context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 1 147k |
|---|---|---|---|---|---|---|
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.This problem is an easier version of Problem G.\n\nThere is a slot machine with three reels.\r\nThe arrangement of sym... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 281 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Takahashi can stop the reels at certain times to make all their displayed characters the same. The goal is to find the minimal total time from the start until all reels are stopped. If impossible, output -1.
Hmm. Let's understand the problem first. Each reel ... |
[
{
"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.Team Takahashi and Team Aoki are playing a baseball game, with Team Takahashi batting first.\nCurrently, the game has ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 431 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about calculating the minimum runs Team Aoki needs to score in the bottom of the ninth inning so that their total is strictly greater than Team Takahashi's.
So, the input gives the runs scored by each team in each inning. For Team Takahashi, there are 9 innings (top of 1-9), an... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: What is the concentration of calcium ions in a solution containing 0.02 M stochiometric Ca-EDTA complex (we assume that the pH is ideal, T = 25 °C). KCa-EDTA = 5x10^10.\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 16 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the concentration of calcium ions (Ca²⁺) in a solution containing 0.02 M stochiometric Ca-EDTA complex. The formation constant (K_Ca-EDTA) for this complex is given as 5 × 10¹⁰. The reaction between calcium ions and EDTA can be represented as:
\[ \text{Ca}^{2+} + \text{EDTA}... |
[
{
"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 | 190 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about finding the maximum possible product of the minimums of two arrays after possibly rearranging one of them. And there are updates which adjust the elements of either array a or b, and after each update, we need to output the maximum possible product modu... |
[
{
"content": "Problem: What is $1^{(2^{235423523})}$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 65 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to compute 1 raised to the power of 2^235423523. Hmm. So the base is 1, and the exponent is a really big number. Wait, but maybe there's a pattern here or some mathematical property that can help me simplify this.
Wait, anything raised to the power of 1 is itself. But wait, if t... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: In a photoelectric experiment a parallel beam of monochromatic... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 160 | JEEBench | {
"expected_answer": "24",
"problem_id": "13",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | ### Solution
Okay, let's tackle this problem step by step. The goal is to find the value of \( n \) in the force equation \( F = n \times 10^{-4} \, \text{N} \), where the force is due to the impact of photoelectrons on the anode.
First, let's understand the setup. We have a cathode emitting photoelectrons when hit 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 integer N between 1 and 9, inclusive, as input.\nConcatenate N copies of the digit N and print the re... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 346 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this programming problem. Let's read the question carefully. The task is to generate an executable Python function that takes an integer N from stdin and prints a string formed by concatenating N copies of the digit N. Oh right, the input is given as a single digit between 1 and 9. 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": 1,
"temperature": 0.7
} | 1 | 2 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have to remove two vertices from a tree exactly twice, and find the maximum number of connected components after those removals. Let me think through the approach here.
First, the problem says that each time we remove a vertex and all its edges. So when you remove... |
[
{
"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 | 156 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about a robot moving in a grid with a script that can be modified when it hits the borders. The robot executes the script k times, and we need to find how many times it ends up at (0,0) after each full cycle of the script. The initial position is (0,0), but w... |
[
{
"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: For a polynomial $g(x)$ with real coefficients, let $m_{g}$ de... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 275 | JEEBench | {
"expected_answer": "3",
"problem_id": "53",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let's tackle this problem. Hmm. The problem is asking for the minimum possible value of the sum of the number of distinct real roots of the first and second derivatives of a polynomial f, where f is in the set S. The set S consists of polynomials of the form (x²-1)^² multiplied by a cubic polynomial a₀ + ... |
[
{
"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 block with mass $M$ is connected by a massless spring with stiffness... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 48 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the motion of a block connected to a spring after a particle of smaller mass is placed on it. The block oscillates about an equilibrium position with small amplitude, and we need to consider two specific cases before placing the particle. The key is to determine how the additio... |
[
{
"content": "Problem: Let \\(O=(0,0)\\), \\(A=\\left(\\tfrac{1}{2},0\\right)\\), and \\(B=\\left(0,\\tfrac{\\sqrt{3}}{2}\\right)\\) be points in the coordinate plane. Let \\(\\mathcal{F}\\) be the family of segments \\(\\overline{PQ}\\) of unit length lying in the first quadrant with \\(P\\) on the \\(x\\)-axi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 11 | AIME24 | {
"expected_answer": "23",
"problem_id": "aime24-11",
"reference_solution": "Begin by finding the equation of the line $\\overline{AB}$ : $y= -\\sqrt{3}x+\\frac{\\sqrt{3}}{2}$ Now, consider the general equation of all lines that belong to $\\mathcal{F}$ . Let $P$ be located at $(a,0)$ and $Q$ be located... | To solve the problem, we need to determine the unique point \( C \) on the segment \( \overline{AB} \) that is not covered by any unit-length segment from the family \( \mathcal{F} \). The family \( \mathcal{F} \) consists of segments \( \overline{PQ} \) where \( P \) is on the \( x \)-axis, \( Q \) is on the \( y \)-a... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 350 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I've got this problem to solve where I need to turn a graph into a cool graph by performing certain operations. The cool graph is either empty or a tree. The operation allows me to choose three distinct vertices a, b, c, and for each of the edges (a,b), (b,c), (c,a), add them if they don't exist or rem... |
[
{
"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 | 346 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where given a sequence of numbers and operators (which can be + or * inserted between them), I have to determine if it's possible to reach a target m. The operators are applied in the usual order, so multiplication first. The challenge is to figure out all possible ways to ins... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and the j-th column... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 367 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this programming problem. Let's read the problem statement carefully.
The problem is about a grid with H rows and W columns. Each cell can be 'o', 'x', or '.' (initially empty). We can change '.' to 'o' any number of times. The goal is to have at least one consecutive sequence ... |
[
{
"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 colour of the $\\mathrm{X}_{2}$ molecules of group 17 elements cha... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 77 | JEEBench | {
"expected_answer": "CD",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Okay, let's see. The problem is about the color change in the X₂ molecules of group 17 elements (halogens) from yellow to violet as we go down the group. And we have to choose the correct reason from the options given.
Hmm. So, the color of a molecule is related to the energy gap between the highest occupied molecular... |
[
{
"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: Gene flow between populations results in\nOptions: A. disruption of Hardy-Weinberg equilibrium in the metapopulation, B. an increased likelihood of s... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | A. |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 126 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the minimum possible length of a string that contains both a and b as a substring and a subsequence, respectively. Hmm. Let me think through the problem step by step.
First, the problem says the string must have a as a substring and b as a subsequence. 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 | 37 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about transforming array a into array b using three types of operations: increase, decrease, or copy an element and append. We need to find the minimum number of operations required.
First, let's understand the operations. Increasing or decreasing elements 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 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": 2,
"temperature": 0.7
} | 2 | 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 an integer B as input and checks if there's a positive integer A such that A^A equals B. If there is, output A; otherwise, output -1. Hmm.
First, the problem is to find A where A^A = B. So for example, in the sample input 27, 3^3 is 27, so A is 3. B... |
[
{
"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: From laboratory measurements we know that a particular spectral line formed by hydrogen appears at a wavelength of 486.1 nanometers (nm). The spectru... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 335 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{I}
Explanation: The problem is about determining the motion of a star based on the shift of a spectral line. The key concept here is the Doppler effect as applied to light.
When a star moves away from us, the light we receive is shifted towards the red end of the spectrum (longer wavelengths), whereas if it mo... |
[
{
"content": "Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | <think>
Okay, let's tackle this problem. Hmm, the problem gives us three equations involving logs and variables x, y, z. My goal is to find the value of the absolute value of log2(x^4 y^3 z^2) expressed as m/n, then add m and n.
First, I need to parse the given equations. Let's write them down again:
1. log2(x/(y z)... |
[
{
"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 plot of the number of neutrons $(N)$ against the number of protons $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 17 | JEEBench | {
"expected_answer": "BD",
"problem_id": "25",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Okay, let's tackle this problem step by step. Hmm, the question is about the possible modes of decay for unstable nuclei with a ratio of neutrons to protons less than 1. So first, I need to understand what each option does and when it happens.
The problem mentions that for atomic numbers Z>20, the plot of neutrons vs ... |
[
{
"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 | 82 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the k-th smallest XOR value over all possible subarrays of length at least 2. Hmm. Let's think about how to approach this.
First, the problem says that for every possible subarray of length 2 or more, compute the minimum XOR between any two elements in 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 | 220 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is about a game between Turtle and Piggy on a sequence. The goal is to find the final value of a_1 after all possible moves, considering both players play optimally. Turtle goes first, wanting to maximize a_1, and Piggy wants to minimize it.
Hmm. The game proceeds by each player... |
[
{
"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 cyanide process of gold extraction involves leaching out gold from... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Okay, let's tackle this problem step by step. The problem is about the cyanide process for gold extraction. We need to figure out which options are correct based on the chemical reactions involved in this process.
First, let's summarize the process as described. The gold ore is leached with CN⁻ ions in the presence of... |
[
{
"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 even length n.\nYou must remove n / 2 elements from nums1 and n / 2 elements from nums2. After th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 150 | 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 remove n/2 elements from each of the two arrays and then find the maximum possible size of the set formed by the remaining elements. Hmm. So the goal is to maximize the number of unique elements in the combined set after the removals.
Wait, right. 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": 1,
"temperature": 0.7
} | 1 | 232 | CodeElo | {
"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 compute the sum of f(a[l..r]) for all possible subarrays of a given array. The function f(b) is the minimum number of operations needed to make the array b a palindrome using two specific operations. Hmm.
First, I need to understand what the functi... |
[
{
"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": 7,
"temperature": 0.7
} | 7 | 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 $\\overline{OI}\\perp\\overline{AM}$ ... | Let's start by analyzing the given problem. We have a triangle \( \triangle ABC \) with circumradius \( R = 13 \) and inradius \( r = 6 \). The circumcenter is \( O \) and the incenter is \( I \). The condition given is \( \overline{IA} \perp \overline{OI} \). We need to find the product \( AB \cdot AC \).
First, let'... |
[
{
"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 threshold.\nFind the length of the longest subarray of nums starting at index l and ending at index... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 52 | 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 longest subarray starting with an even number, followed by elements alternating in parity, and all elements <= the threshold. Hmm, let's think about how to approach this.
First, the subarray must start with an even number. So for each position l in th... |
[
{
"content": "Problem: Find the sum of all complex solutions of the equation\n\\[\\frac{1}{x^2 - 1} + \\frac{2}{x^2 - 2} + \\frac{3}{x^2 - 3} + \\frac{4}{x^2 - 4} = 2010x - 4.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 478 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the equation \(\frac{1}{x^2 - 1} + \frac{2}{x^2 - 2} + \frac{3}{x^2 - 3} + \frac{4}{x^2 - 4} = 2010x - 4\), we need to find all complex solutions and sum them.
First, let's consider the domain of the equation. The denominators \(x^2 - 1\), \(x^2 - 2\), \(x^2 -3\), and \(x^2 -4\) must not be zero. Therefore, \... |
[
{
"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 | 147 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to understand this problem. So, the task is to find all pairs (a, b) for a given n where K1o0n's incorrect method gives the same result as the correct one. Hmm.
The correct answer is n*a - b. But K1o0n calculated it using his wrong method. So, we need to model what his method does. Let's break... |
[
{
"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 | 229 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this programming problem. Let me read the problem statement carefully.
The problem is about finding the k-th maximum weight in all possible paths between two nodes in a graph. The constraints are pretty tight, especially with up to 3e5 queries per test case. So I need an effici... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: An electron is moving along the horizontal axis from the left with a Lorentz factor of 4. A positron is also moving along the horizontal axis, but from the right with a ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 114 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{D} |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider two electrons are in p orbital angular momentum state. Ignoring there spin angular momentum, the coupled angular momentum state of the 2-electron system is repr... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 66 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the joint probability of measuring the orbital angular momentum components \( L_{1z} \) and \( L_{2z} \) for two electrons in a p orbital state, given the coupled angular momentum state \( |l_1, l_2, l, m> = |1, 1, 2, -1> \).
### Step 1: Understanding the Quantum State
The s... |
[
{
"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": 9,
"temperature": 0.7
} | 9 | 16 | AMC23 | {
"expected_answer": "8",
"problem_id": "18",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem of finding how many positive perfect squares less than 2023 are divisible by 5, we can follow these steps:
1. **Identify the form of the perfect squares divisible by 5**: A perfect square divisible by 5 must be the square of a multiple of 5. Let's denote such a number as \((5k)^2\), where \(k\) is... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 499 | JEEBench | {
"expected_answer": "0.25",
"problem_id": "15",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | ### Solution
We need to find the inradius of triangle \(ABC\) given that it is an obtuse-angled triangle with the largest and smallest angles differing by \(\frac{\pi}{2}\), sides in arithmetic progression, and all vertices lying on a circle of radius 1.
First, let's denote the angles of the triangle as \(A\), \(B\),... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Reaction of $\\mathbf{x} \\mathrm{g}$ of $\\mathrm{Sn}$ with $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 355 | JEEBench | {
"expected_answer": "3.57",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | ### Solution
Let's tackle this problem step by step. The goal is to determine the value of x, which represents the mass of tin (Sn) that reacts with HCl to form a salt. Then, this salt reacts with nitrobenzene to produce an organic salt with a mass of 1.29 g.
First, let's understand the chemical reactions involved. ... |
[
{
"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 | 279 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to tackle this problem. Hmm, the problem statement is a bit complex. Let me read through it again and understand what's needed.
So, we have two strongly connected directed graphs, each with n vertices. Each vertex is either incoming (0) or outgoing (1). We need to add exactly n edges between th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a 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": 1,
"temperature": 0.7
} | 1 | 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 integer N can be expressed as 2^x multiplied by 3^y, where x and y are non-negative integers. Let's think about how to approach this.
First, the problem states that N must be a product of powers of 2 and 3. So, any other prime factors besi... |
[
{
"content": "Problem: Let $ABC$ be a triangle inscribed in circle $\\omega$ . Let the tangents to $\\omega$ at $B$ and $C$ intersect at point $D$ , and let $\\overline{AD}$ intersect $\\omega$ at $P$ . If $AB=5$ , $BC=9$ , and $AC=10$ , $AP$ can be written as the form $\\frac{m}{n}$ , wher... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 24 | AIME24 | {
"expected_answer": "113",
"problem_id": "aime24-24",
"reference_solution": "From the tangency condition we have $\\let\\angle BCD = \\let\\angle CBD = \\let\\angle A$ . With LoC we have $\\cos(A) = \\frac{25+100-81}{2*5*10} = \\frac{11}{25}$ and $\\cos(B) = \\frac{81+25-100}{2*9*5} = \\frac{1}{15}$ . Then, ... | <think>
Okay, let's tackle this problem. So, we have a triangle ABC inscribed in a circle ω. The tangents at B and C meet at point D. Then AD intersects ω again at P. We need to find AP in the form m/n, where m and n are coprime, and then get m + n.
Hmm. Let's start by recalling some geometry theorems. Oh right, the p... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a permutation P = (P_1, P_2, \\dots, P_N) of (1, 2, \\dots, N).\nA length-K sequence of indices (i_1, i_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 441 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum i_K - i_1 for a good index sequence of length K in a permutation P. The good sequence is one where the elements form a consecutive integers subset when rearranged. So, for each possible sequence of K elements in the permutation, ordered, I need to check if they form a... |
[
{
"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: $5.00 \\mathrm{~mL}$ of $0.10 \\mathrm{M}$ oxalic acid solutio... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 255 | JEEBench | {
"expected_answer": "0.11",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To determine the concentration of the NaOH solution, we need to analyze the titration data provided. The key is to find the average volume of NaOH used and then use the stoichiometry of the reaction between oxalic acid (H2C2O4) and NaOH to calculate the concentration.
### Step 1: Understand the Reaction
The reaction b... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A word is considered valid if:\n\nIt contains a minimum of 3 characters.\nIt contains only digits (0-9), and English letters (uppercase and lowercase).\nIt inc... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 492 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to generate a Python function that checks if a given word is valid based on certain criteria. Let's see the problem statement again.
The conditions are:
1. The word must have at least 3 characters.
2. It can only contain digits and English letters (uppercase or lowercase).
3. It must have at leas... |
[
{
"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: List-I shows different radioactive decay processes and List-II provides p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 474 | JEEBench | {
"expected_answer": "A",
"problem_id": "31",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | Okay, let's tackle this problem. So, we need to match each radioactive decay process in List-I with the correct emitted particles from List-II. Hmm. Let's remember that in radioactive decay, the mass number changes, and so does the atomic number. So, for each decay, we need to see how the parent nucleus transforms into... |
[
{
"content": "Problem: A rectangular field is enclosed in an athletic track, as shown below. The track consists of two edges of the field, and two semicircles. The length of the track is 400 meters. What is the largest possible area of the field, in square meters?\n\n[asy]\nunitsize(1 cm);\n\nfilldraw((0,0)-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 382 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. So, the problem is about finding the maximum possible area of a rectangular field enclosed by an athletic track. The track has two edges of the rectangle and two semicircles. The total length around the track is 400 meters. We need to maximize the area of the rectangle.
Hmm. Let's star... |
[
{
"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 | 198 | CodeElo | {
"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 check if a string matches a numeric template. The conditions are a bit tricky. Let me break down the problem.
So, the template is an array of numbers. Each test case has this array and a bunch of strings to check. A string matches if:
1. Its length... |
[
{
"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: How many $3 \\times 3$ matrices $M$ with entries from $\\{0,1,2\\}$ are t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 112 | JEEBench | {
"expected_answer": "B",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | Okay, I need to solve this problem where I have to find the number of 3x3 matrices M with entries from {0,1,2} such that the sum of the diagonal entries of M^T M is 5. Let's break this down step by step.
First, let's understand what M^T M is. The matrix product M^T M is a 3x3 matrix where each entry (i,j) is the dot p... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed string s that consists of digits from 0 to 9.\nA string t is called a semi-repetitive if there is at most one consecutive pair of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 20 | 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 longest semi-repetitive substring in a given string. Let's see, the definition says a semi-repetitive string has at most one consecutive pair of the same digits. So the task is to look for the longest substring where there's either no consecutive dupli... |
[
{
"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 | 118 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is to construct the lexicographically largest array such that for any i < j, a_gcd(i,j) is not equal to gcd(a_i, a_j). If that's not possible, output -1.
Hmm. The key condition here is that a_gcd(i,j) must differ from gcd(a_i, a_j). Let's think about what this implies.
First, t... |
[
{
"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 items.\r\nEach of these is one of a pull-tab can, a regular can, or a can opener.\r\nThe i-th item is desc... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 254 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is about selecting M items out of N, which include pull-tab cans, regular cans, and openers. The goal is to maximize the total happiness. Hmm. Let's think about how to model this.
First, let's understand the items. For a pull-tab can (T=0), adding it to our collection gives X_i ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We dilute 20.00 cm3 0.05 M acetic acid with 20.00 cm3 water, then titrate the resulting solution with 0.1M NaOH (25 °C). What will be the value of pH at 25% titration an... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 82 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem step by step. So, the problem is about titrating acetic acid with NaOH, and we need to find the pH at 25% titration and at the equivalence point. Hmm.
First, let's understand the setup. We have 20.00 cm³ of 0.05 M acetic acid (CH₃COOH) and add 20.00 cm³ of water. Then we titrate... |
[
{
"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 | 302 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about arranging stamps (rectangles) on a grid to form a connected region with the minimum possible perimeter. Hmm. So each stamp is placed exactly once, and they can be positioned anywhere. But the key is that when you place a stamp, it's a solid rectangle. The goal is to have al... |
[
{
"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 | 63 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about dividing a grid between Alice and Bob based on their paths. The key is to find the maximum area Alice can get, considering the fountains that Bob can give away, and then compute the impact of each fountain on Alice's area.
First, let's understand the s... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 12 | AIME24 | {
"expected_answer": "321",
"problem_id": "aime24-12",
"reference_solution": "\\[\\prod_{k=0}^{12} \\left(2- 2\\omega^k + \\omega^{2k}\\right) = \\prod_{k=0}^{12} \\left((1 - \\omega^k)^2 + 1\\right) = \\prod_{k=0}^{12} \\left((1 + i) - \\omega^k)((1 - i) - \\omega^k\\right)\\] Now, we consider the polynomial $x... | <think>
Okay, let's tackle this problem. So, we need to find the remainder when the product \(\prod_{k=0}^{12}(2 - 2\omega^k + \omega^{2k})\) is divided by 1000. Here, \(\omega\) is a 13th root of unity, which means \(\omega^{13} = 1\) and \(\omega \neq 1\).
First, let's understand what the terms in the product look ... |
[
{
"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 | 246 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to understand this problem. So the task is to compute for every substring of length exactly k in the given string s, the minimal possible length after performing some compression operations. The compression process involves splitting the string into even-numbered substrings and then writing 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 | 178 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's see. The problem is to find the minimum number of operations required to change all characters in a string to '0's. Each operation involves selecting a non-empty subsequence where adjacent characters are different, then flipping all of them. Hmm.
The example given in the editorial says that the answer is e... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: S)-4-hydroxycyclohex-2-en-1-one is treated with tert-Butyldimethylsilyl chloride and triethylamine, forming product 1.\n\n1 is treated with Ph2CuLi at low temperature, f... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 27 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's work through this problem step by step to determine the structure of product 4.
**Step 1: Treatment of S)-4-hydroxycyclohex-2-en-1-one with tert-Butyldimethylsilyl chloride and triethylamine to form product 1.**
The starting material is (S)-4-hydroxycyclohex-2-en-1-one. When treated with a chlorosilane like ter... |
[
{
"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 | 208 | CodeElo | {
"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 count the number of deterministic max-heaps generated by adding exactly k ones to the nodes along the paths from the root to some nodes. The answer has to be modulo p. Hmm.
First, I need to understand what a deterministic max-heap is. From the descr... |
[
{
"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\\left(\\left(\\log _{2} 9\\right)^... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 142 | JEEBench | {
"expected_answer": "8",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | ### Solution
Let's evaluate the given expression step by step. The expression is:
\[
\left(\left(\log _{2} 9\right)^{2}\right)^{\frac{1}{\log _{2}\left(\log _{2} 9\right)}} \times (\sqrt{7})^{\frac{1}{\log _{4} 7}}
\]
We need to compute each part separately and then multiply the results.
#### First Part: \(\left(\lo... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Astronomers are observing a planet with a radius of 1 Earth radius in a circular orbit, with a transit impact parameter of 0.2, around a star that has a radius 1.5 times... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 194 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's think about this problem step by step. The key here is to determine the maximum orbital period of a second planet that can both transit and occult the star. Both events require the second planet to be in the same orbital plane as the first, which is already given. So the main constraints are the orbital periods t... |
[
{
"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 parallel universe where a magnet can have an isolated North or South pole, Maxwell’s equations look different. But, specifically, which of those equations are diffe... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 3 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | A |
[
{
"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 reaction of $\\mathrm{K}_3\\left[\\mathrm{Fe}(\\mathrm{CN})_6\\right]... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 360 | JEEBench | {
"expected_answer": "C",
"problem_id": "33",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | Okay, let's tackle this problem step by step. The goal is to determine which complex salt (option A-D) is formed as the white precipitate X when K4[Fe(CN)6] is reacted with FeSO4 solution in the absence of air. Then, we need to see how X behaves when exposed to air and how the other reactions relate.
First, let's unde... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two strings s and t of equal length n. You can perform the following operation on the string s:\n\nRemove a suffix of s of length l where 0 < l <... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 92 | 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 ways to transform string s into t in exactly k operations, each of which involves removing a suffix and moving it to the front. The answer has to be modulo 1e9+7. Let's think through this step by step.
First, let me understand the operations... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two arrays of equal length, nums1 and nums2.\nEach element in nums1 has been increased (or decreased in the case of negative) by an integer, repr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 489 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the integer x that when added to each element of nums1 makes it equal to nums2. Hmm. So the problem says that after adding x to every element in nums1, the two arrays become the same. So the key here is to find x such that for all elements i, nums1[i] + x = nums2[i].
Wait, righ... |
[
{
"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 | 136 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find two integers A and B within a range [l, r] such that their GCD is exactly G and the distance |A - B| is maximized. If there are multiple pairs, choose the one with the smallest A. If no pair exists, output -1 -1.
Let me start by understanding the problem ... |
[
{
"content": "Problem: The lengths of two opposite sides of a square are decreased by $40\\%$ while the lengths of the other two sides are increased by $50\\%$ to form a rectangle. By what percent does the square's area decrease?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 67 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's start by considering the original square. Let's denote the side length of the square as \( s \). The area of the square is \( s^2 \).
Now, according to the problem, two opposite sides are decreased by 40%, and the other two are increased by 50%.
First, calculate the new lengths of the sides. For the two opposi... |
[
{
"content": "Problem: Let $a,$ $b,$ $c,$ $d$ be distinct complex numbers such that $|a| = |b| = |c| = |d| = 1$ and $a + b + c + d = 0.$ Find the maximum value of\n\\[|(a + b)(a + c)(a + d)(b + c)(b + d)(c + d)|.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 204 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to find the maximum value of the product \((a + b)(a + c)(a + d)(b + c)(b + d)(c + d)\) given that \(a, b, c, d\) are distinct complex numbers with \(|a| = |b| = |c| = |d| = 1\) and \(a + b + c + d = 0\).
### Approach
1. **Unit Circle Constraint**: Since each complex number has a magnitud... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.N people labeled 1,2,\\dots,N took an exam, and person i scored A_i points.\r\nOnly those who scored at least L points... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 332 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this programming problem. Let's read the problem carefully.
The task is to determine how many people passed the exam. The rules are that anyone who scored at least L points passes. So, given the input, I have to count how many of the A_i values are >= L.
Hmm, right. So the input is N (nu... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums and a positive integer k.\nYou can apply the following operation on the array any number of times:\n\nChoose any e... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 165 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to find the minimum number of bit flips to make the XOR of all elements equal to k. Let's think about this problem step by step.
First, the XOR of all elements in the array should be k after some flips. Each flip operation can change a single bit in any element. So, the goal is to determine which ... |
[
{
"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 permutation A=(A_1,\\ldots,A_N) of (1,2,\\ldots,N).\r\nTransform A into (1,2,\\ldots,N) by performing the following operation between 0 and N-1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 429 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to generate a sequence of swaps that transforms a given permutation into the identity permutation (1, 2, ..., N). The output should be the number of operations K followed by K pairs of indices. Each swap must be between two distinct elements, and each swap is recorded as the pa... |
[
{
"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 | 399 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to understand this problem. So, we need to count the number of n x m matrices where each entry is between 1 and v (inclusive) that satisfy a certain condition. The condition is a bit complex, so I need to break it down.
The condition given is:
The minimum of the maximums of each row (left side)... |
[
{
"content": "Problem: Let $f$ be the unique function defined on the positive integers such that \\[\\sum_{d\\mid n}d\\cdot f\\left(\\frac{n}{d}\\right)=1\\] for all positive integers $n$. What is $f(2023)$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 12 | AMC23 | {
"expected_answer": "96",
"problem_id": "14",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \( f(2023) \), we need to determine the unique function \( f \) defined on the positive integers such that for all positive integers \( n \),
\[
\sum_{d \mid n} d \cdot f\left( \frac{n}{d} \right) = 1.
\]
### Step 1: Understanding the Functional Equation
The given equation involves a sum over all divisors... |
[
{
"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 | 101 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem says that after performing at most one operation (selecting a row and column and turning all their cells to '#'), we need to find the maximum possible size of the largest connected component of '#'s.
So, the first thing I need to do is understand what the opera... |
[
{
"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 nums and andValues of length n and m respectively.\nThe value of an array is equal to the last element of that array.\nYou have to div... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 478 | 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 split the array 'nums' into 'm' contiguous subarrays. Each subarray's AND value must match the corresponding 'andValues' array. And I need to find the minimum possible sum of the values of these subarrays. If it's not possible, return -1.
Hmm. Let 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 | 225 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to find the maximum possible sum of MEX values for all rows and columns in an n x m grid. Each cell is filled with a unique number from 0 to n*m-1. We need to maximize the sum of the MEX of each row and each column.
Hmm, MEX stands for Minimum Excluded Value. So for a row, the M... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Calculate the enthalpy of neutralization when 500 mL 0.2 M HCl, 300 mL 0.3 M H2SO4 and 200 mL 0.5 M Ba(OH)2 are mixed.\nOptions: A) -16.0 kJ, B) -3.80 kcal, C) -11.42 kc... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 133 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B
</pre>
to user provided prompt: [Problem](https://www.reddit.com/r/AskScience/comments/1234567/calculate_the_enthalpy_of_neutralization_when_500/): Calculate the enthalpy of neutralization when 500 mL 0.2 M HCl, 300 mL 0.3 M H2SO4 and 200 mL 0.5 M Ba(OH)2 are mixed.
[Answer](https://www.reddit.com/r/AskScience/comm... |
[
{
"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 | 157 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Robin's brother and mother are visiting, and I have to choose their start days such that the brother's visit overlaps as many jobs as possible, the mother's as few as possible. And if there are multiple options, pick the earliest day for each.
Hmm, let's think about how... |
[
{
"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 | 68 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is about this polyathlon competition where participants are eliminated based on the sports they're skilled in. The order of sports is determined by a cyclic permutation starting from x, then x mod m+1, etc. For each sport x (from 1 to m), we need to determine the winner if the co... |
[
{
"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 | 127 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. Hmm. So the problem is about two movies and n people who watched them. Each person can leave a review for one of the movies. The review's impact depends on their attitude. We need to maximize the minimum rating between the two movies after assigning all people to either movie A or B.
L... |
[
{
"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: Three numbers are chosen at random, one after another with rep... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 328 | JEEBench | {
"expected_answer": "76.25",
"problem_id": "41",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the probabilities \( p_1 \) and \( p_2 \) for two specific events when selecting three numbers with replacement from the set \( S = \{1, 2, \ldots, 100\} \). Then, we will compute the value of \( \frac{625}{4} p_1 \).
### Step 1: Calculate \( p_1 \)
The event \( p_1 \) is 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: According to the Arrhenius equation,\n(A) a high activation energy usu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 16 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "24",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Okay, let's tackle this problem step by step. The question is about the Arrhenius equation, which relates the rate constant of a reaction to temperature and activation energy. The options provided are A to D, and we need to identify which ones are correct based on the Arrhenius equation.
First, let's recall the Arrhen... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed string array words having length n and containing 0-indexed strings.\nYou are allowed to perform the following operation any number o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem where I need to find the maximum number of palindromes in a list of strings after performing any number of swaps between characters. Hmm, let's try to think through this.
First, the key is that we can swap any characters between any positions. So the essence is that we can rearrang... |
[
{
"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: An $\\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 317 | JEEBench | {
"expected_answer": "4",
"problem_id": "17",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | $\textbf{Problem Statement:}$
An $\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential $V$ and then enter a region with a uniform magnetic field perpendicular to their velocities. Determine the ratio of their radii of curvature in th... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The |3,0,0\\rangle state in the standard notation |n,l,m\\rangle of the H -atom in the non-relativistic theory decays to the state |1,0,0\\rangle via two dipole transiti... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 55 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B
|
[
{
"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 concept of bureaucracy has come to have very negative connotationstoday. Discuss those factors you believe are responsiblefor this negative attit... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 168 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{C}
Weber's bureaucratic approach, as outlined in his theory, emphasizes a structured, hierarchical organization with clearly defined roles, rules, and procedures. While this structure can lead to efficiency and predictability, it also has several flaws that contribute to the negative attitudes towards bureaucr... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.An element x of an integer array arr of length m is dominant if freq(x) * 2 > m, where freq(x) is the number of occurrences of x in arr. Note that this definit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 69 | 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 minimum split index in an array such that both resulting subarrays have the same dominant element. The dominant element is the one that occurs more than half the length of the subarray. And the original array has exactly one dominant element... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Astronomers are searching for exoplanets around two stars with exactly the same masses. Using the RV method, they detected one planet around each star, both with masses ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 103 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let’s think about this problem step by step. The key here is to use the radial velocity method and understand the relationship between the orbital periods of the planets and their host stars.
First, the radial velocity method works by measuring the periodic Doppler shift of the star's spectrum. This shift is caused by... |
[
{
"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, where each number in the array appears either once or twice.\nReturn the bitwise XOR of all the numbers that appear twice in the a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 509 | 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 an array of numbers, each appearing once or twice. The task is to compute the XOR of all numbers that appear exactly twice. If none appear twice, return 0.
Hmm. So first, I need to track how many times each number occurs. Then, for those that occur ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a binary string s, partition the string into one or more substrings such that each substring is beautiful.\nA string is beautiful if:\n\nIt doesn't conta... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 65 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to partition a binary string into the minimum number of beautiful substrings. Let's see what that means.
So, a beautiful substring must not have leading zeros and must be a power of 5. Wait, right, because a power of 5 in binary ends with a 1, except for 5^0 whi... |
[
{
"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.We define Extended A strings, Extended B strings, Extended C strings, and Extended ABC strings as follows:\n\n- A stri... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 365 | 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 string S is an Extended ABC string. Let's see the definitions again.
An Extended ABC string is a concatenation of three parts: S_A (Extended A), S_B (Extended B), S_C (Extended C). So the entire string must be S_A followed by S_B followed ... |
[
{
"content": "Problem: How many digits are in the base-ten representation of $8^5 \\cdot 5^{10} \\cdot 15^5$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 17 | AMC23 | {
"expected_answer": "18",
"problem_id": "19",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the number of digits in the base-ten representation of \(8^5 \cdot 5^{10} \cdot 15^5\), we can use the property that the number of digits of a number \(N\) is given by \(\lfloor \log_{10} N \rfloor + 1\). Therefore, we need to compute \(\log_{10} (8^5 \cdot 5^{10} \cdot 15^5)\) and then take the floor of 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: What are the results of fertilization?\nOptions: A. Creation of multiple cells, apoptosis, gene silencing, and evolutionary adaptation, B. Fusion of ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 145 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{E} |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 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 $1$... | <think>
Okay, let's tackle this problem. Hmm. So, we have 25 white and 25 black chips. We need to place some of them on a 5x5 grid such that each cell has at most one chip. Also, in each row, all the chips must be the same color, and similarly for each column. And we need to count all possible valid configurations.
Wa... |
[
{
"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 the function $f:[0,1] \\rightarrow \\mathbb{R}$ be defined... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 309 | JEEBench | {
"expected_answer": "19",
"problem_id": "52",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | ### Solution
Okay, let's tackle this problem step by step. The problem is to compute the sum of the function \( f \left( \frac{k}{40} \right) \) for \( k \) from 1 to 39, and then subtract \( f \left( \frac{1}{2} \right) \). The function \( f \) is given by \( f(x) = \frac{4^x}{4^x + 2} \).
First, I need to find a pat... |
[
{
"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\n\\[\\mathrm{M}=\\left\\{(\\mathrm{x}, \\mathrm{y}) \\in \\mathbb{R} ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 373 | JEEBench | {
"expected_answer": "D",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the number of circles \( C_n \) that lie entirely within the given circle \( M \) and then find the maximum number of these circles that do not intersect. Let's proceed step by step.
First, let's understand the problem setup. The region \( M \) is a circle centered at the or... |
[
{
"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 | 437 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem says that Alice starts at vertex 1, and Bob starts at some vertex p_j on the path from u to v. We need to determine for each j, whether Alice or Bob wins.
First, I need to understand the game rules. The players take turns moving to unvisited neighboring vertice... |
[
{
"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 DDoS-type string is a string of length 4 consisting of uppercase and lowercase English letters satisfying both of th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 195 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to tackle this problem. Hmm, the problem is about calculating the number of strings that can be formed by replacing the '?' in the given string S such that none of them contains a DDoS-type substring. And the DDoS-type substring is defined as a 4-character sequence where the first, second, fourt... |
[
{
"content": "Problem: Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$ , $AC=BD= \\sqrt{80}$ , and $BC=AD= \\sqrt{89}$ . There exists a point $I$ inside the tetrahedron such that the distances from $I$ to each of the faces of the tetrahedron are all equal. This distance can be written in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 28 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-28",
"reference_solution": "Notice that \\(41=4^2+5^2\\), \\(89=5^2+8^2\\), and \\(80=8^2+4^2\\), let \\(A~(0,0,0)\\), \\(B~(4,5,0)\\), \\(C~(0,5,8)\\), and \\(D~(4,0,8)\\). Then the plane \\(BCD\\) has a normal\n\\begin{equation*}\n\\mathbf n:=\\frac14\\overright... | <think>
Okay, let's tackle this problem. So, we have a tetrahedron ABCD with specific edge lengths. We need to find the distance from a point I inside it to all four faces, which is equal. This point I is the incenter of the tetrahedron, right? Because the incenter is equidistant from all faces. So the problem reduces ... |
[
{
"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 of integers nums. Return the length of the longest subarray of nums which is either strictly increasing or strictly decreasing.\n \nExam... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 472 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the length of the longest subarray in nums that is either strictly increasing or strictly decreasing. Hmm. So first, I need to figure out for each element in the array, the maximum length of such a subarray ending at that element. Then the answer would be the maximum of all those... |
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