context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 8
values | metadata dict | model_outputs stringlengths 1 159k |
|---|---|---|---|---|---|---|
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Identify the compound C9H11NO2 using the given data.\nIR: medium to strong intensity bands at 3420 cm-1, 3325 cm-1\nstrong band at 1720 cm-1\n1H NMR: 1.20 ppm (t, 3H); 4... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 46 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's analyze the given data step by step to identify the compound C9H11NO2.
First, let's look at the IR spectrum. The presence of medium to strong bands at 3420 cm-1 and 3325 cm-1 suggests the presence of a hydroxyl (-OH) group because these are typical stretching frequencies for hydroxyl. However, wait, the compound... |
[
{
"content": "Problem: What is the product of all solutions to the equation\n\\[\\log_{7x}2023\\cdot \\log_{289x}2023=\\log_{2023x}2023\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 8 | AMC23 | {
"expected_answer": "1",
"problem_id": "10",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this equation: log₇ₓ 2023 ⋅ log₂₈₉ₓ 2023 = log₂₀₂₃ₓ 2023. Hmm, logarithms with variables as bases... That's a bit tricky. Let me recall some logarithm properties. Oh right, the change of base formula: logₐ b = ln b / ln a. Maybe I can apply that here.
First, let me denote each logarith... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed 2D integer array nums. Initially, your score is 0. Perform the following operations until the matrix becomes empty:\n\nFrom each row ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 10 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have a 2D array, and I have to compute a score by doing some operations. Let's read the problem carefully again.
The steps are: in each operation, first, select the largest number from each row and remove it. Then, among all those selected numbers (one from each row),... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Addition of excess aqueous ammonia to a pink coloured aqueous solution... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 78 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "23",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to work through this problem step by step. So, the problem is about coordination complexes and their properties. Let me start by understanding each part of the question.
First, we have an aqueous solution of X, which is MCl₂·6H₂O (where M is the metal ion) and NH₄Cl. When we add excess aqueous ... |
[
{
"content": "Problem: The asymptotes of a hyperbola are $y = 2x - 3$ and $y = 17 - 2x.$ Also, the hyperbola passes through the point $(4,7).$ Find the distance between the foci of the hyperbola.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 409 | MATH500 | {
"expected_answer": "",
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"subject": null,
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} | To solve the problem, we start by determining the equation of the hyperbola given its asymptotes and a point it passes through. The asymptotes of a hyperbola provide key information about its structure.
The given asymptotes are \( y = 2x - 3 \) and \( y = 17 - 2x \). First, we find the center of the hyperbola, which ... |
[
{
"content": "Problem: For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 37 | AMC23 | {
"expected_answer": "901",
"problem_id": "47",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out for how many integers n the expression sqrt[(log(n²) - (log n)^2)/(log n - 3)] is a real number. Hmm, let's break this down step by step.
First, I remember that for a square root to be real, the argument inside must be non-negative. So, the expression inside the square root, whic... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed string s, a string a, a string b, and an integer k.\nAn index i is beautiful if:\n\n0 <= i <= s.length - a.length\ns[i..(i + a.length... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 163 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find beautiful indices in a string s based on some conditions. Let's see the problem again.
The function is called is_beautiful, and the parameters are s, a, b, k. The steps are:
An index i is beautiful if:
1. i is within the range where i + a.length <= s.len... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N integers A_1, A_2, \\dots, A_N.\r\nAlso, define B_i = A_i \\times A_{i+1}\\ (1 \\leq i \\leq N-1).\nPr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 410 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that takes input from stdin and prints the output as specified. Let's see the problem again.
The input is N integers A_1 to A_N. Then, B_i is A_i multiplied by A_{i+1} for i from 1 to N-1. So, the output should be all B_i values printed in order, space-separated.
First... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi has placed N gifts on a number line. The i-th gift is placed at coordinate A_i.\nYou will choose a half-open... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 313 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes input N and M, followed by a list of A_i coordinates, and determine the maximum number of gifts that can be acquired by choosing a half-open interval [x, x+M). Hmm. The key here is to find the maximum count of gifts that fall into such an interval.
... |
[
{
"content": "Problem: Simplify $\\tan 100^\\circ + 4 \\sin 100^\\circ.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 164 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to simplify this expression: tan(100°) + 4 sin(100°). Hmm, let's see. I remember that tangent is sine over cosine, so tan(100°) is sin(100°)/cos(100°). So substituting that in, the expression becomes sin(100°)/cos(100°) + 4 sin(100°).
I can factor out sin(100°) from both terms. That gives sin(... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A \"strictly binary tree\" is a binary tree in which every node that is not a leaf has two children. Suppose that for a class of strictly binary tree... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 26 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which option best characterizes the height h of any tree in this class of strictly binary trees. Let me start by recalling what a strictly binary tree is. Every node that's not a leaf must have exactly two children. So, such a tree is a full binary tree, right? Because in a full bi... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Match the reactions (in the given stoichiometry of the reactants) in List... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 482 | JEEBench | {
"expected_answer": "D",
"problem_id": "48",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | \boxed{D}
**Solution:**
To solve this problem, we need to determine the correct products for each reaction listed in List-I and match them with the corresponding product codes in List-II. Let's analyze each reaction step by step.
**Reaction (P):**
\[ \mathrm{P}_2\mathrm{O}_3 + 3\mathrm{H}_2\mathrm{O} \rightarrow \]... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A container weighs 3.22 lb force when empty. Filled with water at 60°F the mass of the container and its contents is 1.95 slugs. Find its volume in c... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 212 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the volume of the container in cubic feet. The problem gives me the weight of the empty container and the mass when it's filled with water. Also, the density of water is provided. Hmm, how do I approach this?
First, let me recall some units. The mass of the container when filled... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A container with $1 \\mathrm{~kg}$ of water in it is kept in s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 284 | JEEBench | {
"expected_answer": "8.33",
"problem_id": "18",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, let's see. I need to find the temperature difference between the water and the surroundings after a long time. Hmm, the problem says to ignore the container effects, so I can focus on the water and the heat exchange.
First, the setup: there's 1 kg of water. The sunlight provides an average energy of 700... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this coding problem. Let's read the problem carefully and understand what's required. The problem is about a game between Alice and Bob where they take turns cutting rows or columns off a grid and collecting points based on the chips that are in the cut parts. The goal is to compute the to... |
[
{
"content": "Problem: Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\\%$ on every pair of shoes. Carlos also knew that he had to pay a $7.5\\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 30 | AMC23 | {
"expected_answer": "50",
"problem_id": "36",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. Carlos wants to buy running shoes that are on sale with a 20% discount. Then he has to pay 7.5% sales tax on the discounted price. He has $43. We need to find the original price of the most expensive shoes he can afford.
Hmm, first, let me break down the problem. The steps involved would be:
... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s consisting of only lowercase English letters. In one operation, you can do the following:\n\nSelect any non-empty substring of s, poss... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 35 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the lexicographically smallest string possible by performing exactly one operation on the input string. The operation allows me to replace each character in a selected substring with the previous character in the English alphabet. Hmm.
First, let me understand the problem. For e... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Some standard electrode potentials at $298 \\mathrm{~K}$ are given bel... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 350 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's see. I need to determine which combinations of metals X and Y would result in the dissolution of X when connected in a circuit. The problem mentions that X is dissolved, which means that the cell potential would be positive, favoring the oxidation of X. So, the standard reduction potentials (E°) giv... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider a system with Hamiltonian operator $H = \\varepsilon \\vec{\\sigma}.\\vec{n}$. Here, $\\vec{n}$ is an arbitrary unit vector, $\\varepsilon $ is a constant of di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the eigenvalues of the Hamiltonian operator H = ε(vecσ · vecn). The components of vecσ are Pauli spin matrices. So first, I remember that the Pauli matrices have some specific properties. Each Pauli matrix σ_x, σ_y, σ_z is a 2x2 matrix. The vector vecσ would then be a vector of t... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: \"Oh, I know you,\" the ribonucleoprotein particle says to the nascent chain as they meet. \"Pause there for a minute. Let me show you in; you really need some sugar.\"\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 26 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let me think about this problem. The question is about where a ribonucleoprotein particle (which is an RNA-protein complex, like a snRNP) meets a nascent protein chain. The chain then mentions going to the extracellular space, so we need to figure out the cellular locations involved.
First, the ribonucleoprotein parti... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 147 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each test case n, I have to find the number of pairs (a, b) such that when K1o0n's solution runs, it gives the correct result. The problem is that K1o0n made a mistake in how he interpreted the multiplication and subtraction. So, the question is, for a given n, how m... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 43 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where given a number x, I have to find an array of integers a_0 to a_{n-1} that sum to x using powers of two, with certain constraints. The constraints are that each a_i is either 1, 0, or -1, and there can't be two consecutive non-zero elements. Also, n must be bet... |
[
{
"content": "Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | <think>
Okay, let's see. I have these three equations involving logarithms of positive real numbers x, y, z. The goal is to find the value of |log2(x⁴y³z²)| in the form m/n and then find m+n. Hmm.
First, let me write down the equations clearly. They are:
1. log2(x/(yz)) = 1/2
2. log2(y/(xz)) = 1/3
3. log2(z/(xy)) = 1... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A light beam is propagating through a glass with index of refraction n. The glass is moving at constant velocity v in the same direction as the beam and toward the obser... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 40 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the speed of light in glass relative to the observer in the laboratory when the glass is moving. The problem says the glass has an index of refraction n and is moving at velocity v in the same direction as the light beam towards the observer. The speed of light in vacuum is given a... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let the functions $f:(-1,1) \\rightarrow \\mathbb{R}$ and $g:(-1,1) \\rightarrow(-1,1)$ be defined by\n\\[\nf(... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 298 | JEEBench | {
"expected_answer": "4",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, so I need to figure out the problem where I have to find the sum c + d, where c is the number of points in (-1,1) where the composite function f(g(x)) is not continuous, and d is the number of points where it's not differentiable. Hmm, let's start by understanding the functions given.
First, the function... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A buyer contracted in writing to purchase 1,000 gidgets (which are similar to widgets but are more popular because of their greater durability and- r... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 247 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about the enforceability of a modification to a contract for gidgets. The original contract was in writing, and the parties agreed to change the quantity from 1,000 to 800. But this change was done over the phone. The question is why this modification might be unenforceable.
Fir... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Aristotle claims that:\nOptions: A. vice is in our power, but virtue is not., B. virtue is in our power, and so is vice., C. vice is in our power, an... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 149 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what Aristotle's claim is about vice and virtue being in our power. Let me start by recalling what I know about Aristotle's philosophy. He wrote a lot about ethics and virtue, right? I remember that in his Nicomachean Ethics, he discusses the concept of virtue and vice, and whether... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 239 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Subtangle Game problem. Let me read the problem carefully again. So, the game is played between Tsovak and Narek. They have an array a and a matrix b. The players take turns looking for elements in the matrix. The array a is to be found in order, each element appearing in the matrix. ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 35 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Jellyfish is playing a card game and we have to find the probability that she can empty the draw pile. The problem seems quite complex, so let me try to break it down step by step.
First, let's understand the problem thoroughly. The game works as follows: Jellyfish has ... |
[
{
"content": "Problem: The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? [asy]\ndraw((-.3,-3)--(.1,1)--(-1,0)--(3,0)--cycle);\nlabel(\"$A$\",(.1,1),N);\nlabel(\"$B$\",(-1,0),W);\nlabel(\"$C... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem where I need to find the area of triangle CDE given that the area of triangle ABC is 6 square centimeters, AB is parallel to DE, BD is 4 times BC. Hmm, let's see. First, I remember that when two triangles have parallel bases, their areas are proportional to the lengths of the bases ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We have a large ensemble of 10.000 (ten thousand) identical systems. Each system has a particle that are the same and under the same conditions. Each particle can move a... | {
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} | To determine the numerical value of "a" given the conditions, we need to analyze the wave function provided and the constraints on where particles are found. The wave function is given as:
\[ \psi = \frac{a}{\sqrt{1 + x}} - 0.5i \]
We know that particles were only found between x=1 and x=3, and none outside this inte... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: This question refers to the following information.\n\"I travelled thence to 'Aden, the port of Yemen, on the coast of the ocean. It is surrounded by ... | {
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} | F
\boxed{F} |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 1 | 372 | CodeElo | {
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} | <think>
Okay, let's see. I need to solve this problem where for an array, I have to find the maximum number of non-overlapping beautiful segments. A segment is beautiful if the sum from l to r is zero. And the segments can't overlap. Hmm.
Wait, the problem says "non-overlapping segments of the array a such that each ... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Young's modulus of elasticity $Y$ is expressed in terms of three derived ... | {
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"seed": 2,
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} | 2 | 500 | JEEBench | {
"expected_answer": "A",
"problem_id": "19",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | \boxed{A}
To determine the correct values of \(\alpha\), \(\beta\), and \(\gamma\) for the expression \(Y = c^\alpha h^\beta G^\gamma\), we need to ensure that the dimensions of both sides of the equation match. Let's start by recalling the dimensional formulas of each quantity involved.
First, the dimensions of Youn... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Area of the cross-section of a wire is measured using a screw gauge. The ... | {
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} | 0 | 437 | JEEBench | {
"expected_answer": "C",
"problem_id": "35",
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"subject": "phy",
"type": "MCQ"
} | <think>
Okay, let's see. I need to figure out the diameter and cross-sectional area of the wire using the screw gauge readings provided. Hmm, screw gauges work by combining the main scale reading with the circular scale reading, right? The formula for the measurement is usually something like (Main scale reading + Circ... |
[
{
"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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} | 2 | 50 | CodeElo | {
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"problem_id": "",
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} | <think>
Okay, let's try to figure out how to solve this problem. So the task is to compute the maximum number of 1s that can be obtained in string a (which is a substring of s) using some operations. The operations are based on certain conditions on the characters in a and b (which is a substring of t).
First, let's ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Marcia Baron argues that the artificiality of ticking bomb cases is problematic because\nOptions: A. the artificial assumptions are, in fact, empiri... | {
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} | 0 | 321 | MMLUPro | {
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} | <think>
Okay, let's see. I need to figure out which option best completes Marcia Baron's argument about the problem with ticking bomb cases being artificial. The question is asking why she thinks the artificiality is problematic.
First, I should recall what Marcia Baron's stance is on this. From what I remember, Baro... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: For $a \\in \\mathbb{R},|a|>1$, let\n\\[\n\\lim _{n \\rightarrow \\inf... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 235 | JEEBench | {
"expected_answer": "AD",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to find the possible values of 'a' that satisfy this limit equation. Let me start by understanding the problem step by step.
The given limit is:
\[
\lim _{n \rightarrow \infty}\left(\frac{1+\sqrt[3]{2}+\cdots+\sqrt[3]{n}}{n^{7 / 3}\left(\frac{1}{(a n+1)^{2}}+\frac{1}{(a n+2)^{2}}+\cdots+\frac{... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Find KE of product particles in,\nPi(+) = mu(+) + nu\nhere Pi(+) is stationary.\nRest mass of Pi(+) & mu(+) is 139.6 MeV & 105.7 MeV respectively.\nOptions: A) 7.2 MeV,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 11 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the kinetic energy of the product particles when a pi+ meson decays into a mu+ and a neutrino. The pi+ is stationary, so it's moving with zero initial momentum. The rest masses are given: pi+ is 139.6 MeV, mu+ is 105.7 MeV. The options are the kinetic energies of mu+ and the neut... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array nums and an integer k.\nThe frequency of an element x is the number of times it occurs in an array.\nAn array is called good if ... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 147 | 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 subarray where each element's frequency is <= k. Let's think about how to approach this.
Hmm, the brute force approach would be to check all possible subarrays, calculate their frequencies, and see if they're valid. But that's O(n^2) time, whi... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: The melting point of monoclinic sulfur at a pressure of 1atm is 119.3°C. The change in volume during fusion is 41 cm^3 kg^-1 and\\DeltaH_fusis 422 ca... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 136 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the melting point of monoclinic sulfur when the pressure is increased from 1 atm to 1000 atm. The given data is the melting point at 1 atm (119.3°C), the change in volume during fusion (41 cm³ kg⁻¹), and the latent heat of fusion (ΔH_fus = 422 cal mol⁻¹). The answer choices are A t... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 378 | CodeElo | {
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"problem_id": "",
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} | <think>
Okay, let's see. The problem is about constructing a permutation that maximizes the value of k after performing n operations. Each operation alternates between AND and OR with the current k. The goal is to find the maximum possible k and the permutation that achieves it. Hmm.
First, let's understand the proces... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S consisting of lowercase English letters.\r\nRemove all occurrences of a, e, i, o, u from S an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 264 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that takes input from stdin and then outputs the result after removing all vowels from a given string. The vowels are a, e, i, o, u. Let's think about how to approach this.
First, the function should read the input string. Then, iterate through each character in the stri... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The compound(s) with TWO lone pairs of electrons on the central atom i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 19 | JEEBench | {
"expected_answer": "BC",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Solution:
To determine which compounds have a central atom with two lone pairs of electrons, we need to analyze the Lewis structures of each given molecule. The key is to calculate the total number of valence electrons around the central atom and determine if there are two lone pairs (which would mean 4 valence electro... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Experiencing intense feelings of shame and guilt upon admitting to a counselor that a family problem exists is common among traditional\nOptions: A. ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 446 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which group among the options is most commonly experiencing intense feelings of shame and guilt when admitting a family problem to a counselor. The question is about traditional vs. maybe more modern attitudes towards family issues in different cultures.
Let me start by recalling... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: One mole of a monatomic ideal gas undergoes an adiabatic expan... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | JEEBench | {
"expected_answer": "900",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I need to find the decrease in internal energy of a monatomic ideal gas that undergoes an adiabatic expansion. The volume becomes eight times the initial volume, and the initial temperature is 100 K. The universal gas constant R is given as 8.0 J/mol·K. Hmm, let's think step by step.
First, I remember... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence A=(A_1,\\ldots,A_N) of length N. The elements of A are distinct.\nProcess Q queries in the or... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 404 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where we have a sequence A of distinct elements and process Q queries of two types. Let's think about how to approach this.
First, let's understand the problem. The initial array A is given, and then there are Q queries. Each query is either inserting an element after a given... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 183 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to calculate the number of ways to place n chips on x points such that the cost is exactly m. The cost is defined as the minimum number of chips that remain after performing the operations. Hmm, let's think about how to approach this.
First, let's understand the ... |
[
{
"content": "Problem: For how many ordered pairs $(a,b)$ of integers does the polynomial $x^3+ax^2+bx+6$ have $3$ distinct integer roots?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 27 | AMC23 | {
"expected_answer": "5",
"problem_id": "30",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find out how many ordered pairs (a, b) of integers make the polynomial x³ + ax² + bx + 6 have three distinct integer roots. Hmm, let's think about this.
First, if the polynomial has three distinct integer roots, let's say r, s, t. Then, according to the factor theorem, the polynomial can be... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 126 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see this problem. So, the task is to find the minimum possible length of a string that contains one string a as a substring and another string b as a subsequence. Hmm.
First, I need to understand the problem properly. The string we create must have both a as a substring and b as a subsequence. We ... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 10 | AMC23 | {
"expected_answer": "5",
"problem_id": "12",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the units digit of the sum of the 2023rd row in this triangular array. The problem gives the first five rows, and the rule for forming subsequent rows. Hmm. Let me try to understand the pattern here.
First, looking at the given rows:
Row 1: 1 (sum 1, units digit 1)
Row 2: 1 1 (... |
[
{
"content": "Problem: A line is parameterized by\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} 8 \\\\ -1 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ 3 \\end{pmatrix}.\\]The equation of the line can be expressed in the form $y = mx + b.$ Enter the ordered pair $(m,b).$\nMark your solution with... | {
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} | 0 | 206 | MATH500 | {
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"subject": null,
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} | <think>
Okay, I need to find the equation of the line in the form y = mx + b from the given parametric equations. Let's see. The parametric equations are:
\[
\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \end{pmatrix}.
\]
So, that means for any value of t, x a... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 138 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to make all elements of an array zero by repeatedly choosing an integer x and updating each element to the absolute difference with x. And I can do this up to 40 times. The goal is to find a sequence of x's that achieves this, or determine it's impossible.
First... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid of H rows and W columns, each cell having a side length of 1, and we have N tiles.\nThe i-th tile (1\\... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 405 | 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 place N tiles on an H x W grid such that every cell is covered exactly once. The tiles can be rotated or flipped, but they must fit within the grid without extending. Hmm, let's think about how to approach this.
First, the problem... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: The geometries of the ammonia complexes of $\\mathrm{Ni}^{2+}, \\mathrm{P... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 50 | JEEBench | {
"expected_answer": "A",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, so I need to figure out the geometries of the ammonia complexes for nickel(II), platinum(II), and zinc(II) ions. Hmm, let me start by recalling what I know about complex ion geometries.
First, I remember that the geometry of a complex ion depends on the number of ligands and the coordination number. For... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 11 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each test case, given n and m, I have to count the number of ordered pairs (a, b) such that 1 ≤ a ≤ n and 1 ≤ b ≤ m, and a + b is a multiple of b * gcd(a, b). Hmm, let's think about this.
First, let me rephrase the condition. The condition is that (a + b) mod (b * g... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums having length n.\nYou are allowed to perform a special move any number of times (including zero) on nums. In one s... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 151 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to make all elements of an array equal to a palindromic number with the minimum possible cost. The cost is the sum of the absolute differences between each element and the chosen palindromic number. But wait, no, the cost is calculated by adding |nums[i] - x| for ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A previously healthy 27-year-old nulligravid woman comes to the emergency department because of a 2-day history of moderate-to-severe pain and swelli... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 246 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The patient is a 27-year-old woman who comes to the emergency department with pain and swelling in her left labia. She's sexually active and uses condoms inconsistently. The exam shows a tender, fluctuant mass medial to the labium majus, which is blocking the introital opening. So, first, I nee... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The AtCoder railway line has N stations, numbered 1, 2, \\ldots, N.\nOn this line, there are inbound trains that start... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 438 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if a train stops at a specific station Z when traveling from X to Y on the AtCoder railway. Let's see. The trains are either inbound (starting at 1 and going up to N) or outbound (starting at N and going down to 1).
First, let's understand the probl... |
[
{
"content": "Problem: Janet rolls a standard $6$-sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal $3$? The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive inte... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 18 | AMC23 | {
"expected_answer": "265",
"problem_id": "20",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the probability that Janet's running total equals 3 at some point during her four rolls, we can model the problem using states. Let's define the state as the running total modulo 3, since we are interested in when the total reaches 3. However, considering the possible values each roll can take (1 through 6... |
[
{
"content": "Problem: Simplify the following expression to a simplified fraction: $$\\sqrt{\\dfrac{\\dfrac{5}{\\sqrt{80}}+\\dfrac{\\sqrt{845}}{9}+\\sqrt{45}}{\\sqrt5}}.$$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 331 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to simplify this expression: the square root of (5 over sqrt(80) plus sqrt(845)/9 plus sqrt(45)) all divided by sqrt(5). Hmm, okay, where do I start?
First, maybe I should handle the denominator outside the square root. The entire fraction inside the square root has a denominator of sqr... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 129 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out how to solve this problem. So the task is to compute the number of different possible arrays b that can be formed from all possible arrays a, and then output that count modulo 998244353. Hmm.
First, let's understand the problem properly. Array a consists of integers from 1 to k, ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: For any positive integer $n$, define $f_{n}:(0, \\infty) \\rightarrow ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 170 | JEEBench | {
"expected_answer": "D",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem. So, we have a function \( f_n(x) \) defined as the sum from \( j=1 \) to \( n \) of \( \tan^{-1} \left( \frac{1}{1 + (x+j)(x+j-1)} \right) \). And we need to determine which of the given statements (A) to (D) are true. Hmm, let's start by understanding the function better.
Firs... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 309 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | To solve this problem, we need to minimize the number of inversions when concatenating multiple arrays of length 2 into a single array. The key insight is that the problem can be broken down into handling each pair of elements from consecutive arrays in the permutation.
### Approach
1. **Understanding Inversions**: An... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $P$ be the point on the parabola $y^{2}=4 x$ which is at the short... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 65 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. First, I need to understand what's being asked. The problem involves a parabola and a circle. We have to find a point P on the parabola \(y^2 = 4x\) that is closest to the center S of the circle. Then, there's a point Q on the circle that divides the line segment SP... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Interaction between the bosonic field X and fermions is given by\n\n\\mathcal{L}\\left(y\\right)=-\\lambda{f}\\bar{\\psi}{f}\\left(y\\right)\\left(\\upsilon+X\\left(... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 134 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the kinematically allowed decays of the boson X with a mass of 6 GeV. Let's start by understanding the problem. The interaction term given is \(\mathcal{L} = -\lambda f \bar{\psi}_f(y) (\upsilon + X(y)) \psi_f(y)\). Hmm, so this is a bosonic field X interacting with fermions via so... |
[
{
"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"
} | Solution:
To determine the dimensions of the magnetic field \( [B] \) in terms of the given constants \( e \), \( m_e \), \( h \), and \( k \), we first need to express each constant's dimensions and then find the exponents \( \alpha, \beta, \gamma, \delta \) such that the product \( [e]^{\alpha} [m_e]^{\beta} [h]^{\g... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There are n balls on a table, each ball has a color black or white.\nYou are given a 0-indexed binary string s of length n, where 1 and 0 represent black and w... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 130 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to group all the black balls (which are represented by 1s) to the right and the white balls (0s) to the left with the minimum number of swaps. Let's think about how to approach this.
Hmm. The problem is similar to partitioning elements into two groups. But the ke... |
[
{
"content": "Problem: In how many ways can 5 students be selected from a group of 6 students?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 455 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many ways I can select 5 students from a group of 6. Hmm, let's think. This is a combination problem, right? Because the order in which we select the students doesn't matter. So, the formula for combinations is n choose k, which is n! divided by k! times (n - k)! . Here, n is 6... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 295 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each i from 1 to n, I compute f(i^k, d), sum them all, and mod by 1e9+7. The function f(n, d) gives the number of leaves in the divisor tree T_{n,d}.
First, let's understand what the divisor tree is. The root is n. Each node in layer i generates children which are ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s consisting of lowercase English letters, and you are allowed to perform operations on it. In one operation, you can replace a characte... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 29 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to make a string a palindrome by doing the minimum number of replacements, and if there are multiple possibilities, pick the lexicographically smallest one. Hmm. Let's think about how to approach this.
First, what's a palindrome? A string that reads the same forw... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 145 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to create a permutation of length n such that the sum of f(i) minus the sum of g(i) is maximized. Hmm, f(i) is the sum of elements in the first i elements that are >=k. And g(i) is the sum of elements in the first i elements that are <=m. So the differe... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Use divergence therem to evaluate $\\iint_S \\vec{F} \\cdot d \\vec{S}$ where $\\vec{F} = sin(\\pi x) \\vec{i} + (z y^3)\\vec{j} + (z^2 + 4x)\\vec{k}... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 227 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to evaluate this surface integral using the divergence theorem. Let me start by recalling what the divergence theorem says. It states that the flux of a vector field through a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the sur... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given an integer sequence A = (A_1, A_2, \\dots, A_N).\r\nCalculate the following expression:\n\\displaystyle ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 434 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to calculate the sum of the maximum differences between all pairs of elements in a sequence. The formula given is the double sum where for each i from 1 to N and j from i+1 to N, we compute max(A[j] - A[i], 0) and add it all up. Hmm. Let's think about how to appro... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi will have N penalty kicks in a soccer match.\nFor the i-th penalty kick, he will fail if i is a multiple of ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 418 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to create a Python function that takes input N and outputs a string of 'o's and 'x's based on whether Takahashi succeeds or fails each penalty kick. Let's see.
The problem says that for the i-th kick, he fails if i is a multiple of 3. Wait, wait, wait. Wait, the description says: "For the i-th pen... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given positive integers n and m.\nDefine two integers, num1 and num2, as follows:\n\nnum1: The sum of all integers in the range [1, n] that are not div... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 120 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that calculates the difference between two sums. Let's see. The problem says that num1 is the sum of all integers from 1 to n that are not divisible by m, and num2 is the sum of those that are divisible by m. Then return num1 minus num2.
Hmm. So for each number in 1 to n... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $7 \\overbrace{5 \\cdots 5}^{r} 7$ denote the $(r+2)$ digit number where the first and the last digits are... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 459 | JEEBench | {
"expected_answer": "1219",
"problem_id": "10",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, let's see. The problem is asking for the sum S of a series of numbers, each of which starts and ends with 7, with 5s in between. Then, this sum S is expressed as a fraction where the numerator is a number similar to the series but with 99 fives, plus some m, and the denominator is n. We need to find m + n... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Consider the following statements related to colloids.\n\n(I) Lyophobic c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 506 | JEEBench | {
"expected_answer": "A",
"problem_id": "36",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's tackle this problem step by step. So, the question is asking which combination of statements about colloids is correct. There are four statements labeled (I) to (IV), and we need to figure out which two are both true. Let's go through each one and see.
Starting with statement (I): "Lyophobic colloi... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be a differentia... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 175 | JEEBench | {
"expected_answer": "0.4",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to find the limit as x approaches negative infinity of f(x) for this differential equation. Let me start by understanding the problem. The function f is differentiable, and we know f(0) = 0. The differential equation given is dy/dx = (2 + 5y)(5y - 2). Hmm, first, I should probably separate varia... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a family consisting of person 1, person 2, \\ldots, and person N. For i\\geq 2, person i's parent is person ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 237 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where we have a family tree, and each person can buy insurance that covers them and some number of descendants in the next generations. The goal is to find out how many people are covered by at least one insurance policy.
Hmm. Let's start by understanding the probl... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 287 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the number of starting cities that allow me to conquer all cities according to the given deadlines. Let's think about the problem step by step.
First, let's understand the rules. The game starts at time 1. At time 1, I choose the starting city. Then, 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.There is a grid with 10^9 by 10^9 squares. Let (i, j) denote the square at the (i + 1)-th row from the top and the (j ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 340 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where there's a huge grid of size 10^9 by 10^9, but the color of each cell is determined by some pattern modulo N. The task is to answer Q queries about the number of black squares in a subrectangle. Hmm, how to approach this?
First, let's understand the problem. The grid's c... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two strings s1 and s2, both of length 4, consisting of lowercase English letters.\nYou can apply the following operation on any of the two string... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 87 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to determine if I can swap the characters in s1 and s2 using the allowed operations, which are swapping characters at positions i and j where j - i is exactly 2. And we can do this any number of times on either string. Hmm.
The problem says that both strings are length 4. So each string... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 298 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. This is a coding problem. The task is to determine if the slide show can be arranged properly for each state of the array b, considering the updates. Hmm. Let's start by understanding the problem.
So, the setup is: there's a team of n members in a line. The order of the line is given by array ... |
[
{
"content": "Problem: There exist real numbers $x$ and $y$ , both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$ . Find $xy$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | AIME24 | {
"expected_answer": "25",
"problem_id": "aime24-16",
"reference_solution": "By properties of logarithms, we can simplify the given equation to $x\\log_xy=4y\\log_yx=10$ . Let us break this into two separate equations: \\[x\\log_xy=10\\] \n \\[4y\\log_yx=10.\\] \nWe multiply the two equations to get: \n \\[4xy\\... | <think>
Okay, so I have this problem where I need to find the value of xy given that there exist real numbers x and y greater than 1 such that log_x(y^x) = log_y(x^(4y)) = 10. Hmm, let me start by breaking down these logarithmic expressions.
First, let's recall some logarithm properties. The logarithm of a power is th... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: A person measures the depth of a well by measuring the time interval betw... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 97 | JEEBench | {
"expected_answer": "B",
"problem_id": "7",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | <think>
Okay, let's see. The problem is about calculating the fractional error in the measurement of the well's depth, given some errors in timing and the measurements. Hmm. So the user is asking for the fractional error in L, which is delta L over L, and wants to know which option it's closest to among the given choic... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two arrays of equal length, nums1 and nums2.\nEach element in nums1 has been increased (or decreased in the case of negative) by an integer, repr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 489 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the integer x that, when added to each element of nums1, makes it equal to nums2. The arrays are of the same length, and each element in nums1 is adjusted by x (could be positive or negative). The arrays are considered equal if they have the same integers ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 372 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for an array, I have to find the maximum number of non-overlapping beautiful segments. A segment is beautiful if the sum from a_l to a_r is zero. And the segments can't overlap. Hmm.
Let me think. For each possible segment, if it's beautiful (sum 0), then we can choose ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: In a bimolecular reaction, the steric factor $P$ was experimentally de... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 105 | JEEBench | {
"expected_answer": "AB",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's see. The problem is about a bimolecular reaction where the steric factor P is experimentally determined to be 4.5. We need to figure out which of the given options are correct based on this information. Let me start by recalling what the steric factor P means in the context of chemical reactions.
F... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are at a fruit market with different types of exotic fruits on display.\nYou are given a 1-indexed array prices, where prices[i] denotes the number of coin... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 137 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum coins to buy all the fruits. The offer is that if I buy the i-th fruit, I can get the next i fruits for free. But I can still buy them individually for their price. Hmm. So the problem is to decide which fruits to buy and which to take for free, in a way that minimize... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi has created a game where the player controls a dragon on a coordinate plane.\nThe dragon consists of N parts... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 358 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where a dragon has N parts, and I have to process Q queries. Let's see what the problem says.
The dragon starts with part 1 (head) at (1,0), and each subsequent part i is at (i,0). Then there are queries of two types. Type 1 is moving the head in a certain direction, and the ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: In a study about a pandemic, data of 900 persons was collected... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 378 | JEEBench | {
"expected_answer": "0.8",
"problem_id": "3",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let's see. I need to find the probability that a randomly chosen person has at most one symptom from fever, cough, or breathing problem. The total number of people is 900. So first, I should figure out how many people have each of these symptoms either alone or in combination, and then subtract the ones w... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: A person measures the depth of a well by measuring the time interval betw... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 97 | JEEBench | {
"expected_answer": "B",
"problem_id": "7",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | <think>
Okay, let's see. I need to find the fractional error in the measurement of the well's depth, δL/L, given the errors in time measurement, δT, and the measured depth L. Hmm. The problem says that the person measures the depth by timing how long it takes for the stone to fall to the bottom and the sound to come ba... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: There are three bags $B_{1}, B_{2}$ and $B_{3}$. The bag $B_{1}$ conta... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 206 | JEEBench | {
"expected_answer": "AB",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let's see. I need to solve this probability problem with multiple choices. Hmm, the problem involves three bags, each with different colored balls, and a probability of selecting each bag. Then, a ball is chosen from the selected bag, and we have to find various probabilities. Let me break it down step by... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence A=(A_0,A_1,\\dots,A_{63}) of length 64 consisting of 0 and 1.\nFind A_0 2^0 + A_1 2^1 + \\dot... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 218 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have a sequence A of 64 bits, and I have to compute the sum A0*2^0 + A1*2^1 + ... + A63*2^63. The input is given as 64 space-separated numbers, each either 0 or 1. The output is just the integer result.
Hmm, so the problem is essentially converting a binary number rep... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $\\Gamma$ denote a curve $y=y(x)$ which is in the first quadrant a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 209 | JEEBench | {
"expected_answer": "AB",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I have this problem where a curve Γ is in the first quadrant, passing through the point (1,0). The tangent to Γ at any point P intersects the y-axis at Y_P, and the distance P Y_P is always 1. I need to determine which of the given options are correct based on this condition. Let me think through this ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 216 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Lelle and Flamm have to coordinate their wins to maximize their total score while keeping the match successful. Let's see. The conditions are that after every round, the gcd of their wins must be <=1, and at the end, their wins can't exceed n and m respectively. The scor... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed binary string s having an even length.\nA string is beautiful if it's possible to partition it into one or more substrings such that:... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 121 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum changes to make a binary string beautiful. The conditions are that each substring in the partition must have even length and contain only 1s or 0s. And the total length is even.
Hmm. So the key here is to partition the string into substrings where each has even leng... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The correct statement(s) about the oxoacids, $\\mathrm{HClO}_{4}$ and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 76 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | \boxed{BD}
Let us analyze each statement step by step to determine which are correct regarding the oxoacids HClO₄ and HClO.
**Statement [A]: The central atom in both HClO₄ and HClO is \( sp^3 \) hybridized.**
- For HClO: The central chlorine atom has one oxygen atom bonded and three lone pairs. The electron geometry... |
[
{
"content": "Problem: Find the remainder when $(5x + 9)^{611} + (x + 5)^{11} + (x - 1)^{11} + 3x^2 + 1$ is divided by $x + 2.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 203 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the remainder when this big polynomial is divided by x + 2. Hmm, the remainder theorem says that when a polynomial f(x) is divided by x - c, the remainder is f(c). But here it's x + 2, which is x - (-2), so I should substitute x = -2 into the polynomial. Let me write that down.
The poly... |
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