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 425 187k |
|---|---|---|---|---|---|---|
[
{
"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 | 93 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about calculating the expected value of (f(S))^2 where f(S) is the XOR of all elements in the multiset S. And S is built by inserting each element a_i into S with probability p_i / 10^4.
First, I need to understand what's the expected value of the square of... |
[
{
"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: Put a uniform meter scale horizontally on your extended index ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 246 | JEEBench | {
"expected_answer": "25.6",
"problem_id": "13",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to determine the distance \( x_R \) at which the right finger stops slipping when moving a uniform meter scale between two fingers. The key is to analyze the forces acting on each finger and determine the point where the static frictional force on the right finger equals the dynamic frict... |
[
{
"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 PL/I program uses the EDIT form of input. The declare statementof the program is as follows: DCL(A,B,C,D,E,F) FIXED(5,2) ; GCHAR(15)VAR, H CHAR(4) ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 430 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the values stored in the memory locations A, B, C, D, E, F, G, and H after executing the GETEDIT statement in the PL/I program. The edit form of input specifies how the data is read from the data card into the variables. Let's break down the problem step by step.
### Step 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.You are given a length-N sequence A=(A_1,A_2,\\dots,A_N) consisting of 0, 1, and 2,\r\nand a length-N string S=S_1S_2\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 231 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to compute the sum of mex for all triples (i,j,k) where the substring S[ij] (not sure if that's the right term) is MEX. Wait, the problem says S is a string of M, E, X, and the triple (i,j,k) must satisfy S_i S_j S_k equal to MEX. Oh right, so the three... |
[
{
"content": "Problem: Rectangles $ABCD$ and $EFGH$ are drawn such that $D,E,C,F$ are collinear. Also, $A,D,H,G$ all lie on a circle. If $BC=16$ , $AB=107$ , $FG=17$ , and $EF=184$ , what is the length of $CE$ ? [asy] import graph; unitsize(0.1cm); pair A = (0,0);pair B = (70,0);pair C = (70,16);pai... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 19 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-19",
"reference_solution": "We use simple geometry to solve this problem. [asy] import graph; unitsize(0.1cm); pair A = (0,0);pair B = (107,0);pair C = (107,16);pair D = (0,16);pair E = (3,16);pair F = (187,16);pair G = (187,33);pair H = (3,33); label(\"$A$\", A,... | We are given two rectangles \(ABCD\) and \(EFGH\) such that points \(D, E, C, F\) are collinear, and points \(A, D, H, G\) lie on a circle. The dimensions of \(ABCD\) are \(AB = 107\) and \(BC = 16\), while \(EFGH\) has \(EF = 184\) and \(FG = 17\). We need to find the length of \(CE\).
First, let's determine the coor... |
[
{
"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 of length n where n is the total number of students in the class. The class teacher tries to select a group of stu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 108 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of ways to select a subset of students such that each student is happy according to the given conditions. Hmm. Let me think about the problem again.
So each student i has a number nums[i]. The conditions for happiness are: either the student is selected and the total ... |
[
{
"content": "Problem: What is the degree measure of the acute angle formed by lines with slopes $2$ and $\\frac{1}{3}$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 2 | AMC23 | {
"expected_answer": "45",
"problem_id": "2",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the acute angle formed by two lines with slopes 2 and \(\frac{1}{3}\), we can use the formula for the angle between two lines. The formula for the angle \(\theta\) between two lines with slopes \(m_1\) and \(m_2\) is given by:
\[
\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|
\]
Here, \(m_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 are N roulette wheels.\nThe i-th (1\\leq i\\leq N) wheel has P _ i integers S _ {i,1},S _ {i,2},\\ldots,S _ {i,P... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 262 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Takahashi wants to earn at least M points by playing roulette wheels, and we have to find the expected cost he'll pay using the optimal strategy. Hmm.
So the problem is about expecting the minimal expected cost. The key here is to find which wheels to play in... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 104 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to find the lexicographically smallest string possible after performing all the update operations. But we can rearrange the indices in the array ind and the letters in the string c. So the key is to choose the best order of operations and the best letters to app... |
[
{
"content": "Problem: For every positive integer $n$, let $\\text{mod}_5 (n)$ be the remainder obtained when $n$ is divided by 5. Define a function $f: \\{0,1,2,3,\\dots\\} \\times \\{0,1,2,3,4\\} \\to \\{0,1,2,3,4\\}$ recursively as follows:\n\n\\[f(i,j) = \\begin{cases}\\text{mod}_5 (j+1) & \\text{ if } i = ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 150 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \( f(2015, 2) \), we need to understand the recursive definition of the function \( f \). Let's break down the problem step by step.
The function \( f \) is defined recursively as follows:
\[
f(i,j) = \begin{cases}
\text{mod}_5 (j+1) & \text{if } i = 0 \text{ and } 0 \le j \le 4, \\
f(i-1,1) & \text{if } ... |
[
{
"content": "Problem: Simplify and write the result with a rational denominator: $$\\sqrt{\\sqrt[3]{\\sqrt{\\frac{1}{729}}}}$$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 181 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to simplify this expression and rationalize the denominator. The problem is \sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}. Hmm, let's break this down step by step.
First, let's tackle the innermost part. The expression is the square root of 1/729. So, the square root of (1/729) is 1 over the sq... |
[
{
"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 | 326 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem says that we have to process a series of queries on an array of zeros, and after each query, choose between x_i or y_i, and add or subtract 1. The goal is to minimize the sum of the array after all queries.
First, I need to think about how the choices affect t... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider the Y-component of the intrinsic angular momentum operator, A of a muon be represented by a 2×2 matrix Ay satisfying the eigenvalue equation Ay(φ) = a(φ). Here,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 34 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the eigenvalues and eigenvectors of the operator \( A_y \), which is given by \( A_y = c \cdot S \), where \( S \) is a \( 2 \times 2 \) matrix with specific entries. Let's proceed step by step.
First, let's write down the matrix \( S \). The problem states that the first ro... |
[
{
"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 | 358 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to find possible values of n and m given a shuffled list of their rows and columns. Oh right, the input was originally a grid with n rows and m columns. But someone shuffled all the integers into a single line, and we need to recover n and m.
First, I need to ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 189 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement is a bit complex, so I need to understand it thoroughly.
So, we have n balls arranged in a row. For each i from x to n (x is given as 1), we need to find f(i), which is the number of j's (from 1 to i) such that after performing i-1 operations, the se... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S of length N consisting of lowercase English letters.\nWe denote the i-th character of S by S_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 217 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes input from stdin and outputs a string. The problem is to generate a new string by repeating each character in the input string twice. So for each character in the input, I append it twice to the result. Oh right, and then concatenate all those pairs ... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The trace of a square matrix is defined to be the sum of its diagonal entries. If $A$ is a $2 \\times 2$ matri... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 297 | JEEBench | {
"expected_answer": "5",
"problem_id": "40",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve for the determinant of the matrix \( A \), given that the trace of \( A \) is 3 and the trace of \( A^3 \) is -18, we can use properties of eigenvalues and their relationships with the trace and determinant of the matrix.
### Step 1: Eigenvalues and Trace Relationship
The trace of a matrix is the sum of its e... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 87 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to determine if two strings s1 and s2 of length 4 can be made equal by swapping characters at positions i and j where j-i is 2. So, each swap allows us to swap two characters that are two positions apart.
Hmm, since the strings are of length 4, there are only a few possible swa... |
[
{
"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 | 370 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a matrix where some elements are lakes (negative heights). Sakurako can perform magic that increases the height of a selected square submatrix's main diagonal elements by 1 each time. We need to find the minimum number of magic uses to make all lakes di... |
[
{
"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 | 257 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So the task is to find the minimum number of operations required to turn a given string into an alternating string. The alternating string has even length, and in each even position (like 0-based index, so positions 0, 2, 4...), the characters are the same. Similarly, the odd po... |
[
{
"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 | 347 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that we need to restore the altitudes of a grid such that all rows and columns have the same sum x. The path that was cleared has all its cells set to zero, and we need to assign new values to those cells.
First, I need to understand the constra... |
[
{
"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 sleighs numbered 1,2,\\ldots, N.\nR_i reindeer are required to pull sleigh i.\nAdditionally, each reindeer... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 354 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where there are N sleighs, each requiring R_i reindeers. But each reindeer can pull at most one sleigh. The queries are X, and for each query, I have to find the maximum number of sleighs that can be pulled with X reindeers. Hmm.
So the problem is, given the list o... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 226 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that Turtle needs to choose a subsequence of length m that satisfies two conditions: the a's are non-decreasing, and all b's in the subsequence are distinct. And we have to maximize the sum of the c's. If it's impossible, output -1.
First, I need... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The isotope ${ }_{5}^{12} \\mathrm{~B}$ having a mass 12.014 u undergoes $\\beta$-decay to ${ }_{6}^{12} \\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 8 | JEEBench | {
"expected_answer": "9",
"problem_id": "15",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the maximum kinetic energy of the beta particle emitted when the isotope \(^{12}\text{B}_5\) undergoes beta decay to \(^{12}\text{C}_6^*\), considering the energy conservation in the decay process.
### Step 1: Understanding the Beta Decay Process
Beta decay involves the conv... |
[
{
"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 | 48 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about maximizing the sum of two gcds after swapping elements in certain intervals. So, the task is to find the maximum possible value of gcd(a) + gcd(b) after performing exactly one swap operation (swap a_i and b_i in a range [l, r]). Also, we need to count 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 | 97 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to split a given string of digits connected by '+' signs into as many expressions as there are '+' signs, such that each expression is a sum of two numbers. The goal is to split the string in such a way that the sum of all these expressions is maximized.
First... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 35 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the lexicographically smallest string possible by performing exactly one operation of replacing a substring's characters with their previous letters. Hmm. So the problem is to choose a substring (any length, including the entire string) and decrement each character by one. Then 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 73 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to fix an expression by changing the fewest characters possible. The expression is a string of three characters: two digits and a comparison symbol. The goal is to make it true by modifying as little as done. And if it's already true, leave it be.
Hmm.... |
[
{
"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 uniform wooden stick of mass $1.6 \\mathrm{~kg}$ and length $l$ rests i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 1 | JEEBench | {
"expected_answer": "D",
"problem_id": "2",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to analyze the forces acting on the wooden stick and use trigonometric relationships to find the ratio \( \frac{h}{l} \) and the frictional force \( f \).
### Step 1: Identify Forces
The stick is in equilibrium, so the sum of all forces and moments must be zero. The forces acting on the ... |
[
{
"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 thermodynamics, the $P-V$ work done is given by\n\\[\nw=-\\int d V ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 252 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "25",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine under which conditions the given expression for work \( w \) is applicable. The work done by a system is given by the integral \( w = -\int dV P_{\text{ext}} \). The specific form of \( P_{\text{ext}} \) in the integral suggests that the system's equation of state is being co... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 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 start by introducing variables to simplify the logarithms. Let's set \(y = \log_{2023x} 2023\). Then, using the change of base formula, we can express the other logarithms in terms of \(y\).
First, recall that \(\log_{a}b = \frac{\log... |
[
{
"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 | 246 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about calculating the expected beauty of a matrix b, which is derived from a given matrix a with exactly one error. The beauty is the number of ways to paint the initial 0 matrix into b using exactly f(b) operations, which is the minimum number of operations ... |
[
{
"content": "Problem: Consider the set of complex numbers $z$ satisfying $|1+z+z^{2}|=4$. The maximum value of the imaginary part of $z$ can be written in the form $\\tfrac{\\sqrt{m}}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\nMark your solution with \\boxed\nAnswer:",
"... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 6 | AMC23 | {
"expected_answer": "21",
"problem_id": "7",
"reference_solution": "",
"subject": null,
"type": null
} | We start with the equation \( |1 + z + z^2| = 4 \), where \( z \) is a complex number. Let's express \( z \) in terms of its real and imaginary parts, \( z = x + yi \), where \( x \) and \( y \) are real numbers. Then, we compute \( 1 + z + z^2 \):
\[
1 + (x + yi) + (x + yi)^2
\]
First, expand \( (x + yi)^2 \):
\[
(... |
[
{
"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: Liquids $\\mathbf{A}$ and $\\mathbf{B}$ form ideal solution fo... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 291 | JEEBench | {
"expected_answer": "0.2",
"problem_id": "32",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the vapor pressure of pure liquid B at 25°C given that liquids A and B form an ideal solution. We are provided with the total vapor pressures of two solutions with different mole fractions of A and B.
### Approach
1. **Understanding Ideal Solutions**: For an ideal solution,... |
[
{
"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 | 420 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to compute the XOR of all numbers in a given range [l, r] that are not congruent to k modulo 2^i. Oh right, and Bob's XORificator can compute this for us. But how?
Wait, first, I need to understand what's being asked here. So for each query, we have l, r, i, 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.Snuke the doctor prescribed N kinds of medicine for Takahashi. For the next a_i days (including the day of the prescr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 235 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes stdin and processes some input to find the first day X where the sum of pills for that day and all previous days is <= K. Hmm.
The problem says that for each day a_i, the person has to take b_i pills of the i-th medicine. The first day when the tota... |
[
{
"content": "Problem: What is the value of\n\\[2^3 - 1^3 + 4^3 - 3^3 + 6^3 - 5^3 + \\dots + 18^3 - 17^3?\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 3 | AMC23 | {
"expected_answer": "3159",
"problem_id": "3",
"reference_solution": "",
"subject": null,
"type": null
} | We need to find the value of the sum \(2^3 - 1^3 + 4^3 - 3^3 + 6^3 - 5^3 + \dots + 18^3 - 17^3\). Let's denote this sum as \(S\).
First, observe the pattern in the terms. The sum alternates between even and odd numbers cubed. Specifically, each pair of consecutive terms is of the form \((2k)^3 - (2k-1)^3\) for \(k = 1... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 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 start by introducing variables to simplify the logarithms. Let \(y = \log_x 2023\). Then, using the change of base formula, we can express the logarithms in terms of \(y\).
First, recall that \(\log_{a}b = \frac{\log b}{\log a}\). App... |
[
{
"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: There are three main types of buying situations in an organization, referred to by Robinson, Faris, and Wind (1967) as _____________.\nOptions: A. B... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 374 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the correct term that refers to the three main types of buying situations in an organization as identified by Robinson, Faris, and Wind in 1967. Let's break down the problem step by step.
First, we need to understand the context. The question is about three main types of buy... |
[
{
"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 | 266 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Alice and Bob are playing a game on a tree, and we have to determine who wins based on Alice starting at vertex 1 and Bob starting at each vertex along the path from u to v. The output is the winner for each position of Bob.
First, let's understand the problem. The game... |
[
{
"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 | 131 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about Alice and Bob playing a game with an array. They take turns choosing an index i where the element a_i is at least the current mx, which starts at 0. Then, the player sets a_i to 0 and updates mx to that a_i. The player who can't make a move loses. We need to determine if Al... |
[
{
"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 representing the strength of some heroes. The power of a group of heroes is defined as follows:\n\nLet i_0, i_1, .... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 18 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the sum of the power of all possible non-empty groups of heroes. The power is calculated as the square of the maximum in the group multiplied by the minimum in the group. And since the group can be any non-empty subset, I have to consider all possible subsets. But wait, the probl... |
[
{
"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 $A B C$ be the triangle with $A B=1, A C=3$ and $\\angle B... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 383 | JEEBench | {
"expected_answer": "0.83",
"problem_id": "8",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve for the radius \( r \) of the circle that touches the sides \( AB \) and \( AC \) of the right-angled triangle \( ABC \) (with \( \angle BAC = \frac{\pi}{2} \), \( AB = 1 \), \( AC = 3 \)), and also touches internally the circumcircle of \( \triangle ABC \), we will follow these steps:
1. **Determine the coor... |
[
{
"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: Sucrose has amoleuclarweight of 342 g/mole. At 0°C the Osmo-tic pressure of an aqueous solution of 1 gram of sucrose per 100 cm^3 solvent is 0.649 at... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 405 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to calculate the osmotic pressure of an aqueous solution of sucrose at 0°C using the given data and the simple form of the osmotic pressure equation. Let's break down the steps:
1. **Identify the given values:**
- Molecular weight of sucrose (C12H22O11) is 342 g/mole.
- Osmotic pre... |
[
{
"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.Vanya and Vova are playing a game. Players are given an integer $n$. On their turn, the player can add $1$ to the curr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 5 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that determines the winner of this game between Vanya and Vova. The problem says that for a given integer n, players take turns adding or subtracting 1, with Vanya going first. The goal is to make the number divisible by 3. If after 10 moves Vanya hasn't won, V... |
[
{
"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 | 153 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to find the optimal character replacement in a string such that the number of distinct permutations after the replacement is minimized. Hmm. So the task is to perform exactly one operation where we replace a character at position i with the character at position j (could be same ... |
[
{
"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 | 2 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. The task is to find the maximum number of connected components after performing two vertex removals on a tree. Each removal is such that we remove a vertex and all edges connected to it. So, each operation splits the tree into multiple components. We need to perform this operati... |
[
{
"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 | 106 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding a dividing point (x0, y0) such that when each city is assigned to a merchant based on its coordinates relative to (x0, y0), the minimum number of cities any merchant gets is as large as possible. So, the goal is to maximize the lower bound of 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 'invert sugar', the correct statement(s) is(are)\n(Given: specific... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 56 | JEEBench | {
"expected_answer": "BC",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which statements are correct regarding invert sugar. Let's analyze each option step by step.
### Option (A): "invert sugar" is prepared by acid catalyzed hydrolysis of maltose.
1. **Understanding Invert Sugar**: Invert sugar is formed by the hydrolysis of sucrose into gluco... |
[
{
"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 | 169 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that Arthur can swap opposite knights in a circle to minimize the difference between the maximum and minimum of the pairs. Each pair is (2i-1, 2i) for i from 1 to n. So the goal is to find the minimal possible difference after any number of swaps.... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N strings S_1,S_2,\\ldots,S_N consisting of lowercase English letters.\r\nDetermine if there are distinc... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 223 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that determines if there are two distinct strings in a list such that their concatenation is a palindrome. Hmm. The function will take stdin as input and print Yes or No. Oh right, and the strings are all distinct, so we don't have to worry about duplicates in ... |
[
{
"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 three sequences A=(A_1,\\ldots,A_N), B=(B_1,\\ldots,B_M), and C=(C_1,\\ldots,C_L).\nAdditionally, a sequ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 402 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where for each X_i in the query, I have to determine if there's a triplet (a, b, c) from arrays A, B, C respectively, such that a + b + c = X_i. The challenge is to do this efficiently, especially since Q can be up to 2e5, which is pretty big. So brute-checking each... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are in a store to buy N items. The regular price of the i-th item is P_i yen (the currency in Japan).\nYou have M... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 232 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about buying N items with M coupons. Each coupon can give a discount of D_i on an item whose regular price is at least L_i. We need to find the minimum total cost after applying the coupons optimally.
Hmm. So the goal is to apply the coupons in such a way that the sum of all ite... |
[
{
"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: Anscombe criticizes Sidgwick on the grounds that:\nOptions: A. he supports the principle of consequentialism., B. he endorses the divine law concepti... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 113 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine which criticism Anscombe levels against Sidgwick's ethical theories. Let's analyze each option step by step.
First, background information: Anscombe was a philosopher who critiqued Sidgwick's ethical system, which is part of the ethical theory known as utilitarianism or cons... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You are studying a nuclear decay which converts two heavy nucleons of flavor A to another flavor B, while simultaneously emitting two much lighter particles E and V. In ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 168 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand how the emission of a massless particle affects the energy spectrum of the outgoing particles in a nuclear decay process. Let's break down the problem step by step.
### Original Decay Process
The original process is \(2A \rightarrow 2B + 2E + 2V\). Here, two particles E and... |
[
{
"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: A stationary source emits sound of frequency $f_{0}=492 \\mathrm{~Hz}$. The sound is reflected by a large car ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 73 | JEEBench | {
"expected_answer": "6",
"problem_id": "11",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the beat frequency resulting from the superposition of the original sound wave and the reflected sound wave. The beat frequency is the difference between the frequencies of the two overlapping waves. Let's break down the solution step by step.
### Step 1: Understanding the P... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Let |alpha> be the state describing an electron, such that it is proportional to (1+i) |up> + (2-i) |down>, where |up> and |down> are the eigenstates of the z-projection... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 111 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the probability of measuring the electron in each eigenstate of a given operator and the average value of that operator. Let's proceed step by step.
First, let's understand the given state \( | \alpha > \). The state is a linear combination of the eigenstates \( | \text{up} ... |
[
{
"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 consisting of positive integers.\nReturn the total frequencies of elements in nums such that those elements all have the maximum fr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 160 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes an array of positive integers and returns the total frequencies of elements that have the maximum frequency. Hmm. Wait, the frequency is the number of times each element appears. So first, I need to count how many times each number appears in the arr... |
[
{
"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 $\\ell_{1}$ and $\\ell_{2}$ be the lines $\\vec{r}_{1}=\\lambda(\\hat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 465 | JEEBench | {
"expected_answer": "B",
"problem_id": "16",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the plane \( H_0 \) that contains the line \( \ell_1 \) and maximizes the distance \( d(H_0) \) between the points of the line \( \ell_2 \) and the plane. Let's proceed step by step.
### Step 1: Understanding the Lines
The line \( \ell_1 \) is given by:
\[ \vec{r}_1 = \lambd... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We would like to dissolve (at 25°С) 0.1 g Fe(OH)3 in 100 cm3 total volume. What is the minimum volume (cm3) of a 0.1 M monobasic strong acid that is needed to prepare th... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 162 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum volume of a 0.1 M monobasic strong acid required to dissolve 0.1 g of Fe(OH)3 in 100 cm³ of solution, and then calculate the resulting pH. Let's proceed step by step.
### Step 1: Determine the Solubility of Fe(OH)3
First, we need to find the solubility of Fe(OH)3... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: What is the main source of protein in the British diet?\n \nOptions: A. Milk and milk products, B. Pulses, C. Fish and fish products, D. Soy and soy ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 348 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the main source of protein in the British diet, let's analyze the options provided:
A. Milk and milk products: Dairy contributes protein, but perhaps not the highest amount per serving.
B. Pulses (like beans, lentils): These are good plant proteins but may not be the primary source.
C. Fish and fish pro... |
[
{
"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 $X$ be the set consisting of the first 2018 terms of the a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 144 | JEEBench | {
"expected_answer": "3748",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the number of elements in the union of two arithmetic sequences, \(X\) and \(Y\). Let's start by understanding the structure of each sequence.
### Step 1: Define the Sequences
The first sequence \(X\) starts at 1 with a common difference of 5. The \(n\)-th term of \(X\) can ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let\n\\[\n\\begin{gathered}\nS_{1}=\\{(i, j, k): i, j, k \\in\\{1,2, \... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 363 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the number of elements in each set \( S_1, S_2, S_3, \) and \( S_4 \) and check which of the given statements are true. Let's analyze each set step by step.
### Set \( S_1 \)
\( S_1 \) is the set of all ordered triplets \((i, j, k)\) where each element is in \(\{1, 2, \ldots... |
[
{
"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 | 17 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to find a permutation q that maximizes the number of local maxima in the array a, where a_i is p_i + q_i. And the permutation q can be any possible permutation as long as it's a valid permutation of the given n.
First, I need to understand what a local maximum ... |
[
{
"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 | 98 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about determining the minimum number of turns needed to kill a boss with certain health h, using n attacks each with their own damage and cooldown.
So each turn, we can use all attacks that aren't on cooldown, and each attack can be used multiple times as l... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two 0-indexed integer arrays, cost and time, of size n representing the costs and the time taken to paint n different walls respectively. There a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum cost to paint all walls using both paid and free painters. The problem is that the free painter can only be used if the paid painter is occupied. Hmm.
So, the paid painter takes time[i] units to paint the i-th wall, and costs cost[i]. The free painter takes 1 unit of... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $f(x)=\\frac{1-x(1+|1-x|)}{|1-x|} \\cos \\left(\\frac{1}{1-x}\\rig... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 116 | JEEBench | {
"expected_answer": "AD",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate the left-hand and right-hand limits of the function \( f(x) = \frac{1 - x(1 + |1 - x|)}{|1 - x|} \cos \left( \frac{1}{1 - x} \right) \) as \( x \) approaches 1. Let's break down the problem step by step.
First, let's simplify the expression inside the function \( f(x) \).
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": 0,
"temperature": 0.7
} | 0 | 439 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is that we need to find the string b that Ship sees from inside the store. The original string a is what Ship sees from outside. The transformation from a to b must follow certain rules based on the examples provided.
Hmm, let's look at the examples. For instance, the first input i... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A benzene ring has a carboxylic acid a carbaldehyde and a cyano group all meta to one another. Ortho to the carboxylic acid are a hydroxyl and a dimethyl amino and para ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 42 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's break down the problem step by step to determine the correct IUPAC name for the given molecule.
First, recall that the parent structure is a benzene ring with various substituents. The key is to identify the positions of each substituent correctly. The substituents mentioned are carboxylic acid (COOH), carbaldeh... |
[
{
"content": "Problem: Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$ . Bob's list has 2024 sets. Find the sum of the elements of A.\nMark your solution with \\boxed\nAnswer:",... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 5 | AIME24 | {
"expected_answer": "55",
"problem_id": "aime24-5",
"reference_solution": "Let $k$ be one of the elements in Alices set $A$ of positive integers. The number of sets that Bob lists with the property that their maximum element is k is $2^{k-1}$ , since every positive integer less than k can be in the set or o... | To solve this problem, we need to determine the set \( A \) such that the number of finite nonempty subsets \( B \) of positive integers where the maximum element of \( B \) is in \( A \) is exactly 2024. We then find the sum of the elements of \( A \).
First, let's think about the structure of the problem. Suppose \(... |
[
{
"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: The decomposition reaction $2 \\mathrm{~N}_{2} \\mathrm{O}_{5}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 229 | JEEBench | {
"expected_answer": "2.3",
"problem_id": "29",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the value of \( Y \) such that after \( Y \times 10^3 \) seconds, the pressure inside the cylinder becomes 1.45 atm. The reaction is \( 2 \mathrm{N}_2\mathrm{O}_5(g) \stackrel{\Delta}{\rightarrow} 2 \mathrm{N}_2\mathrm{O}_4(g) + \mathrm{O}_2(g) \), and the rate constant \( k ... |
[
{
"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 | 123 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So the task is, given a permutation array, for each element, remove it and compute the sum of the minimums of all possible subsegments of the resulting array. Oh right, and we need to do this for each element's removal and output all the results.
Hmm. The first thing I need to ... |
[
{
"content": "Problem: Find the roots of $(x - 3)^3 + (x -7)^3 = (2x - 10)^3.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 36 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | We need to find the roots of the equation \((x - 3)^3 + (x - 7)^3 = (2x - 10)^3\). Let's start by simplifying the equation.
First, notice that \(2x - 10 = 2(x - 5)\). So the right-hand side can be written as \((2(x-5))^3 = 8(x-5)^3\). Thus, the equation becomes:
\[
(x-3)^3 + (x-7)^3 = 8(x-5)^3
\]
Let's set \(y = x -... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A spin-half particle is in a linear superposition 0.5|\\uparrow\\rangle+sqrt(3)/2|\\downarrow\\rangle of its spin-up and spin-down states. If |\\uparrow\\rangle and |\\d... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 2 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let’s break this problem down step by step.
First, the particle is in a state which is a linear superposition of spin-up (|\uparrow\rangle) and spin-down (|\downarrow\rangle) states. The coefficients are 0.5 and sqrt(3)/2 respectively. Wait, wait. Wait, the given state is 0.5|\uparrow\rangle + sqrt(3)/2 |\downarrow\r... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Print an arithmetic sequence with first term A, last term B, and common difference D.\nYou are only given inputs for w... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 379 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to generate a Python function that takes stdin and prints an arithmetic sequence based on the given A, B, and D. Let's see.
First, the problem says the input is A B D. So the function will receive these three integers. The output should be the terms of the arithmetic sequence in order, separated 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": 0,
"temperature": 0.7
} | 0 | 67 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that we have to find a sequence b that satisfies certain conditions based on the given a' sequence. So, the input is a sequence with some -1s, and we need to replace the -1s with positive integers such that each consecutive pair either satisfies b... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The stoichiometric reaction of $516 \\mathrm{~g}$ of dimethyldichlorosilane with water results in a tetrameric... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 480 | JEEBench | {
"expected_answer": "222",
"problem_id": "42",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | To solve this problem, we need to determine the weight of the tetrameric cyclic product X obtained from the reaction of dimethyldichlorosilane (DMDCS) with water, given a 75% yield. Let's proceed step by step.
### Step 1: Determine the Molar Mass of Dimethyldichlorosilane (DMDCS)
DMDCS has the formula Si(C₂H₅)₂Cl₂. Le... |
[
{
"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": 6,
"temperature": 0.7
} | 6 | 10 | AMC23 | {
"expected_answer": "5",
"problem_id": "12",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to solve this problem. So, we have a triangular array where each row after the first has 1 at each end, and the interior entries are 1 more than the sum of the two diagonally upper ones from the previous row. The example given for row 4 is 1 5 5 1. Wait, row 4 has 4 elements. The first and last ... |
[
{
"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 computer producing factory has only two plants $T_{1}$ and $T_{2}$. Pla... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 27 | JEEBench | {
"expected_answer": "C",
"problem_id": "40",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the probability that a randomly selected non-defective computer was produced in plant \( T_2 \). Let's break down the problem step by step.
First, define the events:
- \( T_1 \): computer is produced in plant \( T_1 \)
- \( T_2 \): computer is produced in plant \( T_2 \)
- \... |
[
{
"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 happiness of length n, and a positive integer k.\nThere are n children standing in a queue, where the i^th child has happiness value hap... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 458 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have an array of happiness values and I need to select k children in such a way that each time I select a child, the remaining children's happiness decreases by 1. But their happiness can't go below zero. The goal is to maximize the sum of the selected child... |
[
{
"content": "Problem: A $90^\\circ$ rotation around $-4 - 5i$ in the clockwise direction is applied to $3$ (as a complex number). What is the resulting complex number?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 402 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem of rotating the complex number \(3\) (which can be written as \(3 + 0i\)) by \(90^\circ\) clockwise around the point \(-4 - 5i\), we can follow these steps:
1. **Translate the complex plane**: Shift the point \(-4 -5i\) to the origin. This involves subtracting \(-4 -5i\) from each complex number. ... |
[
{
"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 numeric strings num1 and num2 and two integers max_sum and min_sum. We denote an integer x to be good if:\n\nnum1 <= x <= num2\nmin_sum <= di... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 15 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of integers x between num1 and num2 (inclusive) such that their digit sum is between min_sum and max_sum. Hmm. The constraints say that num1 and num2 can be up to 10^22, which is a really big number. So iterating through each number from num1 to num2 isn't feasible. 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.There is an integer sequence A=(A_1,A_2,\\ldots,A_N) of length N, where all elements are initially set to 0. Also, the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 414 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that processes N and Q, then a series of x_i's. The problem is about a sequence A of zeros, and a set S that starts empty. For each query, we add or remove x_i from S, then for each j in S, add the size of S to A_j. Hmm.
So the main things here are keeping tra... |
[
{
"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 | 53 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a maze where Rostam starts at certain cells and gets trapped forever. We need to maximize the number of such starting cells by optimally assigning directions to the '?'s.
So the key idea is that for each cell, we want to determine the directions such ... |
[
{
"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 | 247 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, so the problem is about finding the maximum number of operations Dora can perform. Each operation involves selecting three distinct integers a, b, c from the set s such that their pairwise gcd is 1. Then those three are removed. The question is, how many such operations can... |
[
{
"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 recorded the number of steps he walked for N weeks. He walked A_i steps on the i-th day.\nFind the total... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 222 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Takahashi's steps are given for N weeks, and each week has 7 days. But the input is given as A_1 to A_{7N}, and I have to sum them into weeks. Oh right, the first week is days 1-7, second week 8-14, etc. So for each week i, the sum is from 7*i-6 to 7*i days. Because for ... |
[
{
"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 nonnegative integers $s$ and $r$, let\n\\[\n\\left(\\begin{array}{... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 305 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate the given function \( g(m, n) \) and determine which of the provided statements are true. Let's start by understanding the definitions and breaking down the problem step by step.
First, recall the binomial coefficient definition given:
\[
\left(\begin{array}{ll}
s \\
r
\end{a... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You identified a new ligand-receptor pair initially expressed in the neural crest cells and want to understand the developmental fate of their interaction. The receptor ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 101 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the most likely reason why the green signal (eGFP) is not observed in the mouse model, let's analyze the given information step by step.
First, the construct is a bicistronic lox-Cre vector where the ligand ORF is at the 5' position fused to mCherry, and the receptor ORF is at the 3' position fused to eGF... |
[
{
"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 | 154 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Robin Hood is giving and taking gold. The task is to find out how many people he gives gold to. Hmm. Let me read the problem again to make sure I understand it correctly.
So, the problem says that Robin starts with 0 gold. He encounters n people. For each per... |
[
{
"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 sellers and M buyers in an apple market.\nThe i-th seller may sell an apple for A_i yen or more (yen is th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 251 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum integer X such that the number of sellers who are willing to sell at X or more is greater than or equal to the number of buyers who are willing to buy at X or less. Hmm.
So the problem is about finding the smallest X where the count of sellers with A_i >= X is >= 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 | 283 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to tackle this problem. Hmm, the problem is about counting the number of arrays a_1 to a_n such that each a_i is between 1 and n, and the number of starting cities (i.e., cities i where a_i <= i) that allow a winning strategy is exactly k. The output is for each k from 0 to n the count modulo a ... |
[
{
"content": "Problem: If $a$ is the $x$-intercept, $b$ is the $y$-intercept, and $m$ is the slope of the line with equation $\\frac{x}4 + \\frac{y}{12} = 1$, then what is the value of $a + b + m$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 250 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the x-intercept (a), y-intercept (b), and the slope (m) of the line given by the equation \(\frac{x}{4} + \frac{y}{12} = 1\). Then, we will compute the sum \(a + b + m\).
### Step 1: Find the x-intercept (a)
The x-intercept occurs where \(y = 0\). Substitute \(y = 0\) into 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: Let $S$ be the reflection of a point $Q$ with respect to the plane giv... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 387 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the reflection of a point \( Q \) with respect to a given plane and find the conditions that the reflected point \( S \) must satisfy. Let's proceed step by step.
### Step 1: Understanding the Plane Equation
The plane is given by the equation:
\[
\vec{r} = -(t + p) \hat{i} +... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 262 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the maximum possible rating of the last remaining fighter after a series of battles. Each battle eliminates one fighter and reduces another's rating by the eliminated one's rating. The key here is that the order of battles matters because the re... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 195 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to generate a Python function that solves this problem. Hmm, the problem is about counting the number of valid strings that can be formed by replacing the '?' in S such that none of them contains a DDoS-type string as a subsequence. And we need to compute this modulo 998244353.
First, let's und... |
[
{
"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 $\\tan ^{-1}(x) \\in\\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right)$, for $x \\in \\mathbb{R}$. Then what... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 457 | JEEBench | {
"expected_answer": "3",
"problem_id": "8",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve the equation \(\sqrt{1 + \cos(2x)} = \sqrt{2} \tan^{-1}(\tan x)\) in the given intervals, we will proceed step by step.
First, let's simplify the left-hand side of the equation. We know that \(1 + \cos(2x) = 2 \cos^2(x)\). Therefore,
\[
\sqrt{1 + \cos(2x)} = \sqrt{2 \cos^2(x)} = \sqrt{2} |\cos(x)|.
\]
So the ... |
[
{
"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 an X-ray tube, electrons emitted from a filament (cathode) carrying... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 279 | JEEBench | {
"expected_answer": "AC",
"problem_id": "10",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the effects of changing the filament current \( I \), potential difference \( V \), and separation distance \( d \) on the cutoff wavelength and the wavelengths of characteristic X-rays emitted from an X-ray tube.
### Step 1: Understanding the Factors Affecting X-ray Productio... |
[
{
"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 quantum mechanical system containing a particle of mass $m$ moving in an istropic three dimensional potential of the form $V(r) = 1/2 m \\omega^2 r^2$ corresp... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 124 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the energy of the third excited state and the number of linearly independent eigenfunctions for that energy in a quantum harmonic oscillator system. Let's proceed step by step.
### Step 1: Identify the Potential and Quantum Harmonic Oscillator Energy Levels
The given potenti... |
[
{
"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: How is the parvovirus family targeted to reduce disease?\nOptions: A. By limiting exposure to outdoor environments, B. Social distancing, C. Through ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 180 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's first understand the question. The problem is about how the parvovirus family is targeted to reduce disease. The options provided are various methods or interventions, and we need to identify which one is specifically aimed at reducing parvovirus disease.
Parvoviruses are a famil... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array usageLimits of length n.\nYour task is to create groups using numbers from 0 to n - 1, ensuring that each number, i, is used no... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 77 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes a list called usageLimits and returns the maximum number of groups possible under the given conditions. Hmm. Let me think through the problem carefully.
The conditions are: each group must have distinct numbers, so no duplicates in a group. Each gro... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.