context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 425 187k |
|---|---|---|---|---|---|---|
[
{
"content": "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
} | To solve this problem, we need to understand how the number of stars observed in a region of the sky relates to the distance from the observer. The key here is to recognize the relationship between parallax and distance, and how this affects the number of stars detected.
1. **Parallax and Distance Relationship**: Para... |
[
{
"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 $9s+18-9s=18=1.6s^{2} + 3.2s$ ... | Let's denote the variables and equations based on the problem statement.
First, we know that when Aya walks at speed \( s \) km/h, the total time taken for the walk and coffee shop is 4 hours. The walk is 9 km long. So the time taken for the walk is \( \frac{9}{s} \) hours. The total time including the coffee shop is ... |
[
{
"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... | To solve the problem, we need to find the number of intersections between the graphs of \( y = 4 g(f(\sin (2 \pi x))) \) and \( x = 4 g(f(\cos (3 \pi y))) \). Let's break down the problem step by step.
First, let's understand the functions \( f(x) \) and \( g(x) \).
The function \( f(x) = \left| \left| x \right| - \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 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>
Okay, let's tackle this problem. Hmm, the problem is about finding all possible sums of subarrays (including the empty one) in an array where all but one elements are -1 or 1. The remaining element can be any value. We need to output all possible sums in ascending order, each only once.
First, let's understand... |
[
{
"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>
Okay, let's see. The problem is about Monocarp and Stereocarp preparing for an olympiad. We need to find the maximum possible difference in the number of problems they solve. Let me think through the problem step by step.
So, the key point here is that Monocarp can choose any days he wants to train. But whenev... |
[
{
"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, let's tackle this problem. So, the task is to determine if the Major Oak's leaves count in year n is even. The leaves grow in the i-th year as i^i, and each leaf stays for k years. So, for a given n, we need to sum all the leaves that are present in year n. Then check if that sum is even.
Hmm. Let's thin... |
[
{
"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
} | Let's denote Denali's current number of dogs as \( D = 16 \) and Nate's current number as \( N = 12 \). The pay ratio between Denali and Nate is \( \frac{D}{N} = \frac{16}{12} = \frac{4}{3} \).
According to the problem, the ratio of their pays will remain the same under two scenarios:
1. Denali walks \( 4x \) more dog... |
[
{
"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
} | <think>
Okay, let's see. I need to write a Python function that takes input from stdin and computes the sum of numbers between 1 and K that are not present in the sequence A. Hmm.
So the problem is: given a list of numbers A and a number K, find the sum of all numbers from 1 to K that are not in A. Right.
First, I ne... |
[
{
"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
} | To solve the problem, we need to determine the probability that the distance from \( Q \) to \( R \) is greater than the distance from \( R \) to \( S \) when \( Q \), \( R \), and \( S \) are randomly chosen distinct vertices of a regular icosahedron.
First, we need to understand the structure of the icosahedron. 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: 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
} | To solve this problem, we need to determine according to David Hume's philosophy, the basis of morality. Let's start by understanding Hume's views on morality.
David Hume was a British philosopher known for his empiricist approach, which emphasizes experience and reason. Hume argued that moral distinctions are not der... |
[
{
"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, let's see. We need to fill a 2x3 grid with digits such that the sum of the two numbers formed left to right is 999, and the sum of the three numbers formed top to bottom is 99. Hmm. Let's break this down.
First, the left to right reading gives two numbers. Since it's a 2x3 grid, each row has three digits... |
[
{
"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
} | To solve this problem, we need to determine the threshold energy of high-energy gamma-rays such that their lifetimes in the universe are limited by annihilation with a photon from the Cosmic Microwave Background (CMB).
The key idea here is that when a gamma-ray with energy \( E \) annihilates with a CMB photon, the t... |
[
{
"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
} | We start with the equation:
\[
\frac{\sqrt{2x}}{\sqrt{3x-1}} = \frac{3}{2}
\]
First, we eliminate the denominators by cross-multiplying. This gives:
\[
2 \sqrt{2x} = 3 \sqrt{3x-1}
\]
Next, we square both sides to remove the square roots. Squaring the left side gives \(4 \cdot 2x = 8x\) and squaring the right side g... |
[
{
"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
} | Let's denote the capacity of each glass as 1 unit. Mrs. Jones fills the first three glasses completely, so each of these has 1 unit. The fourth glass is filled to \(\frac{1}{3}\) of a unit. So the total amount of juice is \(3 + \frac{1}{3} = \frac{10}{3}\) units. Since there are four glasses, each should have \(\frac{1... |
[
{
"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, let's tackle this problem step by step. The problem is asking about correct statements regarding the bonding and acidity of certain compounds. Hmm, I need to think about each option carefully.
First, let's look at option [A]: Al(CH3)3. The question says it has three-centre two-electron bonds in its dimer... |
[
{
"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"
} | To solve the equation \( x^{\left(16(\log_5 x)^3 - 68 \log_5 x\right)} = 5^{-16} \), we start by taking the logarithm base 5 of both sides. Let \( y = \log_5 x \). Then \( x = 5^y \), and the equation becomes:
\[
(5^y)^{16y^3 - 68y} = 5^{-16}
\]
Using the property of exponents \((a^b)^c = a^{bc}\), the left side simp... |
[
{
"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
} | To determine Steven Moore's monthly payments for his new car, we need to calculate the monthly installment based on the total cost and the number of months he plans to pay. The formula for calculating the monthly payment on a fixed-rate loan is as follows:
\[ \text{Monthly Payment} = \frac{P \times r \times (1 + r)^n}... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: 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"
} | To solve the given problem, we need to evaluate the expression:
\[
\sec ^{-1}\left(\frac{1}{4} \sum_{k=0}^{10} \sec \left(\frac{7 \pi}{12}+\frac{k \pi}{2}\right) \sec \left(\frac{7 \pi}{12}+\frac{(k+1) \pi}{2}\right)\right)
\]
and find its value correct up to the second decimal digit. Let's proceed step by step.
Fir... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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
} | To solve this problem, we need to determine why Lizette can no longer distinguish the colors of objects in dim light. The key here is understanding how the different types of photoreceptor cells in the retina (cones and rods) function under varying light conditions.
1. **Identify the Type of Photoreceptor Cells**:
... |
[
{
"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, let's tackle this problem. Hmm, the problem is about making an array beautiful with the minimum number of operations. The definition of a beautiful array is that it's symmetric, i.e., b_i = b_{n - i + 1} for all i. And the allowed operations are adding k to any element any number of times. So, the goal is... |
[
{
"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, \\... | We need to find the smallest integer \( b \geq 2 \) such that there are more than ten \( b \)-beautiful integers. A \( b \)-beautiful integer \( n \) must satisfy two conditions:
1. \( n \) has exactly two digits in base \( b \).
2. The sum of these two digits equals \( \sqrt{n} \).
First, let's express \( n \) in ... |
[
{
"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
} | To solve this problem, we need to determine the minimum resolution required to observe at least 30% of the decays of \( X^0 \) particles in a bubble chamber. The key steps involve calculating the decay length of the \( X^0 \) particles and then determining the resolution needed to capture 30% of the decays.
### Step 1... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 143 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about maximizing the product a*b*c by increasing some of the numbers up to 5 times. Hmm. So for each test case, we have three integers a, b, c. Noobish_Monk can choose to increase any of them (a, b, or c) up to 5 times by 1 each. So each time, he picks one of the three and adds 1... |
[
{
"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
} | <think>
Okay, I need to write a Python function that solves this problem. Let's see what the problem says. The task is to check if all the integers in a list are equal. If they are, output Yes, else No. Hmm.
The input is N followed by N numbers. So first, I need to read N, then read the next line as a list of integers... |
[
{
"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
} | To solve this problem, we need to determine the local boundary layer thickness \(\delta\) as a function of \(x\) by substituting the given velocity profile and skin friction coefficient into the integral form of the momentum equation. Let's proceed step by step.
### Step 1: Integral Momentum Equation
The integral form... |
[
{
"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, let's see. The problem is to find the number of distinct arrangements of 2 indistinguishable IMO gold medals and 2 indistinguishable IPhO gold medals in a row. Hmm, so the main thing here is that the medals of the same type are identical, which means different arrangements that only swap the same type's m... |
[
{
"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, let's see. I need to write a Python function that simulates this game between Alice and Bob. The input is an even-length array of integers. The output should be the array formed by the elements they append in each round.
Hmm, the rules are a bit specific. Let's break it down. Each round, first Alice remo... |
[
{
"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, let's see. The problem is to find the maximum distance from the origin we can reach after n moves, given a string of moves that includes 'L', 'R', and underscores. For each underscore, we can choose to go left or right. But the catch is that the choices for each step might not be optimal for all steps. So... |
[
{
"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
} | To solve this problem, we need to determine the type of mirror required to form an image of a headlight lamp filament on a wall 3 meters from the mirror, given that the lamp is 10 cm in front of the mirror. Additionally, we need to calculate the height of the image formed, knowing the object's height is 5 mm.
### Part... |
[
{
"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"
} | To solve this problem, we need to verify each statement step by step. Let's start by analyzing each option.
**Option (A): The points \( P, Q, R, S \) are NOT coplanar.**
To check if the points are coplanar, we can use the scalar triple product. The points are coplanar if the vectors \( \overrightarrow{PQ} \), \( \ove... |
[
{
"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>
Okay, let's see. I need to find the furthest distance from the origin after n moves, given a string of moves that includes L, R, and underscores. The underscores can be either L or R. So the problem is to choose the best possible values for those underscores to maximize the distance.
Hmm. The movement depends ... |
[
{
"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)"
} | To solve this problem, we need to determine the reflection of a point \( Q \) with respect to a given plane and find the conditions that the coordinates of the reflected point \( S \) must satisfy. Let's proceed step by step.
### Step 1: Understanding the Plane Equation
The plane is given by the equation:
\[
\vec{r} =... |
[
{
"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, I need to solve this programming problem. Let's read the problem statement carefully.
So, the problem is about determining if a slideshow can be good after each update to the array b. Each update changes a specific element in b to a new value. For each state of b (initial and after each update), we have ... |
[
{
"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, let's tackle this problem. Hmm, the task is to find a binary string of length n such that the absolute difference between f(t) and g(t) is minimized. Where f(t) is the number of non-empty subsequences made of 0s only, and g(t) is the number of non-empty subsequences that contain at least one 1.
First, 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": 1,
"temperature": 0.7
} | 1 | 258 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the expected value of the product of two elements in a list. The expected value is the sum of all possible products divided by the number of possible pairs. Since the problem says the answer can be written as P/Q, I need to compute this sum and then divide by the combination coun... |
[
{
"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
} | To solve this problem, we need to determine which demographic group among the options is more likely to experience intense feelings of shame and guilt when admitting to a family problem to a counselor. The key here is to recognize cultural stigma and traditional values associated with each group.
Let's analyze each op... |
[
{
"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"
} | To solve this problem, we need to determine the number of sandbags \( N \) that must be thrown out of the hot air balloon so that it rises to a new equilibrium height of 150 meters. The key principles here are Archimedes' principle and the variation of air density with height.
### Step 1: Understanding the Problem
1. ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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
} | To determine the correct condition for the bond length between two nonmetal atoms, let's analyze each option step by step.
A. The point at which the repulsive forces between the two atoms are equal.
- Repulsive forces between atoms would be significant when they are very close. However, if they are too close, the rep... |
[
{
"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, let's see. I need to find the minimum molar concentration of H+ required to prevent the precipitation of ZnS. Hmm. So the problem is about the solubility equilibrium of ZnS in the presence of H+ ions from H2S.
First, I remember that when H+ is present, it can react with the sulfide ions (S2-) from the d... |
[
{
"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, let's see. I need to solve this problem where I have n houses and a bunch of offers. Each offer is a range of houses and a price. The goal is to select non-overlapping offers to maximize the total gold. Hmm, right. So the key here is to find a way to greedily choose the offers such that their ranges don'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": 0,
"temperature": 0.7
} | 0 | 240 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Tsovak and Narek are playing a game with a matrix and an array. The goal is to determine who wins if they both play optimally. Let's try to understand the problem step by step.
So, the setup is that they have a matrix (n x m) and an array a of length l. The players take... |
[
{
"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, let's try to tackle this problem. Hmm, the problem is about counting the number of deterministic max-heaps after performing a certain number of add operations. The add operation increases values on the path from the root to a chosen node. The heap is deterministic if the choices made during the pop operat... |
[
{
"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, let's see. I need to find the minimum time it takes to make the sum of nums1 less than or equal to x. If it's not possible, return -1. Hmm.
So the process is: every second, add nums2[i] to nums1[i] for all i. Then, you can choose one i each second to set to zero. So each operation (the setting to zero) c... |
[
{
"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
} | <think>
Okay, I need to generate a Python function that takes a string S from stdin, changes the last character to 4, and prints the modified string. Let's see.
First, the problem says S ends with 2023. So the last four characters are 2023. Wait, but maybe the string is exactly four characters long? Wait, the constrai... |
[
{
"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
} | To determine the color of light absorbed by the organic compound, we need to understand the relationship between the energy of the light and its wavelength. The energy \( E \) of a photon is related to its wavelength \( \lambda \) by the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant and \(... |
[
{
"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"
} | To solve this problem, we need to determine the atomic number \( Z \) of a Hydrogen-like atom based on the given photoelectric effect data. Let's break down the problem step by step.
### Step 1: Understanding the Photoelectric Effect
The photoelectric effect occurs when photons strike a metal surface, causing electron... |
[
{
"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 objects such that their Lyman alpha emission can be detected with optical ground-based telescopes, we need to consider the atmospheric absorption of light in the Earth's atmosphere. Specifically, the Lyman alpha line at 1216 Angstrom (Å) can be absorbed by neutral hydrogen... |
[
{
"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, let's see. The problem is to find the minimum number of swaps needed to make a permutation simple. A simple permutation is one where every cycle has length at most 2. So, for each cycle in the permutation's cycle decomposition, we need to break it into cycles of size 2 or 1.
Hmm, how do we compute 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 | 54 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Darius has to arrange the stone columns such that their inscription counts are in non-decreasing order. The moves allowed are transferring one inscription between two columns that differ by exactly 1. The goal is to find the minimum number of moves required and output th... |
[
{
"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>
Okay, let's tackle this problem. Hmm, the problem is asking for, given a graph and a set of nodes that need internet, and for each k from 1 to n, the minimum possible total latency when choosing up to k servers. The latency for a node is the maximum edge weight along the path from the node to the server. So 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 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, let's tackle this problem. So, the problem is about Monocarp's hiking journey where he walks a, b, c, a, b, c... kilometers each day. We need to find the day when the total reaches at least n kilometers.
Hmm. Let's think about the pattern here. The days go like 1:a, 2:b, 3:c, 4:a, 5:b, 6:c, and so on. So... |
[
{
"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, let's see. I need to write a Python function that calculates the score based on the operations described. Hmm. The problem says that in each operation, we remove the largest number from each row, then take the highest among those removed, add it to the score, and repeat until the matrix is empty.
So 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>
Okay, I need to solve this problem where I have to find the maximum value of (nums[i] - nums[j]) * nums[k] for all triplets where i < j < k. If all possible triplets are negative, return 0. Let's think about how to approach this.
Hmm, the brute force way would be to check all possible triplets. Since the const... |
[
{
"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>
Okay, I need to solve this problem where I have to find the sum of elements in an array based on the number of set bits in their indices. Let me read the problem again carefully.
So the task is: given a list of integers nums and an integer k, return the sum of the elements whose indices have exactly k set bits... |
[
{
"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
} | To solve for the total area of the shaded region in the given problem, we need to analyze the structure of the rectangle formed by twelve 1 by 1 squares. The rectangle is a 3x4 grid since 3 columns and 4 rows make up 12 squares. The shaded region consists of two triangles formed by diagonals.
First, let's visualize 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: 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)"
} | To solve this problem, we need to analyze the given pyramid \( O P Q R S \) in the first octant. Let's break down the problem step by step.
1. **Understanding the Base Square**: The base \( O P Q R \) is a square with \( O P = 3 \). Since \( O \) is the origin \((0, 0, 0)\), \( P \) is at \((3, 0, 0)\). The diagonal \... |
[
{
"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, let's tackle this problem. Hmm, the problem is about permutations and building a graph based on certain rules. The goal is to find the maximum possible diameter of a connected graph formed this way. Let's break down the problem step by step.
First, I need to understand the definitions of l_i and r_i. For... |
[
{
"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, let's see. I need to find out which options have all four molecules with permanent dipole moments at room temperature. Hmm, so what determines if a molecule has a permanent dipole? Oh right, it's the difference in electronegativity between the atoms and the molecular geometry. If the molecule is polar cov... |
[
{
"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>
Okay, let's see. I need to find the number of good pairs (i,j) where nums1[i] is divisible by nums2[j] multiplied by k. Hmm. So for each element in nums1, I have to check with each element in nums2 whether nums1[i] divisible by (nums2[j] * k). If yes, count it.
The brute force approach would be for each i in n... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: 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>
Okay, let's see. I need to find the total number of molecules in the given list that have at least one covalent bond between two atoms of the same kind. Hmm. So for each molecule, I have to check if there's a double bond or a triple bond between the same elements. Wait, but covalent bonds between the same eleme... |
[
{
"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... | To solve the problem, we start by considering the given product involving the 13th roots of unity. Let \(\omega = e^{2\pi i / 13}\) be a primitive 13th root of unity. The product in question is
\[
\prod_{k=0}^{12}(2 - 2\omega^k + \omega^{2k}).
\]
First, we can factor out a 2 from the terms inside the product:
\[
\p... |
[
{
"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
} | To solve the problem, we 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 \(y^2 = 8x\).
First, let's determine the points of tangency. The circle has radius \(\sqrt{2}\) and is centered at the origin. The parabola opens to the right... |
[
{
"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, let's tackle this problem. Hmm, the problem is about querying the sum of f(b) for various subarrays. The function f(b) is the minimum number of operations needed to make a subarray of length at least k. Each operation allows changing any element to any value. The subarray must be consecutive and have leng... |
[
{
"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, I need to solve this problem where I have to find all the peaks in a mountain array. Let's see. The problem says a peak is an element that's strictly greater than its neighbors. And the first and last elements can't be peaks. So my task is to iterate through the array and find all indices where the elemen... |
[
{
"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
} | To determine the degree of the polynomial \( p(x) \), we start by analyzing the given expression:
\[
p(x) = \frac{(x - b)(x - c)}{(a - b)(a - c)} + \frac{(x - a)(x - c)}{(b - a)(b - c)} + \frac{(x - a)(x - b)}{(c - a)(c - b)}.
\]
Each term in the sum is a rational function where the numerator is a product of two line... |
[
{
"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
} | <think>
Okay, I need to solve this problem where I have to determine if a given number N can be expressed as 2^x * 3^y. The input is N, and the output should be Yes or No. Let's think about how to approach this.
First, the problem says that N must be a product of powers of 2 and 3. So, any prime factors of N besides 2... |
[
{
"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
} | To determine how many positive perfect squares less than 2023 are divisible by 5, we start by understanding the properties of perfect squares divisible by 5. A number divisible by 5 must end in 0 or 5. Therefore, the square must end in 0 or 5. Let's analyze each case.
First, consider perfect squares ending in 0. Such ... |
[
{
"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)"
} | To solve this problem, we need to analyze the given sum \( S_n(x) \) and determine which of the statements (A), (B), (C), or (D) are true. Let's proceed step by step.
First, let's understand the term inside the sum:
\[ \cot^{-1}\left(\frac{1 + k(k+1) x^2}{x}\right). \]
We can simplify this expression. Let's denote:
\... |
[
{
"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, let's see. The problem is about a projectile's range when the acceleration due to gravity changes partway through its flight. Hmm. So the initial setup is that a projectile is fired with speed v and angle θ. The range d is calculated under gravity g. Then, at the highest point, the gravity changes to g', ... |
[
{
"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"
} | To solve this problem, we need to determine the probability that three randomly chosen distinct points from the set \( X \) form a triangle with a positive integer area. Let's break down the solution step by step.
### Step 1: Understanding the Set \( X \)
The set \( X \) is defined by two conditions:
1. \(\frac{x^2}{8... |
[
{
"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, let's see. I need to find the decrease in internal energy of a monatomic ideal gas that's undergoing an adiabatic expansion. The volume becomes eight times bigger, and the initial temperature is 100 K. The universal gas constant is R=8 J/mol*K. Hmm.
First, adiabatic process means no heat exchange with th... |
[
{
"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, let's tackle this problem. So the task is to find the maximum total petals the girl can get by buying flowers such that the difference between any two flowers in the bouquet is at most one. And the cost is the sum of their petals, which must not exceed m. The goal is to maximize the sum.
Hmm, so the prob... |
[
{
"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)"
} | To solve this problem, we need to determine under which conditions the given expression for work \( w \) is applicable. The expression provided is:
\[
w = -\int dV \left( \frac{R T}{V - b} - \frac{a}{V^2} \right)
\]
This expression involves the pressure \( P_{\text{ext}} \) which is given by the van der Waals equatio... |
[
{
"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)"
} | To solve this problem, we need to analyze each option based on the given information and principles of blackbody radiation. Let's proceed step by step.
### Given Data
- Surface area of the body, \( A = 1 \, \mathrm{m}^2 \)
- Normal body temperature, \( T = T_0 + 10 \, \mathrm{K} \) where \( T_0 = 300 \, \mathrm{K} \)
... |
[
{
"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, let's see. I need to find the area of the region defined by the inequalities 0 ≤ x ≤ 9/4, 0 ≤ y ≤ 1, x ≥ 3y, and x + y ≥ 2. Hmm, right. So the region is a polygon, probably a triangle or something more complex. I should graph these inequalities to visualize the shape.
First, let's think about each inequa... |
[
{
"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... | To solve the problem, we need to find the number of intersections between the graphs of \( y = 4 g(f(\sin (2 \pi x))) \) and \( x = 4 g(f(\cos (3 \pi y))) \). Let's break down the problem step by step.
First, understand the functions \( f(x) \) and \( g(x) \):
\[ f(x) = \left| \left| x \right| - \frac{1}{2} \right| \... |
[
{
"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>
Okay, let's tackle this problem. Hmm. So the problem is that Artem wrote a digit d exactly n! times. We need to find which odd digits from 1 to 9 divide this number. The output should be the sorted list of those digits.
First, let's understand the input. For each test case, we have n and d. The number is made ... |
[
{
"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, let's see. I need to write a Python function that calculates the sum of digit differences between all pairs of integers in an array. All the numbers have the same number of digits. Hmm.
So, the digit difference between two numbers is the count of digits that are different in the same positions. Like for ... |
[
{
"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"
} | To solve this problem, we need to determine the amount of water produced during the oxidation of 1 mole of rhombic sulphur (S8) by concentrated HNO3 to a compound with the highest oxidation state of sulphur. The key steps involve identifying the products of the reaction and calculating the stoichiometry of water format... |
[
{
"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)"
} | To solve this problem, we need to evaluate each statement regarding surface properties and determine which ones are correct. Let's analyze each option step by step.
**Option [A]: Adsorption is accompanied by a decrease in enthalpy and decrease in entropy of the system.**
Adsorption involves the process where molecule... |
[
{
"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, I need to solve this problem where I have to find all the peaks in a mountain array. Let's see. The problem says a peak is an element that's strictly greater than its neighbors. And the first and last elements can't be peaks. So my task is to iterate through the array and find all indices where the elemen... |
[
{
"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"
} | To find the value of \(\lim_{x \to \alpha^+} f(g(x))\), we need to evaluate the limit of the composition of functions \(f\) and \(g\) as \(x\) approaches \(\alpha\) from the right. Let's proceed step by step.
First, recall the definitions of the functions \(f\) and \(g\):
\[
f(x) = \sin \left( \frac{\pi x}{12} \right)... |
[
{
"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"
} | To solve this problem, we need to determine the number of moles of HF produced by the complete hydrolysis of 1 mole of the Xe compound P. Let's proceed step by step.
### Step 1: Determine the Formula of Compound P
The problem states that compound P is formed by the reaction of Xe (elemental xenon) and O₂F₂ (dioxidoflu... |
[
{
"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, I need to solve this problem where I have to find the count of stepping numbers between two large numbers, low and high. Stepping numbers are those where each adjacent digit has an absolute difference of 1. And the answer has to be modulo 1e9+7. Hmm.
First, let's understand what a stepping number is. For... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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
} | To determine which reform Baldassare Castiglione would most likely want to institute, we need to carefully analyze his views as outlined in the provided information. Let's break down the key points from the excerpt:
1. **Arms and Physical Training**: Castiglione emphasizes that the principal profession of a courtier s... |
[
{
"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
} | To solve the problem, we start by understanding the relationship between the regular hexagon and the equilateral triangles that make it up. A regular hexagon can indeed be divided into six equilateral triangles, each sharing a side with the hexagon.
Given that the perimeter of one of these equilateral triangles is 21 ... |
[
{
"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>
Okay, let's see. I need to write a Python function that calculates the score based on the operations described. Hmm. The problem says that in each operation, we remove the largest number from each row, then take the highest among those removed, add it to the score, and repeat until the matrix is empty.
So 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 | 186 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to tackle this problem. Hmm, the problem statement says that we have to maximize the score by performing operations where we can increase certain elements of array a up to k times. The score is the maximum of (a_i + median of the remaining elements) for all i. So, the goal is to choose which ele... |
[
{
"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, let's see. So the problem is about finding the minimum time Zhan needs to blend all his fruits. Hmm. Let me read the problem again to make sure I understand it correctly.
The blender can process up to x fruits per second. But in each second, Zhan can put up to y fruits into the blender. Wait, no. Wait, 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": 0,
"temperature": 0.7
} | 0 | 167 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So the task is to find the minimum number of times we need to square elements in the array to make it non-decreasing. If it's impossible, return -1.
Hmm, first, I need to understand what conditions make the array non-decreasing. A non-decreasing array means each element is grea... |
[
{
"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, let's see. I need to solve this problem where I have to find the maximum value of this function f(x) which is the sum of x and all the players who receive the ball during k passes. The challenge is to compute this for each possible x and choose the maximum. But since n can be up to 1e5 and k up to 1e10, a... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print 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, let's see. The problem is about Alice and Bob playing a game with marbles. The goal is to compute Alice's score at the end of the game, considering both play optimally. Hmm.
So, the rules are that each player takes turns removing marbles. Alice goes first. The score is calculated based on the colors they... |
[
{
"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, let's tackle this problem. So the task is to find an array a such that each element a_i AND a_{i+1} equals b_i. If it's not possible, output -1. Hmm.
First, I need to think about the constraints. The array a has to satisfy n conditions (since there are n-1 elements in b). So for each i from 1 to n-1, a[i... |
[
{
"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
} | <think>
Okay, let's see. I need to solve this problem where I have a tree with N vertices, each has a value C_i. The function f(x) is the sum over all i of C_i multiplied by the distance d(x, i). And I need to find the minimum f(v) over all v from 1 to N.
Hmm. The distance here is the number of edges between x and 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: 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
} | To determine which liqueur is used to make a Pink Lady cocktail pink, let's think about the traditional ingredients of this drink. The Pink Lady is a classic cocktail that typically consists of apple brandy, lime juice, and a sweetener. The key here is the color; since the drink is called a Pink Lady, it's likely that ... |
[
{
"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"
} | To determine the increasing order of atomic radii for the Group 13 elements Al, Ga, In, and Tl, we need to consider the trends in atomic radius as we move down the group. Group 13 elements are also known as the boron group, and they include elements with atomic numbers 13 (Al), 31 (Ga), 49 (In), and 81 (Tl).
### 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: 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, I need to find the limit of this complicated expression as x approaches pi/2. Let's start by looking at the numerator and denominator separately.
The numerator is 4√2 (\sin 3x + \sin x). The denominator is [ (2 \sin 2x \sin (3x/2) + \cos (5x/2)) ] minus [ (\sqrt{2} + \sqrt{2} \cos 2x + \cos (3x/2)) ]. S... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 226 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem statement says that Turtle needs to choose a subsequence of length m that satisfies two conditions: the a's are non-decreasing, and all b's in the subsequence are distinct. And we have to maximize the sum of the c's. If it's impossible, return -1.
First, I need... |
[
{
"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
} | To solve this problem, we need to identify the correct reactants for the given name reactions based on the products provided. Let's analyze each reaction step by step.
### Reaction A:
The product is 2,8-dimethylspiro[4.5]decan-6-one. The name suggests that this is a Claisen rearrangement or a related reaction. The Cla... |
[
{
"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
} | <think>
Okay, let's see. I need to write a Python function that takes B from stdin and outputs A if A^A equals B, otherwise -1. Hmm. So the problem is to find if there's a positive integer A where A raised to itself equals B. If such an A exists, return it; else, return -1.
First, let's think about how to find A given... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.