context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 8
values | metadata dict | model_outputs stringlengths 1 186k |
|---|---|---|---|---|---|---|
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums of positive integers and an integer k.\nIn one operation, you can remove the last element of the array and add it to your collectio... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 98 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum number of operations to collect elements 1 to k inclusive. The operations allow me to remove the last element of the array and add it to my collection. Hmm. Wait, but the example shows that when k is 2, the answer is 4. Wait, how does that work? Let me look at the fir... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Calculate the amount of non-Gaussianity(nG) in the Schrödinger cat state using relative entropy measure. The state is defined as,\n|psi> =( cos(phi)|alpha> + sin(phi)|-a... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 166 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to calculate the non-Gaussianity (nG) for a given Schrödinger cat state using the relative entropy measure. Let's break down the steps.
### Step 1: Understanding the State
The state is given by:
\[ |\psi> = \frac{\cos(\phi)|\alpha> + \sin(\phi)|-\alpha>}{N} \]
with normalization factor \... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s consisting only of uppercase English letters.\nYou can apply some operations to this string where, in one operation, you can remove an... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 23 | 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 minimum length of a string after removing as many "AB" or "CD" substrings as possible. The tricky part is that when I remove a substring, it might create new possible "AB" or "CD" pairs, so I need to process that. Hmm.
Let me think about the examples.... |
[
{
"content": "Problem: Find the greatest integer less than $(\\sqrt{7} + \\sqrt{5})^6.$ (Do not use a calculator!)\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 21 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the greatest integer less than \((\sqrt{7} + \sqrt{5})^6\), we can start by considering the conjugate of \(\sqrt{7} + \sqrt{5}\), which is \(\sqrt{7} - \sqrt{5}\). Let's denote \(a = \sqrt{7} + \sqrt{5}\) and \(b = \sqrt{7} - \sqrt{5}\). Then, we have \(a^6 + b^6\) which is an integer because the product of con... |
[
{
"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: Suppose a ${ }_{88}^{226} R a$ nucleus at rest and in ground s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 220 | JEEBench | {
"expected_answer": "135",
"problem_id": "13",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to determine the energy of the emitted gamma photon when the radon-222 nucleus transitions from an excited state to its ground state. We will follow these steps:
1. **Alpha Decay Calculation**: First, we calculate the kinetic energy of the alpha particle emitted during the alpha decay of... |
[
{
"content": "Problem: The sum of the first $n$ terms in the infinite geometric sequence $\\left\\{\\frac{1}{4},\\frac{1}{8},\\frac{1}{16},\\dots \\right\\}$ is $\\frac{255}{512}$. Find $n$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 446 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for \( n \) in the given problem, we need to find the number of terms in the infinite geometric sequence \(\left\{\frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dots \right\}\) whose sum is \(\frac{255}{512}\).
First, identify the parameters of the geometric sequence. The first term \( a \) is \(\frac{1}{4}\), and ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: In an experiment, a researcher reacted ((2,2-dimethylbut-3-en-1-yl)oxy)benzene with hydrogen bromide. After some time, they checked the progress of the reaction using TL... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 22 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the possible products formed when ((2,2-dimethylbut-3-en-1-yl)oxy)benzene reacts with hydrogen bromide (HBr). The reaction results in the reactant spot diminishing and two new spots appearing on the TLC plate. This indicates that the reaction has produced two new compounds, w... |
[
{
"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: $\\quad \\mathrm{H}_{2} \\mathrm{~S}$ (5 moles) reacts completely with acidified aqueous potassium permanganat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 509 | JEEBench | {
"expected_answer": "18",
"problem_id": "42",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | To solve this problem, we need to determine the number of moles of water produced and the number of moles of electrons involved when hydrogen sulfide (H₂S) reacts completely with an acidified potassium permanganate (KMnO₄) solution. Then, we sum these two values to find the final answer.
### Step 1: Write the Balanced... |
[
{
"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 | 20 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to place x 1x1 icons and y 2x2 icons on the minimum number of 5x3 screens. Each screen can have up to 5*3=15 icons. The challenge is figuring out how to pack these icons efficiently.
Hmm, first, I should think about how each screen can be filled. For e... |
[
{
"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 binary array possible of length n.\nAlice and Bob are playing a game that consists of n levels. Some of the levels in the game are impossible t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 484 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Alice and Bob play a game, and I have to find the minimum number of levels Alice should play to have more points than Bob. Let's think through this step by step.
First, let's understand the problem. The possible array tells us if a level is possible (1) or not (0). Alic... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A string of length $1 \\mathrm{~m}$ and mass $2 \\times 10^{-5} \\mathrm{~kg}$ is under tension $T$. When the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 504 | JEEBench | {
"expected_answer": "5",
"problem_id": "27",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve for the tension \( T \) in the string, we need to use the properties of standing waves on a string. The frequencies of the harmonics are related to the length of the string, its tension, and its mass per unit length.
### Step 1: Understand the Harmonic Frequencies
The frequencies of the harmonics (vibration m... |
[
{
"content": "Problem: Every morning Aya goes for a $9$ -kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 15 | AIME24 | {
"expected_answer": "204",
"problem_id": "aime24-15",
"reference_solution": "$\\frac{9}{s} + t = 4$ in hours and $\\frac{9}{s+2} + t = 2.4$ in hours. Subtracting the second equation from the first, we get, $\\frac{9}{s} - \\frac{9}{s+2} = 1.6$ Multiplying by $(s)(s+2)$ , we get $9s+18-9s=18=1.6s^{2} + 3.2s$ ... | To solve this problem, we need to determine the time Aya spends walking and in the coffee shop, then find the total time when she walks at a different speed. Let's break down the problem step by step.
First, we know that Aya walks 9 kilometers. The time taken for the walk at speed \( s \) is 4 hours, which includes \(... |
[
{
"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 string s that consists of digits from 0 to 9.\nA string t is called a semi-repetitive if there is at most one consecutive pair of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 20 | 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 longest semi-repetitive substring in a given string. Let's see. The definition says that a semi-repetitive string has at most one consecutive pair of the same digits. So, if there are two consecutive same digits, that's allowed, but if there's a third ... |
[
{
"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 bar of mass $M=1.00 \\mathrm{~kg}$ and length $L=0.20 \\mathrm{~m}$ is ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 467 | JEEBench | {
"expected_answer": "A",
"problem_id": "21",
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | To solve this problem, we need to analyze the elastic collision between the small mass \( m \) and the bar, considering both the momentum and angular momentum conservation principles. Since the collision is elastic, both linear momentum and angular momentum are conserved.
### Step-by-Step Solution:
1. **Conservation ... |
[
{
"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 | 320 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to choose a subset of games to maximize the expected value of my winnings. The expected value is the product of the product of probabilities divided by 100 for each selected game and the sum of their winnings. Hmm.
Wait, the problem says that the expec... |
[
{
"content": "Problem: What's the largest eight-digit base 2 integer? Express your answer in base 10.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 278 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the largest eight-digit base 2 integer and convert it to base 10, we can follow these steps:
1. **Understanding Base 2**: In base 2 (binary), each digit can be either 0 or 1. The largest number in any base 2 system with \( n \) digits is the one where all digits are 1s. For example, a 3-digit binary numbe... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $S$ be the reflection of a point $Q$ with respect to the plane giv... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 387 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the reflection of a point \( Q \) with respect to a given plane and verify which of the provided options are true based on the coordinates of the reflected point \( S \).
### Step 1: Understand the Plane Equation
The given plane is represented by the parametric equation:
\[
... |
[
{
"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 an experiment to measure the speed of sound by a resonating air col... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 153 | JEEBench | {
"expected_answer": "AC",
"problem_id": "6",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which statements are true based on the given data from the experiment to measure the speed of sound using a resonating air column. Let's go through the problem step by step.
### Step 1: Understand the Experiment
The experiment uses a tuning fork with a known frequency (500 H... |
[
{
"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 | 217 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this lattice optimizing problem. Hmm. The problem is about finding the maximum MEX of a set S as we traverse from (1,1) to (n,n) in a grid graph. The edges have values, and each time we pass an edge, its value is added to S. The goal is to maximize the MEX when we reach the end.... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $P=\\left[\\begin{array}{ccc}1 & 0 & 0 \\\\ 4 & 1 & 0 \\\\ 16 & 4 & 1... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 57 | JEEBench | {
"expected_answer": "B",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to find the matrix \( Q \) such that \( P^{50} - Q = I \), where \( P \) is given and \( I \) is the identity matrix. Then, we need to compute the value of \( \frac{q_{31} + q_{32}}{q_{21}} \).
First, let's analyze the matrix \( P \):
\[ P = \begin{pmatrix} 1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 &... |
[
{
"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 k and an integer x.\nConsider s is the 1-indexed binary representation of an integer num. The price of a number num is the number of i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 159 | 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 integer num such that the sum of the prices of all numbers from 1 to num is <= k. The price of a number is the count of positions i (1-indexed) where i mod x equals 0 and the ith bit in the binary representation of the number is set (1).
Let ... |
[
{
"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 | 12 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is to count the number of ordered pairs (a, b) such that 1 ≤ a ≤ n, 1 ≤ b ≤ m, and b multiplied by the greatest common divisor of a and b is a multiple of a + b. Wait, the condition is b * gcd(a, b) must be divisible by (a + b). Or in mathematical terms, (a + b)... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Mr. Glass borrowed $250 from the ABC Finance Company. He agreed to repay the $250 in five monthly installments, with interest at 3% a month on the fi... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 443 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. Mr. Glass borrowed $250 from ABC Finance Company. He has to pay it back in five monthly installments. The interest is calculated at 3% a month on the first $150 and 2% on the remaining part. I need to find out his total interest cost. Hmm.
Wait, wait. Wait, how does the interest work here? Let... |
[
{
"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 | 57 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Vlad has to create a certain number of rounds, each requiring a problem of a specific difficulty. The input gives the number of existing problems and the number of rounds, along with the difficulties of those existing problems. The goal is to find the minimum number of n... |
[
{
"content": "Problem: In how many ways can 8 people sit around a round table if 3 of the people -- Pierre, Rosa, and Thomas -- all want to sit together? (Two seatings are considered the same if one is a rotation of the other.)\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 32 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem of seating 8 people around a round table where Pierre, Rosa, and Thomas must sit together, we can treat the trio as a single "block" or "super person". This reduces the problem to arranging 6 blocks (the trio plus the other 5 individuals) around a round table, and then arranging the three people wi... |
[
{
"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 $X$ and $Y$ be two events such that $P(X)=\\frac{1}{3}, P(X \\mid ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 88 | JEEBench | {
"expected_answer": "AB",
"problem_id": "43",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine which of the given options are correct based on the provided probabilities. Let's start by analyzing the given information and using probability rules to find the required probabilities.
Given:
- \( P(X) = \frac{1}{3} \)
- \( P(X \mid Y) = \frac{1}{2} \)
- \( P(Y \mid X) = \... |
[
{
"content": "Problem: Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$ . Bob's list has 2024 sets. Find the sum of the elements of A.\nMark your solution with \\boxed\nAnswer:",... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 5 | AIME24 | {
"expected_answer": "55",
"problem_id": "aime24-5",
"reference_solution": "Let $k$ be one of the elements in Alices set $A$ of positive integers. The number of sets that Bob lists with the property that their maximum element is k is $2^{k-1}$ , since every positive integer less than k can be in the set or o... | To solve this problem, we need to determine the set \( A \) of positive integers such that the number of finite nonempty subsets \( B \) of positive integers where the maximum element of \( B \) is in \( A \) is exactly 2024. We then need to find the sum of the elements of \( A \).
### Approach
1. **Understanding the ... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 25 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the correct reactant (A) for the given reaction and the correct sequence of dienes (B) based on their reactivity. Let's break down the problem step by step.
### Step 1: Understanding the Reaction
The reaction involves cyclohexene reacting with a diene (A) to form 8,8-diiodob... |
[
{
"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 remove one occurrence of the smallest element of nums.\nReturn the m... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 188 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to find the minimum number of operations to remove elements from the array so that all remaining elements are at least k. Each operation removes one occurrence of the smallest element. So the problem is about figuring out how many times we need to remove the smallest element until all el... |
[
{
"content": "Problem: Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only $\\frac{1}{3}$ full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 22 | AMC23 | {
"expected_answer": "7",
"problem_id": "25",
"reference_solution": "",
"subject": null,
"type": null
} | Let's denote the capacity of each glass as 1 unit. Mrs. Jones fills the first three glasses completely, so together they have \(3\) units. The fourth glass is filled to \(\frac{1}{3}\) of its capacity, which is \(\frac{1}{3}\) units. Therefore, the total amount of orange juice available is:
\[3 + \frac{1}{3} = \frac{9... |
[
{
"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 $\\mathrm{Pb}\\left(\\mathrm{NO}_{3}\\right)_{2}$ and $\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 449 | JEEBench | {
"expected_answer": "C",
"problem_id": "53",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | <think>
Okay, let's see. I need to figure out which compound forms when the precipitate dissolves upon adding HCl. The reaction is between lead(II) nitrate and sodium chloride. So first, when these two react, they produce a precipitate. What's the precipitate here? Well, lead(II) chloride (PbCl2) is insoluble in water,... |
[
{
"content": "Problem: Evaluate $\\log_264$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 161 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To evaluate \(\log_2 64\), we need to determine the exponent to which the base 2 must be raised to obtain 64. In other words, we need to find \(x\) such that \(2^x = 64\).
Let's think about the powers of 2:
\[
2^1 = 2
\]
\[
2^2 = 4
\]
\[
2^3 = 8
\]
\[
2^4 = 16
\]
\[
2^5 = 32
\]
\[
2^6 = 64
\]
From this, we can see tha... |
[
{
"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: In a radioactive decay process, the activity is defined as $A=-\\frac{d N}{d t}$, where $N(t)$ is the number o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 505 | JEEBench | {
"expected_answer": "16",
"problem_id": "29",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the ratio of the activities \( A_1 \) and \( A_2 \) of two radioactive sources after they have completed their 3rd and 7th half-lives, respectively. The activity of a radioactive source is given by \( A = -\frac{dN}{dt} \), which means that the activity decreases exponentiall... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $f:[0,1] \\rightarrow[0,1]$ be the function defined by $f(x)=\\fra... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 452 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "3",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given function \( f(x) = \frac{x^3}{3} - x^2 + \frac{5}{9}x + \frac{17}{36} \) and determine which of the provided statements about the areas under the horizontal lines \( L_h \) are true. The regions involved are the green region (where \( y > f(x) \)) and the red region (... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Which sequence of reactions from the following options would lead to the high-yield synthesis of 2-(tert-butyl)-1-ethoxy-3-nitrobenzene, beginning with benzene?\nOptions... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 183 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct sequence of reactions to synthesize 2-(tert-butyl)-1-ethoxy-3-nitrobenzene from benzene, let's break down each step required and match it with the given options.
**Target Molecule:** 2-(tert-butyl)-1-ethoxy-3-nitrobenzene. The structure has a tert-butyl group at position 2, an ethoxy group at ... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 109 | JEEBench | {
"expected_answer": "D",
"problem_id": "38",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the position of the point \( S \) relative to the triangle \( PQR \) based on the given vector equations. Let's start by analyzing the given equations step by step.
The given equations are:
1. \(\overrightarrow{O P} \cdot \overrightarrow{O Q} + \overrightarrow{O R} \cdot \ov... |
[
{
"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 $P Q R S$ be a quadrilateral in a plane, where $Q R=1, \\angle P Q... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 420 | JEEBench | {
"expected_answer": "AB",
"problem_id": "9",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the interval(s) that contain the value of \(4 \alpha \beta \sin \theta^{\circ}\) given the quadrilateral \(PQRS\) with specific side lengths and angles. Let's break down the problem step by step.
First, let's analyze the given information:
- \(QR = 1\)
- \(\angle PQR = \angl... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 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 the array after at most k operations. The score is the frequency of the most frequent element in the final array. The operations allowed are incrementing or decrementing any element by 1. Hmm.
Let me think about the examples. In the first... |
[
{
"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 single integer N written on a blackboard.\r\nTakahashi will repeat the following series of operations until... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 381 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Takahashi does some operations on a blackboard with integers, and I have to compute the total amount he spends. The key is that no matter the order of operations, the total payment is the same. Hmm.
The problem says that each operation involves choosing an in... |
[
{
"content": "Problem: Let $S$ be the set of points $(a,b)$ with $0 \\le a,$ $b \\le 1$ such that the equation\n\\[x^4 + ax^3 - bx^2 + ax + 1 = 0\\]has at least one real root. Determine the area of the graph of $S.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 494 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the area of the set \( S \) of points \((a, b)\) where \(0 \le a, b \le 1\) such that the equation \(x^4 + ax^3 - bx^2 + ax + 1 = 0\) has at least one real root, we need to analyze the conditions under which the polynomial \(f(x) = x^4 + ax^3 - bx^2 + ax + 1\) has a real root.
First, let's consider the po... |
[
{
"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 | 338 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem. Let's read the problem carefully.
The task is to find the minimum cost to empty array a by performing operations of two types. The initial k is 1, and each step, we can either increase k (type 1, cost 0) or remove a prefix (type 2, cost m -k). Also, the number of optimal se... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 1 | AMC23 | {
"expected_answer": "36",
"problem_id": "1",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem where positive real numbers \(x\) and \(y\) satisfy \(y^3 = x^2\) and \((y - x)^2 = 4y^2\), we start by analyzing the given equations.
First, let's rewrite the second equation \((y - x)^2 = 4y^2\). Taking the square root of both sides, we get:
\[
y - x = \pm 2y.
\]
This gives us two possible cases... |
[
{
"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.Your refrigerator has N kinds of ingredients. Let us call them ingredient 1, \\dots, ingredient N. You have Q_i grams ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 371 | 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 number of dish servings given the ingredients. Let's see. The problem says that I can make dishes A and B, and each serving of A requires A_i of each ingredient, and B requires B_i. The goal is to use all the ingredients optimally to maximize t... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 30 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the molecular symmetry group of product 3, we need to first figure out the structure of product 3 by following the reactions step by step.
1. **Toluene (C7H8) is treated with nitric acid and sulfuric acid, forming product 1.**
This is a nitration reaction. Nitration of toluene typically results in th... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Substance X, known for incorporating a heavier isotope of one of its constituent elements, reacts violently with liquid Y with the release of a gas W whose molecule cont... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 139 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the cumulative atomic masses of the lightest and heaviest elements present within Substance X. Let's break down the problem step by step.
### Step 1: Analyze the Reaction with Liquid Y
Substance X reacts violently with liquid Y to produce gas W and precipitate G.
- Gas W ha... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $p, q, r$ be nonzero real numbers that are, respectively, the $10^{\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 391 | JEEBench | {
"expected_answer": "B",
"problem_id": "17",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to analyze the given system of linear equations and the relationships between the terms \( p, q, r \) of a harmonic progression. Let's start by understanding the system of equations and the conditions given.
The system of equations is:
1. \( x + y + z = 1 \)
2. \( 10x + 100y + 1000z = 0 ... |
[
{
"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 all electrons spin, only molecules containing unpairedelectrons - only free radicals - giveesrspectra. Why is this? (Hint: Consider the poss... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 241 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand why only molecules containing unpaired electrons (free radicals) give electronic spectra. The key lies in the behavior of electron spins and their contribution to magnetic moments.
First, let's recall that electrons have a spin quantum number, which can be either +1/2 or -1... |
[
{
"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 | 332 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where for each test case, I have to find the maximum possible value of some subsequence of the given array. The value of the array is defined as its size minus the number of set bits in the bitwise OR of all elements. So the goal is to find a subsequence such that when we comp... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Interaction between the bosonic field X and fermions is given by\n\n\\mathcal{L}\\left(y\\right)=-\\lambda{f}\\bar{\\psi}{f}\\left(y\\right)\\left(\\upsilon+X\\left(... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 134 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the kinematically allowed decays of the boson X, we need to consider the possible fermion pairs that can be produced in its decay. The mass of X is 6 GeV, so the decay products must have a total rest mass energy less than or equal to 6 GeV.
The Lagrangian given is \(\mathcal{L} = -\lambda f \bar{\psi} f(... |
[
{
"content": "Problem: $\\overline{BC}$ is parallel to the segment through $A$, and $AB = BC$. What is the number of degrees represented by $x$?\n\n[asy]\ndraw((0,0)--(10,0));\ndraw((0,3)--(10,3));\ndraw((2,3)--(8,0));\ndraw((2,3)--(4,0));\nlabel(\"$A$\",(2,3),N);\nlabel(\"$B$\",(4,0),S);\nlabel(\"$C$\",(8,0),S... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 18 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve for the measure of angle \( x \) in the given geometric configuration, we need to analyze the relationships between the angles formed by the parallel lines and the transversal.
First, let's look at the diagram. The line segment \(\overline{BC}\) is parallel to the segment through \(A\). This means that \(BC\)... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: S)-4-hydroxycyclohex-2-en-1-one is treated with tert-Butyldimethylsilyl chloride and triethylamine, forming product 1.\n\n1 is treated with Ph2CuLi at low temperature, f... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 27 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the structure of product 4, let's follow the reaction steps from product 3 and backtrack through the intermediate products.
Starting with product 3, which is formed from product 2 via LDA and iodomethane. The reaction between an alcohol (product 2) and LDA (a strong base) in the presence of iodomethane wo... |
[
{
"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: In a triangle $A B C$, let $A B=\\sqrt{23}, B C=3$ and $C A=4$. Then what is the value of\n\\[\n\\frac{\\cot A... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 341 | JEEBench | {
"expected_answer": "2",
"problem_id": "54",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve for the value of \(\frac{\cot A + \cot C}{\cot B}\) in triangle \(ABC\) with sides \(AB = \sqrt{23}\), \(BC = 3\), and \(CA = 4\), we will use trigonometric identities and the Law of Cosines.
First, we need to find the angles \(A\), \(B\), and \(C\). However, calculating the exact angles might be complex, so ... |
[
{
"content": "Problem: Let $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c}$ be three vectors such that\n\\[\\mathbf{a} \\times \\mathbf{b} = \\begin{pmatrix} 6 \\\\ -7 \\\\ 3 \\end{pmatrix}, \\quad \\mathbf{a} \\times \\mathbf{c} = \\begin{pmatrix} 4 \\\\ 7 \\\\ 2 \\end{pmatrix}, \\quad \\mathbf{b} \\times \\mathbf{... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 298 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to compute the cross product \((2 \mathbf{b} - \mathbf{a}) \times (3 \mathbf{c} + \mathbf{a})\). We will use vector properties and the given cross products to find the result.
First, let's recall the distributive property of the cross product:
\[
(\mathbf{u} + \mathbf{v}) \times \mathbf{w... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $b_{i}>1$ for $i=1,2, \\ldots, 101$. Suppose $\\log _{e} b_{1}, \\log... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 58 | JEEBench | {
"expected_answer": "B",
"problem_id": "38",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to analyze the relationships between the sequences \(\{b_i\}\) and \(\{a_i\}\) given the conditions in the problem. Let's break down the solution step by step.
### Step 1: Understanding the Arithmetic Progression for \(\log_e b_i\)
Given that \(\log_e b_1, \log_e b_2, \ldots, \log_e b_{1... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You identified a new ligand-receptor pair initially expressed in the neural crest cells and want to understand the developmental fate of their interaction. The receptor ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 101 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the most likely reason for the absence of the green signal (eGFP) in the mouse model, let's analyze the given experimental setup and options step by step.
The construct is a bicistronic lox-Cre vector where the ligand (ORF) is at the 5' end fused to mCherry, and the receptor (ORF) is at the 3' end fused t... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Complete the following reactions and select the major products by considering the steric hindrance, and the stability of the products.\n2-ethyl-2,6-dimethylcyclohexan-1-... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 110 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. So, we need to complete two reactions and determine the major products A and B. Let's start with the first reaction.
The first reaction is between 2-ethyl-2,6-dimethylcyclohexan-1-one and ethyl acrylate in the presence of t-BuOK. Hmm, this looks like an addition reaction follow... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Initially, you have a bank account balance of 100 dollars.\nYou are given an integer purchaseAmount representing the amount you will spend on a purchase in dol... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 83 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to calculate the account balance after a purchase. The key part is figuring out how the purchase amount is rounded to the nearest multiple of 10, and if there's a tie, choose the larger one. Let's think through how to do that.
First, the input is purchaseAmount, ... |
[
{
"content": "Problem: Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\overline{IA}\\perp\\overline{OI}$ , circumradius $13$ , and inradius $6$ . Find $AB\\cdot AC$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 9 | AIME24 | {
"expected_answer": "468",
"problem_id": "aime24-9",
"reference_solution": "By Euler's formula $OI^{2}=R(R-2r)$ , we have $OI^{2}=13(13-12)=13$ . Thus, by the Pythagorean theorem, $AI^{2}=13^{2}-13=156$ . Let $AI\\cap(ABC)=M$ ; notice $\\triangle AOM$ is isosceles and $\\overline{OI}\\perp\\overline{AM}$ ... | Given a triangle \( \triangle ABC \) with circumcenter \( O \), incenter \( I \), circumradius \( R = 13 \), inradius \( r = 6 \), and the condition \( \overline{IA} \perp \overline{OI} \). We need to find the product \( AB \cdot AC \).
First, recall that the incenter \( I \) and circumcenter \( O \) are related in te... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal{P}$ we took crosses one of th... | To solve this problem, we need to determine the difference between the radii of the inner and outer circles formed by the tangency of a torus (donut-shaped surface) with a sphere. The torus is generated by rotating a circle of radius 3 around an axis 6 units away from its center. The sphere has a radius of 11. The toru... |
[
{
"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 | 227 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where for a given set of points on a line, I have to determine if it's possible to add a new integer point such that this new point is the closest to all existing points. The new point must be different from any existing ones.
Hmm, the example given in the problem... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 81 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | To solve this problem, we need to determine the number of lone pairs of electrons on each central atom in the given species and then sum these numbers. Let's go through each species step by step.
### 1. \(\left[\mathrm{TeBr}_{6}\right]^{2-}\)
- **Central atom**: Te (Tellurium)
- **Valence electrons of Te**: Te is in g... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The correct statement(s) related to processes involved in the extracti... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 477 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "35",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate each statement to determine if it correctly describes a process involved in the extraction of metals. Let's go through each option step by step.
**Option (A): Roasting of Malachite produces Cuprite.**
- Malachite (Cu₂CO₃·Cu(OH)₂) is a common ore of copper.
- Roasting is a th... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: In a hotel, four rooms are available. Six persons are to be ac... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 307 | JEEBench | {
"expected_answer": "1080",
"problem_id": "50",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the number of ways to accommodate six persons in four rooms such that each room has at least one person and at most two persons. Let's break down the problem step by step.
### Step 1: Understanding the Constraints
Each room must have at least one person and at most two perso... |
[
{
"content": "Problem: Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$ . Bob's list has 2024 sets. Find the sum of the elements of A.\nMark your solution with \\boxed\nAnswer:",... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 5 | AIME24 | {
"expected_answer": "55",
"problem_id": "aime24-5",
"reference_solution": "Let $k$ be one of the elements in Alices set $A$ of positive integers. The number of sets that Bob lists with the property that their maximum element is k is $2^{k-1}$ , since every positive integer less than k can be in the set or o... | To solve this problem, we need to determine the set \( A \) of positive integers such that the number of finite nonempty subsets \( B \) of positive integers where the maximum element of \( B \) is in \( A \) is exactly 2024. We then need to find the sum of the elements of \( A \).
### Approach
1. **Understanding the ... |
[
{
"content": "Problem: Rectangles $ABCD$ and $EFGH$ are drawn such that $D,E,C,F$ are collinear. Also, $A,D,H,G$ all lie on a circle. If $BC=16$ , $AB=107$ , $FG=17$ , and $EF=184$ , what is the length of $CE$ ? [asy] import graph; unitsize(0.1cm); pair A = (0,0);pair B = (70,0);pair C = (70,16);pai... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 19 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-19",
"reference_solution": "We use simple geometry to solve this problem. [asy] import graph; unitsize(0.1cm); pair A = (0,0);pair B = (107,0);pair C = (107,16);pair D = (0,16);pair E = (3,16);pair F = (187,16);pair G = (187,33);pair H = (3,33); label(\"$A$\", A,... | To solve this problem, we need to determine the length of \( CE \) given the geometric constraints and specific lengths of the sides of the rectangles \(ABCD\) and \(EFGH\).
### Step-by-Step Solution:
1. **Understanding the Geometry**:
- Rectangles \(ABCD\) and \(EFGH\) are such that points \(D, E, C, F\) are coll... |
[
{
"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 | 36 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to verify if a password meets certain conditions. Let's see the requirements again. The password must consist of lowercase letters and digits. Then, no digit should come after a letter. Also, all digits must be in non-decreasing order, and all letters must be in n... |
[
{
"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 | 288 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this tree pruning problem. The goal is to make all leaves in the tree equidistant from the root (which is always node 1) with the minimum number of operations. Each operation is removing a leaf and its adjacent edge. So the problem is to find the smallest number of such operatio... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 176 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have two arrays a and b, and I can perform k operations. In each operation, I choose an index i, add a_i to my score, then set a_i to max(0, a_i - b_i). The goal is to maximize the total score after k operations. Hmm.
First, I need to think about how to app... |
[
{
"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 symmetries must be respected by all operators in the SMEFT?\n\n1. Lorentz Symmetry\n2. Poincare symmetry\n3. CP symmetry\n4. CPT symmetry\nOptions... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 65 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine which symmetries must be respected by all operators in the Standard Model Effective Field Theory (SMEFT), we need to consider the fundamental principles that the theory must adhere to.
1. **Lorentz Symmetry**: This symmetry is crucial for any theory involving particles and their interactions, especially 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 projector with a lens of 40 cm focal length illuminates an object slide 4.0 cm long and throws an image upon a screen 20 m from the lens. What is t... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 431 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to find the size of the projected image using the lens. Let me think. The problem says that the projector's lens has a focal length of 40 cm. The object slide is 4.0 cm long. The screen is 20 meters away from the lens. So I need to find the image size.
Hmm, I rem... |
[
{
"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 | 21 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to decode a string that was encoded using a specific method. Let me try to understand the encoding process first.
So the encoding process works by first creating a string r that contains all the distinct letters of the original string s, sorted in alphabetical or... |
[
{
"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 buyer signed a contract to purchase a tract of land from a seller. The contract was signed on May 1, 2006, and the closing is set for June 15, 2006... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 371 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine when the seller became or will become the owner of the land, we need to analyze the timeline and the applicable statute of limitations.
First, let's outline the key events:
1. The rancher died intestate on September 1, 1960.
2. The nephew, who is under 21 at the time (since he was born on October 1, 1954... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two 0-indexed integer arrays, nums1 and nums2, both having length n.\nYou are allowed to perform a series of operations (possibly none).\nIn an o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 126 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have two arrays, nums1 and nums2, and I can swap their elements at the same index. The goal is to make sure that the last element of nums1 is the maximum in nums1, and the last element of nums2 is the maximum in nums2. I have to find the minimum number of swaps needed,... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given two positive integers n and x.\nReturn the number of ways n can be expressed as the sum of the x^th power of unique positive integers, in other words, th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 64 | 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 number of ways to express a given number n as the sum of x-th powers of unique positive integers. And the result has to be modulo 10^9 +7. Hmm. Let's think about how to approach this.
First, the problem is similar to dynamic programming because each n... |
[
{
"content": "Problem: The weight of $\\frac{1}{3}$ of a large pizza together with $3 \\frac{1}{2}$ cups of orange slices is the same as the weight of $\\frac{3}{4}$ of a large pizza together with $\\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\\frac{1}{4}$ of a pound. What is the weight, i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 9 | AMC23 | {
"expected_answer": "4",
"problem_id": "11",
"reference_solution": "",
"subject": null,
"type": null
} | Let's denote the weight of a large pizza as \( P \) pounds and the weight of a cup of orange slices as \( O \) pounds. According to the problem, \( O = \frac{1}{4} \) pound.
The problem states that the weight of \(\frac{1}{3}\) of a large pizza plus \(3 \frac{1}{2}\) cups of orange slices is equal to the weight of \(... |
[
{
"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 $P$ be a point in the first octant, whose image $Q$ in the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 177 | JEEBench | {
"expected_answer": "8",
"problem_id": "48",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the length of the segment \( PR \) where \( P \) is a point in the first octant, and \( R \) is its image in the \( xy \)-plane. The point \( Q \) is the image of \( P \) in the plane \( x + y = 3 \), meaning the line segment \( PQ \) is perpendicular to this plane, and the 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 th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 222 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's tackle this problem. Hmm, the problem is about calculating the sum of f(i) for i from 0 to m, where f(i) is the maximum possible value of x after performing some operations starting with x = i. The operations involve choosing a sequence and updating x using the mex of x and the elements of that sequ... |
[
{
"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 is formed when 5-butylnona-2,6-diene is heated?\nOptions: A) 5-ethyl-4-methyldeca-2,6-diene, B) 5-ethylundeca-2,6-diene, C) 5-ethyl-4-me... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 126 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine which molecule is formed when 5-butylnona-2,6-diene is heated, we need to consider the possible reaction mechanisms and product structures.
First, let's recall that heating alkenes can lead to various reactions, such as polymerization, but in the presence of certain conditions (like the presence of a suit... |
[
{
"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 | 311 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem. Let's read the description carefully.
The problem is about combining two strongly connected directed graphs (each with n vertices) such that when we add exactly n edges between them, certain conditions are met. The added edges must connect vertices from different graphs, eac... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Let there be a diatomic molecule, with elements X and Y, that can be modeled using the quantum rotation-vibration model (or non-rigid rotor model). If the molecule is in... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 62 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the momentum of a photon that can cause a diatomic molecule to transition from its fundamental state to the next state with the lowest possible energy. This involves understanding the energy levels of the molecule under the quantum rotation-vibration model.
### Approach
1. *... |
[
{
"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 an exam structured as follows.\n\n- The exam consists of N rounds called round 1 to N.\n- In each round, you ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 285 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes input from stdin and calculates the minimum score needed in the last round to achieve a final grade of X or higher. Hmm.
The problem says that the final grade is the sum of all scores except the highest and lowest. Wait, but in the example given, fo... |
[
{
"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 | 45 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this XORificator problem. Hmm. The task is to find the maximum number of special columns (columns with exactly one 1) by possibly inverting some rows using the XORificator. And also output which rows to invert.
First, I need to understand how inverting a row affects the columns... |
[
{
"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.AtCoder Inc. sells glasses and mugs.\nTakahashi has a glass with a capacity of G milliliters and a mug with a capacity... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 343 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to write a Python function that takes input K, G, M and after performing the operation K times, outputs how much water is in the glass and mug. The operation steps are a bit tricky, so I need to understand them properly.
The problem says that each time you perform the operation, you do ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Your laptop keyboard is faulty, and whenever you type a character 'i' on it, it reverses the string that you have written. Typing other characters works as exp... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 67 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where my laptop's keyboard reverses the string whenever I type an 'i'. So, the task is to simulate typing each character of the input string s, but whenever an 'i' is encountered, the current string is reversed. But wait, how does the typing work? Let's think about the example... |
[
{
"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.\nWe call a subarray of an array complete if the following condition is satisfied:\n\nThe number of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 50 | 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 number of complete subarrays. A complete subarray is one where the number of distinct elements in the subarray is the same as the whole array. Hmm, let's think about how to approach this.
First, the problem is to count all subarrays where the distinct... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Identify compound E in the following reaction scheme.\nCompound A, when reacted with HCN, produces compound B.\nCompound B, upon reduction with H2 in the presence of Pd,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 128 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to identify compound E in the given reaction scheme by analyzing the transformations and the provided hints. Let's break down the problem step by step.
1. **Reaction Scheme Analysis**:
- **Compound A → B (with HCN)**: This suggests that compound A is an unsaturated compound that can r... |
[
{
"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 | 368 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where Alice divides the pockets into boxes and then plays a game with Jack. The goal is to find out how many ways Alice can divide the boxes so that she wins, assuming both play optimally. The answer should be modulo 998,244,353.
Hmm. Let's start by understanding t... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array nums.\nReturn an integer that is the maximum distance between the indices of two (not necessarily different) prime numbers in nu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 476 | 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 distance between indices of prime numbers in an array. Let's think about how to approach this.
First, the problem says the maximum distance between two primes. So, for example, if there are primes at indices i and j, the distance is |i-j|. But... |
[
{
"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 | 82 | 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 k-th smallest value of all possible subarrays of length >=2. The value is determined by the minimum xor between any two elements in the subarray. Hmm.
First, let's understand the problem. For each possible subarray of length at least 2, compute the mi... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 128 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. So the problem is about maximizing the experience points by crafting and melting weapons. Hmm. Let me read the problem statement again.
The key points are: each time you craft a weapon, you gain 1 experience. Each time you melt it, you gain another 1. So each craft-melt pair gives 2 points. Bu... |
[
{
"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 | 168 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to solve this problem where I have to find the minimum number of cases in an ancient language based on certain rules. Hmm. Let's read the problem carefully.
The language's words consist of the first c letters of the Latin alphabet. Each word has a case determined by its last letter. The... |
[
{
"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.Your refrigerator has N kinds of ingredients. Let us call them ingredient 1, \\dots, ingredient N. You have Q_i grams ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 371 | 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 number of dishes I can make given the ingredients. Let's think about the problem step by step.
So, the problem says there are N ingredients. For each dish type, A and B, each requires a certain amount of each ingredient. But the catch is that ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The CORRECT statement(s) for cubic close packed (ccp) three dimensiona... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 53 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate each statement related to the cubic close packed (ccp) three-dimensional structure and determine which ones are correct. Let's analyze each option step by step.
### Option (A): The number of nearest neighbors of an atom in the topmost layer is 12.
1. **Understanding Nearest N... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A 0-indexed array derived with length n is derived by computing the bitwise XOR (⊕) of adjacent values in a binary array original of length n.\nSpecifically, f... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 22 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where given a derived array, I have to determine if there exists a binary original array that when processed forms the derived array. The processing is based on XOR of adjacent elements with a twist for the last element. Let me think through this.
First, let me understand the... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: The base of a solid is a circular disk with radius 3 . Find the volume of the solid if parallel cross-sections perpendicular to the base are isoscele... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 466 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the volume of a solid whose base is a circular disk with radius 3. The cross-sections perpendicular to the base are isosceles right triangles with the hypotenuse lying along the base of the circle.
First, let's visualize the solid. The base is a circle of radius 3. For each cross... |
[
{
"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.Takahashi has recorded the number of steps he walked for N weeks. He walked A_i steps on the i-th day.\nFind the total... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 222 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to calculate the total steps Takahashi walked each week. Let's see. The input is N, which is the number of weeks, and then there's a list of 7N numbers. Each week consists of 7 days, so the first week is days 1-7, the second week 8-14, and so on. My task is to sum... |
[
{
"content": "Problem: There is a unique sequence of integers $a_1, a_2, \\cdots a_{2023}$ such that\n\\[\\tan2023x = \\frac{a_1 \\tan x + a_3 \\tan^3 x + a_5 \\tan^5 x + \\cdots + a_{2023} \\tan^{2023} x}{1 + a_2 \\tan^2 x + a_4 \\tan^4 x \\cdots + a_{2022} \\tan^{2022} x}\\]whenever $\\tan 2023x$ is defined. ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 15 | AMC23 | {
"expected_answer": "-1",
"problem_id": "17",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we start by recognizing that the given equation is a trigonometric identity. The left-hand side is \(\tan(2023x)\), and the right-hand side is a complex fraction involving a power series in \(\tan x\). Our goal is to determine the coefficient \(a_{2023}\) in the numerator.
First, recall the mult... |
[
{
"content": "Problem: Determine if the graph of the equation below is a parabola, circle, ellipse, hyperbola, point, line, two lines, or empty.\n\n$\\left(\\frac x2 - 3\\right)^2 + y^2 = 10$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 358 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the type of conic section represented by the equation \(\left(\frac{x}{2} - 3\right)^2 + y^2 = 10\), we can analyze the form of the equation and compare it to the standard forms of conic sections.
First, let's rewrite the equation in a more recognizable form. The given equation is:
\[
\left(\frac{x}{2} -... |
[
{
"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: In a radioactive decay chain reaction, ${ }_{90}^{230} \\mathrm{Th}$ nucleus decays into ${ }_{84}^{214} \\mat... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 431 | JEEBench | {
"expected_answer": "2",
"problem_id": "20",
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | To solve this problem, we need to determine the ratio of the number of alpha (\(\alpha\)) particles to beta (\(\beta^{-}\)) particles emitted during the decay of a thorium-230 (\({ }_{90}^{230} \mathrm{Th}\)) nucleus into lead-214 (\({ }_{84}^{214} \mathrm{Pb}\)) through a series of radioactive decays. However, the pro... |
[
{
"content": "Problem: Two numbers, $x$ and $y$ are selected at random from the interval $(0,3)$. What is the probability that a triangle with sides of length 1, $x$, and $y$ exists?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 381 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the probability that a triangle with sides of length 1, \(x\), and \(y\) can be formed when \(x\) and \(y\) are selected randomly from the interval \((0,3)\), we need to use the triangle inequality theorem. The triangle inequality theorem states that for any three lengths to form a triangle, the sum of any... |
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