metal carbony... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 129 | JEEBench | {
"expected_answer": "BC",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate the given statements about binary transition metal carbonyl compounds, specifically focusing on iron (Fe) and nickel (Ni) compounds. Let's analyze each statement step by step.
### Statement (A): Total number of valence shell electrons at the metal center in \(\mathrm{Fe}(\mat... |
[
{
"content": "Problem: Louis and Jack are sharing a pie. Louis eats $\\frac{1}{5}$ of the pie, and Jack eats $\\frac{2}{3}$ of the pie. How much of the pie do Louis and Jack eat altogether?\nMark your solution with \\boxed\nAnswer:",
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] | {
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} | <think>
Okay, let's see. Louis and Jack are sharing a pie. Louis eats 1/5 of it, and Jack eats 2/3. I need to find out how much they eat altogether. Hmm, right, I should add those two fractions together. But wait, adding fractions requires a common denominator, right?
So, the denominators here are 5 and 3. The least c... |
[
{
"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 $\\mathrm{Pb}\\left(\\mathrm{NO}_{3}\\right)_{2}$ and $\\... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 449 | JEEBench | {
"expected_answer": "C",
"problem_id": "53",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's tackle this problem step by step. So, the reaction between lead(II) nitrate and sodium chloride in water produces a precipitate, and when hydrochloric acid is added, the precipitate dissolves. We need to figure out which complex ion is formed that leads to the dissolution.
First, I remember that wh... |
[
{
"content": "Problem: What is the probability that a randomly selected integer in the set $$\\{1,2,3,\\ldots,100\\}$$ is divisible by 2 and not divisible by 3? Express your answer as a common fraction.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
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] | {
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"seed": 0,
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} | 0 | 162 | MATH500 | {
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Okay, I need to find the probability that a randomly selected integer from the set {1,2,3,...,100} is divisible by 2 and not divisible by 3. Let's break this down step by step.
First, I know that probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. The... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 426 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where we have a rectangular parallelepiped made of unit cubes of different colors, and we can perform cyclic shifts in any of the three directions. The goal is to count how many different parallelepipeds can be formed such that no two are equal after any combination of cyclic ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi is growing a plant. Its height at the time of germination is 0\\,\\mathrm{cm}. Considering the day of germin... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 448 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's see. The problem is about finding the first day when the plant's height is strictly greater than Takahashi's height. Hmm. So the plant grows every night by 2^i cm on day i. So the height after each day's night is the sum of 2^0 + 2^1 + ... + 2^i. Oh right, that's a geometric series. The sum up to da... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi participated in N contests and earned a performance P_i in the i-th contest.\nHe wants to choose some (at le... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 320 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Takahashi wants to maximize his rating by choosing some contests. Let's see what the problem says.
So the rating is calculated as R. The formula is (sum of (0.9)^(k-i) * Q_i) divided by the sum of (0.9)^(k-i) for all chosen contests, minus 1200 divided by the square roo... |
[
{
"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 batteryPercentages having length n, denoting the battery percentages of n 0-indexed devices.\nYour task is to test each... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 143 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to create a Python function based on the given problem. Let's read through the problem again to make sure I understand it correctly.
The task is to test devices in order from 0 to n-1. For each device i, if the battery percentage is greater than 0, we increment the count of tested devices. Then, f... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal{P}$ we took crosses one of th... | To solve this problem, we need to determine the difference between the radii of the inner and outer circles formed by the tangent points when a torus \( T \) with radius 3 is internally and externally tangent to a sphere \( S \) with radius 11. The result should be expressed as a fraction \(\frac{m}{n}\) in simplest fo... |
[
{
"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: Reaction of $\\mathbf{x} \\mathrm{g}$ of $\\mathrm{Sn}$ with $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 356 | JEEBench | {
"expected_answer": "1.23",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <begiinhide>
Okay, let's try to solve this problem step by step. So, the problem is about a chemical reaction where tin (Sn) reacts with HCl to form a salt, and then that salt reacts with nitrobenzene (with some HCl) to produce another salt. We need to find the value of y, which is the mass of nitrobenzene used.
Firs... |
[
{
"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 string s that consists of digits from 0 to 9.\nA string t is called a semi-repetitive if there is at most one consecutive pair of the... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 20 | 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 length of the longest semi-repetitive substring in a given string s. Let's think about what a semi-repetitive string is. From the examples, it looks like a semi-repetitive string can have at most one pair of consecutive same digits. So, if there are tw... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: What is the index of hydrogen deficiency of the product obtained when 2-formyl-5-vinylcyclohex-3-enecarboxylic acid is reacted with red phosphorus and excess of HI?\nOpt... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 182 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | \boxed{C} |
[
{
"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: In a triangle $A B C$, let $A B=\\sqrt{23}, B C=3$ and $C A=4$. Then what is the value of\n\\[\n\\frac{\\cot A... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 341 | JEEBench | {
"expected_answer": "2",
"problem_id": "54",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, let's see. I need to find the value of (cot A + cot C) / cot B in triangle ABC where the sides are AB = √23, BC = 3, and CA = 4. Hmm. I remember that cotangent is related to the sides of the triangle. Oh right, the cotangent of an angle in a triangle can be expressed using the sides. Let me think.
The fo... |
[
{
"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 | 438 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for a given integer n, I have to find the number of ordered pairs (a, b) of positive integers such that a = n - b. Hmm, let's think.
Wait, since a and b are positive integers, then both a and b must be greater than zero. So for a = n - b, how many possible pairs are 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,
"seed": 0,
"temperature": 0.7
} | 0 | 241 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Alice and Bob are in different rooms, and we have to lock doors between rooms so that they can't reach each other. The goal is to find the minimum number of doors to lock for each test case.
First, let me understand the problem better. The rooms are arranged in a row fr... |
[
{
"content": "Problem: Points $A$ and $B$ lie on the graph of $y=\\log_{2}x$. The midpoint of $\\overline{AB}$ is $(6, 2)$. What is the positive difference between the $x$-coordinates of $A$ and $B$? The final answer can be written in the form $m \\sqrt{n}$, where $m$ and $n$ are relatively prime positive integ... | {
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} | 0 | 19 | AMC23 | {
"expected_answer": "9",
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} | To solve this problem, we start by letting the coordinates of points \(A\) and \(B\) be \((x_1, y_1)\) and \((x_2, y_2)\) respectively. Since both points lie on the graph of \(y = \log_2 x\), their coordinates must satisfy this equation. Therefore, we have:
\[
y_1 = \log_2 x_1 \quad \text{and} \quad y_2 = \log_2 x_2
\]... |
[
{
"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... | {
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} | 0 | 245 | CodeElo | {
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} | <think>
Okay, I need to solve this problem where Iris builds a tree by adding vertices and edges, and for each step, I have to determine the binary depth. The binary depth is the minimum d such that the tree can be turned into a full binary tree of depth d by adding some edges. If it's impossible, it's -1.
First, let'... |
[
{
"content": "Problem: Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\overline{IA}\\perp\\overline{OI}$ , circumradius $13$ , and inradius $6$ . Find $AB\\cdot AC$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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"seed": 2,
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} | 2 | 9 | AIME24 | {
"expected_answer": "468",
"problem_id": "aime24-9",
"reference_solution": "By Euler's formula $OI^{2}=R(R-2r)$ , we have $OI^{2}=13(13-12)=13$ . Thus, by the Pythagorean theorem, $AI^{2}=13^{2}-13=156$ . Let $AI\\cap(ABC)=M$ ; notice $\\triangle AOM$ is isosceles and $\\overline{OI}\\perp\\overline{AM}$ ... | To solve for \( AB \cdot AC \) in the given triangle \( \triangle ABC \) with circumcenter \( O \), incenter \( I \), and the condition \( \overline{IA} \perp \overline{OI} \), we can use properties of the triangle's circles and some algebraic manipulations.
First, recall that the circumcenter \( O \) is the center of... |
[
{
"content": "Problem: If $\\log_6 (x-y) + \\log_6 (x+y) = 2$ and $\\log_y 5x = 2$, then find $x$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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} | 0 | 464 | MATH500 | {
"expected_answer": "",
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} | To solve the given problem, we start by analyzing the equations provided:
1. \(\log_6 (x-y) + \log_6 (x+y) = 2\)
2. \(\log_y 5x = 2\)
First, let's simplify the first equation. Using the properties of logarithms, specifically the sum of logarithms property, we can combine the two logarithms into a single logarithm:
\... |
[
{
"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 | 58 | CodeForces | {
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} | <think>
Okay, I need to solve this problem where Simurgh's warriors each have a time segment they're on watch, and I have to assign colors to them such that at any time where multiple are on watch, there's at least one unique color. The goal is to find the minimum number of colors needed and the assignment.
Hmm, let's... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"seed": 1,
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} | 1 | 159 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Okay, let's tackle this problem. The task is to help the Sheriff of Nottingham defend against Robin Hood's attack by strategically strengthening camps to maximize the remaining gold. Hmm, let's think about how to approach this.
First, the problem states that each camp can be strengthened by taking gold from its neighb... |
[
{
"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 $\\alpha, \\beta$ and $\\gamma$ be real numbers such that ... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 330 | JEEBench | {
"expected_answer": "1.00",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. We need to find the value of \( |\mathrm{M}| \), the determinant of matrix \( M \). First, let me recall that the system of linear equations is consistent, which means the determinant of the coefficient matrix must be zero. The coefficient matrix here is:
\[
A = \b... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A eukaryotic cell evolved a mechanism to turn macromolecular building blocks into energy. The process occurs in mitochondria, which are cellular energy factories. In the... | {
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} | <think>
Okay, let's see. The problem is about figuring out which experiment won't help discover the mitochondrial role of a new anti-diabetes drug. The drug is tested on HEK293 cell lines. The options are transformation with recombinant luciferase and measuring light after adding luciferin, flow cytometry with a specif... |
[
{
"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 cis $\\mathrm{N}-\\mathrm{Mn}-\\ma... | {
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} | 0 | 228 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. We need to determine the total number of cis N-Mn-Cl bond angles in the cis-[Mn(en)₂Cl₂] complex. Hmm, first, I need to visualize the structure of this complex.
The complex has a Mn(II) ion at the center. The ligands are two ethylenediamine (en) molecules and two c... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 0 | 16 | CodeForces | {
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"problem_id": "",
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} | <think>
Okay, I need to solve this problem where I have to find a permutation q that minimizes the number of pairs (i,j) such that the sum from p_i to p_j equals the sum from q_i to q_j. Hmm. Let's think.
First, let's understand the problem better. The problem is about minimizing the number of equal sum subarrays betw... |
[
{
"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 string s having an even length n.\nYou are also given a 0-indexed 2D integer array, queries, where queries[i] = [a_i, b_i, c_i, d_i].... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 134 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about checking if we can make the string a palindrome by rearranging certain substrings. The catch is that the string is split into two parts, the first half and the second half, and each query allows rearranging a substring in the first half and another in the second half. 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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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 79 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Alice, Bob, and Charlie have to share a cake without any conflict. Each of them values different pieces, and the goal is to give each a contiguous slice of the cake such that each gets at least a certain minimum value. Let's think about how to approach this.
First, 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 | 23 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out this problem. So, Alice and Bob are playing a game with a list of booleans. They take turns adding 'and' or 'or' operators between the booleans, with Alice going first. The goal is to determine if Alice can make the final expression evaluate to true, assuming both play optimally.
Hmm. 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 309 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's see. The problem is about maximizing the Fibonacciness of an array by choosing the value of a3. The array is a1, a2, a3, a4, a5. The Fibonacciness is the number of indices i (from 1 to 3) where a[i+2] equals the sum of a[i] and a[i+1]. So we need to set a3 such that as many of the first three positions (i=1... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 47 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Narek and ChatGPT are scoring points based on some strings. Let me read through the problem again to make sure I understand everything.
So, the problem states that Narek is creating problems by selecting some of the n strings (each of length m) and concatenating them. T... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Calculate the enthalpy of formation of (CH3)2C=CH-CH2-CH(CH3)-CH2-CH=C(CH3)2. Given,\nEnthalpy of atomization of carbon = 1000 kJ/mol.\nBond energy of H-H = 100 kJ/mol\n... | {
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} | 0 | 91 | GPQADiamond | {
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"problem_id": "",
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"type": null
} | <think>
Okay, I need to calculate the enthalpy of formation for the given hydrocarbon. The structure is (CH3)2C=CH-CH2-CH(CH3)-CH2-CH=C(CH3)2. Let me start by figuring out the formula of the compound to determine the number of each type of bond.
First, let's break down the structure step by step. The main chain seems ... |
[
{
"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 | 433 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where Eralim, the mafia boss, is having a tournament with his n fighters. Each battle eliminates one fighter and reduces the rating of the other. The goal is to find the maximum possible rating of the last remaining fighter if they choose the battles optimally.
Hmm, let's think. So e... |
[
{
"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 are N buildings aligned in a row. The i-th building from the left has a height of H_i.\nDetermine if there is a ... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 444 | LiveCodeBench | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that solves this problem. Let's see what the problem is. So, there are N buildings in a row, each with a certain height. The first building is the leftmost. We need to find if any building to the right of it is taller. If there is such a building, we need to find the left... |
[
{
"content": "Problem: Let \\(b\\ge 2\\) be an integer. Call a positive integer \\(n\\) \\(b\\text-\\textit{eautiful}\\) if it has exactly two digits when expressed in base \\(b\\) and these two digits sum to \\(\\sqrt n\\). For example, \\(81\\) is \\(13\\text-\\textit{eautiful}\\) because \\(81 = \\underlin... | {
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"seed": 0,
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} | 0 | 13 | AIME24 | {
"expected_answer": "211",
"problem_id": "aime24-13",
"reference_solution": "We write the base- $b$ two-digit integer as $\\left( xy \\right)_b$ .\nThus, this number satisfies\n \\[ \\left( x + y \\right)^2 = b x + y \\] \nwith $x \\in \\left\\{ 1, 2, \\cdots , b-1 \\right\\}$ and $y \\in \\left\\{ 0, 1, \\... | To solve this problem, we need to find the smallest integer \( b \ge 2 \) such that there are more than ten \( b \)-beautiful numbers. A \( b \)-beautiful number \( n \) has exactly two digits in base \( b \), and the sum of these digits equals \( \sqrt{n} \).
### Step-by-Step Solution:
1. **Understanding the Problem... |
[
{
"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 | 273 | CodeElo | {
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} | <think>
Okay, I need to solve this problem where Little John's milk satisfaction days are being tracked. Let me think about the problem again. So, each day he gets certain pints of milk, and he can only drink up to m pints a day. But he always drinks the freshest milk first. The milk's freshness lasts for k days. So, i... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Consider a thin square plate floating on a viscous liquid in a large t... | {
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"seed": 0,
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} | 0 | 151 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "2",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the forces acting on the floating plate and the stresses involved when it's pulled horizontally. Let's break down each statement step by step.
### Step 1: Understanding the Setup
- A thin square plate is floating on a viscous liquid in a large tank.
- The liquid's height \( h ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a 0-indexed 2D integer matrix grid of size n * m, we define a 0-indexed 2D matrix p of size n * m as the product matrix of grid if the following conditio... | {
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} | 1 | 94 | LiveCodeBench | {
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} | <think>
Okay, I need to solve this problem where I have to generate a product matrix based on the given grid. Each element in the product matrix p[i][j] is the product of all elements in the grid except grid[i][j], and then take that product modulo 12345. Hmm, let's think about how to approach this.
First, the example... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Imagine an operator $\\vec{P}$ of a system have components $P_x, P_y$ and $P_z$. The matrix form of the operator $P_x$ has components in the first row as $(0, \\hbar/\\... | {
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} | 1 | 154 | GPQADiamond | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the uncertainty ΔP_z for the P_z operator. The uncertainty is given by the formula ΔP_z = sqrt<⟨P_z²⟩ - ⟨P_z⟩²>. Hmm, so first I need to calculate the expected value of P_z squared and the square of the expected value of P_z.
Wait, the state vector given is |ψ⟩ = (-1/2, 1/√2, -1... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 252 | CodeElo | {
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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 count the number of brilliant subarrays in an array. A brilliant subarray is one that can be turned into a consecutive set through the given operations. Let me think about how to approach this.
First, let's understand the problem better. The operations allow u... |
[
{
"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 voltage will be induced in a wire loop when the magnetic field within that loop\nOptions: A. is amplified, B. converts to magnetic energy, C. is pa... | {
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} | 0 | 498 | MMLUPro | {
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} | <think>
Okay, I need to figure out which option is correct regarding when a voltage is induced in a wire loop due to a changing magnetic field. Let's think about Faraday's law of induction. Faraday's law states that the induced electromotive force (EMF) in any closed loop is directly proportional to the rate of change ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 384 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this Peak Productivity Forces problem. Let me read through the description carefully.
So the problem is about transforming permutation a into permutation b using a specific operation. The operation allows us to cyclically shift parts of the permutation. The steps are: choose an index i, then shi... |
[
{
"content": "Problem: Triangle $ABC$ has side lengths in arithmetic progression, and the smallest side has length $6.$ If the triangle has an angle of $120^\\circ,$ Find the area of $ABC$. The final answer can be simplified in the form $m \\sqrt{n}$, where $m$ and $n$ are positive integers and $n$ without squa... | {
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"max_new_tokens": 32768,
"seed": 7,
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} | 7 | 29 | AMC23 | {
"expected_answer": "18",
"problem_id": "33",
"reference_solution": "",
"subject": null,
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} | To solve this problem, we start by noting that the sides of triangle \(ABC\) are in arithmetic progression. Let the sides be \(a\), \(a+d\), and \(a+2d\) where \(a\) is the smallest side. Given that the smallest side is 6, we have \(a = 6\). Thus, the sides are \(6\), \(6+d\), and \(6+2d\).
We also know that the trian... |
[
{
"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 | 94 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to compute the sum of f(i^k, d) for i from 1 to n, modulo 1e9+7. Let me first understand the problem.
The problem defines a divisor tree T_{n,d}. The root is n. For each layer, each node has children which are all possible distinct divisors of the node's value. The leave... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 303 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Stalin Sort problem. Let's read the problem carefully. The task is to determine the minimum number of integers that must be removed from an array to make it vulnerable. An array is vulnerable if you can sort it in non-increasing order by repeatedly applying Stalin Sort to any of its s... |
[
{
"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: Each of the following options contains a set of four molecules. Identi... | {
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"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 194 | JEEBench | {
"expected_answer": "BD",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine which options contain molecules with permanent dipole moments at room temperature, we need to analyze each molecule's structure and bonding. A permanent dipole moment occurs when there's an uneven distribution of electrons due to differences in electronegativity between atoms in the molecule, and the molec... |
[
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"content": "Problem: There are an infinite number of vectors $\\mathbf{v}$ such that\n\\[\\begin{pmatrix} 1 \\\\ 2 \\\\ -5 \\end{pmatrix} \\times \\mathbf{v} = \\begin{pmatrix} 90 \\\\ 30 \\\\ 30 \\end{pmatrix}.\\]Find the vector $\\mathbf{v}$ that has the smallest magnitude.\nMark your solution with \\boxed\... | {
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Okay, I need to find a vector \(\mathbf{v}\) such that when it's crossed with \(\begin{pmatrix}1 \\ 2 \\ -5\end{pmatrix}\), the result is \(\begin{pmatrix}90 \\ 30 \\ 30\end{pmatrix}\), and among all possible vectors \(\mathbf{v}\), I need the one with the smallest magnitude. Hmm, how do I approach this?
First... |
[
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Okay, I need to solve this problem where I have to pick 8 elements from a list to form four points of a rectangle with maximum area. Let's think about how to approach this.
First, the rectangle's sides are parallel to the coordinate axes. So, the four points will have coordinates where x's and y's are paired. ... |
[
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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: What is the total number of isomers, considering both structur... | {
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Okay, so 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 breaking down what this problem is asking.
First, I remember that cyclic ethers are ethers where the oxygen atom is part of a ring structure. Th... |
[
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} | Okay, I need to solve this permutation problem where for each pair of indices i and j (i < j), I have to check if the product of the elements pi and pj is divisible by the product of i and j. The goal is to count all such valid pairs.
Hmm, the problem statement mentions that the permutation p is given, and for each pa... |
[
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} | To solve this problem, we need to determine the number of different deterministic max-heaps that can be formed by applying exactly \( k \) operations (additions) to a perfect binary tree of size \( 2^n - 1 \). The solution must consider the constraints and properties of deterministic max-heaps and compute the result mo... |
[
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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 maximum possible value of the final element in the array after performing a series of operations where each operation involves merging two elements and appending their floored average to the array. The key insight is to recognize that the optimal strategy is to s... |
[
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"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... | {
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} | <think>
Okay, I need to solve this problem where Takahashi has to move from the start point to the goal point on a grid, using medicines to increase his energy. The challenge is to determine if he can reach the goal given the constraints. Let's break down the problem and figure out how to approach writing the Python fu... |
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