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 9 157k |
|---|---|---|---|---|---|---|
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 323 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where Monocarp is trying to take cards from a deck, and each subsequent card he takes has to be either the same as the previous one or one greater. The goal is to maximize the number of cards he can take, given that the number of distinct values he can hav... |
[
{
"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": "",
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"subject": null,
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} | \boxed{D}
The principle of comparative advantage applies where productive units have different relative efficiencies. This can occur in various contexts, such as international trade, domestic trade, or even within a company. The key factor is the difference in efficiency, not the type of trade or geographical location... |
[
{
"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>
Okay, let's see. The problem is about seating monkeys in a classroom with two rows of seats. Each row has m seats. There are a, b, and c monkeys with specific preferences: a want to sit in the first row, b in the second row, and c have no preference. We need to maximize the number of seated monkeys by assigning... |
[
{
"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 figure out the average intensity of light at a distance of 22 cm from a convex lens that's receiving sunlight with an intensity of 1.3 kW/m². The lens has a focal length of 20 cm. Hmm, let's see. I remember that convex lenses focus light to a point, right? So if sunlight is coming in and 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. The answer choices are given, and I need to pick the correct one. Let me start by recalling what factors affect the probability of a planet transiting its host star.
From wha... |
[
{
"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 says that 3,3,6-trimethylhepta-1,5-dien-4-one is treated with 1 equivalent of meta-chloroperbenzoic acid, and two products are formed in a 1:1 ratio. Then, in a separate vessel, methyllithium is treated with copper(I)iodide, and excess ... |
[
{
"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, so I need to figure out which of the statements A, B, C, D are true given the matrices E, P, and F. Let me take this step by step. First, let me recall what each of these statements is claiming.
Starting with statement (A): It says two things. First, that F equals PEP, and second, that P squared is the 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 | 122 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this monster killing problem. Let me start by understanding the problem statement properly.
We have a tree with n vertices, each containing a monster with a certain number of attack points. The goal is to determine the minimum possible health decrement after 10^100 ro... |
[
{
"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 here about a rectangular box with distinct edge lengths a, b, and c. The problem gives me three different pieces of information: 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, w... |
[
{
"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, so I need to figure out how much copper sulfate (CuSO₄) is needed to completely consume the gas Q produced by dissolving 1.24 grams of white phosphorus in a NaOH solution. Hmm, let me start by recalling what I know about chemical reactions involving phosphorus and copper sulfate.
First, white phosphorus ... |
[
{
"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, let's see. I need to solve this problem about treeks, squigs, and goolees. The problem gives me two equations and asks me to find how many treeks equal the weight of one squig. Hmm. Let me write down the information step by step.
First, the problem states: "Ten treeks weigh as much as three squigs and on... |
[
{
"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
} | <think>
Okay, so I need to figure out how to find the N-th smallest integer that can be expressed as the sum of exactly three repunits. Let me start by understanding the problem better.
First, what's a repunit? A repunit is a number like 1, 11, 111, 1111, etc., where all the digits are 1. So, each repunit is composed ... |
[
{
"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 two parameters: a list of words and a character x. The function should return the indices of all words that contain the character x. The order of the indices doesn't matter, and I should make sure the code works for any valid input given the constraints.
F... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: 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 happening here. We have a hydrogen atom that absorbs a photon, gets excited from n=1 to n=4, and then immediately emits a photon and drops to a lower energy state n=m. We need to figure out which of the given options are cor... |
[
{
"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. We need to evaluate each statement (A to D) and determine which ones are correct. I'll go through each option one by one, explaining my reasoning.
**Statement A:**
\[
\left[\text{FeCl}_4\right]^{-} \text{has tetrahedral geometry.}
\]
First, I remember that the geom... |
[
{
"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 figure out how to solve this problem where I have to determine if a number x is a Harshad number, which means it's divisible by the sum of its digits. If it is, I should return the sum of the digits; otherwise, return -1. The constraints are that x is between 1 and 100, inclusive. Let me brea... |
[
{
"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 number of operations Q. The operations are pairs of characters (c_i, d_i), meaning that every occurrence of c_i in S should be replaced with d_i. The function should perform all these operations in order and then print the resulting string.... |
[
{
"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>
Okay, so I need to solve this problem where I have cards with numbers from 1 to n, and I can buy up to k new cards. The goal is to partition all the cards into decks of the same size, with no two cards of the same value in the same deck. I need to find the maximum possible size of a deck after buying the new ca... |
[
{
"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 of group 17 elements changes from yellow to violet as we go down the group. The options given are about physical states, ionization energy, π*-σ* gap, and HOMO-LUMO gap. Let me think step by step.
First, group 17 elements are the halogens: fluorine, c... |
[
{
"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 | {
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} | To solve the equation \(10^x - 10 = 9990\), we start by isolating the term with \(10^x\).
First, add 10 to both sides of the equation:
\[
10^x - 10 + 10 = 9990 + 10
\]
Simplifying both sides, we get:
\[
10^x = 10000
\]
Next, we recognize that 10000 can be written as a power of 10. Specifically, \(10000 = 10^4\). The... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 198 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Kristina has an array and some strings, and we have to check if each string matches the template. The template has specific rules: the length must match the array's size, each number in the array corresponds to a character in the string, and vice versa. So, if... |
[
{
"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 the letters 'a', 'b', and 'c' into the order 'abc' by swapping two cards at most once. The problem gives me a few test cases and asks me to determine for each case if it's possible. Let me start by understanding the problem step by step.
First, t... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"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
} | Okay, so I need to solve this problem where we have a string t of length m and another string s of length n. We have to determine for each i from 1 to n-1 whether the pair (s[1..i], s[i+1..n]) is beautiful. A pair is beautiful if we can split the string t into parts where each part is either equal to the first string o... |
[
{
"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": "",
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"subject": null,
"type": null
} | \boxed{A}
The factors that affect the rate of transpiration include temperature, humidity, and air currents. These environmental conditions directly impact the movement of water vapor from the plant to the atmosphere. Transpiration is a crucial process in plants, involved in water uptake, nutrient transport, and cooli... |
[
{
"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
} | <think>
Okay, so I need to figure out how to solve this problem where we have a string S and perform a series of operations on it. Let me start by understanding the problem step by step.
First, the problem says we have a string S of length N, consisting of uppercase and lowercase English letters. Then we perform Q ope... |
[
{
"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>
Okay, so I need to figure out who wins the Prime Split Game given different configurations of stone piles. Let me start by understanding the problem deeply.
The game involves two players, Alice and Bob, taking turns to remove and split piles. The key steps are: choosing k (1 ≤ k ≤ n/2), removing k piles, and ... |
[
{
"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
} | Okay, let's try to tackle this problem step by step. So, the problem is about folding a segment on a number line from either left to right (LTR) or right to left (RTL) such that each operation uses a prime number. The goal is to find the number of folding sequences that result in the shortest possible interval. The ans... |
[
{
"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
} | <think>
Okay, so I need to figure out how to solve this problem. Let me read it again to make sure I understand what's being asked.
We have a sequence A of length 3N, where each number from 1 to N occurs exactly three times. For each number i from 1 to N, we need to find the index of its middle occurrence, which is ca... |
[
{
"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
} | Okay, let's try to figure out this problem step by step. So, we have two frogs, Alice and Bob, on different lily pads in a row from 1 to n. They take turns jumping left or right, but they can't occupy the same lily pad. The player who can't make a move loses. We need to determine if Alice can guarantee a win.
First, l... |
[
{
"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 figure out how to solve this problem where I have a 2D integer array, and I have to perform these operations until the matrix is empty. Then return the final score. Let me try to break it down step by step.
First, the problem says: Start with a 0-indexed 2D integer array `nums`. Initially, t... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"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
} | Okay, so I need to figure out the first year when the spider plushie exchange process becomes stable. Let me start by understanding the problem again.
Each spider starts with 1 plushie. Every year, if a spider has at least one plushie, they give exactly one to the spider specified by `r_i`. All transfers happen at 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,
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Okay, so I need to solve this problem where I have to assign unique integers from 1 to 2n to the n vertices of a tree such that the absolute difference between the values of any two adjacent vertices isn't a prime number. If such an assignment isn't possible, I should print -1.
First, let me understand the pr... |
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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.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... | {
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Okay, so I need to figure out who wins this game between Takahashi and Aoki based on the given rules and input. Let me start by understanding the problem step by step.
First, there are N cards, each with two numbers: A_i on the front and B_i on the back. Players take turns removing pairs of cards where either ... |
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"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:",
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Okay, so I have this problem here about complex numbers. Let me read it again to make sure I understand. It says: For complex numbers u = a + bi and v = c + di, where i is the square root of -1, define a binary operation u ⊗ v = ac + bd i. Then, suppose z is a complex number such that z ⊗ z = z² + 40. We need t... |
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"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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... | {
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Okay, so I need to figure out what day of the week April 1, 2011, was. The problem says February 2011 had 28 days and March had 31 days. Hmm, wait, 2011 is not a leap year, right? Because 2011 divided by 4 is 502.75, so it's not divisible by 4. So February had 28 days, which matches the problem statement. March... |
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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.Snuke the doctor prescribed N kinds of medicine for Takahashi. For the next a_i days (including the day of the prescr... | {
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Okay, so I need to figure out the first day when Takahashi has to take 8 or fewer pills. Let me start by understanding the problem again.
We have N medicines, each with a day when he has to take them. For each medicine, there's a day a_i and a number of pills b_i. The day of the prescription is day 1. We need... |
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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Okay, so I need to figure out how to generate a permutation p of length n such that the minimum number of carriage return operations required to transform the initial all -1 array a into p is the same regardless of whether Misuki uses the left-to-right typewriter or the right-to-left typewriter. If such a permu... |
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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: Two men are walking along a horizontal straight line in the sa... | {
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Okay, let's see. There are two men walking in the same direction, and a third man standing still. All three are in a vertical plane. The front man is moving at 1 m/s, the one behind at 2 m/s. They're both blowing whistles that emit 1430 Hz sound. The speed of sound is 330 m/s. At the moment when the two walking... |
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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 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... | {
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Okay, so I need to figure out if I can split an even-length integer array into two parts, each with distinct elements. Let me start by understanding the problem properly.
First, the array has an even number of elements, so splitting it into two equal parts is straightforward. The challenge is ensuring that eac... |
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"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... | {
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"problem_id": "39",
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"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to solve the equation √3 sec x + cosec x + 2(tan x - cot x) = 0 in the set S, which is all x in (-π, π) excluding 0, π/2, and -π/2. Then sum all the distinct solutions and choose the correct answer from the given options.
First, let me recall the definitions of the trigonometric functions invol... |
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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 number of 4-digit integers in the closed interval ... | {
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"problem_id": "7",
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} | <think>
Okay, so I need to figure out how many 4-digit integers between 2022 and 4482 inclusive can be formed using the digits 0, 2, 3, 4, 6, and 7. Let me start by understanding the problem step by step.
First, the numbers we're considering are 4-digit numbers from 2022 to 4482. That means the numbers range from 2022... |
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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Okay, so I need to solve this problem where four Roman merchants want to divide up cities based on their coordinates. The goal is to find a dividing point (x₀, y₀) such that the smallest number of cities any one merchant gets is maximized. In other words, they want to split the cities as evenly as possible.
L... |
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"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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... | {
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Okay, so I need to figure out the diameter of the largest pollen particles that remain in suspension after 1 hour when 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 think about this step by step.
First, I remember that when particles are susp... |
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"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: 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... | {
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Okay, so I need to figure out the probability that the atom decays in the next 150 minutes given that it hasn't decayed yet after 50 minutes. The problem states that the decay probability within 100 minutes is 32%. Hmm, let's break this down step by step.
First, I know that decay problems often involve exponen... |
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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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"problem_id": "",
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Okay, so I need to figure out whether Skibidus can sort the array 'a' in non-decreasing order by performing the given operation a finite number of times. The operation is: for each index i from 1 to n, choose an integer j (1 to m) and set a_i := b_j - a_i.
First, let's parse the problem. The problem mentions ... |
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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.Takahashi, a young baseball enthusiast, has been a very good boy this year, so Santa has decided to give him a bat or ... | {
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Okay, let's see. I need to create a Python function that takes two inputs, B and G, which are the costs of a bat and a glove respectively. Then, depending on which one is more expensive, the function should print either "Bat" or "Glove". The problem states that B and G are different integers between 1 and 1000.... |
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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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"seed": 0,
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"problem_id": "",
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Okay, so I need to solve this problem where I have a tree with n vertices, and I can choose two vertices a and b, then remove all the vertices on the path from a to b, including a and b themselves. The goal is to find the maximum number of connected components that can be formed after removing that path.
Firs... |
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"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: 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... | {
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Okay, so I need to figure out the minimum energy of this system. Let's see. There are 13 identical particles, each with charge 2e. Wait, 12 of them are fixed at 2 meters from point P, and the 13th one is at P. So, we have a central charge at P and 12 charges arranged at a distance of 2 meters from P. Since all ... |
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"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:",
... | {
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Okay, so I have this problem about two gears. One gear turns 33 and 1/3 times per minute, and the other one turns 45 times per minute. Both start with a mark pointing due north. I need to find after how many seconds they will both have their marks pointing due north again. Hmm, let me think.
First, I should pr... |
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"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. ... | {
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"problem_id": "17",
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Okay, so I have this problem here about a sequence of integers \( a_1, a_2, \ldots, a_{2023} \) such that the tangent of 2023x can be expressed as a fraction where the numerator is a polynomial in tan x with only odd-powered terms up to tan^{2023}, and the denominator is a polynomial in tan^2 x with even-powere... |
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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Okay, so I need to solve this problem where we have a string t and another string s. The task is to determine for each prefix of s (from length 1 to n-1) whether the pair (s[1:i], s[i+1:n]) is beautiful. A pair is considered beautiful if the original string t can be split into parts where each part is either th... |
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
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Okay, so I need to solve this problem where I have to find the number of integers n in the range 10^l to 10^r (not inclusive) such that D(k*n) = k*D(n), where D(n) is the sum of the digits of n, and k is a given integer. The answer has to be modulo 10^9 + 7. Let me try to break this down step by step.
First, l... |
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"content": "Problem: What is the smallest number which is one less than twice its reciprocal?\nMark your solution with \\boxed\nAnswer:",
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} | To find the smallest number that is one less than twice its reciprocal, we start by defining the number as \( x \). The problem states that this number is one less than twice its reciprocal. The reciprocal of \( x \) is \( \frac{1}{x} \), so twice the reciprocal is \( \frac{2}{x} \). Therefore, the equation we need 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 the ... | {
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} | Okay, let's try to tackle this problem step by step. So, we have two cows, Bessie and Elsie, racing across n islands. The setup includes main bridges and alternative bridges. Bessie can only use main bridges, while Elsie can use both. The goal is to determine for each starting position s (from 1 to n-1), whether Bessie... |
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"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... | {
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"seed": 2,
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} | 2 | 108 | JEEBench | {
"expected_answer": "C",
"problem_id": "37",
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"subject": "math",
"type": "MCQ"
} | <think>
To find the equation of the plane passing through the point \((1,1,1)\) and perpendicular to the planes \(2x + y - 2z = 5\) and \(3x - 6y - 2z = 7\), we need to determine the normal vector of the desired plane. The normal vector of the plane we seek must be perpendicular to the normal vectors of the given plane... |
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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.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... | {
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Okay, so I need to solve this problem where I have a binary string S of length N, and I have to compute a certain sum over all pairs of indices (i, j) where i ≤ j. The sum involves a function f(i, j) which is defined recursively using the NAND operator. The goal is to compute the total sum and print the result.... |
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"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... | {
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} | 0 | 223 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "20",
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"subject": "chem",
"type": "MCQ(multiple)"
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Okay, so I need to figure out which of the options A to D about aqua regia are correct. Let me start by recalling what I know about aqua regia.
First, aqua regia is a mixture of concentrated hydrochloric acid (HCl) and concentrated nitric acid (HNO3). The ratio is typically 3:1 by volume, which matches option... |
[
{
"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:",
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Okay, so Jackson has this paintbrush that makes a narrow strip, right? The width of the strip is 6.5 millimeters. And he has enough paint to make a strip that's 25 meters long. The question is asking how many square centimeters of paper Jackson could cover with paint. Hmm, let me think through this step by step... |
[
{
"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, so I need to figure out how to arrange the icons on the minimum number of screens for Little Rosie's phone desktop. Each screen is a 5x3 grid, right? So each screen has 15 cells. The problem is asking for the minimum number of screens needed given the number of 1x1 icons (x) and 2x2 icons (y).
First, le... |
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"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You identified a new quorum-sensing peptide in the bacteria Lactobacillus acidophilus. You are highly interested if its role in intercellular communication is conserved ... | {
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Okay, so I need to figure out which protein complex the question is asking about. The problem says that when they treat yeast Saccharomyces cerevisiae with the quorum-sensing peptide from Lactobacillus acidophilus, they observe the formation of the shmoo. Then they want to study the proteome of the active chrom... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | Okay, so I need to figure out how to solve this problem where A-Ju wants to rebuild her castle into a point-symmetric convex polygon, and we need to find the minimum area of the symmetric difference between the original and the new polygon. The cost is proportional to this area, so minimizing it is key.
First, let me ... |
[
{
"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... | {
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Okay, so I need to figure out which of these options correctly states Hund's rule. Let me start by recalling what I know about Hund's rule from my chemistry class.
Hund's rule is about electron configuration in atoms. It deals with how electrons fill orbitals. Let me think... I remember that electrons prefer ... |
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"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 ... | {
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} | 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 minimum current drawn from the battery when these two inductors and a resistor are connected in parallel. Let me start by understanding the problem.
First, the circuit has two inductors, L1 and L2, each with their own inductance and internal resistance. Then ... |
[
{
"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... | {
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} | 2 | 150 | GPQADiamond | {
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"problem_id": "",
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} | <think>
Okay, so I need to figure out the probability that the measurement of the observable represented by matrix P will yield 0 at time t, given that the system's state at time t is the column matrix [-1, 2, 1]^T. Hmm, let me recall how to calculate probabilities in quantum mechanics.
First, the state of the system ... |
[
{
"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"
}
] | {
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"max_new_tokens": 32768,
"seed": 4,
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} | 4 | 25 | AMC23 | {
"expected_answer": "50",
"problem_id": "28",
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} | <think>
Okay, let's see. I need to solve this problem about complex numbers. The problem says that for complex numbers u = a + bi and v = c + di, they define a binary operation u ⊗ v = ac + bdi. Then, it says that if z is a complex number such that z ⊗ z = z² + 40, what is |z|²? They want the answer boxed.
First, let ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 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 they need to make sure that after every round, the greatest common divisor (gcd) of their wins is at most 1. The match also has to end with Lelle having at... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"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 figure out the minimum number of operations required to transform the original arrays into the target arrays using the given operation. Let me start by understanding the problem.
First, the operation allows us to insert an element at the beginning of any array, then shift all subsequent elem... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 197 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python function that takes a grid as input and finds the positions of the cells that spell out "snuke" in order, either vertically, horizontally, or diagonally. The grid is given with H rows and W columns, and each cell contains a lowercase English letter. The function should output ... |
[
{
"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... | {
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"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. The triangle has two sides on the x-axis and the line x + y + 1 = 0. Also, the orthocenter of the triangle is given as (1,1). The answer choices are provided, so I need to figure out which one is correct.
First, ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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 ... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | \boxed{J}
**Explanation:**
A CPA (Certified Public Accountant) who fraudulently issues an unqualified opinion on a corporation's materially misstated financial statements can be liable to both corporate shareholders and corporate bondholders. The key factors determining liability include the presence of fraudulent 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": 1,
"temperature": 0.7
} | 1 | 201 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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} | Okay, so I need to solve this problem where I have to find the maximum size of a complex subset of segments. A complex subset is one where all subsets have the same size, and any two segments in the same subset intersect, while segments in different subsets don't intersect.
The problem is given as a set of segments [... |
[
{
"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 with three differentiable functions: f, g, and h. The functions are defined from the real numbers to the real numbers. The problem gives me specific equations: f(x) = x³ + 3x + 2, and then g(f(x)) = x for all x in R. Also, h(g(g(x))) = x for all x in R. Then there are four opti... |
[
{
"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
} | \boxed{A} |
[
{
"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 solve this geometry problem involving two circles, C1 and C2, and their common tangents. Let me start by understanding the problem step by step.
First, C1 is a circle with radius 1 centered at the origin (0,0). C2 is a circle with radius r, centered at point A = (4,1). The key here is that 1... |
[
{
"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 set M. Let me start by understanding the problem step by step.
First, M is a disk in the plane defined by x² + y² ≤ r², where r is given as (2¹⁹⁹ - 1)√2 / 2¹⁹⁸. Let me compute that value first.
Simplify r: (2¹⁹⁹ - 1)√2 / 2¹⁹⁸. Since 2¹⁹... |
[
{
"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 how to solve this problem where Kosuke has to make a permutation simple by swapping elements, and we need to find the minimum number of operations required. Let me start by understanding the problem thoroughly.
First, the problem states that a permutation is simple if for every in... |
[
{
"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, so I need to figure out which of the statements A, B, C, D are false. Let's go through each one step by step.
Starting with statement A: $\arg(-1 - i) = \frac{\pi}{4}$. Hmm. The principal argument of a complex number is the angle in the interval $(-\pi, \pi]$. Let's recall that for a complex number $a + ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given 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
} | <think>
Okay, so I need to figure out if it's possible to rearrange N strings of length M into a new order T_1, T_2, ..., T_N such that each consecutive pair (T_i, T_{i+1}) can be made equal by altering exactly one character. The characters can be changed to any lowercase English letter. The strings are given, and 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.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
} | <think>
Okay, let me try to figure out this problem. So, the AtCoder Kingdom has a festival for N days, and they launch fireworks on M days, specifically on the A1, A2, ..., AM days. It's guaranteed that the last day, AM, is the same as N. We need to find for each day i from 1 to N, how many days later from day i the n... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: On complete hydrogenation, natural rubber produces\n(A) ethylene-propylen... | {
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"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 has the chemical formula C5H8. Isoprene is an alkene, meaning it has a double bond between the fifth and six... |
[
{
"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>
Okay, so I need to solve this problem where I have a string of digits from 1 to 9, and I have to calculate the minimum length of the string after performing a compression operation on all contiguous substrings of length k. The problem is described in the HTML, and I need to implement it in Python. Let me try 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 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
} | Okay, so I need to figure out how to solve this problem where Kevin has to perform division operations on the array `a` using the array `b` to make all elements of `a` equal to 1. The goal is to find the minimum number of operations required. Let me try to break this down step by step.
First, let's understand the prob... |
[
{
"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 need to solve this geometry problem involving an obtuse triangle with angles in arithmetic progression. The problem states that the difference between the largest and smallest angle is π/2, and all vertices lie on a circle with radius 1. We need to find (64a)^2 where a is the area of the triangle. Hm... |
[
{
"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
} | <think>
Okay, so I need to create a Python function that takes two positive integers, A and B, as input from stdin, and then prints the result of A raised to the power of B plus B raised to the power of A. Let me start by understanding the problem step by step.
First, the problem states that A and B are positive integ... |
[
{
"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>
Okay, let's see. I need to figure out how to solve this problem where Kmes has to divide cards into the minimum number of bad segments, each of which can't have a subset of cards whose product equals x. The goal is to help Kmes figure this out so he can enjoy his herring under a fur coat.
First, let me parse ... |
[
{
"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": "",
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"subject": null,
"type": null
} | <think>
Okay, so I have this problem here where I need to find the sum of all possible values of n given a sequence of positive real numbers (a₁, a₂, ..., aₙ) that satisfy these three conditions:
1. The sum of all a_i is 96.
2. The sum of the squares of all a_i is 144.
3. The sum of the cubes of all a_i is 216.
Hmm, ... |
[
{
"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 by how many times the diffusion coefficient of an ideal gas increases when the absolute temperature is quadrupled and the pressure is doubled. The problem states that the diffusion coefficient is proportional to both the mean free path and the mean speed of the gas molecules. Let m... |
[
{
"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
} | <think>
Okay, so I need to figure out how many days in a year of AtCoder have "repdigits" dates. Let me start by understanding the problem properly.
First, AtCoder's year has N months. Each month i has D_i days. A repdigit date means that both the month number i and the day number j have the same digit in their decim... |
[
{
"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 every integer time t that is covered by at least one interval has exactly one interval that is uniquely colored there. The problem is similar to a graph coloring problem where each interval is a vertex and edges... |
[
{
"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 "Bit Game (Hard Version)" problem. Let me read through the description again carefully to make sure I understand what's being asked.
The problem is about Alice and Bob playing a game where they take turns removing stones from piles. Each pile has a certain number of stones initia... |
[
{
"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, so I need to figure out the ratio of the number of anions to cations in the new structure Z, which is derived from the original ionic solid M X with a NaCl structure. Let me break down the problem step by step according to the given instructions.
First, I should recall the structure of NaCl. Sodium chlor... |
[
{
"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 figure out the percentage error in the energy stored when two capacitors are connected in series. The given values are C1 = 2000 ± 10 pF and C2 = 3000 ± 15 pF. The voltage applied is V = 5.00 ± 0.02 V. Hmm, let's start by recalling the formula for energy stored in a capacitor.
I remember th... |
[
{
"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,
"temperature": 0.7
} | 2 | 130 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to figure out which of the statements A to D are correct. The problem is about compounds from group 15 elements, which I think are the nitrogen family (N, P, As, Sb, Bi). Each statement compares different compounds in terms of their basicity, covalency, boiling point, and bond strength. I need 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: Let us consider a system of units in which mass and angular momentum a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 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 the dimensions of linear momentum, energy, force, and power in a system where mass and angular momentum are dimensionless. The given length has a dimension of L. Let me start by recalling the basic dimensions in physics. Usually, mass (M), length (L), time (T), and angular momentum... |
[
{
"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 the given options could be the modulus of a complex number z, given that both the real and imaginary parts of (\(\bar{z}\)^2 + \(\frac{1}{z^2}\)) are integers. Hmm, let's break this down step by step.
First, let me recall that if z is a complex number, then \(\bar{z}\) is... |
[
{
"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 figure out how to solve this problem where I have to find the sum of the squares of all special elements in an array. Let me start by understanding the problem again.
We have a 1-indexed integer array `nums` of length `n`. An element `nums[i]` is called special if `i` divides `n` (i.e., `n %... |
[
{
"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 how to solve this problem where Egor is playing a game with a deck of cards, and I have to determine the maximum number of rounds he can win. Let me start by understanding the problem again.
**Problem Statement:**
Egor has a deck of n cards. Each card has a number a_i. He wants 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 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 if it's possible to make the two bags equal by moving numbers around. Let me start by understanding the problem again.
We have two bags. The first bag starts with n numbers, and the second is empty. We can do two operations:
1. Move a number from the first bag to the second.
2. I... |
[
{
"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
} | \boxed{A}
Product differentiation is a key concept in monopolistic competition. It refers to the process by which firms distinguish their products from those of their competitors. This differentiation can take various forms, such as varying product features, quality, design, or pricing. The importance of product diffe... |
[
{
"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 from uranium-238, then thorium-234, then protactinium-234, then something called Z, which is then decaying into thorium-230. The question is about identifying what kind of particles or radiation x1, x2, x3, x4 are, an... |
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