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 180k |
|---|---|---|---|---|---|---|
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Identify the compound C9H11NO2 using the given data.\nIR: medium to strong intensity bands at 3420 cm-1, 3325 cm-1\nstrong band at 1720 cm-1\n1H NMR: 1.20 ppm (t, 3H); 4... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 46 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's see. The problem is to identify the compound C9H11NO2 based on the given spectroscopic data. Let's break down the information step by step.
First, the molecular formula is C9H11NO2. So the compound has 9 carbon atoms, 11 hydrogen, 1 nitrogen, and 2 oxygen. Let's check each option to see which matches.
Option A:... |
[
{
"content": "Problem: What is the product of all solutions to the equation\n\\[\\log_{7x}2023\\cdot \\log_{289x}2023=\\log_{2023x}2023\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 8 | AMC23 | {
"expected_answer": "1",
"problem_id": "10",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the equation \(\log_{7x}2023 \cdot \log_{289x}2023 = \log_{2023x}2023\), we start by letting \(y = \log_{2023} 2023\). Since \(\log_{a} a = 1\), we know \(y = 1\). However, this might not directly help, so let's consider a substitution.
Let \(a = \log_{2023} 2023 = 1\). Then the equation can be rewritten usin... |
[
{
"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 programming problem. Let's read the problem carefully.
So the task is to compute a score based on a matrix. The process is: in each step, remove the largest element from each row, add the maximum of those removed elements to the score. Repeat until the matrix is empty. The goal is to... |
[
{
"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 figure out this problem step by step. So, the problem is about some metal complexes and their reactions. Let's see what each part says.
First, the problem statement says that when we add excess aqueous ammonia to a pink solution of X (which is MCl2·6H2O) and NH4Cl, in the presence of air, we... |
[
{
"content": "Problem: The asymptotes of a hyperbola are $y = 2x - 3$ and $y = 17 - 2x.$ Also, the hyperbola passes through the point $(4,7).$ Find the distance between the foci of the hyperbola.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 409 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the distance between the foci of a hyperbola given its asymptotes and a point it passes through. Let's proceed step by step.
### Step 1: Determine the Center of the Hyperbola
The asymptotes of a hyperbola are given by the equations \( y = 2x - 3 \) and \( y = 17 - 2x \). The... |
[
{
"content": "Problem: For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 37 | AMC23 | {
"expected_answer": "901",
"problem_id": "47",
"reference_solution": "",
"subject": null,
"type": null
} | To determine for how many integers \( n \) the given expression represents a real number, we need to analyze the conditions under which the expression inside the square root is non-negative and the denominator is non-zero. The expression is:
\[
\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}}
\]
First, let's simplif... |
[
{
"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, let's see. I need to find all the beautiful indices in the string s. A beautiful index i is one where the substring starting at i matches a, and there's a j where the substring j matches b, and the absolute difference between i and j is at most k.
Hmm. So the steps I need to take are:
First, find all p... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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, let's see. I need to write a Python function that reads some input, computes the product of consecutive elements in a list, and outputs those products. Hmm.
So the problem says that given N integers A_1 to A_N, we have to compute B_i as A_i multiplied by A_{i+1} for each i from 1 to N-1. Then output all ... |
[
{
"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. The problem is to find the maximum number of gifts that can be covered by a half-open interval [x, x + M) of length exactly M. So, the interval is of fixed length M, and we need to choose x such that as many gifts as possible are in this interval.
Hmm. So, the first thing I need to think about... |
[
{
"content": "Problem: Simplify $\\tan 100^\\circ + 4 \\sin 100^\\circ.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 164 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To simplify the expression \(\tan 100^\circ + 4 \sin 100^\circ\), we can use trigonometric identities to combine the terms. Let's proceed step by step.
First, recall that \(\tan \theta = \frac{\sin \theta}{\cos \theta}\). So, \(\tan 100^\circ = \frac{\sin 100^\circ}{\cos 100^\circ}\). Substituting this into the expres... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A \"strictly binary tree\" is a binary tree in which every node that is not a leaf has two children. Suppose that for a class of strictly binary tree... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 26 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the height \( h \) of a strictly binary tree such that the ratio of the lengths of any two root-to-leaf paths is bounded by a constant \( c \). The goal is to find the best characterization of \( h \) in terms of the number of nodes \( N \).
### Approach
1. **Understanding S... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: 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"
} | Okay, I need to solve this problem where I have to match the reactions from List-I to their corresponding products in List-II. Let's see. The problem says that each reaction in List-I has a specific stoichiometry, and I need to find out which product is formed based on that.
First, I should look at each reaction in Li... |
[
{
"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
} | Let's see. The problem is to find the volume of a container when it's filled with water. The container's weight when empty is 3.22 lb. When filled with water at 60°F, the total mass is 1.95 slugs. The density of water is 62.4 lb/ft³. We need to compute the volume in cubic feet.
Hmm. Let's think. The key here is to fin... |
[
{
"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. The problem is about a container with 1 kg of water that's being heated by sunlight. We need to find the temperature difference between the water and the surroundings after a long time. Hmm.
So, the key points here are understanding how the heat is absorbed and then how it's lost through cooli... |
[
{
"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 problem where Alice and Bob are playing a game by cutting rows and columns from a grid and earning points based on the chips in the cut parts. The goal is to compute the total points each earns after all moves. Let's think about how to approach this.
First, let's understand the probl... |
[
{
"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. The problem is about calculating the original price of a pair of shoes that Carlos can afford after a discount and including tax. So, the steps I need to take are: first, understand the discount and tax application, then reverse-engineer the original price based on the amount Carlos has.
Hmm. ... |
[
{
"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. The operation allows selecting any non-empty substring and converting each character to the previous one in the alphabet. So, for example, 'b' becomes 'a', and 'a' becomes 'z'.
Hmm, the goal is ... |
[
{
"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, I need to solve this problem where I have to determine the correct combination of X and Y metals such that X gets dissolved when their solutions are connected. Let's see.
The problem says that when we connect the metal rods of X and Y via a wire, X starts to dissolve. So, that means that in the galvanic... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider a system with Hamiltonian operator $H = \\varepsilon \\vec{\\sigma}.\\vec{n}$. Here, $\\vec{n}$ is an arbitrary unit vector, $\\varepsilon $ is a constant of di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the eigenvalues of the Hamiltonian operator \( H = \varepsilon \vec{\sigma} \cdot \vec{n} \), where \(\vec{\sigma}\) are the Pauli spin matrices, \(\vec{n}\) is a unit vector, and \(\varepsilon\) is a constant with energy dimensions.
### Approach
1. **Understanding the Hamil... |
[
{
"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's think about the problem step by step. The problem is about a ribonucleoprotein particle (which is likely a ribosome) and a nascent chain (a growing polypeptide). The interaction between them occurs in a specific cellular location, and the chain is about to go somewhere else. We need to figure out where they met 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": 0,
"temperature": 0.7
} | 0 | 147 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. Hmm, the problem statement is a bit complex, so I need to make sure I understand it correctly.
So, the main idea is that K1o0n's solution to the problem gives the correct answer for some pairs (a, b) even though he made a mistake in his approach. The correct answer is n*a - b. But K1o0... |
[
{
"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 find an array of 1s, 0s, and -1s such that their sum with appropriate powers of 2 equals the given x. Also, the array can't have two non-zero consecutive elements. Hmm.
Wait, the constraints for the array are that for any i from 0 to n-2, either a_i is 0, or a_i+1 is 0. So, no two co... |
[
{
"content": "Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | To solve this problem, we start by analyzing the given system of logarithmic equations involving \(x, y, z\). The equations are:
1. \(\log_2\left(\frac{x}{yz}\right) = \frac{1}{2}\)
2. \(\log_2\left(\frac{y}{xz}\right) = \frac{1}{3}\)
3. \(\log_2\left(\frac{z}{xy}\right) = \frac{1}{4}\)
First, we convert these logari... |
[
{
"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
} | Let's think about this problem step by step. So, the problem is about a light beam propagating through a glass that's moving at a constant velocity v towards the observer. We need to find the speed of light in the glass relative to the observer in the laboratory frame.
Hmm. The key here is to apply the velocity additi... |
[
{
"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, I need to solve this problem where I have to find the number of points where the composite function f(g(x)) is not continuous (c) and not differentiable (d), then compute c + d. Let's break this down step by step.
First, let's understand the functions involved.
The function f(x) is |2x - 1| + |2x + 1|. ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A buyer contracted in writing to purchase 1,000 gidgets (which are similar to widgets but are more popular because of their greater durability and- r... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 247 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | J. There was no written agreement to the modification. The problem states that the initial agreement was in writing, but the modification was made via a telephone conversation. For contracts that require a written agreement, any changes must be in writing to be enforceable. Since the original contract's terms (quantity... |
[
{
"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
} | To solve this problem, we need to understand Aristotle's view on the control of vice and virtue. Let's break down the problem.
The problem states that we need to determine which option correctly represents Aristotle's claim. The key here is to recall Aristotle's specific stance on the malleability of moral attributes.... |
[
{
"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 problem where Tsovak and Narek are playing a game with an array and a matrix. The goal is to determine who wins given optimal play from both. Let's try to understand the problem step by step.
So, the setup is: there's an array a of length l, and a matrix b of size n x m. The players ... |
[
{
"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 programming problem. Let's read the problem carefully and understand what's required.
So the problem is about a card game scenario where Jellyfish is playing a game similar to Slay the Spire. The setup is that there are n cards, each with a power c_i. The binary string s determines w... |
[
{
"content": "Problem: The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? [asy]\ndraw((-.3,-3)--(.1,1)--(-1,0)--(3,0)--cycle);\nlabel(\"$A$\",(.1,1),N);\nlabel(\"$B$\",(-1,0),W);\nlabel(\"$C... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the area of triangle CDE given that the area of triangle ABC is 6 square centimeters and that AB is parallel to DE. Additionally, we know that BD is 4 times BC.
Let's start by analyzing the given information. Since AB is parallel to DE, triangles ABC and CDE are similar by ... |
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{
"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 value of 'a' in the given wave function, we need to ensure that the wave function is normalized. This means that the total probability of finding the particle in the given interval (x=1 to x=3) must equal 1.
The wave function is given by:
\[ \psi(x) = \frac{a}{\sqrt{1 + x}} - 0.5i \]
The normalizatio... |
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{
"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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} | After carefully analyzing the given information from Ibn Battuta's account, I need to determine which option best explains the direct development of the economic system described in the journal. Let's break down the key points from the passage.
The passage describes the port of 'Aden, located on the coast of the ocean... |
[
{
"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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} | <think>
Okay, let's see. I need to solve this problem where I have to find the maximum number of non-overlapping beautiful segments in an array. A beautiful segment is one where the sum from the start to the end is zero. Hmm.
So the problem is, given an array, split it into as many non-overlapping segments as possible... |
[
{
"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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"expected_answer": "A",
"problem_id": "19",
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"subject": "phy",
"type": "MCQ"
} | <think>
Okay, let's see. The problem is to find the correct exponents for the gravitational constant G, Planck's constant h, and the speed of light c in the expression for Young's modulus Y. So Y = c^α h^β G^γ. We need to determine the values of α, β, and γ.
Hmm, right. Young's modulus is a measure of the stiffness of... |
[
{
"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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"expected_answer": "C",
"problem_id": "35",
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"subject": "phy",
"type": "MCQ"
} | <think>
Okay, I need to solve this problem where I have to find the diameter and cross-sectional area of a wire using the given screw gauge readings. Let's start by understanding the problem.
The problem statement says that the cross-section is measured using a screw gauge. The screw gauge has a main scale and a circu... |
[
{
"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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"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, let's try to figure out this problem. So, the task is to compute for multiple queries on substrings of s and t, the maximum number of 1s in the a string after performing certain operations. The operations are based on the machine's rules. Hmm.
First, I need to understand the operations thoroughly. The ma... |
[
{
"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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} | B |
[
{
"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, let's see. We need to find the value(s) of a such that the given limit equals 54. Hmm. The limit is
\[
\lim_{n \to \infty} \left( \frac{1 + \sqrt[3]{2} + ... + \sqrt[3]{n}}{n^{7/3} \left( \frac{1}{(a n +1)^2} + ... + \frac{1}{(a n +n)^2} \right)} \right) = 54.
\]
First, I need to figure out how to simp... |
[
{
"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,... | {
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} | 1 | 11 | GPQADiamond | {
"expected_answer": "",
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} | To solve this problem, we need to determine the kinetic energies of the muon (μ+) and the neutrino (ν) produced when a stationary pi-plus (π+) particle decays. The decay process is π+ → μ+ + ν.
### Approach
1. **Conservation of Energy and Momentum**: Since the π+ is initially stationary, the total energy and momentum ... |
[
{
"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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} | <think>
Okay, let's see. I need to find the longest subarray where each element's frequency is <= k. Hmm. So the problem is similar to the sliding window technique where we track frequencies and adjust the window based on some condition. The condition here is that if any element's frequency exceeds k, we need to move t... |
[
{
"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... | {
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} | To solve this problem, we need to determine the melting point of monoclinic sulfur when the pressure is increased from 1 atm to 1000 atm. The given data includes the melting point at 1 atm, the change in volume during fusion, and the enthalpy of fusion.
### Approach
The problem can be approached using the Clapeyron e... |
[
{
"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 | 378 | CodeElo | {
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} | <think>
Okay, so I need to solve this problem where I have to construct a permutation of numbers from 1 to n such that after performing a series of operations (bitwise AND for odd steps and OR for even steps), the final value of k is maximized. Hmm. Let's think about how to approach this.
First, let's understand the p... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S consisting of lowercase English letters.\r\nRemove all occurrences of a, e, i, o, u from S an... | {
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"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 solve this problem where I have to remove all the vowels from a given string. Let's see. The vowels are a, e, i, o, u. So the task is to go through each character in the input string and exclude any of those vowels. The output should be the resulting string after removing all these vowels.
Hmm.... |
[
{
"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)"
} | <think>
Okay, let's see. The problem is to find which of the given compounds have two lone pairs of electrons on the central atom. Hmm. So, I need to analyze each molecule and count the lone pairs around the central atom.
Wait, the central atom's valence electrons plus any non-bonding pairs (lone pairs) are what dete... |
[
{
"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,
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} | 0 | 446 | MMLUPro | {
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} | B |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: One mole of a monatomic ideal gas undergoes an adiabatic expan... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 159 | JEEBench | {
"expected_answer": "900",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, I need to solve this problem where a monatomic ideal gas undergoes an adiabatic expansion. The volume becomes eight times the initial, and I have to find the decrease in internal energy. Let's think through this step by step.
First, remember that for an ideal gas, the internal energy depends only on temp... |
[
{
"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,
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} | 1 | 404 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to process a series of insert and delete operations on a sequence. The challenge is to handle these operations efficiently because the constraints are pretty tight—up to 2e5 operations. So, using a regular list data structure might not work because inserting and d... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 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 count the number of placements of n chips on x points with a certain cost m. The cost is the minimum number of chips left after performing operations. Let me try to understand the problem first.
So, the operations allowed are moving or transforming chips. 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, let's see. The problem is to find the number of ordered pairs (a, b) such that the polynomial x³ + ax² + bx +6 has three distinct integer roots. Hmm. So, the polynomial must have three distinct integer roots, which means when we factor it, it's (x - r)(x - s)(x - t), where r, s, t are distinct integers. 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": 1,
"temperature": 0.7
} | 1 | 126 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to find the minimal length of a string that contains both a and b as a substring and subsequence respectively. Let me think about how to approach this.
First, let's understand the problem. We need a string S such that:
1. a is a substring of S. So, the characters of a m... |
[
{
"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. The problem is about a triangular array of integers. The first few rows are given, and we need to find the units digit of the sum of the 2023rd row. Hmm. Let's think about how the rows are structured.
Looking at the examples:
Row 1: 1 → sum is 1. Units digit 1.
Row 2: 1 1 → sum 2. Units digit... |
[
{
"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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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 206 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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} | To find the equation of the line in the form \( y = mx + b \), we start with the given parametric equations. The parametric equations are derived from the line's parameterization:
\[
\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \end{pmatrix}
\]
This means tha... |
[
{
"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,
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"problem_id": "",
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Okay, let's see. So the problem is to find a sequence of operations that makes all elements of an array zero. Each operation involves choosing an x, then replacing each element with the absolute difference between itself and x. We need to do this in at most 40 steps, or return -1 if impossible.
Hmm. Let me thi... |
[
{
"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, let's see. I need to determine if the given tiles can be placed on the grid such that every cell is covered exactly once. Hmm. So the problem is about tiling a grid with various tiles, each of which can be rotated or flipped. The key points are that each tile must fit exactly into the grid without overlap... |
[
{
"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... | {
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"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, let's see. The problem is about the geometries of ammonia complexes of different metal ions. So, I need to figure out the correct geometry for each of these: nickel(II), platinum(II), and zinc(II) when they form complexes with ammonia.
Hmm. Let's start by recalling the coordination numbers and the corres... |
[
{
"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 | 11 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem. So, the task is to count the number of ordered pairs (a, b) where 1 ≤ a ≤ n, 1 ≤ b ≤ m, and a + b is a multiple of b multiplied by the gcd of a and b. Hmm, that's a bit tricky. Let me break it down.
First, let's rephrase the condition. The condition is (a + b) mod (b... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums having length n.\nYou are allowed to perform a special move any number of times (including zero) on nums. In one s... | {
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"seed": 2,
"temperature": 0.7
} | 2 | 151 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the minimum cost to make all elements in an array equal to a palindromic number. The cost is the sum of the absolute differences between each element and the chosen palindromic number. Hmm, let's think.
First, the problem states that the array must become... |
[
{
"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,
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} | 0 | 246 | MMLUPro | {
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"problem_id": "",
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} | B
The patient's symptoms suggest a possible abscess or infected cyst in the labia. The presence of a tender, fluctuant mass indicates that it's a collection of pus, which is a sign of infection. The most appropriate next step is to perform incision and drainage (option B) to relieve the pressure and allow the pus to d... |
[
{
"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... | {
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"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 programming problem. Let's read the problem carefully.
So the problem is about a railway line with N stations. There are inbound trains that start at station 1 and go to 2, 3, ..., N. Outbound trains start at N and go to N-1, N-2, ..., 1. Takahashi is traveling from X to Y using eith... |
[
{
"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
} | <think>
Okay, let's see. The problem is about calculating the probability that at some point during 4 rolls of a die, the running total equals 3. Hmm. So we need to find all possible sequences of 4 dice rolls where the sum reaches 3 at least once during the process. Then, divide that by the total possible outcomes (whi... |
[
{
"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": "",
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"subject": null,
"type": null
} | To simplify the given expression, we need to break it down step by step. The expression is:
\[
\sqrt{\dfrac{\dfrac{5}{\sqrt{80}} + \dfrac{\sqrt{845}}{9} + \sqrt{45}}{\sqrt{5}}}
\]
First, let's simplify each term inside the numerator of the fraction. The numerator consists of three terms: \(\dfrac{5}{\sqrt{80}}\), \(\... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 129 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem. So, the task is to determine the number of distinct arrays b that can be formed from all possible arrays a of size n, where each element is between 1 and k, and every integer from 1 to k appears at least once. The array b is constructed by, for each element a_i, findi... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: For any positive integer $n$, define $f_{n}:(0, \\infty) \\rightarrow ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 170 | JEEBench | {
"expected_answer": "D",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the function \( f_n(x) \) defined as the sum of inverse tangent terms. Let's break down each statement and check its validity.
### Statement (A)
The statement claims that \(\sum_{j=1}^{5} \tan^2(f_j(0)) = 55\). Let's compute \( f_j(0) \) for each \( j \).
For \( f_j(x) \):
\[... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 309 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is to arrange n arrays, each of length 2, into a single array such that when they are concatenated in some order, the number of inversions is minimized. Hmm. The key is to find the permutation of the arrays that gives the least inversions.
Wait, each array is of length 2. So whe... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $P$ be the point on the parabola $y^{2}=4 x$ which is at the short... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 65 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to find the point \( P \) on the parabola \( y^2 = 4x \) that is closest to the center \( S \) of the given circle. Then, determine the point \( Q \) on the circle that divides the line segment \( SP \) internally. Finally, check the given options to determine which are correct.
### Step... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Interaction between the bosonic field X and fermions is given by\n\n\\mathcal{L}\\left(y\\right)=-\\lambda{f}\\bar{\\psi}{f}\\left(y\\right)\\left(\\upsilon+X\\left(... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 134 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the possible decays of the boson X, we need to consider the interaction term given in the problem. The interaction is between the bosonic field X and a fermion field, which is described by the Lagrangian term:
\[
\mathcal{L} = -\lambda f \bar{\psi} (y) (\upsilon + X(y)) \psi_f (y)
\]
Here, \( f \) is a f... |
[
{
"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"
} | <think>
Okay, let's see. I need to find the values of alpha, beta, gamma, and delta such that the product of e^alpha * m_e^beta * h^gamma * k^delta gives the magnetic field's dimension. Then sum those exponents and get the answer.
Hmm. So first, I should figure out the dimensions of each of these constants in terms of... |
[
{
"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 find the minimum number of swaps to group all the black balls (1s) to the right and white balls (0s) to the left. Let's think about how to approach this.
So, the problem is similar to separating two types of elements with the minimum number of adjacent swaps. ... |
[
{
"content": "Problem: In how many ways can 5 students be selected from a group of 6 students?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 455 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem of selecting 5 students from a group of 6, we can use the concept of combinations. The number of ways to choose k elements from a set of n elements without regard to the order is given by the binomial coefficient, which is calculated as C(n, k) = n! / (k! * (n - k)!).
In this problem, we need to f... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 295 | 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 sum of f(i^k, d) for all i from 1 to n, modulo 1e9+7. And f(n, d) is the number of leaves in that divisor tree.
First, I need to understand what f(n, d) represents. From the description, the leaves are the d-th layer nodes.... |
[
{
"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 turn a string into a palindrome with the least number of changes, and if there are multiple options, pick the lex smallest one. Let's think about how to approach this.
First, the main idea is to make the string a palindrome by changing as few characters as pos... |
[
{
"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 try to figure out this problem. So, we need to construct a permutation of length n such that the sum of f(i) minus the sum of g(i) for all i from 1 to n is maximized.
First, I need to understand what f(i) and g(i) represent.
From the description, f(i) is the sum of all elements in the prefix of ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Use divergence therem to evaluate $\\iint_S \\vec{F} \\cdot d \\vec{S}$ where $\\vec{F} = sin(\\pi x) \\vec{i} + (z y^3)\\vec{j} + (z^2 + 4x)\\vec{k}... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 227 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to evaluate the surface integral of the vector field \(\vec{F}\) over the surface \(S\) of a box. The box is defined by the ranges \(-1 \le x \le 2\), \(0 \le y \le 1\), and \(1 \le z \le 4\). The surface integral can be computed using the Divergence Theorem, which states that the integra... |
[
{
"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 compute the sum over all pairs (i,j) where i < j of max(A_j - A_i, 0). Hmm. Let's think about how to approach this efficiently because the constraints are up to 4e5 elements, so O(N^2) is definitely not going to work. That's way too slow. So I need a smarter ap... |
[
{
"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, let's see. The problem is about generating a string where each character is 'o' if the penalty kick is successful, and 'x' otherwise. The rule is that if the index (i) is a multiple of 3, he fails. Otherwise, he succeeds. Wait, but wait, the indices start from 1, right? Because in the sample input 7, the ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given 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, let's see. I need to write a Python function that calculates the difference between two sums: one for numbers not divisible by m and the other for those divisible. Hmm.
So the steps are: first, compute the sum of numbers from 1 to n that are not divisible by m. Then compute the sum of those that are. Sub... |
[
{
"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 to find the sum S of a series of numbers that start with 7, followed by a bunch of 5s, then ending with 7. Each term in the sum increases the number of 5s by one. For example, the first term is 77 (two digits, r=0?), then 757 (three digits, r=1?), and so on up to r=98, which woul... |
[
{
"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"
} | Let's analyze each statement one by one to determine which ones are correct.
Statement (I): Lyophobic colloids are not formed by simple mixing of dispersed phase and dispersion medium.
- Lyophobic colloids are those where the dispersed phase has a weak affinity for the dispersion medium. They are less stable compared... |
[
{
"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, I need to solve this problem where I have to find the limit of f(x) as x approaches negative infinity, given that f is a differentiable function with f(0) = 0 and satisfies the differential equation dy/dx = (2 + 5y)(5y - 2). Let's think through this step by step.
First, let's understand the differential ... |
[
{
"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 I have a family tree, and some insurances that cover certain people and their descendants. The goal is to find out how many people are covered by at least one insurance. Hmm.
So the input gives the number of people N and the number of insurances M. Then there... |
[
{
"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 a winning strategy. Let me read the problem statement carefully again.
So the setup is: there are n cities in a row. At time 1, I conquer one city (the starting city). Then, each subsequent time (from 2 to n), I ca... |
[
{
"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, let's see. So the problem is about a grid that's infinitely big, but each cell's color is determined by a pattern of size N x N. So the color of (i,j) is determined by (i mod N, j mod N). And we have to answer Q queries, each asking for the number of black squares in a rectangle defined by (A,B) as the 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 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. The problem is to determine if two strings of length 4 can be made equal by performing certain operations. The allowed operation is choosing two indices i and j where j-i is 2, then swapping the characters at those positions. So, the operation can be applied any number of times on either 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 try to figure out this problem. So, the task is to determine for each state of the array b (initial and after each update) whether it's possible to rearrange the team members such that each slide i is presented by b_i. The constraints are that the members are in a line, and after each presentation, ... |
[
{
"content": "Problem: There exist real numbers $x$ and $y$ , both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$ . Find $xy$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | AIME24 | {
"expected_answer": "25",
"problem_id": "aime24-16",
"reference_solution": "By properties of logarithms, we can simplify the given equation to $x\\log_xy=4y\\log_yx=10$ . Let us break this into two separate equations: \\[x\\log_xy=10\\] \n \\[4y\\log_yx=10.\\] \nWe multiply the two equations to get: \n \\[4xy\\... | To solve the given problem, we need to find the values of \( x \) and \( y \) such that both \( \log_x(y^x) = 10 \) and \( \log_y(x^{4y}) = 10 \). Then, we need to compute the product \( xy \).
### Approach
1. **Understanding the Logarithmic Equations**:
- The first equation \( \log_x(y^x) = 10 \) can be rewritten ... |
[
{
"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 depth of a well when we measure it using the time interval between dropping a stone and hearing the sound. Hmm. So the main idea here is that the time measured includes both the time the stone takes to fall to the bottom and the time ... |
[
{
"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, let's see. So the problem is that we have two arrays of the same length, and we need to find the integer x such that when we add x to each element of nums1, it becomes equal to nums2. The arrays are considered equal if they have the same elements with the same frequencies. So, the task is to find x.
Hmm.... |
[
{
"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, let's see. So the problem is to find the maximum number of non-overlapping beautiful segments in an array. A beautiful segment is one where the sum of the elements in that segment is zero. And we need to find the maximum number of such segments that don't overlap. Hmm.
First, I need to understand what a ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: 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 understanding the steric factor P in a bimolecular reaction. So, P is given as 4.5, and we have to choose the correct options based on that.
Hmm, first, I need to recall what the steric factor P represents. Oh right, in collision theory, the frequency factor (or collision ... |
[
{
"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. So the problem is about buying fruits where each fruit has a certain price, and there's this offer where if you buy the i-th fruit, you get the next i fruits for free. But you can choose to buy those free ones later if it's better. We need to find the minimum coins required to get all the fruit... |
[
{
"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, let's see. So the problem is about a dragon made up of N parts. The head is part 1, and each subsequent part follows the one in front. So when the head moves, the next part moves to where the head was before the move, and so on. For queries of type 2, we need to find the coordinates of part p.
Hmm, the c... |
[
{
"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. The problem gives a lot of data about various combinations of symptoms. Hmm.
First, I should understand the problem. The total number of people is 900. Each person has some combination of three possible sympt... |
[
{
"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, I need to solve this problem where I have to find the fractional error in the depth of the well measurement. Let's see. The problem says that the person measures the time interval between dropping a stone and hearing the sound. The depth is calculated using that time, considering both the time it takes fo... |
[
{
"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 problem where there are three bags, each with different combinations of red and green balls. The probabilities of selecting each bag are given, and I need to determine which of the four options are correct.
First, let's understand the problem. We have to calculate various... |
[
{
"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 to compute the sum of a sequence of bits multiplied by their corresponding powers of two. Let me think about how to approach this.
So the input is a sequence of 64 bits, A_0 to A_63. The output is the sum of each A_i multiplied by 2^i. Wait, wait, no. Wait, the p... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $\\Gamma$ denote a curve $y=y(x)$ which is in the first quadrant a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 209 | JEEBench | {
"expected_answer": "AB",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which of the given options correctly describe the curve \(\Gamma\) under the given conditions. Let's break down the problem step by step.
### Problem Analysis
The curve \(\Gamma\) passes through the point \((1, 0)\). For any point \(P(x, y)\) on \(\Gamma\), the tangent at \(... |
[
{
"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, let's try to figure out this problem. So, the task is to maximize the score l*W_L + f*W_F under certain constraints. The main constraints are that after every round, the GCD of W_L and W_F must be ≤1. And at the end, W_L ≤n and W_F ≤m. Also, the rounds can stop whenever they want. Hmm.
First, I need to u... |
[
{
"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 number of changes required to make a binary string beautiful. The conditions for a beautiful string are that it can be partitioned into substrings of even length, each consisting of all 0s or all 1s. Hmm.
So the problem is to modify the string such that after changes... |
[
{
"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)"
} | Let's analyze each statement one by one to determine the correct options.
[A] The central atom in both HClO4 and HClO is sp3 hybridized.
For HClO4 (perchloric acid):
The central atom is Cl. Let's count the atoms around Cl. Cl has four bonds (four O atoms) and no lone pairs. So, sp3 hybridization.
For HClO (hypochlor... |
[
{
"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, I need to find the remainder when this polynomial is divided by x+2. Let's see. The problem is to compute (5x+9)^611 + (x+5)^11 + (x-1)^11 + 3x² + 1 mod x+2.
Hmm. The remainder when dividing by x+2 is the same as evaluating the polynomial at x = -2. Because of the Remainder Theorem. So the idea is to sub... |
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