context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 1 123k |
|---|---|---|---|---|---|---|
[
{
"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 | 323 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the maximum number of cards Monocarp can take from the deck given the rules. Let me try to break down the problem step by step.
First, let's understand the problem again. We have a deck of n cards, each with a number from 1 to 10^9. The game starts with Monocarp taking any card on... |
[
{
"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: Does the principle of comparative advantage apply only to international trade?\nOptions: A. No, it is a principle that applies only to consumer choic... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 91 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | The principle of comparative advantage is a fundamental concept in economics that applies to any situation where individuals, businesses, or nations specialize in the production of goods or services in which they have a relative efficiency compared to others. It was first introduced by David Ricardo in 1817 and is prim... |
[
{
"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 | 440 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let's tackle this problem. So, we have a classroom with two rows, each having m seats. There are a + b + c monkeys in total, where a prefer the first row, b prefer the second row, and c have no preference. The goal is to maximize the number of monkeys seated, considering their preferences and the seat ... |
[
{
"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: Sunlight of intensity $1.3 \\mathrm{~kW} \\mathrm{~m}^{-2}$ is... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 127 | JEEBench | {
"expected_answer": "130",
"problem_id": "13",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I need to find the average intensity of light at a distance of 22 cm from a convex lens. The given data is: the incident sunlight has an intensity of 1.3 kW/m², the lens has a focal length of 20 cm, and the lens aperture is much smaller than the focal length. Also, we can ignore energy loss due to the ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Researchers are attempting to detect transits of two Earth-like planets: Planet_1 and Planet_2. They have limited observing time and want to observe the one that has the... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 14 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which planet, Planet_1 or Planet_2, has a higher probability of transiting based on the given information. Let me start by recalling what affects the probability of a planet transiting its star. From what I remember, the probability of a planet transiting depends mainly on the plan... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: 3,3,6-trimethylhepta-1,5-dien-4-one is treated with 1 equivalent of meta-chloroperbenzoic acid. Two different products are formed, in approximately a 1:1 ratio.\n\nIn a ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 94 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem step by step. So, the first part involves treating 3,3,6-trimethylhepta-1,5-dien-4-one with 1 equivalent of meta-chloroperbenzoic acid (mCPBA). This should oxidize some of the carbon-hydrogen bonds in the molecule. Since mCPBA is a strong oxidizing agent, it can conver... |
[
{
"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: For any $3 \\times 3$ matrix $M$, let $|M|$ denote the determinant of ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 334 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. First, I need to understand each part of the question and verify the truthfulness of each statement. The matrices given are E, P, and F. Q is a nonsingular matrix, so we know that Q is invertible. Let's start with each option one by one.
**Option (A):** The stateme... |
[
{
"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 | 122 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to minimize the health decrement when battling monsters on a tree. The problem is a bit complex, but let's break it down step by step.
First, let's understand the problem. We have a tree with n vertices, each containing a monster with a certain number of attack points. In each... |
[
{
"content": "Problem: A rectangular box $P$ has distinct edge lengths $a$, $b$, and $c$. The sum of the lengths of all $12$ edges of $P$ is $13$, the areas of all $6$ faces of $P$ is $\\frac{11}{2}$, and the volume of $P$ is $\\frac{1}{2}$. Find the length of the longest interior diagonal connecting two vertic... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 26 | AMC23 | {
"expected_answer": "13",
"problem_id": "29",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem about a rectangular box with distinct edge lengths a, b, and c. The sum of all 12 edges is 13, the total area of all 6 faces is 11/2, and the volume is 1/2. I need to find the length of the longest interior diagonal, which should be in the form m/n where m and n are relatively prime... |
[
{
"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: Dissolving $1.24 \\mathrm{~g}$ of white phosphorous in boiling... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 404 | JEEBench | {
"expected_answer": "2.38",
"problem_id": "41",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's try to figure out this problem step by step. So, we have 1.24 grams of white phosphorous dissolved in a boiling NaOH solution under an inert atmosphere, which produces a gas Q. Then, we need to find out how much CuSO₄ is required to completely consume this gas Q. Hmm, let's break this down.
First, ... |
[
{
"content": "Problem: Ten treeks weigh as much as three squigs and one goolee. Two treeks and one goolee are equal in weight to one squig. The combined weight of how many treeks equals the weight of one squig?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 81 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many treeks equal the weight of one squig. Let me start by writing down the information given in the problem.
First, the problem says that ten treeks weigh as much as three squigs and one goolee. So, that would be: 10 treeks = 3 squigs + 1 goolee. Let me note that down as equ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A repunit is an integer whose digits are all 1 in decimal representation. The repunits in ascending order are 1, 11, 1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 348 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
def find_n_th_sum_of_three_repunits(N):
def generate_repunits(length):
return int('1' * length)
def find_next_sum(current_sum, next_repunit):
return current_sum + next_repunit
def is_sum_of_three_repunits(n):
count = 0
while n > 0:
if n >= generate_r... |
[
{
"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 of strings words and a character x.\nReturn an array of indices representing the words that contain the character x.\nNote that... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 129 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python function that takes a list of words and a character x, then returns the indices of all words that contain x. Let me think step by step how to approach this.
First, the function should probably iterate through each word in the list. For each word, check if the character x is p... |
[
{
"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 free hydrogen atom after absorbing a photon of wavelength $\\lambda_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 219 | JEEBench | {
"expected_answer": "AD",
"problem_id": "8",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to tackle this problem step by step. First, I need to understand what's being asked here. We have a free hydrogen atom that absorbs a photon of wavelength λ_a, which excites it from the n=1 state to n=4. Then, the electron immediately jumps to a higher state n=m by emitting a photon of wavelengt... |
[
{
"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: Choose the correct statement(s) among the following:\n(A) $\\left[\\ma... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 253 | JEEBench | {
"expected_answer": "AC",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. The question is asking to choose the correct statement(s) from the given options about the geometries, hybridizations, and magnetic moments of some coordination compounds. Let me go through each option one by one and analyze them.
Starting with option (A): $\left[\... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.An integer divisible by the sum of its digits is said to be a Harshad number. You are given an integer x. Return the sum of the digits of x if x is a Harshad n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 469 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python function that checks if a given integer x is a Harshad number. If it is, the function should return the sum of its digits; otherwise, it should return -1. Let me think about how to approach this step by step.
First, let me recall what a Harshad number is. A Harshad number is ... |
[
{
"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 of length N consisting of lowercase English letters.\nYou will perform an operation Q times o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 392 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python function that takes a string S and a series of operations, then applies those operations to S and prints the result. Let me break down the problem step by step.
First, the problem states that we have a string S of length N, initially consisting of lowercase English letters. T... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 275 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have cards with different numbers, and I can buy some additional cards. The goal is to partition all the cards into decks with the maximum possible size, such that no deck has two cards with the same number. Let me try to break this down step by step.
First, let... |
[
{
"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 colour of the $\\mathrm{X}_{2}$ molecules of group 17 elements cha... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 77 | JEEBench | {
"expected_answer": "CD",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out why the color of X₂ molecules from group 17 elements changes from yellow to violet as we go down the group. Let me start by recalling some basics about group 17 elements, which are the halogens: fluorine, chlorine, bromine, iodine, and astatine. Their molecular structures are all d... |
[
{
"content": "Problem: If $10^x - 10 = 9990,$ what is $x$ equal to?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 262 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve the equation \(10^x - 10 = 9990\). Hmm, let's see. First, I should probably rewrite the equation to make it easier to solve for \(x\). If I add 10 to both sides, that would get rid of the minus 10 on the left. Let me try that:
\(10^x - 10 + 10 = 9990 + 10\)
Simplifying both sides:
\(... |
[
{
"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 | 198 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have a template array `a` and several strings, and we have to check if each string matches the template based on the given conditions. Let me try to break this down step by step.
First, let me understand the problem again. For each test case, we have an array `... |
[
{
"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 three cards with letters $\\texttt{a}$, $\\texttt{b}$, $\\texttt{c}$ placed in a row in some order. You can ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 0 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether it's possible to rearrange three cards with letters a, b, and c in a row to become "abc" by swapping two cards at most once. The problem gives multiple test cases, and for each, I should output "YES" if possible and "NO" otherwise. Let me start by 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 193 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have two strings, s and t, and I need to check for each possible split of t into two parts (one starting at the beginning up to some index i and the other from index i+1 to the end), whether these two parts are "beautiful". A pair is beautiful if every part in 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: What factors affect the rate of transpiration?\nOptions: A. Temperature, humidity, and air currents, B. Plant species, root depth, and wind speed, C.... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 445 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine which factors affect the rate of transpiration, I recall that transpiration is the process by which water moves through a plant and evaporates from aerial parts, primarily the leaves. The rate of transpiration is influenced by both environmental and plant factors.
1. **Environmental Factors**:
- **Temp... |
[
{
"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 of length N consisting of uppercase and lowercase English letters.\nLet us perform Q operatio... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 261 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
def process_operations(N, S, Q, operations):
for t, x, c in operations:
if t == 1:
S = S[:x - 1] + c + S[x:]
elif t == 2:
S = S.lower()
elif t == 3:
S = S.upper()
return S
def main():
N = int(input())
S = input().strip()
Q = in... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 142 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out this Prime Split Game problem. Let me try to understand the rules and requirements first.
We have two players, Alice and Bob, taking turns to play. There are n piles of stones, each with a certain number of stones. On each turn, the player must:
1. Choose an integer k where 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": 2,
"temperature": 0.7
} | 2 | 268 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a segment on a number line from [ℓ, r], and we can fold it either from left to right (LTR) or right to left (RTL) such that the sum of the endpoints is a prime number. The goal is to find the number of folding sequences that result in the shortest possible int... |
[
{
"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 A=(A_1,A_2,\\dots,A_{3N}) of length 3N where each of 1,2,\\dots, and N occurs exactly three t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 219 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the middle occurrence of each number in the sequence and then sort the numbers based on these middle indices. Here's a step-by-step plan and the corresponding Python function:
1. **Parse the Input**: First, we need to read the value of N and the sequence A. Since the length of 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 345 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether Alice can guarantee a win against Bob in this frog game. Let me start by understanding the problem better.
We have a row of n lilypads numbered from 1 to n. Alice and Bob start on different lilypads, a and b respectively. They take turns jumping left or right, but they can... |
[
{
"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 2D integer array nums. Initially, your score is 0. Perform the following operations until the matrix becomes empty:\n\nFrom each row ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 10 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a function that calculates the final score based on the given matrix. Let me try to break down the problem step by step.
First, the problem says that we have a 2D integer array, which is basically a matrix. Each element in the matrix is a non-negative integer. The goal is to perform o... |
[
{
"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 | 445 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have n spiders, each starting with 1 plushie. Every year, each spider that has at least one plushie gives exactly one plushie to another spider specified by r_i. We need to find the first year when the distribution of plushies stabilizes, meaning no spider's cou... |
[
{
"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 | 424 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have to assign unique integers from 1 to 2n to each vertex of a tree such that the absolute difference of the values of any two connected vertices is not a prime number. If such an assignment is possible, I need to provide the array; otherwise, print -1.
First,... |
[
{
"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 and Aoki are playing a game using N cards. The front side of the i-th card has A_i written on it, and the ba... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 449 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the winner of the game between Takahashi and Aoki, we need to analyze the given cards and simulate the optimal moves for both players. The key idea is to check whether there's a pair of cards that can be removed (either front sides are the same or back sides are the same) and then recursively determine the... |
[
{
"content": "Problem: For complex number $u = a+bi$ and $v = c+di$ (where $i=\\sqrt{-1}$), define the binary operation\n$u \\otimes v = ac + bdi$\nSuppose $z$ is a complex number such that $z\\otimes z = z^{2}+40$. What is $|z|^2$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | AMC23 | {
"expected_answer": "50",
"problem_id": "28",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem here about complex numbers. Let me read it again to make sure I get all the details.
It says: For complex numbers u = a + bi and v = c + di, the binary operation u ⊗ v is defined as ac + bd i. So, that's like a combination of the real parts and the imaginary parts multiplied toget... |
[
{
"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: February of 2011 has 28 days and March has 31 days. On what day of the week will next month, April, begin?\nOptions: A. Wednesday, B. Sunday, C. Thur... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 147 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what day of the week April 1, 2011, is. Hmm, let's see. February 2011 has 28 days, and March has 31, so starting from February 1, 2011, which is a Sunday (since February 1 is a Sunday, right?), let me count the days. Wait, actually, I should probably start from the beginning of the... |
[
{
"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.Snuke the doctor prescribed N kinds of medicine for Takahashi. For the next a_i days (including the day of the prescr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 235 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | from heapq import heappush, heappop
def find_first_day_with_k_pills_or_less():
import sys
input = sys.stdin.read
data = list(map(int, input().split()))
N, K = data[:2]
data = data[2:]
a = data[:N]
b = data[N:]
medicines = list(zip(a, b))
medicines.sort()
medicine_days = []... |
[
{
"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 | 205 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have to generate a permutation of length n such that the minimum number of carriage return operations needed to make the array equal to this permutation is the same regardless of whether we use the left-to-right or right-to-left typewriter. If it's impossible, we 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: Two men are walking along a horizontal straight line in the sa... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 125 | JEEBench | {
"expected_answer": "5",
"problem_id": "8",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Alright, let me try to figure out this problem step by step. So, we have two men walking in a straight line, one in front and the other behind. The front man is moving at 1.0 m/s, and the back man is moving at 2.0 m/s. There's a third man standing 12 meters above them, forming a vertical plane with the two walk... |
[
{
"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 of even length. You have to split the array into two parts nums1 and nums2 such that:\n\nnums1.length == nums2.length == nu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 186 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if we can split the given array `nums` into two parts, each containing `nums.length / 2` elements, such that both parts have distinct elements. Here's the step-by-step approach to achieve this:
1. **Check Element Frequency**: First, we need to check how many times each eleme... |
[
{
"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: Let $S=\\left\\{x \\in(-\\pi, \\pi): x \\neq 0, \\pm \\frac{\\pi}{2}\\rig... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 26 | JEEBench | {
"expected_answer": "C",
"problem_id": "39",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to solve this equation: √3 sec x + cosec x + 2(tan x - cot x) = 0, and find the sum of all distinct solutions in the set S, which is (-π, π) excluding 0, π/2, -π/2. Let me start by understanding the equation step by step.
First, let's rewrite all the trigonometric functions in terms of sine and... |
[
{
"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 4-digit integers in the closed interval ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 382 | JEEBench | {
"expected_answer": "569",
"problem_id": "7",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to find how many 4-digit integers between 2022 and 4482 can be formed using the digits 0, 2, 3, 4, 6, and 7. Let me break this down step by step.
First, let's clarify the range. The numbers start at 2022 and go up to 4482. So, we need to count all 4-digit numbers within this interval that can 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 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 106 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where four Roman merchants need to divide up cities based on a dividing point (x₀, y₀). The goal is to find the point (x₀, y₀) that maximizes the minimum number of cities any merchant would get. If I understand correctly, this is about minimizing the maximum load among t... |
[
{
"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: Spherical particles of pollen are shakenup in water and allowed to stand. The depth of water is 2 cm. What is the diameter of the largest particles r... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 496 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the diameter of the largest pollen particles that remain in suspension 1 hour after they're shaken up in water. The depth of the water is 2 cm, and the density of the pollen is 1.8 g/cm³. Hmm, let's start by recalling some principles related to sedimentation or particle separation ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We want to observe a decay of a single atom (atomic nucleus). It is possible to obtain this atom (e.g., from a beta decay of another atom) and start monitoring right awa... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 73 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the probability that an atom will decay in the next 150 minutes, given that it hasn't decayed in the first 50 minutes. The problem states that the decay probability within 100 minutes is 32%. Hmm, let's break this down step by step.
First, if the probability of decay within 100 mi... |
[
{
"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 | 405 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether I can sort the array 'a' in non-decreasing order by using the operation where for each element in 'a', I can subtract it from some element in 'b'. Since m is 1, that means for each a_i, I can choose one b_j (which is just b_1 here since m=1) and set a_i = b_j - a_i.
First... |
[
{
"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, a young baseball enthusiast, has been a very good boy this year, so Santa has decided to give him a bat or ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 351 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def which_item():
B, G = map(int, input().split())
if B > G:
print("Bat")
else:
print("Glove")
which_item()
``` |
[
{
"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 | 379 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a tree with n vertices, and we can choose two vertices a and b, remove all vertices on the path from a to b, including a and b themselves. The goal is to find the maximum number of connected components we can achieve. Hmm, interesting.
First, let me try to un... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider an isolated system of 13 identical particles each with charge 2e and negligible mass. 12 of these charges are\nconstrained to stay at 2 m from a point P. The 13... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 179 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the minimum energy of this isolated system. Let me try to understand the problem first. There are 13 identical particles, each with charge 2e. Wait, but 12 of them are constrained to stay 2 meters from a point P, and the 13th one is fixed at P. Hmm, so all these particles are charged, an... |
[
{
"content": "Problem: One gear turns $33\\frac{1}{3}$ times in a minute. Another gear turns 45 times in a minute. Initially, a mark on each gear is pointing due north. After how many seconds will the two gears next have both their marks pointing due north?\nMark your solution with \\boxed\nAnswer:",
... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 287 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem where two gears are turning, and I need to find out after how many seconds both of their marks will point due north again. Let me try to break this down step by step.
First, let me make sure I understand the problem. There are two gears. The first gear turns 33 and 1/3 times in a m... |
[
{
"content": "Problem: There is a unique sequence of integers $a_1, a_2, \\cdots a_{2023}$ such that\n\\[\\tan2023x = \\frac{a_1 \\tan x + a_3 \\tan^3 x + a_5 \\tan^5 x + \\cdots + a_{2023} \\tan^{2023} x}{1 + a_2 \\tan^2 x + a_4 \\tan^4 x \\cdots + a_{2022} \\tan^{2022} x}\\]whenever $\\tan 2023x$ is defined. ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 15 | AMC23 | {
"expected_answer": "-1",
"problem_id": "17",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem here where there's a unique sequence of integers \( a_1, a_2, \ldots, a_{2023} \) such that the tangent of 2023x can be expressed as a fraction involving alternating sequences of odd and even powers of tangent x, multiplied by these coefficients. The question is asking for the value... |
[
{
"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 | 193 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have a string t and another string s. For each i from 1 to n-1, I need to check if the pair of strings (s[1:i+1], s[i+1:n]) is beautiful. A pair is beautiful if I can split t into parts where each part is either x or y.
First, let me try to understand 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 99 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have to find the number of integers n in the range [10^l, 10^r) such that the sum of the digits of k*n equals k times the sum of the digits of n. And then output the answer modulo 10^9 + 7.
First, let me parse the problem again to make sure I understand it. The f... |
[
{
"content": "Problem: What is the smallest number which is one less than twice its reciprocal?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 341 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the smallest number that is one less than twice its reciprocal. Hmm, let me try to parse this problem. Let's see. The number is one less than twice its reciprocal. So, if I call the number x, then twice its reciprocal would be 2*(1/x), and the number itself is one less than that. So, the... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 18 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether Bessie can win the race starting from each possible starting island. Let me try to break down the problem step by step.
First, let's understand the setup. There are n islands connected by main bridges and m alternative bridges. The main bridges connect each island i to isl... |
[
{
"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 equation of the plane passing through the point $(1,1,1)$ and perpend... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 108 | JEEBench | {
"expected_answer": "C",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to find the equation of the plane that passes through the point (1,1,1) and is perpendicular to both planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7. Hmm, let me think.
First, I remember that if a plane is perpendicular to two other planes, its normal vector should be the cross product of the norm... |
[
{
"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 of length N consisting of 0 and 1.\r\nIt describes a length-N sequence A=(A _ 1,A _ 2,\\ldots... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 242 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compute the sum over all pairs (i, j) where 1 ≤ i ≤ j ≤ N of the function f(i, j). The function f(i, j) is defined recursively using the NAND operator. The key steps involve understanding the recursive definition and efficiently computing the sum without directly iterating over all 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: With reference to aqua regia, choose the correct option(s)\n(A) Aqua r... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 223 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of these options are correct regarding aqua regia. Let me start by recalling what aqua regia is. From what I remember, aqua regia is a mixture of nitric acid and hydrochloric acid, right? The name "aqua regia" means "royal water," and it's known for its ability to dissolve pr... |
[
{
"content": "Problem: Jackson's paintbrush makes a narrow strip with a width of $6.5$ millimeters. Jackson has enough paint to make a strip $25$ meters long. How many square centimeters of paper could Jackson cover with paint?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 34 | AMC23 | {
"expected_answer": "1625",
"problem_id": "44",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many square centimeters of paper Jackson can cover with his paintbrush. Let me start by understanding the problem step by step.
First, the paintbrush makes a strip that's 6.5 millimeters wide. That seems pretty narrow. Jackson has enough paint to make a strip that's 25 meters ... |
[
{
"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 | 20 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of screens required to place x 1x1 icons and y 2x2 icons on a 5x3 grid. Each screen is 5x3, so each screen has 5*3=15 cells. The problem is asking for the minimal number of screens needed.
Let me start by understanding the constraints. Each 1x1 icon takes 1 cel... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You identified a new quorum-sensing peptide in the bacteria Lactobacillus acidophilus. You are highly interested if its role in intercellular communication is conserved ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 151 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which complex from the given options is least likely to be observed in the assay when studying active chromatin in the shmoo. Let me start by recalling what each complex does.
First, the pre-initiation complex (PIC) is involved in the initiation of transcription in eukaryotes. It ... |
[
{
"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 | 274 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have to find the minimum area of the symmetric difference between the original convex polygon and another convex polygon that is point symmetric. The goal is to minimize the area difference, which is calculated as the sum of the areas added and subtracted when tr... |
[
{
"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: Hund's rule requires that\nOptions: A. all electrons must have opposite spins in an orbital, B. no two electrons can have the same four quantum numbe... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 359 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which statement correctly explains Hund's rule. Let me start by recalling what Hund's rule is about. From my chemistry class, I remember that it's related to how electrons fill orbitals in an atom. The key idea is about the distribution of electrons in orbitals to minimize energy. ... |
[
{
"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: Two inductors $L_{1}$ (inductance $1 \\mathrm{mH}$, internal resistance $3 \\Omega$ ) and $L_{2}$ (inductance ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 11 | JEEBench | {
"expected_answer": "8",
"problem_id": "18",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | <think>
Okay, so I need to find the ratio of the maximum to the minimum current drawn from the battery in this parallel circuit with two inductors and a resistor. Let me start by understanding the problem step by step.
First, the circuit has two inductors, L1 and L2, connected in parallel with a resistor R, all across... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The state of a system at time t is given by the column matrix having elements (-1, 2, 1). An observable of the system is represented by the matrix operator P having elem... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 150 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the probability that the measurement of the observable P will yield 0 at time t. The system's state is given by the column matrix (-1, 2, 1). Hmm, first, let me make sure I understand the problem correctly.
The system's state is a vector, right? So that would be |ψ⟩ = [ -1, 2, 1 ]^T. A... |
[
{
"content": "Problem: For complex number $u = a+bi$ and $v = c+di$ (where $i=\\sqrt{-1}$), define the binary operation\n$u \\otimes v = ac + bdi$\nSuppose $z$ is a complex number such that $z\\otimes z = z^{2}+40$. What is $|z|^2$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 25 | AMC23 | {
"expected_answer": "50",
"problem_id": "28",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I have this problem about complex numbers. The question defines a binary operation called "⊗" for two complex numbers u and v. Specifically, u⊗v is defined as ac + bdi, where u = a + bi and v = c + di. Then, there's a complex number z such that when you do z⊗z, it equals z squared plus 40. I ne... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 215 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Lelle and Flamm are having a performance match with multiple rounds. Each round either Lelle or Flamm wins, and the goal is to maximize the total score while ensuring that the match is successful. The success conditions are that after every round, the greatest common ... |
[
{
"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 | 287 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have n arrays, each of length m. Each array has distinct elements, and I can perform operations where I choose an array and an integer x, then add x to the beginning of the array, set x to the last element, and remove the last element. The goal is to transform each ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H horizontal rows and W vertical columns. Each cell has a lowercase English letter written on it... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 197 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find a sequence of five consecutive cells in a grid (either vertically, horizontally, or diagonally) that contain the letters 's', 'n', 'u', 'k', and 'e' in that order. The cells must form a contiguous set, meaning each consecutive pair of cells shares either a side or a corner. Additi... |
[
{
"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 a triangle $\\Delta$ whose two sides lie on the $x$-axis and the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 324 | JEEBench | {
"expected_answer": "B",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to find the equation of the circle that passes through the vertices of triangle Δ, given that two of its sides lie on the x-axis and the line x + y + 1 = 0, and the orthocenter is at (1,1). Hmm, let's break this down step by step.
First, since two sides of the triangle are on the x-axis and 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: To which of the following parties will a CPA be liable if the CPA fraudulently issues an unqualified opinion on a corporation's materially misstated ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the liability of a CPA who fraudulently issues an unqualified opinion on a corporation's materially misstated financial statements, we need to consider the potential victims of such fraud.
1. **Corporate Shareholders**: Shareholders generally rely on the accuracy of financial statements when making inves... |
[
{
"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 | 201 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have a bunch of segments, and I need to find the maximum size of a complex subset. A complex subset is one where all the segments are the same size, and any two segments intersect if and only if they are in the same subset.
First, let me parse the problem again... |
[
{
"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}, \\quad g: \\mathbb{R} \\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 34 | JEEBench | {
"expected_answer": "BC",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I have this problem here where I need to figure out which of the given options are correct. The problem states that we have three differentiable functions: f, g, and h. Their definitions are:
- f(x) = x³ + 3x + 2
- g(f(x)) = x
- h(g(g(x))) = x
And we need to determine the derivatives of g and h at ce... |
[
{
"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: The Oral Torah, in its written form, is known as what?\nOptions: A. Mishnah, B. Tanakh, C. Talmud, D. Pentateuch, E. Gemara, F. Zohar, G. Ketuvim, H.... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 481 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what the Oral Torah is called in its written form. Hmm, let me start by recalling what I know about the Torah. The Torah is the sacred text of Judaism, right? It's the first part of the Tanakh, which is the Hebrew Bible. The Torah is also sometimes referred to as the Pentateuch, wh... |
[
{
"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: Let $C_{1}$ be the circle of radius 1 with center at the origin. Let $C_{2}$ be the circle of radius $r$ with ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 497 | JEEBench | {
"expected_answer": "2",
"problem_id": "13",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, so I need to find the value of \( r^2 \) given that the distance from point \( B \) (where the line joining the midpoints of the common tangents \( PQ \) and \( ST \) meets the x-axis) to point \( A \) (the center of circle \( C_2 \)) is \( \sqrt{5} \). Let me try to break this down step by step.
First, ... |
[
{
"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: Let\n\\[\\mathrm{M}=\\left\\{(\\mathrm{x}, \\mathrm{y}) \\in \\mathbb{R} ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 374 | JEEBench | {
"expected_answer": "B",
"problem_id": "50",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to figure out how many of the circles D_n are inside the bigger circle M. Let me start by understanding the problem step by step.
First, M is defined as all points (x, y) in R² such that x² + y² ≤ r², where r is given as ((2¹⁹⁹ - 1)√2)/2¹⁹⁸. Let me simplify that expression to get a better sense... |
[
{
"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 | 373 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of operations needed to make a permutation simple. The problem is given a permutation, we can swap any two elements any number of times, and we need to make sure that for every i, either p_i = i or p_{p_i} = i. Hmm, interesting. Let me try to break this down step... |
[
{
"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: For a non-zero complex number $z$, let $\\arg (z)$ denote the principa... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 137 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. The question is asking which of the given statements are false. We need to analyze each one carefully. Let me start by recalling some basic concepts about complex numbers and their arguments.
First, the principal argument of a complex number \( z \), denoted \( \ar... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N strings S_1,S_2,\\dots,S_N, each of length M, consisting of lowercase English letter. Here, S_i are p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 198 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
def check_rearrangement():
N, M = map(int, input().split())
strings = [input().strip() for _ in range(N)]
# Check if all strings have the same set of characters
unique_chars = set(strings[0])
for s in strings[1:]:
unique_chars.update(s)
if len(unique_chars) > 26:
... |
[
{
"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 AtCoder Kingdom holds a festival for N days. On M of these days, namely on the A_1-th, A_2-th, \\dots, A_M-th days... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 291 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def calculate_days_until_fireworks():
import sys
input = sys.stdin.read
data = list(map(int, input().split()))
N = data[0]
M = data[1]
A = data[2:M + 1]
A.append(N) # Ensure A_M = N
result = [0] * N
for i in range(N):
index = next((j for j, x in enumerate(A) if... |
[
{
"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: On complete hydrogenation, natural rubber produces\n(A) ethylene-propylen... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 15 | JEEBench | {
"expected_answer": "A",
"problem_id": "23",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, so I need to figure out what product is formed when natural rubber undergoes complete hydrogenation. Let me start by recalling what natural rubber is. Natural rubber is a polymer of isoprene, which is a five-carbon compound. The chemical formula for natural rubber is (C5H8)n, where n is a large number, ty... |
[
{
"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 | 233 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have a string of digits from 1 to 9, and I need to calculate the minimum length of a string that can be obtained by splitting a contiguous substring of length k into an even number of non-empty parts and then repeating each part a number of times equal to the nex... |
[
{
"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 | 398 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where Kevin has to perform division operations on two sequences of numbers. The goal is to make all elements of the first sequence equal to 1 by choosing the smallest possible element in a segment of the second sequence and dividing each element in that segment by the sm... |
[
{
"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: Consider an obtuse angled triangle $A B C$ in which the differ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 498 | JEEBench | {
"expected_answer": "1008",
"problem_id": "14",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I have this problem here about an obtuse triangle ABC with some specific properties. Let me try to parse through it step by step.
First, the problem states that it's an obtuse-angled triangle, meaning one of its angles is greater than 90 degrees. The difference between the largest and the smallest an... |
[
{
"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 positive integers A and B.\r\nPrint the value A^B+B^A.\n\nInput\n\nThe input is given from Standard Inpu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 279 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
import sys
def compute_power_sum():
# Read input from stdin
A, B = map(int, sys.stdin.readline().split())
# Compute A^B and B^A
a_power_b = A ** B
b_power_a = B ** A
# Sum them and print the result
result = a_power_b + b_power_a
print(result)
# Call the function to ... |
[
{
"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 | 148 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to divide these cards into the minimum number of bad segments such that no segment can multiply to give the integer x. Let me start by understanding the problem step by step.
First, the problem states that we have n cards with prices, and each price is an integer. We need t... |
[
{
"content": "Problem: Let $(a_1, a_2, \\dots, a_n)$ be a sequence of positive real numbers, such that\n\\[\\sum_{i = 1}^n a_i = 96, \\quad \\sum_{i = 1}^n a_i^2 = 144, \\quad \\sum_{i = 1}^n a_i^3 = 216.\\]Find the sum of all possible values of $n.$\nMark your solution with \\boxed\nAnswer:",
"role": "user... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 136 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem where I need to find the sum of all possible values of n given three conditions about a sequence of positive real numbers. The sequence is (a1, a2, ..., an). The conditions are:
1. The sum of the terms is 96: a1 + a2 + ... + an = 96.
2. The sum of the squares is 144: a1² + a2² + ..... |
[
{
"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 diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | JEEBench | {
"expected_answer": "4",
"problem_id": "33",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, so I need to figure out how the diffusion coefficient of an ideal gas changes when the temperature is increased 4 times and the pressure is increased 2 times. The problem states that the diffusion coefficient is proportional to both the mean free path and the mean speed of the gas molecules. Let me start ... |
[
{
"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.AtCoder Kingdom uses a calendar whose year has N months.\nMonth i (1\\leq i\\leq N) has D _ i days, from day 1 of mont... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 322 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
def count_repeated_digits(n, days):
def is_repeated_digit(day, month):
return len(set(str(day) + str(month))) == 1
total_days = 0
for i in range(1, n + 1):
for j in range(1, days[i - 1] + 1):
if is_repeated_digit(j, i):
total_days += 1
return tota... |
[
{
"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 | 59 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of colors required to color the intervals such that each time point is covered by exactly one color. The problem is similar to a previous one but with more constraints. Let me start by breaking down the problem.
First, the input consists of multiple test cases, ... |
[
{
"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 | 308 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Alice and Bob are playing a game with stone piles. The goal is to count the number of ways Bob can win if both players play optimally. The key points are:
1. Each pile has a value \(a_i\) and a maximum number of stones \(b_i\). The actual number of stones \(x_i\) can... |
[
{
"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: Consider an ionic solid $\\mathbf{M X}$ with $\\mathrm{NaCl}$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 133 | JEEBench | {
"expected_answer": "3",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's try to figure out this problem step by step. So, we have an ionic solid MX with a NaCl structure. The task is to modify this structure following the given instructions and then find the ratio of the number of anions to the number of cations in the new structure Z. Alright, let's start by understandi... |
[
{
"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: Two capacitors with capacitance values $C_{1}=2000 \\pm 10 \\m... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 282 | JEEBench | {
"expected_answer": "1.3",
"problem_id": "15",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I need to find the percentage error in the calculation of the energy stored in two capacitors connected in series. The capacitors have values \( C_1 = 2000 \pm 10 \, \text{pF} \) and \( C_2 = 3000 \pm 15 \, \text{pF} \), and the applied voltage is \( V = 5.00 \pm 0.02 \, \text{V} \). Hmm, let's break t... |
[
{
"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: Based on the compounds of group 15 elements, the correct statement(s) ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 130 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of these statements about compounds of group 15 elements are correct. Let me go through each one step by step.
First, let me recall that group 15 elements are nitrogen (N), phosphorus (P), arsenic (As), antimony (Sb), and bismuth (Bi). As we move down the group, the element... |
[
{
"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 us consider a system of units in which mass and angular momentum a... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 185 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "11",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of these statements are correct given that in this system of units, mass and angular momentum are dimensionless. The length has a dimension of L. Let me start by recalling how dimensions work in physics. Usually, dimensions are derived from the fundamental quantities like mas... |
[
{
"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 $\\bar{z}$ denote the complex conjugate of a complex number $z$. I... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 422 | JEEBench | {
"expected_answer": "A",
"problem_id": "11",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of these options could be the modulus of a complex number z, given that when you take the complex conjugate of z, square it, and add the reciprocal of z squared, both the real and imaginary parts are integers. Hmm. Let me start by breaking down the problem step by step.
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 1-indexed integer array nums of length n.\nAn element nums[i] of nums is called special if i divides n, i.e. n % i == 0.\nReturn the sum of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 42 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a function that takes a list of integers called `nums` and returns the sum of the squares of all the special elements in the list. A special element is defined as one where its index divides the length of the list. Let me try to break this down step by step.
First, let me make sure 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 | 73 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the maximum number of rounds Egor can win with his deck of cards. Let me try to break this down step by step.
First, let me parse the problem again. Egor has a deck of n cards, each with a number a_i. He wants to play rounds where he takes a non-zero number of cards from the top. ... |
[
{
"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 | 42 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether it's possible to make the two bags contain the same numbers by performing the given operations. Let me try to break down the problem step by step.
First, the problem states that we have two bags. The first bag initially has n numbers, and the second is empty. We can do two... |
[
{
"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 is the importance of product differentiationin monopolistic competition?\nOptions: A. Product differentiation defines monopolistic competition a... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 327 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | A. |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 195 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to figure out this problem step by step. So, we have a decay sequence starting with uranium-238 (U-238) and ending with thorium-230 (Th-230). The sequence goes through three decays: first to thorium-234 (Th-234), then to protactinium-234 (Pa-234), and then to some element Z, which finally decays... |
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