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 1.54k 439k |
|---|---|---|---|---|---|---|
[
{
"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"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"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, let's tackle this problem step by step. The question is about finding the number of values \( n \) where \( f(x) = \sin(7\pi \cdot \sin(5x)) \) is zero in the interval \( 0 < x < 2\pi \), and then determining how many of those \( n \) points \( t \) are points where the graph is tangent to the x-axis. Fin... |
[
{
"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, let's try to figure out this problem. So, the task is to count the number of non-empty strings t (t is not "a") such that the string s can be partitioned into some substrings where each is either t or "a", and at least one of them is t.
Hmm, right. Let's think about the problem step by step. The key is t... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 40 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the number of permutations of size n that can be split into q operations as specified. The problem seems a bit complex, but let's break it down step by step.
First, understanding the problem. The initial array is a permutation of size n. We perform q operations, each time splitt... |
[
{
"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's see. I need to find the maximum cost path from (1,1) to (2,n) in a 2xN matrix. The path can move right or down, but the columns can be swapped any number of times. The cost is the sum of all cells in the path except the last. Wait, wait. Wait, the path has (n+1) cells? Because it starts at (1,1) and... |
[
{
"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, I need to solve this problem where I have to construct a permutation of numbers 1 to n such that the value of k, which is built by applying bitwise AND on odd steps and OR on even steps, is maximized. Let's think through this step by step.
First, let's understand how the operations work. For each element... |
[
{
"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, I need to solve this problem where for each candidate i, I have to find the minimum number of candidates that need to be excluded so that candidate i wins the election. Let me think through this step by step.
First, let's understand the problem. The election works as follows: each candidate's original vo... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 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, let's try to figure out this question step by step. So, the problem is about which mutant groups of mice (G1 to G6) would have significantly different levels of high-affinity OVA-specific antibodies that have undergone somatic hypermutation (SHM) compared to wild-type mice. The answer choices are from A t... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 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 Al1, Al2, and Rga1 based on the given data. Hmm, the question is about interpreting the effect of adding different molecules on the enzyme Zma1's kcat, which measures how efficiently the enzyme converts molecule A to B. Higher kcat means the enzyme works faster und... |
[
{
"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-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 111 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to calculate the sum of the scores of all non-empty subsequences of a given array A. The score is defined based on the length of the subsequence. If the length is a multiple of M, the score is the XOR of all elements in the subsequence raised to the power K. Other... |
[
{
"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 ... | {
"do_sample": false,
"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 step by step. Let me start by understanding what's given and what's being asked.
First, there's a circle C₁ defined by the equation x² + y² = 3, which is centered at the origin O. It intersects a parabola x² = 2y at a point P in the first quadrant. Then, there's ... |
[
{
"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, let's see. I need to solve this programming problem. Let's read the problem carefully.
The problem is about a cake divided into pieces by vertical and horizontal cuts. The goal is to find the minimum and maximum number of strawberries in any piece after the cake is divided. The constraints are that the s... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 198 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to check if a string matches a given template array. Let's think about what the conditions mean.
So, the template array a is a list of numbers. A string s matches if:
1. The length of s is equal to the length of a. That's straightforward. So for each test case, ... |
[
{
"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... | {
"do_sample": false,
"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, let's try to tackle this problem step by step. Hmm, so we have a weak monobasic acid. The limiting molar conductivity at 298 K is given as 4 × 10² S·cm²·mol⁻¹. The question is asking for the degree of dissociation α of the acid in solution, given that the molar conductivity is y × 10² S·cm²·mol⁻¹. Also, w... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 324 | LiveCodeBenchV5 | {
"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 some elements in the array are -1, and I can replace each -1 with either x or y once. The goal is to choose x and y such that the maximum absolute difference between adjacent elements after replacement is minimized. Hmm.
First, I need to understand how replac... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 87 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to find the number of ways to maximize the final value of c by choosing either adding a_i or taking the absolute value after adding a_i. And the answer has to be modulo 998244353.
Hmm, the problem says that the maximum possible final value is k, and we... |
[
{
"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, I need to solve this problem where I have to find the minimum total weight of a walk that visits each vertex at least once. Hmm. Let me think. So, a walk can traverse edges multiple times, and each time an edge is used, its weight is added. The goal is to find the path (or walk) that covers all vertices w... |
[
{
"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 selecting a team of 4 members from a debate club that has 6 girls and 4 boys. The team needs to include a captain, who can be any one of the 4 members. Additionally, the team must include at most one boy. The question is asking for the number of ways to select such a team, ... |
[
{
"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, let's see. I need to solve this problem where Alice and Bob are dividing a grid, and I have to compute two things: the maximum area Alice can get without any fountains, and for each fountain, the additional area she can get if she gets that fountain. Hmm.
First, let's understand the problem. The grid is ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 351 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Iris and Dora are playing a game to set the values of some nodes in a tree. The goal is to determine the maximum score Iris can achieve by choosing optimally, assuming Dora also plays optimally. The score is the number of leaves with non-zero weight after all ? are fille... |
[
{
"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... | {
"do_sample": false,
"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. There are four statements to evaluate, and I need to figure out which ones are correct. Let's go through each one individually, starting with option A.
**Option A: Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones.**
First, I need to r... |
[
{
"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... | {
"do_sample": false,
"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. The question is about which corporate structure satisfies the requirements of Alex and Tyler. Let me break down their requirements first.
1) Equal control over the company. So, the structure needs to allow both partners equal voting rights or some form of control.
2) Alex wants payments via sa... |
[
{
"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,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The question is about the three main types of buying situations in an organization as referred to by Robinson, Faris, and Wind in 1967. The options are A to J, and I need to pick the correct one.
First, I need to recall what I know about organization buying. From my studies, Robinson, Faris, a... |
[
{
"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 Python function called minKey that takes three integers num1, num2, num3 and returns their key as a four-digit number. The key is generated by taking the minimum of the i-th digits of each number after padding them with leading zeros to four digits. Then, after generating all... |
[
{
"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 figure out the average kinetic energy of air molecules at 300 K and the typical speed of nitrogen molecules in air. Let me start by recalling some basic thermodynamics and kinetic theory concepts.
First, the average kinetic energy of molecules in a gas is given by the formula (3/2)kT, where ... |
[
{
"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... | {
"do_sample": false,
"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... | <think>
Okay, let's try to work through this question step by step. The question is about hypermutator strains of Pseudomonas aeruginosa and how their increased mutagenesis rate affects the frequency of mucoid variants, specifically related to mutations in the mucA gene. The answer choices are A to E, and I need to fig... |
[
{
"content": "Problem: Find the greatest common divisor of $3339$, $2961$, and $1491$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 89 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <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 think about how to approach this.
I remember that to find the GCD of two numbers, the Euclidean algorithm is really effe... |
[
{
"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,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Alice and Bob are taking turns cutting parts of a grid and collecting points based on the chips in the cut sections. The challenge is to compute the total points each of them earns based on the sequence of moves they make.
First, let's understand the problem step by ste... |
[
{
"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:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_rationale": null,
"reference_solution": "",
"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 this.
First, the equation is quadratic in both x and y. Maybe I can f... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 116 | CodeElo | {
"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 to find the maximum number of operations possible. Each operation involves selecting an element a[i] = i, then removing a[i] and a[i+1]. The challenge is to maximize the number of such operations. Hmm.
So the key here is to model the problem in a way t... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N cities in a certain country.\nYou will travel from your office in city 1 to a destination in city N, via z... | {
"do_sample": false,
"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, let's see. I need to find the minimum time to travel from city 1 to city N, using either company car or train. The transitions are allowed only from car to train in a city. So the problem is about finding the shortest path considering these constraints.
Hmm. So the cities are nodes, and each edge has two... |
[
{
"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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} | <think>
Okay, let's see. The problem is asking for the energy of the Relativistic Heavy Ion Collider (RHIC) such that the speed of nucleus X, which is Li with 3 neutrons, is 0.96c. The options are given, and I need to figure out which one is correct. Hmm, let's start by understanding what's being asked here.
First, I ... |
[
{
"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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"seed": 0,
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} | 0 | 195 | MATH500 | {
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} | <think>
Okay, so I have this problem here where I need to find p(0) + p(4) for a monic polynomial of degree 4. Three of the roots are given as 1, 2, and 3. Since it's a monic polynomial, I know that the leading coefficient is 1. Let me think about how to approach this.
First, since it's a monic quartic polynomial and ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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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"max_new_tokens": 32768,
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} | 1 | 25 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where we have N+2 cells, with N stones initially in cells 1 to N, and two empty cells at the end. The goal is to rearrange the stones to match the desired T string. Each operation allows me to take two adjacent stones and move them into the two empty cells, maintain... |
[
{
"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,
"temperature": 0.7
} | 2 | 363 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where given a sequence A, I have to find the maximum possible size of a Pyramid Sequence that can be formed by performing certain operations. The allowed operations are: decrease a term by 1, or remove the first or last element. The Pyramid Sequence has a specific structure: i... |
[
{
"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,
"temperature": 0.7
} | 5 | 28 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-28",
"reference_rationale": null,
"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. The edges AB and CD are both √41, AC and BD are both √80, and BC and AD are both √89. The question is asking for the distance from a point I inside the tetrahedron to all four faces, which is the inradius of the tetrahedron. Once ... |
[
{
"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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"problem_id": "",
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} | <think>
Okay, I need to solve this problem where I have to maximize the MEX of an array after performing any number of operations. Each operation allows me to choose an index and add x to that element. The goal is to find the maximum possible MEX after optimally choosing how to perform these operations.
Hmm, let's sta... |
[
{
"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",
"reference_rationale": null,
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"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where a parabola is rotated 60 degrees counterclockwise around the origin, and I have to find the y-coordinate of the unique intersection point in the fourth quadrant between the original parabola and its image. The answer is in the form (a - sqrt(b))/c, and then I need to ... |
[
{
"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,
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to figure out how many possible values of c there are such that the sum of the first n terms of an arithmetic progression starting with c and common difference 2 is equal to half the sum of the first n terms of a geometric progression starting with c and common ratio 2. Let me break this down st... |
[
{
"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,
"temperature": 0.7
} | 0 | 83 | CodeForces | {
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"problem_id": "",
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} | <think>
Okay, I need to solve this problem where I have to count the number of nondegenerate right triangles formed by three distinct points. Let's think about how to approach this.
First, the problem says that a right triangle is nondegenerate if the three points form a triangle, which means they can't be colinear. 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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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 163 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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"subject": null,
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} | <think>
Okay, let's see. The problem is to compute these binomial coefficients using the wrong formula that akshiM wrote. Wait, the correct formula for binomial coefficients is C(n, k) = n! / (k! * (n - k)!). But here, the wrong formula is something else? Wait, the problem says that the code should compute the coeffici... |
[
{
"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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"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this programming problem. The problem is about calculating the sum of mex values for certain triplets (i,j,k) in a sequence. The condition for including a triplet is that the substring S_i S_j S_k is "MEX".
First, I need to understand what the mex function does. The mex of thr... |
[
{
"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,
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, let's see. I need to find the value of x, which is the mass of tin (Sn) that reacts with HCl to form a salt. Then, this salt reacts with y grams of nitrobenzene (which I think is a key here) to produce 1.29 grams of an organic salt. Hmm. The problem mentions that the reaction is quantitative, so all the s... |
[
{
"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 | {
"expected_answer": "",
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} | <think>
Okay, I need to solve this problem where I have to count the number of connected sensor regions. The sensors are connected if they are adjacent horizontally, vertically, or diagonally. So, the problem is essentially asking for the number of such connected regions. Hmm, right. So, this sounds like a union-find (... |
[
{
"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,
"type": null
} | <think>
Okay, I need to solve this problem where I have to maximize the sum of two GCDs of arrays a and b after swapping elements, but each swap costs some coins. The coins spent must be ≤ d. And for multiple d values, output the maximum possible sum for each.
First, let's understand the problem. We can swap a_i and b... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Discuss thetonotopicorganization of our auditory system.\nOptions: A. Tonotopic organization describes the layout of taste buds on the tongue and the... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 229 | 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 correct answer to the question about tonotopic organization in the auditory system. Let's start by breaking down the question. The problem is asking me to discuss the tonotopic organization of the auditory system, and then choose the correct option from the given choices.
Fir... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: 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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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 167 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
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! The force between two point charges is given by Coulomb's law. The formula is F = k * |q1*q2| / r², where k is the Coulomb constant, q1 and q2 are the magnitudes 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}\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, let's try to tackle this problem. Hmm, the question is about finding the force per unit area on the x = d plane due to a time-varying magnetic field perturbation. The setup involves a surface current in the x=0 plane, with different regions: a region of infinite permeability (μ → ∞) for x < 0, a supercond... |
[
{
"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 | 30 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the minimum number of steps to paint all vertices blue using two chess pieces, PA and PB. Let's try to understand the problem step by step.
So the problem says that initially, all vertices are white. Then PA starts at a and PB starts at b. In each step, f... |
[
{
"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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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 128 | HLESubset | {
"expected_answer": "B",
"problem_id": "670285bc39fbddbbfdaffdfe",
"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, let's tackle this question. The question is asking what kind of conceptual metaphor is expressed by "my love for humanity," based on the framework from "Conceptual Metaphor in Everyday Language." The answer choices are A through E, with A being Conceptual metaphor, B Physical metaphor, C Orientational met... |
[
{
"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,
"temperature": 0.7
} | 2 | 67 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if a sequence can be completed based on the given rules. Let me start by understanding the problem thoroughly.
So the problem says that the original sequence a has some elements replaced with -1. For each consecutive pair in the original sequence, on... |
[
{
"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 | 92 | CodeElo | {
"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 to count the number of minimal-length attack plans to capture all towers. Hmm. The problem is a bit complex, so I need to break it down step by step.
First, the problem statement says that each operation allows me to capture a new tower R along with so... |
[
{
"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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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 51 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where a truck has two fuel tanks, and I have to calculate the maximum distance it can travel. Let's see the problem statement again. The main tank has 'mainTank' liters, and the additional tank has 'additionalTank' liters. The truck uses fuel at 10 km per liter. The key thing ... |
[
{
"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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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 81 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, let's see. I need to find the sum of the number of lone pairs on the central atom for four different species: [TeBr6]²⁻, [BrF2]+, SNF3, and [XeF3]⁻. Hmm. Alright, so first, I remember that to determine the number of lone pairs on the central atom, I need to figure out the Lewis structure of each molecule ... |
[
{
"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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"max_new_tokens": 32768,
"seed": 7,
"temperature": 0.7
} | 7 | 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 start by understanding the problem step by step.
First, the torus T is formed by rotating a circle with radius 3 around an axis that's in the plane of the circle and is 6 units away from the center of the circle. So, the torus has a majo... |
[
{
"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}, \\... | {
"do_sample": false,
"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 find the value of \( |\vec{a} \times \vec{b}|^2 \) given the conditions in the problem. Let me start by understanding the problem step by step.
First, let's parse the given information. We have a triangle \( PQR \). The vectors are defined as follows:
- \( \vec{a} = \overrightarrow{QR} \)
- ... |
[
{
"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... | <think>
Okay, so I need to figure out the next best step if the stapler gets stuck on the base of the appendix during a laparoscopic appendectomy. Let me start by understanding the problem. The surgeon fired the stapler across the base, the staples went off, and now the stapler is stuck. They've tried all troubleshooti... |
[
{
"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))). Hmm, let's start by understanding what these functions look like.
First, let me parse the functions f and g. The problem defines f(x) = ||x| - 1/2| and g(x) = ||x| - 1/4|. Wait, those are abs... |
[
{
"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, I need to solve this problem where given two strings S and T of the same length, I have to find the minimal-length array X such that after each step, the string is changed by replacing one character and added to X. And among those minimal-length arrays, choose the lexicographically smallest one.
Hmm, let... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 105 | LiveCodeBenchV5 | {
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} | <think>
Okay, let's see. I need to write a Python function that determines if the mayoral election is already decided based on the current votes and the remaining possible votes. Hmm.
The problem says that the outcome is decided if even after all remaining votes are added to the current counts, one candidate still has... |
[
{
"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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} | <think>
Okay, I need to solve this problem where I have to find the lex smallest array possible by swapping elements that have an XOR less than 4. Let's think through this step by step.
First, let's understand the problem. The key point is that two elements can be swapped if their XOR is <4. The goal is to arrange the... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Consider the lines $\\mathrm{L}_1$ and $\\mathrm{L}_2$ defined... | {
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"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's see. I need to find the value of λ² such that the distance between R' and S' is √270. Hmm, the problem involves loci, perpendicular bisectors, and distances. Let me break it down step by step.
First, let me understand the given lines L₁ and L₂. The equations are:
L₁: x√2 + y - 1 = 0
L₂: x√2 - y ... |
[
{
"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\... | {
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"seed": 1,
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} | 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, let's tackle this question about the standard Japanese pitch accent pattern for the word 「弟」. Hmm, I remember that pitch accent in Japanese is really important for meaning. So first, I need to recall what the different patterns are and how they apply to this word.
The answer choices are Heiban, Atamadaka... |
[
{
"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... | {
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} | 1 | 98 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, let's see. I need to find the minimum number of operations to collect elements 1 through k. The operation is to remove the last element of the array and add it to my collection. So the problem is about choosing which elements to take from the end of the array in the optimal order.
Hmm, the key here is th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given eight integers S_1,S_2,\\dots, and S_8,\r\nprint Yes if they satisfy all of the following three conditions, and ... | {
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"seed": 1,
"temperature": 0.7
} | 1 | 227 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, let's see. I need to write a Python function that reads eight integers from stdin and checks if they meet three conditions. The function should print "Yes" or "No" based on whether all conditions are satisfied. Hmm.
First, let's break down the three conditions.
Condition 1: The sequence must be monoton... |
[
{
"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... | {
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"seed": 0,
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} | 0 | 345 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, I need to solve this problem where Bob has to break n locks with certain energy requirements. The time taken depends on how the sword's energy builds up over time. Let's think through how to approach this.
First, let's understand the process. Each lock requires a certain amount of energy. The sword's ene... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 325 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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} | <think>
Okay, let's try to figure out how to solve this problem. So the task is to minimize the disturbance, which is the number of adjacent pairs where the topics are the same. We can perform any number of swaps where we swap the i-th element with the (n-i+1)-th element. The goal is to find the minimal possible distur... |
[
{
"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... | {
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"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. The problem mentions that there are three rectangles shown in the diagram, but I don't have the diagram. Hmm, but maybe I... |
[
{
"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 the equation p₀ - p = (7/(2N)) ρ v_t². The problem is about a train moving through a tunnel, and the pressure difference between the front and the region between the train's sides and the tunnel walls is given in terms of N. Let me start by understanding all the c... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 128 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, let's see. So the problem is about calculating F(i) for each i from 1 to n. F(i) is the number of black integers reachable from i. And from the description, it seems that the reachable numbers form a cycle in the permutation. Because when you apply the permutation multiple times, you end up in a cycle. So... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 319 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
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} | <think>
Okay, let's see. I need to solve this problem where I have to count the number of pairs (i,j) such that when you remove the elements at i and j, the sum of the remaining elements is between x and y, inclusive. Hmm. So the sum of the array minus a_i and a_j should be >=x and <=y.
Wait, the problem says the sum ... |
[
{
"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, so I need to compute the value of this integral:
∫₀^∞ [ (2p - e^{-p/4} + 2p⁷ + 2pe^{-p} + e^{p/4}) / √( max_{S ∈ SPD₇ : [sum_{i=1}^7 λ_i²(f₂(S))] ≤ p²} 4f₁(S) ) ] dp
Hmm, this looks really complicated. Let me try to break it down step by step.
First, let's understand the components of the integrand. Th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array 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, I need to solve this problem where I have to maximize the points by choosing enemies to either gain energy or points. Let me think through the problem step by step.
So the problem says that each enemy has a certain energy value. The initial currentEnergy is given. The operations are:
Either choose an un... |
[
{
"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[/... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 389 | MATH500 | {
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} | <think>
Okay, so I have this problem here about triangle RST. The Asymptote code shows a right triangle with a right angle at R. Wait, let me check that. The Asymptote code says "draw(rightanglemark(R,S,T,10));", so the right angle is at R. So triangle RST is a right-angled triangle with right angle at R. The hypotenus... |
[
{
"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,
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} | <think>
Okay, 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 here is one that has at least m distinct elements. Hmm. Let's think about how to approach this.
So first, the problem is about sliding windows, right? Because we need to c... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence of N positive integers A = (A_1, A_2, \\dots ,A_N), where each element is at least 2. Anna an... | {
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"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, let's try to figure out this problem. So, the task is to determine whether Anna or Bruno wins the game when both play optimally. The game is about taking turns to replace an element in the array with one of its proper divisors. The player who can't make a move loses.
Hmm. Let's start by understanding the... |
[
{
"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... | {
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"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. So, the patient is a 64-year-old woman with a bunch of medical issues. The main complaints are lesions in her inframammary folds, which are the folds under the breasts. The physician describes large bullae (which are fluid-filled blisters), erythematous skin (rednes... |
[
{
"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, let's see. I need to find the vapor pressure of pure liquid B. The problem says that liquids A and B form an ideal solution at 25°C. There are two solutions with mole fractions of A being 0.25 and 0.50, and their total vapor pressures are 0.3 bar and 0.4 bar respectively. Hmm, so ideal solution means that... |
[
{
"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... | {
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"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, so I need to figure out what the consequence is of having this algorithm A for DomSet that uses an oracle for #IndSet. The options are A to E. Let me start by recalling what each problem is and what the algorithm A's properties imply.
First, Dominating Set (DomSet) is a problem where, given a graph G and... |
[
{
"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 try to figure out this problem step by step. So, the question is about two reactions performed by an organic chemist, and then combining the products for HPLC analysis. The key is to determine how many peaks the chemist would observe in both the chiral HPLC and the normal-phase HPLC columns. The opt... |
[
{
"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... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 326 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the minimum possible sum of an array after performing certain operations a limited number of times. Let's see. The operations are dividing by 2 (rounded up) and subtracting k. Both operations can be applied to any index, but each at most a certain number o... |
[
{
"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]\... | {
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"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, I need to figure out which sequence of commands transforms the initial array into the given final array and identify the hidden symbols. Let's break this down step by step.
First, let's understand the problem. The initial array is a 2x2 matrix. Each command applies a transformation that affects the array... |
[
{
"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, let's try to figure out how to solve this problem. So the task is to find the minimum number of operations (either dyeing a 2x2 subgrid white or dyeing a whole row white) to turn all cells in the grid white. Hmm. Let's start by understanding the problem thoroughly.
The grid is n x n. For each row i, 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 try to figure out this problem step by step. The question is about the internal energy and speed of sound in an ideal gas at thermodynamic equilibrium. The options compare the speed of sound (vn) and internal energy (Un) for different numbers of degrees of freedom (n). We need to determine which of ... |
[
{
"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, I need to solve this programming problem. Let's read the problem carefully.
The problem is about N people on a road. Each person starts at a unique position X_i, sorted from west to east. The tasks are Q queries where each query is: move the T_i-th person to G_i. For each query, we need to compute the mi... |
[
{
"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, I need to solve this problem where I have to find the longest common subsegment between two XOR sequences. Let's think about how to approach this.
First, the problem says that for each test case, given x and y, find the maximum m where there exists some i and j such that a_i, a_{i+1}, ..., a_{i+m-1} are ... |
[
{
"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's try to figure out this problem. The question is about which assumptions imply the "impulse" approximation in nuclear calculations. The options are combinations of four statements, and we need to pick the correct combination. Let's break down each option and see.
First, I need to recall what the imp... |
[
{
"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, let's try to figure out how to solve this problem. So the problem is about determining after each query whether it's possible to sort the permutation using certain swap operations based on the string s.
First, I need to understand the operations allowed here. The operations are swapping adjacent element... |
[
{
"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, I need to solve this problem where I have to find the number of possible infection sequences given the positions of infected children. The key points are that once a child is infected, it can spread to adjacent uninfected children, but each second only one new child can get infected. The answer should be ... |
[
{
"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, let's see. So the problem is about maximizing the score by performing k operations on elements of array a. Each operation lets me choose an index i, add a_i to the score, then set a_i to max(0, a_i - b_i). The goal is to find the maximum possible score after exactly k operations.
Hmm, first, I need to th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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 finding the maximum product possible by adding 1 to exactly one digit in the array. The function needs to read from stdin and output the result for each test case.
Hmm, the input starts with t test cases. For each test case, we have n digits, and we can choose any one of t... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 148 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to compute the alternating sum of a sequence of integers. Let's think about how to approach this.
The problem says that the signs alternate starting with a plus. So for the first element, it's +, then - for the next, + for the third, and so on. So the sign depend... |
[
{
"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, I need to solve this problem where I have to generate a string of vowels such that the number of palindrome subsequences is minimized. Let's think about how to approach this.
First, the problem says that the string must consist of vowels only (a, e, i, o, u). Then, we need to find a string of length n 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: 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 about a cube. Let me read it again carefully to make sure I understand all the parts.
We have a cube Q with vertices in 3D space where each coordinate is either 0 or 1. So, the cube has 8 vertices, right? Then, F is the set of all twelve lines that are the face di... |
[
{
"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. Let me start by understanding the problem step by step.
First, the function f(x) is defined piecewise on the interval [0,1]. It has four different linear segments, each with their own equati... |
[
{
"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 to find a sequence of operations to make a cyclic array balanced, or determine it's impossible. The operations are a bit tricky, but the editorial gives some insight. Let me break this down step by step.
First, the problem says that each operation incr... |
[
{
"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. The question is asking how many boxes have neither pens nor pencils. Hmm. Let me try to figure this out step by step.
First, let's parse the information given. There are five boxes with pencils. Let me note 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 | 224 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where we have a dynamic set that supports insertions, deletions, and k-load queries. The k-load is the smallest d such that the interval [d, d+k-1] is not fully covered by the set. So, for each query of type '?', I have to find the minimal d where there's a gap of at least k c... |
[
{
"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's see. I need to write a Python function that takes a list of distinct integers and distributes them into two arrays based on certain conditions. The first two elements go to arr1 and arr2 respectively. Then for each subsequent element, if the last element of arr1 is greater than arr2's, append to arr... |
[
{
"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 determine which of the options (A) through (D) are correct. The function f is defined on (0, ∞) and is differentiable. It satisfies the differential equation f'(x) = 2 - [f(x)/x] for all x > 0, and it's given that f(1) ≠ 1. The options involve limits and inequal... |
[
{
"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 start by understanding the problem statement carefully.
We have a torus T formed by revolving a circle with radius 3 around an axis in its plane that's 6 units away from the center of the circle. So, the major radius of the torus (the dis... |
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