context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 12
values | metadata dict | model_outputs stringlengths 436 155k |
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[
{
"content": "Problem: There are $n$ values of $x$ in the interval $0<x<2\\pi$ where $f(x)=\\sin(7\\pi\\cdot\\sin(5x))=0$. For $t$ of these $n$ values of $x$, the graph of $y=f(x)$ is tangent to the $x$-axis. Find $n+t$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
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] | {
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"seed": 9,
"temperature": 0.7
} | 9 | 23 | AIME25 | {
"expected_answer": "149",
"problem_id": "II-9",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to find the number of values n where the function f(x) = sin(7π·sin(5x)) is zero in the interval 0 < x < 2π. Then, out of these n values, I have to find how many points t where the graph is tangent to the x-axis. Finally, add n and t together to get the answer.... |
[
{
"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 | 88 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this coding problem where I have to count the number of nonempty strings t (where t is not "a") such that the given string s can be partitioned into substrings that are either t or "a", and there's at least one substring that's t. Let me try to understand the problem step by step.
Firs... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 40 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem about valid permutations based on the operations described. Let me try to understand the problem step by step.
We start with a permutation of size n. Then we perform q operations where each operation splits an array into two parts, and we record the maximum elements of eac... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 104 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out this problem. So, we have a 2xN grid, each cell has an integer. We can swap any two columns any number of times, and then we need to find the maximum cost path from (1,1) to (2,N). The cost is the sum of all cells in the path.
First, let me understand the operations. Swapping tw... |
[
{
"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 | 378 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Alya has to construct a permutation of numbers 1 to n such that after performing a series of bitwise operations (AND for odd indices and OR for even indices), the final value of k is maximized. Let me try to break this down step by step.
First, let me make sure I und... |
[
{
"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 | 49 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this elections problem where I have to determine, for each candidate, the minimum number of candidates that need to be excluded so that candidate i wins. Let me try to break this down step by step.
First, let's understand the problem. We have n candidates, each with a certain number of... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nEffective antibody production by B cells of the mammalian adaptive immune system is criti... | {
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"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 120 | HLESubset | {
"expected_answer": "B",
"problem_id": "670013827794cc36bc974f27",
"reference_rationale": "B cell production of high-affinity antibodies requires class-switching and somatic hypermutation (SHM). For the induction of an adaptive immune response as well as high-affinity antibody production against a target antigen... | <think>
Okay, so I need to figure out which groups of mice would have different levels of high-affinity OVA-specific antibodies that have undergone somatic hypermutation (SHM) after injection with OVA and CpG. Let me start by recalling what each of these genes do and how their mutations might affect the immune response... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nTo improve the catalytic efficiency of enzyme Zma1, which converts molecule A to B resear... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 223 | HLESubset | {
"expected_answer": "G",
"problem_id": "671d9e9d29e7fde7166e474d",
"reference_rationale": "1. Metals.\nIt is known that divalent metal ions function as cofactors of enzymes.\nThe presence of MgCl2 increases kcat so MgCl2 is a cofactor.\nCucl2 and Cacl2 decrease kcat so CuCl2 and CaCl2 are inhibitors. Cu ions and... | <think>
Okay, let's try to figure out the functions of molecules Al1, Al2, and Rga1 based on the experiment results. The question is about the catalytic efficiency (kcat) of the enzyme Zma1 under different conditions. The answer choices suggest different possibilities, so I need to analyze each condition step by step.
... |
[
{
"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 positive integers N, M, K, and a sequence of non-negative integers: A=(A_1,A_2,\\ldots,A_N).\nFor a non-... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 111 | LiveCodeBenchV5 | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to calculate the sum of the scores of all non-empty subsequences of a given sequence A. The score of a subsequence is defined based on its length relative to M and K. Let me try to break this down step by step.
First, let's understand the problem statement aga... |
[
{
"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 circle $C_{1}: x^{2}+y^{2}=3$, with centre at $O$, intersects the ... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 35 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "48",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to solve this geometry problem. Let me start by understanding what's given and what's being asked.
First, there's the circle C₁: x² + y² = 3. The center is at O, which I assume is the origin (0,0) because the standard equation of a circle is (x - h)² + (y - k)² = r², and if there are no h or k,... |
[
{
"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 rectangular cake with some strawberries on the xy-plane. The cake occupies the rectangular area \\lbrace (x... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 210 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a rectangular cake with strawberries on it, and we're supposed to cut the cake into pieces with vertical and horizontal cuts, then find the minimum and maximum number of strawberries that could be in any of the pieces. Let me try to break this down step by ste... |
[
{
"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 | 198 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Kristina has an array 'a' with n integers, and m strings. Each string needs to be checked if it matches the template defined by the array. The conditions are that the length of the string must equal the length of the array, and there's a one-to-one correspondence betw... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: At $298 \\mathrm{~K}$, the limiting molar conductivity of a we... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 353 | JEEBench | {
"expected_answer": "0.22",
"problem_id": "25",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I have this problem about molar conductivity and degree of dissociation. Let me try to parse through it step by step.
First, the problem states that at 298 K, the limiting molar conductivity of a weak monobasic acid is 4 × 10² S cm² mol⁻¹. Then, for an aqueous solution of the acid, the degree of diss... |
[
{
"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. Some values in nums are missing and are denoted by -1.\nYou can choose a pair of positive integers (x, y) exactly once... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 324 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to figure out how to minimize the maximum absolute difference between adjacent elements in an array where some elements are missing (denoted by -1). I can replace all the missing elements with either x or y once, choosing the pair (x, y) that gives the smallest possible maximum differenc... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 87 | CodeElo | {
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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have an array of integers, and for each element, we can either add it to a current value c or take the absolute value after adding it. The goal is to find the number of unique procedures that result in the maximum possible value of c. The answer needs to be modulo ... |
[
{
"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 weighted simple directed graph with N vertices and M edges.\r\nThe vertices are numbered 1 to N, and the i-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 374 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem. The task is to determine if there's a walk that visits every vertex at least once in a directed graph, and if so, find the minimum total weight of such a walk. The graph has N vertices and M edges, with possible negative weights but no negative cycles. Th... |
[
{
"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: A debate club consists of 6 girls and 4 boys. A team of 4 members is to b... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 25 | JEEBench | {
"expected_answer": "A",
"problem_id": "38",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, let's see. The problem is about a debate club with 6 girls and 4 boys. We need to select a team of 4 members, and this team has to include a captain. The key condition here is that the team can have at most one boy. The question is asking for the number of ways to select such a team. The options are A) 38... |
[
{
"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_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this Field Division problem where Alice and Bob are dividing a field, and I have to calculate the maximum number of cells Alice can get under two scenarios: one where Bob doesn't give her any fountains, and another where he gives her each fountain one by one, and see how much each gift ... |
[
{
"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 | 351 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Iris and Dora are playing a game on a tree. The goal is to determine the final score of the tree after both play optimally. Let me try to understand the problem step by step.
First, let's recap the problem. We have a tree rooted at vertex 1. Each vertex has a value o... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Which of the following statement(s) is(are) true?\n(A) Monosaccharides... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 196 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "29",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | <think>
Okay, let's tackle this problem step by step. So, there are four statements here, labeled A through D, and I need to figure out which ones are true. Let me go through each one individually.
Starting with statement (A): "Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones." Hmm, monos... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nTwo business partners named Alex and Tyler are looking to incorporate a company in Ontari... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 216 | HLESubset | {
"expected_answer": "C",
"problem_id": "671c6a1aacee876e82d4bc0e",
"reference_rationale": "This questions deals with incorporations and corporate structuring, and presents a type of matter that is very common. For the purposes of keeping the answer options a reasonable length, only the three rights that are req... | <think>
Okay, let's see. Alex and Tyler want to set up a company in Ontario with specific requirements. Let me go through each of their needs and then check the answer choices.
First, they need equal control. So, the structure should allow both Alex and Tyler to have equal say in decisions. That probably means they ea... |
[
{
"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: There are three main types of buying situations in an organization, referred to by Robinson, Faris, and Wind (1967) as _____________.\nOptions: A. B... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 374 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the answer to this question about the three main types of buying situations in an organization as referred to by Robinson, Faris, and Wind (1967). The options are A through J, and I have to pick the correct one.
First, let me recall what I know about organizational buying. I remem... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given three positive integers num1, num2, and num3.\nThe key of num1, num2, and num3 is defined as a four-digit number such that:\n\nInitially, if any ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to create a function that takes three positive integers and returns their key based on the smallest digits in each position. The key is a four-digit number, so even if the input numbers have fewer digits, they get padded with leading zeros. Then, for each digit position (from the first 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 is the average kinetic energy of air molecules at a temperature of 300° K? What would be a typical speed for nitrogen molecules, which are the m... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 201 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the average kinetic energy of air molecules at 300 K and the typical speed of nitrogen molecules in air. Let me start with the average kinetic energy.
I remember that the average kinetic energy per molecule in an ideal gas is given by the formula (3/2)kT, where k is the Boltzmann const... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nGiven that some environmental conditions of chronic infections favor the emergence of hyp... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 473 | HLESubset | {
"expected_answer": "C",
"problem_id": "673a8c2e4e2e35b51a27fafd",
"reference_rationale": "Conversion to the mucoid phenotype in hypermutator strains of Pseudomonas aeruginosa can be increased because of an increased mutation frequency on the mucA gene. However, most of mutations of the mucA gene observed in hyp... | Explanation: The question is about the effect of hypermutator strains of Pseudomonas aeruginosa on the frequency of mucoid variants, specifically regarding mutations in the mucA gene. Hypermutator strains are known to have increased rates of mutation. The mucoid phenotype is commonly associated with mutations in the mu... |
[
{
"content": "Problem: Find the greatest common divisor of $3339$, $2961$, and $1491$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 89 | MATH500 | {
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} | <think>
Okay, so I need to find the greatest common divisor (GCD) of three numbers: 3339, 2961, and 1491. Hmm, GCD is the largest number that divides all of them without leaving a remainder. Let me remember how to do this. I think the Euclidean algorithm is the way to go here, but since there are three numbers, maybe I... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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} | <think>
Okay, so I need to solve this Cutting Game problem where Alice and Bob take turns cutting rows or columns off a grid and earning points based on the chips that are on the cut part. The goal is to compute the total points each player earned after all moves are made. Let me try to break this down.
First, let me ... |
[
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such that $12x^2 - xy - 6y^2 = 0$.\nMark your solution with \\boxed\nAnswer:",
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] | {
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"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_rationale": null,
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"subject": null,
"type": null
} | <think>
Okay, so I need to find the number of ordered pairs (x, y) where both x and y are integers between -100 and 100, inclusive, and they satisfy the equation 12x² - xy - 6y² = 0. Hmm, let's start by understanding the equation and how to approach it.
First, the equation is quadratic in both x and y. Maybe I can fac... |
[
{
"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 | 116 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have an array of integers, and we can perform operations where we remove two adjacent elements, but only if they meet a certain condition. The goal is to find the maximum number of such operations we can perform. Let me try to understand the problem step by step.
... |
[
{
"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 cities in a certain country.\nYou will travel from your office in city 1 to a destination in city N, via z... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 309 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum time to travel from city 1 to city N, using a combination of company car and train. Let me start by understanding the problem.
First, there are N cities, and we start at city 1 and need to get to city N. We can use either a company car or a train between any two cities... |
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{
"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 energy of the Relativistic Heavy Ion Collider (RHIC) so that the speed of the nucleus X is equal to 0.96c?\n\nKnowing that X is defined as Li with 3 neutrons... | {
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Okay, so I need to find the energy of the Relativistic Heavy Ion Collider (RHIC) where the speed of the nucleus X is 0.96 times the speed of light, c. The nucleus X is defined as Li with 3 neutrons. Hmm, let me break this down step by step.
First, I should recall that the energy of a particle moving at a relat... |
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{
"content": "Problem: Let $p(x)$ be a monic polynomial of degree 4. Three of the roots of $p(x)$ are 1, 2, and 3. Find $p(0) + p(4).$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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Okay, so I need to find p(0) + p(4) where p(x) is a monic polynomial of degree 4. They told me three of the roots are 1, 2, and 3. Hmm, monic means the leading coefficient is 1, right? So the polynomial should look like (x - 1)(x - 2)(x - 3)(x - a), where 'a' is the fourth root. But wait, since it's degree 4 an... |
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{
"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+2 cells arranged in a row. Let cell i denote the i-th cell from the left.\nThere is one stone placed in ea... | {
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} | 1 | 25 | LiveCodeBenchV5 | {
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"subject": null,
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} | <think>
Okay, so I need to figure out if it's possible to transform the initial configuration of stones (given by string S) into the target configuration (given by string T) using the allowed operations. If possible, find the minimum number of operations required. Let me start by understanding the problem step by step.... |
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{
"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.For a positive integer k, the Pyramid Sequence of size k is a sequence of length (2k-1) where the terms of the sequenc... | {
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"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 363 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
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} | <think>
Okay, so I need to figure out how to solve this problem where I have a sequence A of length N, and I want to find the maximum possible length of a Pyramid Sequence I can get by performing operations: decreasing a term by 1 or removing the first or last term. The Pyramid Sequence has to be of the form 1,2,...,k-... |
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{
"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 ... | {
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"max_new_tokens": 32768,
"seed": 5,
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} | 5 | 28 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-28",
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"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... | <think>
Okay, so I have this problem about a tetrahedron ABCD with specific edge lengths: AB and CD are both √41, AC and BD are √80, and BC and AD are √89. The question says there's a point I inside the tetrahedron where the distances from I to each of the faces are all equal. That distance needs to be found in the for... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 297 | CodeElo | {
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} | <think>
Okay, so I need to solve this problem where I have to maximize the mex of an array by performing operations that add x to a chosen index any number of times. Let me try to understand what exactly the problem is asking for.
First, the mex of an array is the smallest non-negative integer not present in the array... |
[
{
"content": "Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and... | {
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"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
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} | <think>
Okay, so I need to solve this problem where a parabola y = x² - 4 is rotated 60 degrees counterclockwise around the origin, and then find the unique intersection point in the fourth quadrant where the original parabola and its image intersect. The answer should be in the form (a - sqrt(b))/c, and I need to find... |
[
{
"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 $a_{1}, a_{2}, a_{3}, \\ldots$ be a sequence of positive i... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 272 | JEEBench | {
"expected_answer": "1",
"problem_id": "50",
"reference_rationale": null,
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"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to figure out how many possible values of c there are such that the equation 2 times the sum of the first n terms of an arithmetic progression (AP) with first term c and common difference 2 equals the sum of the first n terms of a geometric progression (GP) with first term c and common ratio 2. ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 83 | CodeForces | {
"expected_answer": "",
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} | <think>
Okay, so I need to figure out how to count the number of non-degenerate right triangles that can be formed from n points on a 2D plane. The points are distinct, and their y-coordinates are between 0 and 1. Hmm, right triangles have one 90-degree angle, so the three points must satisfy the Pythagorean theorem. B... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"seed": 1,
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} | 1 | 163 | CodeForces | {
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} | <think>
Okay, so I need to solve this problem where AkshiM used the wrong formula for binomial coefficients, and we have to compute his "wrong" coefficients modulo 10^9 + 7. The example given in the editorial shows that the wrong formula results in C[n][k] = 2^k, which is interesting. Let me try to understand why that ... |
[
{
"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 length-N sequence A=(A_1,A_2,\\dots,A_N) consisting of 0, 1, and 2,\r\nand a length-N string S=S_1S_2\... | {
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"seed": 1,
"temperature": 0.7
} | 1 | 231 | LiveCodeBench | {
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} | <think>
Okay, let me try to figure out how to approach this problem. The goal is to compute the sum of the mex values for all triples (i, j, k) where the substring S[i]S[j]S[k] is "MEX". The mex of a set of numbers is the smallest non-negative integer not in that set. The sequence A has elements 0, 1, 2, and S is a str... |
[
{
"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 $... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 355 | JEEBench | {
"expected_answer": "3.57",
"problem_id": "27",
"reference_rationale": null,
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"subject": "chem",
"type": "Numeric"
} | <think>
Alright, let's tackle this problem step by step. First, I need to understand what's going on here. We have a reaction between tin (Sn) and hydrochloric acid (HCl) to produce a salt. Then, the entire amount of that salt reacts with nitrobenzene (C6H3N2O) in the presence of some HCl to form another organic salt, ... |
[
{
"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 zero or more sensors placed on a grid of H rows and W columns. Let (i, j) denote the square in the i-th row ... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 307 | LiveCodeBench | {
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} | <think>
Okay, so I need to figure out how to solve this problem where sensors are placed on a grid, and they interact with adjacent sensors (horizontally, vertically, or diagonally). The goal is to find the number of "super sensors" when they interact with each other. Each group of interacting sensors counts as one sup... |
[
{
"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 | 19 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
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} | <think>
Okay, so I need to solve this problem where I have two arrays, a and b, each of length n. I can swap elements between a and b, but each swap costs c_i coins. The goal is to maximize the sum of the greatest common divisors (GCDs) of the two arrays after some swaps, without spending more than d coins total. And w... |
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{
"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: Discuss thetonotopicorganization of our auditory system.\nOptions: A. Tonotopic organization describes the layout of taste buds on the tongue and the... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 229 | MMLUPro | {
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"problem_id": "",
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"subject": null,
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} | <think>
Okay, so I need to figure out which option correctly explains the tonotopic organization. Let me start by recalling what I know about the auditory system.
I remember that the ear has parts that help detect sound. The basilar membrane is a key part in the inner ear where hair cells convert sound waves into ele... |
[
{
"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 negative point charge of 10^-6 coulomb is situated in air at theorigin of a rectangular coordinate system. A second negativepoint charge of 10^-4 c... | {
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} | 0 | 167 | MMLUPro | {
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Okay, so I need to figure out the force on the second charge. Let me start by recalling what I know about electric forces. Oh, right! Coulomb's Law! It states that the force between two charged particles is proportional to the product of their charges divided by the square of the distance between them. The form... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nA surface current of infinite extent in the$y$ and $z$ directions, $\\vec{K}(x = 0, t) = ... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 234 | HLESubset | {
"expected_answer": "B",
"problem_id": "671eeb53c1a668a6c81e5993",
"reference_rationale": "1. In the superconducting region, Maxwell's equations in their time-varying form are given by:\n$\\vec{J} = \\varepsilon_0 \\frac{\\partial \\vec{E}}{\\partial t}, \\quad \\nabla \\times \\vec{H} = \\varepsilon_0 \\omega_p... | <think>
Okay, so I need to find the force per unit area on the x = d plane due to the time-varying boundary condition for the magnetic field. Let me start by recalling that the force per unit area (stress) on a surface is given by the张量形式的电磁力，可能涉及电场和磁场的本构方程。不过，通常力的计算可能需要考虑电磁力的公式，比如 Lorentz 力，但这里的问题可能更偏向于通过 Maxwell 方程组来... |
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"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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"seed": 0,
"temperature": 0.7
} | 0 | 30 | CodeElo | {
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"problem_id": "",
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} | <think>
Okay, so I need to solve this problem where we have a tree with n vertices, and two chess pieces, PA and PB. The goal is to paint all vertices blue as quickly as possible using these two pieces. Let me try to understand the problem step by step.
First, all vertices start white. PA is on vertex a, PB is on vert... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nWhat kind of conceptual metaphor is expressed by \"my love for humanity\", according to \... | {
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"seed": 1,
"temperature": 0.7
} | 1 | 128 | HLESubset | {
"expected_answer": "B",
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"reference_rationale": "Lakoff and Johnson use the term 'physical metaphor' in this paper for the most common, almost undetectable type of metaphor used to make it possible to talk about abstract things in simpler terms such as 'the brutality of ... | <think>
Okay, so the question is asking about the type of conceptual metaphor expressed by "my love for humanity" according to the book "Conceptual Metaphor in Everyday Language". The answer choices are A through E. Let me think through this step by step.
First, I need to recall what the different types of metaphors 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... | {
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"max_new_tokens": 32768,
"seed": 2,
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"problem_id": "",
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} | <think>
Okay, so I need to solve this problem where there's a sequence that's incomplete, with some elements missing (replaced by -1), and the conditions are that for each adjacent pair, either the left one is half the right one (rounded down) or the right one is half the left one (rounded down). The goal is to fill in... |
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"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": 1,
"temperature": 0.7
} | 1 | 92 | CodeElo | {
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"problem_id": "",
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} | <think>
Okay, so I need to solve this Tower Capturing problem. Let me try to understand the problem first. We have n towers at distinct points, no three collinear, no four concyclic. Initially, we own two towers, say P and Q. The goal is to capture all towers by using operations where we pick two owned towers (P and Q)... |
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A truck has two fuel tanks. You are given two integers, mainTank representing the fuel present in the main tank in liters and additionalTank representing the f... | {
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} | 0 | 51 | LiveCodeBench | {
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Okay, so I need to figure out the maximum distance a truck can travel given two fuel tanks. The main tank has 'mainTank' liters, and the additional tank has 'additionalTank' liters. The truck uses 10 km per liter. The key thing here is that every time the main tank uses 5 liters of fuel, if the additional tank ... |
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{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the sum of the number of lone pairs of electrons on each central atom in the following species?\n$\\le... | {
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"seed": 1,
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} | 1 | 81 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_rationale": null,
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"subject": "chem",
"type": "Integer"
} | <think>
Okay, so I need to find the sum of the number of lone pairs of electrons on each central atom in these four species: [TeBr₆]²⁻, [BrF₂]⁺, SNF₃, and [XeF₃]⁻. Hmm, let's take each one by one.
Starting with [TeBr₆]²⁻. First, I should figure out the structure of tellurium bromide hexafluoride ion. Tellurium is the... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
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"seed": 7,
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} | 7 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
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"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal... | <think>
Okay, so I need to solve this problem about a torus (which is like a donut shape) and a sphere. The problem says that when the torus rests on the inside of the sphere S, it's internally tangent along a circle with radius r_i, and when it rests on the outside, it's externally tangent along a circle with radius r... |
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{
"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 triangle $P Q R$, let $\\vec{a}=\\overrightarrow{Q R}, \\... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 274 | JEEBench | {
"expected_answer": "108",
"problem_id": "52",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to solve this vector problem in triangle PQR. Let me first parse the given information. The vectors a, b, and c are the sides QR, RP, and PQ respectively. Their magnitudes are given: |a| = 3, |b| = 4. Also, there's a ratio involving dot products that equals the ratio of |a| to |a| + |b|. The goa... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nYou’re doing a laparoscopic appendectomy. You fire your stapler across the base of the ap... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 500 | HLESubset | {
"expected_answer": "A",
"problem_id": "6766662d37a605e5d7cb9ee8",
"reference_rationale": "Taking a little cecum is easy, harmless, and happens often in an appendectomy. Best of all once you divide it, the appendix is now free and you can just pull out the stapler with the appendix attached.",
"reference_solut... | Explanation: When performing a laparoscopic appendectomy, using a stapler to secure the appendix is a standard step. However, if the stapler gets stuck on the base of the appendix despite troubleshooting, the next step is critical. The stapler being stuck could compromise the blood supply to the appendix if not address... |
[
{
"content": "Problem: Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$ . Find the number of intersections of the graphs of \\[y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 g(f(\\cos (3 \\pi y))).\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 26 | AIME24 | {
"expected_answer": "385",
"problem_id": "aime24-26",
"reference_rationale": null,
"reference_solution": "If we graph $4g(f(x))$ , we see it forms a sawtooth graph that oscillates between $0$ and $1$ (for values of $x$ between $-1$ and $1$ , which is true because the arguments are between $-1$ and ... | <think>
Okay, so I need to find the number of intersections between the graphs of y = 4g(f(sin(2πx))) and x = 4g(f(cos(3πy))). The functions f and g are defined as f(x) = ||x| - 1/2| and g(x) = ||x| - 1/4|. Hmm, these are absolute value functions, so their graphs are going to be V-shaped, but with multiple reflections ... |
[
{
"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 strings S and T consisting of lowercase English letters. Here, S and T have equal lengths.\nLet X be... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 130 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where we have two strings S and T of the same length, and we want to transform S into T by changing one character each time and appending the new S to an array X. We need the array X to have the minimum number of elements, and if there are multiple such ar... |
[
{
"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 mayoral election is being held in AtCoder City. The candidates are Takahashi and Aoki.\nThere are N valid votes cast... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 105 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out how to solve this problem. So, the question is about determining if the outcome of a mayoral election between Takahashi and Aoki is already decided based on the current vote counts and the total number of valid votes. The election has N valid votes, which is an odd number, T votes... |
[
{
"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 | 6 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to find the lexicographically smallest array by swapping elements as long as their XOR is less than 4. Hmm, let me start by understanding what exactly the problem is asking for.
First, lexicographical order means that we want the smallest possible array where ... |
[
{
"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 lines $\\mathrm{L}_1$ and $\\mathrm{L}_2$ defined... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 332 | JEEBench | {
"expected_answer": "9.00",
"problem_id": "45",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, let me try to work through this problem step by step. It's a bit involved, but I'll take it one piece at a time.
First, let's parse the problem:
We have two lines, L₁ and L₂, defined by the equations:
L₁: x√2 + y - 1 = 0
L₂: x√2 - y + 1 = 0
There's a fixed constant λ, and C is the locus of points P ... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nWhat is the standard Japanese pitch accent pattern of 「弟」?\n\nAnswer Choices:\nA. Heiban\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 19 | HLESubset | {
"expected_answer": "D",
"problem_id": "66e97fd756455f341c7849c3",
"reference_rationale": "「弟」(Hepburn Transliteration: otouto) is Japanese for \"younger brother\" and follows the Odaka (尾高) pitch accent pattern in standard Japanese. This can be verified in any source of pitch accent information, such as the “NH... | <think>
Okay, so the question is about the standard Japanese pitch accent pattern for the word "弟" (dī). Let me think about how to approach this. First, I remember that in Japanese, pitch accent, or "yöngun" (音高), refers to the pattern of syllable stress in a word. Each syllable can be either high or low pitch, and the... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums of positive integers and an integer k.\nIn one operation, you can remove the last element of the array and add it to your collectio... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 98 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to figure out the minimum number of operations required to collect the elements 1, 2, ..., k from the array nums. The operation is defined as removing the last element and adding it to my collection. So, each time I perform an operation, I'm effectively moving the last element of the arr... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given eight integers S_1,S_2,\\dots, and S_8,\r\nprint Yes if they satisfy all of the following three conditions, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 227 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python function that checks if eight integers given as input satisfy three conditions: the sequence is monotonically non-decreasing, all numbers are between 100 and 675 inclusive, and each number is a multiple of 25. The function should print "Yes" if all three conditions are met, an... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Bob is stuck in a dungeon and must break n locks, each requiring some amount of energy to break. The required energy for each lock is stored in an array called... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 345 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum time Bob needs to break all the locks. Let me start by understanding the problem step by step.
First, Bob has to break n locks, each with a certain strength. The energy of his sword starts at 0, and every minute, the energy increases by a factor X. Initially, X is 1. 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": 2,
"temperature": 0.7
} | 2 | 325 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to minimize the disturbance in a line of students by swapping pairs of students. The disturbance is the number of adjacent students with the same topic of interest. The allowed operation is to swap the i-th student with the (n-i+1)-th student any number of times.
First, let m... |
[
{
"content": "Problem: Find the number of rectangles that can be formed inside a fixed regular dodecagon ( $12$ -gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles. [asy] unitsize(0.6 inch); for(int i=0; i<360; i+=30) { d... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 14 | AIME24 | {
"expected_answer": "315",
"problem_id": "aime24-14",
"reference_rationale": null,
"reference_solution": "By Furaken There are two kinds of such rectangles: those whose sides are parallel to some edges of the regular 12-gon (Case 1), and those whose sides are not (Case 2). For Case 1, WLOG assume that the rect... | <think>
Okay, so I need to find the number of rectangles that can be formed inside a regular dodecagon (12-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. Hmm, let's start by understanding the problem better.
First, a regular dodecagon has 12 equal sides and angles. All the ... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A train with cross-sectional area $S_{t}$ is moving with speed $v_{t}$ inside a long tunnel of cross-sectional... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 277 | JEEBench | {
"expected_answer": "9",
"problem_id": "2",
"reference_rationale": null,
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | <think>
Okay, so I need to figure out the value of N in this problem about the train moving through a tunnel. Let me start by understanding the setup.
We have a train with cross-sectional area S_t moving at speed v_t. The tunnel has a cross-sectional area S_0, which is four times S_t. The problem says that almost 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 128 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where Sakurako has a permutation of numbers and colors for each element. The function F(i) is the number of black-colored numbers reachable from i. The challenge is to compute F(i) for each i in the permutation. Let me try to break this down step by step.
First, let me und... |
[
{
"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 | 319 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to count the number of interesting pairs (i, j) in a sequence a. The conditions are that i < j, and after removing elements at positions i and j, the sum of the remaining elements is between x and y (inclusive). Wait, no, the problem says "at least x and at mos... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nLet $\\mathbb{R}, \\mathbb{C}$ represent the spaces of real and complex numbers, respect... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 28 | HLESubset | {
"expected_answer": "I",
"problem_id": "66eaa401c7a3252f0f3fe535",
"reference_rationale": "consider \n$$b(p)= \\underset{ \\left\\{ \\textbf{S} \\in \n \\textbf{SPD}_{7}:\\left[ \\sum_{i=1}^{7} \\lambda_i^2(f_2(\\textbf{S})) \\right] \\leq p^2 \\right\\}}{\\max} f_1(\\textbf{S}) \\\\\n$$\n\n\\begin{enumera... | <think>
Okay, let's try to tackle this problem step by step. First, I need to understand what each part of the integral is asking. The integral is from p=0 to infinity, and the integrand is a complicated fraction. Let me break it down.
The denominator of the fraction is sqrt( [ max over S in SPD_7 with sum_{i=1}^7 λ_i... |
[
{
"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 enemyEnergies denoting the energy values of various enemies.\nYou are also given an integer currentEnergy denoting the amount of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 93 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to maximize the points by strategically choosing which enemies to attack or to take energy from. Let me start by understanding the problem step by step.
First, the rules: I can either attack an unmarked enemy (which gives 1 point and reduces my energy by that enemy's energy) o... |
[
{
"content": "Problem: In $\\triangle{RST}$, shown, $\\sin{R}=\\frac{2}{5}$. What is $\\sin{T}$?\n\n[asy]\npair R,S,T;\nT = (0,0);\nS = (2,0);\nR = (2,sqrt(21));\ndraw(R--S--T--R);\ndraw(rightanglemark(R,S,T,10));\nlabel(\"$T$\",T,SW);\nlabel(\"$S$\",S,SE);\nlabel(\"$R$\",R,NE);\nlabel(\"$5$\",(R+T)/2,NW);\n[/... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 389 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem here about triangle RST. They told me that sin R is 2/5, and I need to find sin T. Hmm, let's see. First, let me visualize the triangle based on the Asymptote code. The right angle is at R, right? Because it's a right-angled triangle with the right angle marked at R. So, triangle RS... |
[
{
"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 and two positive integers m and k.\nReturn the maximum sum out of all almost unique subarrays of length k of nums. If no su... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 82 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to find the maximum sum of an almost unique subarray of length k. An almost unique subarray is one that has at least m distinct elements. The function should take in the array nums, and the integers m and k, and return the maximum sum. If no such subarray exist... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence of N positive integers A = (A_1, A_2, \\dots ,A_N), where each element is at least 2. Anna an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 118 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out who wins this game between Anna and Bruno when they play optimally. The game is about taking turns to replace a number in the sequence with one of its proper divisors. The person who can't make a move loses. Let's break it down step by step.
First, let me understand the game mecha... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nA 64-year-old woman, para 4 gravida 1, arrives at a dermatology and plastic surgery group... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 144 | HLESubset | {
"expected_answer": "A",
"problem_id": "670c775842b25f65425c86c2",
"reference_rationale": "This patient's history of using alkylating agent chemotherapeutics (cyclophosphamide most likely for the ductal carcinoma) and bullae in the axilla are the main features that make the diagnosis lean towards malignancy-rela... | <think>
Okay, let's try to figure out this diagnosis. The patient is a 64-year-old woman with a lot of medical issues. The main complaint is about lesions in her inframammary folds, which are the areas under her breasts. The dermatology issues mentioned include large bullae (blisters) in the axillary folds (under the 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: Liquids $\\mathbf{A}$ and $\\mathbf{B}$ form ideal solution fo... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 291 | JEEBench | {
"expected_answer": "0.2",
"problem_id": "32",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the vapor pressure of pure liquid B at 25°C. The problem says that liquids A and B form an ideal solution for all compositions at that temperature. There are two solutions: one with 0.25 mole fractions of A and another with 0.50 mole fractions of A. The total vapor pressures of these two... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nConsider the following two computational problems:\n\n1. $\\mathsf{DomSet}$.\nInput: A gr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 76 | HLESubset | {
"expected_answer": "C",
"problem_id": "66f760ebf206a49e129c7ed9",
"reference_rationale": "To avoid confusion: The answer is NOT B, since the second problem is on *counting* $\\ell$-independent sets, which is #W[1]-complete, and the connection between W[2] and #W[1] is not known.\n\nInstead, the only consequence... | <think>
Okay, let's try to figure out this problem step by step. So, we have two problems here: DOMSet and #IndSet. The question is about the consequences of having an algorithm A for DOMSet that uses an oracle for #IndSet with certain restrictions. The answer choices are about different hypotheses and hierarchy collap... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: An organic chemist performs two reactions.\nReaction I:\n(S)-5-methoxyhexan-3-one is treated with LAH followed by an acidic workup.\nReaction II:\nPentane-2,4-dione is t... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 125 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem step by step. First, I need to understand what each reaction does and the products formed. Then, I have to figure out how the products would behave in both normal-phase HPLC and chiral HPLC. The key here is determining the number of peaks each product contributes to the chromatog... |
[
{
"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 and three integers k, op1, and op2.\nYou can perform the following operations on nums:\n\nOperation 1: Choose an index i an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 326 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to minimize the sum of an array by performing two types of operations. Let me start by understanding the problem thoroughly.
We have an array of integers, `nums`, and three parameters: `k`, `op1`, and `op2`. The goal is to apply a combination of two operations to the array ele... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nStarting with this initial array:\n\ninitial_array = [\n ['◬','◑'],\n ['◪','▨']\n]\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 441 | HLESubset | {
"expected_answer": "E",
"problem_id": "673668e658bad7ba89d4ad54",
"reference_rationale": "The correct answer is:\n\nscale 2, roll 0 1, rotate clockwise, flip lr, transpose, scale 2, roll 1 2, rotate counterclockwise, flip ud, roll 0 3, antidiagonal_transpose, scale 2, rotate clockwise, roll 0 8, flip ud, roll 1... | <think>
Okay, let's try to figure out which sequence of commands transforms the initial array into the final one described. The problem involves applying a series of operations: scale, roll, rotate, flip, transpose, and antidiagonal transpose. Each operation affects the array's structure and the positions of specific 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 134 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this grid puzzle problem. Let me read it again carefully. The problem is about an n x n grid where each row i has the first a_i cells black and the rest white. We can perform two operations: dye a 2x2 subgrid white or dye an entire row white. The goal is to make all cells white with the... |
[
{
"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: An ideal gas is in thermodynamic equilibrium. The number of degrees of fr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 502 | JEEBench | {
"expected_answer": "C",
"problem_id": "21",
"reference_rationale": null,
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | <think>
Okay, let's see. The problem is about an ideal gas in thermodynamic equilibrium. We have to do with the number of degrees of freedom, n, and how that affects the speed of sound, v_n, and the internal energy, U_n. The question gives four options and asks which one is correct when the temperature and pressure are... |
[
{
"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 road extending east and west, and N persons are on the road.\nThe road extends infinitely long to the east ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 138 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum total number of movements required for all persons to reach their respective destinations. Let me try to break down the problem.
First, the setup: there's a road that extends infinitely east and west from the origin. There are N people initially at positions X₁, X₂, ..... |
[
{
"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 | 53 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have two numbers x and y, and two sequences a and b. Each sequence is defined by a_n = n XOR x and b_n = n XOR y. The goal is to find the length of the longest common subsegment between these two sequences.
First, let me make sure I understand what a common subseg... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A common approximation made in many-body nuclear calculations of some interaction (for example an electroweak interaction) is to suppose that nucleons in a nucleus behav... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 19 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to work through this problem step by step. The question is about the assumptions that lead to the "impulse approximation" in nuclear calculations. The options are combinations of four statements, and I need to figure out which ones imply the approximation.
First, I should recall what the impul... |
[
{
"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 | 359 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where QED has a permutation and a string of L's and R's. The goal is to determine after each query whether the permutation can be sorted into non-decreasing order using the allowed operations based on the current string. Let me try to break this down step by step.
First, l... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer n and a 0-indexed integer array sick which is sorted in increasing order.\nThere are n children standing in a queue with positions 0 t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 146 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to solve this problem where we have n children in a queue, some infected (given by the sick array), and we need to count the number of possible infection sequences modulo 10^9 + 7. Let me start by understanding the problem better.
First, the setup: there are n children in a li... |
[
{
"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 | 176 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have two arrays, a and b, each of length n. My goal is to maximize the score by performing k operations. In each operation, I can choose an index i, add a_i to my score, and then set a_i to max(0, a_i - b_i). The challenge is to figure out the optimal way to choose ... |
[
{
"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.Slavic is preparing a present for a friend's birthday. He has an array $a$ of $n$ digits and the present will be the p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 1 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about Slavic wanting to maximize the product of his digits by adding 1 to exactly one of them. Hmm. So, for each test case, we have an array of digits, and we need to find the maximum product possible after adding 1 to one digit. Let me try to break this down.
First, the input. ... |
[
{
"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 | 148 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a Python program that calculates the alternating sum of a sequence of numbers. The problem says that the signs alternate starting with a plus. So for example, if the numbers are 1, 2, 3, 17, the alternating sum would be 1 - 2 + 3 - 17, which equals -15. Let me make sure I understand 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 44 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to generate a string of vowels (a, e, i, o, u) with the minimal number of palindrome subsequences. Let me start by understanding the problem better.
First, the problem states that we need to minimize the number of palindrome subsequences in a string of length n. The example gi... |
[
{
"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 $Q$ be the cube with the set of vertices $\\left\\{\\left(x_{1}, x_{2... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 454 | JEEBench | {
"expected_answer": "A",
"problem_id": "5",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Okay, so I need to solve this geometry problem involving a cube and some lines. Let me try to parse the problem first.
We have a cube Q with vertices at all combinations of (x1, x2, x3) where each xi is either 0 or 1. So that's the unit cube in 3D space. Then, F is the set of all twelve lines that are the diag... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $n \\geq 2$ be a natural number and $f:[0,1] \\rightarrow \\mathbb{R}$ be the function defined by\n\n$$\nf... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 458 | JEEBench | {
"expected_answer": "8",
"problem_id": "9",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, so I need to find the maximum value of the function f(x) given that the area under the curve from x=0 to x=1 is 4. The function f(x) is defined piecewise in four intervals, each with different expressions. Let me try to parse this step by step.
First, let me note that n is a natural number greater than o... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 383 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have a cyclic array of odd length n, and I can perform operations that increase a_i by 1, a_{i+1} by 1, and a_{i-1} by 2. The goal is to make all elements equal, or determine if it's impossible. The example input has several test cases, and the output shows ... |
[
{
"content": "Problem: Roslyn has ten boxes. Five of the boxes contain pencils, four of the boxes contain pens, and two of the boxes contain both pens and pencils. How many boxes contain neither pens nor pencils?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 404 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. Roslyn has ten boxes. Some of them have pencils, some have pens, and some have both. I need to figure out how many boxes have neither pens nor pencils. Hmm, let's break this down.
First, the problem says five boxes have pencils, four have pens, and two have both pens and pencils. Wait, 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": 2,
"temperature": 0.7
} | 2 | 224 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a set of numbers that can undergo insertions, deletions, and queries for the k-load. The k-load is the smallest number d such that the interval [d, d + k - 1] is not entirely contained in the set.
First, let me make sure I understand the problem correctly. T... |
[
{
"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 1-indexed array of distinct integers nums of length n.\nYou need to distribute all the elements of nums between two arrays arr1 and arr2 using ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 189 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out how to solve this problem. So, we have a list of numbers, and we need to distribute them into two arrays, arr1 and arr2, following specific rules. The goal is to return the concatenated result of these two arrays after applying the distribution rules.
First, let's recap the prob... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $f:(0, \\infty) \\rightarrow \\mathbb{R}$ be a differentiable func... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 30 | JEEBench | {
"expected_answer": "A",
"problem_id": "43",
"reference_rationale": null,
"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 four options (A) through (D) are correct based on the given differential equation and the condition that f(1) ≠ 1. Let me start by understanding the problem step by step.
First, the function f is defined on the interval (0, ∞) and maps t... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
"reference_rationale": null,
"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal... | <think>
Okay, so I need to solve this problem about a torus and a sphere. Let me try to visualize it first. The torus is made by rotating a circle with radius 3 around an axis that's 6 units away from the center of the circle. So, the distance from the center of the circle to the axis is 6, which means the torus has a ... |
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