context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 1 200k |
|---|---|---|---|---|---|---|
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 244 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out who will win the game between Alice and Bob based on the number of stones in each pile. The key here is to determine the Grunty values for each pile size and see if the overall XOR of these values is non-zero (Alice wins) or zero (Bob wins).
First, let's recall that in combinator... |
[
{
"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: At $298 \\mathrm{~K}$, the limiting molar conductivity of a we... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 353 | JEEBench | {
"expected_answer": "0.22",
"problem_id": "25",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's try to figure out this problem step by step. So, we have a weak monobasic acid at 298 K. The limiting molar conductivity of this acid is given as 4 × 10² S·cm²·mol⁻¹. Then, in an aqueous solution, the degree of dissociation is α, and the molar conductivity is y × 10² S·cm²·mol⁻¹. When we dilute this... |
[
{
"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: $$\n\\beta=2 \\pi c \\tilde{\\omega}_{\\mathrm{obs}}\\left(\\frac{\\mu}{2 D}\\right)^{1 / 2}\n$$\nGiven that $\\tilde{\\omega}_{\\mathrm{obs}}=2886 \... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 428 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to calculate β using the given formula. Let me first write down the formula again to make sure I have it right:
β = 2πc * ω̃_{obs} * (μ / (2D))^{1/2}
Hmm, let's see. The problem gives ω̃_{obs} as 2886 cm⁻¹ and D as 440.2 kJ·mol⁻¹ for H³⁵Cl. I need to calculate β. The answer should be in units ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.The imbalance number of a 0-indexed integer array arr of length n is defined as the number of indices in sarr = sorted(arr) such that:\n\n0 <= i < n - 1, and\n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 46 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to calculate the sum of imbalance numbers for all subarrays of the given list nums. Let me start by understanding the problem step by step.
First, the imbalance number of a subarray is defined as the number of indices in its sorted version (sarr) where the difference between 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 a 0-indexed integer array nums and a positive integer k.\nYou can do the following operation on the array any number of times:\n\nChoose any two ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 114 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the sum of squares of k elements after performing the given operations on the array. The operations allow me to choose any two indices i and j, then update nums[i] to the bitwise AND of i and j, and nums[j] to the bitwise OR of i and j.
First, let's try to underst... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array nums of length n.\nThe distinct difference array of nums is an array diff of length n such that diff[i] is equal to the number ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 16 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem of finding the distinct difference array. Let me try to understand the problem again.
We have a 0-indexed array nums of length n. The distinct difference array, diff, is supposed to have for each index i, the number of distinct elements in the suffix num... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: ChIP-seq on a PFA-fixed sample with an antibody to the IKAROS transcription factor in human B cells followed by next-generation sequencing and standard quality control, ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 13 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let me try to figure out this ChIP-seq problem. So, the question is about where we might find ChIP peaks that disappear when using PFA+DSG fixation instead of just PFA. The options are repeats, random locations, introns of large genes, or active promoters and enhancers. Hmm.
First, I need to recall wh... |
[
{
"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: Consider the cube in the first octant with sides $O P, O Q$ an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 178 | JEEBench | {
"expected_answer": "0.5",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let me try to figure out this problem step by step. So, we have a cube in the first octant with sides OP, OQ, and OR each of length 1 along the x, y, and z axes respectively. The center of the cube is at point S(1/2, 1/2, 1/2). We need to find the value of |(p × q) × (r × t)| where p, q, r, and t are vect... |
[
{
"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: Consider the equation\n\\[\n\\int_{1}^{e} \\frac{\\left(\\log _{\\math... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 384 | JEEBench | {
"expected_answer": "CD",
"problem_id": "9",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of the statements A, B, C, or D are true regarding the given integral equation. The integral is from 1 to e of [ (√(ln x)) / (x * (a - (ln x)^(3/2))^2) ] dx, and it's supposed to equal 1. The parameter a is in (-∞, 0) ∪ (1, ∞). Let me try to work through this step by step.
F... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: On dissolving $0.5 \\mathrm{~g}$ of a non-volatile non-ionic s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 199 | JEEBench | {
"expected_answer": "1.02",
"problem_id": "34",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the depression of freezing point of benzene when 0.5 grams of a non-volatile, non-ionic solute is added to 39 grams of benzene. The given data includes the molar mass of benzene as 78 g/mol and the molal freezing point depression constant as 5.12 K kg/mol. The initial vapor pressure of b... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 302 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Pak Chanek has to set up internet connections in a village represented as a graph. The goal is to find the minimum total latency for each possible number of servers \( k \) from 1 to \( n \). Each house can be connected to at most one server, and the latency for a hou... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Substances 1-6 undergo an electrophilic substitution reaction with an excess of bromine (it is assumed that only one monobromo derivative is formed):\n1) С6H5-CH3\n2) C6... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 170 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let me try to figure out the correct order for the weight fraction of the yield of the para-isomer. So, we have six substances, all of which are monobromo derivatives of benzene. The reaction is electrophilic substitution with excess bromine, so I know that bromine usually attacks the benzene ring in e... |
[
{
"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: Consider the lines $\\mathrm{L}_1$ and $\\mathrm{L}_2$ defined... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 332 | JEEBench | {
"expected_answer": "9.00",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let me try to figure out this problem step by step. First, let's understand what's given and what's required.
We have two lines, L1 and L2, defined by the equations:
L1: x√2 + y - 1 = 0
L2: x√2 - y + 1 = 0
There's a constant λ, and C is the locus of points P such that the product of the distances from... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 154 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many people Robin Hood gives gold to based on the rules given. Let me start by understanding the problem step by step.
First, the problem says there are n people, starting from 1 to n. Each person has a_i gold. Robin Hood starts with 0 gold. The threshold k is given, so if a_i... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: When n = 11, what is the value of 10 – (n + 6)?\nOptions: A. 3, B. 0, C. 5, D. –7, E. -5, F. 1, G. 27, H. 7, I. -3, J. 15",
"role": "user"
}
] | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 144 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see here. The problem is asking for the value of 10 minus (n plus 6) when n is 11. The options are given from A to J, and I need to figure out which one is the correct answer. Let me break this down step by step.
First, let's make sure I understand the expression correctly. The problem says 10 – (n... |
[
{
"content": "Problem: Suppose that $a$, $b$, $c$ and $d$ are positive integers satisfying all of the following relations.\n\\[abcd=2^6\\cdot 3^9\\cdot 5^7\\]\n\\[\\text{lcm}(a,b)=2^3\\cdot 3^2\\cdot 5^3\\]\n\\[\\text{lcm}(a,c)=2^3\\cdot 3^3\\cdot 5^3\\]\n\\[\\text{lcm}(a,d)=2^3\\cdot 3^3\\cdot 5^3\\]\n\\[\\tex... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 32 | AMC23 | {
"expected_answer": "3",
"problem_id": "41",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to solve this problem step by step. We need to find the greatest common divisor (gcd) of four positive integers a, b, c, and d, given their products, least common multiples (lcm) in various pairs, and their overall product. Let me start by recalling some number theory concepts.
First, I know th... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: If the line $x=\\alpha$ divides the area of region $R=\\left\\{(x, y) ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 118 | JEEBench | {
"expected_answer": "BC",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out for which value of α between 0 and 1 the vertical line x = α divides the area of the region R into two equal parts. The region R is defined by the inequalities 0 ≤ x ≤ 1, and for each x, y is between x³ and x. So, it's like a region between the curves y = x³ and y = x from x=0 to x... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: In an experiment to determine the acceleration due to gravity $g$, the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 46 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "9",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to tackle this problem step by step. First, I need to understand what's being asked here. The question is about determining the acceleration due to gravity (g) using the given formula for the time period (T) of a certain motion. The formula provided is \( T = 2\pi \sqrt{\frac{7(R - r)}{5g}} \). ... |
[
{
"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: Consider the lines $\\mathrm{L}_1$ and $\\mathrm{L}_2$ defined... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 333 | JEEBench | {
"expected_answer": "77.14",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let's try to tackle this problem step by step. First, let me make sure I understand what's being asked. We have two lines, L1 and L2, given by the equations:
L1: x√2 + y - 1 = 0
L2: x√2 - y + 1 = 0
These lines are part of a locus C where for any point P, the product of the distances from P to L1 and L... |
[
{
"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 | 380 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of coins required to defeat a monster with health z using a weapon that starts with 0 damage. The operations are: increasing the damage by 1 (costing x coins) and attacking the monster with the current damage (costing y coins). There's a restriction that we can't... |
[
{
"content": "Problem: How many digits are in the base-ten representation of $8^5 \\cdot 5^{10} \\cdot 15^5$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 17 | AMC23 | {
"expected_answer": "18",
"problem_id": "19",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many digits are in the base-ten representation of this number: \(8^5 \cdot 5^{10} \cdot 15^5\). Hmm, let me start by breaking it down.
First, I remember that the number of digits in a number can be found by taking the logarithm base 10 of the number and then adding 1, and the... |
[
{
"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: If $M=\\left(\\begin{array}{rr}\\frac{5}{2} & \\frac{3}{2} \\\\ -\\frac{3... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 427 | JEEBench | {
"expected_answer": "A",
"problem_id": "16",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to find which matrix is equal to M raised to the 2022nd power. The matrix M is given as:
M = [ [5/2, 3/2], [-3/2, -1/2] ]
Hmm, let me think. First, maybe I should check if this matrix is diagonalizable or if it has any special properties that could make exponentiating it easier. For example, i... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A tin chloride $\\mathrm{Q}$ undergoes the following reactions (not ba... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 190 | JEEBench | {
"expected_answer": "AB",
"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, we have a tin chloride Q that undergoes three different reactions, and each reaction produces a different product: X, Y, or Z. The problem gives us some information about the products and asks us to determine which of the given options are correct. Le... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.An array is considered special if every pair of its adjacent elements contains two numbers with different parity.\nYou are given an array of integers nums. Ret... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 501 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out if an array is special. A special array is defined as one where every pair of adjacent elements has different parity. That means, if one number is even, the next one has to be odd, and vice versa. Let me try to break this down step by step.
First, let me recall what parity means. ... |
[
{
"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 $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be a differentiable function such that $f(0)=0, f\\left(\\frac{\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 90 | JEEBench | {
"expected_answer": "2",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, so I need to find the limit as x approaches 0 of the function g(x), which is defined as an integral from x to π/2 of [f'(t) cosec t - cot t cosec t f(t)] dt. Hmm, let me start by understanding the problem step by step.
First, let's recall that f is a differentiable function with f(0) = 0 and f(π/2) = 3. ... |
[
{
"content": "Problem: If Rosa's age is divided by 2, 3, 4, or 6, the remainder is 1. If her age is divided by 7, the remainder is 0. She is less than 75 years old. How many years old is Rosa?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 149 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out Rosa's age based on the given conditions. Let me start by breaking down the problem step by step.
First, the problem says that when Rosa's age is divided by 2, 3, 4, or 6, the remainder is 1 in each case. Then, when her age is divided by 7, there's no remainder, meaning 7 is a div... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: How many of the stars listed below would be detectable using the ESPRESSO spectrograph, when it is coupled with one of the 8m VLT telescopes at the Paranal Observatory? ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 186 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many of these stars listed (Canopus, Polaris, and the four others) would be detectable using the ESPRESSO spectrograph on the 8m VLT telescopes at Paranal. The key is to check if each star's signal-to-noise ratio (S/N) is at least 10 per binned pixel after a 1-hour exposure.
F... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $f:\\left[-\\frac{1}{2}, 2\\right] \\rightarrow \\mathbb{R}$ and $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 63 | JEEBench | {
"expected_answer": "BC",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let me try to figure out this problem step by step. So, we have two functions here: f(x) and g(x). Both are defined on the interval [-1/2, 2]. The function f(x) is given as [x² - 3], which is the greatest integer less than or equal to x² - 3. Then g(x) is defined as |x| times f(x) plus |4x - 7| times f(x)... |
[
{
"content": "Problem: The area of triangle $ABC$ is equal to $a^2 - (b - c)^2,$ where $a,$ $b,$ and $c$ are the sides of triangle $ABC,$ as usual. Compute $\\tan A.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 483 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find tan A given that the area of triangle ABC is equal to \( a^2 - (b - c)^2 \). Hmm, let me start by recalling some formulas related to the area of a triangle and trigonometric identities.
First, the standard formula for the area of a triangle is \( \frac{1}{2}bc \sin A \). Maybe I can se... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.For a positive integer X, the Dragon String of level X is a string of length (X+3) formed by one L, X occurrences of o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 360 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python function that takes a positive integer N as input and prints the Dragon String of level N. The Dragon String is supposed to have a length of (N + 3) and consists of one 'L', N number of 'o's, one 'n', and one 'g' in that specific order. Let me make sure I understand the proble... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Astronomers are studying a system of three exoplanets (Planet1, Planet2, and Planet3) with circular orbits discovered through the TTV method. They have found that the ra... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 41 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to figure out by what factor the orbital period of Planet3 is larger than that of Planet1, given the temperature ratios and mass ratios, with all planets having the same albedo of 0.3. Hmm.
First, I remember that for exoplanets, their equilibrium temperature is related to their distanc... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: In an X-ray tube, electrons emitted from a filament (cathode) carrying... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 279 | JEEBench | {
"expected_answer": "AC",
"problem_id": "10",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, let me try to figure out this problem step by step. So, we have an X-ray tube where electrons are emitted from a filament (cathode) with current I, hit a target (anode) at distance d, which is kept at a potential V higher than the cathode. The X-rays emitted are continuous and characteristic. Now, the con... |
[
{
"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: For how many positive integral values of x ≤ 100 is 3^x − x^2 divisible by 5?\nOptions: A. 25, B. 50, C. 15, D. 20, E. 10, F. 35, G. 40, H. 55, I. 30... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 334 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out for how many positive integers x ≤ 100 the expression 3^x - x² is divisible by 5. That means when you divide 3^x - x² by 5, there's no remainder. So, another way of saying that is that 3^x ≡ x² mod 5. Hmm, modular arithmetic. Let me recall how exponents work in modular arithmetic. ... |
[
{
"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 weighted undirected complete graph with N vertices numbered from 1 to N. The edge connecting vertices ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 273 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where we have a complete graph with N vertices, and each edge has a weight D_{i,j}. We need to choose some edges such that their endpoints are pairwise distinct, and maximize the total weight. Hmm, let's see.
First, let me parse the problem again. The gra... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.This is an interactive problem (a type of problem where your program interacts with the judge program through Standard... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 368 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where there are N bottles of juice, one of which is spoiled. The goal is to identify the spoiled bottle by giving some bottles to friends and then seeing which ones make them sick. The challenge is to use the minimum number of friends necessary.
First, l... |
[
{
"content": "Problem: Every morning Aya goes for a $9$ -kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 15 | AIME24 | {
"expected_answer": "204",
"problem_id": "aime24-15",
"reference_solution": "$\\frac{9}{s} + t = 4$ in hours and $\\frac{9}{s+2} + t = 2.4$ in hours. Subtracting the second equation from the first, we get, $\\frac{9}{s} - \\frac{9}{s+2} = 1.6$ Multiplying by $(s)(s+2)$ , we get $9s+18-9s=18=1.6s^{2} + 3.2s$ ... | <think>
Okay, let's try to figure out this problem step by step. So, Aya walks 9 kilometers every morning and stops at a coffee shop. We need to find out how long it takes her when she walks at s + 0.5 km/h, including the time she spends in the coffee shop, which is t minutes.
First, let's parse the information 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 88 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Yunli has an array and can perform operations to make subarrays consecutive. The goal is to calculate the sum of f(b) for all possible consecutive subarrays within a given range for each query. The function f(b) is the minimum number of operations needed to make a con... |
[
{
"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 | 342 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many operations Alice needs to perform to turn her array into a permutation by replacing the maximum element with the MEX each time. Let me start by understanding the problem step by step.
First, Alice's array is constructed using the formula \( a_i = b \times (i - 1) + c \) f... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $\\ell_{1}$ and $\\ell_{2}$ be the lines $\\vec{r}_{1}=\\lambda(\\hat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 465 | JEEBench | {
"expected_answer": "B",
"problem_id": "16",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, let's tackle this problem step by step. First, I need to understand what's being asked here. We have two lines, ℓ₁ and ℓ₂, given in vector form. Then, we need to consider all planes H that contain ℓ₁. For each plane H, we find the smallest distance d(H) between points on ℓ₂ and H. The plane H₀ is the one ... |
[
{
"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 $L_{1}$ and $L_{2}$ be the following straight lines.\n\\[\nL_{1}: ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 269 | JEEBench | {
"expected_answer": "AB",
"problem_id": "47",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let me try to solve this problem step by step. So, we have two lines, L1 and L2, given in parametric form. Then there's a line L that lies in the plane containing L1 and L2, passes through their intersection point, and bisects the acute angle between L1 and L2. We need to find which statements among A, B,... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 388 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many times the number 1543 appears in all layers of a carpet when traversed clockwise. The carpet is given as an n x m grid, where n and m are both even integers. Each cell contains a digit from 0 to 9. The problem states that we need to check how many times 1543 appears in the... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 185 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to find a permutation q that minimizes the number of pairs of indices (i, j) where the sum of the subarray from p_i to p_j is equal to the sum of the subarray from q_i to q_j. The original permutation p is given, and I need to construct q such that these sums (... |
[
{
"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 | 65 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the score in this game between Turtle and Piggy. Let me start by understanding the problem again.
Turtle picks a number x between l and r, inclusive. Then Piggy keeps dividing x by some integer p (greater than or equal to 2) that divides x, each time increasing the... |
[
{
"content": "Problem: Cities $A$ and $B$ are $45$ miles apart. Alicia lives in $A$ and Beth lives in $B$. Alicia bikes towards $B$ at 18 miles per hour. Leaving at the same time, Beth bikes toward $A$ at 12 miles per hour. How many miles from City $A$ will they be when they meet?\nMark your solution with \\box... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 0 | AMC23 | {
"expected_answer": "27",
"problem_id": "0",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so there's this problem where Alicia and Beth are biking towards each other from cities A and B, which are 45 miles apart. Alicia is going at 18 mph, and Beth at 12 mph. I need to find out how many miles from city A they'll meet. Hmm, let's see.
First, since they're moving towards each other, their spee... |
[
{
"content": "Problem: Simplify $\\frac{1}{5}\\cdot \\frac{8}{7}\\div \\frac{12}{20}$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 256 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to simplify the expression \(\frac{1}{5} \cdot \frac{8}{7} \div \frac{12}{20}\). Hmm, let me think about how to approach this step by step. First, I remember that dividing fractions is the same as multiplying by their reciprocals. So, maybe I can rewrite the division part as multiplication. Let ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 451 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we're given an array of integers, and we have to find the maximum possible value of some subsequence. The value is defined as the size of the subsequence minus the number of set bits in the bitwise OR of all elements in the subsequence.
First, let me parse the examp... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 224 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about Ksyusha and the Loaded Set. Let me try to understand the problem first. We have a set of integers initially containing n distinct integers. Then there are m operations: insert, remove, or query the k-load of the set. The k-load is the smallest positive integer d such ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums consisting of integers. You are also given a 2D array queries, where queries[i] = [pos_i, x_i].\nFor query i, we first set nums[pos... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 506 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have an array `nums` and a series of queries. Each query updates an element in `nums` at position `pos_i` to `x_i`, and then we need to find the maximum sum of a non-adjacent subsequence of the updated `nums`. Then, sum up all these maximum sums for each query and ... |
[
{
"content": "Problem: What is the degree measure of the acute angle formed by lines with slopes $2$ and $\\frac{1}{3}$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 2 | AMC23 | {
"expected_answer": "45",
"problem_id": "2",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the acute angle between two lines with slopes 2 and 1/3. Hmm, let me recall how angles between lines relate to their slopes. I think there's a formula involving the arctangent of the absolute value of the difference in slopes divided by 1 plus the product of the slopes. Wait, is that rig... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 137 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of coins required to buy all the fruits in the market. The problem says that if I buy the i-th fruit at price prices[i], I can get the next i fruits for free. But even if I can get them for free, I might still need to buy them to get a new offer. Hmm, interesting... |
[
{
"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.Aoki, an employee at AtCoder Inc., has his salary for this month determined by an integer N and a sequence A of length... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 315 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the expected value of Aoki's salary based on the given process and then find its modulo 998244353. Let me start by understanding the problem step by step.
First, Aoki is rolling an N-sided die, starting with x = 0. Each time he rolls, if the result y is greater than the current x,... |
[
{
"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 temperature of a black body given in List-I with an appropriate... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 475 | JEEBench | {
"expected_answer": "C",
"problem_id": "32",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | <think>
Okay, let's tackle this problem step by step. First, I need to recall what a black body is and how its temperature relates to the wavelength of peak emission. The key here is Wien's Law, which states that the peak wavelength (λ_max) of a black body's emission is inversely proportional to its temperature (T). Ma... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a binary string s that contains at least one '1'.\nYou have to rearrange the bits in such a way that the resulting binary number is the maximum o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 102 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to generate the maximum odd binary number from a given binary string that has at least one '1'. Let me start by understanding the problem again.
The key points are:
1. The input is a binary string with at least one '1'.
2. We need to rearrange the bits such that the resulting... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The crystalline form of borax has\n(A) tetranuclear $\\left[\\mathrm{B... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 18 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let me try to figure out the correct answers for the problem about the crystalline form of borax. So, the question is about the structure of borax, which is sodium tetraborate decahydrate, but the problem is referring to its anhydrous form for the crystalline structure. Let me go through each option one b... |
[
{
"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 rhombohedral crystal, with the interatomic distance of 10 Angstrom and the angles $\\quad\\alpha=\\beta=\\gamma=30^{0}$. What is the interplanar distance of t... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 187 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the interplanar distance of the (111) plane in a rhombohedral crystal. The interatomic distance is given as 10 Angstrom, and all the angles α, β, γ are 30 degrees. Hmm, let's start by recalling what I know about rhombohedral crystals.
First, rhombohedral is a type of crystal system wher... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 212 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many ways the game can happen where Suneet ends up as the winner. Let me start by understanding the problem again. Each player has two cards, and they take turns flipping one card each. The one who flips a higher number wins the round. If they flip the same number, no one wins.... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A flat plate is moving normal to its plane through a gas under the act... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 68 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "1",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to figure out this problem step by step. So, we have a flat plate moving normal to its plane through a gas, under the action of a constant force F. The gas is at very low pressure, and the plate's speed v is much less than the average speed u of the gas molecules. We need to check which of the o... |
[
{
"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 $R S$ be the diameter of the circle $x^{2}+y^{2}=1$, where $S$ is ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 36 | JEEBench | {
"expected_answer": "AC",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, let's try to tackle this geometry problem step by step. First, let me parse the problem again to make sure I understand all the components.
We have a circle given by the equation \(x^2 + y^2 = 1\). The diameter \(RS\) is such that \(S\) is the point \((1, 0)\). Since \(RS\) is the diameter, the other end... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 353 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have an array, and we want to count the number of subarrays that can be made consecutive by adding elements using the given operations. The key is to recognize that the consecutive set must have an arithmetic progression with an odd common difference, which is a po... |
[
{
"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: Choose the correct option(s) from the following\n(A) Natural rubber is... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 226 | JEEBench | {
"expected_answer": "BC",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let me try to figure out which of these options are correct. Hmm, starting with option A: Natural rubber is polyisoprene containing trans alkene units. I remember that natural rubber is indeed a polymer of isoprene, which is a five-carbon compound. But wait, isoprene usually has a double bond, right? So w... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | To solve the problem of determining the maximum number of rounds Monocarp can survive after each query, we need to consider how distributing artifacts to heroes affects the total damage over rounds. The key idea is to maintain the balance between the number of artifacts and heroes and calculate the total damage contrib... |
[
{
"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.N AtCoder users have gathered to play AtCoder RPS 2. The i-th user's name is S_i and their rating is C_i.\nAtCoder RPS... | {
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"problem_id": "",
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} | <think>
Okay, so I need to figure out the winner of this AtCoder RPS 2 game based on the given rules. Let me start by understanding the problem step by step.
First, the game involves N users. Each user has a name (S_i) and a rating (C_i). The key point here is that the users are assigned numbers from 0 to N-1 based on... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 198 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
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} | <think>
Okay, so I need to figure out how many starting cities allow me to win the game based on the given deadlines. Let me start by understanding the problem again.
We have n cities in a row, numbered from 1 to n. At time 1, I choose a starting city. Then, each subsequent time step from 2 to n, I can choose a city ... |
[
{
"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: According to one theory, the power of Ancestral Pueblo elites emerged when certain groups:\nOptions: A. created intricate pottery and jewelry., B. di... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 383 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
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} | <think>
Okay, so I need to figure out which option best explains how the power of Ancestral Pueblo elites emerged according to the theory mentioned. Let me start by recalling what I know about the Ancestral Pueblo people. They were ancient inhabitants of the southwestern United States, primarily in what is now Arizona,... |
[
{
"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) for cubic close packed (ccp) three dimensiona... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 53 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of these statements are correct about the cubic close packed (ccp) structure. Let me start by recalling what I know about ccp.
First, cubic close packed is another way of saying face-centered cubic (FCC), right? Because when you pack atoms in a cube, the most efficient way ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 1 | 378 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, so I need to solve this problem where for each query, I have to find the maximum modulus m such that all elements in the given range are equal modulo m. The key idea here seems to be that m must divide the difference between any two consecutive elements in the range. Therefore, m is the greatest common di... |
[
{
"content": "Problem: Let $P(x)$ be a quadratic polynomial with real coefficients satisfying $x^2 - 2x + 2 \\le P(x) \\le 2x^2 - 4x + 3$ for all real numbers $x$, and suppose $P(11) = 181$. Find $P(16)$.\nMark your solution with \\boxed\nAnswer:",
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] | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 412 | MATH500 | {
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} | <think>
Okay, so I have this problem here where I need to find P(16) for a quadratic polynomial P(x) that satisfies certain inequalities for all real numbers x. The polynomial also has real coefficients, and I know that P(11) = 181. Let me try to break this down step by step.
First, let's parse the problem statement a... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Which of the following statements are true concerning a comparison between ARCH(q) and GARCH(1,1) models?\n\ni) The ARCH(q) model is likely to be the... | {
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"problem_id": "",
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Okay, let's try to figure out this problem step by step. So, we need to compare the ARCH(q) model and the GARCH(1,1) model and see which statements about them are true. The options are given, and we have to choose the correct combination. Let me start by recalling what each model is.
First, the ARCH(q) model s... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The solubility of a salt of weak acid (AB) at $\\mathrm{pH} 3$... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 136 | JEEBench | {
"expected_answer": "4.47",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the solubility of the salt AB at pH 3, which is given as Y × 10⁻³ mol L⁻¹. The solubility product (K_sp) of AB is 2 × 10⁻¹⁰, and the acid dissociation constant (K_a) of HB is 1 × 10⁻⁸. Hmm, let's break this down step by step.
First, I remember that when a salt of a weak acid dissolves i... |
[
{
"content": "Problem: A $90^\\circ$ rotation around the origin in the counter-clockwise direction is applied to $7 + 2i.$ What is the resulting complex number?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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} | 0 | 28 | MATH500 | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, so I need to figure out what happens when I rotate the complex number 7 + 2i by 90 degrees counterclockwise around the origin. Hmm, complex numbers and rotations... I remember that rotating a complex number can be done by multiplying it by a certain complex number. Let me recall.
First, a rotation by 90 ... |
[
{
"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 | 130 | CodeElo | {
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"problem_id": "",
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} | <think>
Okay, so I need to figure out how to solve this problem where we have a matrix and we can paint rows red or columns blue. The cost is based on how many actions we take, and if we take multiple actions at the same time, the cost is the square of the number of actions. The goal is to process a series of queries w... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 334 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
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} | <think>
Okay, so I need to solve this problem where we have an integer sequence, and after each update (increasing an element by x), we need to find the length of the longest good subarray. A good subarray is defined by the condition: MEX(c) - (OR of elements in c) = 1.
First, let's parse the problem again. The seque... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: What is meant by a gene pool, balanced polymorphism, and genetic load?\nOptions: A. Gene pool is the total number of organisms in a population; balan... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the correct answer regarding gene pools, balanced polymorphism, and genetic load. Let me start by understanding each term individually and then see how they fit together.
First, a **gene pool**. From what I remember, the gene pool refers to all the genetic information carried by a... |
[
{
"content": "Problem: Positive real numbers $x$ and $y$ satisfy $y^3=x^2$ and $(y-x)^2=4y^2$. What is $x+y$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 1 | AMC23 | {
"expected_answer": "36",
"problem_id": "1",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have two positive real numbers, x and y, that satisfy two equations: y³ = x² and (y - x)² = 4y². The question is asking for x + y. Alright, let me start by writing down the equations again to make sure I have them right.
First equation: y³ = x².
Second equation: ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 213 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about checking if a permutation is a valid DFS order after swapping two elements. Let me try to break it down step by step.
First, the problem says we have a tree with n vertices, and a permutation of [1, 2, ..., n]. We need to answer q queries where each query swaps two ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 29 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the maximum possible value that the array can be changed to using Mocha's operations. Let me start by understanding the problem again.
Chamo gives Mocha an array of n positive integers. Mocha can perform operations where she selects a subarray (between indices l and r, inclusive)... |
[
{
"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 | 302 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a graph with n houses and m internet cables. Each cable has a certain latency. There are p houses that need internet, and we can install servers in at most k houses. The goal is to find the minimum total latency for each k from 1 to n.
First, let me understan... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array nums consisting of positive integers.\nA partition of an array into one or more contiguous subarrays is called good if no two s... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 140 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where I have to find the number of good partitions in an array. A good partition is one where no two subarrays have the same number. The answer should be modulo 10^9 + 7. Let me try to break this down step by step.
First, let me understand the problem aga... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Astronomers are studying a star with a 1.5 solar radius and 1.1 solar masses. When the star's surface is not covered by dark spots, its Teff is 6000K. However, when 40% ... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 51 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem step by step. So, the question is about the ratio of neutral titanium atoms in two energy levels, level 1 and level 2, in a star's photosphere. The ratio decreases when the star has dark spots, and we need to find the factor by which this ratio changes when comparing t... |
[
{
"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 solid horizontal surface is covered with a thin layer of oil... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 154 | JEEBench | {
"expected_answer": "6.3",
"problem_id": "7",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, let me try to figure out this problem step by step. So, we have a rectangular block with mass 0.4 kg on a surface with a thin layer of oil. An impulse of 1.0 N is applied at t=0, which makes the block start moving along the x-axis with a velocity given by v(t) = v₀ e^(-t/τ), where τ is 4 seconds. We need ... |
[
{
"content": "Problem: Let $f$ be the unique function defined on the positive integers such that \\[\\sum_{d\\mid n}d\\cdot f\\left(\\frac{n}{d}\\right)=1\\] for all positive integers $n$. What is $f(2023)$?\nMark your solution with \\boxed\nAnswer:",
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}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 12 | AMC23 | {
"expected_answer": "96",
"problem_id": "14",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the function f defined on positive integers such that for every positive integer n, the sum over all divisors d of n of d times f(n/d) equals 1. Then, specifically, I need to find f(2023). Hmm, let's start by understanding the problem.
First, the function f is uniquely defined by the eq... |
[
{
"content": "Problem: Let $z = 2 + \\sqrt{2} - (3 + 3 \\sqrt{2})i$, and let $c = 2 - 3i$. Let $w$ be the result when $z$ is rotated around $c$ by $\\frac{\\pi}{4}$ counter-clockwise.\n\n[asy]\nunitsize(0.6 cm);\n\npair C, W, Z;\n\nZ = (2 + sqrt(2), -3 - 3*sqrt(2));\nC = (2,-3);\nW = rotate(45,C)*(Z);\n\ndraw(... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 15 | MATH500 | {
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"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the result of rotating the complex number z = 2 + √2 - (3 + 3√2)i around the complex number c = 2 - 3i by π/4 radians counter-clockwise. Hmm, rotating complex numbers... I remember that rotation can be achieved by multiplying by a complex exponential. Let me recall the formula.
If you 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: For the following electrochemical cell at $298 \\mathrm{~K}$,\n$\\mathrm{... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 49 | JEEBench | {
"expected_answer": "D",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, so I need to solve this problem about an electrochemical cell. Let me start by understanding the given information and the question. The cell is Pt(s) | H₂(g, 1 bar) | H⁺(aq, 1 M) || M⁴⁺(aq), M²⁺(aq) | Pt(s). The cell potential E_cell is given as 0.092 V when the ratio [M²⁺]/[M⁴⁺] is 10^x. We are given th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N people numbered 1 through N.\nEach person has a integer score called programming ability; person i's progr... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 255 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many more points person 1 needs to have more points than everyone else. Let me read the problem again to make sure I understand it correctly.
The problem says there are N people, each with a programming ability score, P_i. We need to find the minimum non-negative integer x suc... |
[
{
"content": "Problem: The weight of $\\frac{1}{3}$ of a large pizza together with $3 \\frac{1}{2}$ cups of orange slices is the same as the weight of $\\frac{3}{4}$ of a large pizza together with $\\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\\frac{1}{4}$ of a pound. What is the weight, i... | {
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"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 9 | AMC23 | {
"expected_answer": "4",
"problem_id": "11",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the weight of a large pizza. The problem says that the weight of 1/3 of a pizza plus 3 1/2 cups of orange slices is equal to the weight of 3/4 of a pizza plus 1/2 cup of orange slices. Also, each cup of orange slices weighs 1/4 of a pound. Hmm. Alright, let's break this down step... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The conductance of a $0.0015 \\mathrm{M}$ aqueous solution of a weak monobasic acid was determined by using a ... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 80 | JEEBench | {
"expected_answer": "6",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, let me try to figure out this problem step by step. So, we need to find the limiting molar conductivity (Λm°) of a weak monobasic acid in aqueous solution. The given information includes the conductance of a 0.0015 M solution, the geometry of the conductivity cell, and the pH of the solution. The answer s... |
[
{
"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.N people numbered 1 through N tossed a coin several times. We know that person i's tosses resulted in A_i heads and B... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 229 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to write a Python function that can sort N people based on their success rates from their coin tosses. The input is given as N pairs of integers A_i and B_i, where A_i is the number of heads and B_i is the number of tails for person i. The success rate for each person is A_i divided by (A_i + B_... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Determine the product obtained when 3,4-dimethylhexanedial is reacted with the following set of reagents:\n\n1. KOH, H2O, THF, Heat\n2. CH3CH2MgBr, H3O+\n3. PCC, CH2Cl2\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 89 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the product when 3,4-dimethylhexanedial is reacted with four different sets of reagents. Let me take each one step by step.
First, let's recall what 3,4-dimethylhexanedial looks like. The structure has a hexane chain with two methyl groups attached at the 3rd and 4th carbon atoms... |
[
{
"content": "Problem: A rectangular box $P$ has distinct edge lengths $a$, $b$, and $c$. The sum of the lengths of all $12$ edges of $P$ is $13$, the areas of all $6$ faces of $P$ is $\\frac{11}{2}$, and the volume of $P$ is $\\frac{1}{2}$. Find the length of the longest interior diagonal connecting two vertic... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 26 | AMC23 | {
"expected_answer": "13",
"problem_id": "29",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about a rectangular box with distinct edge lengths a, b, and c. The problem gives three pieces of information: the sum of all the edges is 13, the sum of the areas of all the faces is 11/2, and the volume is 1/2. Then I have to find the length of the longest interior diagon... |
[
{
"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: Suppose ${X_n:n\\geq 1}$ be independent and exponentially distributed with parameter 1. what is the probability $P(\\limsup _{n \\rightarrow infty} X... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 214 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the probability that the limit superior of X_n divided by log(n) equals 1, where X_n are independent exponential random variables with parameter 1. Let me try to recall what limit superior means here. The limsup of a sequence is the largest limit point of the sequence. So, in this case, ... |
[
{
"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 | 232 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to calculate the sum of the function f(a[l..r]) for all subarrays of the given array a. The function f(b) is the minimum number of operations required to make the array b a palindrome. The operations allowed are either merging two adjacent elements by adding th... |
[
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 2 | 324 | CodeForces | {
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} | <think>
Okay, so I need to figure out how to solve this problem where Sakurako can increase the height of mountains along a diagonal by 1 each time she uses her magic. The goal is to make sure all the lakes (which are mountains with negative heights) disappear, and we need the minimum number of times she has to use her... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $Q$ be the cube with the set of vertices $\\left\\{\\left(x_{1}, x_{2... | {
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} | 1 | 454 | JEEBench | {
"expected_answer": "A",
"problem_id": "5",
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"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to find the maximum distance between a line from set F (the twelve face diagonals) and a line from set S (the four main space diagonals) in a cube Q with vertices at all combinations of (0,0,0), (0,0,1), ..., (1,1,1). The answer choices are given, so I need to figure out which one is correct.
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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} | 0 | 269 | CodeElo | {
"expected_answer": "",
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"subject": null,
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} | <think>
Okay, so I need to solve this problem where we have a town with people whose wealth is given, and the richest person finds some extra gold. We need to determine the minimum amount of gold (x) that the richest person must find so that more than half of the population becomes unhappy. The unhappiness condition is... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 189 | CodeElo | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, so I need to solve this problem where we have a row of balls with numbers on them, and we perform some operations where we merge two balls based on their values. The function f(i) is defined as the number of starting positions j (from 1 to i) such that after performing i-1 merge operations starting from j... |
[
{
"content": "Problem: In a certain isosceles right triangle, the altitude to the hypotenuse has length $4\\sqrt{2}$. What is the area of the triangle?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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} | 0 | 434 | MATH500 | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, so I need to find the area of an isosceles right triangle where the altitude to the hypotenuse is 4√2. Hmm, let me start by recalling what an isosceles right triangle is. It's a triangle with two legs of equal length and a hypotenuse. The angles are 45°, 45°, and 90°. Right?
Now, the problem mentions the... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 161 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a forest of k trees, and we want to remove subtrees from them such that the bitwise OR of the sizes of the removed subtrees is maximized. Let me try to figure out how to approach this.
First, let me parse the problem again. We have a collection of trees (a fo... |
[
{
"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: Find a cosine series which represents f(x) in 0 \\leq x \\leq \\pi if f(x) is defined as f(x) = 00 \\leq x < (\\pi / 2) f(x) = 1(\\pi / 2) < x \\leq ... | {
"do_sample": true,
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} | 0 | 354 | MMLUPro | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which of these options is the correct cosine series representation of the function f(x) defined as 0 for 0 ≤ x < π/2 and 1 for π/2 < x ≤ π. Hmm, cosine series usually involves expanding a function in terms of cosines, which are even functions, so that makes sense here since f(x) is... |
[
{
"content": "Problem: Positive real numbers $x$ and $y$ satisfy $y^3=x^2$ and $(y-x)^2=4y^2$. What is $x+y$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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"max_new_tokens": 32768,
"seed": 6,
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} | 6 | 1 | AMC23 | {
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"problem_id": "1",
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"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where positive real numbers x and y satisfy two equations: y³ = x² and (y - x)² = 4y². I need to find x + y. Hmm, let me think step by step.
First, let's write down the given equations again to make sure I have them right.
1. y³ = x²
2. (y - x)² = 4y²
Since both x and y ... |
[
{
"content": "Problem: Roslyn has ten boxes. Five of the boxes contain pencils, four of the boxes contain pens, and two of the boxes contain both pens and pencils. How many boxes contain neither pens nor pencils?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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"max_new_tokens": 32768,
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} | 0 | 404 | MATH500 | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, so Roslyn has ten boxes in total. Let me break down the problem step by step. First, five of the boxes have pencils, four have pens, and two have both pens and pencils. The question is asking how many boxes contain neither pens nor pencils. Hmm, okay, so I need to find the number of boxes that don't have ... |
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