context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 1 200k |
|---|---|---|---|---|---|---|
[
{
"content": "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: In the chemical reaction between stoichiometric quantities of $\\mathrm{KMnO}_{4}$ and $\\mathrm{KI}$ in weakl... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 286 | JEEBench | {
"expected_answer": "6",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, so I need to figure out how many moles of I2 are released when 4 moles of KMnO4 are consumed in the reaction with KI. Alright, let's start by recalling what the reaction between KMnO4 and KI is. I know that potassium permanganate (KMnO4) reacts with potassium iodide (KI) in a redox reaction. The products ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a weighted undirected graph G with N vertices, numbered 1 to N. Initially, G has no edges.\nYou will per... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 437 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem. Let me start by understanding the requirements again. We have a weighted undirected graph G with N vertices. Initially, there are no edges. We perform M operations where each operation adds edges between all pairs of vertices in a given subset S_i, with e... |
[
{
"content": "Problem: Find the modulo $7$ remainder of the sum $1+3+5+7+9+\\dots+195+197+199.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 366 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the remainder when the sum of all the odd numbers from 1 to 199 is divided by 7. Let me start by understanding the problem step by step.
First, the sequence given is 1, 3, 5, 7, 9, ..., 195, 197, 199. This is an arithmetic sequence where each term increases by 2. To find the sum of thi... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N intervals of real numbers. The i-th (1 \\leq i \\leq N) interval is [l_i, r_i]. Find the number of pai... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 456 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where I have N intervals, and I need to find the number of pairs (i, j) such that the i-th and j-th intervals intersect. Let me start by understanding the problem again.
First, the input is N followed by N pairs of integers l_i and r_i, which define the s... |
[
{
"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.\nYou can perform any number of operations, where each operation involves selecting a subarray of the array and re... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 139 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the maximum length of a non-decreasing array that can be made by replacing any number of subarrays with their sums. The problem is a bit tricky, but let me try to break it down step by step.
First, let me recall what a non-decreasing array is. In a non-decreasing array, each eleme... |
[
{
"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 | 274 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out for each query of targets from l to r whether the Sheriff can prevent Robin Hood from winning. The game is played optimally by both players, so if the Sheriff can force a tie or a win, it's "NO", otherwise "YES".
First, let me understand the problem. There are n targets with poin... |
[
{
"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 | 178 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to insert a lowercase letter into Monocarp's password to make it as strong as possible based on the typing time. The typing time has different rates: 2 seconds for the first character and 1 second for each subsequent character if it's the same as the previous one, or 2 seconds ... |
[
{
"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 | 100 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about "Good Subarray". Let me try to understand the problem first.
We are given an integer array `a` of size `n`. A good array is one that can be obtained by starting with any single integer and repeatedly adding the integer, or the integer ±1, to the end of the array. So,... |
[
{
"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 | 251 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of coins required to defeat a monster with health z using a weapon that has damage d. The cost to increase the damage by 1 is x coins, and the cost to attack is y coins. Also, I can't increase the damage more than k times in a row. Let me try to break this down 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 | 36 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to verify whether a given password is strong based on Monocarp's criteria. Let me start by understanding the problem again. The password must meet four conditions:
1. Consist only of lowercase Latin letters and digits.
2. No digit comes after a letter. So, after each letter, there must be anoth... |
[
{
"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 | 135 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have an array with mostly -1 and 1, but possibly one element that's different (x), and I need to find all possible sums of subarrays. The problem says that each test case can be solved in O(n), but I need to figure out how to do that. Let me start by understanding 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 203 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have n cities in a row, numbered 1 to n. We start by conquering one city at time 1, and then at each subsequent time step up to n, we can choose a city adjacent to the ones already conquered. The goal is to count the number of arrays [a₁, a₂, ..., aₙ] where each a_... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 303 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about making an array vulnerable using the minimum number of deletions. The definition of a vulnerable array is that you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays. The key insight from the editorial is that an array is ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 284 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out this problem. So, we have an array `a` of length `n` and an even integer `k` (2 ≤ k ≤ n). We need to split the array into exactly `k` non-empty subarrays. Then, all the subarrays with even indices (second, fourth, ..., k-th) are concatenated into a single array `b`. After that, 0 ... |
[
{
"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: On a frictionless horizontal plane, a bob of mass $m=0.1 \\mathrm{~kg}$ is attached to a spring with natural l... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 433 | JEEBench | {
"expected_answer": "6",
"problem_id": "25",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | <think>
Okay, so I need to find the integer closest to n, where the time period T of the oscillation is given as nπ seconds. The problem involves a mass attached to a spring with two different spring constants depending on the length, and it's oscillating on a frictionless plane. Let me try to break this down step by s... |
[
{
"content": "Problem: A line is parameterized by\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} 8 \\\\ -1 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ 3 \\end{pmatrix}.\\]The equation of the line can be expressed in the form $y = mx + b.$ Enter the ordered pair $(m,b).$\nMark your solution with... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 206 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the equation of the line given in parametric form and express it in the form y = mx + b. The parametric equations are:
\[
\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \end{pmatrix}
\]
Hmm, parametric equations usually define x ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A solution is prepared by mixing $0.01 \\mathrm{~mol}$ each of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 402 | JEEBench | {
"expected_answer": "10.02",
"problem_id": "39",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the pH of a solution made by mixing equal molar amounts (0.01 mol each) of H2CO3, NaHCO3, Na2CO3, and NaOH in 100 mL of water. The given pKa1 and pKa2 for H2CO3 are 6.37 and 10.32, respectively. Hmm, let's start by understanding the problem step by step.
First, let's list all the compon... |
[
{
"content": "Problem: Let $a,$ $b,$ $c,$ and $d$ be positive real numbers such that $a + b + c + d = 10.$ Find the maximum value of $ab^2 c^3 d^4.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 470 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the maximum value of \( ab^2 c^3 d^4 \) given that \( a + b + c + d = 10 \) and all variables are positive real numbers. Hmm, this looks like an optimization problem with a constraint. I remember that for such problems, methods like Lagrange multipliers can be useful. But since this is 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 | 165 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this bouquet problem where the girl wants to buy a bouquet with the maximum number of petals without spending more than m coins. The flowers have different numbers of petals, and the difference between any two flowers in the bouquet can't exceed one petal. Let me try to figure out how 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: A three input information channel with all three input symbols equally probable, is defined by the channel matrix, \\vert0.50.30.2\\vert \\vert0.20.3... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 154 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the error probability, P_E, for this three-input information channel. The channel matrix is given as:
First input:
0.5 | 0.3 | 0.2
Second input:
0.2 | 0.3 | 0.5
Third input:
0.3 | 0.3 | 0.4
All three input symbols are equally probable, so each input has a probability of 1/3. Th... |
[
{
"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 pricing policies results in establishment of a price to external customers higher than the competitive price for a given indus... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 133 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to figure out which of these pricing policies results in setting a price higher than the competitive price. The options are A through I, as listed. Let me go through each one and try to understand what they are.
First, Competitive pricing (Option A). That sounds like just matching the 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 | 40 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to compute the bitwise XOR of the median of all "good" sequences of length n with elements less than m. The problem is a bit complex, so I need to break it down step by step.
First, let's understand what makes a sequence "good". The definition says that for al... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array of positive integers nums.\nIn one operation, you can swap any two adjacent elements if they have the same number of set bits. ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 175 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out if I can sort the array by swapping adjacent elements that have the same number of set bits. Let me start by understanding the problem again.
First, the operation allowed is swapping two adjacent elements if they have the same number of set bits (which is the number of 1s in thei... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array nums of non-negative integers, and two integers l and r.\nReturn the count of sub-multisets within nums where the sum of elemen... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 105 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where I have to count the number of sub-multisets (which are like multisets but allow repeated elements) of the array `nums` such that the sum of elements in each subset falls within the inclusive range `[l, r]`. The answer should be modulo `10^9 + 7` beca... |
[
{
"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 | 358 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether Alice can win the game given different binary strings. The game is about placing AND or OR operators between the bits such that Alice wants the final expression to be True, and Bob wants it to be False. They take turns inserting these operators, with Alice going first. The ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Consider the following reversible reaction,\n\\[\n\\mathrm{A}(... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 168 | JEEBench | {
"expected_answer": "8500",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the absolute value of ΔG° for the reaction A(g) + B(g) ⇌ AB(g) at 300 K. The problem states that the activation energy of the backward reaction exceeds that of the forward reaction by 2 RT. Also, the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction. ... |
[
{
"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 there is a monopolistically competitive industry with firms enjoying above-normal profits, what will probably happen to costs as other firms enter... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 122 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out what happens to costs in a monopolistically competitive industry when other firms enter, given that the existing firms are already making above-normal profits. Let me start by recalling what monopolistic competition is.
In a monopolistically competitive industry, there are many f... |
[
{
"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.Takahashi has decided to give one gift to Aoki and one gift to Snuke.\r\nThere are N candidates of gifts for Aoki,\r\n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 199 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out if Takahashi can choose a gift for Aoki and one for Snuke such that their values differ by at most D, and also get the maximum possible sum of their values. Let me try to break this down step by step.
First, let's understand the problem. We have N gifts for Aoki with values A_1, A... |
[
{
"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": 4,
"temperature": 0.7
} | 4 | 16 | AMC23 | {
"expected_answer": "8",
"problem_id": "18",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many positive perfect squares less than 2023 are divisible by 5. Let me start by understanding what the question is asking.
First, a perfect square is a number that's the square of an integer. So numbers like 1 (1²), 4 (2²), 9 (3²), etc. The problem wants me to count all such... |
[
{
"content": "Problem: Consider the paths of length $16$ that follow the lines from the lower left corner to the upper right corner on an $8\\times 8$ grid. Find the number of such paths that change direction exactly four times, as in the examples shown below. [asy] size(10cm); usepackage(\"tikz\");label(\"... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 20 | AIME24 | {
"expected_answer": "294",
"problem_id": "aime24-20",
"reference_solution": "We divide the path into eight “ $R$ ” movements and eight “ $U$ ” movements. Five sections of alternative $RURUR$ or $URURU$ are necessary in order to make four “turns.” We use the first case and multiply by $2$ . <br/>\nFor $U$ ,... | <think>
Okay, so I need to find the number of paths of length 16 that go from the lower left corner to the upper right corner on an 8x8 grid, changing direction exactly four times. Hmm, let's start by understanding the problem.
First, an 8x8 grid means that to go from the bottom-left corner (let's call it (0,0)) to th... |
[
{
"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 array nums containing positive integers. We define a function encrypt such that encrypt(x) replaces every digit in x with the largest ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 479 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a function that takes an integer array called nums and returns the sum of the encrypted elements. Each element in the array is encrypted by replacing every digit with the largest digit in that element. Hmm, let me try to break this down step by step.
First, I need to understand how th... |
[
{
"content": "Problem: In the $xy$-plane, a circle of radius $4$ with center on the positive $x$-axis is tangent to the $y$-axis at the origin, and a circle with radius $10$ with center on the positive $y$-axis is tangent to the $x$-axis at the origin. What is the slope of the line passing through the two point... | {
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} | 4 | 23 | AMC23 | {
"expected_answer": "7",
"problem_id": "26",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to solve this problem step by step. So, we have two circles in the xy-plane. The first one has a radius of 4, is centered on the positive x-axis, and is tangent to the y-axis at the origin. The second circle has a radius of 10, is centered on the positive y-axis, and is tangent to the x-axis at ... |
[
{
"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 instantaneous voltages at three terminals marked $X, Y$ and $Z$ ar... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 98 | JEEBench | {
"expected_answer": "AD",
"problem_id": "9",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out the RMS voltage between points X and Y, and then between Y and Z, given their instantaneous voltage equations. Let me start by recalling what the problem is asking.
First, the voltages at each terminal are sinusoidal functions. For terminal X, it's straightforward: V_X = V_0 sin(... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.An array is considered special if every pair of its adjacent elements contains two numbers with different parity.\nYou are given an array of integers nums. Ret... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 501 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out if an array is "special" based on the given definition. The problem says that an array is special if every pair of its adjacent elements has two numbers with different parity. Parity here probably refers to whether the numbers are even or odd. So, basically, each consecutive pair 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... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 96 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the center of a Manhattan circle given a grid with '#' characters representing the circle's points. Let me start by understanding the problem.
First, a Manhattan circle is defined as all points (a, b) that are within a certain radius 'r' from the center (h, k). The Manhattan dista... |
[
{
"content": "Problem: Calculate the maximum area of an isosceles trapezoid that has legs of length $1$ and one base twice as long as the other. The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m^2+n^2$?\nMark your solution with \\box... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 24 | AMC23 | {
"expected_answer": "13",
"problem_id": "27",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the maximum area of an isosceles trapezoid with legs of length 1, where one base is twice as long as the other. The answer should be in the form m/n, with m and n coprime, and then compute m² + n². Alright, let's start by recalling what an isosceles trapezoid is. It's a trapezoid with th... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 343 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how Alice can cut the cake into m+1 pieces such that each of the m creatures gets a piece with at least v tastiness, and Alice maximizes her own piece. If it's impossible, return -1. Let me start by understanding the problem step by step.
First, the cake has n sections with tastin... |
[
{
"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 | 221 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Turtle wants to reorder a string to maximize the number of good pairs. Let me try to understand the problem step by step.
First, the problem defines what a "good pair" is. A good pair (i, j) is either a pair where s_i = s_j (i.e., the characters at positions i and j... |
[
{
"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 | 273 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem of finding all trophic balance species in an ecosystem modeled as a directed graph. Let me start by understanding the key components here.
First, the problem defines two main concepts:
1. **Independent Trophic Group (ITG):** A set of species (nodes) wher... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 314 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum time required for a dump truck to level the sand in a given segment of sections from l_i to r_i. Each section has an initial height, some are positive (hills) and some are negative (pits). The truck can move between adjacent sections, take sand from a section (decrease ... |
[
{
"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: An integer c is a common divisor of two integers x and y if and only if c is a divisor of x and c is a divisor of y. Which of the following sets of i... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 185 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which of these options could be the set of all common divisors of two integers. Let me start by recalling that a common divisor of two integers x and y is an integer c such that c divides both x and y. The problem states that such a c must be a divisor of both x and y individually.... |
[
{
"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 | 400 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where we have a binary string and we can perform some operations to generate other binary strings, and we need to count how many distinct non-empty strings we can produce. The answer should be modulo 998,244,353. Let me try to break this down step by step.... |
[
{
"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 | 443 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where there's a grid constructed from two arrays, and then we have some queries about whether we can perform a specific operation to make the beauty of the grid equal to a given value. The operation is removing all elements in a specified row and column, effectively setting... |
[
{
"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 | 19 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have n balls, each with a value a_i, and we perform operations where we merge elements from the set S = {1, 2, ..., i} into a single element. The function f(i) counts how many starting elements j (from 1 to i) can end up alone after i-1 operations. The key is to fi... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 36 | AMC23 | {
"expected_answer": "6",
"problem_id": "46",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out on how many of the 11 disjoint open intervals, after removing the roots of the polynomial P(x), the polynomial is positive. Let me start by understanding the problem step by step.
First, the polynomial given is P(x) = (x - 1)^1 * (x - 2)^2 * (x - 3)^3 * ... * (x - 10)^10. So, this... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Identify the correct sequence of reagents for the synthesis of [1,1'-bi(cyclopentylidene)]-2-one starting from 1,5-dichloropentane.\nOptions: A) 1. Na, ether\n2. Cl2/hv\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 80 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let's tackle this problem. So, we need to figure out the correct sequence of reagents to convert 1,5-dichloropentane into [1,1'-bi(cyclopentylidene)]-2-one. Hmm, okay. Let me start by understanding the target compound and the starting material.
First, the starting material is 1,5-dichloropentane. That... |
[
{
"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 | 181 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the value at the root of a tree by performing operations where I increase the value at a vertex and decrease the values at its subtree nodes. Let me start by understanding the problem step by step.
First, the problem gives a tree with n vertices, numbered 1 to n, w... |
[
{
"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 sizes n and m, respectively.\nConsider calculating the following values:\n\nThe number of indices... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 135 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem. Let me read the prompt again carefully. We have two integer arrays, nums1 and nums2, with lengths n and m respectively. The task is to find two values:
1. The number of indices i (from 0 to n-1) where the element nums1[i] appears at least once in nums2.
... |
[
{
"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 potential energy of a particle of mass $m$ at a distance $r$ from ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 120 | JEEBench | {
"expected_answer": "BC",
"problem_id": "1",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of the statements (A) to (D) are true regarding the speed \( v \) of a particle moving in a circular orbit and its angular momentum \( L \) given the potential energy \( V(r) = \frac{k r^2}{2} \).
First, let me recall that potential energy is related to the force through the... |
[
{
"content": "Problem: Let $a$ be a positive real number such that all the roots of\n\\[x^3 + ax^2 + ax + 1 = 0\\]are real. Find the smallest possible value of $a.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 19 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the smallest possible value of a positive real number a such that all the roots of the cubic equation x³ + a x² + a x + 1 = 0 are real. Hmm, let's see.
First, since the equation is a cubic with real coefficients, and all roots are real, then I remember that for cubic equations, if all ... |
[
{
"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": 3,
"temperature": 0.7
} | 3 | 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... | <think>
Okay, so I need to find the probability that a regular octagon, with each vertex independently colored red or blue with equal chance, can be rotated so that all blue vertices end up at positions where there were originally red vertices. Hmm, that sounds a bit tricky, but let me try to break it down.
First, let... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 190 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have two arrays, a and b, each of length n. We need to compute the maximum possible product P = ∏_{i=1}^n min(a_i, b_i) after rearranging b. Then there are q modifications where we can either increase a_x or b_x by 1, and after each modification, we need to compute... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Compound A (C3H6) undergoes bromination in the presence of carbon tetrachloride to form compound B. When compound B reacts with alcoholic KOH, it forms compound C. Passi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 99 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem step by step. So, we have Compound A, which is C3H6. That's propene, right? Because propane is C3H8, so propene would be C3H6. It undergoes bromination in the presence of carbon tetrachloride to form Compound B. Bromination usually adds Br atoms to the molecule. Since ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The correct statement(s) related to the metal extraction processes is(... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 322 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "33",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. Each option seems to relate to different metal extraction processes, so I need to analyze each one carefully.
Starting with option (A): A mixture of PbS and PbO undergoes self-reduction to produce Pb and SO₂. Hmm, self-reduction usually means that the mixture reduc... |
[
{
"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 total number of compounds having at least one brid... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 164 | JEEBench | {
"expected_answer": "6",
"problem_id": "25",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to figure out how many of these given compounds have at least one bridging oxo group. Hmm, first, I should remember what a bridging oxo group is. From what I recall, an oxo group is a group containing oxygen and a positive charge, like a hydroxyl group (OH) or a peroxyl group (O2). A bridging ox... |
[
{
"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 array nums of length n and a positive integer k.\nThe power of an array of integers is defined as the number of subsequences with thei... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 482 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where I have to calculate the sum of the power of all subsequences of an integer array `nums` with a target sum `k`. The power of a subsequence is the number of its subsequences that sum up to `k`. The answer should be modulo `10^9 + 7` because it might be... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 66 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "49",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I have this system of linear equations to analyze:
1. \( a x + 2 y = \lambda \)
2. \( 3 x - 2 y = \mu \)
And I need to figure out which of the statements (A) to (D) are correct. Let me take each one step by step.
First, let me recall that for a system of linear equations, the number of solutions dep... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A cubical solid aluminium (bulk modulus $=-V \\frac{d P}{d V}=... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 283 | JEEBench | {
"expected_answer": "0.24",
"problem_id": "16",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I need to figure out the change in the edge length of a solid aluminum cube when it's submerged in the ocean at a depth of 5 km. The cube has an edge length of 1 meter on the Earth's surface. The problem gives me the bulk modulus of aluminum as 70 GPa, the density of water as 1000 kg/m³, and the accele... |
[
{
"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 $7 \\overbrace{5 \\cdots 5}^{r} 7$ denote the $(r+2)$ digit number where the first and the last digits are... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 459 | JEEBench | {
"expected_answer": "1219",
"problem_id": "10",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, let me try to figure out this problem. So, the problem is about adding a bunch of numbers that start and end with 7, with all the middle digits being 5, and then expressing the sum as a fraction where the numerator is another such number (with 99 fives) plus some number m, and the denominator is n. We nee... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: \"Oh, I know you,\" the ribonucleoprotein particle says to the nascent chain as they meet. \"Pause there for a minute. Let me show you in; you really need some sugar.\"\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 26 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out where the ribonucleoprotein particle and the nascent chain met, and where the chain is heading. The problem mentions a conversation between a ribonucleoprotein particle and a nascent chain. Ribonucleoprotein particles are complexes of RNA and proteins, often involved in mRNA proces... |
[
{
"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 following compounds will exhibit optical activity?\n\n(Z)-1-chloro-2-methylbut-1-ene\n(3aR,7aS,E)-8-(chloromethylene)hexahydro-4,7-methanoisobenzofuran-1... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 15 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many of these compounds are optically active. Let me start by recalling that optical activity, or chirality, depends on whether a molecule has a non-superimposable mirror image. That is, if a molecule is not symmetrical, it can rotate plane-polarized light, which is what makes ... |
[
{
"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: In what way does Lamarck's theory of acquired characteristicsnot agree with present evidence?\nOptions: A. Acquired characteristics are inherited thr... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 417 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which option best explains why Lamarck's theory of acquired characteristics doesn't align with current evidence. Let me start by recalling what Lamarck believed. He thought that traits acquired during an organism's lifetime could be passed on to its offspring. For example, if a gir... |
[
{
"content": "Problem: What is the area of the region in the coordinate plane defined by\n$| | x | - 1 | + | | y | - 1 | \\le 1$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 39 | AMC23 | {
"expected_answer": "8",
"problem_id": "49",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the area of the region defined by the inequality | |x| - 1 | + | |y| - 1 | ≤ 1 in the coordinate plane. Hmm, this looks a bit complicated with all the absolute values, but maybe I can break it down step by step.
First, let me recall that absolute value equations often create V-shaped gr... |
[
{
"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": 9,
"temperature": 0.7
} | 9 | 37 | AMC23 | {
"expected_answer": "901",
"problem_id": "47",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out for how many integers \( n \) the given expression is a real number. The expression is:
\[
\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}}
\]
First, let me recall that for a square root to be a real number, the expression inside the square root must be non-negative. So, the fra... |
[
{
"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 | 369 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Kevin has a binary string s and he wants to transform it into another string t, which can have '0', '1', or '?' characters. The operations allowed are swapping adjacent blocks of the same character. The goal is to find the minimum number of operations required, or det... |
[
{
"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 | 319 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have a sequence of integers and two bounds x and y. I need to count the number of pairs (i, j) such that when I remove the elements at i and j, the sum of the remaining elements is at least x and at most y. The constraints are pretty large—n can be up to 200,000 and... |
[
{
"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 non-empty string S consisting of uppercase and lowercase English letters. Determine whether the follow... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 369 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def check_uppercase(S):
if S[0].isupper() and all(s.islower() for s in S[1:]):
print("Yes")
else:
print("No")
# Call the function after the definition
check_uppercase(input()) |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A supernova occurred in our Galaxy. Part of the supernova ejecta is moving directly towards the center of the Galaxy. Both the ejecta part and the Galaxy are inertial fr... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 122 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so there's this problem about a supernova ejecta moving towards the center of the Galaxy, and we need to find the distance it travels in the Galaxy's reference frame when 50 seconds pass in the ejecta's reference frame. Hmm, let's break this down.
First, the problem mentions that both the ejecta part and... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The surface of copper gets tarnished by the formation of coppe... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 167 | JEEBench | {
"expected_answer": "-14.6",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the minimum partial pressure of H₂ gas, p_H₂, required to prevent the oxidation of copper by water vapor at 1250 K. Then, I have to compute the natural logarithm of that pressure. Let me start by understanding the problem step by step.
First, the reaction given is:
2 Cu(s) + H₂O(g) → C... |
[
{
"content": "Problem: Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and\n \\[a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 10 | AIME24 | {
"expected_answer": "601",
"problem_id": "aime24-10",
"reference_solution": "$ab(a+b)+bc(b+c)+ac(a+c)=300(ab+bc+ac)-3abc=6000000, 100(ab+bc+ac)-abc=2000000$ Note that \n $(100-a)(100-b)(100-c)=1000000-10000(a+b+c)+100(ab+bc+ac)-abc=0$ . Thus, $a/b/c=100$ . There are $201$ cases for each but we need to subtrac... | <think>
Okay, so I need to find the number of triples of nonnegative integers (a, b, c) such that a + b + c = 300 and the sum of their pairwise products squared equals 6,000,000. That is, a²b + a²c + b²a + b²c + c²a + c²b = 6,000,000. Hmm, that seems like a lot of terms, but maybe there's a pattern or a substitution I ... |
[
{
"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 order of the oxidation state of the phosphorus atom in $\\mathrm{H}_{... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 102 | JEEBench | {
"expected_answer": "C",
"problem_id": "23",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, so I need to figure out the order of the oxidation states of the phosphorus atoms in these four compounds: H₃PO₂, H₃PO₃, H₃PO₄, and H₄P₂O₆. The answer choices are given, so I need to determine the oxidation state for each compound and then arrange them from highest to lowest oxidation state. Let me start ... |
[
{
"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 | 38 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about nested segments. Let me try to understand the problem first. We have a set S of segments [l_i, r_i] where each segment is distinct and the set is good. A good set has the property that any two segments either don't overlap or one is fully contained within the other. W... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 102 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this strange matrix problem. Let me try to understand the requirements first. The matrix has to satisfy two conditions for any two distinct rows i and j:
1. For every set of columns (x₁, x₂, ..., xₖ), the bitwise AND of the elements in those columns for rows i and j is 0.
2. For every ... |
[
{
"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 | 341 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out if Alice will ever meet the Red Queen based on her movement pattern. Let's start by understanding the problem. Alice starts at (0,0) and the Red Queen is at (a,b). Alice's movement is determined by a string s which repeats indefinitely. Each character in s is one of N, E, S, W (nor... |
[
{
"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 | 283 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether Milya can rearrange the elements in array a such that there are at least 3 distinct elements in array c, where c_i = a_i + b_i. Let me start by understanding the problem.
First, both arrays a and b are good arrays. That means for each element x in a or b, x appears at leas... |
[
{
"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 | 222 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Turtle can change a value x by taking the mex of some sequence, and we have to compute the sum of f(i) from i=0 to m, where f(i) is the maximum x after some operations starting with i. Hmm, let me try to understand.
First, let's parse the problem again. There are n s... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array receiver of length n and an integer k.\nThere are n players having a unique id in the range [0, n - 1] who will play a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 95 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where we have a list of receivers and we need to maximize the sum after passing the ball k times. Let me try to understand the problem step by step.
First, the problem is about choosing a starting player (x) such that when we pass the ball k times startin... |
[
{
"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: Natural boron is made up of 20 per cent^10B and 80 per cent 11 B. What is the approximate atomic weight of natural boron on the scale of 16 units for... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 477 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the approximate atomic weight of natural boron on a scale where 16 units correspond to the atomic weight of oxygen (O). Let me start by recalling some basic concepts.
First, natural boron is a mixture of two isotopes: boron-10 (²⁰% abundance) and boron-11 (80% abundance). The ato... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 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, so I need to solve this geometry problem. Let me read it again carefully.
We have triangle ABC inscribed in circle ω. The tangents to ω at B and C intersect at point D. Then line AD intersects ω again at P. We are given the lengths AB = 5, BC = 9, AC = 10, and we need to find AP in the form m/n where m a... |
[
{
"content": "Problem: There exist real numbers $x$ and $y$ , both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$ . Find $xy$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 16 | AIME24 | {
"expected_answer": "25",
"problem_id": "aime24-16",
"reference_solution": "By properties of logarithms, we can simplify the given equation to $x\\log_xy=4y\\log_yx=10$ . Let us break this into two separate equations: \\[x\\log_xy=10\\] \n \\[4y\\log_yx=10.\\] \nWe multiply the two equations to get: \n \\[4xy\\... | <think>
Okay, so I need to solve this problem where there exist real numbers x and y, both greater than 1, such that log base x of y^x equals 10 and log base y of x^(4y) also equals 10. Then I have to find xy. Hmm, logarithms, exponents... Let me break this down step by step.
First, let's write down the equations give... |
[
{
"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 | 157 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out how to solve this problem. So, we have two visitors: Robin's brother and Mrs. Hood. Each needs to stay for 'd' consecutive days, and we need to choose the starting day for each such that the brother's visit overlaps the maximum number of distinct jobs, and Mrs. Hood's visit overla... |
[
{
"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 | 27 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have multiple planets with intervals of vulnerability, and we can expand their intervals by 1 unit either left or right. The goal is to compute the sum of the scores for all non-empty subsets of planets. The score of a subset is the minimum number of expansions nee... |
[
{
"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 | 177 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of roads that must be maintained on Penacony to ensure that all pairs of friends can still travel between each other. Let me start by understanding the problem.
First, the setup: There are n houses arranged in a circle, with each house connected to its immediate... |
[
{
"content": "Problem: What is the product of all solutions to the equation\n\\[\\log_{7x}2023\\cdot \\log_{289x}2023=\\log_{2023x}2023\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 8 | AMC23 | {
"expected_answer": "1",
"problem_id": "10",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this equation:
\[
\log_{7x}2023 \cdot \log_{289x}2023 = \log_{2023x}2023
\]
Hmm, logarithms with different bases. Let me recall some logarithm properties. Maybe I can convert them all to the same base to make it easier? Let's see.
First, I remember that \(\log_a b = \frac{\ln b}{\ln... |
[
{
"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 have a sequence A=(A_1,A_2,\\dots,A_N) of length N. Initially, all the terms are 0.\r\nUsing an integer K given in... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 221 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | # Generate an executable Python function based on the given prompt.
import heapq
from typing import List
def compute_f(A: List[int], K: int) -> int:
# Convert the list A into a max-heap to sort it in descending order.
max_heap = [-a for a in A] # Negative because Python's heap is min-heap by default.
hea... |
[
{
"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 | 263 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which restaurant the person hasn't visited yet. They've already gone to five different restaurants from Monday to Thursday, each day visiting a different one. Now, on Friday, they need to go to the remaining one. Since there are five restaurants in total, numbered 1 to 5, and they'... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A sample $(5.6 \\mathrm{~g})$ containing iron is completely di... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 357 | JEEBench | {
"expected_answer": "1.87",
"problem_id": "29",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let me try to figure out how to solve this problem. So, we have a sample of iron that's 5.6 grams. It's dissolved in cold dilute HCl to make a 250 mL solution. Then, when we take 25 mL of that solution and titrate it with 0.03 M KMnO4, we need 12.5 mL of the KMnO4 solution to reach the endpoint. We need 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: Find the interest charge on a $600 loan at 6% for 60 days. Find the total amount due.\nOptions: A. $612, B. $600, C. $620, D. $624, E. $606, F. $615,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 372 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the interest charge on a $600 loan at 6% for 60 days, and then find the total amount due. Let me start by recalling how interest works. There's simple interest, which is calculated using the formula I = P * R * T, where I is the interest, P is the principal amount, R is the rate, a... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Large clouds of neutral hydrogen in deep space absorb the light from background quasars at Lyman alpha wavelength ~1216 Angstrom. Estimate the lower limit on the redshif... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 129 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the lower limit on the redshift of quasars that can be detected with optical ground-based telescopes by considering the absorption of Lyman alpha wavelength (~1216 Angstrom) by neutral hydrogen clouds. The options given are 2.4, 1.2, 3, and 1.9. Hmm, let me think through this step ... |
[
{
"content": "Problem: How many positive two-digit integers are factors of both 100 and 150?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 180 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many positive two-digit integers are factors of both 100 and 150. Hmm, let me start by understanding what the question is asking. It wants two-digit numbers that divide both 100 and 150 without leaving a remainder. In other words, these numbers are common factors of 100 and 150... |
[
{
"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 | 153 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem called "Med-imize" where we have an array and we can repeatedly remove a subarray of size k, and we want to maximize the median of the remaining array. The problem gives a good example of how the median is calculated, and there are some test cases provided. Let me try to fi... |
[
{
"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 | 87 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have an array of integers, and we start with c = 0. For each element in the array, we can either add it to c or take the absolute value of c after adding it. We want to find the number of unique procedures that result in the maximum possible value of c, modulo 9982... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A light beam is propagating through a glass with index of refraction n. The glass is moving at constant velocity v in the same direction as the beam and toward the obser... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 40 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let me try to figure out this problem. So, we have a light beam traveling through a glass medium with index of refraction n. The glass is moving at a constant velocity v in the same direction as the beam and towards the observer. We need to find the speed of light in the glass relative to the observer in ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: This question refers to the following information.\n\"I travelled thence to 'Aden, the port of Yemen, on the coast of the ocean. It is surrounded by ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 381 | MMLUPro | {
"expected_answer": "",
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"subject": null,
"type": null
} | <think>
Okay, let's try to figure out which option led directly to the development of the economic system described in the journal. The passage is about Aden, a port in Yemen, as described by Ibn Battuta around 1325-1354 CE. The question is asking which of the given options was the direct cause of the economic system 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 279 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about complex segments. Let me read the description again to make sure I understand it. A complex set of segments can be partitioned into subsets where each subset has the same size, and two segments intersect if and only if they're in the same subset. The goal is to find 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": 1,
"temperature": 0.7
} | 1 | 54 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to distribute bets across different outcomes such that the total coins bet are strictly less than the coins received if any outcome wins. Let me start by understanding the problem better.
Each test case has multiple outcomes, each with a multiplier (k_i). For each outcome, if ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: If $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ is a differentiable funct... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 115 | JEEBench | {
"expected_answer": "AC",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I have this problem here where I need to figure out which of the options A to D are correct based on the given conditions. Let me start by restating the problem to make sure I understand it.
We have a differentiable function f: ℝ → ℝ such that its derivative f'(x) is always greater than 2f(x) for all ... |
[
{
"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 | 239 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out who wins between Tsovak and Narek in this game. Let me start by understanding the problem again. They have an array a and a matrix b. The game is played in turns: Tsovak starts, then Narek, then Tsovak again, etc. Each turn, a player has to find the next element of the array in the... |
[
{
"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 two grids, each with N rows and N columns, referred to as grid A and grid B.\r\nEach cell in the grids c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 432 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which cell is different between two grids, grid A and grid B. Both grids have N rows and N columns, and each cell contains a lowercase English letter. The problem states that they differ in exactly one cell, so I need to find the coordinates (i, j) where the characters are differen... |
[
{
"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 binary string s of length n on which you can apply two types of operations:\n\nChoose an index i and invert all characters from index... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 30 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum cost to make all characters in a binary string equal using two types of operations. Let me try to understand the problem first.
We have a binary string, which means it's made up of only 0s and 1s. The goal is to make all the characters the same, either all 0s or all 1... |
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