context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 8
values | metadata dict | model_outputs stringlengths 1 888k |
|---|---|---|---|---|---|---|
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Identify the compound C9H11NO2 using the given data.\nIR: medium to strong intensity bands at 3420 cm-1, 3325 cm-1\nstrong band at 1720 cm-1\n1H NMR: 1.20 ppm (t, 3H); 4... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 46 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's see. The problem is to identify the compound C9H11NO2 using the given data. The data includes IR and 1H NMR spectra.
First, I need to look at the structure of the compound. The formula is C9H11NO2. So the compound has 9 carbon atoms, 11 hydrogen, 1 nitrogen, and 2 oxygen.
The IR spectrum shows medium to strong... |
[
{
"content": "Problem: What is the product of all solutions to the equation\n\\[\\log_{7x}2023\\cdot \\log_{289x}2023=\\log_{2023x}2023\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 8 | AMC23 | {
"expected_answer": "1",
"problem_id": "10",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the equation \(\log_{7x}2023 \cdot \log_{289x}2023 = \log_{2023x}2023\), we need to use properties of logarithms. Let's start by simplifying each term.
First, recall that \(\log_b a = \frac{\log_c a}{\log_c b}\) for any base \(c\). Using this, we can rewrite each logarithm in the equation with a common base, ... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 10 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def maxSumAfterPartitioning(nums):
n, m = len(nums), max(len(row) for row in nums)
dp = [[0] * (m + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for j in range(1, m + 1):
max_value = 0
for k in range(j):
max_value = max(max_value, nums[i - 1][k])
... |
[
{
"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: Addition of excess aqueous ammonia to a pink coloured aqueous solution... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 78 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "23",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, I need to understand the reactions and properties of the complexes mentioned. Let's start by analyzing each part of the problem.
First, the aqueous solution of \(\mathrm{MCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) (X) and \(\mathrm{NH}_{4} \mathrm{Cl}\) when treated with excess aqueous ammonia ... |
[
{
"content": "Problem: The asymptotes of a hyperbola are $y = 2x - 3$ and $y = 17 - 2x.$ Also, the hyperbola passes through the point $(4,7).$ Find the distance between the foci of the hyperbola.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 409 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the distance between the foci of the hyperbola, we need to follow these steps:
1. **Determine the center of the hyperbola**: The asymptotes are given as \(y = 2x - 3\) and \(y = 17 - 2x\). The center is the intersection point of these two lines. To find the intersection, we solve the system of equations:
\[... |
[
{
"content": "Problem: For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 37 | AMC23 | {
"expected_answer": "901",
"problem_id": "47",
"reference_solution": "",
"subject": null,
"type": null
} | To determine for how many integers \( n \) the given expression represents a real number, we need to analyze the expression step by step. The expression is:
\[
\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}}
\]
First, let's simplify the numerator. The term \(\log (n^2)\) can be rewritten using the logarithm power r... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed string s, a string a, a string b, and an integer k.\nAn index i is beautiful if:\n\n0 <= i <= s.length - a.length\ns[i..(i + a.length... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 163 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def beautiful_indices(s, a, b, k):
def find_substring_indices(substring):
indices = []
for i in range(len(s) - len(substring) + 1):
if s[i:i+len(substring)] == substring:
indices.append(i)
return indices
a_indices = find_substring_indices(a)
b_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.You are given N integers A_1, A_2, \\dots, A_N.\r\nAlso, define B_i = A_i \\times A_{i+1}\\ (1 \\leq i \\leq N-1).\nPr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 410 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def generate_b_values():
import sys
input = sys.stdin.read
N = int(input())
A = list(map(int, input().split()))
B = [A[i] * A[i + 1] for i in range(N - 1)]
print(*B)
generate_b_values()
``` |
[
{
"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 has placed N gifts on a number line. The i-th gift is placed at coordinate A_i.\nYou will choose a half-open... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 313 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the maximum number of gifts that can be acquired, we need to choose a half-open interval [x, x+M) on the number line. The key is to maximize the number of gifts within this interval. Let's think about how to approach this problem.
First, the problem can be broken down into two parts: finding the optimal starti... |
[
{
"content": "Problem: Simplify $\\tan 100^\\circ + 4 \\sin 100^\\circ.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 164 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To simplify the expression \(\tan 100^\circ + 4 \sin 100^\circ\), we can use trigonometric identities. Let's start by expressing \(\tan 100^\circ\) in terms of sine and cosine. We know that \(\tan \theta = \frac{\sin \theta}{\cos \theta}\), so \(\tan 100^\circ = \frac{\sin 100^\circ}{\cos 100^\circ}\). Substituting thi... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A \"strictly binary tree\" is a binary tree in which every node that is not a leaf has two children. Suppose that for a class of strictly binary tree... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 26 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand the structure of a strictly binary tree and the given condition about the ratio of root-to-leaf paths. Let's break it down step by step.
First, a strictly binary tree is a binary tree where every non-leaf node has exactly two children. This means that the number of nodes at... |
[
{
"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: Match the reactions (in the given stoichiometry of the reactants) in List... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 482 | JEEBench | {
"expected_answer": "D",
"problem_id": "48",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To solve this problem, we need to determine the correct products for each reaction in List-I and match them with the corresponding entries in List-II. Let's analyze each reaction step by step.
### Reaction (P)
\[
\mathrm{P}_{2} \mathrm{O}_{3} + 3 \mathrm{H}_{2} \mathrm{O} \rightarrow
\]
This reaction seems to involve ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A container weighs 3.22 lb force when empty. Filled with water at 60°F the mass of the container and its contents is 1.95 slugs. Find its volume in c... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 212 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | I need to find the volume of the container when it's filled with water. Let's start by understanding the problem. The empty container weighs 3.22 lb force. When filled with water at 60°F, the total mass (container plus water) is 1.95 slugs. The density of water at 60°F is 62.4 lb force/ft³.
First, I need to convert th... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A container with $1 \\mathrm{~kg}$ of water in it is kept in s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 284 | JEEBench | {
"expected_answer": "8.33",
"problem_id": "18",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to find the temperature difference between the water and the surroundings after a long time. Let's break it down step by step.
### Step 1: Determine the Power Absorbed by the Water
The container has an effective area of \(0.05 \, \mathrm{m}^2\) through which it receives sunlight. The ave... |
[
{
"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 | 25 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def calculate_points(a, b, n, m, chip_positions, moves):
grid = [[0] * a for _ in range(b)]
for x, y in chip_positions:
grid[y-1][x-1] = 1
points_alice = 0
points_bob = 0
for move in moves:
direction, k = move[0], move[1]
if direction == 'U':
for row i... |
[
{
"content": "Problem: Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\\%$ on every pair of shoes. Carlos also knew that he had to pay a $7.5\\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 30 | AMC23 | {
"expected_answer": "50",
"problem_id": "36",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the original price of the most expensive shoes Carlos could afford, we need to account for the discount and sales tax. Let's denote the original price as \( P \).
First, the shoes are on sale with a 20% reduction. So the discounted price is \( 0.8P \). Then, a 7.5% sales tax is applied to this discounted ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s consisting of only lowercase English letters. In one operation, you can do the following:\n\nSelect any non-empty substring of s, poss... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 35 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the lexicographically smallest string after performing the operation exactly once, we need to consider the effect of the substring replacement on the entire string. The operation converts each character in a substring to the previous character in the alphabet. So, 'b' becomes 'a', 'c' becomes 'b', etc., and 'a'... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Some standard electrode potentials at $298 \\mathrm{~K}$ are given bel... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 350 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine the correct combination of metals \( \mathbf{X} \) and \( \mathbf{Y} \) that result in the dissolution of \( \mathbf{X} \), we need to analyze their electrode potentials. The solution contains \( 0.001 \, \text{M} \) of \( \mathbf{X}^{2+} \) and \( 0.1 \, \text{M} \) of \( \mathbf{Y}^{2+} \).
First, the ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider a system with Hamiltonian operator $H = \\varepsilon \\vec{\\sigma}.\\vec{n}$. Here, $\\vec{n}$ is an arbitrary unit vector, $\\varepsilon $ is a constant of di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the eigenvalues of the Hamiltonian operator \( H = \varepsilon \vec{\sigma} \cdot \vec{n} \), we need to analyze the structure of the operator. Let's start by understanding the components.
The Pauli spin matrices are:
\[
\sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad
\sigma_y = \begin{pmatrix} ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: \"Oh, I know you,\" the ribonucleoprotein particle says to the nascent chain as they meet. \"Pause there for a minute. Let me show you in; you really need some sugar.\"\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 26 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | C) ribosome to the proteasome
The dialogue between the ribonucleoprotein particle and the nascent chain suggests that the chain is entering a cellular structure, possibly a protein complex. The mention of "need some sugar" might refer to the requirement of an energy source, which could be related to the Golgi apparatu... |
[
{
"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 | 147 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to understand how K1o0n's solution works and under what conditions it gives the correct answer. Let's start by looking at the problem description.
The question is asking for the number of apples left with Noobish_Monk after he returns some to his friends. He has \( n \) friends, each givi... |
[
{
"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 | 43 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to find an array of integers that meets certain conditions. Let me start by understanding the requirements.
The problem states that for a given positive integer \( x \), I need to find an array \( a_0, a_1, \ldots, a_{n-1} \) such that:
1. The length \( n \) is between 1 and 32, inclusiv... |
[
{
"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 = \\... | To solve the given system of equations, we start by analyzing each equation. The equations are:
\[
\log_2\left(\frac{x}{yz}\right) = \frac{1}{2}
\]
\[
\log_2\left(\frac{y}{xz}\right) = \frac{1}{3}
\]
\[
\log_2\left(\frac{z}{xy}\right) = \frac{1}{4}
\]
First, we can use the properties of logarithms to rewrite each equ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A light beam is propagating through a glass with index of refraction n. The glass is moving at constant velocity v in the same direction as the beam and toward the obser... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 40 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the speed of light in a moving glass medium relative to an observer in the laboratory, we need to consider the index of refraction and the velocity of the glass.
First, the index of refraction \( n \) relates the speed of light in the medium to the speed in vacuum. Given that the speed of light in vacuum ... |
[
{
"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 the functions $f:(-1,1) \\rightarrow \\mathbb{R}$ and $g:(-1,1) \\rightarrow(-1,1)$ be defined by\n\\[\nf(... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 298 | JEEBench | {
"expected_answer": "4",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve the problem, we need to analyze the functions \( f \) and \( g \), and their composite \( f \circ g \). Let's start by understanding each function.
The function \( f(x) = |2x-1| + |2x+1| \). Let's break this down. The expressions inside the absolute values are linear. The critical points are where each linear... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A buyer contracted in writing to purchase 1,000 gidgets (which are similar to widgets but are more popular because of their greater durability and- r... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 247 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | J
The correct answer is J: there was no written agreement to the modification. The original contract was in writing, but the change in quantity from 1,000 to 800 gidgets was discussed via telephone. For modifications to a contract that's subject to the statute of frauds (which gidgets might be considered, given the si... |
[
{
"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: Aristotle claims that:\nOptions: A. vice is in our power, but virtue is not., B. virtue is in our power, and so is vice., C. vice is in our power, an... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 149 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | The correct answer is B. According to Aristotle's ethical theory, both virtue and vice are in our power. He believed that humans have the ability to choose and act in a virtuous or vicious way. So, the correct statement would be that both are in our power. Let me check the other options to make sure.
Option A says vir... |
[
{
"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 | 239 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def game_winner(l, n, m, a, b):
# a is the array to look for
# b is the matrix
# Tsovak starts, then Narek, etc.
# For each element in a, find in b, mark as visited.
# Then, for each player's turn, they need to find their element in the remaining matrix.
# If a player can't find their ... |
[
{
"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 | 35 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to understand the game dynamics and how the cards are played. Let's start by breaking down the problem.
The game is called "Slay the Spire" and involves managing a hand of cards and a draw pile. The goal is to empty either the hand or the draw pile. The cards are numbered from 1 to \( n \... |
[
{
"content": "Problem: The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? [asy]\ndraw((-.3,-3)--(.1,1)--(-1,0)--(3,0)--cycle);\nlabel(\"$A$\",(.1,1),N);\nlabel(\"$B$\",(-1,0),W);\nlabel(\"$C... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to find the area of triangle CDE given that the area of triangle ABC is 6 square centimeters and that AB is parallel to DE. Also, BD is 4 times BC.
First, let's understand the structure. Since AB is parallel to DE, triangles ABC and CDE are similar by the AA (Angle-Angle) similarity crite... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We have a large ensemble of 10.000 (ten thousand) identical systems. Each system has a particle that are the same and under the same conditions. Each particle can move a... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 38 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the numerical value of "a" from the given problem, we need to analyze the wave function and the conditions provided. Let's start by understanding the setup.
The problem states that the particles are in a region where x ranges from 1 to 3. The wave function is given as:
\[
\psi = \frac{a}{\sqrt{1 + x}} - 0... |
[
{
"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: This question refers to the following information.\n\"I travelled thence to 'Aden, the port of Yemen, on the coast of the ocean. It is surrounded by ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 381 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | F |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 372 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to find the maximum number of non-overlapping beautiful segments in the given array. Let me think through the steps.
First, a beautiful segment is defined as one where the sum of all elements from start to end is zero. So, the main idea is to find all such segments and then select the max... |
[
{
"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: Young's modulus of elasticity $Y$ is expressed in terms of three derived ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 500 | JEEBench | {
"expected_answer": "A",
"problem_id": "19",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To determine the correct values of \(\alpha\), \(\beta\), and \(\gamma\) for the expression of Young's modulus of elasticity \(Y\) in terms of the gravitational constant \(G\), Planck's constant \(h\), and the speed of light \(c\), we need to ensure that the dimensions on both sides of the equation match.
First, let's... |
[
{
"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: Area of the cross-section of a wire is measured using a screw gauge. The ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 437 | JEEBench | {
"expected_answer": "C",
"problem_id": "35",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To determine the diameter and cross-sectional area of the wire using the given screw gauge measurements, we need to analyze the data provided. Let's start by understanding the screw gauge's structure and how the readings relate to the actual dimensions.
### Screw Gauge Parameters
- **Pitch of the main scale**: $0.5 \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 | 50 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def compute_max_ones(s, t, queries):
n = len(s)
max_ones = [0] * (n + 1)
for i in range(n - 2, -1, -1):
max_ones[i] = max_ones[i + 1] + (s[i] == '1')
for i in range(n - 2, -1, -1):
if s[i] == '1' and s[i + 2] == '0' and t[i + 1] == '0':
max_ones[i] = max(max_ones[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: Marcia Baron argues that the artificiality of ticking bomb cases is problematic because\nOptions: A. the artificial assumptions are, in fact, empiri... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 321 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | I think the correct answer here is option A. The problem is that the assumptions made in ticking bomb cases, like the artificiality Marcia Baron refers to, are actually based on empirical claims that are important for the debate. So if we dismiss them as purely artificial, we might miss their actual value. But wait, 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: For $a \\in \\mathbb{R},|a|>1$, let\n\\[\n\\lim _{n \\rightarrow \\inf... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 235 | JEEBench | {
"expected_answer": "AD",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate the given limit and find the possible values of \(a\). Let's break down the problem step by step.
First, let's look at the limit expression:
\[
\lim _{n \rightarrow \infty}\left(\frac{1+\sqrt[3]{2}+\cdots+\sqrt[3]{n}}{n^{7 / 3}\left(\frac{1}{(a n+1)^{2}}+\frac{1}{(a n+2)^{2}... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Find KE of product particles in,\nPi(+) = mu(+) + nu\nhere Pi(+) is stationary.\nRest mass of Pi(+) & mu(+) is 139.6 MeV & 105.7 MeV respectively.\nOptions: A) 7.2 MeV,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 11 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the KE of product particles in the reaction where Pi(+) is stationary and converts to mu(+) and nu, we need to use the given rest masses. The rest mass of Pi(+) is 139.6 MeV, and mu(+) is 105.7 MeV. The equation is Pi(+) → mu(+) + nu.
Since the Pi(+) is stationary, the total energy after the reaction would 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 integer array nums and an integer k.\nThe frequency of an element x is the number of times it occurs in an array.\nAn array is called good if ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 147 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the length of the longest good subarray in the given integer array `nums` where each element's frequency is <= k, I can use the sliding window technique. Here's the plan:
1. **Initialize a frequency map**: To keep track of how many times each element appears in the current window.
2. **Sliding window**: Use tw... |
[
{
"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 melting point of monoclinic sulfur at a pressure of 1atm is 119.3°C. The change in volume during fusion is 41 cm^3 kg^-1 and\\DeltaH_fusis 422 ca... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 136 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | I need to find the melting point of monoclinic sulfur at 1000 atm. Let's look at the given information. The standard conditions are 1atm and 119.3°C. The change in volume during fusion is 41 cm³ kg⁻¹ and the fusion enthalpy is 422 cal mol⁻¹.
First, I should consider how pressure affects the melting point. Generally, f... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 378 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to construct a permutation \( p \) of integers \( 1, 2, \ldots, n \) that maximizes the value of \( k \) after performing a series of operations. Let's break down the problem.
### Problem Statement
Given an integer \( n \), we perform \( n \) operations where:
- For odd \( i \), \( k = k... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S consisting of lowercase English letters.\r\nRemove all occurrences of a, e, i, o, u from S an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 264 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def remove_vowels(s):
result = ''
for c in s:
if c not in 'aeiou':
result += c
print(result)
remove_vowels(input()) |
[
{
"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 compound(s) with TWO lone pairs of electrons on the central atom i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 19 | JEEBench | {
"expected_answer": "BC",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine which compounds have a central atom with two lone pairs of electrons, we need to analyze the Lewis structures of each. Let's go through each option step by step.
**Option (A): BrF₅**
- The central atom is bromine (Br).
- Br has 7 valence electrons.
- Each F atom contributes 1 electron, so 5 F atoms give 5... |
[
{
"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: Experiencing intense feelings of shame and guilt upon admitting to a counselor that a family problem exists is common among traditional\nOptions: A. ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 446 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | I think the correct answer here is C. African-Americans. The question is asking about the experience of intense shame and guilt when admitting a family problem to a counselor. These feelings are common in many cultural groups, but research has shown that African-Americans may be particularly susceptible.
Let me expla... |
[
{
"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: One mole of a monatomic ideal gas undergoes an adiabatic expan... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | JEEBench | {
"expected_answer": "900",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to find the decrease in internal energy of a monatomic ideal gas when it undergoes an adiabatic expansion where the volume becomes eight times its initial value. Let's start by recalling some key properties.
First, the internal energy \( U \) of an ideal gas depends on temperature \( T \... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence A=(A_1,\\ldots,A_N) of length N. The elements of A are distinct.\nProcess Q queries in the or... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 404 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def process_sequence():
import sys
class Node:
def __init__(self, value):
self.value = value
self.next = None
class LinkedList:
def __init__(self):
self.head = None
def insert_after(self, x, y):
current = self.head
... |
[
{
"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 | 183 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to understand the cost function and how the operations affect the chip placements. Let's start by breaking down the problem.
The goal is to find the number of ways to place exactly \( n \) chips in points from 1 to \( x \) such that the cost is equal to \( m \). The cost is defined as the... |
[
{
"content": "Problem: For how many ordered pairs $(a,b)$ of integers does the polynomial $x^3+ax^2+bx+6$ have $3$ distinct integer roots?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 27 | AMC23 | {
"expected_answer": "5",
"problem_id": "30",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the number of ordered pairs \((a, b)\) for which the polynomial \(x^3 + ax^2 + bx + 6\) has three distinct integer roots, we need to follow a systematic approach.
First, let's denote the three distinct integer roots by \(r, s, t\). Since these are roots of the polynomial, the polynomial can be expressed 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": 1,
"temperature": 0.7
} | 1 | 126 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to find the minimum possible length of a string that contains one string as a substring and another as a subsequence. Let's break it down.
First, the problem states that for each test case, we have two strings: a and b. We need to form a new string that includes a as a substring and b as ... |
[
{
"content": "Problem: Rows 1, 2, 3, 4, and 5 of a triangular array of integers are shown below.\n1\n1 1\n1 3 1\n1 5 5 1\n1 7 11 7 1\nEach row after the first row is formed by placing a 1 at each end of the row, and each interior entry is 1 greater than the sum of the two numbers diagonally above it in the prev... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 10 | AMC23 | {
"expected_answer": "5",
"problem_id": "12",
"reference_solution": "",
"subject": null,
"type": null
} | To find the unit's digit of the sum of the 2023 numbers in the 2023rd row of the given triangular array, let's first understand the pattern. The array starts with the first row as 1, each subsequent row starts and ends with 1, and interior entries are the sum of the two numbers directly above them plus 1.
Wait, the pr... |
[
{
"content": "Problem: A line is parameterized by\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} 8 \\\\ -1 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ 3 \\end{pmatrix}.\\]The equation of the line can be expressed in the form $y = mx + b.$ Enter the ordered pair $(m,b).$\nMark your solution with... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 206 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To convert the given parameterized line into the form \( y = mx + b \), I need to eliminate the parameter \( t \) and express \( y \) in terms of \( x \). Let's start by looking at the parameterized equation:
\[
\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \en... |
[
{
"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 | 138 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
import sys
from typing import List
def make_all_zeros(a: List[int], max_operations: int) -> int:
n = len(a)
if n == 1:
return 1 if a[0] == 0 else 0
operations = 0
while operations < max_operations:
possible_x = set()
for i in range(n):
for j in range(i + 1... |
[
{
"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 of H rows and W columns, each cell having a side length of 1, and we have N tiles.\nThe i-th tile (1\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 405 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | from itertools import product
from typing import List, Tuple, Set, Dict, FrozenSet
from copy import copy
def solve(h: int, w: int, n: int, a: List[int], b: List[int]) -> bool:
grid = [[0 for _ in range(w)] for _ in range(h)]
placed = set()
def place_tile(x: int, y: int, a: int, b: int, rot: int) -> None:
... |
[
{
"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 geometries of the ammonia complexes of $\\mathrm{Ni}^{2+}, \\mathrm{P... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 50 | JEEBench | {
"expected_answer": "A",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To determine the geometries of the ammonia complexes for \(\mathrm{Ni}^{2+}\), \(\mathrm{Pt}^{2+}\), and \(\mathrm{Zn}^{2+}\), we need to consider the electron configurations and the ligand field theory. Let's go through each step.
First, the ammonia (NH₃) ligand has a trigonal pyramidal shape, but when it's used as 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 | 11 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to write a Python program that calculates the number of ordered pairs (a, b) that meet the given conditions. Let me start by understanding the problem.
The conditions are:
1. \(1 \le a \le n\) and \(1 \le b \le m\).
2. \(a + b\) is a multiple of \(b \cdot \gcd(a, b)\).
First, I need to b... |
[
{
"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 having length n.\nYou are allowed to perform a special move any number of times (including zero) on nums. In one s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 151 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the minimum possible total cost to make the array `nums` equalindromic. Let's break down the problem step by step.
### Understanding the Goal
An array is considered equalindromic if all its elements are equal to a palindromic number. The task is to choose a palindromic number `y`... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A previously healthy 27-year-old nulligravid woman comes to the emergency department because of a 2-day history of moderate-to-severe pain and swelli... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 246 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B. Incision and drainage. The patient has a tender, fluctuant mass, which suggests an abscess. The most appropriate management is incision and drainage. The other options, like antibiotics, may be considered but are less urgent. Since the mass is causing introital compromise, immediate incision and drainage would be ne... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The AtCoder railway line has N stations, numbered 1, 2, \\ldots, N.\nOn this line, there are inbound trains that start... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 438 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def check_station_stop():
import sys
input = sys.stdin.readline
N, X, Y, Z = map(int, input().split())
# Determine the direction of the train (inbound or outbound)
if X < Y:
# Inbound train stops at stations 2,3,...,N
if Z > X and Z < Y:
print('Yes')
e... |
[
{
"content": "Problem: Janet rolls a standard $6$-sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal $3$? The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive inte... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 18 | AMC23 | {
"expected_answer": "265",
"problem_id": "20",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the probability that Janet's running total will equal 3 at some point during her 4 rolls, we need to consider all possible sequences of rolls that result in a total of 3. Let's break this down step by step.
First, the possible individual rolls are 1, 2, 3, 4, 5, 6. The running total is the sum of all roll... |
[
{
"content": "Problem: Simplify the following expression to a simplified fraction: $$\\sqrt{\\dfrac{\\dfrac{5}{\\sqrt{80}}+\\dfrac{\\sqrt{845}}{9}+\\sqrt{45}}{\\sqrt5}}.$$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 331 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To simplify the given expression, we need to handle the nested fractions and square roots step by step. Let's start by breaking down the problem.
The expression is:
\[
\sqrt{\dfrac{\dfrac{5}{\sqrt{80}}+\dfrac{\sqrt{845}}{9}+\sqrt{45}}{\sqrt5}}
\]
First, let's focus on the denominator of the main fraction, which is \(... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 129 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of distinct arrays \( b \) that can be generated from all possible arrays \( a \) of length \( n \) with values in the range 1 to \( k \). The construction of \( b \) is based on the distance to the closest element that is different from the current element in \( a... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: For any positive integer $n$, define $f_{n}:(0, \\infty) \\rightarrow ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 170 | JEEBench | {
"expected_answer": "D",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given function and the statements carefully. Let's start by understanding the function \( f_n(x) \).
The function is defined as:
\[
f_{n}(x)=\sum_{j=1}^{n} \tan ^{-1}\left(\frac{1}{1+(x+j)(x+j-1)}\right) \text { for all } x \in(0, \infty)
\]
First, let's simplify the argu... |
[
{
"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 | 309 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to concatenate the given arrays in a way that minimizes the number of inversions in the resulting array. Let's start by understanding the problem.
Each array has two elements. The concatenation of \( n \) such arrays would result in a single array of length \( 2n \). An inversion in an a... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $P$ be the point on the parabola $y^{2}=4 x$ which is at the short... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 65 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to go through several steps. Let's start by understanding the given equations and what's being asked.
First, the parabola is given by \( y^2 = 4x \). The circle's equation is \( x^2 + y^2 - 4x - 16y + 64 = 0 \). We need to find the point \( P \) on the parabola that is closest to the cen... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Interaction between the bosonic field X and fermions is given by\n\n\\mathcal{L}\\left(y\\right)=-\\lambda{f}\\bar{\\psi}{f}\\left(y\\right)\\left(\\upsilon+X\\left(... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 134 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the kinematically allowed decays of the boson X at the lowest order, we need to look at the possible interactions between the bosonic field X and the fermions. The given Lagrangian is:
\[
\mathcal{L}\left(y\right)=-\lambda{f}\bar{\psi}{f}\left(y\right)\left(\upsilon+X\left(y\right)\right)\psi_{f}\left(y\r... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$, ele... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 432 | JEEBench | {
"expected_answer": "4",
"problem_id": "22",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To find the value of \(\alpha + \beta + \gamma + \delta\) where the magnetic field \(B\) is expressed in terms of the given constants, we need to determine the dimensions of each constant first.
The constants are:
- Electric charge \(e\) (dimensions: [e])
- Electron mass \(m_e\) (dimensions: [m])
- Planck's constant \... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There are n balls on a table, each ball has a color black or white.\nYou are given a 0-indexed binary string s of length n, where 1 and 0 represent black and w... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 130 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the minimum number of steps to group all black balls (represented by '1's) to the right and all white balls (represented by '0's) to the left. Let's think about the structure of the string here.
First, let's consider the final configuration. The desired state is to have all '1's ... |
[
{
"content": "Problem: In how many ways can 5 students be selected from a group of 6 students?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 455 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the number of ways to select 5 students from a group of 6, we can use the concept of combinations. The combination formula is given by \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \), where \( n \) is the total number of students, and \( r \) is the number of students to be selected.
In this problem, \( n = 6 \)... |
[
{
"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 | 295 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
from math import gcd
from collections import defaultdict
mod = 10**9 + 7
def count_leaves(n, d):
leaves = 0
for i in range(1, n + 1):
leaves += count_divisors(i, d)
return leaves % mod
def count_divisors(x, d):
divisors = set()
for i in range(1, int(x**0.5) + 1):
if x % ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s consisting of lowercase English letters, and you are allowed to perform operations on it. In one operation, you can replace a characte... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 29 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def make_palindrome(s):
n = len(s)
operations = 0
for i in range(n // 2):
if s[i] != s[n - i - 1]:
operations += 1
if operations == 0:
return s
min_operations = operations
for i in range(n):
for j in range(i + 1, n):
s_list = list(s)
... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 145 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to construct a permutation that maximizes the value of the expression \(\sum_{i=1}^n f(i) - \sum_{i=1}^n g(i)\). Let's start by understanding the functions \(f(i)\) and \(g(i)\).
The function \(f(i)\) is the sum of all numbers in the prefix of length \(i\) that are not less than \(k\). S... |
[
{
"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: Use divergence therem to evaluate $\\iint_S \\vec{F} \\cdot d \\vec{S}$ where $\\vec{F} = sin(\\pi x) \\vec{i} + (z y^3)\\vec{j} + (z^2 + 4x)\\vec{k}... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 227 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To evaluate the surface integral using the divergence theorem, we first need to compute the divergence of the vector field \(\vec{F}\). The divergence is given by the sum of the partial derivatives of each component with respect to their respective variables. Let's calculate that step by step.
The vector field is:
\[
... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given an integer sequence A = (A_1, A_2, \\dots, A_N).\r\nCalculate the following expression:\n\\displaystyle ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 434 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def calculate_expression():
import sys
from itertools import combinations
# Read the input
N = int(input())
A = list(map(int, input().split()))
# Calculate the expression using combinations
total_sum = sum(max(A[j] - A[i], 0) for i, j in combinations(range(N), 2))
# Output t... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi will have N penalty kicks in a soccer match.\nFor the i-th penalty kick, he will fail if i is a multiple of ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 418 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def penalty_kicks():
N = int(input())
result = ''
for i in range(1, N + 1):
if i % 3 == 0:
result += 'x'
else:
result += 'o'
print(result)
penalty_kicks() |
[
{
"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 positive integers n and m.\nDefine two integers, num1 and num2, as follows:\n\nnum1: The sum of all integers in the range [1, n] that are not div... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 120 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def calculate_difference(n, m):
num1 = sum(x for x in range(1, n+1) if x % m != 0)
num2 = sum(x for x in range(1, n+1) if x % m == 0)
return num1 - num2
``` |
[
{
"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 $7 \\overbrace{5 \\cdots 5}^{r} 7$ denote the $(r+2)$ digit number where the first and the last digits are... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 459 | JEEBench | {
"expected_answer": "1219",
"problem_id": "10",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve this problem, we need to first understand the structure of the numbers involved. The given problem defines a number as $7 \overbrace{5 \cdots 5}^{r} 7$, which represents a number with the first and last digits as 7, and the middle $r$ digits as 5. So, for example, when $r=1$, the number is 757; when $r=2$, it'... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Consider the following statements related to colloids.\n\n(I) Lyophobic c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 506 | JEEBench | {
"expected_answer": "A",
"problem_id": "36",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To determine the correct set of statements related to colloids, let's analyze each statement one by one.
**Statement (I):** Lyophobic colloids are not formed by simple mixing of dispersed phase and dispersion medium.
- Lyophobic colloids are typically formed when the dispersed phase particles have a strong affinity f... |
[
{
"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 $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be a differentia... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 175 | JEEBench | {
"expected_answer": "0.4",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the given problem, we need to find the value of \(\lim_{x \rightarrow -\infty} f(x)\) where the function \(f: \mathbb{R} \rightarrow \mathbb{R}\) is differentiable, satisfies \(f(0) = 0\), and the differential equation \(\frac{dy}{dx} = (2 + 5y)(5y - 2)\).
First, let's analyze the differential equation. The e... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a family consisting of person 1, person 2, \\ldots, and person N. For i\\geq 2, person i's parent is person ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 237 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def count_covered_people():
N, M = map(int, input().split())
parents = list(map(int, input().split()))
covered = set([1])
insurance_covered = [set() for _ in range(M + 1)]
for i in range(1, M + 1):
x, y = map(int, input().split())
insurance_covered[i] = set(range(1, y + 2)... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 287 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to determine the number of starting cities that allow a winning strategy based on the given deadlines. Let's break down the problem step by step.
### Understanding the Problem
The cities are numbered from 1 to \( n \). The goal is to conquer each city \( i \) by time \( a_i \). The rules ... |
[
{
"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 10^9 by 10^9 squares. Let (i, j) denote the square at the (i + 1)-th row from the top and the (j ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 340 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def count_black_squares(N, queries):
# Precompute the color pattern for each cell based on the given N x N grid
pattern = [[0] * N for _ in range(N)]
for i in range(N):
for j in range(N):
color = P[i % N][j % N]
pattern[i][j] = 1 if color == 'B' else 0
# Functi... |
[
{
"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 s1 and s2, both of length 4, consisting of lowercase English letters.\nYou can apply the following operation on any of the two string... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 87 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine if two strings, s1 and s2, can be made equal using the specified operation, we need to check their characters in specific positions. The operation allows swapping characters at positions i and i+2.
First, let's look at the example. For s1 = "abcd" and s2 = "cdab", the solution involves two steps. The fir... |
[
{
"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 | 298 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
from typing import List
from dataclasses import dataclass
@dataclass
class Member:
id: int
position: int
def is_good_slideshow(n: int, m: int, a: List[Member], b: List[Member]) -> bool:
member_to_position = {member.id: member.position for member in a}
for i in range(m):
if b[i] not i... |
[
{
"content": "Problem: There exist real numbers $x$ and $y$ , both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$ . Find $xy$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | AIME24 | {
"expected_answer": "25",
"problem_id": "aime24-16",
"reference_solution": "By properties of logarithms, we can simplify the given equation to $x\\log_xy=4y\\log_yx=10$ . Let us break this into two separate equations: \\[x\\log_xy=10\\] \n \\[4y\\log_yx=10.\\] \nWe multiply the two equations to get: \n \\[4xy\\... | To solve the given problem, we need to find the value of \( xy \) where both \( x \) and \( y \) are real numbers greater than 1, and they satisfy the equations:
\[
\log_x\left(y^x\right) = 10 \quad \text{and} \quad \log_y\left(x^{4y}\right) = 10
\]
First, let's simplify each logarithmic expression.
For the first e... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: A person measures the depth of a well by measuring the time interval betw... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 97 | JEEBench | {
"expected_answer": "B",
"problem_id": "7",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To determine the fractional error in the measurement of the well's depth, we need to first understand how the depth is calculated based on the given measurements. The person measures the time interval \( T \) between dropping the stone and hearing the sound. The depth \( L \) can be calculated using the formula that ac... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 489 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def find_integer_x(nums1, nums2):
# Subtract each element of nums1 from the corresponding element in nums2
differences = [nums2[i] - nums1[i] for i in range(len(nums1))]
# Find the common difference between the two arrays
x = differences[0]
for diff in differences[1:]:
x = diff - x
... |
[
{
"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 | 372 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to find the maximum number of non-overlapping beautiful segments in an array. Let's start by understanding what makes a segment beautiful. A segment is considered beautiful if the sum of all its elements is zero.
First, I'll need to generate all possible segments in the array and then fin... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: In a bimolecular reaction, the steric factor $P$ was experimentally de... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 105 | JEEBench | {
"expected_answer": "AB",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to understand the role of the steric factor \( P \) in a bimolecular reaction. Let's start by recalling some key concepts.
The Arrhenius equation relates the frequency factor (also known as the pre-exponential factor) \( A \) to the activation energy \( E_a \):
\[ k = A e^{-\frac{E_a}{RT... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are at a fruit market with different types of exotic fruits on display.\nYou are given a 1-indexed array prices, where prices[i] denotes the number of coin... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 137 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the minimum number of coins required to purchase all the fruits. Let's think about the optimal strategy here.
First, the problem states that if you purchase the i-th fruit for prices[i] coins, you can get the next i fruits for free. So, the key here is to decide which fruit to p... |
[
{
"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 has created a game where the player controls a dragon on a coordinate plane.\nThe dragon consists of N parts... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 358 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def dragon_game():
N, Q = map(int, input().split())
parts = [[i, 0] for i in range(1, N+1)]
head = parts[0]
for _ in range(Q):
query = input().split()
if query[0] == '1':
direction = query[1]
if direction == 'U': dx, dy = 0, 1
elif direction ... |
[
{
"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 study about a pandemic, data of 900 persons was collected... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 378 | JEEBench | {
"expected_answer": "0.8",
"problem_id": "3",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To find the probability that a person has at most one symptom, we need to consider the different scenarios where the person has zero, one, or two symptoms, but not all three. Let's start by understanding the data.
The total number of persons is 900. The counts for each symptom and their combinations are given. Let's d... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: A person measures the depth of a well by measuring the time interval betw... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 97 | JEEBench | {
"expected_answer": "B",
"problem_id": "7",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To determine the fractional error in the measurement of the well's depth, we need to consider how the errors in time and the derived depth affect the final result. Let's start by understanding the relationship between the variables.
The depth of the well, \( L \), can be calculated using the time interval \( T \) and ... |
[
{
"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: There are three bags $B_{1}, B_{2}$ and $B_{3}$. The bag $B_{1}$ conta... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 206 | JEEBench | {
"expected_answer": "AB",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to use the given information about the balls in each bag and the probabilities of selecting each bag. Let's break down each part step by step.
First, let's recall the structure:
- Bag \( B_1 \): 5 red, 5 green. Probability of selecting \( B_1 \) is \( \frac{3}{10} \).
- Bag \( B_2 \): 3 ... |
[
{
"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_0,A_1,\\dots,A_{63}) of length 64 consisting of 0 and 1.\nFind A_0 2^0 + A_1 2^1 + \\dot... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 218 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def compute_value():
import sys
from functools import reduce
# Read the input sequence
sequence = list(map(int, input().split()))
# Compute the value using bitwise operations
value = reduce(lambda acc, x: (acc << 1) | x, sequence)
# Print the result as an integer
print(value... |
[
{
"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 $\\Gamma$ denote a curve $y=y(x)$ which is in the first quadrant a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 209 | JEEBench | {
"expected_answer": "AB",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to use the given condition that the length of \( P Y_P \) is 1 for each point \( P \) on the curve \( \Gamma \). Let's break down the steps.
First, the point \( P \) is on the curve, so let's denote it as \( P(x, y) \). The tangent to the curve at \( P \) has a slope of \( y'(x) \). 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": 2,
"temperature": 0.7
} | 2 | 216 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to write a Python program that finds the maximum total score for a successful performance. Let's start by understanding the requirements.
### Problem Overview
The performance has rounds where either Lelle or Flamm wins. The match is successful if after every round, the greatest common di... |
[
{
"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 binary string s having an even length.\nA string is beautiful if it's possible to partition it into one or more substrings such that:... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 121 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to make sure that the binary string can be partitioned into substrings where each substring is either all '0's or all '1's and has an even length. Let's think about the structure of such a string.
First, if a string is already made up of alternating blocks of '0's and '1's with each bloc... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The correct statement(s) about the oxoacids, $\\mathrm{HClO}_{4}$ and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 76 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine the correct statements about the oxoacids HClO4 and HClO, let's analyze each option step by step.
**Option [A]: The central atom in both HClO4 and HClO is sp3 hybridized.**
First, let's look at the structure of each acid. The central atom in HClO4 is chlorine. To determine the hybridization, we need to c... |
[
{
"content": "Problem: Find the remainder when $(5x + 9)^{611} + (x + 5)^{11} + (x - 1)^{11} + 3x^2 + 1$ is divided by $x + 2.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 203 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the remainder when the polynomial \( P(x) = (5x + 9)^{611} + (x + 5)^{11} + (x - 1)^{11} + 3x^2 + 1 \) is divided by \( x + 2 \), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial \( P(x) \) by a linear polynomial \( x - c \) is \( P(c) \). Here, t... |
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