context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 1 147k |
|---|---|---|---|---|---|---|
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In a specific region of the sky, astronomers have observed that the number of stars varies with parallax as 1/plx^5. How does the number of stars in that region of the s... | {
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} | 1 | 192 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | Let's think about this problem step by step. The problem states that the number of stars varies with parallax as 1/plx^5. We need to find how the number of stars changes with distance (per unit range of distance, r).
First, I need to recall the relationship between parallax and distance. Parallax is inversely proport... |
[
{
"content": "Problem: Every morning Aya goes for a $9$ -kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk... | {
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"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 15 | AIME24 | {
"expected_answer": "204",
"problem_id": "aime24-15",
"reference_solution": "$\\frac{9}{s} + t = 4$ in hours and $\\frac{9}{s+2} + t = 2.4$ in hours. Subtracting the second equation from the first, we get, $\\frac{9}{s} - \\frac{9}{s+2} = 1.6$ Multiplying by $(s)(s+2)$ , we get $9s+18-9s=18=1.6s^{2} + 3.2s$ ... | Let's break down the problem step by step. The goal is to find the time Aya takes when walking at a speed of \( s + \frac{1}{2} \) kilometers per hour, including the time she spends in the coffee shop.
First, we need to determine the original time spent walking when she walks at speed \( s \). The total time given is ... |
[
{
"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"
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] | {
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"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 26 | AIME24 | {
"expected_answer": "385",
"problem_id": "aime24-26",
"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 $1$ ). Thus by precariously dr... | To solve the problem, we need to find the number of intersections between the graphs of \( y = 4g(f(\sin(2\pi x))) \) and \( x = 4g(f(\cos(3\pi y))) \). Let's start by analyzing the functions \( f \) and \( g \).
First, let's understand \( f(x) = \left| \left| x \right| - \frac{1}{2} \right| \). This function maps any... |
[
{
"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 | 135 | CodeForces | {
"expected_answer": "",
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} | <think>
Okay, let's tackle this problem. Hmm. The problem says that we have an array where all elements are either 1 or -1 except for at most one element. Our task is to find all possible sums of subarrays (including empty) and output them sorted. Each sum should appear only once even if multiple subarrays give it.
Wa... |
[
{
"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 | 316 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Okay, let's see. The problem is about Monocarp and Stereocarp practicing problems each day. Monocarp can choose any day to practice, but Stereocarp has to practice the next day if he did on a previous day. The goal is to maximize the difference between Monocarp's total and Stereocarp's total.
Hmm. So for each day exce... |
[
{
"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 | 268 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, I need to solve this problem where Robin wants to know if the Major Oak has an even number of leaves in year n. Let's see the problem statement again.
So, the tree grows i^i leaves in the i-th year. Each leaf stays for k years. So, leaves from year i are present in years i to i + k - 1. We need to count ... |
[
{
"content": "Problem: Denali and Nate work for a dog walking business and are paid for each dog they walk. Denali is responsible for $16$ dogs and Nate is responsible for $12$ dogs. Under the company's new policy, they will be assigned or unassigned new dogs in groups of $x$ dogs. The ratio of Denali's pay to ... | {
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"max_new_tokens": 32768,
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} | 0 | 22 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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} | Let's start by defining the variables and understanding the problem. Denali's original number of dogs is 16, and Nate's is 12. The new policy changes the number of dogs in groups of x. We need to find x such that the ratio of Denali's pay to Nate's pay remains the same under two different scenarios: one where Denali ge... |
[
{
"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 positive integers A=(A_1,A_2,\\dots,A_N) of length N and a positive integer K.\nFind the s... | {
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} | 2 | 411 | LiveCodeBench | {
"expected_answer": "",
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} | <think>
Okay, let's see. I need to solve this problem where I have to find the sum of all numbers from 1 to K that are not present in the given array A. The input is N, K, followed by the array A. The constraints are tight, especially since K can be up to 2e9, which means we can't just iterate from 1 to K and check eac... |
[
{
"content": "Problem: If $A$ and $B$ are vertices of a polyhedron, define the distance $d(A,B)$ to be the minimum number of edges of the polyhedron one must traverse in order to connect $A$ and $B$. For example, if $\\overline{AB}$ is an edge of the polyhedron, then $d(A, B) = 1$, but if $\\overline{AC}$ and $... | {
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"seed": 8,
"temperature": 0.7
} | 8 | 11 | AMC23 | {
"expected_answer": "29",
"problem_id": "13",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the probability that the distance from vertex \( Q \) to \( R \) is greater than the distance from \( R \) to \( S \) in a regular icosahedron. The answer should be in the form \(\frac{m}{n}\) where \( m \) and \( n \) are relatively prime, and we provide \( m + n \).
First,... |
[
{
"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: According to Hume, morality is ultimately based on:\nOptions: A. cultural norms., B. social agreements., C. reason., D. personal beliefs., E. individ... | {
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} | \boxed{I} |
[
{
"content": "Problem: Find the number of ways to place a digit in each cell of a 2x3 grid so that the sum of the two numbers formed by reading left to right is $999$ , and the sum of the three numbers formed by reading top to bottom is $99$ . The grid below is an example of such an arrangement because $8+99... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 2 | AIME24 | {
"expected_answer": "45",
"problem_id": "aime24-2",
"reference_solution": "Consider this table: $\\begin{array}{|c|c|c|} \\hline a & b & c \\\\ \\hline d & e & f\\\\ \\hline \\end{array}$ We note that $c+f = 9$ , because $c+f \\leq 18$ , meaning it never achieves a unit's digit sum of $9$ otherwise. Since no... | <think>
Okay, let's tackle this problem. So, we have a 2x3 grid, and we need to place digits in each cell such that the sum of the two numbers formed left to right is 999, and the sum of the three numbers formed top to bottom is 99. Hmm, right.
First, let's understand the structure. The twox three grid has 6 cells. T... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The universe is filled with the Cosmic Microwave Background. Consider the annihilation of high energy \\gamma-rays with a photon from the CMB Radiation into electron-pos... | {
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"seed": 0,
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} | 0 | 6 | GPQADiamond | {
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} | B
</stream> |
[
{
"content": "Problem: If $\\frac{\\sqrt{2x}}{\\sqrt{3x-1}}=\\frac32$, solve for $x$. Express your answer in simplest fractional form.\nMark your solution with \\boxed\nAnswer:",
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] | {
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} | 0 | 305 | MATH500 | {
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} | $\frac{\sqrt{2x}}{\sqrt{3x-1}} = \frac{3}{2}$
Square both sides to eliminate the square roots:
$\left(\frac{\sqrt{2x}}{\sqrt{3x-1}}\right)^2 = \left(\frac{3}{2}\right)^2$
This simplifies to:
$\frac{2x}{3x-1} = \frac{9}{4}$
Cross multiply to get:
$4 * 2x = 9 * (3x - 1)$
Which is:
$8x = 27x - 9$
Bring all terms ... |
[
{
"content": "Problem: Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only $\\frac{1}{3}$ full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into t... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | AMC23 | {
"expected_answer": "7",
"problem_id": "25",
"reference_solution": "",
"subject": null,
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} | Let's start by determining the total amount of orange juice Mrs. Jones has. She fills the first three glasses completely. Let's denote the capacity of each glass as \( C \). So, the total juice is \( 3C \). However, the fourth glass is only \( \frac{1}{3} \) full, which means she has poured \( \frac{1}{3}C \) into it. ... |
[
{
"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: Among the following, the correct statement(s) is(are)\n[A] $\\mathrm{A... | {
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} | 0 | 106 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Okay, let's tackle this problem step by step. The problem is about understanding the bonding and acidity of certain compounds. Let's look at each option one by one.
First, the problem mentions dimeric structures and three-centre two-electron bonds. So, I need to recall what those are. Three-centre two-electron bonds a... |
[
{
"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 product of all positive real values of $x$ satisfying the equation\n\\[\nx^{\\left(16\\left(\\log ... | {
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} | 1 | 415 | JEEBench | {
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"problem_id": "4",
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"subject": "math",
"type": "Integer"
} | To solve the equation \(x^{\left(16\left(\log _{5} x\right)^{3}-68 \log _{5} x\right)}=5^{-16}\), we start by taking the logarithm base 5 of both sides. This will help us simplify the equation.
Let \(y = \log_5 x\). Then the equation becomes:
\[x^{\left(16y^3 - 68y\right)} = 5^{-16}.\]
Since \(x = 5^y\), substituting ... |
[
{
"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: Steven Moore purchased a new car for $3,462.20, including taxes and all other charges. He wishes to pay for it in 35 months. Find his monthly payment... | {
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} | 0 | 329 | MMLUPro | {
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} | <think>
Okay, I need to solve this problem where Steven Moore is buying a car for $3,462.20 and wants to pay it off in 35 months. I have to calculate his monthly payment. Let's think about the possible approach here.
Hmm, the question is asking for the monthly payment, so it's a division problem. The total cost divide... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the value of\n\\[\n\\sec ^{-1}\\left(\\frac{1}{4} \\su... | {
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"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 241 | JEEBench | {
"expected_answer": "0",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the given problem, we need to evaluate the expression:
\[
\sec^{-1}\left( \frac{1}{4} \sum_{k=0}^{10} \sec \left( \frac{7\pi}{12} + \frac{k\pi}{2} \right) \sec \left( \frac{7\pi}{12} + \frac{(k+1)\pi}{2} \right) \right)
\]
and find its value within the interval \([- \frac{\pi}{4}, \frac{3\pi}{4}]\).
### Ste... |
[
{
"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: Lizette and her family watch the sunset over the ocean. While walking home in the increasing darkness, Lizette notices that she can no longer disting... | {
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} | B
Lizette is struggling to see colors in the dimming light. The correct explanation here is related to the difference in light sensitivity between cones and rods in the retina. Cones are specialized for color vision and require more light to function properly, while rods are better for black-and-white vision and can w... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 106 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's try to figure out this problem. So, the task is to find the minimum number of operations to make an array beautiful by shuffling and adding k multiple times. Hmm.
First, what's a beautiful array? Oh right, it's symmetric. For every i, the element at position i must equal the element at position n-i... |
[
{
"content": "Problem: Let \\(b\\ge 2\\) be an integer. Call a positive integer \\(n\\) \\(b\\text-\\textit{eautiful}\\) if it has exactly two digits when expressed in base \\(b\\) and these two digits sum to \\(\\sqrt n\\). For example, \\(81\\) is \\(13\\text-\\textit{eautiful}\\) because \\(81 = \\underlin... | {
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"max_new_tokens": 32768,
"seed": 7,
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} | 7 | 13 | AIME24 | {
"expected_answer": "211",
"problem_id": "aime24-13",
"reference_solution": "We write the base- $b$ two-digit integer as $\\left( xy \\right)_b$ .\nThus, this number satisfies\n \\[ \\left( x + y \\right)^2 = b x + y \\] \nwith $x \\in \\left\\{ 1, 2, \\cdots , b-1 \\right\\}$ and $y \\in \\left\\{ 0, 1, \\... | To solve this problem, we need to determine the smallest integer \( b \geq 2 \) such that there are more than ten \( b \)-beautiful numbers. A \( b \)-beautiful number is a positive integer \( n \) that can be expressed as a two-digit number in base \( b \) where the sum of its digits equals the square root of \( n \).... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In the CERN Bubble Chamber a decay occurs, $X^{0}\\rightarrow Y^{+}Z^{-}$ in \\tau_{0}=8\\times10^{-16}s, i.e. the proper lifetime of X^{0}. What minimum resolution is n... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 68 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, let's tackle this problem. So, the problem is about observing particle decays in a bubble chamber. The question is asking for the minimum resolution needed to capture at least 30% of the decays. Hmm. Let's think about what factors influence this.
First, the decay is X^0 → Y^+ Z^-. The proper lifetime of ... |
[
{
"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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} | 2 | 143 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"type": null
} | Okay, let's see. The problem is about increasing three numbers a, b, c by at most 5 ones each, and we need to maximize their product. So, the goal is to figure out how to distribute the increments among the three numbers to get the maximum product after doing up to 5 increments.
Hmm. Let's think about possible approac... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N integers A _ 1,A _ 2,\\ldots,A _ N.\nIf their values are all equal, print Yes; otherwise, print No.\n\... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 299 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this programming problem. Let's read the problem carefully.
The task is to check if all the given N integers are equal. If they are, print "Yes"; otherwise, print "No".
Hmm, so the steps are: first, read N from input. Then read the list of N numbers. Then check if all elements in the lis... |
[
{
"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: For a steady, turbulent, constant property, two dimensional boundarylayer-type flow over a flat plate at zero angle of approach, the velocity profile... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 340 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | <think>
Okay, I need to solve this problem where I have to find the local boundary layer thickness δ as a function of x using the given velocity profile and skin friction equation. Let's see the problem statement again.
The velocity profile is u = v (y/δ)^1/7. The skin friction coefficient is C_f = 0.045 (v/ρV)^1/4. A... |
[
{
"content": "Problem: A mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row. How many distinct arrangements are possible?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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} | 0 | 269 | MATH500 | {
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"problem_id": "",
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} | To solve this problem, we need to determine the number of distinct arrangements possible for 2 indistinguishable IMO gold medals and 2 indistinguishable IPhO gold medals when placed in a row.
Let's break down the problem step by step.
1. **Identify the Total Items**: We have 4 medals in total. Among them, 2 are ide... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums of even length and there is also an empty array arr. Alice and Bob decided to play a game where in every round Ali... | {
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} | <think>
Okay, let's see. I need to solve this problem where Alice and Bob are playing a game with the array. The task is to determine the order in which elements are added to the arr array based on their moves. Hmm.
So the rules are: In each round, Alice and Bob each remove the minimum element from nums. Then Bob appe... |
[
{
"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 string moves of length n consisting only of characters 'L', 'R', and '_'. The string represents your movement on a number line starting from th... | {
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"seed": 2,
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} | 2 | 91 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about finding the furthest point from the origin after n moves, where each move can be left, right, or whatever (since '_' can be either). So, the key here is to maximize the distance by choosing the best possible directions for each step.
Hmm, the furthest distance would be ach... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: (a) What type of mirror is required to form an image, on a wall 3 m from the mirror, of the filament of a headlight lamp 10 cm in front of the mirror... | {
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} | 0 | 105 | MMLUPro | {
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} | To solve this problem, we need to determine the type of mirror and the height of the image formed by a headlight lamp placed in front of a mirror. The problem involves applying the mirror formula and magnification formula to find the solution.
### Part (a): Determining the Mirror Type
1. **Given Data**:
- Object d... |
[
{
"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 the position vectors of the points $P, Q, R$ and $S$ be $\\vec{a}=\\h... | {
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} | 0 | 488 | JEEBench | {
"expected_answer": "B",
"problem_id": "4",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to verify each of the given statements about the points P, Q, R, and S with their respective position vectors. Let's go through each option step by step.
### Option (A): Check if points P, Q, R are coplanar
Points are coplanar if the vectors formed by them are linearly dependent. For 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 a string moves of length n consisting only of characters 'L', 'R', and '_'. The string represents your movement on a number line starting from th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 91 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about finding the furthest point from the origin after n moves. The moves are given as a string, where each character can be L, R, or _. For each step, if the character is L or _, we can move left, and R or _ allows moving right. So I need to find the maximum possible distance fr... |
[
{
"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 $S$ be the reflection of a point $Q$ with respect to the plane giv... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 387 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the reflection of a point \( Q \) across a given plane and then find the relationship between the coordinates of \( Q \) and its reflection \( S \).
### Step 1: Understanding the Plane Equation
The given plane is represented by the vector equation:
\[
\vec{r} = -(t + p) \hat... |
[
{
"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 | 299 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem. Let's read through the problem statement again to make sure I understand it correctly.
The problem is about determining if a slide show can be presented under certain conditions. Each slide is presented by the front member of the line. After each slide, we can move that memb... |
[
{
"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 | 22 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find a binary string of length n such that the oneness (absolute difference between f(t) and g(t)) is minimized. Hmm. Let's understand what f and g represent.
So, f(t) is the number of non-empty subsequences consisting solely of 0s. For example, in "000", there are 3 elements, 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 258 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the expected value of the product of two elements chosen uniformly at random from an array. Then, I have to output that as a fraction modulo 1e9+7. Hmm.
First, the expected value formula. For a pair of elements a and b, the expected value is the average of all possible products.... |
[
{
"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: Experiencing intense feelings of shame and guilt upon admitting to a counselor that a family problem exists is common among traditional\nOptions: A. ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 446 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B |
[
{
"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 hot air balloon is carrying some passengers, and a few sandbags of mass $1 \\mathrm{~kg}$ each so that its t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 278 | JEEBench | {
"expected_answer": "4",
"problem_id": "4",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | $\textbf{Problem Analysis}$
Okay, let's tackle this problem. Hmm. So, the problem is about a hot air balloon and figuring out how many sandbags to throw out so that the balloon rises to a higher altitude. The key here is understanding the balance of forces acting on the balloon at equilibrium and how the air density ch... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: The bond length between any two nonmetal atoms is achieved under which of the following conditions?\nOptions: A. The point at which the repulsive for... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 224 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | D
The correct answer is D. The bond length between two nonmetal atoms is determined when the total interatomic potential energy is at its minimum. This is because at this point, the attractive forces between the atoms (due to the attraction between nuclei and electrons, and between electrons of the two atoms) are bala... |
[
{
"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: An acidified solution of $0.05 \\mathrm{M} \\mathrm{Zn}^{2+}$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 293 | JEEBench | {
"expected_answer": "0.2",
"problem_id": "36",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | ### Solution
Okay, let's see. I need to find the minimum molar concentration of H+ required to prevent ZnS precipitation. Hmm. So the problem is about the solubility equilibrium of ZnS in an acidified solution. The key here is to set up the reaction and determine the conditions under which precipitation doesn't happen.... |
[
{
"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 representing the number of houses on a number line, numbered from 0 to n - 1.\nAdditionally, you are given a 2D integer array offers... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 85 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to maximize the gold earned by selecting non-overlapping intervals of houses from the offers. Hmm. Let's think about how to approach this.
The problem resembles the classic interval selection problem where you pick non-overlapping intervals to maximize the sum... |
[
{
"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 | 240 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this Subtangle Game problem. Hmm. So the problem is about a game between Tsovak and Narek. They take turns finding elements in a matrix, and the way they choose cells affects whose turn it is next. The goal is to determine who wins if both play optimally.
Let me read the proble... |
[
{
"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 | 33 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to understand this problem. So, we need to count the number of different deterministic max-heaps created by performing exactly k add operations. Each add operation increments all nodes on the path from the root to a chosen node v by 1. The heap is deterministic if the pop operations are unique 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 two 0-indexed integer arrays nums1 and nums2 of equal length. Every second, for all indices 0 <= i < nums1.length, value of nums1[i] is increment... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 80 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out how to solve this problem. So the problem says that we have two arrays, nums1 and nums2. Every second, all elements in nums1 are incremented by their corresponding nums2 values. Then, we can choose one element each second (after the increments) and set it to zero. Our goal is to fi... |
[
{
"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 string S consisting of lowercase English letters and digits.\nS is guaranteed to end with 2023.\r\nCha... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 356 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to take a string S that ends with '2023' and change the last character to '4'. Then print the modified string. Hmm, so the input is S, which is a string that ends with 2023. The output is S with the last character replaced by 4.
Wait, so for example, if the input is 'hello2023',... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A textile dye containing an extensively conjugated pi-electrons emits light with energy of 2.3393 eV. What color of light is absorbed by the organic compound?\nOptions: ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 29 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | C |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 470 | JEEBench | {
"expected_answer": "3",
"problem_id": "25",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | $\textbf{Problem Analysis}$
Okay, I need to solve this problem where a Hydrogen-like atom with atomic number Z emits photons when electrons transition from n=4 to n=3. These photons are then used in a photoelectric effect experiment on a metal. The maximum kinetic energy of the photoelectrons is given as 1.95 eV. The p... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Large clouds of neutral hydrogen in deep space absorb the light from background quasars at Lyman alpha wavelength ~1216 Angstrom. Estimate the lower limit on the redshif... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 129 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B) 1.2
The Lyman-alpha line at 1216 Angstroms (Å) is a critical feature in studying distant objects. The problem asks for the lower limit on the redshift \( z \) such that this line can be detected with optical ground-based telescopes.
Redshift is a measure of how much the wavelength of light is stretched due to 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 | 327 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is to find the minimum number of swaps needed to make a permutation simple. A simple permutation is one where every element either is in its original position or is part of a pair. So, for each cycle in the permutation, we need to split it into cycles of size 1 or 2.
First, I need... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 54 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about rearranging the columns so that their inscriptions are in non-decreasing order using the minimum number of moves. Each move allows us to transfer one inscription between two columns that differ by exactly one. So, the challenge is to find a sequence of such moves that sorts... |
[
{
"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 | 301 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm. So the problem is about finding the optimal way to place servers in up to k houses so that the total latency for all p houses that need internet is minimized. And we have to do this for each k from 1 to n.
First, I need to understand the problem thoroughly. The key points ... |
[
{
"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 | 317 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about Monocarp walking on a journey where he alternates between three different distances each day. The question is to find the day when his total distance is at least n kilometers. Hmm.
So the pattern is a, b, c, a, b, c, etc. So every three days, he covers a + b + c kilometers... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed 2D integer array nums. Initially, your score is 0. Perform the following operations until the matrix becomes empty:\n\nFrom each row ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 10 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about calculating a score by removing the largest numbers from each row repeatedly. Hmm. So, in each step, we take the largest number from each row, collect all those numbers, find the maximum among them, add that to the score, and then remove those elements from the rows. Wait, ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums.\nReturn the maximum value over all triplets of indices (i, j, k) such that i < j < k. If all such triplets have a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 115 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the maximum value from all possible triplets (i, j, k) where i < j < k. The value is calculated as (nums[i] - nums[j]) * nums[k]. Hmm. Let's think about how to approach this.
First, the problem says that for every possible triplet that's ordered, we need ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array nums and an integer k.\nReturn an integer that denotes the sum of elements in nums whose corresponding indices have exa... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 106 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to compute the sum of elements in a list based on the number of set bits in their indices. Let me read the problem again carefully.
So the input is a list of integers nums and an integer k. The task is to find all indices in nums where the binary representation o... |
[
{
"content": "Problem: Twelve 1 by 1 squares form a rectangle, as shown. What is the total area of the shaded region? [asy]\nsize(4cm);defaultpen(linewidth(0.75));\n\n// Filled portions\nfill((0, 4)--(0, 0)--(2, 0)--cycle, gray(0.75));\nfill((0, 4)--(3, 4)--(3, 0)--cycle, gray(0.75));\n\n// grid\nint j;\nfor (j... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 210 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem of finding the total area of the shaded region in the given rectangle, we will follow a step-by-step approach. The problem states that twelve 1 by 1 squares form a rectangle, and we need to determine the area of the shaded regions.
First, let's visualize the problem. The rectangle is formed by 12 ... |
[
{
"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: Consider a pyramid $O P Q R S$ located in the first octant $(x \\geq 0... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 29 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "42",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given pyramid and determine which of the provided statements are correct. Let's proceed step by step.
### Step 1: Understanding the Pyramid Structure
The pyramid \(O P Q R S\) has its base \(O P Q R\) as a square in the first octant. The edges \(O P\) and \(O R\) lie along... |
[
{
"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 | 118 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about permutations and constructing a graph based on certain rules. The goal is to find the maximum possible diameter of a connected graph or return -1 if no connected graph is possible.
First, I need to understand the problem thoroughly. Let's break down t... |
[
{
"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: Each of the following options contains a set of four molecules. Identi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 194 | JEEBench | {
"expected_answer": "BD",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which molecules in each option possess a permanent dipole moment at room temperature. A permanent dipole moment arises when there is an uneven distribution of electrons in a molecule, typically due to differences in electronegativity between atoms or molecular geometry.
### ... |
[
{
"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 2 integer arrays nums1 and nums2 of lengths n and m respectively. You are also given a positive integer k.\nA pair (i, j) is called good if nums1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 504 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to find the number of good pairs between two arrays based on certain conditions. Hmm, the problem says a pair (i,j) is good if nums1[i] is divisible by (nums2[j] multiplied by k). And I have to return the total count of such pairs.
So first, 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: Among $\\mathrm{B}_{2} \\mathrm{H}_{6}, \\mathrm{~B}_{3} \\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 197 | JEEBench | {
"expected_answer": "4",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | Okay, let's tackle this problem. The task is to determine how many molecules from the given list contain a covalent bond between two atoms of the same kind. Hmm, right. So first, I need to parse each molecule's formula and check if any two atoms in that molecule are the same and form a covalent bond. But wait, covalent... |
[
{
"content": "Problem: Let $\\omega\\neq 1$ be a 13th root of unity. Find the remainder when\n \\[\\prod_{k=0}^{12}(2-2\\omega^k+\\omega^{2k})\\] \nis divided by 1000.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 12 | AIME24 | {
"expected_answer": "321",
"problem_id": "aime24-12",
"reference_solution": "\\[\\prod_{k=0}^{12} \\left(2- 2\\omega^k + \\omega^{2k}\\right) = \\prod_{k=0}^{12} \\left((1 - \\omega^k)^2 + 1\\right) = \\prod_{k=0}^{12} \\left((1 + i) - \\omega^k)((1 - i) - \\omega^k\\right)\\] Now, we consider the polynomial $x... | <think>
Okay, let's tackle this problem. So, we need to find the remainder when the product \(\prod_{k=0}^{12}(2 - 2\omega^k + \omega^{2k})\) is divided by 1000. Here, \(\omega\) is a 13th root of unity, which means \(\omega^{13} = 1\) and \(\omega \neq 1\).
First, let's understand what the terms in the product look ... |
[
{
"content": "Problem: The circle $x^2 + y^2 = 2$ and the parabola $y^2 = 8x$ have two common tangents, forming four points of tangency. Find the area of the quadrilateral formed by the four points of tangency.\n\n[asy]\nunitsize(0.8 cm);\n\nreal upperparab (real x) {\n return (sqrt(8*x));\n}\n\nreal lowerpar... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 445 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to find the area of the quadrilateral formed by the four points of tangency where the circle \(x^2 + y^2 = 2\) and the parabola \(y^2 = 8x\) intersect their common tangents.
### Step 1: Find the Equations of the Common Tangents
The circle \(x^2 + y^2 = 2\) has its center at the origin \((... |
[
{
"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 | 87 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I've got this programming problem to solve. Let's read through it carefully. The problem is about calculating the sum of f(b) for all subarrays within a given range [l, r]. The function f(b) is the minimum number of operations needed to make a consecutive subarray of length at least k in b. Each operat... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array mountain. Your task is to find all the peaks in the mountain array.\nReturn an array that consists of indices of peaks in the g... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 144 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find all the peaks in a mountain array. Let's see, the problem says a peak is an element that's strictly greater than its neighbors. And the first and last elements can't be peaks. So the steps I need to take are:
First, I need to iterate through each element ... |
[
{
"content": "Problem: Let $a,$ $b,$ and $c$ be distinct real numbers. Find the degree of the polynomial\n\\[p(x) = \\frac{(x - b)(x - c)}{(a - b)(a - c)} + \\frac{(x - a)(x - c)}{(b - a)(b - c)} + \\frac{(x - a)(x - b)}{(c - a)(c - b)}.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 317 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the degree of the polynomial \( p(x) \), we need to analyze each term individually and then sum their degrees, considering possible reductions due to cancellation of terms.
The given polynomial is:
\[
p(x) = \frac{(x - b)(x - c)}{(a - b)(a - c)} + \frac{(x - a)(x - c)}{(b - a)(b - c)} + \frac{(x - a)(x - ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a positive integer N.\r\nIf there are integers x and y such that N=2^x3^y, print Yes; otherwise, print N... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 300 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to determine if a given integer N can be expressed as 2^x multiplied by 3^y, where x and y are non-negative integers. Let's think about how to approach this.
First, the problem states that N must be a product of powers of 2 and 3. So, any other prime factors besi... |
[
{
"content": "Problem: How many positive perfect squares less than $2023$ are divisible by $5$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 16 | AMC23 | {
"expected_answer": "8",
"problem_id": "18",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem of finding how many positive perfect squares less than 2023 are divisible by 5, we can follow these steps:
1. **Identify the form of the numbers**: A perfect square divisible by 5 must be a multiple of 25. Because if a square is divisible by 5, then the number being squared must be divisible by 5.... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: For any positive integer $n$, let $S_{n}:(0, \\infty) \\rightarrow \\m... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 338 | JEEBench | {
"expected_answer": "AB",
"problem_id": "51",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement given about the function \( S_n(x) = \sum_{k=1}^{n} \cot^{-1} \left( \frac{1 + k(k+1) x^2}{x} \right) \).
### Step 1: Simplify the General Term
First, let's simplify the argument of the \(\cot^{-1}\) function in each term of the sum. For each \(k\),
\[
\frac{1 +... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A projectile is fired from horizontal ground with speed $v$ an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 397 | JEEBench | {
"expected_answer": "0.95",
"problem_id": "26",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | ### Solution
Okay, let's tackle this problem step by step. The problem is about a projectile that's fired from the ground with a certain speed and angle. The Earth's gravity changes at the highest point, and we need to find out how the range changes. Hmm, exciting!
First, let's recall the basic projectile motion formu... |
[
{
"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 $X=\\left\\{(x, y) \\in \\mathbb{Z} \\times \\mathbb{Z}: \\frac{x^{2}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 455 | JEEBench | {
"expected_answer": "B",
"problem_id": "6",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | Okay, I need to solve this problem. Let's start by understanding the set X. The problem states that X is the set of integer pairs (x, y) that satisfy two conditions: x²/8 + y²/20 < 1 and y² <5x. I need to find all such pairs first.
Wait, the first inequality is x²/8 + y²/20 < 1. Let me think about what this represents... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: One mole of a monatomic ideal gas undergoes an adiabatic expan... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | JEEBench | {
"expected_answer": "900",
"problem_id": "12",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | ### Solution
Okay, let's tackle this problem step by step. So, we have a monatomic ideal gas going through an adiabatic expansion where the volume increases by a factor of 8. The initial temperature is 100 K, and we need to find the decrease in internal energy in Joules. Hmm. Right. Let's think about the adiabatic proc... |
[
{
"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 | 165 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where the girl wants to buy flowers for her bouquet with maximum total petals without exceeding her coins m. The constraint is that the difference in petals between any two flowers in the bouquet can't be more than 1. Let's think about how to approach this.
First, let's under... |
[
{
"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: In thermodynamics, the $P-V$ work done is given by\n\\[\nw=-\\int d V ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 252 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "25",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Okay, let's see. The problem is about determining which conditions apply to the given integral expression for work. The key here is to understand where the integrand comes from.
The integrand in the given equation is \( P_{\text{ext}} \), which for a real gas might not be just the ideal gas law. The van der Waals equ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A human body has a surface area of approximately $1 \\mathrm{~m}^{2}$.... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 69 | JEEBench | {
"expected_answer": "C",
"problem_id": "4",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each option based on the given information and relevant physical principles, particularly those related to blackbody radiation and thermodynamics.
### Option Analysis
**Option [A]: The amount of energy radiated by the body in 1 second is close to 60 Joules.**
Given:
- Stefan... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: The area of the region\n\\[\n\\left\\{(x, y): 0 \\leq x \\leq \\frac{9}{4... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 325 | JEEBench | {
"expected_answer": "A",
"problem_id": "38",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | Okay, I need to find the area of the region defined by those inequalities. Let's visualize the feasible region step by step.
First, let's list all the constraints:
1. \(0 \leq x \leq \frac{9}{4}\)
2. \(0 \leq y \leq 1\)
3. \(x \geq 3y\)
4. \(x + y \geq 2\)
The feasible region is the intersection of all these constra... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 26 | AIME24 | {
"expected_answer": "385",
"problem_id": "aime24-26",
"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 $1$ ). Thus by precariously dr... | To solve this problem, we need to determine the number of intersections between the graphs of the functions \( y = 4g(f(\sin(2\pi x))) \) and \( x = 4g(f(\cos(3\pi y))) \).
First, let's understand the functions \( f \) and \( g \).
The function \( f(x) = \left| \left| x \right| - \frac{1}{2} \right| \). This functi... |
[
{
"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 | 134 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where Artem writes the digit d exactly n! times. We need to find all the odd digits from 1 to 9 that divide this huge number. The constraints are tight, with n up to 1e9, so we can't compute n! directly. We need a smarter approach.
Let me think about the problem. The number is d repe... |
[
{
"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 consisting of positive integers where all integers have the same number of digits.\nThe digit difference between two integers is th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 502 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to calculate the sum of digit differences between all pairs of numbers in the given array. Hmm. The digit difference is the count of different digits in the same positions. So for each pair, compare their digits one by one, count how many are different, and sum all those counts.
First, ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the amount of water produced (in g) in the oxidation o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 227 | JEEBench | {
"expected_answer": "288",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | ### Solution
The problem involves calculating the amount of water produced during the oxidation of rhombic sulfur (sulfur, S) by concentrated nitric acid (HNO3) to a compound with the highest possible oxidation state of sulfur. The key here is to determine the balanced chemical equation for this reaction and then calcu... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The correct statement(s) about surface properties is(are)\n[A] Adsorpt... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 103 | JEEBench | {
"expected_answer": "AB",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | Okay, I need to solve this problem where I have to determine which of the given statements about surface properties are correct. Let's go through each option one by one and analyze them.
First, let's look at option [A]: Adsorption is accompanied by a decrease in enthalpy and a decrease in entropy of the system. Adsorp... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array mountain. Your task is to find all the peaks in the mountain array.\nReturn an array that consists of indices of peaks in the g... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 144 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find all the peaks in a mountain array. Let's see, the problem says a peak is an element that's strictly greater than its neighbors, and the first and last elements can't be peaks. So the first thing I need to do is iterate through the array from the second ele... |
[
{
"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 $\\alpha$ be a positive real number. Let $f: \\mathbb{R} \... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 377 | JEEBench | {
"expected_answer": "0.5",
"problem_id": "2",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | ### Solution
We need to find the value of the limit \(\lim_{x \to \alpha^+} f(g(x))\) where \(f(x) = \sin\left(\frac{\pi x}{12}\right)\) and \(g(x) = \frac{2 \log_e(\sqrt{x} - \sqrt{\alpha})}{\log_e(e^{\sqrt{x}} - e^{\sqrt{\alpha}})}\).
First, let's analyze the function \(g(x)\). We need to compute \(g(x)\) as \(x\) a... |
[
{
"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: The reaction of $\\mathrm{Xe}$ and $\\mathrm{O}_{2} \\mathrm{~F}_{2}$ gives a Xe compound $\\mathbf{P}$. What ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 440 | JEEBench | {
"expected_answer": "4",
"problem_id": "40",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | To solve this problem, we need to determine the number of moles of hydrofluoric acid (HF) produced when 1 mole of an unknown compound P is completely hydrolyzed. The key is to first figure out the structure of P based on the reaction between xenon (Xe) and oxygen difluoride (O₂F₂).
### Step 1: Determine the Formula of... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given two positive integers low and high represented as strings, find the count of stepping numbers in the inclusive range [low, high].\nA stepping number is a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 79 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to count stepping numbers between two large numbers given as strings. A stepping number is one where each adjacent digit differs by exactly 1. And the answer has to be modulo 1e9+7.
First, I remember that the constraints are big because the numbers can be up to ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: This question refers to the following information.\nI am of opinion that the principal and true profession of the Courtier ought to be that of arms; ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 197 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | D
Explanation: Let's see. The problem is to determine which reform Castiglione would most likely want to institute based on the provided passage. Let's break down the key points from the text.
First, the passage discusses the ideal Courtier, which is a man of arms, well-versed in various skills. The main aspects are:... |
[
{
"content": "Problem: A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the triangles is 21 inches, what is the perimeter, in inches, of the regular hexagon?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 5 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the perimeter of a regular hexagon given the perimeter of one of its equilateral triangles. Let's break down the problem step by step.
1. **Understand the Structure**: A regular hexagon can be divided into six equilateral triangles. Each of these triangles shares a common si... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed 2D integer array nums. Initially, your score is 0. Perform the following operations until the matrix becomes empty:\n\nFrom each row ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 10 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about calculating a score by removing the largest numbers from each row repeatedly. Hmm. So, in each step, we take the largest number from each row, collect all of them, find the maximum among those, add that to the score. Then remove those elements from the rows. Wait, but 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 186 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem. Hmm, the problem says we have two arrays, a and b. We can perform operations where we select an index i with b_i = 1 and increase a_i by 1. Each operation counts towards k, and we can do this at most k times. Then, our score is the maximum of a_i plus the median of th... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 261 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's see. The problem is about finding the minimum time Zhan needs to blend all fruits. Let's parse the problem carefully.
So, each second, Zhan can add up to y fruits to the blender. Then, the blender works for one second, blending min(x, c) fruits, where c is the current count in the blender. After blending, ... |
[
{
"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 | 167 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the minimum number of squaring operations required to make an array non-decreasing. Let's think through the problem step by step.
First, the problem allows us to square any element as many times as needed, but each squaring counts as one operation. The go... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed integer array receiver of length n and an integer k.\nThere are n players having a unique id in the range [0, n - 1] who will play a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 95 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is about finding the maximum value of this function f(x) where x is the starting player, and the ball is passed k times. The function sums up all the player IDs involved in those passes, including the starting player. We need to choose the best starting player to maximize this su... |
[
{
"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 | 75 | CodeForces | {
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} | <think>
Okay, let's see. I need to solve this problem where Alice and Bob are playing a game with marbles of different colors. The goal is to compute Alice's final score under optimal play from both. Hmm.
The problem says that Alice gets points for each color she has at least one marble of, and an additional point 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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} | 0 | 137 | CodeElo | {
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} | <think>
Okay, I need to solve this problem where I'm given an array b of n-1 elements, and I have to construct a good array a of n elements such that each b_i is equal to a_i AND a_{i+1}. If it's not possible, I should output -1. Let's think about how to approach this.
First, let's understand the constraints. For each... |
[
{
"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 tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects vertices A_i and B_... | {
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} | 1 | 420 | LiveCodeBench | {
"expected_answer": "",
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} | <think>
Okay, I need to solve this programming problem. Let's read the problem carefully.
So, the problem is about a tree with N vertices. Each vertex has a value C_i. We need to compute for each vertex x, the sum of C_i multiplied by the distance between x and i (d(x, i)) for all i from 1 to N. Then, find the minimum... |
[
{
"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 liqueur is used to make a Pink Lady cocktail pink?\nOptions: A. grenadine, B. pernod, C. rum, D. raspberry liqueur, E. pink lemonade, F. schnapp... | {
"do_sample": true,
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} | 0 | 489 | MMLUPro | {
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} | A. |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: The increasing order of atomic radii of the following Group 13 elements i... | {
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} | 0 | 13 | JEEBench | {
"expected_answer": "B",
"problem_id": "21",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | $\boxed{A}$
Let me start by understanding the problem. I need to determine the correct order of atomic radii for the Group 13 elements. The options given are different permutations, and I have to choose the correct one.
First, let's recall that Group 13 elements are also known as the Boron group. They include aluminu... |
[
{
"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 value of the limit\n\\[\n\\lim _{x \\rightarrow \\frac{\\pi}{2}} \\frac{4 \\sqrt{2}(\\sin 3 x+\\si... | {
"do_sample": false,
"max_new_tokens": 32768,
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} | 0 | 299 | JEEBench | {
"expected_answer": "8",
"problem_id": "42",
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"subject": "math",
"type": "Integer"
} | To solve the given limit problem, we need to evaluate:
\[
\lim _{x \rightarrow \frac{\pi}{2}} \frac{4 \sqrt{2}(\sin 3 x + \sin x)}{\left(2 \sin 2x \sin \frac{3x}{2} + \cos \frac{5x}{2}\right) - \left(\sqrt{2} + \sqrt{2} \cos 2x + \cos \frac{3x}{2}\right)}
\]
### Step 1: Simplify the numerator
The numerator is \(4\sqrt... |
[
{
"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 | 226 | CodeElo | {
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"problem_id": "",
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} | <think>
Okay, let's see. So the problem is where we have to select a subsequence of length m from the given sequences a, b, c. The subsequence needs to satisfy two conditions: the a's are non-decreasing in the selected indices, and all the b's in those indices are distinct. And we need to find the maximum sum of c's fo... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Name reactions in chemistry refer to a specific set of well-known chemical reactions that are typically named after their discoverers or the scientists who made signific... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 24 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"type": null
} | Let's see. The first reaction is A + H2SO4 → 2,8-dimethylspiro[4.5]decan-6-one. Hmm. So this is the AIE reaction, right? The AIE reaction involves the treatment of a spiro compound with sulfuric acid, which usually leads to the formation of a lactone. So the reactant A here is likely the primary alcohol form of the spi... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given an integer B.\nIf there exists a positive integer A such that A^A = B, print its value; otherwise, outpu... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 317 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
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} | <think>
Okay, let's see. I need to write a Python function that takes an integer B as input and checks if there's a positive integer A such that A^A equals B. If there is, output A; otherwise, output -1. Hmm.
First, the problem is to find A where A^A = B. So for example, in the sample input 27, 3^3 is 27, so A is 3. F... |
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