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 455k |
|---|---|---|---|---|---|---|
[
{
"content": "Problem: Let\n\\[f(x) = (\\arccos x)^2 + (\\arcsin x)^2.\\]Find the range of $f(x).$ All functions are in radians.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 431 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the range of the function \( f(x) = (\arccos x)^2 + (\arcsin x)^2 \), we start by recalling the trigonometric identity that relates the arccosine and arcsine functions. Specifically, for any \( x \) in the domain of both functions, we have:
\[
\arccos x + \arcsin x = \frac{\pi}{2}.
\]
Let's denote \( \theta =... |
[
{
"content": "Problem: In the $xy$-plane, a circle of radius $4$ with center on the positive $x$-axis is tangent to the $y$-axis at the origin, and a circle with radius $10$ with center on the positive $y$-axis is tangent to the $x$-axis at the origin. What is the slope of the line passing through the two point... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 23 | AMC23 | {
"expected_answer": "7",
"problem_id": "26",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the slope of the line passing through the two points where the two circles intersect. Let's start by defining the equations of the circles.
The first circle has a radius of 4 and is centered on the positive x-axis. Since it is tangent to the y-axis at the origin, its center m... |
[
{
"content": "Problem: How many ordered pairs of positive real numbers $(a,b)$ satisfy the equation\n\\[(1+2a)(2+2b)(2a+b) = 32ab?\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 13 | AMC23 | {
"expected_answer": "1",
"problem_id": "15",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the equation \((1+2a)(2+2b)(2a+b) = 32ab\) for ordered pairs \((a, b)\) of positive real numbers, we start by expanding and simplifying the left-hand side.
First, expand the product step by step. Let's denote the left-hand side as \(L = (1+2a)(2+2b)(2a+b)\).
First, expand \((1+2a)(2+2b)\):
\[
(1+2a)(2+2b) = ... |
[
{
"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 | 265 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the winner of a game played on a tree. The game involves two players, Alice and Bob, who take turns moving along the edges of the tree. The player who cannot make a move loses. The problem provides a tree structure and a path from vertex \( u \) to \( v \), and we need to det... |
[
{
"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 bus is in operation. The number of passengers on the bus is always a non-negative integer.\nAt some point in time, t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 377 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def min_passengers():
N = int(input())
A = list(map(int, input().split()))
current = 0
min_pass = 0
for i in range(N):
current += A[i]
if current < 0:
min_pass += abs(current)
current = 0
print(min_pass)
min_passengers() |
[
{
"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 | 445 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the first year in which the distribution of plushies among spiders becomes stable. A year is considered stable if each spider has the same number of plushies as they did in the previous year.
### Approach
1. **Problem Analysis**: Each spider gives one plushie to another spi... |
[
{
"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 | 384 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
# Precompute powers of 2 up to 10^6
pow2 = [1]
for _ in range(1, 10**6):
pow2.append(pow2[-1] * 2 % 998244353)
def count_ways():
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
l = 0
# Count initial trivial pockets ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: From this information compute: a) The current ratio. b) The quick asset ratio. c) The net working capital. 1. Current Assets: Current Liabilities Cas... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compute the current ratio, quick asset ratio, and net working capital using the provided financial data.
First, let's list out the given values:
- **Current Assets**: $93,600
- **Current Liabilities**: $58,500
- Breakdown: Cash ($22,150), Marketable Securities ($16,000), Accounts Re... |
[
{
"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 positive integer x is called a 321-like Number when it satisfies the following condition.\n\n- The digits of x are s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 284 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <script>
def is_321_like(n):
digits = []
while n > 0:
digits.append(n % 10)
n = n // 10
d = len(digits)
for i in range(d - 1):
if digits[i] <= digits[i + 1]:
return False
return True
n = int(input())
if is_321_like(n):
print("Yes")
else:
print("No")
</scr... |
[
{
"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 | 21 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to determine the maximum score achievable by optimally shuffling the array \(a\). The score is calculated as the sum of \(c_i - b_i\) for each element, where \(b_i\) is the minimum prefix sum up to index \(i\), and \(c_i\) is the maximum prefix sum up to index \(i\).
First, let's understa... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: α-β unsaturated carbonyls have a much more electrophilic carbon double bond. These double bonds act as a good Lewis acid and react with nucleophiles to produce enolate i... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 152 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's start by understanding the Michael addition reaction. The Michael reaction occurs when a β,γ-unsaturated carbonyl compound (the Michael acceptor) reacts with a nucleophile (the Michael donor) to form an enolate ion. The nucleophile attacks the β-carbon, leading to a resonance-stabilized intermediate.
Looking at ... |
[
{
"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 | 180 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to help Monocarp restore a regular bracket sequence by placing brackets on the odd positions, such that the cost is minimized. The cost is calculated as the sum of the distances between each pair of corresponding opening and closing brackets. Hmm.
First, let me understand the problem 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 348 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum time required for the crow to teleport to a position greater than or equal to \(\ell\), given the positions of the scarecrows and the teleportation distance \(k\). The solution involves a dynamic approach where we calculate the optimal positions of the scarecrows ... |
[
{
"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 | 172 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to transform a given undirected graph into a cool graph by performing at most \(2 \cdot \max(n, m)\) operations. A graph is considered cool if either it has no edges or it is a tree. The operations allow us to add or remove edges by selecting three distinct vertices \(a\), \(b\), and \(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": 1,
"temperature": 0.7
} | 1 | 190 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum possible value of the product \( P = \prod_{i=1}^n \min(a_i, b_i) \) after each modification to the arrays \( a \) and \( b \). The goal is to compute \( P \) modulo \( 998,244,353 \) for each test case and after every modification.
### Approach
1. **Initial Setu... |
[
{
"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 previously healthy 27-year-old nulligravid woman comes to the emergency department because of a 2-day history of moderate-to-severe pain and swelli... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 246 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | B
The patient presents with a tender, fluctuant mass in the left labia, which is consistent with an abscess. The differential diagnosis could include a Bartholin's gland abscess, a hymen hematoma (though she's nulligravid), or a serous cyst. However, given the symptoms and physical exam, the most likely diagnosis is a... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: The reaction of $\\mathrm{K}_3\\left[\\mathrm{Fe}(\\mathrm{CN})_6\\right]... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 360 | JEEBench | {
"expected_answer": "C",
"problem_id": "33",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To solve this problem, we need to determine the correct formula for the white precipitate X formed when \(\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\) reacts with \(\mathrm{FeSO}_4\) in the absence of air. Let's break down the problem step by step.
### Step 1: Understand the Reactions Given
1. **Turnbull's 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 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 113 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of button presses required to guarantee obtaining at least \( k \) cans of lemonade from a vending machine with \( n \) slots. Each slot initially contains a known number of cans, and each button press on a slot either removes a can (if present) or nothing ... |
[
{
"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 | 257 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, I need to determine the minimum number of operations required to make all elements of an array have the same parity. In each operation, I can select a pair of indices with elements of different parities, replace the smaller one with the sum of the two elements, and repeat until all elements share... |
[
{
"content": "Problem: Rows 1, 2, 3, 4, and 5 of a triangular array of integers are shown below.\n1\n1 1\n1 3 1\n1 5 5 1\n1 7 11 7 1\nEach row after the first row is formed by placing a 1 at each end of the row, and each interior entry is 1 greater than the sum of the two numbers diagonally above it in the prev... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 10 | AMC23 | {
"expected_answer": "5",
"problem_id": "12",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the units digit of the sum of the 2023rd row in a triangular array where each row is constructed based on specific rules. Let's start by understanding the pattern in the given rows.
The first few rows are:
1
1 1
1 3 1
1 5 5 1
1 7 11 7 1
Each interior entry in a row is 1 gre... |
[
{
"content": "Problem: How many positive whole-number divisors does 196 have?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 3 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the number of positive whole-number divisors of 196, we start by finding its prime factorization.
First, we check if 196 is divisible by the smallest prime number, 2. Since 196 is even, we divide by 2:
\[ 196 \div 2 = 98 \]
So, 2 is a factor. Next, we factor 98. Again, 98 is even, so we divide by 2:
\[ 9... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A compound with the molecular formula C8H9NO and the given NMR data is reacted with the following set of reagents:\n\n1. NaNO2 + HCl\n2. H2O\n3. aq. KOH, Heat \n\n1H-NMR... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 149 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's start by analyzing the given NMR data. The 1H NMR spectrum shows peaks at 9.72 (t, 1H), 6.98 (d, 2H), 6.51 (d, 2H), 6.27 (bs, 2H), and 3.66 (d, 2H).
First, the aromatic protons (6.98, 6.51, 6.27 ppm) suggest the presence of phenyl rings. The multiplicity of doublets (d) for these peaks indicates they are part o... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 197 | JEEBench | {
"expected_answer": "4",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To determine the total number of molecules containing a covalent bond between two atoms of the same kind among the given list, we need to analyze each compound individually. The compounds are:
1. **B\(_2\)H\(_6\)** (Borane)
2. **B\(_3\)N\(_3\)H\(_6\)** (Borazine)
3. **N\(_2\)O** (Dinitrogen monoxide)
4. **N\(_2\)O\(_4... |
[
{
"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. A pair of indices i, j where 0 <= i < j < nums.length is called beautiful if the first digit of nums[i] and the l... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 36 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that counts the number of beautiful pairs in an array. Let me think about how to approach this.
First, the problem defines a beautiful pair as two indices i and j (with i < j) where the first digit of nums[i] and the last digit of nums[j] are coprime. So, for each pair, ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Michael reaction is a chemical process in organic chemistry where a nucleophile adds to a molecule containing a specific carbon-carbon double bond (C=C) adjacent to ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 18 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct products for the given Michael reactions, let's analyze each reaction step by step.
**First Reaction:**
Reactants: methyl 2-oxocyclohexane-1-carboxylate + (NaOEt, THF, 2,4-dimethyl-1-(vinylsulfinyl)benzene)
The Michael donor here is the vinylsulfinyl group (C=CS(O)Et). The nucleophile would b... |
[
{
"content": "Problem: How many ways are there to put 5 balls in 2 boxes if the balls are not distinguishable and neither are the boxes?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 226 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the number of ways to put 5 indistinguishable balls into 2 indistinguishable boxes, we need to consider the different possible distributions of the balls. Since the balls and boxes are indistinguishable, the order of the boxes doesn't matter. This is a problem of partitioning the number 5 into up to two pa... |
[
{
"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, an integer array queries, and an integer x.\nFor each queries[i], you need to find the index of the queries[i]^th occurren... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 510 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each query in queries, I have to find the index of the queries[i]-th occurrence of x in the nums array. If there are fewer than that number of occurrences, return -1.
Let me think. So first, the straightforward approach would be to loop through each query and for e... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a string s, return the maximum length of a substring such that it contains at most two occurrences of each character.\n \nExample 1:\n\nInput: s = \"bcbb... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 465 | 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 length of a substring in a given string such that each character in the substring appears at most twice. Let's think about how to approach this.
First, I remember that sliding window techniques are often used for problems where you need to fin... |
[
{
"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: Calamine, malachite, magnetite and cryolite, respectively, are\n(A) $\\ma... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 189 | JEEBench | {
"expected_answer": "C",
"problem_id": "20",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To determine the correct answer, we need to identify each compound listed in the options and match them with the given minerals: calamine, malachite, magnetite, and cryolite. Let's go through each option step by step.
First, let's recall the chemical formulas of common minerals:
1. **Calamine**: Also known as zinc ca... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: which of the following molecules has c3h symmetry?\ntriisopropyl borate\nquinuclidine\nbenzo[1,2-c:3,4-c':5,6-c'']trifuran-1,3,4,6,7,9-hexaone\ntriphenyleno[1,2-c:5,6-c'... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 8 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine which molecule has a C3h symmetry, I need to understand the symmetry elements involved. C3h symmetry implies that the molecule has a three-fold rotational axis (C3) and a horizontal plane of symmetry (σh) that includes this axis. Additionally, there must be a perpendicular plane of symmetry (σv) that meets... |
[
{
"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 | 94 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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"type": null
} | </html>
To solve the "Maximum Multiple Sum" problem, we need to find an integer \( x \) in the range \( 2 \leq x \leq n \) that maximizes the sum of multiples of \( x \) less than or equal to \( n \). The sum is given by \( x + 2x + 3x + \dots + kx \), where \( kx \leq n \).
### Approach
1. **Understanding the Sum**:... |
[
{
"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 integer array nums of length n.\nAn element nums[i] of nums is called special if i divides n, i.e. n % i == 0.\nReturn the sum of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 42 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that calculates the sum of the squares of all special elements in a given array. Let me start by understanding the problem again.
A special element is defined as nums[i] where i divides n, meaning n % i == 0. So for each index i (starting from 1, since it's 1-indexed), c... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider a system with Hamiltonian operator $H = \\varepsilon \\vec{\\sigma}.\\vec{n}$. Here, $\\vec{n}$ is an arbitrary unit vector, $\\varepsilon $ is a constant of di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 184 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the eigenvalues of the Hamiltonian operator \( H = \varepsilon \vec{\sigma} \cdot \vec{n} \), where \(\vec{n}\) is a unit vector and \(\vec{\sigma}\) represents the Pauli spin matrices, we need to analyze the structure of the operator.
First, recall that the Pauli matrices \(\vec{\sigma} = (\sigma_x, \sig... |
[
{
"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 | 388 | CodeForces | {
"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 f(i) for i from 0 to m. Let me start by understanding the problem.
First, the function f(i) is defined as the maximum value of x after performing any number of operations starting from the initial value i. Each operation allows choosing a se... |
[
{
"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 | 432 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum time required for Zhan to blend all his fruits using his blender. The blender can mix up to \( x \) fruits per second, and Zhan can add up to \( y \) fruits per second. The key is to figure out the optimal strategy for adding fruits to the blender and blending the... |
[
{
"content": "Problem: The square root of $t$ is greater than $2$ and less than $3.5$. How many integer values of $t$ satisfy this condition?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 468 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine how many integer values of \( t \) satisfy the condition that the square root of \( t \) is greater than 2 and less than 3.5, we start by translating the problem into mathematical inequalities:
\[
2 < \sqrt{t} < 3.5
\]
Next, we eliminate the square root by squaring all parts of the inequality. Since squa... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given an array of strings words and a string s, determine if s is an acronym of words.\nThe string s is considered an acronym of words if it can be formed by c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 84 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to write a Python function that checks if a string 's' is an acronym formed by the first characters of each word in the list 'words'. Let me think about how to approach this.
First, the function should probably check if the length of 's' is the same as the number of words in the list. If not, it 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": 0,
"temperature": 0.7
} | 0 | 14 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for given n points on the x-axis, I have to compute how many points are contained in exactly k_i segments for each query. Let me think through this step by step.
First, the points are given in increasing order, and each segment is between x_i and x_j where i < j. So eac... |
[
{
"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 coins representing coins of different denominations and an integer k.\nYou have an infinite number of coins of each denomination... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 477 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to generate the k-th smallest amount that can be made using the given coins, where each coin can be used infinitely, but they can't be combined. Hmm. Let's start by understanding the problem.
First, the coins are [3,6,9] in the example. Each coin can generate multiples of thei... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 2D boolean matrix grid.\nReturn an integer that is the number of right triangles that can be made with the 3 elements of grid such that all of ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 497 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to count the number of right triangles in a 2D grid of booleans. Let me think about how to approach this.
First, the problem defines a right triangle as a set of three elements where one is in the same row as another and the same column as a third. So, the right ... |
[
{
"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.\nYou can perform the following operation on the array at most k times:\n\nChoose any index i fro... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 131 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to maximize the score of an array by performing at most k operations. The score is the frequency of the most frequent element. Let me think about how to approach this.
First, the problem says that each operation can either increase or decrease an element by 1. 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": 1,
"temperature": 0.7
} | 1 | 19 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum possible sum of the greatest common divisors (GCDs) of two arrays after performing at most \( d \) swaps. Each swap allows exchanging elements \( a_i \) and \( b_i \) but costs \( c_i \) coins. The goal is to compute this maximum sum for each of \( q \) different ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and the j-th column... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 367 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def solve():
import sys
input = sys.stdin.readline
H, W, K = map(int, input().split())
S = [input().strip() for _ in range(H)]
# Check horizontal possibilities
dp_h = [0] * (W + 1)
for i in range(H):
consecutive = 0
for j in range(W):
if S[i][j] == 'o'... |
[
{
"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 gas is enclosed in a cylinder with a movable frictionless piston. Its i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 44 | JEEBench | {
"expected_answer": "C",
"problem_id": "3",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the amount of heat supplied to the system during the two-step process (isobaric expansion followed by isochoric process) and compare it to the heat supplied in the adiabatic process. However, the problem only asks for the heat supplied in the two-step process. Let's proceed 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 0 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out how to approach this problem. The task is to find the number of minimal coprime segments within a given range [l, r]. From the problem statement and the example, I understand that a minimal coprime segment is one where the start and end points are coprime, and there's no smaller 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 | 251 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Iris has a tree with certain constraints and she needs to compute the maximum possible sum of distances after each event. Let me break down the problem step by step.
First, the tree has n vertices numbered from 1 to n in a depth-first search (DFS) order. The edges have ... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: An $\\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 317 | JEEBench | {
"expected_answer": "4",
"problem_id": "17",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To determine the ratio \( \frac{r_S}{r_\alpha} \) of the radii of the circular orbits of the sulfur ion and the \(\alpha\)-particle in a magnetic field, we will follow these steps:
1. **Determine the velocities after acceleration:**
Both particles are accelerated through the same potential \( V \). The kinetic ener... |
[
{
"content": "Problem: Positive real numbers $x$ and $y$ satisfy $y^3=x^2$ and $(y-x)^2=4y^2$. What is $x+y$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 1 | AMC23 | {
"expected_answer": "36",
"problem_id": "1",
"reference_solution": "",
"subject": null,
"type": null
} | We start with the given equations: \(y^3 = x^2\) and \((y - x)^2 = 4y^2\). Let's expand and simplify the second equation.
First, expand \((y - x)^2 = 4y^2\):
\[
(y - x)^2 = y^2 - 2xy + x^2 = 4y^2
\]
Rearrange terms to isolate \(x^2\):
\[
y^2 - 2xy + x^2 = 4y^2 \implies x^2 - 2xy + y^2 = 4y^2 \implies x^2 - 2xy - 3y^2... |
[
{
"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: Consider the following lists:\nList-I\n(I) $\\left\\{x \\in\\left[-\\frac... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 389 | JEEBench | {
"expected_answer": "B",
"problem_id": "15",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the number of elements in each set listed in List-I and match them with the corresponding options in List-II. Let's analyze each equation and interval step by step.
**List-I Analysis:**
1. **Set (I):** \(\left\{x \in\left[-\frac{2 \pi}{3}, \frac{2 \pi}{3}\right]: \cos 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 tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects vertices A_i and B_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 420 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have a tree with N vertices and a list of integers C. The goal is to find the vertex v that minimizes the function f(v), which is the sum over all i of C_i multiplied by the distance d(v, i) between v and each vertex i.
First, let me understand what's given. The inpu... |
[
{
"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 integers, num and t.\nAn integer x is called achievable if it can become equal to num after applying the following operation no more than t t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 28 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is to find the maximum possible achievable number x, given an initial num and t operations. The operations allow us to either increase or decrease x and num by 1 each, but we can do this at most t times. Hmm.
First, let me try to understand what's happening here. The key point i... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 47 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum possible value of \( \text{score}_n - \text{score}_c \) by selecting a subset of strings from the given set. Let's break down the problem and the solution step by step.
### Key Insight:
1. **Narek's Score (\( \text{score}_n \))**:
- Narek's score is incremente... |
[
{
"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.\nIn one operation, you can pick any index i of nums such that 0 <= i < nums.length - 1 and repla... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 168 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to create a Python function that solves this problem. The goal is to apply at most k operations to minimize the bitwise OR of the remaining elements in the array. Each operation replaces two adjacent elements with their bitwise AND.
Hmm. So the key here is that each operation reduces t... |
[
{
"content": "Problem: The proper divisors of 12 are 1, 2, 3, 4 and 6. A proper divisor of an integer $N$ is a positive divisor of $N$ that is less than $N$. What is the sum of the proper divisors of the sum of the proper divisors of 284?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 12 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to find the sum of the proper divisors of the sum of the proper divisors of 284. Let's break this down step by step.
First, we need to determine the sum of the proper divisors of 284. Proper divisors are positive divisors of a number that are less than the number itself.
Let's start by f... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A methanol solution of (R)-(+)-Limonene is stirred with Pd/C under a Hydrogen atmosphere. After 1 equivalent of hydrogen is consumed, product 1 is isolated as the major ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 12 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{D} |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: 7-(tert-butoxy)bicyclo[2.2.1]hepta-2,5-diene is combined with 2 equivalents of 5,6-bis(dibromomethyl)cyclohexa-1,3-diene and sodium iodide at elevated temperature, formi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 71 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's start by understanding the transformations step by step.
First, the initial compound is 7-(tert-butoxy)bicyclo[2.2.1]hepta-2,5-diene. Let's visualize its structure. The parent skeleton is a 7-membered ring with 2 and 5 as the double bonds. The 7-position is substituted with a tert-butoxy group. The structure mig... |
[
{
"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 $|M|$ denote the determinant of a square matrix $M$. Let $g:\\left... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 388 | JEEBench | {
"expected_answer": "AC",
"problem_id": "14",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve the problem, we need to determine the maximum and minimum values of the function \( g(\theta) \) defined on the interval \(\left[0, \frac{\pi}{2}\right]\), then use these values to construct a quadratic polynomial \( p(x) \) whose roots are these maximum and minimum values, and finally evaluate certain express... |
[
{
"content": "Problem: Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ and $BC$ of triangle $ABC$ , respectively. $2024$ circles of radius $1$ can be arranged in the same manner. The inradius of triangle $ABC$ can be expressed as $\\frac{m}{n}$ , w... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 22 | AIME24 | {
"expected_answer": "197",
"problem_id": "aime24-22",
"reference_solution": "Draw an altitude from both end circles of the diagram with the circles of radius one, and call the lengths you get drawing the altitudes of the circles down to $BC$ $a$ and $b$ . Now we have the length of side $BC$ of being $(2)... | To solve the problem, we need to determine the inradius of triangle \(ABC\) given that eight circles of radius 34 are arranged such that two are tangent to sides \(AB\) and \(BC\) respectively, and 2024 circles of radius 1 are arranged similarly. The key is to find a relationship between the number of circles and the i... |
[
{
"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 furniture store had a truck that an employee of the store used to deliver furniture to the store's customers. One afternoon while the employee was ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 259 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{D} |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the total number of isomers, considering both structur... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 231 | JEEBench | {
"expected_answer": "10",
"problem_id": "32",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To determine the total number of isomers (both structural and stereoisomers) of cyclic ethers with the molecular formula \(\mathrm{C}_4\mathrm{H}_8\mathrm{O}\), we will follow a systematic approach.
### Step 1: Understand the Structure of Cyclic Ethers
Cyclic ethers are cyclic molecules containing an oxygen atom 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 the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 422 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of operations required to make all elements of the array equal to 1. The array starts as all zeros. We have two types of operations:
1. **Type 1**: Choose an index \( i \) where \( a_i = 0 \) and set \( a_i = 1 \). This operation increases the number of co... |
[
{
"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: Although corporate profit maximization is not directly prescribed by major normative theories to which normative theory is it most similar?\nOptions:... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 12 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | \boxed{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 positive integers of length N: A=(A_1,A_2,\\ldots,A_N). Find the number of triples of posi... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 274 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <script>
def count_triples():
import sys
input = sys.stdin.read
n = int(input())
a = list(map(int, input().split()))
# Create a dictionary to track the positions of each element
pos = {}
for i, x in enumerate(a):
if x not in pos:
pos[x] = []
pos[x].append(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: For how many values of $p$, the circle $x^{2}+y^{2}+2 x+4 y-p=0$ and the coordinate axes have exactly three co... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 89 | JEEBench | {
"expected_answer": "2",
"problem_id": "44",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To determine the number of values of \( p \) for which the circle \( x^2 + y^2 + 2x + 4y - p = 0 \) intersects the coordinate axes in exactly three points, we need to analyze the conditions under which the circle touches or intersects the axes.
First, rewrite the equation of the circle in standard form by completing 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": 0,
"temperature": 0.7
} | 0 | 225 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum number of inversions in an interesting permutation of length \( n \) given \( m \) intervals. A permutation is considered interesting if for each interval \([l_i, r_i]\), we can choose an integer \( k_i \) such that \( l_i \le k_i < r_i \), and the following condi... |
[
{
"content": "Problem: Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers are randomly chosen from $S.$ She wins a prize if at least two of her numbers were $2$ of the randomly chosen numbers, and wins the grand prize if all four of her numbers were the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 18 | AIME24 | {
"expected_answer": "116",
"problem_id": "aime24-18",
"reference_solution": "This is a conditional probability problem. Bayes' Theorem states that \n \\[P(A|B)=\\dfrac{P(B|A)\\cdot P(A)}{P(B)}\\] in other words, the probability of $A$ given $B$ is equal to the probability of $B$ given $A$ times the proba... | To solve this problem, we need to determine the probability that Jen wins the grand prize given that she won a prize. Let's break this down step by step.
First, let's define the events:
- \( G \): Jen wins the grand prize (all 4 of her numbers are chosen).
- \( W \): Jen wins a prize (at least 2 of her numbers are cho... |
[
{
"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 treatment of galena with $\\mathrm{HNO}_{3}$ produces a gas that i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 408 | JEEBench | {
"expected_answer": "AD",
"problem_id": "48",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which statements are correct about the gas produced when galena (PbS) reacts with nitric acid (HNO₃). Let's go through each option step by step.
First, let's write the balanced chemical equation for the reaction between galena and nitric acid. Galena (PbS) reacts with HNO₃ t... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A pendulum consists of a bob of mass $m=0.1 \\mathrm{~kg}$ and... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 346 | JEEBench | {
"expected_answer": "0.16",
"problem_id": "10",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to determine the kinetic energy \( K \) of the pendulum just after the bob lifts off the floor. Let's break down the problem step by step.
### Step 1: Understand the Initial Conditions
- The pendulum bob has mass \( m = 0.1 \, \text{kg} \).
- The string length is \( L = 1.0 \, \text{m} \... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 157 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the optimal start days for Robin's brother and mother such that the brother's visit overlaps with the maximum number of distinct jobs, and the mother's visit overlaps with the minimum number of distinct jobs. If there are multiple possible days, the earliest one should be cho... |
[
{
"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 the decay sequence,\n${ }_{92}^{238} \\mathrm{U} \\stackrel{-\\math... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 195 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each step of the decay sequence and determine the nature of the particles or radiation emitted at each step. Let's go through each decay step by step.
The given decay sequence is:
\[
_{92}^{238} \text{U} \xrightarrow{-\text{x}_1} _{90}^{234} \text{Th} \xrightarrow{-\text{x}_2}... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 359 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out this problem. So, we have a permutation p of length n, and a string s of the same length consisting of L and R. The problem allows QED to perform certain swaps based on the characters in s. The goal is to check after each query if the permutation can be sorted in non-decreasing order using... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Dienes are organic compounds with two adjacent double bonds in their structure, and they exhibit unique reactivity due to their conjugated pi-electron system. They play ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct reactant A and the reactivity sequence of dienes, let's analyze the problem step by step.
First, the given reaction is cyclohexene reacting with A to form 8,8-diiodobicyclo[4.2.0]octan-7-one. The product is a cyclic ketone with two iodine atoms. The key here is understanding the reactivity of ... |
[
{
"content": "Problem: Let $x,$ $y,$ and $z$ be positive real numbers such that $xyz(x + y + z) = 1.$ Find the minimum value of\n\\[(x + y)(y + z).\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 332 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the minimum value of \((x + y)(y + z)\) given that \(x, y, z\) are positive real numbers satisfying \(xyz(x + y + z) = 1\), we start by introducing new variables to simplify the expression. Let \(a = x + y\), \(b = y + z\), and \(c = z + x\). Note that \(a, b, c > 0\) because \(x, y, z\) are positive. Also, the... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 364 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to help Kevin select four sticks from a given set to form an isosceles trapezoid. If no such selection exists, we should output -1. Let's break down the problem and the solution approach.
### Key Insights:
1. **Isosceles Trapezoid Conditions**: An isosceles trapezoid can be formed if two... |
[
{
"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 | 340 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the strength of an array described by a sequence of pairs after each prefix of the pairs is considered. The strength is defined as the number of seconds it takes for the array to become empty under the effect of cosmic rays. Each second, all elements that are either at the be... |
[
{
"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.The programming contest World Tour Finals is underway, where N players are participating, and half of the competition ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 296 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
input = sys.stdin.readline
def func():
N, M = map(int, input().split())
A = list(map(int, input().split()))
S = [input().strip() for _ in range(N)]
def calc(i):
# Player i's solved problems
solved = set()
for j in range(M):
if S[i][j] == 'o':
... |
[
{
"content": "Problem: A list of positive integers has the following properties: $\\bullet$ The sum of the items in the list is $30$ . $\\bullet$ The unique mode of the list is $9$ . $\\bullet$ The median of the list is a positive integer that does not appear in the list itself. Find the sum of the squares... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 1 | AIME24 | {
"expected_answer": "236",
"problem_id": "aime24-1",
"reference_solution": "The third condition implies that the list's size must be an even number, as if it were an odd number, the median of the list would surely appear in the list itself. Therefore, we can casework on what even numbers work. Say the size is 2.... | To solve this problem, we need to determine a list of positive integers that satisfies the given conditions and then compute the sum of their squares. Let's break down the conditions step by step.
1. **Sum of the items is 30.**
2. **The unique mode is 9.** This means that 9 appears more frequently than any other numbe... |
[
{
"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": 1,
"temperature": 0.7
} | 1 | 502 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to create a Python function that calculates the sum of digit differences between all pairs of integers in an array. Each number in the array has the same number of digits. Hmm.
First, the digit difference between two numbers is the count of positions where their digits differ. For examp... |
[
{
"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 positive integer x is called a 321-like Number when it satisfies the following condition.\n\n- The digits of x are s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 284 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | def is_321_like(N):
digits = [int(d) for d in str(N)]
return all(digits[i] > digits[i+1] for i in range(len(digits)-1))
if __name__ == '__main__':
N = int(input())
print('Yes' if is_321_like(N) else 'No') |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 81 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | To determine the sum of the number of lone pairs of electrons on each central atom in the given species, we need to analyze each molecular formula step by step. The species are \(\left[\mathrm{TeBr}_{6}\right]^{2-}\), \(\left[\mathrm{BrF}_{2}\right]^{+}\), \(\mathrm{SNF}_{3}\), and \(\left[\mathrm{XeF}_{3}\right]^{-}\)... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: List-I shows different radioactive decay processes and List-II provides p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 474 | JEEBench | {
"expected_answer": "A",
"problem_id": "31",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to determine the correct particles emitted during each radioactive decay process listed in List-I by analyzing the changes in atomic numbers and mass numbers. Let's go through each decay reaction step by step.
**List-I Entries:**
1. **P) \( {}_{92}^{238} U \rightarrow {}_{91}^{234} \tex... |
[
{
"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 | 130 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where there's a matrix and multiple queries adding color restrictions. The goal is to find the minimum cost to paint the matrix according to these restrictions. The operations are painting entire rows red or columns blue, and the cost depends on how many actions are... |
[
{
"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_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Alice and Bob are playing a game on a grid, taking turns cutting rows or columns to earn points based on the chips in the cut sections. The task is to compute the total points each player earned based on the initial grid and the sequence of moves.
First, let me understa... |
[
{
"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 current carrying wire heats a metal rod. The wire provides a constant p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 182 | JEEBench | {
"expected_answer": "A",
"problem_id": "3",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To determine the heat capacity of the metal rod, we need to start by understanding the relationship between power, heat capacity, and temperature change. The power \( P \) provided by the wire is the rate at which energy is supplied to the rod. The heat capacity \( C \) is the amount of heat required to raise the tempe... |
[
{
"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 option(s) regarding the complex $\\left[\\mathrm{Co}(\\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 162 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the complex \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3+}\) where \(\text{en} = \mathrm{H}_2\mathrm{NCH}_2\mathrm{CH}_2\mathrm{NH}_2\). Let's break down each option step by step.
### Step 1: Determine the Coo... |
[
{
"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: Galena (an ore) is partially oxidized by passing air through i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 165 | JEEBench | {
"expected_answer": "6.47",
"problem_id": "26",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the weight of lead (Pb) produced per kilogram of oxygen (O₂) consumed in the given chemical process. The process involves the partial oxidation of galena (PbS) followed by self-reduction. Let's break down the problem step by step.
### Step 1: Write the Balanced Chemical Equa... |
[
{
"content": "Problem: The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? [asy]\ndraw((-.3,-3)--(.1,1)--(-1,0)--(3,0)--cycle);\nlabel(\"$A$\",(.1,1),N);\nlabel(\"$B$\",(-1,0),W);\nlabel(\"$C... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we start by analyzing the given information. The area of triangle \(ABC\) is 6 square centimeters. We know that \(AB \parallel DE\) and \(BD = 4BC\). We need to find the area of triangle \(CDE\).
First, since \(AB \parallel DE\), triangles \(ABC\) and \(CDE\) are similar by the AA (Angle-Angle) s... |
[
{
"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 $X$ be the set consisting of the first 2018 terms of the a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 144 | JEEBench | {
"expected_answer": "3748",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To determine the number of elements in the set \(X \cup Y\), we need to find the union of the two arithmetic progressions (APs) and count the distinct terms. Let's start by defining the two sequences.
**Step 1: Define the arithmetic progressions.**
- **Set \(X\):** The first term \(a_1 = 1\) and common difference \(d... |
[
{
"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 | 346 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if it's possible to craft an artifact using the given magical materials by applying a specific operation any number of times. The operation allows us to increase the count of one material by 1 and decrease the count of every other material by 1. The key is to check if we can ... |
[
{
"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 | 78 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to select a subset of vertices from a tree such that:
1. The subset is connected.
2. Every integer from 1 to n appears at least once in the subset.
3. The total cost (sum of 2^vertex) is minimized.
### Approach
The problem involves selecting vertices with specific constraints. The key in... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: toluene is treated with nitric acid and sulfuric acid, forming product 1.\n\n1 is treated with MnO2 and H2SO4, forming product 2.\n\n2 is treated with acetone and aqueou... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 30 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's work through this step by step to determine the molecular symmetry group of product 3.
First, let's identify the reagents and products involved in each step:
1. **Step 1**: Toluene (C7H8) is treated with nitric acid and sulfuric acid. This likely results in the nitration of toluene, forming **nitrotoluene** (C7... |
[
{
"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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 106 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "30",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze each statement step by step, focusing on the nature of the bonds in the dimeric structures and the Lewis acidity of the molecules involved.
**Option [A]: \(\text{Al}(\text{CH}_3)_3\) has three-centre two-electron bonds in its dimeric structure.**
First, consider the dimeric s... |
[
{
"content": "Problem: What is the degree measure of the acute angle formed by lines with slopes $2$ and $\\frac{1}{3}$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 2 | AMC23 | {
"expected_answer": "45",
"problem_id": "2",
"reference_solution": "",
"subject": null,
"type": null
} | To find the degree measure of the acute angle formed by lines with slopes \(2\) and \(\frac{1}{3}\), we can use the formula for the tangent of the angle between two lines. The formula is:
\[
\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|
\]
where \(m_1\) and \(m_2\) are the slopes of the two lines. Here, ... |
[
{
"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 | 208 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine a valid way to assign fillings to BBQ buns such that no filling is used exactly once, and the distance between any two buns with the same filling is a perfect square. If no such assignment exists, return -1.
### Approach
Let's break down the problem:
1. **Constraints Analy... |
[
{
"content": "Problem: Find the largest possible real part of \\[(75+117i)z+\\frac{96+144i}{z}\\] where $z$ is a complex number with $|z|=4$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
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"seed": 9,
"temperature": 0.7
} | 9 | 21 | AIME24 | {
"expected_answer": "540",
"problem_id": "aime24-21",
"reference_solution": "Let $z=a+bi$ such that $a^2+b^2=4^2=16$ . The expression becomes: \\[(75+117i)(a+bi)+\\dfrac{96+144i}{a+bi}.\\] Call this complex number $w$ . We simplify this expression. \\begin{align*}\nw&=(75+117i)(a+bi)+\\dfrac{96+144i}{a+bi} \... | Given the problem: Find the largest possible real part of \((75+117i)z + \frac{96+144i}{z}\) where \(z\) is a complex number with \(|z|=4\). Mark your solution with \boxed.
1. **Express \(z\) in terms of its real and imaginary parts:**
Since \(|z| = 4\), we can write \(z = 4e^{i\theta} = 4(\cos\theta + i\sin\theta)... |
[
{
"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 | 372 | CodeForces | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | ```python
import sys
input = sys.stdin.readline
def solve():
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
dp = [[0] * (n + 1) for _ in range(n + 1)]
def dfs(l, r):
if l > r:
return 0
if ... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 377 | JEEBench | {
"expected_answer": "0.5",
"problem_id": "2",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To find the value of \(\lim_{x \to \alpha^+} f(g(x))\), we need to evaluate the limit step by step. Let's start by understanding the functions \(f\) and \(g\).
Given:
\[
f(x) = \sin \left( \frac{\pi x}{12} \right)
\]
\[
g(x) = \frac{2 \log_e (\sqrt{x} - \sqrt{\alpha})}{\log_e (e^{\sqrt{x}} - e^{\sqrt{\alpha}})}
\]
Fi... |
[
{
"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 happens to neurotransmitters once they have \"done their job?\"\nOptions: A. Neurotransmitters diffuse away and are exhaled, B. Neurotransmitter... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 219 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | \boxed{I} |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 291 | 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 smallest number of light bulbs n such that after performing a series of flips based on divisibility, exactly k bulbs remain on. Let me think through this step by step.
First, let me understand the problem again. Initially, all bulbs are on. For each i... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Sigmatropic rearrangement is a class of pericyclic reactions. In these reactions, the terminal pi bond migrates into the sigma bond. Cope and Claisen rearrangements are ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 48 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | Let's tackle these reactions step by step.
Starting with the first reaction: 1,1-dimethoxyethan-1-amine + but-3-en-2-ol + (H+ + Heat) → A.
The reactants are 1,1-dimethoxyethan-1-amine (an amine with two methoxy groups and a terminal amino group) and but-3-en-2-ol (an alcohol with a double bond at C3 and a hydroxyl ... |
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