context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 12
values | metadata dict | model_outputs stringlengths 1 112k |
|---|---|---|---|---|---|---|
[
{
"content": "Problem: There are $n$ values of $x$ in the interval $0<x<2\\pi$ where $f(x)=\\sin(7\\pi\\cdot\\sin(5x))=0$. For $t$ of these $n$ values of $x$, the graph of $y=f(x)$ is tangent to the $x$-axis. Find $n+t$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 23 | AIME25 | {
"expected_answer": "149",
"problem_id": "II-9",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we first need to determine the values of \(x\) in the interval \(0 < x < 2\pi\) where \(f(x) = \sin(7\pi \sin(5x)) = 0\).
The function \(\sin(7\pi \sin(5x)) = 0\) implies that:
\[7\pi \sin(5x) = k\pi \quad \text{for integer } k.\]
This simplifies to:
\[\sin(5x) = \frac{k}{7}.\]
The range of \(\si... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 88 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of nonempty strings \( t \neq \texttt{"a"} \) that can partition the given string \( s \) such that each substring is either \( t \) or \(\texttt{"a"}\), and at least one substring is \( t \).
### Thought Process:
1. **Identify all possible substrings** of the giv... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 40 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand how the operations affect the permutation and how we can use the given sequences to determine the number of valid permutations. Here's a step-by-step approach:
1. **Understand the Operations**: Each operation splits an array into two parts and writes the maximum values of t... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 104 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we can follow the editorial's approach to calculate the maximum cost of a path. Here's the step-by-step plan:
1. **Calculate the sum of the maximum values** for each column, i.e., for each column, take the maximum of the two values in that column.
2. **Iterate through each possible column** that... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 378 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to construct a permutation that maximizes the value of \( k \) after performing the given operations. Let's break down the thought process:
1. **Odd Operations**: For odd indices, \( k \) is updated using the bitwise AND operation. This means we want to ensure that the bits that are set ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 49 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of candidates that need to be excluded for each candidate to win the elections. Here's a step-by-step thought process:
1. **Sort the Votes**: We need to sort the votes in ascending order to easily determine the candidates that can be excluded to make the c... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nEffective antibody production by B cells of the mammalian adaptive immune system is criti... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 120 | HLESubset | {
"expected_answer": "B",
"problem_id": "670013827794cc36bc974f27",
"reference_rationale": "B cell production of high-affinity antibodies requires class-switching and somatic hypermutation (SHM). For the induction of an adaptive immune response as well as high-affinity antibody production against a target antigen... | Explanation: To determine which groups of mutant mice would have a significantly different titer of high-affinity OVA-specific antibodies that have undergone somatic hypermutation (SHM), we need to understand the function of the proteins targeted by the mutations. AID (Activation-Induced Cytidine Deaminase) is crucial ... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nTo improve the catalytic efficiency of enzyme Zma1, which converts molecule A to B resear... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 223 | HLESubset | {
"expected_answer": "G",
"problem_id": "671d9e9d29e7fde7166e474d",
"reference_rationale": "1. Metals.\nIt is known that divalent metal ions function as cofactors of enzymes.\nThe presence of MgCl2 increases kcat so MgCl2 is a cofactor.\nCucl2 and Cacl2 decrease kcat so CuCl2 and CaCl2 are inhibitors. Cu ions and... | Explanation: Let's analyze the results to understand the function of Al1, Al2, and Rga1 based on the provided data.
1. **Al1 and Al2**: Both Al1 and Al2 show significant increases in kcat when added to the enzyme in the presence of the standard buffer. Specifically, adding 5 mM Al1 increases kcat to 1000/second, while... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given positive integers N, M, K, and a sequence of non-negative integers: A=(A_1,A_2,\\ldots,A_N).\nFor a non-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 111 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | ```python
def calculate_xor_score(N, M, K, A):
MOD = 998244353
# Initialize the dp table
dp = [[0] * (1 << 20) for _ in range(M + 1)]
dp[0][0] = 1 # Base case: empty subsequence
# Calculate the XOR scores for all subsequences
for a in A:
for length in range(M, 0, -1):
f... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The circle $C_{1}: x^{2}+y^{2}=3$, with centre at $O$, intersects the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 35 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "48",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to follow a step-by-step approach. Let's start by finding the coordinates of the point \(P\) where the circle \(C_1\) intersects the parabola \(C\).
1. **Find the coordinates of \(P\):**
The circle \(C_1\) is given by \(x^2 + y^2 = 3\). The parabola \(C\) is given by \(x^2 = 2y\). Sub... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a rectangular cake with some strawberries on the xy-plane. The cake occupies the rectangular area \\lbrace (x... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 210 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def min_max_strawberries():
import sys
input = sys.stdin.read
W, H = map(int, input().split())
N = int(input())
points = [tuple(map(int, input().split())) for _ in range(N)]
A = int(input())
vertical_lines = list(map(int, input().split()))
B = int(input())
horizontal_lines ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 198 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to carefully analyze the conditions for a string to match the template. The key points are:
1. The length of the string must match the length of the array.
2. The mapping of characters to numbers and vice versa must be consistent.
Here's a step-by-step approach:
1. **Read Input**: We n... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: At $298 \\mathrm{~K}$, the limiting molar conductivity of a we... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 353 | JEEBench | {
"expected_answer": "0.22",
"problem_id": "25",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to understand the relationship between molar conductivity, degree of dissociation, and the effect of dilution on molar conductivity.
1. **Limiting Molar Conductivity and Degree of Dissociation:**
The limiting molar conductivity, $\Lambda_m^0$, is given as $4 \times 10^2 \, \text{S cm}... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array of integers nums. Some values in nums are missing and are denoted by -1.\nYou can choose a pair of positive integers (x, y) exactly once... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 324 | LiveCodeBenchV5 | {
"expected_answer": "",
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} | ```python
def minAbsoluteDifference(nums):
n = len(nums)
# Replace -1 with a value that doesn't affect sorting
for i in range(n):
if nums[i] == -1:
nums[i] = float('inf')
# Sort the array
nums.sort()
# Replace inf back with -1
for i in range(n):
if nums[... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 87 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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"subject": null,
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} | To solve this problem, we need to understand how the value of \( c \) changes based on the operations we perform. The key observation here is that the absolute value operation can be seen as a decision point that can either amplify or negate the current value of \( c \).
### Thought Process:
1. **Understanding the Pr... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a weighted simple directed graph with N vertices and M edges.\r\nThe vertices are numbered 1 to N, and the i-... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 374 | LiveCodeBench | {
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} | To solve this problem, we need to find a walk that visits each vertex at least once and minimizes the total weight of the edges traversed. Given the constraints, a brute-force approach can be used to check all possible walks. However, for larger graphs, this approach may not be efficient. Here, we will use a brute-forc... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: A debate club consists of 6 girls and 4 boys. A team of 4 members is to b... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 25 | JEEBench | {
"expected_answer": "A",
"problem_id": "38",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to consider the constraint that the team must include at most one boy. This means we have two cases to consider: the team includes no boys, or the team includes exactly one boy.
**Case 1: The team includes no boys.**
In this case, the team is composed entirely of girls. There are 6 girl... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 63 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum size of Alice's plot for different scenarios. Here's the thought process:
1. **Calculate the initial maximum size of Alice's plot (`alpha`)**:
- Alice's plot must include the bottom-right cell (`n, 1`).
- To maximize her plot, Alice should ideally follow th... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 351 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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"subject": null,
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} | To solve this problem, we need to understand how the score of the tree changes based on the values of the vertices. The key points are:
1. The score of a leaf depends on the path from the root to the leaf and the transitions between `0` and `1`.
2. If the root's value is already decided, we can directly compute the sc... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Which of the following statement(s) is(are) true?\n(A) Monosaccharides... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 196 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "29",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine which of the statements (A) through (D) are true, let's analyze each one:
(A) Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones.
- Monosaccharides are the simplest carbohydrates and cannot be broken down further through hydrolysis. They are already in their simplest form. The... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nTwo business partners named Alex and Tyler are looking to incorporate a company in Ontari... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 216 | HLESubset | {
"expected_answer": "C",
"problem_id": "671c6a1aacee876e82d4bc0e",
"reference_rationale": "This questions deals with incorporations and corporate structuring, and presents a type of matter that is very common. For the purposes of keeping the answer options a reasonable length, only the three rights that are req... | Explanation:
Let's analyze each option to see which one meets all the requirements specified:
1. **Equal control**: Both partners must have equal voting rights.
2. **Alex's salary**: Alex should receive payments via salary.
3. **Tyler's dividends**: Tyler should receive payments via dividends.
4. **Option to bring in... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: There are three main types of buying situations in an organization, referred to by Robinson, Faris, and Wind (1967) as _____________.\nOptions: A. B... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 374 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | J |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given three positive integers num1, num2, and num3.\nThe key of num1, num2, and num3 is defined as a four-digit number such that:\n\nInitially, if any ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def generate_key(num1: int, num2: int, num3: int) -> int:
# Convert numbers to strings and pad with leading zeros to ensure they are 4 digits
num1_str = str(num1).zfill(4)
num2_str = str(num2).zfill(4)
num3_str = str(num3).zfill(4)
key = ""
# Iterate through each digit positi... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: What is the average kinetic energy of air molecules at a temperature of 300° K? What would be a typical speed for nitrogen molecules, which are the m... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 201 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | A |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nGiven that some environmental conditions of chronic infections favor the emergence of hyp... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 473 | HLESubset | {
"expected_answer": "C",
"problem_id": "673a8c2e4e2e35b51a27fafd",
"reference_rationale": "Conversion to the mucoid phenotype in hypermutator strains of Pseudomonas aeruginosa can be increased because of an increased mutation frequency on the mucA gene. However, most of mutations of the mucA gene observed in hyp... | Explanation: Hypermutator strains of Pseudomonas aeruginosa have a higher rate of mutation compared to normal strains. This increased mutation rate can lead to a higher frequency of various phenotypes, including mucoid variants. The mucoid phenotype is primarily caused by mutations in the mucA gene. With increased muta... |
[
{
"content": "Problem: Find the greatest common divisor of $3339$, $2961$, and $1491$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 89 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
"type": null
} | To find the greatest common divisor (GCD) of \(3339\), \(2961\), and \(1491\), we can use the Euclidean algorithm, which involves repeated division and taking remainders. We will first find the GCD of the first two numbers, and then use that result to find the GCD with the third number.
### Step 1: Find the GCD of \(3... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to keep track of the remaining grid and the chips in it after each move. We will use a 2D array to represent the grid and a set to store the positions of the chips. For each move, we will update the grid and the set of chip positions accordingly.
Here's the step-by-step plan:
1. **Initi... |
[
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such that $12x^2 - xy - 6y^2 = 0$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we start with the given equation:
\[12x^2 - xy - 6y^2 = 0.\]
First, we rearrange the equation:
\[12x^2 - xy - 6y^2 = 0.\]
We can factor this quadratic equation in terms of \(x\). To do this, we look for two numbers that multiply to \(12 \cdot (-6y^2) = -72y^2\) and add up to \(-y\). These number... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 116 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the maximum number of operations we can perform on the array. Each operation involves finding an index \(i\) where \(a_i = i\) and removing \(a_i\) and \(a_{i+1}\) from the array.
### Thought Process:
1. **Identify Valid Operations**: We need to iterate through the array and fin... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N cities in a certain country.\nYou will travel from your office in city 1 to a destination in city N, via z... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 309 | LiveCodeBench | {
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"subject": null,
"type": null
} | To solve this problem, we can use dynamic programming. We will maintain two arrays `dp_car` and `dp_train` where `dp_car[i]` represents the minimum time to reach city `i` using a car and `dp_train[i]` represents the minimum time to reach city `i` using a train. We will iterate through each city and update these arrays ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: What is the energy of the Relativistic Heavy Ion Collider (RHIC) so that the speed of the nucleus X is equal to 0.96c?\n\nKnowing that X is defined as Li with 3 neutrons... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 31 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | A |
[
{
"content": "Problem: Let $p(x)$ be a monic polynomial of degree 4. Three of the roots of $p(x)$ are 1, 2, and 3. Find $p(0) + p(4).$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 195 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Given that \( p(x) \) is a monic polynomial of degree 4 with roots 1, 2, and 3, we can express \( p(x) \) in the form:
\[
p(x) = (x-1)(x-2)(x-3)(x-r)
\]
where \( r \) is the fourth root of the polynomial.
To find \( p(0) + p(4) \), we first need to determine \( p(0) \) and \( p(4) \).
1. **Finding \( p(0) \):**
\[
p(... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N+2 cells arranged in a row. Let cell i denote the i-th cell from the left.\nThere is one stone placed in ea... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 25 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we can use a breadth-first search (BFS) approach to find the minimum number of operations required to transform the initial state `S` into the target state `T`. Here's the Python function that implements this approach:
```python
from collections import deque
def min_operations(N, S, T):
# I... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.For a positive integer k, the Pyramid Sequence of size k is a sequence of length (2k-1) where the terms of the sequenc... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 363 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | ```python
import sys
def find_max_pyramid_size():
input = sys.stdin.read
data = input().split()
n = int(data[0])
sequence = list(map(int, data[1:]))
max_val = max(sequence)
count = sequence.count(max_val)
# Check if we can form a pyramid of size 2*max_val-1
if count >= 2 ... |
[
{
"content": "Problem: Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$ , $AC=BD= \\sqrt{80}$ , and $BC=AD= \\sqrt{89}$ . There exists a point $I$ inside the tetrahedron such that the distances from $I$ to each of the faces of the tetrahedron are all equal. This distance can be written in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 28 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-28",
"reference_rationale": null,
"reference_solution": "Notice that \\(41=4^2+5^2\\), \\(89=5^2+8^2\\), and \\(80=8^2+4^2\\), let \\(A~(0,0,0)\\), \\(B~(4,5,0)\\), \\(C~(0,5,8)\\), and \\(D~(4,0,8)\\). Then the plane \\(BCD\\) has a normal\n\\begin{equation*}\n... | To solve the problem, we need to determine the volume of the tetrahedron \(ABCD\) and use the fact that the point \(I\) is the incenter of the tetrahedron, meaning the distances from \(I\) to each face are equal to the inradius \(r\).
First, we calculate the volume of the tetrahedron using the Cayley-Menger determinan... |
[
{
"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 | 297 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand how to maximize the MEX (minimum excluded value) by optimally performing the given operations. Here’s the thought process:
1. **Initial Observation**: The MEX of an array is the smallest non-negative integer that is not present in the array. By adding a fixed value `x` to a... |
[
{
"content": "Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we first need to determine the equation of the parabola after it is rotated $60^\circ$ counterclockwise around the origin. The rotation transformation can be represented by the equations:
\[ x' = x \cos \theta - y \sin \theta \]
\[ y' = x \sin \theta + y \cos \theta \]
For $\theta = 60^\circ$, we ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $a_{1}, a_{2}, a_{3}, \\ldots$ be a sequence of positive i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 272 | JEEBench | {
"expected_answer": "1",
"problem_id": "50",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to first express the sequences \(a_n\) and \(b_n\) in terms of \(c\) and \(n\).
The arithmetic progression \(a_n\) has the first term \(a_1 = c\) and common difference 2. The general term of the arithmetic progression is:
\[
a_n = c + (n-1) \cdot 2 = c + 2n - 2
\]
The geometric progress... |
[
{
"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 | 83 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to count the number of nondegenerate right triangles that can be formed from the given points. A right triangle in this context is one where one of the angles is 90 degrees. This means that the dot product of the vectors formed by the points must be zero.
Given the constraints, a brute-f... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 163 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we can follow these steps:
1. **Input Handling**: Read the number of test cases `t`, followed by two lists of integers `n` and `k` which represent the parameters for the binomial coefficient calculation.
2. **Pattern Recognition**: Recognize that the erroneous formula for the binomial coefficien... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a length-N sequence A=(A_1,A_2,\\dots,A_N) consisting of 0, 1, and 2,\r\nand a length-N string S=S_1S_2\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 231 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to follow these steps:
1. Parse the input to get the sequence `A` and the string `S`.
2. Identify all tuples `(i, j, k)` such that `1 ≤ i < j < k ≤ N` and `S_iS_jS_k = "MEX"`.
3. For each identified tuple, compute the `mex` value of the corresponding elements in `A`.
4. Sum up all the `m... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Reaction of $\\mathbf{x} \\mathrm{g}$ of $\\mathrm{Sn}$ with $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 355 | JEEBench | {
"expected_answer": "3.57",
"problem_id": "27",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the amount of tin (Sn) that reacted with HCl to produce a salt, which then reacted with nitrobenzene to produce an organic salt.
First, let's identify the reactants and the products involved in the reactions:
1. **Reaction of Sn with HCl:**
\[
\mathrm{Sn} + 2\mathrm{H... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are zero or more sensors placed on a grid of H rows and W columns. Let (i, j) denote the square in the i-th row ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 307 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def count_sensors():
from collections import defaultdict
# Read input
H, W = map(int, input().split())
grid = [input() for _ in range(H)]
# Function to check if two cells are adjacent
def is_adjacent(x1, y1, x2, y2):
return max(abs(x1 - x2), abs(y1 - y2)) == 1
# Function... |
[
{
"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 | 19 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to consider the following steps:
1. **Preprocessing**: Calculate the initial GCD values for the arrays `a` and `b`.
2. **Sorting and Segment Tree**: Use a segment tree to efficiently manage the swaps and their costs.
3. **Query Handling**: For each query, determine the maximum GCD sum by... |
End of preview. Expand in Data Studio
YAML Metadata Warning:empty or missing yaml metadata in repo card
Check out the documentation for more information.
mlfoundations-dev/Qwen2.5-7B-Instruct_eval_2e29
Precomputed model outputs for evaluation.
Evaluation Results
Summary
| Metric | AIME24 | AMC23 | MATH500 | MMLUPro | JEEBench | GPQADiamond | LiveCodeBench | CodeElo | CodeForces | AIME25 | HLE | LiveCodeBenchv5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Accuracy | 15.0 | 53.5 | 70.6 | 43.0 | 33.6 | 23.7 | 33.0 | 5.1 | 9.9 | 8.0 | 11.8 | 17.2 |
AIME24
- Average Accuracy: 15.00% ± 0.85%
- Number of Runs: 10
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 13.33% | 4 | 30 |
| 2 | 16.67% | 5 | 30 |
| 3 | 20.00% | 6 | 30 |
| 4 | 16.67% | 5 | 30 |
| 5 | 16.67% | 5 | 30 |
| 6 | 13.33% | 4 | 30 |
| 7 | 13.33% | 4 | 30 |
| 8 | 13.33% | 4 | 30 |
| 9 | 16.67% | 5 | 30 |
| 10 | 10.00% | 3 | 30 |
AMC23
- Average Accuracy: 53.50% ± 1.38%
- Number of Runs: 10
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 60.00% | 24 | 40 |
| 2 | 50.00% | 20 | 40 |
| 3 | 50.00% | 20 | 40 |
| 4 | 57.50% | 23 | 40 |
| 5 | 57.50% | 23 | 40 |
| 6 | 55.00% | 22 | 40 |
| 7 | 50.00% | 20 | 40 |
| 8 | 55.00% | 22 | 40 |
| 9 | 45.00% | 18 | 40 |
| 10 | 55.00% | 22 | 40 |
MATH500
- Accuracy: 70.60%
Accuracy Questions Solved Total Questions 70.60% 353 500
MMLUPro
- Average Accuracy: 43.00% ± 0.00%
- Number of Runs: 1
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 43.00% | 215 | 500 |
JEEBench
- Average Accuracy: 33.59% ± 0.48%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 34.22% | 176.25 | 515 |
| 2 | 34.13% | 175.75 | 515 |
| 3 | 32.43% | 167.0 | 515 |
GPQADiamond
- Average Accuracy: 23.74% ± 0.24%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 23.23% | 46 | 198 |
| 2 | 23.74% | 47 | 198 |
| 3 | 24.24% | 48 | 198 |
LiveCodeBench
- Average Accuracy: 33.01% ± 0.83%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 32.49% | 166 | 511 |
| 2 | 31.90% | 163 | 511 |
| 3 | 34.64% | 177 | 511 |
CodeElo
- Average Accuracy: 5.12% ± 1.03%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 7.16% | 28 | 391 |
| 2 | 4.35% | 17 | 391 |
| 3 | 3.84% | 15 | 391 |
CodeForces
- Average Accuracy: 9.93% ± 0.71%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 8.83% | 40 | 453 |
| 2 | 9.71% | 44 | 453 |
| 3 | 11.26% | 51 | 453 |
AIME25
- Average Accuracy: 8.00% ± 1.43%
- Number of Runs: 10
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 6.67% | 2 | 30 |
| 2 | 6.67% | 2 | 30 |
| 3 | 20.00% | 6 | 30 |
| 4 | 3.33% | 1 | 30 |
| 5 | 10.00% | 3 | 30 |
| 6 | 3.33% | 1 | 30 |
| 7 | 6.67% | 2 | 30 |
| 8 | 6.67% | 2 | 30 |
| 9 | 10.00% | 3 | 30 |
| 10 | 6.67% | 2 | 30 |
HLE
- Average Accuracy: 11.85% ± 0.23%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 11.33% | 58 | 512 |
| 2 | 12.30% | 63 | 512 |
| 3 | 11.91% | 61 | 512 |
LiveCodeBenchv5
- Average Accuracy: 17.16% ± 0.39%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 17.89% | 66 | 369 |
| 2 | 16.53% | 61 | 369 |
| 3 | 17.07% | 63 | 369 |
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