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": "Problem: Let $\\mathbf{A}$ be a matrix such that\n\\[\\mathbf{A} \\begin{pmatrix} 3 \\\\ 1 \\\\ 0 \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ 4 \\\\ -3 \\end{pmatrix} \\quad \\text{and} \\quad \\mathbf{A} \\begin{pmatrix} -5 \\\\ 2 \\\\ 2 \\end{pmatrix} = \\begin{pmatrix} 0 \\\\ -5 \\\\ -5 \\end{pmat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 205 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \(\mathbf{A} \begin{pmatrix} -13 \\ 3 \\ 4 \end{pmatrix}\), we need to express the vector \(\begin{pmatrix} -13 \\ 3 \\ 4 \end{pmatrix}\) as a linear combination of the vectors \(\begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix}\) and \(\begin{pmatrix} -5 \\ 2 \\ 2 \end{pmatrix}\). Let's denote these vectors as \(... |
[
{
"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 string S consisting of lowercase English letters is a good string if and only if it satisfies the following property... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 423 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that checks if a given string is a good string according to the problem's definition. Hmm. The definition says that for a string to be good, for every integer i >=1, there are exactly zero or exactly two different letters that appear exactly i times. So, for ea... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 13 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So the task is to find the maximum score by selecting some elements in an array such that no two adjacent elements are selected. The score is the maximum value of the selected elements plus the number of elements selected. Hmm, right.
So the problem is similar to a dynamic prog... |
[
{
"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 | 71 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So, the question is whether, between the two scores that Dima remembers, there was never a point where the scores were equal. And we need to check if it's possible that the score changes in such a way that during his absence, there were no equal scores.
Hmm. The key here is to ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 9 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that Alice needs to cut the cake into m+1 pieces such that each of the m creatures gets a piece with at least v taste, and Alice's piece is the remaining part. We need to maximize Alice's taste. If it's impossible, output -1.
First, let's underst... |
[
{
"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 | 176 | 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 number of days until all vertices have a message. The graph's edges appear each day with certain probabilities, and each day a vertex gets the message if at least one of its adjacent vertices had it the previous day.
First, I ... |
[
{
"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: What is the total number of distinct $x \\in[0,1]$ for which $\\int_{0}^{x} \\frac{t^{2}}{1+t^{4}} d t=2 x-1$?... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 39 | JEEBench | {
"expected_answer": "1",
"problem_id": "52",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, let's see. I need to find the number of x in [0,1] such that the integral from 0 to x of (t²/(1 + t⁴)) dt equals 2x -1. Hmm. Alright, so first I should check if there's a function whose derivative is the integrand. Oh right, maybe a substitution. Let me think. The integrand is (t²)/(1 + t⁴). Let's try sub... |
[
{
"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.On a blackboard, there are N sets S_1,S_2,\\dots,S_N consisting of integers between 1 and M. Here, S_i = \\lbrace S_{i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 201 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where we have N sets on a blackboard, and we can merge them by combining two that share at least one element. The goal is to find the minimum number of operations to get a set that contains both 1 and M. If it's impossible, return -1.
Hmm. So first, I need to model... |
[
{
"content": "Problem: Let $G$ and $H$ denote the centroid and orthocenter of triangle $ABC,$ respectively. Let $F$ be the midpoint of $\\overline{GH}.$ Express $AF^2 + BF^2 + CF^2$ in terms of the side lengths $a,$ $b,$ $c$ and circumradius $R$ of triangle $ABC.$\nMark your solution with \\boxed\nAnswer:",
... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 425 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \( AF^2 + BF^2 + CF^2 \) in terms of the side lengths \( a, b, c \) and circumradius \( R \) of triangle \( ABC \), we will use vector geometry and properties of the centroid and orthocenter.
First, recall that the centroid \( G \) of a triangle divides each median in the ratio 2:1. The orthocenter \( H \... |
[
{
"content": "Problem: Let $F_1$ and $F_2$ be the foci of the ellipse $kx^2 + y^2 = 1,$ where $k > 1$ is a constant. Suppose that there is a circle which passes through $F_1$ and $F_2$ and which lies tangent to the ellipse at two points on the $x$-axis. Compute $k.$\nMark your solution with \\boxed\nAnswer:",
... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 108 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | We start by analyzing the given ellipse equation \(kx^2 + y^2 = 1\). To put this into the standard form of an ellipse, we rewrite it as:
\[
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
\]
where \(a^2 = \frac{1}{k}\) and \(b^2 = 1\). Since \(k > 1\), we have \(a^2 = \frac{1}{k} < 1\) and \(b^2 = 1\). Thus, the ellipse is hor... |
[
{
"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 | 394 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to construct a permutation of length n such that the sum of the minimum of all subarrays of length k is minimized. Hmm. So, for each test case with n and k, we need to generate such a permutation.
The example given: For 4 2, the output is 3 1 2 4. Let's see why. The subarrays ar... |
[
{
"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 do astronomers think Jupiter generates its internal heat?\nOptions: A. the gravitational pull from its moons, B. heat produced by its magnetic fi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 93 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine how astronomers think Jupiter generates its internal heat, let's evaluate each option step by step.
Option A: Gravitational pull from its moons. While Jupiter's moons do exert gravitational forces, this is not considered the primary source of internal heat. The gravitational interaction between Jupiter an... |
[
{
"content": "Problem: Let $f(x)=|x-p|+|x-15|+|x-p-15|,$ where $0 < p < 15.$ Determine the minimum value taken by $f(x)$ for $x$ in the interval $p \\leq x\\leq15.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 489 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the minimum value of the function \( f(x) = |x - p| + |x - 15| + |x - (p + 15)| \) for \( x \) in the interval \( p \leq x \leq 15 \), where \( 0 < p < 15 \), we need to analyze the function step by step.
First, let's understand the function. The function \( f(x) \) is the sum of three absolute values. Ea... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 51 | 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 number of connected components in a graph constructed from a matrix. The matrix is formed by cyclic shifts of the input array. Then, edges are added between vertices (i,j) if certain conditions are met. The challenge is to compute this effic... |
[
{
"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 binary array nums.\nWe call a subarray alternating if no two adjacent elements in the subarray have the same value.\nReturn the number of alter... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 470 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the number of alternating subarrays in a binary array. Let's think about how to approach this.
First, the problem defines an alternating subarray as one where no two adjacent elements are the same. So, like [0,1] is alternating, but [0,0,1] isn't. The exa... |
[
{
"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 | 320 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the task is to select a subset of games such that the product of their probabilities (each divided by 100) and the sum of their winnings is maximized. Oh right, the key here is that the product of the probabilities is multiplied by the sum of winnings. So, we need to choose... |
[
{
"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 increasing order of atomic radii of the following Group 13 elements i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 13 | JEEBench | {
"expected_answer": "B",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To determine the increasing order of atomic radii for the Group 13 elements aluminum (Al), gallium (Ga), indium (In), and thallium (Tl), we need to consider the trends in atomic radius as we move down the group.
Group 13 elements are part of the p-block and have valence electrons in the p orbital. As we move down the... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.In a mystic dungeon, n magicians are standing in a line. Each magician has an attribute that gives you energy. Some magicians can give you negative energy, whi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 500 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is about finding the maximum possible energy you can gain by starting at some magician in a line and then teleporting with k jumps. Each time you absorb the energy of the current magician, and then jump k steps. The process repeats until you can't jump anymore.
Hmm. So the key ... |
[
{
"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: Replacing a “failure identity” with a “success identity” is a goal of treatment for practitioners of _______ therapy.\nOptions: A. Adlerian, B. reali... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 216 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to identify the type of therapy that aims to replace a "failure identity" with a "success identity" as a primary goal of treatment. Let's evaluate each option step by step to determine the correct answer.
A. Adlerian therapy: This approach focuses on preventing maladjustment and promotin... |
[
{
"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 crystalline form of borax has\n(A) tetranuclear $\\left[\\mathrm{B... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 18 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to understand the structure of borax, which is the crystalline form of sodium tetraborate, Na2B4O7·10H2O. Let's analyze each option step by step.
**Option (A): Tetranuclear \([B_4O_5(OH)_4]\^{2-}\) unit.**
This option refers to the structure of the borate ion. Let's break it down. The b... |
[
{
"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 race through checkpoints 1,2,\\dots,N in this order on a coordinate plane.\nThe coordinates of checkpoint i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 269 | 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 find the minimum possible value of the total distance plus a penalty based on the number of checkpoints skipped. The checkpoints are arranged in order 1 to N, and you can skip some in between. So the path is like 1 → ... → N, but you can choose which... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 316 | 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 minimum number of button presses needed to get at least k cans of lemonade from a vending machine with n slots. Each slot has a certain number of cans initially. The buttons are mixed up, so pressing a button corresponding to a slot gives yo... |
[
{
"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 ate N plates of sushi at a sushi restaurant. The color of the i-th plate is represented by a string C_i.\nT... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 228 | 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 computes the total price based on the given conditions. Hmm. The problem says that each plate's color is checked against the D list. If it's in the D list, use the corresponding P value. Otherwise, use P0. Then sum all the prices.
So first... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal{P}$ we took crosses one of th... | To solve this problem, we need to determine the difference between the radius of the circle along which the torus is internally tangent to the sphere and the radius of the circle along which it is externally tangent. Let's break down the problem step by step.
### Step 1: Understanding the Torus and Sphere Configuratio... |
[
{
"content": "Problem: Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ and $BC$ of triangle $ABC$ , respectively. $2024$ circles of radius $1$ can be arranged in the same manner. The inradius of triangle $ABC$ can be expressed as $\\frac{m}{n}$ , w... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 22 | AIME24 | {
"expected_answer": "197",
"problem_id": "aime24-22",
"reference_solution": "Draw an altitude from both end circles of the diagram with the circles of radius one, and call the lengths you get drawing the altitudes of the circles down to $BC$ $a$ and $b$ . Now we have the length of side $BC$ of being $(2)... | We start by analyzing the arrangement of the circles in triangle \(ABC\). The problem states that eight circles of radius 34 are sequentially tangent, with two of them tangent to \(AB\) and \(BC\) respectively. The goal is to determine the inradius of triangle \(ABC\) given that 2024 circles of radius 1 can be arranged... |
[
{
"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 nums consisting of positive integers.\nThere are two types of operations that you can apply on the array any number of times:\n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 107 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum number of operations to make the array empty by removing elements in pairs or triplets. Hmm. The problem is to minimize the steps. So, the key is to figure out how to represent the counts of each number in a way that allows us to use as many triplets as possible, but ... |
[
{
"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 $s, t, r$ be non-zero complex numbers and $L$ be the set of soluti... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 171 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given equation \( s z + t \bar{z} + r = 0 \) where \( z = x + i y \) and \( \bar{z} = x - i y \). Let's break down the problem step by step.
First, substitute \( z \) and \( \bar{z} \) into the equation:
\[ s(x + i y) + t(x - i y) + r = 0 \]
Expand this expression:
\[ 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": 1,
"temperature": 0.7
} | 1 | 299 | 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 a line of members and a slide show. Each slide must be presented by a specific member (from the b array). After each slide, we can move the front member to any position in the line. The goal is to check, after each update to the b arr... |
[
{
"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 | 192 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So, the question is about Alex and his shower time. The problem says that we need to determine if there's a free interval of at least 's' minutes in a day of 'm' minutes, considering his existing tasks.
Hmm. So, the input gives multiple test cases. For each test case, we have n... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be a differentia... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 176 | JEEBench | {
"expected_answer": "2",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the given problem, we start by analyzing the functional equation satisfied by the differentiable function \( f: \mathbb{R} \rightarrow \mathbb{R} \) with \( f(0) = 1 \):
\[
f(x + y) = f(x) f'(y) + f'(x) f(y) \quad \text{for all } x, y \in \mathbb{R}.
\]
First, we differentiate both sides of the equation with... |
[
{
"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 string T of length 3 consisting of uppercase English letters is an airport code for a string S of lowercase English ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 421 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if a given T is an airport code for S. Let's read the problem carefully.
So, the definition says that T is an airport code for S if we can derive T from S using one of two methods:
1. Take a subsequence of length 3 from S (not necessarily contiguous... |
[
{
"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 | 182 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this programming problem. Let's read the problem carefully.
So, Monocarp starts at level 1. He fights monsters in order from 1 to n. For each monster, if his current level is strictly higher than the monster's level, the monster flees. Otherwise, he fights. After every k-th fig... |
[
{
"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 is initially at his house and is about to visit Aoki's house.\nThere are N bus stops numbered 1 to N between... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 278 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Takahashi is trying to get to Aoki's house as early as possible by catching buses. The input gives the structure of the bus routes and stops, then some queries asking for the earliest arrival time given a departure time from home.
Hmm. The steps I need to tak... |
[
{
"content": "Problem: Calculate the maximum area of an isosceles trapezoid that has legs of length $1$ and one base twice as long as the other. The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m^2+n^2$?\nMark your solution with \\box... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 24 | AMC23 | {
"expected_answer": "13",
"problem_id": "27",
"reference_solution": "",
"subject": null,
"type": null
} | We need to find the maximum area of an isosceles trapezoid with legs of length 1 and the upper base being twice as long as the lower base. The area should be expressed in the form \(\frac{m}{n}\) with \(m\) and \(n\) relatively prime, and we must determine \(m^2 + n^2\).
First, let's denote the lengths of the bases. L... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H rows and W columns. Initially, all cells are painted with color 0.\nYou will perform the follow... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 409 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where after performing a series of row or column paint operations on a grid, I have to count the number of cells for each existing color and output them in ascending order. Hmm.
The input gives H, W, M. Then M operations. Each operation is either painting a row wit... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $S=\\{1,2,3, \\ldots, 9\\}$. For $k=1,2, \\ldots, 5$, let $N_{k}$ be ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 113 | JEEBench | {
"expected_answer": "D",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the sum of the number of subsets of \( S = \{1, 2, 3, \ldots, 9\} \) that contain exactly \( k \) odd numbers for \( k \) from 1 to 5. The total number of such subsets is \( N_1 + N_2 + N_3 + N_4 + N_5 \).
First, let's identify the odd and even numbers in \( S \):
- The odd ... |
[
{
"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.\nConsider performing the following operation until s becomes empty:\n\nFor every alphabet character from 'a' to 'z', remove the first... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 180 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about this process where you remove the first occurrence of each character in the string, one by one. And we need to find the string right before the last operation, when it's reduced to empty. Hmm.
So, the example given is "aabcbbca" which becomes "abbca" then "ba" then empty. ... |
[
{
"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": 7,
"temperature": 0.7
} | 7 | 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\\... | We start with the given equations \(\log_x(y^x) = 10\) and \(\log_y(x^{4y}) = 10\). Let's tackle each equation step by step.
First, consider the equation \(\log_x(y^x) = 10\). Using the properties of logarithms, we can rewrite this as:
\[ x \log_x y = 10. \]
Similarly, the second equation \(\log_y(x^{4y}) = 10\) can b... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 374 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem says we have an array a of length n. Each operation allows us to pick an index i from 2 to n-1, and either decrease a[i-1] by 1 and increase a[i+1] by 1, or decrease a[i+1] by 1 and increase a[i-1] by 1. After each operation, all elements must remain non-negativ... |
[
{
"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: Which of these factors increases the risk for lung cancer?\n\nOptions: A. Saturated fat, B. High fiber diet, C. Eating citrus fruits, D. Alcohol, E. ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 447 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine which factor increases the risk for lung cancer, let's evaluate each option step by step:
A. Saturated fat: While a high intake of saturated fats is linked to various health issues, including cardiovascular disease, there's no strong evidence directly linking it to lung cancer. So this is unlikely.
B. Hi... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Four identical spin-1/2 particles are placed in a one-dimensional infinite potential well of length L. Calculate the energies of the ground state, first excited state, a... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 44 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let me think about this problem step by step. So, we have four identical spin-1/2 particles in a 1D infinite potential well of length L. The energy levels for each particle would be determined by their quantum numbers. Since they're identical, we have to consider the Pauli exclusion principle, which states that no two ... |
[
{
"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 | 119 | 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 multiset containing a single number n into a multiset containing only ones. The allowed operations are: take a number u from the set, remove it, and add up to k numbers such that their sum is equal to u. ... |
[
{
"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 | 150 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about Tim's answer sheet and maximizing the number of correct answers. So the input is a string of 4n characters, each being A, B, C, D, or ?. And we need to determine the maximum possible correct answers by changing the '?'s optimally.
Hmm. The key here is that for each of 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": 0,
"temperature": 0.7
} | 0 | 280 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this complex segments problem. Let's read the problem statement carefully.
So, the problem is about finding the maximum size of a subset of segments that forms a complex set. A complex set is one where all subsets have the same size, and any two segments in the same subset must intersect.... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Compound A shows two signals in the proton NMR, a triplet at 0.9 ppm for 6H and a quartet at 1.3 ppm for 4H. It undergoes monobromination to form compound B. B reacts wi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 115 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's break down the problem step by step to determine the correct compound D.
1. **Identify Compound A:**
- Proton NMR shows a triplet at 0.9 ppm (6H) and a quartet at 1.3 ppm (4H).
- The triplet suggests a structure where a proton is adjacent to two other protons (like in a methine group, -CH2-CH2-CH2-... but ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array of integers nums, and an integer target.\nReturn the length of the longest subsequence of nums that sums up to target. If no su... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 109 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the longest subsequence in an array that sums up to a target. If there's no such subsequence, return -1. Hmm, let's think about how to approach this.
First, I remember that a subsequence doesn't require consecutive elements, just maintaining order. 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: The potential energy of a particle of mass $m$ at a distance $r$ from ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 120 | JEEBench | {
"expected_answer": "BC",
"problem_id": "1",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given potential energy function and apply the principles of circular motion and angular momentum. Let's proceed step by step.
1. **Given Potential Energy**: The potential energy \( V(r) \) is given by \( V(r) = \frac{k r^2}{2} \), where \( k \) is a positive constant.
2. ... |
[
{
"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 solve for the dimensions of the magnetic field \( [B] \) in terms of the given constants \( e \), \( m_e \), \( h \), and \( k \), we need to express \( [B] \) as a product of these dimensions raised to some exponents and then determine those exponents by comparing dimensions on both sides of the equation.
First, l... |
[
{
"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 particle of mass $m$ is moving in the $x y$-plane such that its velocit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 501 | JEEBench | {
"expected_answer": "A",
"problem_id": "20",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the force \(\vec{F}\) acting on a particle of mass \(m\) moving in the \(xy\)-plane with a given velocity vector \(\overrightarrow{\mathrm{v}} = \alpha (y \hat{x} + 2x \hat{y})\). The force can be found using Newton's second law, which states that \(\vec{F} = m \vec{a}\), whe... |
[
{
"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 6. It is guaranteed that the first three characters of S are ABC and the last three... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 426 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that checks if a given string S is one of the valid abbreviations. The string S is 6 characters long, starts with ABC, and ends with two digits. The valid ones are from ABC001 to ABC349, but excluding ABC316. Oh right, because ABC316 is not included in the list... |
[
{
"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 | 168 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem seems a bit complex at first glance. Let me read the description carefully.
So, the problem is about Monocarp distributing artifacts to heroes and determining how many rounds he can survive after each query. Each query adds either a hero or an artifact. The bat... |
[
{
"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: Starting at time $t=0$ from the origin with speed $1 \\mathrm{~ms}^{-1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 281 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given conditions and determine which statements are correct. Let's start by understanding the particle's motion.
The particle's trajectory is given by the equation \( y = \frac{x^2}{2} \). This is a parabolic path. The particle starts at the origin (0,0) with a speed of \(... |
[
{
"content": "Problem: In the state of Coinland, coins have values $6,10,$ and $15$ cents. Suppose $x$ is the value in cents of the most expensive item in Coinland that cannot be purchased using these coins with exact change. What is the sum of the digits of $x?$\nMark your solution with \\boxed\nAnswer:",
... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 28 | AMC23 | {
"expected_answer": "11",
"problem_id": "32",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for the largest value that cannot be formed using coins of 6, 10, and 15 cents, we need to determine the Frobenius number for these denominations. The Frobenius number is the largest monetary amount that cannot be obtained using any combination of coins of specified denominations.
First, we note that all thre... |
[
{
"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.Two characters x and y are called similar characters if and only if one of the following conditions is satisfied:\n\n-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 202 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if two strings S and T are similar based on the given rules. Let's see the problem statement again.
So, two characters x and y are similar if one of the following is true:
1. They are the same.
2. One is '1' and the other is 'l'.
3. One is '0' and th... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A grantor executed a deed by which he conveyed his apartment building for a consideration of one dollar, receipt of which was acknowledged, \"to my s... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 322 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to analyze the legal structure of the deed and determine the nature of the brother's interest during the son's lifetime. Let's break down the problem step by step.
The deed conveys the apartment building "to my son for life, then to my uncle for life, but if my uncle moves to another sta... |
[
{
"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 non-negative integer k. There exists a staircase with an infinite number of stairs, with the lowest stair numbered 0.\nAlice has an integer jum... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 503 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of ways Alice can reach stair k. The problem seems a bit tricky, but maybe I can break it down step by step.
First, let's understand the setup. Alice starts at stair 1. Each operation, when she's on stair i, she can either go down to i-1 (but can't use this consecutiv... |
[
{
"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 | 242 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about Alice and Bob splitting items based on their costs. Bob can increase the costs a bit, but he can't decrease them. The goal is to find the minimum possible score Alice gets minus Bob's, given that both play optimally. Hmm.
So the approach from the editorial suggests that we... |
[
{
"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: Of the following choices the one most likely to be preferred by supply-side economists would be\nOptions: A. lower taxes on household income., B. a t... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 218 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine which economic policy supply-side economists are most likely to support. Supply-side economics focuses on stimulating economic growth by encouraging production and investment. Key principles include reducing tax rates, especially on businesses and high-income individuals, to ... |
[
{
"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.\nWe want to group the indices so for each index i in the range [0, n - 1], it is assigned to exactly ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 118 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the minimum number of groups required to assign indices of an array such that each group has all the same numbers in the array, and the difference between the sizes of any two groups is at most 1. Hmm.
Let me think about the examples. In the first example... |
[
{
"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 electronic configurations in List-I with appropriate metal comp... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 483 | JEEBench | {
"expected_answer": "D",
"problem_id": "49",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's see. I need to match the electronic configurations in List-I with the appropriate metal complex ions in List-II. Hmm. Let's start by understanding each configuration.
First, let's recall that the d-subshell has 5 orbitals: t2g (three orbitals) and eg (two). So the notation like t2g^x means x electr... |
[
{
"content": "Problem: The weight of $\\frac{1}{3}$ of a large pizza together with $3 \\frac{1}{2}$ cups of orange slices is the same as the weight of $\\frac{3}{4}$ of a large pizza together with $\\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\\frac{1}{4}$ of a pound. What is the weight, i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 9 | AMC23 | {
"expected_answer": "4",
"problem_id": "11",
"reference_solution": "",
"subject": null,
"type": null
} | Let's denote the weight of a large pizza as \( P \) pounds. The weight of orange slices is given in cups, and each cup weighs \( \frac{1}{4} \) of a pound. So, \( 3 \frac{1}{2} \) cups is equal to \( \frac{7}{2} \) cups. Therefore, the weight of \( 3 \frac{1}{2} \) cups of orange slices is \( \frac{7}{2} \times \frac{1... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: How many stereoisomers are there for the compound 6-chloro-9-ethyl-2-methylundeca-3,7-dien-5-ol?\nOptions: A) 8, B) 4, C) 32, D) 16\nAnswer:",
"role": "user"
}
] | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 144 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | To determine the number of stereoisomers for the compound 6-chloro-9-ethyl-2-methylundeca-3,7-dien-5-ol, we need to consider the number of chiral centers and the possible configurations at each of them. Let's break down the compound step by step.
First, let's identify the chiral centers. A chiral center is a carbon at... |
[
{
"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 cities in a certain country.\nYou will travel from your office in city 1 to a destination in city N, via z... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 309 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum time to travel from city 1 to city N using either company car or train. The transportation rules are that once you switch from car to train, you can't switch back. So the path could involve only car, only train, or a combination where you switch once. But once you swi... |
[
{
"content": "Problem: A list of positive integers has the following properties: $\\bullet$ The sum of the items in the list is $30$ . $\\bullet$ The unique mode of the list is $9$ . $\\bullet$ The median of the list is a positive integer that does not appear in the list itself. Find the sum of the squares... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 1 | AIME24 | {
"expected_answer": "236",
"problem_id": "aime24-1",
"reference_solution": "The third condition implies that the list's size must be an even number, as if it were an odd number, the median of the list would surely appear in the list itself. Therefore, we can casework on what even numbers work. Say the size is 2.... | To solve this problem, we need to determine a list of positive integers that meets the given properties and then compute the sum of their squares. Let's break down the problem step by step.
### Properties of the List
1. **Sum of the Items**: The sum is 30.
2. **Unique Mode**: The number 9 appears more frequently than ... |
[
{
"content": "Problem: One line is defined by\n\\[\\begin{pmatrix} 3 \\\\ -10 \\\\ 1 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ -9 \\\\ -2 \\end{pmatrix}.\\]Another line is defined by\n\\[\\begin{pmatrix} -5 \\\\ -3 \\\\ 6 \\end{pmatrix} + u \\begin{pmatrix} 4 \\\\ -18 \\\\ -4 \\end{pmatrix}.\\]These two lines ... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 288 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | To find the distance between two parallel lines in 3D space, we can use the formula involving the cross product of their direction vectors and the vector connecting a point from each line. Let's go through the steps.
First, identify the direction vectors of both lines. For the first line, the direction vector is \(\be... |
[
{
"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: Suppose\n\\[\n\\operatorname{det}\\left[\\begin{array}{cc}\n\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 238 | JEEBench | {
"expected_answer": "6.2",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the given problem, we need to evaluate the determinant of a 2x2 matrix and use the condition that the determinant is zero to find the sum \(\sum_{k=0}^{n} \frac{{ }^{n} C_{k}}{k+1}\).
The matrix is:
\[
\begin{bmatrix}
\sum_{k=0}^{n} k & \sum_{k=0}^{n} {n \choose k} k^2 \\
\sum_{k=0}^{n} {n \choose k} k & \sum... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A solution curve of the differential equation $\\left(x^{2}+x y+4 x+2 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 33 | JEEBench | {
"expected_answer": "AD",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which of the given statements about the solution curve of the differential equation \(\left(x^{2}+x y+4 x+2 y+4\right) \frac{d y}{d x} - y^{2} = 0\) with \(x > 0\) and passing through the point \((1,3)\) are correct. Let's proceed step by step.
First, we start by analyzing 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... | {
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"seed": 2,
"temperature": 0.7
} | 2 | 63 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about dividing a field between Alice and Bob, where Alice starts from the left or top side, moves right or down, and must end on the right or bottom side. The goal is to maximize the number of cells she can cover. Also, there are fountains that Bob can give 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... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 9 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, so the problem is about a game between Alice and Bob with coins arranged in a circle. Each coin can be up or down. The players take turns choosing a facing-up coin, remove it, and flip the two adjacent coins. The goal is to determine who wins if both play optimally.
First,... |
[
{
"content": "Problem: There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of a $5\\times5$ grid such that: each cell contains at most one chip all chips in the same row and all ch... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 8 | AIME24 | {
"expected_answer": "902",
"problem_id": "aime24-8",
"reference_solution": "The problem says \"some\", so not all cells must be occupied.\nWe start by doing casework on the column on the left. There can be 5,4,3,2, or 1 black chip. The same goes for white chips, so we will multiply by 2 at the end. There is $1$... | To solve this problem, we need to determine the number of ways to place chips on a \(5 \times 5\) grid such that each cell contains at most one chip, all chips in the same row and column have the same color, and no additional chip can be placed without violating these conditions. The chips are indistinguishable within ... |
[
{
"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 $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^{5}$ in the expansion of $\\left(a x^{2}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 462 | JEEBench | {
"expected_answer": "3",
"problem_id": "13",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve the problem, we need to find the value of \(2b\) given that the coefficient of \(x^5\) in the expansion of \(\left(ax^2 + \frac{70}{27bx}\right)^4\) is equal to the coefficient of \(x^{-5}\) in the expansion of \(\left(ax - \frac{1}{bx^2}\right)^7\).
### Step 1: Expand \(\left(ax^2 + \frac{70}{27bx}\right)^4\... |
[
{
"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 programming contest World Tour Finals is underway, where N players are participating, and half of the competition ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 296 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to generate a Python function that takes stdin as input and prints the output. The problem is about players in a programming contest and how many more problems they need to solve to exceed all others' current scores. Hmm.
First, the function needs to read N and M from the input. Then th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array nums consisting of positive integers.\nThere are two types of operations that you can apply on the array any number of times:\n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 107 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum number of operations to make the array empty by removing elements in pairs or triplets. Hmm. The problem is to minimize the steps. So, the key here is to figure out the optimal way to use pairs and triplets to remove as many elements as possible with each operation.
... |
[
{
"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 the van der Waals parameters for chlorine to calculate approximate values of the Boyle temperature of chlorine.\nOptions: A. $1.25 \\times 10^3$ ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 160 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to calculate the Boyle temperature of chlorine using its van der Waals parameters. The Boyle temperature is the temperature at which the compressibility becomes infinite, which occurs when the pressure derived from the van der Waals equation becomes zero. Let's go through the steps in det... |
[
{
"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 option(s) regarding the complex $\\left[\\mathrm{Co}(\\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 162 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem about the complex [Co(en)(NH3)3(H2O)]3+. Hmm, I need to figure out which of the options are correct. Let me start by breaking down the problem.
First, I remember that en is a bidentate ligand. Wait, en is ethylenediamine, right? So each en molecule can form two coordinate covale... |
[
{
"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 is playing a game.\nThe game consists of N stages numbered 1,2,\\ldots,N. Initially, only stage 1 can be pla... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 382 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about finding the minimum time needed to reach stage N in a game. Each stage from 1 to N-1 can be cleared with two options: either spend A_i seconds to get to the next stage, or spend B_i seconds to jump to stage X_i. We need to choose the optimal path that minimizes the total ti... |
[
{
"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 | 108 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about creating a set of problems such that each participant from a city with a lower index solves strictly more problems than those from higher cities. And the topics of the problems must all be distinct. Oh right, and the answer has to be 5n or fewer problem... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.We have N books numbered 1 to N.\r\nBook i assumes that you have read C_i books, the j-th of which is book P_{i,j}: yo... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 268 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this programming problem. Let's read the problem carefully.
The problem is about reading books in a specific order. Each book i requires you to read C_i books first, which are given in the list P_{i,1} to P_{i,C_i}. We need to find the minimal set of books to read so that book 1 is includ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are three cards with letters $\\texttt{a}$, $\\texttt{b}$, $\\texttt{c}$ placed in a row in some order. You can ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 0 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if it's possible to arrange the cards into 'abc' by performing at most one swap. Let's think about how to approach this.
So the problem says that each test case is a string of three characters, each being a, b, or c. We can pick two cards and swap th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N people gathered for an event called Flowing Noodles. The people are lined up in a row, numbered 1 to N in ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 283 | 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 people lined up, and M events happen where at time T_i, a quantity W_i is poured. The front person gets it, steps out, and returns at time T_i + S_i. The goal is to calculate how much each person ends up with after all events.
Hmm. The challenge h... |
[
{
"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: In a historical experiment to determine Planck's constant, a metal surfac... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 0 | JEEBench | {
"expected_answer": "B",
"problem_id": "1",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine Planck's constant \( h \) using the given data on the wavelengths of incident light and the corresponding stopping potentials. The key is to use the photoelectric effect equation, which relates the energy of the incident photon to the stopping potential and the work function ... |
[
{
"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 | 414 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about minimizing the range of an array after performing certain operations. Each operation allows Dora to increase an element by a or b. The range is the max minus min, so our goal is to find the minimal possible range after any number of operations.
First, ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 341 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that Lelle and Flamm need to coordinate their wins such that after each round, the gcd of their scores is at most 1. And the final scores must be within n and m respectively. The goal is to maximize the total score, which is l * W_L + f * W_F.
Fi... |
[
{
"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 | 190 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where for each test case, given a two-digit number, I have to compute the sum of its digits. Hmm.
So the input is t test cases, each with a two-digit number. The output should be the sum for each of those numbers. Right.
First, I need to read the number of test ca... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Which of the following inequalities is/are TRUE?\n(A) $\\int_{0}^{1} x... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 270 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To determine which of the given inequalities are true, we need to evaluate each integral and compare it to the given values. Let's tackle each integral one by one.
### Option (A): \(\int_{0}^{1} x \cos x \, dx \geq \frac{3}{8}\)
First, compute the integral \(\int x \cos x \, dx\). We use integration by parts:
Let \(u... |
[
{
"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 | 287 | CodeForces | {
"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 carefully.
So, we have n arrays, each of length m. Each element in these arrays is unique. The allowed operation is kind of a shift: when you choose an array and an x, you insert x at the beginning of that ... |
[
{
"content": "Problem: Let $N$ be the greatest four-digit positive integer with the property that whenever one of its digits is changed to $1$ , the resulting number is divisible by $7$ . Let $Q$ and $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$ . Find $Q+R$ .\nMark ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 6 | AIME24 | {
"expected_answer": "699",
"problem_id": "aime24-6",
"reference_solution": "We note that by changing a digit to $1$ for the number $\\overline{abcd}$ , we are subtracting the number by either $1000(a-1)$ , $100(b-1)$ , $10(c-1)$ , or $d-1$ . Thus, $1000a + 100b + 10c + d \\equiv 1000(a-1) \\equiv 100(b-1... | To solve this problem, we need to find the greatest four-digit number \( N \) such that changing any one of its digits to 1 results in a number divisible by 7. Then, we need to compute \( Q + R \) where \( Q \) and \( R \) are the quotient and remainder respectively when \( N \) is divided by 1000.
### Approach
1. **U... |
[
{
"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 average kinetic energy of air molecules at a temperature of 300° K? What would be a typical speed for nitrogen molecules, which are the m... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 201 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine two things: the average kinetic energy of air molecules at 300 Kelvin and the typical speed of nitrogen molecules in air. Let's approach each part step by step.
### Part 1: Average Kinetic Energy
The average kinetic energy (\(KE_{avg}\)) of a gas molecule can be calculated u... |
[
{
"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 | 62 | 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 find the minimum number of operations to make all elements of an array equal. The operation is kind of tricky: for each operation, you choose an index i, decrease a_i by 2 and increase a_{(i mod n)+1} by 1. Hmm.
So the problem is that after performi... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: \"Scientist aims to run quantitative polymerase chain reaction (qPCR) on some samples. He first wants to make a calibration curve so he took positive control with known ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 92 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand the principles of quantitative Polymerase Chain Reaction (qPCR) and the factors that can influence the accuracy and precision of the results. The key points to consider here are the calibration curve, efficiency, slope, and the biological and technical replicates.
First, le... |
[
{
"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 | 321 | 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 minimum time to make the two screens display s and t. The actions allowed are appending a character to a screen or copying from one screen to another, overwriting the destination.
So, the key is to figure out the optimal sequence of these ... |
[
{
"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: For the following cell,\n\\[\n\\mathrm{Zn}(s)\\left|\\mathrm{ZnSO}_{4}(a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 99 | JEEBench | {
"expected_answer": "B",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's see. I need to find the expression for ΔG when the concentration of Zn²+ is 10 times that of Cu²+. The given options involve Faraday's constant F, gas constant R, temperature T, and the standard cell potential E°cell = 1.1 V. Hmm.
First, I remember that the cell potential E is related to Gibbs free... |
[
{
"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 phrenic nerves innervate the\nOptions: A. diaphragm., B. diaphragm and pericardium., C. diaphragm, parietal pleura, pericardium and abdominal mus... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 161 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine which structures are innervated by the phrenic nerves. The phrenic nerves are part of the peripheral nervous system and are primarily associated with the diaphragm. However, their distribution extends to other structures in the thorax and upper abdomen. Let's break down the o... |
[
{
"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 bound system of two nucleons (NN) in a 1S0 state which emit a particle X of intrinsic parity -1. Pauli statistics require that the isospin, angular momentum, ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 108 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine which of the given partial wave options is not permitted when two nucleons in a 1S0 state emit a particle X with intrinsic parity -1. The key is to ensure that the conservation of angular momentum and parity is maintained.
First, let's break down the problem step by step.
1... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 61 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, so the task is to determine if we can transform matrix a into matrix b by swapping rows and swapping columns any number of times. Oh right, and each swap can be either rows or columns, but you can do them in any order.
First, I need to think about what properties are pres... |
[
{
"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 nitrogen containing compound produced in the reaction of $\\mathrm... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 55 | JEEBench | {
"expected_answer": "BD",
"problem_id": "29",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the correct options regarding the nitrogen-containing compound produced when \(\mathrm{HNO}_3\) reacts with \(\mathrm{P}_4\mathrm{O}_{10}\). Let's break down the problem step by step.
First, we need to write the balanced chemical equation for the reaction between \(\mathrm{H... |
[
{
"content": "Problem: Let \\(O=(0,0)\\), \\(A=\\left(\\tfrac{1}{2},0\\right)\\), and \\(B=\\left(0,\\tfrac{\\sqrt{3}}{2}\\right)\\) be points in the coordinate plane. Let \\(\\mathcal{F}\\) be the family of segments \\(\\overline{PQ}\\) of unit length lying in the first quadrant with \\(P\\) on the \\(x\\)-axi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 11 | AIME24 | {
"expected_answer": "23",
"problem_id": "aime24-11",
"reference_solution": "Begin by finding the equation of the line $\\overline{AB}$ : $y= -\\sqrt{3}x+\\frac{\\sqrt{3}}{2}$ Now, consider the general equation of all lines that belong to $\\mathcal{F}$ . Let $P$ be located at $(a,0)$ and $Q$ be located... | To solve this problem, we need to determine the unique point \( C \) on the line segment \(\overline{AB}\) that is not covered by any other unit segments from the family \(\mathcal{F}\). The goal is to find \( OC^2 \) where \( O \) is the origin, and express it as a fraction \(\frac{p}{q}\) in simplest terms, then comp... |
[
{
"content": "Problem: Calculate the maximum area of an isosceles trapezoid that has legs of length $1$ and one base twice as long as the other. The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m^2+n^2$?\nMark your solution with \\box... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 24 | AMC23 | {
"expected_answer": "13",
"problem_id": "27",
"reference_solution": "",
"subject": null,
"type": null
} | We are given the problem of finding the maximum area of an isosceles trapezoid with legs of length 1 and one base twice as long as the other. The solution requires determining the optimal dimensions to maximize the area, which can be expressed as a fraction \(\frac{m}{n}\) in simplest terms, and then finding \(m^2 + n^... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.This problem has a similar setting to Problem G. Differences in the problem statement are indicated in red.\nThere is ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 355 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to compute the expected value of the number of green connected components after randomly choosing a red cell and repainting it green. Then output this value modulo 998244353. Hmm. Let's break this down.
First, the problem says the expected value. Expected value i... |
[
{
"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 $M=\\left(a_{i j}\\right), i, j \\in\\{1,2,3\\}$, be the $3 \\time... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 489 | JEEBench | {
"expected_answer": "BC",
"problem_id": "5",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given \(3 \times 3\) matrix \(M\) where each entry \(a_{ij}\) is 1 if \(j+1\) is divisible by \(i\), and 0 otherwise. Let's construct this matrix first.
### Step 1: Construct the Matrix \(M\)
For each entry \(a_{ij}\), check if \(j+1\) is divisible by \(i\). Let's compute ... |
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