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 8 169k |
|---|---|---|---|---|---|---|
[
{
"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: S Select the best translation into predicate logic. Some kind people help some endangered species. (Ex: x is endangered; Kx: x is kind; Px: x is a p... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 203 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the best translation of the sentence "Some kind people help some endangered species" into predicate logic. The given options are A to F, and each has different logical structures. Let me start by breaking down the original sentence.
The main components are:
- Some kind people (K... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two arrays of strings wordsContainer and wordsQuery.\nFor each wordsQuery[i], you need to find a string from wordsContainer that has the longest ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 468 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each word in wordsQuery, I have to find the corresponding word in wordsContainer that shares the longest common suffix. If there are multiple such words, I pick the shortest one, and if lengths are same, the first one in the container. Then return the indices of thos... |
[
{
"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 | 130 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | </html>
To solve this problem, we need to compute the expected value of the product of two randomly chosen elements from an array. The expected value is given by the formula \(\frac{\sum_{i < j} a_i \cdot a_j}{\binom{n}{2}}\), where \(n\) is the number of elements in the array. The result should be expressed as \(P \c... |
[
{
"content": "Problem: There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of a $5\\times5$ grid such that: each cell contains at most one chip all chips in the same row and all ch... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 8 | AIME24 | {
"expected_answer": "902",
"problem_id": "aime24-8",
"reference_solution": "The problem says \"some\", so not all cells must be occupied.\nWe start by doing casework on the column on the left. There can be 5,4,3,2, or 1 black chip. The same goes for white chips, so we will multiply by 2 at the end. There is $1$... | To solve this problem, we need to determine the number of ways to place 25 indistinguishable white chips and 25 indistinguishable black chips into a 5x5 grid such that each cell contains at most one chip, all chips in the same row and column have the same color, and adding any additional chip would violate these condit... |
[
{
"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 three integers start, finish, and limit. You are also given a 0-indexed string s representing a positive integer.\nA positive integer x is called... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 161 | 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 number of powerful integers between start and finish, inclusive. A powerful integer is defined as one that ends with a given string s, and each of its digits is less than or equal to a given limit. Hmm.
First, let's understand the constraints. The sta... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N sticks with several balls stuck onto them. Each ball has a lowercase English letter written on it.\nFor ea... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 240 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine the number of different sticks based on the letters written on their balls. Let's see the problem again. Each stick has balls with letters, and two sticks are the same if their letter sequences are equal or reversed. So the task is to count how many u... |
[
{
"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.AtCoder Shop has N products.\r\nThe price of the i-th product (1\\leq i\\leq N) is P _ i.\r\nThe i-th product (1\\leq ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 239 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to create a Python function that solves this problem. The problem is about determining if there's a product that is strictly superior to another. Strictly superior means that product i is better than product j in all functions, and either the price of i is lower than j or j has some addi... |
[
{
"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 | 189 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | </e>
To solve this problem, we need to determine Iris's final lucky value based on her observation process. The key insight is to understand how the segments of stars change with each round of observation and how the lucky value accumulates based on the segments she observes.
### Approach
The problem involves a recurs... |
[
{
"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 | 311 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if it's possible to draw exactly n new edges between two strongly connected directed graphs such that the following conditions are met:
1. The ends of any added edge lie in different graphs.
2. From each outgoing vertex of the first graph, exactly one added edge originates.
3... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Consider a triangle $\\Delta$ whose two sides lie on the $x$-axis and the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 324 | JEEBench | {
"expected_answer": "B",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the equation of the circle passing through the vertices of triangle \(\Delta\), given that two of its sides lie on the \(x\)-axis and the line \(x + y + 1 = 0\), and its orthocenter is \((1,1)\).
### Step-by-Step Solution:
1. **Identify the vertices of the triangle:**
- ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In an inactive state, a transcription factor subunit awaits an activation signal from the membrane phosphorylation cascade. Upon phosphorylation on the Ser residues in t... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 157 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's break down the problem step by step.
First, we need to understand the normal function of the transcription factor subunit. In its inactive state, it's waiting for an activation signal from the membrane phosphorylation cascade. Once phosphorylated on Ser residues in the transactiv... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: How many of the stars listed below would be detectable using the ESPRESSO spectrograph, when it is coupled with one of the 8m VLT telescopes at the Paranal Observatory? ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 186 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to determine how many of the listed stars can be detected by the ESPRESSO spectrograph when coupled with an 8m VLT telescope at Paranal. The criteria is a signal-to-noise ratio (S/N) of at least 10 per binned pixel during a 1-hour exposure.
First, I should recall how the signal-to-noise... |
[
{
"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 | 236 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out how to approach this problem. So, the problem is about David trying to avoid being caught by multiple teachers in a one-dimensional classroom. They take turns moving, and David wants to maximize the number of moves until he's caught, while the teachers want to minimize that number. We need... |
[
{
"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 | 95 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Jane has a list of problems, and she solved all except the last one. The goal is to determine her problem-solving skill level, which is an integer x. If the skill level is x, then she can solve problems with difficulty up to x. So, if x is her skill, then she can solve 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: The World Health Organization recommends zinc supplements for which groups of people?\n\nOptions: A. Men with high physical activity levels, B. All w... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 84 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer, let's analyze each option based on the World Health Organization's (WHO) recommendations for zinc supplements.
First, we need to recall that zinc is essential for immune function, wound healing, and overall growth. Deficiencies can lead to conditions like stunting in children, diarrhea... |
[
{
"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 | 373 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Line Breaks problem. Let me read the problem statement carefully.
So, Kostya has a text with n words. He has two strips. The first strip can hold m characters, and the second one is unlimited. He has to choose a number x such that the first x words fit on the first strip. The goal i... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Two quantum states with energies E1 and E2 have a lifetime of 10^-9 sec and 10^-8 sec, respectively. We want to clearly distinguish these two energy levels. Which one of... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 0 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to figure out which energy difference would allow two quantum states with given lifetimes to be clearly resolved. Let me start by recalling the relevant physics here.
The lifetime of a quantum state is related to the energy uncertainty through the Heisenberg uncertainty principle. The formula is ... |
[
{
"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. We say that two integers x and y form a prime number pair if:\n\n1 <= x <= y <= n\nx + y == n\nx and y are prime numbers\n\nReturn ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 58 | 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 prime pairs (x, y) such that x + y = n, x and y are primes, and x <= y. Then return them sorted by x in a 2D list. Let's think about how to approach this.
First, the constraints are up to 1e6, so precomputing primes up to n might be feasible. Sieve of... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Choose the correct statement(s) among the following.\n(A) $\\mathrm{Sn... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 290 | JEEBench | {
"expected_answer": "AB",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine the correct statements, we need to analyze each option step by step.
**Option (A):** $\mathrm{SnCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}$ is a reducing agent.
- Tin(II) chloride (SnCl₂) is known to be a reducing agent because it can gain electrons. When it is oxidized, it forms SnCl₄. So this statement i... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider an isolated system of 13 identical particles each with charge 2e and negligible mass. 12 of these charges are\nconstrained to stay at 2 m from a point P. The 13... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 179 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{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 an N \\times N grid. Let (i,j) denote the cell in the i-th row from the top and the j-th column from the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 335 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out how to approach this problem. So, we have an N x N grid where each cell can be either 'o' or 'x'. The task is to find the number of triples of cells that meet certain conditions. Let's break down the conditions again.
First, the triple must consist of three distinct cells. All thr... |
[
{
"content": "Problem: Each vertex of a regular octagon is independently colored either red or blue with equal probability. The probability that the octagon can then be rotated so that all of the blue vertices end up at positions where there were originally red vertices is $\\tfrac{m}{n}$ , where $m$ and $n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 25 | AIME24 | {
"expected_answer": "371",
"problem_id": "aime24-25",
"reference_solution": "Notice that the question's condition mandates all blues to go to reds, but reds do not necessarily have to go to blue. Let us do casework on how many blues there are. If there are no blues whatsoever, there is only one case. This case i... | To solve this problem, we need to determine the probability that a regular octagon, with each vertex independently colored red or blue, can be rotated such that all blue vertices were originally at positions with red vertices. This implies that after rotation, each blue vertex must have been a red vertex in the origina... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: At time $t=0$, a disk of radius $1 \\mathrm{~m}$ starts to rol... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 395 | JEEBench | {
"expected_answer": "0.52",
"problem_id": "23",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. So, a disk starts rolling without slipping, and a stone is stuck to it. At t=0, the contact point is where the disk meets the plane. After some time, the stone detaches and flies off tangentially. We need to find the maximum height it reaches, specifically the value... |
[
{
"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 position vector $\\vec{r}$ of a particle of mass $m$ is given by t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 6 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which of the given statements about the particle are true at \( t = 1 \) second. We will do this by calculating the velocity, angular momentum, force, and torque step by step.
### Step 1: Calculate the Velocity \(\vec{v}(t)\)
The velocity vector is the time derivative of the... |
[
{
"content": "Problem: Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\overline{IA}\\perp\\overline{OI}$ , circumradius $13$ , and inradius $6$ . Find $AB\\cdot AC$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 9 | AIME24 | {
"expected_answer": "468",
"problem_id": "aime24-9",
"reference_solution": "By Euler's formula $OI^{2}=R(R-2r)$ , we have $OI^{2}=13(13-12)=13$ . Thus, by the Pythagorean theorem, $AI^{2}=13^{2}-13=156$ . Let $AI\\cap(ABC)=M$ ; notice $\\triangle AOM$ is isosceles and $\\overline{OI}\\perp\\overline{AM}$ ... | To solve for \( AB \cdot AC \) in the given triangle \( \triangle ABC \) with circumcenter \( O \), incenter \( I \), and the condition \( \overline{IA} \perp \overline{OI} \), we start by using the given information about the circumradius \( R = 13 \) and inradius \( r = 6 \).
First, recall that the distance \( OI \)... |
[
{
"content": "Problem: Find the largest $x$-value at which the graphs of $f(x)=e^{3x^2-|\\lfloor x \\rfloor|!}+\\binom{22+735235|\\lfloor x \\rfloor |}{2356}+\\phi(|\\lfloor x \\rfloor|+1)+72x^4+3x^3-6x^2+2x+1$ and $g(x)=e^{3x^2-|\\lfloor x \\rfloor|!}+\\binom{22+735235|\\lfloor x \\rfloor |}{2356}+\\phi(|\\lfl... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 188 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the largest \( x \)-value at which the graphs of \( f(x) \) and \( g(x) \) intersect, we start by analyzing the given functions. Both functions \( f(x) \) and \( g(x) \) have the same terms except for the \( x^3 \) and \( x^2 \) terms. Specifically, the only difference is in the \( x^3 \) coefficient and 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": 1,
"temperature": 0.7
} | 1 | 75 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's see. So the problem is about Alice and Bob playing a game with marbles of different colors. The goal is to calculate Alice's score at the end of the game when both play optimally. The score depends on the colors of marbles each player has taken.
Hmm. Let me read the editorial again. Oh right, the key idea... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 317 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that reads an integer B from standard input and determines if there's a positive integer A such that A^A equals B. If such an A exists, output it; otherwise, output -1. The constraints are 1 ≤ B ≤ 10^18, which is a big range. Let's think about how to approach this.
First... |
[
{
"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 | 393 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | </html>
To solve this problem, we need to determine if Kevin can unlock a combination lock by reducing its initial value \( x \) to zero using specific operations. The operations allowed are either removing two consecutive digits '3' from \( x \) (if possible) or subtracting 33 from \( x \) (if \( x \geq 33 \)).
### K... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given three integers a, b, and n, return the maximum value of (a XOR x) * (b XOR x) where 0 <= x < 2^n.\nSince the answer may be too large, return it modulo 10... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 127 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where given three integers a, b, and n, I have to find the maximum value of (a XOR x) * (b XOR x) for 0 <= x < 2^n. And then return that maximum modulo 1e9+7. Hmm.
First, let's think about what XOR does. XOR is a bitwise operation. When you XOR two numbers, each bit is 1 if e... |
[
{
"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 $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 109 | JEEBench | {
"expected_answer": "D",
"problem_id": "38",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the position of point \( S \) relative to triangle \( PQR \) given the vector equation. Let's start by analyzing the given equation.
The equation provided is:
\[
\overrightarrow{OP} \cdot \overrightarrow{OQ} + \overrightarrow{OR} \cdot \overrightarrow{OS} = \overrightarrow{O... |
[
{
"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 k and an integer x.\nConsider s is the 1-indexed binary representation of an integer num. The price of a number num is the number of i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where given k and x, I have to find the maximum integer num such that the sum of the prices of numbers from 1 to num is <= k. The price of a number is the count of positions i where i mod x == 0 and the ith bit in the binary representation of the number is set (1).
Hmm, let'... |
[
{
"content": "Problem: Let $a,$ $b,$ $c,$ $d$ be positive real numbers. Find the minimum value of\n\\[(a + b + c + d) \\left( \\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c} + \\frac{1}{d} \\right).\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 289 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the minimum value of the expression \((a + b + c + d) \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} \right)\), we can use the Cauchy-Schwarz inequality. The Cauchy-Schwarz inequality in the form we need here states that for any real numbers \(x_i\) and \(y_i\), \((\sum x_i^2)(\sum y_i^2) \geq (\s... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The compound(s) which generate(s) $\\mathrm{N}_{2}$ gas upon thermal d... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 128 | JEEBench | {
"expected_answer": "BC",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine which compounds generate \(\mathrm{N}_2\) gas upon thermal decomposition below \(300^\circ \mathrm{C}\), we need to analyze each option by considering their decomposition reactions and the conditions under which they occur.
**Option (A): \(\mathrm{NH}_4 \mathrm{NO}_3\)**
This compound is ammonium nitrate... |
[
{
"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 | 411 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where after each query, which flips a single character in the binary string, I have to calculate the sum of f(b) over all non-empty subsequences of s, modulo 998244353. Hmm. Let's think about the function f(t). The function f(t) is the minimum number of contiguous identical character ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Consider an obtuse angled triangle $A B C$ in which the differ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 498 | JEEBench | {
"expected_answer": "1008",
"problem_id": "14",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. We need to find the value of \((64a)^2\) for an obtuse-angled triangle \(ABC\) with some specific properties. Let's break down the information given and the steps required.
First, the triangle is obtuse-angled, meaning one of its angles is greater than \(\pi/2\) (9... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: For a reaction taking place in a container in equilibrium with its sur... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 104 | JEEBench | {
"expected_answer": "BD",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, I need to figure out which statements are correct regarding the effect of temperature on the equilibrium constant K for reactions, especially in terms of entropy changes. Let's start by recalling the relationship between entropy, temperature, and equilibrium constants.
The equilibrium constant K is conne... |
[
{
"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: On complete hydrogenation, natural rubber produces\n(A) ethylene-propylen... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 15 | JEEBench | {
"expected_answer": "A",
"problem_id": "23",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's see. The question is about what natural rubber produces when it's completely hydrogenated. Hmm. I remember that natural rubber is a polymer made from isoprene units. The chemical formula for isoprene is C5H8. When you hydrogenate a polymer, you add hydrogen atoms to the double bonds in the polymer 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: Consider the hyperbola\n\\[\n\\frac{x^{2}}{100}-\\frac{y^{2}}{64}=1\n\\]\nwith foci at $S$ and $S_{1}$, where ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 418 | JEEBench | {
"expected_answer": "7",
"problem_id": "7",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve the given problem, we start by analyzing the hyperbola equation and its properties. The hyperbola is given by:
\[
\frac{x^2}{100} - \frac{y^2}{64} = 1
\]
First, we identify the key parameters of the hyperbola. The standard form of a hyperbola centered at the origin is:
\[
\frac{x^2}{a^2} - \frac{y^2}{b^2} =... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Two compounds A and B are treated separately with hydrochloric acid, sodium nitrite, and water. Through the mentioned treatment two different diketones are produced. Sel... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 138 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to figure out which starting materials A and B would produce the given diketones when treated with sodium nitrite, hydrochloric acid, and water. The reactions probably involve a Claisen condensation or something similar. Let me think about the structures of the diketones first.
The firs... |
[
{
"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 $P$ be a point in the first octant, whose image $Q$ in the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 177 | JEEBench | {
"expected_answer": "8",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the length of the segment \( PR \), where \( P \) is a point in the first octant, \( Q \) is its image in the plane \( x + y = 3 \), and \( R \) is the image of \( P \) in the \( xy \)-plane. Let's proceed step by step.
### Step 1: Determine the coordinates of \( Q \)
Given ... |
[
{
"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: How can the public debt exert an inflationary pressure on the economy?\nOptions: A. Public debt increases the value of the currency, leading to defla... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 103 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{C} |
[
{
"content": "Problem: The equation\n\\[x^{10}+(13x-1)^{10}=0\\,\\]has 10 complex roots $r_1,$ $\\overline{r}_1,$ $r_2,$ $\\overline{r}_2,$ $r_3,$ $\\overline{r}_3,$ $r_4,$ $\\overline{r}_4,$ $r_5,$ $\\overline{r}_5,$ where the bar denotes complex conjugation. Find the value of\n\\[\\frac 1{r_1\\overline{r}_1}+... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 101 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the given problem, we start by analyzing the equation \(x^{10} + (13x - 1)^{10} = 0\). This equation can be rewritten as:
\[x^{10} = - (13x - 1)^{10}.\]
Taking the 10th root of both sides, we get:
\[x = \pm (13x - 1) e^{i k \pi / 5} \quad \text{for} \quad k = 0, 1, 2, \ldots, 9.\]
However, this approach mi... |
[
{
"content": "Problem: Cities $A$ and $B$ are $45$ miles apart. Alicia lives in $A$ and Beth lives in $B$. Alicia bikes towards $B$ at 18 miles per hour. Leaving at the same time, Beth bikes toward $A$ at 12 miles per hour. How many miles from City $A$ will they be when they meet?\nMark your solution with \\box... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 0 | AMC23 | {
"expected_answer": "27",
"problem_id": "0",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. Two people, Alicia and Beth, are starting from cities A and B which are 45 miles apart. Alicia is biking towards B at 18 miles per hour, and Beth is biking towards A at 12 miles per hour. I need to find out how many miles from city A they will meet.
Hmm, so the key here is to figure out how lo... |
[
{
"content": "Problem: A group of $N$ students, where $N < 50$, is on a field trip. If their teacher puts them in groups of 8, the last group has 5 students. If their teacher instead puts them in groups of 6, the last group has 3 students. What is the sum of all possible values of $N$?\nMark your solution with ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 201 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of students \( N \) such that when divided by 8, the remainder is 5, and when divided by 6, the remainder is 3. Additionally, \( N \) must be less than 50.
First, we can express the given conditions using congruences:
\[
N \equiv 5 \pmod{8}
\]
\[
N \equiv 3 \pmod{... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 159 | JEEBench | {
"expected_answer": "900",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <begiin solution>
Okay, let's tackle this problem step by step. So, we need to find the decrease in internal energy of a monatomic ideal gas that undergoes an adiabatic expansion. The volume becomes eight times the initial, and the initial temperature is 100 K. The universal gas constant is given as 8.0 J/mol·K.
Firs... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: In a circuit, a metal filament lamp is connected in series wit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 348 | JEEBench | {
"expected_answer": "60",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem step by step. We need to find the phase angle \(\varphi\) between the current and the supply voltage in a circuit with a metal filament lamp and a capacitor connected in series. The supply is 200V, 50Hz, and the power consumed by the lamp is 500W with a voltage drop of 100V. Let'... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $n \\geq 2$ be a natural number and $f:[0,1] \\rightarrow \\mathbb{R}$ be the function defined by\n\n$$\nf... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 458 | JEEBench | {
"expected_answer": "8",
"problem_id": "9",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, let's see. I need to find the maximum value of the function \( f(x) \) given that the area under the curve from \( x=0 \) to \( x=1 \) is 4. The function is defined in four different pieces. Hmm. First, I should calculate the area under each piece and set their sum equal to 4. Then find the value of \( n ... |
[
{
"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: If Mr. Hammer's disposable income last year was $5,000 and his total expenditures were 4,600, what was his propensity to save?\nOptions: A. 7%, B. 3%... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 343 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine Mr. Hammer's propensity to save, we first need to calculate his savings. Propensity to save is the ratio of savings to disposable income.
Step 1: Calculate savings.
Savings = Disposable Income - Total Expenditures
Given Disposable Income = $5,000 and Total Expenditures = $4,600
Savings = $5,000 - $4,600 ... |
[
{
"content": "Problem: In quadrilateral $ABCD$, angle $BAD$ and angle $CDA$ are trisected as shown. What is the degree measure of angle $AFD$?\n\n[asy]\nsize(150);\npair A , B, C, D; A = (0,0); B = (2, 4); C = (7,4); D = (7, -2);\ndraw( (0,0)--(2,4) -- (7,4) -- (7, -2)-- cycle);\nlabel(\"$A$\", A, SW);\nlabel(\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 94 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for the measure of angle \(AFD\) in the given quadrilateral \(ABCD\), we start by analyzing the information provided and the properties of angles in geometric figures.
First, we note that angle \(BAD\) and angle \(CDA\) are trisected. This means they are each divided into three equal parts. Let's denote the 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 | 442 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to count the number of ordered pairs (x, y) that satisfy certain conditions. Let me read the problem again carefully.
So the conditions are:
1. x has to be between l1 and r1 inclusive.
2. y has to be between l2 and r2 inclusive.
3. There exists a non-negative integer n 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 210 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where Chloe wants to create a perfect binary tree isomorphic to Penchick's tree. The challenge is to find the minimum depth d of Chloe's tree. Let me think about how to approach this.
First, let's understand the problem. Penchick's tree is given as a rooted tree with n vertices, root... |
[
{
"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 | 390 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Turtle and Inversions problem. Let me read through the description carefully.
So the problem is about finding the maximum number of inversions in a permutation that satisfies certain interval conditions. The permutation is considered interesting if for each interval [l_i, r_i], 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 | 92 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this Tower Capturing problem. Let's start by understanding the problem statement.
So, there are n towers at distinct points. Initially, we own towers 1 and 2. We can perform operations where we pick two owned towers P and Q, and an unowned tower R. The circle through P, Q, R must contain all n 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 | 327 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Monocarp is adding heroes and artifacts to his army and wants to know after each query the maximum number of rounds he can survive. The battle proceeds with the dragon dealing damage each round, and the battle ends when all heroes are dead. The key is to determine, after... |
[
{
"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 $a, \\lambda, \\mu \\in \\mathbb{R}$. Consider the system of linea... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 66 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given system of linear equations for different values of \(a\), \(\lambda\), and \(\mu\). The system is:
\[
\begin{aligned}
& a x + 2 y = \lambda \\
& 3 x - 2 y = \mu
\end{aligned}
\]
### Step 1: Determine the conditions for unique solutions
A system of linear equations h... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Observations of a quasar across the electromagnetic spectrum are being carried out. Focusing on the near infrared and optical spectrum, there is a peak at wavelength of ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 158 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about determining the comoving distance of a quasar based on some given parameters. Hmm. The quasar is observed in the near-infrared and optical spectrum, with a peak at 790 nm. The flux drops at shorter wavelengths. So the wavelength here is 790 nm, which is in the infrared part... |
[
{
"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 | 33 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. The task is to determine if two given strings s and t can be transformed into the same string by replacing their wildcards ( '-' and '*' ) under certain rules. Hmm. Let's think about the conditions under which s and t can be made equal after replacement.
First, the rules for replacemen... |
[
{
"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.On a two-dimensional plane, Takahashi is initially at point (0, 0), and his initial health is H. M items to recover h... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 204 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to create a Python function that models Takahashi's movement and health based on the given inputs. The goal is to determine if he can complete all N moves without collapsing due to negative health. Hmm.
First, the input is read from stdin. The function should take stdin as input and pri... |
[
{
"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: Which of the following is(are) NOT the square of a $3 \\times 3$ matri... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 86 | JEEBench | {
"expected_answer": "BD",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, I need to figure out which of these matrices is NOT the square of a 3x3 matrix with real entries. Let's think about what it means for a matrix to be a square. If a matrix A squared is A^2, then it's the product of A with itself. But how does this affect the entries?
First, let's look at the main 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": 1,
"temperature": 0.7
} | 1 | 149 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out this problem. So, the task is to compute MEOW(a) for a given array a. The MEOW function is defined as the sum over all distinct subsets b of a, of the MEX(b, |b| + 1). Hmm. First, I need to understand what MEX means here.
The MEX of a set S and a number k is the k-th positive integer not ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 134 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this Grid Puzzle problem. Let's read the problem carefully. The task is to convert all cells in an n x n grid to white using the minimum number of operations. The operations allowed are dyeing a 2x2 subgrid white or dyeing an entire row white.
First, let's understand the initial setup. 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: Pine Co. purchased land for $450000 as a factory site. An existing building on the site was razed before construction began. Additional information i... | {
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} | 0 | 286 | MMLUPro | {
"expected_answer": "",
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"subject": null,
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} | <think>
Okay, let's see. The problem is about calculating the capitalized cost of the completed factory building for Pine Co. So, I need to figure out which expenses should be included in the cost basis of the new building.
First, the land was purchased for $450,000. Then, the existing building was razed, which cost ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"temperature": 0.7
} | 0 | 286 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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} | To solve this problem, we need to determine the minimum possible total cost of operations required to move tokens in two graphs such that the cost of each operation is minimized. The cost of each operation is defined as the absolute difference between the vertices chosen for movement in both graphs during each step. If... |
[
{
"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 | 216 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where Arul has a binary array and he wants to find the sum of the medians of all possible subsequences of length k, with the result modulo 1e9+7. Hmm, let's think about how to approach this.
First, let's understand the problem. The median of a subsequence is the middle element when t... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $\\beta$ be a real number. Consider the matrix\n\\[\nA=\\left(\\begin{array}{ccc}\n\\beta & 0 & 1 \\\\\n2 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 417 | JEEBench | {
"expected_answer": "3",
"problem_id": "6",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, let's tackle this problem step by step. We need to find the value of \(9\beta\) given that the matrix \(A = \left(\begin{smallmatrix}\beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2\end{smallmatrix}\right)\) satisfies the condition that \(A^7 - (\beta -1)A^6 - \beta A^5\) is a singular matrix.
First, I remembe... |
[
{
"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,
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"seed": 1,
"temperature": 0.7
} | 1 | 71 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's see. The problem is about bridge renovation. There are three bridges with different widths: 18, 21, and 25 units. Each bridge needs n planks. The planks are sold in 60-unit length. The workers can cut planks but not join them. So the goal is to buy the minimum number of 60-unit planks such that when cut, ea... |
[
{
"content": "Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
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"seed": 6,
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} | 6 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | To solve the given system of equations, we start by converting the logarithmic equations into exponential form. The first equation is:
\[
\log_2\left(\frac{x}{yz}\right) = \frac{1}{2} \implies \frac{x}{yz} = 2^{1/2} = \sqrt{2}
\]
Similarly, the second equation:
\[
\log_2\left(\frac{y}{xz}\right) = \frac{1}{3} \impli... |
[
{
"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.Given an integer X between -10^{18} and 10^{18}, inclusive, print \\left\\lceil \\dfrac{X}{10} \\right\\rceil.\r\nHere... | {
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"seed": 0,
"temperature": 0.7
} | 0 | 406 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to create a Python function that reads an integer X from standard input and prints the ceiling of X divided by 10. Hmm, the ceiling function. Oh right, in Python, the math.ceil function does that. But wait, I have to make sure to import math then.
Wait, the problem says to take stdin as input. So ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence A=(A_0,A_1,\\dots,A_{63}) of length 64 consisting of 0 and 1.\nFind A_0 2^0 + A_1 2^1 + \\dot... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 218 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to create a Python function that reads a sequence of 64 bits (each 0 or 1) from standard input and calculates the integer value they represent. The sequence is A = (A_0, A_1, ..., A_{63}), and the value is computed as the sum of A_i * 2^i for i from 0 to 63.
First, the input is given as a single ... |
[
{
"content": "Problem: Janet rolls a standard $6$-sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal $3$? The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive inte... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 18 | AMC23 | {
"expected_answer": "265",
"problem_id": "20",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. Janet rolls a die four times and wants the running total to equal 3 at some point. Hmm. So the problem is to find the probability that during those four rolls, the sum up to that point hits exactly 3. And then we need to express that probability as a fraction m/n and find m+n.
First, I need to... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: If a charge q is placed d distance away from the center of a grounded conducting sphere of radius R. Calculate the net potential energy of this system.\nOptions: A) U=- ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 50 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the net potential energy of the system where a charge \( q \) is placed a distance \( d \) from the center of a grounded conducting sphere of radius \( R \), we need to consider the interaction between the charge and the induced charges on the sphere.
### Step-by-Step Solution:
1. ** grounded conducting spher... |
[
{
"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 matrix grid of size n * n with values in the range [1, n^2]. Each integer appears exactly once except a which appears twic... | {
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"seed": 2,
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} | 2 | 149 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the two numbers in the grid: one that's repeated (a) and one that's missing (b). The grid is n x n, and the numbers are from 1 to n², with a appearing twice and b once. Hmm.
First, how do I find a and b? Let's think. Since the numbers are from 1 to n², maybe I can use the fact t... |
[
{
"content": "Problem: Suppose $\\sin D = 0.7$ in the diagram below. What is $DE$? [asy]\npair D,E,F;\nF = (0,0);\nD = (sqrt(51),7);\nE = (0,7);\ndraw(D--E--F--D);\ndraw(rightanglemark(D,E,F,15));\nlabel(\"$D$\",D,NE);\nlabel(\"$E$\",E,NW);\nlabel(\"$F$\",F,SW);\nlabel(\"$7$\",(E+F)/2,W);\n[/asy]\nMark your sol... | {
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"seed": 0,
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} | 0 | 14 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the length of DE in the given right triangle DEF. The problem states that sin D equals 0.7. Hmm. Let's recall what sine represents in a right triangle. Sine of an angle is opposite over hypotenuse. So for angle D, the opposite side is DE, and the hypotenuse is FD. So sin D = DE /... |
[
{
"content": "Problem: For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 37 | AMC23 | {
"expected_answer": "901",
"problem_id": "47",
"reference_solution": "",
"subject": null,
"type": null
} | To determine for how many integers \( n \) the expression
\[
\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}}
\]
represents a real number, we need to ensure that the argument of the square root is non-negative. This requires the fraction
\[
\frac{\log (n^2) - (\log n)^2}{\log n - 3}
\]
to be greater than or equa... |
[
{
"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 | 415 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to determine if a melody is perfect based on the intervals between its notes. Let me read the problem statement again carefully.
So, the problem says that a melody is perfect if every adjacent pair of notes has an interval of either 5 or 7 semitones. The input consists o... |
[
{
"content": "Problem: Let ABCDEF be a convex equilateral hexagon in which all pairs of opposite sides are parallel. The triangle whose sides are extensions of segments AB, CD, and EF has side lengths 200, 240, and 300. Find the side length of the hexagon.\nMark your solution with \\boxed\nAnswer:",
"role":... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 4 | AIME24 | {
"expected_answer": "80",
"problem_id": "aime24-4",
"reference_solution": "Draw a good diagram!\nLet $AF \\cap BC$ , $BC \\cap DE$ , and $AF \\cap DE$ be K, L, and M, respectively. Let $KL=200, KM=300, ML=240$ . Notice that all smaller triangles formed are all similar to the larger $(200,240,300)$ triangl... | To solve for the side length of the convex equilateral hexagon \(ABCDEF\) given that the triangle formed by extending its opposite sides has side lengths 200, 240, and 300, we can use properties of similar triangles and the geometry of the hexagon.
First, recall that in a convex equilateral hexagon with all pairs of o... |
[
{
"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 | 328 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | </html>
To solve this problem, we need to find two perpendicular line segments AB and CD on a coordinate plane, each with integer coordinates, lengths at least K, and within given bounds X and Y. The key challenge is ensuring the segments are perpendicular and meet the length constraints.
### Approach
1. **Understandi... |
[
{
"content": "Problem: You are playing a game. A $2 \\times 1$ rectangle covers two adjacent squares (oriented either horizontally or vertically) of a $3 \\times 3$ grid of squares, but you are not told which two squares are covered. Your goal is to find at least one square that is covered by the rectangle. A \... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 35 | AMC23 | {
"expected_answer": "4",
"problem_id": "45",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of turns required to ensure that at least one of the guessed squares is covered by a hidden \(2 \times 1\) rectangle on a \(3 \times 3\) grid. The rectangle can be either horizontal or vertical, and we are to find a strategy that guarantees success in the f... |
[
{
"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 is the acceleration of gravity on the moon's surface, g_m (as compared to the acceleration of gravity on the earth surface,g_e) if the diame... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 308 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem step by step. First, part (a) asks for the acceleration due to gravity on the moon's surface (g_m) compared to Earth's (g_e). The problem gives that the moon's diameter is one-quarter of Earth's, so the radius is also one-quarter. And the moon's density is two-thirds of Earth'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": 0,
"temperature": 0.7
} | 0 | 237 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Narek and ChatGPT are scoring points based on some strings. Let me read through the problem again to make sure I understand everything.
So, the problem states that Narek is creating problems using some strings, and ChatGPT creates n problems each of length m. Then, Nare... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Very large number of neutrinos produced by the Sun reach the Earth (very large flux of neutrinos, defined as the number of neutrinos per cm^2, per second).\n\nLet us ass... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 180 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure this out. The problem is about the flux of neutrinos from the Sun, specifically looking at two energy bands: 700-800 keV (band 1) and 800-900 keV (band 2). The key here is that the pp-III branch in the Sun's core is hypothetical stopped, but other reactions remain. Also, neutrino flavo... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Which of the following is the correct characteristic of arteries?\nOptions: A. They carry blood towards the heart., B. They always carry deoxygenated... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 252 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to figure out which option correctly describes arteries. Let me start by recalling what I know about the circulatory system.
Arteries are blood vessels that carry blood away from the heart, right? So that would mean option C is correct. Let me check the other options to make sure there's nothing ... |
[
{
"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": 4,
"temperature": 0.7
} | 4 | 22 | AMC23 | {
"expected_answer": "7",
"problem_id": "25",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine how much juice Mrs. Jones must pour from each of the first three glasses into the fourth glass so that all four glasses have the same amount of juice. Let's break down the problem step by step.
1. **Define Variables:**
- Let the total capacity of each glass be \(1\) unit.... |
[
{
"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 | 152 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's see. The problem is about Alyona assembling a square jigsaw puzzle over several days. Each day, she adds a certain number of pieces around the central piece, completing layers. She's happy if at the end of the day there are no unfinished layers, meaning the puzzle forms a complete square. The task is to fin... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N types of beans, one bean of each type. The i-th type of bean has a deliciousness of A_i and a color of C_i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 416 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about choosing a color of beans to eat such that the minimum deliciousness of the beans of that color is maximized. Hmm. So, the key here is to group the beans by their color and then for each color, find the minimum deliciousness among the beans in that group. Then, we need to 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 | 195 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have a binary array and I have to find the sum of the medians of all possible subsequences of length k, which is odd. And then output the sum modulo 1e9+7. Hmm.
First, let's understand the problem. The median of an odd-length array is the middle element when sorted. So for a ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: \"1,2-Rearrangement reaction in which vicinal diols are allowed to react with acid is called Pinacol Pinacolone rearrangement reaction. This reaction proceeds through th... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 33 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to figure out the correct products of the Pinacol rearrangement for the given starting compounds. Let me start by recalling how the Pinacol Pinacolone rearrangement works. So, vicinal diols (diols that are adjacent) when treated with an acid like H+ undergo a rearrangement. The reaction involves th... |
[
{
"content": "Problem: When the roots of the polynomial \n\\[P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \\cdot \\cdot \\cdot (x-10)^{10}\\]\nare removed from the number line, what remains is the union of $11$ disjoint open intervals. On how many of these intervals is $P(x)$ positive?\nMark your solution with \\boxed\nAnsw... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 36 | AMC23 | {
"expected_answer": "6",
"problem_id": "46",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine on how many of the 11 disjoint open intervals resulting from removing the roots of the polynomial \( P(x) \) the polynomial \( P(x) \) remains positive.
First, let's analyze the polynomial \( P(x) \). The polynomial is given by:
\[
P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \cdots (x-1... |
[
{
"content": "Problem: What is the smallest positive integer $n$ such that all the roots of $z^4 + z^2 + 1 = 0$ are $n^{\\text{th}}$ roots of unity?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 46 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for the smallest positive integer \( n \) such that all the roots of the polynomial \( z^4 + z^2 + 1 = 0 \) are \( n \)-th roots of unity, we start by finding the roots of the given polynomial.
First, let's solve the equation \( z^4 + z^2 + 1 = 0 \). We can make a substitution to simplify this equation. Let \... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $\\beta$ be a real number. Consider the matrix\n\\[\nA=\\left(\\begin{array}{ccc}\n\\beta & 0 & 1 \\\\\n2 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 417 | JEEBench | {
"expected_answer": "3",
"problem_id": "6",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, let's see. I need to find the value of 9β given that the matrix A raised to certain powers, minus some terms, is a singular matrix. Hmm. So first, what does it mean for a matrix to be singular? Oh right, a matrix is singular if its determinant is zero. So the problem is saying that the determinant of A^7 ... |
[
{
"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 | 390 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Okay, I need to solve this XORificator problem. Let's read the problem carefully. So, the task is to compute the XOR of all integers x in the range [l, r] that do not satisfy x ≡ k mod 2^i. Hmm. So first, I need to understand when a number x is considered interesting. The problem states that x is interesting if x ≢ k m... |
[
{
"content": "Problem: How many digits are in the base-ten representation of $8^5 \\cdot 5^{10} \\cdot 15^5$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
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"seed": 7,
"temperature": 0.7
} | 7 | 17 | AMC23 | {
"expected_answer": "18",
"problem_id": "19",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find out how many digits are in the base-ten representation of \(8^5 \cdot 5^{10} \cdot 15^5\). Hmm, let's think about how to approach this.
First, I remember that the number of digits of a positive integer \(n\) is given by \(d(n) = \lfloor \log_{10} n \rfloor + 1\). So, my plan is to comp... |
[
{
"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.A graph with (k+1) vertices and k edges is called a level-k\\ (k\\geq 2) star if and only if:\n\n- it has a vertex tha... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 206 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to figure out how to determine the number and levels of the initial stars given a tree T. The problem says that the tree is formed by starting with stars and then adding edges between two disconnected vertices with degree 1 each time. So, the initial stars are level-k stars, which have a... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The study of quantum mechanics deals with a lot of matrices. Consider the following matrices. \n\nW = (0, 0, 1; 0, 1, 0; 1, 0, 0), \nX = (i, -1, 2i; 1, 0, 1; 2i, -1, -i... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 178 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to figure out which statement is correct about these matrices W, X, Y, Z in the context of quantum mechanics. Let's start by recalling what we know about quantum mechanics and matrices.
In quantum mechanics, observables are Hermitian matrices. So, checking if any of these matrices are ... |
[
{
"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 | 424 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | </html>
To solve this problem, we need to construct an array of unique integers from 1 to 2n such that the absolute difference of the values of any two connected nodes in the tree is not a prime number. If no such array exists, we should report that.
### Approach
The key insight is to assign values to the nodes in suc... |
[
{
"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 | 319 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if it's possible to draw exactly n new edges between two strongly connected directed graphs such that the following conditions are met:
1. The ends of any added edge lie in different graphs.
2. From each outgoing vertex of the first graph, exactly one added edge originates.
3... |
[
{
"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 | 357 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Kinich tries to maximize his score by selecting pairs of indices in an array. The score increments each time he picks two indices i and j where a_i equals a_j, and they haven't been chosen before. Let's think about how to approach this.
First, let's understand the probl... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You identified a new quorum-sensing peptide in the bacteria Lactobacillus acidophilus. You are highly interested if its role in intercellular communication is conserved ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 151 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{C} |
[
{
"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 | 10 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if Alice can trade her card from type 1 to type n by trading with the Queen, King, or Jack of Hearts. Each player has a permutation of card preferences, and Alice can only trade if she values the received card more than the one she is willing to trade. We need to check if Ali... |
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