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": "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.This problem is an easier version of Problem G.\n\nThere is a slot machine with three reels.\r\nThe arrangement of sym... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 281 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Here's the Python function to solve the problem. The function is designed to be self-contained and follows the guidelines provided. It takes the input from standard input, processes it, and prints the result.
```python
import sys
def find_min_time(M, reels):
# Convert the list of reels into a list of tuples cont... |
[
{
"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.Team Takahashi and Team Aoki are playing a baseball game, with Team Takahashi batting first.\nCurrently, the game has ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 431 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
def min_runs_needed():
import sys
input = sys.stdin.read
data = input().strip().split()
A = list(map(int, data[:9]))
B = list(map(int, data[9:]))
total_A = sum(A)
total_B = sum(B)
remaining_B = total_A - total_B
if remaining_B >= 0:
return max(0, (total_... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: What is the concentration of calcium ions in a solution containing 0.02 M stochiometric Ca-EDTA complex (we assume that the pH is ideal, T = 25 °C). KCa-EDTA = 5x10^10.\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 16 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the concentration of calcium ions in a solution that has a 0.02 M concentration of the Ca-EDTA complex. The given dissociation constant for the complex is KCa-EDTA = 5 × 10¹⁰. Hmm, let's break this down step by step.
First, I remember that the Ca-EDTA complex can dissociate into calcium... |
[
{
"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 | 190 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have two arrays, a and b, both of length n. The goal is to find the maximum product P = product of min(a_i, b_i) after rearranging b. Then, there are q modifications where each can either increase a_x by 1 or b_x by 1, and after each modification, I need to output t... |
[
{
"content": "Problem: What is $1^{(2^{235423523})}$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 65 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what 1 raised to the power of 2 raised to the power of 235423523 is. Hmm, let's start by breaking down the problem step by step.
First, the expression is 1^(2^235423523). Let me recall some basic exponent rules. I know that any number raised to any power is still 1 if the base is... |
[
{
"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: In a photoelectric experiment a parallel beam of monochromatic... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 160 | JEEBench | {
"expected_answer": "24",
"problem_id": "13",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, let's try to solve this problem step by step. First, let me read through the problem again to make sure I understand all the details.
We have a photoelectric experiment where a parallel beam of monochromatic light with a power of 200 W is incident on a perfectly absorbing cathode. The work function of th... |
[
{
"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 an integer N between 1 and 9, inclusive, as input.\nConcatenate N copies of the digit N and print the re... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 346 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def concatenate_digit_n():
n = int(input().strip())
result = str(n) * n
print(result)
# Call the function
concatenate_digit_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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 2 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have a tree with n vertices, and we need to remove two vertices exactly twice each, and find the maximum number of connected components we can get. Hmm. Let me try to understand the problem first.
First, the tree structure. A tree with n vertices has n-1 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 156 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where there's a robot in a rectangle, moving according to a script. The script is a string of moves: L, R, U, D, which make the robot move left, right, up, or down. But if the robot tries to go outside the rectangle, it flips all the Ls and Rs or all the Us and Ds. Then it ... |
[
{
"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: For a polynomial $g(x)$ with real coefficients, let $m_{g}$ de... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 275 | JEEBench | {
"expected_answer": "3",
"problem_id": "53",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Alright, so I need to find the minimum possible value of the sum of the number of distinct real roots of a polynomial f and its second derivative f'' in the set S. The set S consists of polynomials of the form (x² - 1)² multiplied by a cubic polynomial with real coefficients. Let me break this down step by 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: A block with mass $M$ is connected by a massless spring with stiffness... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 48 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to tackle this problem step by step. So, we have a block of mass M oscillating on a massless spring with stiffness constant k, attached to a rigid wall. The block is moving without friction on a horizontal surface, and it's oscillating with small amplitude A around an equilibrium position x₀. No... |
[
{
"content": "Problem: Let \\(O=(0,0)\\), \\(A=\\left(\\tfrac{1}{2},0\\right)\\), and \\(B=\\left(0,\\tfrac{\\sqrt{3}}{2}\\right)\\) be points in the coordinate plane. Let \\(\\mathcal{F}\\) be the family of segments \\(\\overline{PQ}\\) of unit length lying in the first quadrant with \\(P\\) on the \\(x\\)-axi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 11 | AIME24 | {
"expected_answer": "23",
"problem_id": "aime24-11",
"reference_solution": "Begin by finding the equation of the line $\\overline{AB}$ : $y= -\\sqrt{3}x+\\frac{\\sqrt{3}}{2}$ Now, consider the general equation of all lines that belong to $\\mathcal{F}$ . Let $P$ be located at $(a,0)$ and $Q$ be located... | <think>
Okay, so I need to solve this problem where there are points O, A, and B in the coordinate plane. O is at (0,0), A is at (1/2, 0), and B is at (0, sqrt(3)/2). Then there's this family of segments PQ, which are unit lengths in the first quadrant, with P on the x-axis and Q on the y-axis. The question is about a ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 350 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have an undirected graph with n vertices and m edges. The goal is to make the graph cool by performing operations where I choose three distinct vertices a, b, and c, and for each of the edges (a,b), (b,c), and (c,a), I either add or remove them if they exist or don'... |
[
{
"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 | 346 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether it's possible to insert plus and multiplication signs into a sequence of numbers such that the sum equals a given target. The problem allows using only these two operations, and we have to follow the order of operations where multiplication happens before addition. The inpu... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and the j-th column... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 367 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if it's possible to make a contiguous subgrid of size KxK entirely of 'o's by changing cells from '.' to 'o', and if possible, find the minimum number of operations needed. Here's the step-by-step approach:
1. **Understand the Problem**:
- We have an HxW grid with some ce... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 77 | JEEBench | {
"expected_answer": "CD",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Alright, let me try to figure out why the color of X₂ molecules changes from yellow to violet as we go down group 17. Hmm, okay, so the question is about group 17 elements, which are the halogens: fluorine, chlorine, bromine, iodine, and astatine. Their molecular forms, like F₂, Cl₂, Br₂, I₂, and At₂, are diato... |
[
{
"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: Gene flow between populations results in\nOptions: A. disruption of Hardy-Weinberg equilibrium in the metapopulation, B. an increased likelihood of s... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's recall what gene flow is and its effects on populations. Gene flow refers to the transfer of genetic material from one population to another. This can happen through migration, where individuals move between populations, leading to the exchange of genes.
Now, let's analyze each ... |
[
{
"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 | 126 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have two strings, a and b, and I need to find the minimum length of a string that contains a as a substring and b as a subsequence. Hmm, let's break this down step by step.
First, let me understand the problem again. For each test case, we have two strings a and 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 37 | CodeElo | {
"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 array a into array b using the three allowed operations: increasing or decreasing an element in a, or copying an element from a and appending it to the end. The problem is given multiple test cases, each with their own n, a, 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 an integer B.\nIf there exists a positive integer A such that A^A = B, print its value; otherwise, outpu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 317 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import math
def find_A(B):
def is_perfect_power(n, k):
return n == k**k
A = 1
while A**A <= B:
if is_perfect_power(B, A):
return A
A += 1
return -1
def main():
B = int(input().strip())
result = find_A(B)
print(result)
if __name__ == "__main__":
mai... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: From laboratory measurements we know that a particular spectral line formed by hydrogen appears at a wavelength of 486.1 nanometers (nm). The spectru... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 335 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what conclusion we can draw from the fact that the wavelength of a hydrogen spectral line in a star's spectrum is different from the one in the laboratory. Let me recall what I know about spectral lines and redshifts.
First, in the laboratory, we have the rest wavelength of the hy... |
[
{
"content": "Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | <think>
Okay, so I need to solve this system of logarithmic equations and then find the value of |log₂(x⁴y³z²)|. Let me start by writing down the given equations again to make sure I have them right:
1. log₂(x / (yz)) = 1/2
2. log₂(y / (xz)) = 1/3
3. log₂(z / (xy)) = 1/4
Hmm, each equation is a logarithm equal to a 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 plot of the number of neutrons $(N)$ against the number of protons $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 17 | JEEBench | {
"expected_answer": "BD",
"problem_id": "25",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Alright, let me try to figure out this problem. So, the question is about the modes of decay for unstable nuclei where the ratio of neutrons to protons (N/P) is less than 1. And we need to determine which of the given options (A, B, C, D) are possible modes of decay.
First, I remember that in stable nuclei, 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": 2,
"temperature": 0.7
} | 2 | 82 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have an array of non-negative integers, and I need to find the k-th smallest value over all subarrays of length at least 2. The value of a subarray is defined as the minimum value of a_i XOR a_j where l ≤ i < j ≤ r.
First, let me try to understand the problem. For... |
[
{
"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 | 220 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out this game where Turtle and Piggy take turns modifying a sequence. The goal is to determine the value of the first element, a₁, when both players play optimally. Let me try to break this down step by step.
First, let's understand the game rules again. The sequence starts with lengt... |
[
{
"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 cyanide process of gold extraction involves leaching out gold from... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out the correct options for this cyanide process of gold extraction problem. Let me start by recalling what I know about the cyanide process.
First, the cyanide process, also known as the Werner process, is used to extract gold from its ores. The key steps involve dissolving the gold... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two 0-indexed integer arrays nums1 and nums2 of even length n.\nYou must remove n / 2 elements from nums1 and n / 2 elements from nums2. After th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 150 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the size of the set s after removing n/2 elements from both nums1 and nums2. Then, the remaining elements are inserted into the set. The goal is to return the maximum possible size of this set. Let me break this down step by step.
First, let's understand the proble... |
[
{
"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 | 232 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have to calculate the sum of the minimum number of operations needed to make each subarray a palindrome. Hmm, okay. Let me try to break this down step by step.
First, let me understand the problem better. We have an array 'a' with n integers. For each subarray f... |
[
{
"content": "Problem: Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\overline{IA}\\perp\\overline{OI}$ , circumradius $13$ , and inradius $6$ . Find $AB\\cdot AC$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 9 | AIME24 | {
"expected_answer": "468",
"problem_id": "aime24-9",
"reference_solution": "By Euler's formula $OI^{2}=R(R-2r)$ , we have $OI^{2}=13(13-12)=13$ . Thus, by the Pythagorean theorem, $AI^{2}=13^{2}-13=156$ . Let $AI\\cap(ABC)=M$ ; notice $\\triangle AOM$ is isosceles and $\\overline{OI}\\perp\\overline{AM}$ ... | <think>
Okay, so I need to find the product AB·AC in triangle ABC where the circumradius R is 13, the inradius r is 6, and the circumcenter is O with the incenter I such that IA is perpendicular to OI. Hmm, let me start by recalling some relevant theorems and formulas.
First, I remember that in any triangle, the circu... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums and an integer threshold.\nFind the length of the longest subarray of nums starting at index l and ending at index... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 52 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to write a function that finds the longest subarray in nums where the first element is even, the subsequent elements alternate in parity (even and odd), and all elements are less than or equal to the threshold. Let me break this down step by step.
First, let me understand the problem again. ... |
[
{
"content": "Problem: Find the sum of all complex solutions of the equation\n\\[\\frac{1}{x^2 - 1} + \\frac{2}{x^2 - 2} + \\frac{3}{x^2 - 3} + \\frac{4}{x^2 - 4} = 2010x - 4.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 478 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve the equation:
\[
\frac{1}{x^2 - 1} + \frac{2}{x^2 - 2} + \frac{3}{x^2 - 3} + \frac{4}{x^2 - 4} = 2010x - 4
\]
and find the sum of all complex solutions. Hmm, let's start by understanding the equation. It's a combination of rational functions on the left side and a linear function on 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": 2,
"temperature": 0.7
} | 2 | 147 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many pairs (a, b) exist for each given n where K1o0n's solution accidentally converts the multiplication and subtraction steps into string operations but still manages to get the correct numerical result. Hmm, let me break this down.
First, let's understand K1o0n's mistake. He... |
[
{
"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 | 229 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this graph problem where I have a connected weighted undirected graph, and there are queries about the k-th maximum weight of edges on paths from a to b. The challenge is that for each query, we need to find the smallest weight such that among all paths from a to b, the k-th maximum wei... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: An electron is moving along the horizontal axis from the left with a Lorentz factor of 4. A positron is also moving along the horizontal axis, but from the right with a ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 114 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the angle between the two photons produced when an electron and a positron annihilate. The problem mentions that the electron has a Lorentz factor of 4 and the positron has a Lorentz factor of 2. After the collision, each photon is moving in a different direction: one upper-right a... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider two electrons are in p orbital angular momentum state. Ignoring there spin angular momentum, the coupled angular momentum state of the 2-electron system is repr... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 66 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let me try to figure out this problem. So, we have two electrons in p-orbital angular momentum states, and we need to find the joint probability that both L₁ᶻ and L₂ᶻ (the z-components of their angular momenta) are -ħ. Hmm, okay. Let me start by recalling some quantum mechanics basics.
First, each ele... |
[
{
"content": "Problem: How many positive perfect squares less than $2023$ are divisible by $5$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 16 | AMC23 | {
"expected_answer": "8",
"problem_id": "18",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many positive perfect squares less than 2023 are divisible by 5. Hmm, let's start by recalling what a perfect square is. A perfect square is a number that can be expressed as the square of an integer. So, like 1, 4, 9, 16, and so on.
First, I need to find all the perfect squa... |
[
{
"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 | 499 | JEEBench | {
"expected_answer": "0.25",
"problem_id": "15",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I have this problem here about an obtuse-angled triangle ABC where the sides are in arithmetic progression, the vertices lie on a circle of radius 1, and the difference between the largest and smallest angles is π/2. I need to find the inradius of the triangle. Hmm, let me try to break this down step b... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Reaction of $\\mathbf{x} \\mathrm{g}$ of $\\mathrm{Sn}$ with $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 355 | JEEBench | {
"expected_answer": "3.57",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Alright, let me try to figure out this problem step by step. So, we have a reaction where tin (Sn) reacts with HCl to form a salt. Then, that salt reacts with nitrobenzene (which has a mass of y g) in the presence of HCl to produce 1.29 g of an organic salt quantitatively. We need to find the value of x, which ... |
[
{
"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 | 279 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether it's possible to add exactly n directed edges between two strongly connected graphs such that each outgoing vertex in one graph connects to an incoming vertex in the other graph, and vice versa, with the additional constraint that the length of any cycle in the resulting gr... |
[
{
"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 positive integer N.\r\nIf there are integers x and y such that N=2^x3^y, print Yes; otherwise, print N... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 300 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Here's a Python function that solves the problem as described. The function checks if the given integer N can be expressed as 2^x multiplied by 3^y for some non-negative integers x and y. If such x and y exist, the function prints "Yes"; otherwise, it prints "No".
The approach involves factorizing N into its prime fa... |
[
{
"content": "Problem: Let $ABC$ be a triangle inscribed in circle $\\omega$ . Let the tangents to $\\omega$ at $B$ and $C$ intersect at point $D$ , and let $\\overline{AD}$ intersect $\\omega$ at $P$ . If $AB=5$ , $BC=9$ , and $AC=10$ , $AP$ can be written as the form $\\frac{m}{n}$ , wher... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 24 | AIME24 | {
"expected_answer": "113",
"problem_id": "aime24-24",
"reference_solution": "From the tangency condition we have $\\let\\angle BCD = \\let\\angle CBD = \\let\\angle A$ . With LoC we have $\\cos(A) = \\frac{25+100-81}{2*5*10} = \\frac{11}{25}$ and $\\cos(B) = \\frac{81+25-100}{2*9*5} = \\frac{1}{15}$ . Then, ... | <think>
Alright, let me try to figure out this problem. So, we have triangle ABC inscribed in a circle ω. The tangents at B and C intersect at point D, and then the line AD intersects the circle again at point P. We need to find the length of AP, which is expressed as m/n, and then find m + n where m and n are relative... |
[
{
"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 permutation P = (P_1, P_2, \\dots, P_N) of (1, 2, \\dots, N).\nA length-K sequence of indices (i_1, i_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 441 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | from collections import defaultdict, Counter
from typing import List
def find_min_iK_i1(N: int, K: int, P: List[int]) -> int:
def is_good_sequence(i1: int, iK: int) -> bool:
subsequence = sorted(P[i1:iK+1])
consecutive = list(range(subsequence[0], subsequence[0] + K))
return subsequence == ... |
[
{
"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: $5.00 \\mathrm{~mL}$ of $0.10 \\mathrm{M}$ oxalic acid solutio... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 255 | JEEBench | {
"expected_answer": "0.11",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the concentration of the NaOH solution. The problem says that we have 5.00 mL of 0.10 M oxalic acid, and we're titrating it with NaOH using phenolphthalein as an indicator. The volumes of NaOH used in five experiments are given: 12.5, 10.5, 9.0, 9.0, 9.0 mL. Hmm, let me think about how t... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A word is considered valid if:\n\nIt contains a minimum of 3 characters.\nIt contains only digits (0-9), and English letters (uppercase and lowercase).\nIt inc... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 492 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to create a function that checks if a given word is valid based on certain criteria. Let me break down the requirements first. The function should return `true` if the word is valid and `false` otherwise. The validation rules are:
1. The word must be at least 3 characters long.
2. It can onl... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: List-I shows different radioactive decay processes and List-II provides p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 474 | JEEBench | {
"expected_answer": "A",
"problem_id": "31",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | <think>
Okay, so I need to figure out which emitted particles correspond to each of these radioactive decay processes. Let me start by recalling some basic concepts about radioactivity.
First, there are three main types of radioactive decay: alpha (α), beta plus (β+), and beta minus (β-). Each type involves the emiss... |
[
{
"content": "Problem: A rectangular field is enclosed in an athletic track, as shown below. The track consists of two edges of the field, and two semicircles. The length of the track is 400 meters. What is the largest possible area of the field, in square meters?\n\n[asy]\nunitsize(1 cm);\n\nfilldraw((0,0)-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 382 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the largest possible area of a rectangular field that's enclosed by an athletic track. The track consists of two edges of the field and two semicircles. The total length of the track is 400 meters. Hmm, let me visualize this. The field is a rectangle with a track around it, which include... |
[
{
"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 | 198 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a template array and several strings, and we need to check if each string matches the template based on certain conditions. Let me try to break this down step by step.
First, let me restate the problem in my own words. We have an array of integers (the templa... |
[
{
"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: How many $3 \\times 3$ matrices $M$ with entries from $\\{0,1,2\\}$ are t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 112 | JEEBench | {
"expected_answer": "B",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to figure out how many 3x3 matrices with entries from {0,1,2} have the property that the sum of the diagonal entries of M^T M is 5. Hmm. Let's start by understanding what M^T M means.
First, M is a 3x3 matrix, so M^T is its transpose. Multiplying M^T by M should give another 3x3 matrix where t... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed string s that consists of digits from 0 to 9.\nA string t is called a semi-repetitive if there is at most one consecutive pair of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 20 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the length of the longest semi-repetitive substring in a given string s. Let me try to break down the problem and figure out how to approach it.
First, let me recall the definition: a semi-repetitive string has at most one consecutive pair of the same digits. So, if there are two or mor... |
[
{
"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 | 118 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let's tackle this problem. So, we need to find the lexicographically largest integer array of length n where each element is from a given set S, and the condition that for all pairs i < j, the element at the gcd(i, j) index is not equal to the gcd of the elements at indices i and j. If such an array do... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N items.\r\nEach of these is one of a pull-tab can, a regular can, or a can opener.\r\nThe i-th item is desc... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 254 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to maximize the total happiness by selecting M items out of N, considering the types of items and their associated happiness. The key steps involve:
1. **Categorizing Items**: Differentiate between pull-tab cans (T=0), regular cans (T=1), and can openers (T=2). Regular cans require a can... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We dilute 20.00 cm3 0.05 M acetic acid with 20.00 cm3 water, then titrate the resulting solution with 0.1M NaOH (25 °C). What will be the value of pH at 25% titration an... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 82 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the pH at 25% titration and at the equivalence point when we dilute 20.00 cm³ of 0.05 M acetic acid with 20.00 cm³ of water, then titrate it with 0.1 M NaOH. Hmm, let's break this down step by step.
First, let's understand the problem. We start with 20.00 cm³ of 0.05 M acetic acid... |
[
{
"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 | 302 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where I have to arrange a set of rectangular stamps on an infinite grid, each stamp exactly once, and minimize the perimeter of the connected black region. The key here is to figure out how to place these stamps to minimize the total perimeter. Let me try to break this d... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 63 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where Alice and Bob are dividing a field, which is a grid of size n x m. There are k fountains on this field, and Alice wants to divide the field in such a way that she gets as many cells as possible. The tricky part is that Bob can give one of the fountains to Alice, an... |
[
{
"content": "Problem: Let $\\omega\\neq 1$ be a 13th root of unity. Find the remainder when\n \\[\\prod_{k=0}^{12}(2-2\\omega^k+\\omega^{2k})\\] \nis divided by 1000.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 12 | AIME24 | {
"expected_answer": "321",
"problem_id": "aime24-12",
"reference_solution": "\\[\\prod_{k=0}^{12} \\left(2- 2\\omega^k + \\omega^{2k}\\right) = \\prod_{k=0}^{12} \\left((1 - \\omega^k)^2 + 1\\right) = \\prod_{k=0}^{12} \\left((1 + i) - \\omega^k)((1 - i) - \\omega^k\\right)\\] Now, we consider the polynomial $x... | <think>
Okay, so I need to find the remainder when the product \(\prod_{k=0}^{12}(2-2\omega^k+\omega^{2k})\) is divided by 1000, where \(\omega\) is a 13th root of unity but not equal to 1. Hmm, let's break this down step by step.
First, since \(\omega\) is a 13th root of unity, that means \(\omega^{13} = 1\), right? ... |
[
{
"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 | 246 | CodeForces | {
"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, and I need to compute the minimum length of a compressed string for all its contiguous substrings of length exactly k. The compression operation involves splitting the string into an even number of non-empty substrings and then writing th... |
[
{
"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 | 178 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let me try to figure out this problem. So, we have a string consisting of 0s and 1s. The task is to change all the characters to 0s by performing the minimum number of operations. Each operation allows us to select a non-empty subsequence where no two adjacent characters are the same, then flip their b... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: S)-4-hydroxycyclohex-2-en-1-one is treated with tert-Butyldimethylsilyl chloride and triethylamine, forming product 1.\n\n1 is treated with Ph2CuLi at low temperature, f... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 27 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out the structure of product 4 step by step. The problem gives a series of reactions starting from S)-4-hydroxycyclohex-2-en-1-one and ending with product 4, which is formed by treating the previous product with aqueous HCl. We need to determine the structure of product 4 from the give... |
[
{
"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 | 208 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have a perfect binary tree of size \(2^n - 1\), and each node has a value. The goal is to count the number of different deterministic max-heaps created by applying the "add" operation exactly \(k\) times. Then, modulo the given prime \(p\).
First, let me parse ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the value of\n\\[\n\\left(\\left(\\log _{2} 9\\right)^... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 142 | JEEBench | {
"expected_answer": "8",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to solve this expression:
\[
\left(\left(\log _{2} 9\right)^{2}\right)^{\frac{1}{\log _{2}\left(\log _{2} 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _{4} 7}}
\]
Hmm, let me break it down step by step. First, I need to handle each part separately and then multiply them together. Let's start wit... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Astronomers are observing a planet with a radius of 1 Earth radius in a circular orbit, with a transit impact parameter of 0.2, around a star that has a radius 1.5 times... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 194 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out this problem. So, we have a planet with 1 Earth radius orbiting a star that's 1.5 times the Sun's radius. The first planet has a transit impact parameter of 0.2 and an orbital period of 3 days. Then there's a second planet with 2.5 times Earth's radius, and we need to find its max... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In a parallel universe where a magnet can have an isolated North or South pole, Maxwell’s equations look different. But, specifically, which of those equations are diffe... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 3 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let me try to figure out which of Maxwell's equations are different in a parallel universe where magnets can have isolated North or South poles. Hmm, okay. First, I remember that in our universe, magnets always have both North and South poles, so the magnetic field is divergence-free. But in this hypot... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: The reaction of $\\mathrm{K}_3\\left[\\mathrm{Fe}(\\mathrm{CN})_6\\right]... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 360 | JEEBench | {
"expected_answer": "C",
"problem_id": "33",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Alright, let me try to figure out this problem step by step. So, we have a scenario where different iron complexes are formed when FeSO4 solution is reacted with different reagents. The question is asking about the identity of precipitate X, which is formed when K4[Fe(CN)6] is reacted with FeSO4 in the absence ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two strings s and t of equal length n. You can perform the following operation on the string s:\n\nRemove a suffix of s of length l where 0 < l <... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 92 | 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 you can transform string s into t using exactly k operations, each of which involves moving a suffix to the front. And I need to return the number of ways to do this modulo 10^9 + 7. Let me start by understanding the problem step by step.
First, the... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two arrays of equal length, nums1 and nums2.\nEach element in nums1 has been increased (or decreased in the case of negative) by an integer, repr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 489 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out a function that can find the integer x such that when you add x to each element in nums1, it becomes equal to nums2. Both arrays are the same length, and all the elements are non-negative. The result should be the same for all elements, so x should be the same number added to ea... |
[
{
"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 | 136 | 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 two integers A and B within a given range [l, r] such that their GCD is G and the difference |A - B| is maximized. If there are multiple pairs with the same maximum distance, I should choose the one where A is minimized. If no such pair exists, I sho... |
[
{
"content": "Problem: The lengths of two opposite sides of a square are decreased by $40\\%$ while the lengths of the other two sides are increased by $50\\%$ to form a rectangle. By what percent does the square's area decrease?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 67 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem here about a square that's being transformed into a rectangle. The lengths of two opposite sides are decreased by 40%, and the other two sides are increased by 50%. I need to find out by what percent the area of the square decreases. Hmm, let me think step by step.
First, let's rec... |
[
{
"content": "Problem: Let $a,$ $b,$ $c,$ $d$ be distinct complex numbers such that $|a| = |b| = |c| = |d| = 1$ and $a + b + c + d = 0.$ Find the maximum value of\n\\[|(a + b)(a + c)(a + d)(b + c)(b + d)(c + d)|.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 204 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem where I need to find the maximum value of the expression |(a + b)(a + c)(a + d)(b + c)(b + d)(c + d)| given that a, b, c, d are distinct complex numbers on the unit circle (so |a| = |b| = |c| = |d| = 1) and their sum is zero, meaning a + b + c + d = 0. Hmm, that sounds pretty involv... |
[
{
"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.N people labeled 1,2,\\dots,N took an exam, and person i scored A_i points.\r\nOnly those who scored at least L points... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 332 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def count_passed():
N, L = map(int, input().split())
scores = list(map(int, input().split()))
passed_count = sum(1 for score in scores if score >= L)
print(passed_count)
count_passed() |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums and a positive integer k.\nYou can apply the following operation on the array any number of times:\n\nChoose any e... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 165 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out the minimum number of bit flips required to make the XOR of all elements in the array equal to k. Let me start by understanding the problem step by step.
First, the XOR operation. The XOR of a bunch of numbers is the result of bitwise XOR on all their binary representations. Th... |
[
{
"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 permutation A=(A_1,\\ldots,A_N) of (1,2,\\ldots,N).\r\nTransform A into (1,2,\\ldots,N) by performing the following operation between 0 and N-1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 429 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python function that takes a permutation of numbers from 1 to N and transforms it into the sequence (1, 2, ..., N) by swapping elements. The function should output the number of swaps needed and the pairs of indices swapped each time. Let me think about how to approach this.
First, ... |
[
{
"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 | 399 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Kevin wants to befriend matrices that satisfy a certain condition. The condition is that the minimum of the maximums of each row should be greater than or equal to the maximum of the minimums of each column. Hmm, that's a bit confusing. Let me try to parse that again.... |
[
{
"content": "Problem: Let $f$ be the unique function defined on the positive integers such that \\[\\sum_{d\\mid n}d\\cdot f\\left(\\frac{n}{d}\\right)=1\\] for all positive integers $n$. What is $f(2023)$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 12 | AMC23 | {
"expected_answer": "96",
"problem_id": "14",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to find the value of f(2023) where f is a unique function defined on positive integers such that the sum over all divisors d of n of d times f(n/d) equals 1 for all positive integers n. Hmm, okay. Let me try to parse this step by step.
First, the problem states that f is a function on positi... |
[
{
"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 | 101 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have a grid of rows and columns with some cells being '#' and others being '.'. The task is to perform at most one operation where I can choose any row and any column, and set all cells in that row and column to '#'. Then, I need to find the maximum possible size of... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two arrays nums and andValues of length n and m respectively.\nThe value of an array is equal to the last element of that array.\nYou have to div... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 478 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to divide the array `nums` into `m` contiguous subarrays such that the bitwise AND of each subarray equals the corresponding value in `andValues`. The goal is to minimize the sum of the values of these subarrays. If it's not possible, return -1.
First, let me parse the prob... |
[
{
"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 | 225 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the sum of the Minimum Excluded (MEX) values for all rows and columns in an n x m table. Each cell must contain a unique number from 0 to (n*m - 1). The MEX of a set is the smallest non-negative integer not present in the set. The total score is the sum of the MEX v... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Calculate the enthalpy of neutralization when 500 mL 0.2 M HCl, 300 mL 0.3 M H2SO4 and 200 mL 0.5 M Ba(OH)2 are mixed.\nOptions: A) -16.0 kJ, B) -3.80 kcal, C) -11.42 kc... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 133 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to calculate the enthalpy of neutralization when these three acids and base are mixed. Let me start by recalling that the enthalpy of neutralization is the heat released when an acid and a base react to form water. The standard enthalpy of neutralization for strong acids and strong bases is usua... |
[
{
"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 | 157 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Robin's brother and mother are visiting, and he has to choose the start day for each visit such that the brother's visit overlaps with the maximum number of jobs, and the mother's visit overlaps with the minimum number of jobs. If there are multiple days, he should ch... |
[
{
"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 | 68 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the winner of this polyathlon competition for each starting sport. The problem is a bit complex, but let me break it down step by step.
First, the input: we have n participants and m sports. Each participant has a binary string of length m, indicating their skills. The i-th partic... |
[
{
"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 | 127 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the minimum rating of two movies based on the reviews from viewers. Each viewer has an attitude towards each movie, which can be liked (1), neutral (0), or disliked (-1). The problem allows assigning each viewer to review either the first or the second movie. The go... |
[
{
"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: Three numbers are chosen at random, one after another with rep... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 328 | JEEBench | {
"expected_answer": "76.25",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Alright, let's tackle this problem step by step. The question is asking for the value of \(\frac{625}{4} p_{1}\), where \(p_{1}\) is the probability that the maximum of three randomly chosen numbers (with replacement) from the set \(\{1, 2, 3, \ldots, 100\}\) is at least 81.
First, I need to understand what \... |
[
{
"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: According to the Arrhenius equation,\n(A) a high activation energy usu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 16 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "24",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Alright, let me try to work through this problem step by step. So, the question is about the Arrhenius equation, and we have four options to consider. The goal is to figure out which of these statements are correct based on the Arrhenius equation. Let me recall what the Arrhenius equation is. If I remember corr... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed string array words having length n and containing 0-indexed strings.\nYou are allowed to perform the following operation any number o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out the maximum number of palindromes I can get from the given list of words by swapping characters between different words. Let me start by understanding the problem better.
First, the goal is to maximize the number of palindromes in the list by swapping characters between any two... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: An $\\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 317 | JEEBench | {
"expected_answer": "4",
"problem_id": "17",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | <think>
Okay, so I have this problem here where there's an α-particle and a singly charged sulfur ion. Both are initially at rest and get accelerated through a potential V. Then, they enter a region with a uniform magnetic field perpendicular to their velocities, causing them to move in circular orbits. The question is... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The |3,0,0\\rangle state in the standard notation |n,l,m\\rangle of the H -atom in the non-relativistic theory decays to the state |1,0,0\\rangle via two dipole transiti... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 55 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which transition route and probability are correct for the decay of the |3,0,0⟩ state to the |1,0,0⟩ state via two dipole transitions. Let me start by recalling some basics about atomic transitions and dipole transitions.
First, in non-relativistic quantum mechanics, the Hydrogen ... |
[
{
"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 concept of bureaucracy has come to have very negative connotationstoday. Discuss those factors you believe are responsiblefor this negative attit... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 168 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | The negative attitude toward bureaucracy can be attributed to several factors. First, Weber's bureaucratic approach is often criticized for its lack of regard for individual needs and its assumption that humans are predictable, which can lead to a dehumanizing work environment (C). Additionally, the strict adherence to... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.An element x of an integer array arr of length m is dominant if freq(x) * 2 > m, where freq(x) is the number of occurrences of x in arr. Note that this definit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 69 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out the minimum index to split the array so that both halves have the same dominant element. Let me start by understanding the problem step by step.
First, the definition of a dominant element: an element x in the array is dominant if its frequency multiplied by 2 is greater than t... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Astronomers are searching for exoplanets around two stars with exactly the same masses. Using the RV method, they detected one planet around each star, both with masses ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 103 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many times longer the orbital period of planet #2 is compared to planet #1. Both stars have the same mass as the Sun, and each has a Neptune-mass planet in a circular orbit. The key difference is the periodic shift of the spectral line in the star's spectrum due to the planet's... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums, where each number in the array appears either once or twice.\nReturn the bitwise XOR of all the numbers that appear twice in the a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 509 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to write a Python function that takes an array of numbers as input. Each number in the array either appears once or twice. The function should return the bitwise XOR of all numbers that appear twice, or 0 if no number appears twice. Let me think through this step by step.
First, I need to fi... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a binary string s, partition the string into one or more substrings such that each substring is beautiful.\nA string is beautiful if:\n\nIt doesn't conta... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 65 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to partition a binary string into the minimum number of beautiful substrings. Each substring has to be a binary representation of a power of 5 and can't have leading zeros. If it's impossible, return -1. Let me start by understanding the problem better.
First, powers of 5 i... |
[
{
"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.We define Extended A strings, Extended B strings, Extended C strings, and Extended ABC strings as follows:\n\n- A stri... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 365 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def is_extended_abc(s):
i = 0
while i < len(s):
count = 1
while i + 1 < len(s) and s[i] == s[i + 1]:
count += 1
i += 1
if s[i] not in 'ABC':
return 'No'
if count == 1:
return 'No'
if s[i] == 'A':
a_count = count
... |
[
{
"content": "Problem: How many digits are in the base-ten representation of $8^5 \\cdot 5^{10} \\cdot 15^5$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 17 | AMC23 | {
"expected_answer": "18",
"problem_id": "19",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many digits are in the base-ten representation of \(8^5 \cdot 5^{10} \cdot 15^5\). Hmm, let me start by breaking this down.
First, maybe I should simplify the expression step by step. Let's see, \(8^5\) is 8 raised to the 5th power, \(5^{10}\) is 5 to the 10th, and \(15^5\) 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 are the results of fertilization?\nOptions: A. Creation of multiple cells, apoptosis, gene silencing, and evolutionary adaptation, B. Fusion of ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 145 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which of these options correctly describes the results of fertilization. Let me start by recalling what fertilization is. Fertilization is the process where two gametes (usually a sperm and an egg) fuse, leading to the formation of a zygote. This zygote then divides and differentia... |
[
{
"content": "Problem: There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of a $5\\times5$ grid such that: each cell contains at most one chip all chips in the same row and all ch... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 8 | AIME24 | {
"expected_answer": "902",
"problem_id": "aime24-8",
"reference_solution": "The problem says \"some\", so not all cells must be occupied.\nWe start by doing casework on the column on the left. There can be 5,4,3,2, or 1 black chip. The same goes for white chips, so we will multiply by 2 at the end. There is $1$... | <think>
Okay, so I have this problem where I need to find the number of ways to place 25 white chips and 25 black chips on a 5x5 grid. The conditions are that each cell can have at most one chip, and all chips in the same row or column must be the same color. Also, placing any additional chip would violate one of these... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let the function $f:[0,1] \\rightarrow \\mathbb{R}$ be defined... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 309 | JEEBench | {
"expected_answer": "19",
"problem_id": "52",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to find the value of this sum: f(1/40) + f(2/40) + ... + f(39/40) minus f(1/2), where the function f(x) is 4^x divided by (4^x + 2). Hmm. Let me start by understanding the function and the problem better.
First, let's write down the function again to make sure I have it right. f(x) = 4^x / (4^x... |
[
{
"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 | 373 | JEEBench | {
"expected_answer": "D",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, let's try to tackle this problem step by step. First, let me make sure I understand what's being asked here.
We have a set M, which is a disk in the plane with center at the origin (0,0) and radius r = 1025/513. So, M is all points (x, y) such that x² + y² ≤ (1025/513)². That's straightforward.
Then 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": 2,
"temperature": 0.7
} | 2 | 437 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the winner of this game where Alice and Bob move along a tree, starting from different vertices and trying to avoid being stuck with no moves. The problem is given multiple test cases, each with a tree and a path from u to v. For each vertex along that path, I have to determine 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.A DDoS-type string is a string of length 4 consisting of uppercase and lowercase English letters satisfying both of th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 195 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
import sys
def count_non_ddos_strings(input_str):
MOD = 998244353
n = len(input_str)
dp = [0] * (n + 1)
dp[0] = 1
for i in range(1, n + 1):
if input_str[i - 1] == '?':
dp[i] = (dp[i - 1] * 52) % MOD
else:
if input_str[i - 1].islower() or input_str[... |
[
{
"content": "Problem: Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$ , $AC=BD= \\sqrt{80}$ , and $BC=AD= \\sqrt{89}$ . There exists a point $I$ inside the tetrahedron such that the distances from $I$ to each of the faces of the tetrahedron are all equal. This distance can be written in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 28 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-28",
"reference_solution": "Notice that \\(41=4^2+5^2\\), \\(89=5^2+8^2\\), and \\(80=8^2+4^2\\), let \\(A~(0,0,0)\\), \\(B~(4,5,0)\\), \\(C~(0,5,8)\\), and \\(D~(4,0,8)\\). Then the plane \\(BCD\\) has a normal\n\\begin{equation*}\n\\mathbf n:=\\frac14\\overright... | <think>
Okay, so I need to find the distance from a point I inside a tetrahedron ABCD to each of its faces, given the edge lengths. The tetrahedron has edges AB, CD, AC, BD, BC, AD with lengths √41, √41, √80, √80, √89, √89 respectively. The point I is the incenter, equidistant from all faces, and the distance is to be ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array of integers nums. Return the length of the longest subarray of nums which is either strictly increasing or strictly decreasing.\n \nExam... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 472 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the length of the longest subarray in nums that's either strictly increasing or strictly decreasing. Let me start by understanding the problem step by step.
First, the function should take an array of integers, `nums`, and return the length of the longest subarray that is either s... |
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