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 123k |
|---|---|---|---|---|---|---|
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In a specific region of the sky, astronomers have observed that the number of stars varies with parallax as 1/plx^5. How does the number of stars in that region of the s... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 192 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out this problem. So, the question is about how the number of stars in a specific region of the sky changes with distance, given that the number of stars varies with parallax as 1/plx^5. Hmm, I need to recall how parallax relates to distance in astronomy.
First, parallax is the appar... |
[
{
"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": 9,
"temperature": 0.7
} | 9 | 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 solve this problem step by step. So, Aya goes for a 9-kilometer walk every morning. When she walks at a constant speed of \( s \) kilometers per hour, the total time she takes for the walk and the coffee shop is 4 hours. Similarly, when she walks at \( s + 2 \) kilometers per hour, the total ... |
[
{
"content": "Problem: Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$ . Find the number of intersections of the graphs of \\[y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 g(f(\\cos (3 \\pi y))).\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 26 | AIME24 | {
"expected_answer": "385",
"problem_id": "aime24-26",
"reference_solution": "If we graph $4g(f(x))$ , we see it forms a sawtooth graph that oscillates between $0$ and $1$ (for values of $x$ between $-1$ and $1$ , which is true because the arguments are between $-1$ and $1$ ). Thus by precariously dr... | <think>
Okay, let's try to tackle this problem step by step. The question is asking for the number of intersections between the graphs of two functions:
1. \( y = 4g(f(\sin(2\pi x))) \)
2. \( x = 4g(f(\cos(3\pi y))) \)
Where the functions \( f(x) = ||x| - \frac{1}{2}|| \) and \( g(x) = ||x| - \frac{1}{4}|| \). The n... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 135 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let's tackle this problem step by step. The problem is about finding all possible sums of subarrays in an array where most elements are either -1 or 1, except for one element which can be any integer between -10^9 and 10^9. The goal is to find all distinct subarray sums and output them in ascending ord... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 316 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to maximize the difference between the number of problems Monocarp and Stereocarp solve. The key here is that Monocarp can choose which days to practice on, but if he practices on a particular day, Stereocarp will practice the next day. But wait, actually, the problem says i... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 268 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether the Major Oak will have an even number of leaves in year n. The problem states that the tree grows i^i leaves in the i-th year, and each leaf stays for k years. So, the number of leaves on the tree in any given year is the sum of all leaves from the previous k years. Wait, ... |
[
{
"content": "Problem: Denali and Nate work for a dog walking business and are paid for each dog they walk. Denali is responsible for $16$ dogs and Nate is responsible for $12$ dogs. Under the company's new policy, they will be assigned or unassigned new dogs in groups of $x$ dogs. The ratio of Denali's pay to ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about Denali and Nate, who walk dogs for a living. Let me read the problem again carefully to make sure I understand it.
Denali is responsible for 16 dogs, and Nate is responsible for 12 dogs. The company has a new policy where they assign or unassign new dogs in groups of... |
[
{
"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 of positive integers A=(A_1,A_2,\\dots,A_N) of length N and a positive integer K.\nFind the s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 411 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
def find_missing_sum():
N, K = map(int, input().split())
A = list(map(int, input().split()))
total_sum = K * (K + 1) // 2
missing_sum = 0
present = set(A)
for i in range(1, K + 1):
if i not in present:
missing_sum += i
print(missing_sum)
find_missing_sum(... |
[
{
"content": "Problem: If $A$ and $B$ are vertices of a polyhedron, define the distance $d(A,B)$ to be the minimum number of edges of the polyhedron one must traverse in order to connect $A$ and $B$. For example, if $\\overline{AB}$ is an edge of the polyhedron, then $d(A, B) = 1$, but if $\\overline{AC}$ and $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 11 | AMC23 | {
"expected_answer": "29",
"problem_id": "13",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the probability that the distance between Q and R is greater than the distance between R and S in a regular icosahedron. Hmm, let's start by understanding the structure of a regular icosahedron. It has 12 vertices, 30 edges, and 20 triangular faces, right? Each face is an equilateral tri... |
[
{
"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 Hume, morality is ultimately based on:\nOptions: A. cultural norms., B. social agreements., C. reason., D. personal beliefs., E. individ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 18 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out according to Hume, what morality is based on. Let me recall what I know about Hume's philosophy. I remember that he was a Scottish philosopher from the 18th century, and he wrote a lot about morality and the human mind. Hmm, let's start by recalling some key concepts from his works... |
[
{
"content": "Problem: Find the number of ways to place a digit in each cell of a 2x3 grid so that the sum of the two numbers formed by reading left to right is $999$ , and the sum of the three numbers formed by reading top to bottom is $99$ . The grid below is an example of such an arrangement because $8+99... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 2 | AIME24 | {
"expected_answer": "45",
"problem_id": "aime24-2",
"reference_solution": "Consider this table: $\\begin{array}{|c|c|c|} \\hline a & b & c \\\\ \\hline d & e & f\\\\ \\hline \\end{array}$ We note that $c+f = 9$ , because $c+f \\leq 18$ , meaning it never achieves a unit's digit sum of $9$ otherwise. Since no... | <think>
Okay, so I need to figure out how many ways there are to fill a 2x3 grid with digits such that when you read each row left to right, the sum of those two rows is 999, and when you read each column top to bottom, the sum of those three columns is 99. Hmm, let me parse this again.
Wait, actually, the problem say... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The universe is filled with the Cosmic Microwave Background. Consider the annihilation of high energy \\gamma-rays with a photon from the CMB Radiation into electron-pos... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 6 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the energy of gamma-rays where their lifetimes are limited by annihilating with a photon from the Cosmic Microwave Background (CMB). The average photon energy of the CMB is given as 10^-3 eV. Let me recall some physics concepts here.
First, the annihilation process is γγ → e+e-. F... |
[
{
"content": "Problem: If $\\frac{\\sqrt{2x}}{\\sqrt{3x-1}}=\\frac32$, solve for $x$. Express your answer in simplest fractional form.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 305 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve the equation \(\frac{\sqrt{2x}}{\sqrt{3x-1}} = \frac{3}{2}\) for \(x\). Hmm, let me start by understanding what the problem is asking. It wants me to find the value of \(x\) that makes the ratio of the square root of \(2x\) to the square root of \(3x - 1\) equal to \(\frac{3}{2}\).
Fi... |
[
{
"content": "Problem: Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only $\\frac{1}{3}$ full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | AMC23 | {
"expected_answer": "7",
"problem_id": "25",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. Mrs. Jones has four identical glasses, and she wants to pour orange juice into them. The first three glasses are filled completely, but the fourth one is only 1/3 full. Now, she needs to take some juice from the first three glasses and put it into the fourth glass so that all four glasses have ... |
[
{
"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: Among the following, the correct statement(s) is(are)\n[A] $\\mathrm{A... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 106 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of these statements are correct regarding the bonding in some aluminum and boron compounds. Let me start by recalling what three-center two-electron (3c-2e) bonds are. From what I remember, 3c-2e bonds occur when two atoms share a pair of electrons, but those electrons are si... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the product of all positive real values of $x$ satisfying the equation\n\\[\nx^{\\left(16\\left(\\log ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 415 | JEEBench | {
"expected_answer": "1",
"problem_id": "4",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Alright, let's tackle this problem step by step. The equation given is:
\[
x^{\left(16\left(\log _{5} x\right)^{3}-68 \log _{5} x\right)}=5^{-16}
\]
We need to find the product of all positive real values of \( x \) that satisfy this equation. Hmm, exponents with logarithms can be tricky, but maybe we can sim... |
[
{
"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: Steven Moore purchased a new car for $3,462.20, including taxes and all other charges. He wishes to pay for it in 35 months. Find his monthly payment... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 329 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out Steven Moore's monthly payment for his new car. The total cost is $3,462.20, and he wants to pay it off in 35 months. Hmm, let me think. I remember that to calculate monthly payments, you can use the formula for an installment loan. The formula is:
\[ \text{Monthly Payment} = \fra... |
[
{
"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: What is the value of\n\\[\n\\sec ^{-1}\\left(\\frac{1}{4} \\su... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 241 | JEEBench | {
"expected_answer": "0",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to find the value of this inverse secant function. The expression inside the sec⁻¹ is a sum of some secant terms, averaged somehow. Let me try to parse this step by step.
First, the problem is asking for the value of sec⁻¹ of the average (since it's multiplied by 1/4) of the product of secant 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: Lizette and her family watch the sunset over the ocean. While walking home in the increasing darkness, Lizette notices that she can no longer disting... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 472 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out why Lizette can't see colors in the dim light when she's walking home after sunset. Let me start by recalling what I know about how our eyes work in different lighting conditions.
First, I remember that there are two types of light-sensitive cells in the retina: rods and cones. Ro... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 106 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to make an array beautiful by adding a certain value k to one of its elements, possibly multiple times. The array is considered beautiful if it's symmetric, meaning the element at position i is equal to the element at position n - i + 1 for all i. The goal is t... |
[
{
"content": "Problem: Let \\(b\\ge 2\\) be an integer. Call a positive integer \\(n\\) \\(b\\text-\\textit{eautiful}\\) if it has exactly two digits when expressed in base \\(b\\) and these two digits sum to \\(\\sqrt n\\). For example, \\(81\\) is \\(13\\text-\\textit{eautiful}\\) because \\(81 = \\underlin... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 13 | AIME24 | {
"expected_answer": "211",
"problem_id": "aime24-13",
"reference_solution": "We write the base- $b$ two-digit integer as $\\left( xy \\right)_b$ .\nThus, this number satisfies\n \\[ \\left( x + y \\right)^2 = b x + y \\] \nwith $x \\in \\left\\{ 1, 2, \\cdots , b-1 \\right\\}$ and $y \\in \\left\\{ 0, 1, \\... | <think>
Okay, so I need to find the smallest integer \( b \geq 2 \) such that there are more than ten \( b \)-beautiful integers. A \( b \)-beautiful integer is a positive integer \( n \) that has exactly two digits in base \( b \), and the sum of those two digits equals \( \sqrt{n} \).
First, let's parse the problem... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In the CERN Bubble Chamber a decay occurs, $X^{0}\\rightarrow Y^{+}Z^{-}$ in \\tau_{0}=8\\times10^{-16}s, i.e. the proper lifetime of X^{0}. What minimum resolution is n... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 68 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum resolution needed to observe at least 30% of the decays of X⁰ in the CERN Bubble Chamber. The given options are all different distances, and I need to determine which one is correct. Let me start by recalling some basic concepts.
First, the proper lifetime of X⁰ is giv... |
[
{
"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 | 143 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the maximum value of a × b × c that Noobish_Monk can achieve by increasing any of the integers a, b, or c by 1 at most 5 times. Each test case gives three integers, and we have to do this process at most 5 times total across all integers. Wait, actually, the problem says "at most 5... |
[
{
"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,\\ldots,A _ N.\nIf their values are all equal, print Yes; otherwise, print No.\n\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 299 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def check_all_equal():
import sys
input = sys.stdin.read
data = input().split()
N = int(data[0])
A = data[1:]
A = [int(a) for a in A]
if len(set(A)) == 1:
print('Yes')
else:
print('No')
check_all_equal() |
[
{
"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 a steady, turbulent, constant property, two dimensional boundarylayer-type flow over a flat plate at zero angle of approach, the velocity profile... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 340 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the local boundary layer thickness δ as a function of x for this given problem. Let me start by recalling what the integral form of the momentum equation is. For boundary layer flow, the integral momentum equation is usually derived by integrating the Navier-Stokes equations over t... |
[
{
"content": "Problem: A mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row. How many distinct arrangements are possible?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 269 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many distinct ways there are to arrange 2 indistinguishable IMO gold medals and 2 indistinguishable IPhO gold medals in a single row. Hmm, let me start by recalling some combinatorics basics.
First, when dealing with permutations of objects where some are identical, the formu... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums of even length and there is also an empty array arr. Alice and Bob decided to play a game where in every round Ali... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 148 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a function that simulates this game between Alice and Bob. Let me try to break down the problem step by step.
First, the input is a list of integers called `nums`, which has an even number of elements. The goal is to return an array `arr` that contains the elements removed by Bob and ... |
[
{
"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 moves of length n consisting only of characters 'L', 'R', and '_'. The string represents your movement on a number line starting from th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 91 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the furthest distance from the origin on a number line based on the moves given. The moves are a string with characters 'L', 'R', and '_', and I have to determine how far I can go left or right depending on these characters. Let me break this down step by step.
First, let me under... |
[
{
"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) What type of mirror is required to form an image, on a wall 3 m from the mirror, of the filament of a headlight lamp 10 cm in front of the mirror... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 105 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what type of mirror is needed here and then find the height of the image. Let me start by recalling some basics about mirrors.
First, the problem mentions a headlight lamp filament, which is the object, and we want to form an image of it on a wall 3 meters away from the mirror. T... |
[
{
"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 the position vectors of the points $P, Q, R$ and $S$ be $\\vec{a}=\\h... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 488 | JEEBench | {
"expected_answer": "B",
"problem_id": "4",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to figure out which of these statements is true given the position vectors for points P, Q, R, and S. Let me start by writing down all the vectors clearly:
- Point P: \(\vec{a} = \hat{i} + 2\hat{j} - 5\hat{k}\)
- Point Q: \(\vec{b} = 3\hat{i} + 6\hat{j} + 3\hat{k}\)
- Point R: \(\vec{c} = \frac... |
[
{
"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 moves of length n consisting only of characters 'L', 'R', and '_'. The string represents your movement on a number line starting from th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 91 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out the furthest distance from the origin on a number line based on the given moves. The moves string consists of 'L', 'R', and '_' characters. Each of these has specific meanings for the direction I can move. Let me break it down.
First, the problem states that for each move i (fr... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $S$ be the reflection of a point $Q$ with respect to the plane giv... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 387 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to find the reflection of point Q with respect to a given plane. The position vector of Q is 10i + 15j + 20k, and the reflected point S has a position vector αi + βj + γk. The plane is given by the equation r = -(t + p)i + tj + (1 + p)k, where t and p are real parameters. Hmm, let me try to pars... |
[
{
"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 | 299 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where there's a team of n members presenting m slides. The members are initially lined up in a certain order, and after each slide is presented, we can move the front member to any position in the line. The question is whether the presentation can be made good by possibly m... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 22 | CodeForces | {
"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 binary string of length n such that the oneness is minimized. Oneness is defined as the absolute difference between the number of non-empty subsequences with only 0s (f(t)) and the number of non-empty subsequences with at least one 1 (g(t)). The goal ... |
[
{
"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 | 258 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to find the expected value of the product of two elements from an array. The problem gives me an array of integers, and I have to calculate the expected value of the product when two elements are randomly picked. The result should be in the form of P/Q and then multiplied by Q inverse modulo ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Experiencing intense feelings of shame and guilt upon admitting to a counselor that a family problem exists is common among traditional\nOptions: A. ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 446 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | I think the answer is C. African-Americans. So my final response is \boxed{C}. |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A hot air balloon is carrying some passengers, and a few sandbags of mass $1 \\mathrm{~kg}$ each so that its t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 278 | JEEBench | {
"expected_answer": "4",
"problem_id": "4",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | <think>
Okay, so I need to figure out how many sandbags, N, are thrown out of the hot air balloon so that it rises from 100 meters to 150 meters. Each sandbag has a mass of 1 kg, and the original total mass was 480 kg. The volume of the balloon remains V, which is unchanged. The density of air varies with height accord... |
[
{
"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 bond length between any two nonmetal atoms is achieved under which of the following conditions?\nOptions: A. The point at which the repulsive for... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 224 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out under which condition the bond length between two nonmetal atoms is achieved. Let me start by recalling what bond length means. Bond length is the distance between the nuclei of two atoms in a molecule. It's determined by the balance between the attractive and repulsive forces betw... |
[
{
"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: An acidified solution of $0.05 \\mathrm{M} \\mathrm{Zn}^{2+}$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 293 | JEEBench | {
"expected_answer": "0.2",
"problem_id": "36",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the minimum molar concentration of H+ required to prevent the precipitation of ZnS in an acidified solution that's already 0.05 M in Zn²+ and saturated with 0.1 M H2S. The given constants are Ksp for ZnS as 1.25 × 10⁻²² and the overall dissociation constant for H2S, which is K1K2, as 1 ×... |
[
{
"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 n representing the number of houses on a number line, numbered from 0 to n - 1.\nAdditionally, you are given a 2D integer array offers... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 85 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the amount of gold I can earn by selling houses to buyers. Each buyer has an offer with a start house, end house, and the amount of gold they're willing to pay. The goal is to select the offers that give the most gold without overlapping houses. Let me think through... |
[
{
"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 | 240 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out who wins this Subtangle game between Tsovak and Narek. The problem is a bit complex, but let me try to break it down step by step.
First, the game involves an array `a` and a matrix `b`. The players take turns looking for elements of `a` in the matrix. Each time a player finds an... |
[
{
"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 | 33 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have a perfect binary tree with size \(2^n - 1\), and each node is assigned a value. The task is to count the number of different deterministic max-heaps produced by applying the "add" operation exactly \(k\) times. Then, modulo the given prime \(p\).
First, let me... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two 0-indexed integer arrays nums1 and nums2 of equal length. Every second, for all indices 0 <= i < nums1.length, value of nums1[i] is increment... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 80 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem. Let me start by understanding the problem statement again.
We have two integer arrays, nums1 and nums2, of the same length. Every second, each element in nums1 is incremented by the corresponding element in nums2. Then, we can choose one index and set 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.You are given a string S consisting of lowercase English letters and digits.\nS is guaranteed to end with 2023.\r\nCha... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 356 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```
def change_last_character():
S = input().strip()
last_index = S.rfind('2023')
if last_index != -1:
modified_string = S[:last_index + 4] + '4'
print(modified_string)
change_last_character()
``` |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A textile dye containing an extensively conjugated pi-electrons emits light with energy of 2.3393 eV. What color of light is absorbed by the organic compound?\nOptions: ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 29 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what color of light is absorbed by an organic compound that emits light with an energy of 2.3393 eV. Hmm, let me start by recalling some basic concepts about light, energy, and colors.
First, I remember that the energy of a photon is related to its wavelength by the equation E = (... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 470 | JEEBench | {
"expected_answer": "3",
"problem_id": "25",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | <think>
Okay, so I need to find the atomic number Z of a Hydrogen-like atom. The problem says that when photons are emitted from transitions between n=4 and n=3 levels in this atom, they are used in a photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons is 1.95 eV, and the... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Large clouds of neutral hydrogen in deep space absorb the light from background quasars at Lyman alpha wavelength ~1216 Angstrom. Estimate the lower limit on the redshif... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 129 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To estimate the lower limit on the redshift of quasars such that their Lyman alpha emission can be detected with optical ground-based telescopes, we need to consider the Lyman alpha wavelength and how redshift affects the observed wavelength.
The Lyman alpha line is at ~1216 Angstroms in the rest frame of the quasar. ... |
[
{
"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 | 327 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of operations needed to make a given permutation simple. A permutation is simple if every element p_i is either equal to i or p_{p_i} = i. Hmm, that's an interesting condition. So, the task is to take a permutation and perform the least number of swaps (where eac... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 54 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where Darius has to arrange stone columns in non-decreasing order of the number of inscriptions by transferring inscriptions between columns. Each move must adjust the number of inscriptions by exactly 1 in two columns. The goal is to find the number of moves and the seq... |
[
{
"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 | 301 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have a village represented as a graph with n houses, m internet cables, and p houses that need internet. The task is to determine, for each k from 1 to n, the minimum total latency required to connect all the houses that need internet by installing servers in 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 317 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out on which day Monocarp will complete his journey by walking at least n kilometers. The problem gives me three integers a, b, c for the first three days, and then the pattern repeats every three days. So, every subsequent three days, he walks a + b + c kilometers.
First, let me par... |
[
{
"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, so I need to create a function that calculates the final score based on the given 2D integer array. Let me try to break down the problem step by step.
First, the problem says that we have a 0-indexed 2D integer array called `nums`. Our initial score is 0. We need to perform two main operations until 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 a 0-indexed integer array nums.\nReturn the maximum value over all triplets of indices (i, j, k) such that i < j < k. If all such triplets have a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 115 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to solve this problem. The goal is to find the maximum value of the expression (nums[i] - nums[j]) * nums[k] where the indices i, j, k are all less than each other (i < j < k). If all possible triplets give a negative value, then the answer should be 0. Let me break this dow... |
[
{
"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 an integer k.\nReturn an integer that denotes the sum of elements in nums whose corresponding indices have exa... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 106 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to write a function that takes a list of integers `nums` and an integer `k`, and returns the sum of elements in `nums` where their indices have exactly `k` set bits in binary. Let me think through this step by step.
First, let me recall that the set bits in an integer's binary representation... |
[
{
"content": "Problem: Twelve 1 by 1 squares form a rectangle, as shown. What is the total area of the shaded region? [asy]\nsize(4cm);defaultpen(linewidth(0.75));\n\n// Filled portions\nfill((0, 4)--(0, 0)--(2, 0)--cycle, gray(0.75));\nfill((0, 4)--(3, 4)--(3, 0)--cycle, gray(0.75));\n\n// grid\nint j;\nfor (j... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 210 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the total area of the shaded region in this problem. The figure is made up of twelve 1 by 1 squares, forming a rectangle. There are two gray-filled regions, and I have to calculate their combined area. Let me try to visualize this step by step.
First, let's understand the structure of t... |
[
{
"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 a pyramid $O P Q R S$ located in the first octant $(x \\geq 0... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 29 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to solve this problem about a pyramid O P Q R S in the first octant. Let me start by visualizing the pyramid. The base O P Q R is a square with OP = 3. So, since O is the origin, P is at (3, 0, 0), Q is at (3, 3, 0), R is at (0, 3, 0), and O is at (0, 0, 0). Then, the point S is directly above t... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 118 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have a permutation p of length n, and a string s of length n with characters L, R, or ?. Based on s, I add edges to a graph, either (i, l_i) or (i, r_i) for each i. The task is to find the maximum possible diameter of a connected graph that can be formed. If it's no... |
[
{
"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: Each of the following options contains a set of four molecules. Identi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 194 | JEEBench | {
"expected_answer": "BD",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of these options have all four molecules with a permanent dipole moment at room temperature. Hmm, let's start by recalling what a permanent dipole moment means. A molecule has a permanent dipole moment if there's a separation of electric charge, meaning it's not symmetrically... |
[
{
"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 2 integer arrays nums1 and nums2 of lengths n and m respectively. You are also given a positive integer k.\nA pair (i, j) is called good if nums1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 504 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to write a function that counts the number of good pairs between two integer arrays, nums1 and nums2, where each pair (i, j) is good if nums1[i] is divisible by nums2[j] multiplied by some positive integer k. Let me break this down step by step.
First, let's parse the problem again to make 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: Among $\\mathrm{B}_{2} \\mathrm{H}_{6}, \\mathrm{~B}_{3} \\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 197 | JEEBench | {
"expected_answer": "4",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Alright, let me try to figure out this problem. So, we have a list of molecules: B₂H₆, B₃N₃H₆, N₂O, N₂O₄, H₂S₂O₃, and H₂S₂O₈. We need to find how many of these molecules contain a covalent bond between two atoms of the same kind. Hmm, okay. Let me start by recalling what a covalent bond is. A covalent bond form... |
[
{
"content": "Problem: Let $\\omega\\neq 1$ be a 13th root of unity. Find the remainder when\n \\[\\prod_{k=0}^{12}(2-2\\omega^k+\\omega^{2k})\\] \nis divided by 1000.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 12 | AIME24 | {
"expected_answer": "321",
"problem_id": "aime24-12",
"reference_solution": "\\[\\prod_{k=0}^{12} \\left(2- 2\\omega^k + \\omega^{2k}\\right) = \\prod_{k=0}^{12} \\left((1 - \\omega^k)^2 + 1\\right) = \\prod_{k=0}^{12} \\left((1 + i) - \\omega^k)((1 - i) - \\omega^k\\right)\\] Now, we consider the polynomial $x... | <think>
Okay, so I need to find the remainder when the product \(\prod_{k=0}^{12}(2-2\omega^k+\omega^{2k})\) is divided by 1000, where \(\omega\) is a 13th root of unity but not equal to 1. Hmm, let me start by understanding what exactly this product looks like.
First, since \(\omega\) is a primitive 13th root of uni... |
[
{
"content": "Problem: The circle $x^2 + y^2 = 2$ and the parabola $y^2 = 8x$ have two common tangents, forming four points of tangency. Find the area of the quadrilateral formed by the four points of tangency.\n\n[asy]\nunitsize(0.8 cm);\n\nreal upperparab (real x) {\n return (sqrt(8*x));\n}\n\nreal lowerpar... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 445 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the area of the quadrilateral formed by the four points of tangency between the circle \(x^2 + y^2 = 2\) and the parabola \(y^2 = 8x\). Hmm, let me start by understanding the problem step by step.
First, let's recall that the points of tangency are where the circle and the parabola touc... |
[
{
"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 | 87 | 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 a of length n, and we need to handle q queries. Each query is a range [l, r], and for each query, we need to compute the sum of f over all subarrays starting from index l + k - 1 up to r. The function f(b) is the minimum number of operations needed to... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array mountain. Your task is to find all the peaks in the mountain array.\nReturn an array that consists of indices of peaks in the g... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 144 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find all the peaks in a mountain array. Let me think. A peak is an element that's strictly bigger than its neighbors, right? And the first and last elements can't be peaks because they don't have both neighbors. Got it. So, the function should go through the array, check each element (except ... |
[
{
"content": "Problem: Let $a,$ $b,$ and $c$ be distinct real numbers. Find the degree of the polynomial\n\\[p(x) = \\frac{(x - b)(x - c)}{(a - b)(a - c)} + \\frac{(x - a)(x - c)}{(b - a)(b - c)} + \\frac{(x - a)(x - b)}{(c - a)(c - b)}.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 317 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the degree of the polynomial p(x) given by the sum of three terms. Each term is a product of two linear factors in the numerator and a product of two linear factors in the denominator. Let me write down the expression again to make sure I have it right:
p(x) = [(x - b)(x - c)] / [(a - b... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a positive integer N.\r\nIf there are integers x and y such that N=2^x3^y, print Yes; otherwise, print N... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 300 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
import math
def check_integer(N):
while N % 2 == 0:
N //= 2
while N % 3 == 0:
N //= 3
return N == 1
def main():
N = int(input().strip())
if check_integer(N):
print('Yes')
else:
print('No')
if __name__ == '__main__':
main()
```
The function `check... |
[
{
"content": "Problem: How many positive perfect squares less than $2023$ are divisible by $5$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 16 | AMC23 | {
"expected_answer": "8",
"problem_id": "18",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many positive perfect squares less than 2023 are divisible by 5. Hmm, let's start by recalling what a perfect square is. A perfect square is a number that can be expressed as the square of an integer. So, like 1, 4, 9, 16, and so on. So, the problem is asking for how many of th... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: For any positive integer $n$, let $S_{n}:(0, \\infty) \\rightarrow \\m... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 338 | JEEBench | {
"expected_answer": "AB",
"problem_id": "51",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Alright, let me try to tackle this problem step by step. So, we have a function \( S_n(x) \) defined as the sum from \( k=1 \) to \( n \) of \( \cot^{-1}\left( \frac{1 + k(k+1) x^2}{x} \right) \). We need to check which of the given statements A, B, C, D are true. Let's go through each one carefully.
**Stateme... |
[
{
"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 projectile is fired from horizontal ground with speed $v$ an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 397 | JEEBench | {
"expected_answer": "0.95",
"problem_id": "26",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I have this problem about a projectile that's fired from the ground with speed v and angle θ. The range in the original region with gravity g is d. Then, when the projectile reaches the highest point of its trajectory, it enters a region where the acceleration due to gravity is reduced to g' = g/0.81, ... |
[
{
"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 $X=\\left\\{(x, y) \\in \\mathbb{Z} \\times \\mathbb{Z}: \\frac{x^{2}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 455 | JEEBench | {
"expected_answer": "B",
"problem_id": "6",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to find the probability that three randomly chosen points from set X form a triangle with a positive integer area. Let me start by understanding the problem step by step.
First, the set X is defined as all integer pairs (x, y) such that two inequalities hold:
1. \(\frac{x^2}{8} + \frac{y^2}{20}... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: One mole of a monatomic ideal gas undergoes an adiabatic expan... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | JEEBench | {
"expected_answer": "900",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I need to find the decrease in internal energy of a monatomic ideal gas when it undergoes an adiabatic expansion, where the volume becomes eight times its initial value. The initial temperature is 100 K, and the universal gas constant R is 8.0 J mol⁻¹ K⁻¹. Hmm, let's break this down step by step.
Firs... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 165 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where a girl wants to buy the most beautiful bouquet. The bouquet should have flowers where the difference in the number of petals between any two flowers doesn't exceed 1. Also, the total cost (which is the number of coins spent) can't exceed m. The goal is to maximize the... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: In thermodynamics, the $P-V$ work done is given by\n\\[\nw=-\\int d V ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 252 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "25",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Alright, let me try to figure out this problem. So, the question is about the work done in a thermodynamic process, given by the integral equation:
\[
w = -\int dV \left( \frac{RT}{V - b} - \frac{a}{V^2} \right)
\]
And we need to determine which of the following options this equation is applicable to:
(A) 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: A human body has a surface area of approximately $1 \\mathrm{~m}^{2}$.... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 69 | JEEBench | {
"expected_answer": "C",
"problem_id": "4",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Alright, let me try to work through this problem step by step. So, we have a human body with a surface area of about 1 m². The normal body temperature is 10 K above the room temperature, which is given as 300 K. They also tell us that σT₀⁴ = 460 Wm⁻², where σ is the Stefan-Boltzmann constant. The question is as... |
[
{
"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 area of the region\n\\[\n\\left\\{(x, y): 0 \\leq x \\leq \\frac{9}{4... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 325 | JEEBench | {
"expected_answer": "A",
"problem_id": "38",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to find the area of the region defined by these inequalities: 0 ≤ x ≤ 9/4, 0 ≤ y ≤ 1, x ≥ 3y, and x + y ≥ 2. Hmm, let me visualize this step by step.
First, let me sketch the coordinate system and plot the boundaries of each inequality. Since x is between 0 and 9/4 (which is 2.25) and y is betw... |
[
{
"content": "Problem: Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$ . Find the number of intersections of the graphs of \\[y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 g(f(\\cos (3 \\pi y))).\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 26 | AIME24 | {
"expected_answer": "385",
"problem_id": "aime24-26",
"reference_solution": "If we graph $4g(f(x))$ , we see it forms a sawtooth graph that oscillates between $0$ and $1$ (for values of $x$ between $-1$ and $1$ , which is true because the arguments are between $-1$ and $1$ ). Thus by precariously dr... | <think>
Alright, let me try to figure out this problem. So, we have two functions defined as \( f(x) = ||x| - \frac{1}{2}|\) and \( g(x) = ||x| - \frac{1}{4}|\). Then, we need to find the number of intersections between the graphs of \( y = 4g(f(\sin(2\pi x))) \) and \( x = 4g(f(\cos(3\pi y))) \).
First, let me unders... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 134 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let's tackle this problem. So, we have a number written on the board which is the digit `d` written exactly `n!` times. We need to find which odd digits (from 1 to 9) divide this number. The key point is that the number is a repetition of the digit `d` for `n!` times.
First, let me understand the pro... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums consisting of positive integers where all integers have the same number of digits.\nThe digit difference between two integers is th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 502 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a function that calculates the sum of digit differences between all pairs of integers in an array where each integer has the same number of digits. Let me start by understanding the problem step by step.
First, the function should take an array of positive integers called `nums`. All ... |
[
{
"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: What is the amount of water produced (in g) in the oxidation o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 227 | JEEBench | {
"expected_answer": "288",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to figure out how much water is produced when 1 mole of rhombic sulfur is oxidized by concentrated nitric acid (HNO₃) to form a compound with the highest oxidation state of sulfur. Then, I have to give the answer in grams, rounded to two decimal places. Alright, let's start breaking this down st... |
[
{
"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 surface properties is(are)\n[A] Adsorpt... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 103 | JEEBench | {
"expected_answer": "AB",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. The question is asking about the correct statement(s) regarding surface properties. There are four options provided, and I need to figure out which ones are accurate. Let me start by recalling what each term and concept means.
First, let's look at option [A]: "Adso... |
[
{
"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 mountain. Your task is to find all the peaks in the mountain array.\nReturn an array that consists of indices of peaks in the g... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 144 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find all the peaks in a mountain array. Let me start by understanding what a peak is. The problem says a peak is an element that is strictly greater than its neighboring elements. Also, the first and last elements can't be peaks. Got it. So, for each element in the array, I need to check if i... |
[
{
"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 $\\alpha$ be a positive real number. Let $f: \\mathbb{R} \... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 377 | JEEBench | {
"expected_answer": "0.5",
"problem_id": "2",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to find the limit as x approaches α from the right of f(g(x)), where f(x) is sin(πx/12) and g(x) is this logarithmic expression. Let me start by understanding the components here.
First, let's write down what f(g(x)) is. Since f(x) = sin(πx/12), then f(g(x)) = sin(πg(x)/12). So, the limit becom... |
[
{
"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 reaction of $\\mathrm{Xe}$ and $\\mathrm{O}_{2} \\mathrm{~F}_{2}$ gives a Xe compound $\\mathbf{P}$. What ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 440 | JEEBench | {
"expected_answer": "4",
"problem_id": "40",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, so I need to figure out how many moles of HF are produced when 1 mole of compound P is completely hydrolyzed. Hmm, let me start by understanding the problem step by step.
First, the problem mentions that the reaction between Xe (xenon) and O₂F₂ (dioxygen difluoride) forms a Xe compound called P. Then, wh... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given two positive integers low and high represented as strings, find the count of stepping numbers in the inclusive range [low, high].\nA stepping number is a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 79 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the count of stepping numbers between two integers low and high, inclusive. A stepping number is one where each adjacent digit differs by exactly 1. The problem mentions that the answer should be modulo 10^9 + 7, and both low and high are positive integers represented as strings. Their l... |
[
{
"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.\nI am of opinion that the principal and true profession of the Courtier ought to be that of arms; ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 197 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which reform Baldassare Castiglione would most likely want to institute based on the information provided. Let me start by recalling what his main ideas were from the excerpt.
First, he emphasizes that the principal profession of a courtier should be arms, meaning he should be sk... |
[
{
"content": "Problem: A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the triangles is 21 inches, what is the perimeter, in inches, of the regular hexagon?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 5 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem here: A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the triangles is 21 inches, what is the perimeter of the regular hexagon in inches? Hmm, let me think about how to approach this.
First, let's recall what a regular hexagon is. A regul... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 10 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to create a Python function that calculates the final score based on the given matrix. Let me try to break down the problem step by step.
First, the problem states that we have a 2D integer array, `nums`, which is 0-indexed. Our goal is to perform operations until the matrix becomes empty. T... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 186 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have an array a of length n and a binary array b of the same length. The goal is to maximize the score by performing operations where I can increase the value of a[i] by 1 when b[i] is 1, up to k times. The score is defined as the maximum of (a[i] + median(c_i)) for... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 261 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum time required for Zhan to blend all his fruits using his blender. Let me try to break down the problem step by step.
First, let's understand the problem. Zhan has n fruits, and his blender can mix up to x fruits per second. In each second, Zhan can put up to y fruits i... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 167 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of operations required to make an array non-decreasing by squaring elements. Let me start by understanding the problem.
First, the problem states that we have an array of integers, and we can perform an operation where we take any element at index i and replace ... |
[
{
"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 receiver of length n and an integer k.\nThere are n players having a unique id in the range [0, n - 1] who will play a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 95 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the function f(x) which is the sum of x and all the players who receive the ball over k passes. The goal is to choose the starting player x such that f(x) is as large as possible. Let me try to break this down step by step.
First, let me understand the problem bett... |
[
{
"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 | 75 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out Alice's score in this marble game. Let me start by understanding the problem again.
We have n marbles, each with a color c_i. The players take turns, with Alice going first. Each player tries to maximize (Alice) or minimize (Bob) Alice's score. The score is calculated as follows: ... |
[
{
"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 | 137 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to reconstruct an array a such that each element b_i is the bitwise AND of a_i and a_{i+1}. If possible, I need to find such an array a, otherwise report that it's impossible. Let me try to break this down step by step.
First, let's understand the problem. Giv... |
[
{
"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 tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects vertices A_i and B_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 420 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the minimum value of the function \( f(v) = \sum_{i=1}^{N} (C_i \times d(v, i)) \) where \( d(v, i) \) is the distance from vertex \( v \) to vertex \( i \) in a given tree.
The steps to solve this problem are as follows:
1. **Tree Representation**: First, represent the tree us... |
[
{
"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 liqueur is used to make a Pink Lady cocktail pink?\nOptions: A. grenadine, B. pernod, C. rum, D. raspberry liqueur, E. pink lemonade, F. schnapp... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 489 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which liqueur is used to make a Pink Lady cocktail pink. Let me start by recalling what a Pink Lady cocktail is. From my memory, it's a classic cocktail that's typically made with a combination of spirits and fruit-flavored liqueurs. The color is supposed to be pink, which gives it... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: The increasing order of atomic radii of the following Group 13 elements i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 13 | JEEBench | {
"expected_answer": "B",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, so I need to figure out the increasing order of atomic radii for the Group 13 elements: aluminum (Al), gallium (Ga), indium (In), and thallium (Tl). Hmm, let's start by recalling some basic concepts about atomic radii and the periodic table.
First, I remember that atomic radius generally increases as you... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the value of the limit\n\\[\n\\lim _{x \\rightarrow \\frac{\\pi}{2}} \\frac{4 \\sqrt{2}(\\sin 3 x+\\si... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 299 | JEEBench | {
"expected_answer": "8",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, so I need to find the limit as x approaches π/2 of this expression involving sine and cosine terms. Let me write it down again to make sure I have it right:
\[
\lim _{x \rightarrow \frac{\pi}{2}} \frac{4 \sqrt{2}(\sin 3 x+\sin x)}{\left(2 \sin 2 x \sin \frac{3 x}{2}+\cos \frac{5 x}{2}\right)-\left(\sqrt{... |
[
{
"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 | 226 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have three sequences: a, b, and c, each of length n. The task is to choose a subsequence of length m from the indices 1 to n, such that the elements in sequence a are non-decreasing, and all elements in sequence b are distinct. Then, I need to maximize the sum of th... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Name reactions in chemistry refer to a specific set of well-known chemical reactions that are typically named after their discoverers or the scientists who made signific... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 24 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the reactants for these two name reactions. Let me start by recalling some common name reactions and their typical reactants. The first reaction is A + H2SO4 --> 2,8-dimethylspiro[4.5]decan-6-one. The second one is B + BuLi + H+ --> 4-methyl-1-phenylpent-3-en-1-ol. Hmm, let's take ... |
[
{
"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 B.\nIf there exists a positive integer A such that A^A = B, print its value; otherwise, outpu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 317 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | from math import isqrt
def find_A(B):
if B == 1: return 1
for A in range(2, isqrt(B) + 1):
if B % A == 0:
exponent = 1
while True:
if A ** exponent == B:
return A
elif A ** exponent > B:
break
... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.