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 658k |
|---|---|---|---|---|---|---|
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Identify the compound C9H11NO2 using the given data.\nIR: medium to strong intensity bands at 3420 cm-1, 3325 cm-1\nstrong band at 1720 cm-1\n1H NMR: 1.20 ppm (t, 3H); 4... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 46 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to identify the compound C9H11NO2 based on the given IR and NMR data. Let's break down the information step by step.
First, let's consider the molecular formula C9H11NO2. This tells us the compound has 9 carbon atoms, 11 hydrogen, 1 nitrogen, and 2 oxygen atoms. Now, let's look at the IR... |
[
{
"content": "Problem: What is the product of all solutions to the equation\n\\[\\log_{7x}2023\\cdot \\log_{289x}2023=\\log_{2023x}2023\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 8 | AMC23 | {
"expected_answer": "1",
"problem_id": "10",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the equation \(\log_{7x}2023 \cdot \log_{289x}2023 = \log_{2023x}2023\), we start by introducing a substitution to simplify the logarithmic expressions. Let \(y = \log_{7x}2023\). Then, using the change of base formula, we can express \(\log_{289x}2023\) in terms of \(y\). Since \(289x = (7x)^2 \cdot x = 7^2 x... |
[
{
"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: Among $\\left[\\mathrm{I}_{3}\\right]^{+},\\left[\\mathrm{SiO}_{4}\\right]^{4-}, \\mathrm{SO}_{2} \\mathrm{Cl}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 510 | JEEBench | {
"expected_answer": "5",
"problem_id": "43",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | To determine the number of species with \( sp^3 \) hybridization, we need to analyze each compound's central atom and its hybridization state. Let's go through each species step by step.
1. **\[ \text{I}_3^+ \]**
Central atom: Iodine (I).
Charge: +1.
Lewis structure: Iodine has 7 valence electrons, each... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S of length N consisting of lowercase English letters.\nWe denote the i-th character of S by S_... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 217 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to generate a new string by concatenating the input string in a specific pattern. The new string should consist of each character in the input string repeated twice, followed by the input string itself again. For example, if the input string is "beginner" (8 characters), the output is "bb... |
[
{
"content": "Problem: The asymptotes of a hyperbola are $y = 2x - 3$ and $y = 17 - 2x.$ Also, the hyperbola passes through the point $(4,7).$ Find the distance between the foci of the hyperbola.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 409 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to determine the distance between the foci of a hyperbola given its asymptotes and a point it passes through. Let's proceed step by step.
First, recall that the equations of the asymptotes of a hyperbola provide information about its orientation and center. The given asymptotes are \( y =... |
[
{
"content": "Problem: For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 37 | AMC23 | {
"expected_answer": "901",
"problem_id": "47",
"reference_solution": "",
"subject": null,
"type": null
} | To determine for how many integers \( n \) the expression
\[
\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}}
\]
represents a real number, we need to ensure that the argument of the square root is non-negative and that the denominator is not zero. Let's break this down step by step.
First, let's simplify the numer... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $X$ be the set consisting of the first 2018 terms of the a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 144 | JEEBench | {
"expected_answer": "3748",
"problem_id": "45",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the number of elements in the union of two arithmetic sequences, \(X\) and \(Y\), each consisting of 2018 terms. The goal is to find how many unique elements are present in either \(X\) or \(Y\).
### Step 1: Define the Arithmetic Sequences
**Sequence \(X\):**
- First term: \... |
[
{
"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 extremes of temperature in New York, over a period of 50 years, differ by 116 Fahrenheit degrees. Express this 50 years, differ by 116 Fahrenheit... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 387 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To convert the temperature difference from Fahrenheit to Celsius, we can use the formula that relates the two scales. The formula to convert a temperature difference (Δ) from Fahrenheit to Celsius is:
\[ \Delta C = \frac{5}{9} \times \Delta F \]
Given that the temperature difference in Fahrenheit is 116 degrees, we c... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: For a complex number $z$, let $\\operatorname{Re}(z)$ denote the real part of $z$. Let $S$ be the set of all c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 294 | JEEBench | {
"expected_answer": "8",
"problem_id": "37",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To solve the given problem, we start by analyzing the equation \( z^4 - |z|^4 = 4i z^2 \). Let \( z = x + yi \) where \( x \) and \( y \) are real numbers. Then, \( |z|^4 = (x^2 + y^2)^2 \) and \( z^2 = (x + yi)^2 = x^2 - y^2 + 2xyi \). Similarly, \( z^4 \) can be computed as \( (z^2)^2 = (x^2 - y^2 + 2xyi)^2 \).
Firs... |
[
{
"content": "Problem: Simplify $\\tan 100^\\circ + 4 \\sin 100^\\circ.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 164 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To simplify \(\tan 100^\circ + 4 \sin 100^\circ\), we start by using trigonometric identities and properties of angles in different quadrants.
First, note that \(100^\circ\) is in the second quadrant. In the second quadrant, the tangent function is negative, and the sine function is positive. So, \(\tan 100^\circ = -\... |
[
{
"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 $S=\\left\\{x \\in(-\\pi, \\pi): x \\neq 0, \\pm \\frac{\\pi}{2}\\rig... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 26 | JEEBench | {
"expected_answer": "C",
"problem_id": "39",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve the equation \(\sqrt{3} \sec x + \operatorname{cosec} x + 2(\tan x - \cot x) = 0\) for \(x \in S = \left\{x \in (-\pi, \pi): x \neq 0, \pm \frac{\pi}{2}\right\}\), we start by expressing all trigonometric functions in terms of sine and cosine.
First, recall the definitions:
\[
\sec x = \frac{1}{\cos x}, \quad... |
[
{
"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 | 358 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the winner of a game where Alice and Bob take turns inserting logical operators ('and' or 'or') between a sequence of boolean values. The goal is to predict the outcome assuming both players play optimally.
### Approach
1. **Understanding the Game Dynamics**:
- Alice want... |
[
{
"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 $A P(a ; d)$ denote the set of all the terms of an infinit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 212 | JEEBench | {
"expected_answer": "157",
"problem_id": "50",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the problem, we need to find the intersection of three arithmetic progressions (APs) and determine the parameters \(a\) and \(d\) such that the intersection forms another AP. The given APs are \(AP(1, 3)\), \(AP(2, 5)\), and \(AP(3, 7)\).
First, let's write down the general terms of each AP:
- \(AP(1, 3)\) ha... |
[
{
"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 | 36 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to verify if a password meets certain criteria. Let's see. The problem says the password is strong if it meets four conditions. Let me read them again carefully.
First, the password can only have lowercase Latin letters and digits. Wait, the input is supposed to consist of those characters only. B... |
[
{
"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 and a dictionary of words dictionary. You have to break s into one or more non-overlapping substrings such that each substri... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 13 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to split the string into substrings that exist in the dictionary, and minimize the extra characters left. Hmm. Let's think about the approach here.
So, the problem is similar to the word break problem, but instead of just checking if it's possible, we need to fin... |
[
{
"content": "Problem: Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\\%$ on every pair of shoes. Carlos also knew that he had to pay a $7.5\\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 30 | AMC23 | {
"expected_answer": "50",
"problem_id": "36",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the original price of the most expensive pair of shoes Carlos can afford, we need to account for the discount and sales tax. Let's break down the problem step by step.
1. **Define Variables:**
Let \( P \) be the original price of the shoes.
2. **Apply the Discount:**
The shoes are discounted by 20%... |
[
{
"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: According to the Arrhenius equation,\n(A) a high activation energy usu... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 16 | JEEBench | {
"expected_answer": "BCD",
"problem_id": "24",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To solve this problem, we need to evaluate each statement in the context of the Arrhenius equation. The Arrhenius equation relates the rate constant (k) of a chemical reaction to the absolute temperature (T), activation energy (Ea), and the pre-exponential factor (A). The equation is typically written as:
k = A e^(-Ea... |
[
{
"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 arrays of equal length, nums1 and nums2.\nEach element in nums1 has been increased (or decreased in the case of negative) by an integer, repr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 489 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the integer x that when added to each element of nums1 results in nums2. The key insight here is that the difference between corresponding elements in nums1 and nums2 must be the same x. This is because adding the same x to each element of nums1 should transform it into nums2... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Consider a system with Hamiltonian operator $H = \\varepsilon \\vec{\\sigma}.\\vec{n}$. Here, $\\vec{n}$ is an arbitrary unit vector, $\\varepsilon $ is a constant of di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the eigenvalues of the Hamiltonian \( H = \varepsilon \vec{\sigma} \cdot \vec{n} \), where \( \vec{\sigma} \) are the Pauli matrices and \( \vec{n} \) is a unit vector, we need to analyze the properties of the Pauli matrices and their dot product.
First, recall that the Pauli matrices are \( 2 \times 2 \) matr... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: \"Oh, I know you,\" the ribonucleoprotein particle says to the nascent chain as they meet. \"Pause there for a minute. Let me show you in; you really need some sugar.\"\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 26 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's think through this problem step by step. The dialogue between the ribonucleoprotein particle (which is likely a ribosome) and the nascent chain (the growing polypeptide chain) provides key clues.
First, the ribosome says, "Pause there for a minute. Let me show you in; you really need some sugar." This suggests ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two 0-indexed integer arrays nums1 and nums2 of sizes n and m, respectively.\nConsider calculating the following values:\n\nThe number of indices... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 135 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine how many elements in nums1 appear in nums2 and vice versa. The solution involves counting the occurrences of each element in both arrays and then checking for overlaps.
### Approach
1. **Count Elements in nums1**: Create a frequency dictionary (using a list since elements ca... |
[
{
"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 people labeled 1 to N, who have played several one-on-one games without draws. Initially, each person star... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 422 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the final score of person N given the final scores of the first N-1 persons. Each person's score changes by +1 for a win and -1 for a loss. The key insight is that the total sum of all scores (including the unknown score of person N) must be even because each game contributes... |
[
{
"content": "Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | To solve the given system of equations involving logarithms, we start by converting the logarithmic equations into exponential form. The equations are:
1. \(\log_2\left(\frac{x}{yz}\right) = \frac{1}{2}\)
2. \(\log_2\left(\frac{y}{xz}\right) = \frac{1}{3}\)
3. \(\log_2\left(\frac{z}{xy}\right) = \frac{1}{4}\)
Each of... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A light beam is propagating through a glass with index of refraction n. The glass is moving at constant velocity v in the same direction as the beam and toward the obser... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 40 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the speed of light in a moving glass medium relative to an observer in the laboratory. Let's break down the concepts involved here.
First, recall that the speed of light in a medium with index of refraction \( n \) is \( c/n \), where \( c \) is the speed of light in a vacuu... |
[
{
"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 weighted undirected graph G with N vertices, numbered 1 to N. Initially, G has no edges.\nYou will per... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 437 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if a weighted undirected graph constructed through a series of operations is connected and, if so, compute the total weight of the edges in its minimum spanning tree (MST). The key challenges are handling the dynamic addition of edges efficiently and ensuring we can track the... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Consider one mole of helium gas enclosed in a container at ini... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 247 | JEEBench | {
"expected_answer": "1.77",
"problem_id": "16",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to calculate the work done during both the isothermal and adiabatic expansions and then find the ratio between them. Let's proceed step by step.
### Step 1: Isothermal Expansion
For an isothermal expansion of an ideal gas, the work done is given by:
\[ W_{\text{iso}} = nRT \ln \left( \fr... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A farmer $F_{1}$ has a land in the shape of a triangle with ve... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 149 | JEEBench | {
"expected_answer": "4",
"problem_id": "50",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the value of \( n \) such that the area taken away by farmer \( F_2 \) is exactly 30% of the area of triangle \( \triangle PQR \). The region taken away lies between the line segment \( PQ \) and the curve \( y = x^n \).
First, let's calculate the area of \( \triangle PQR \)... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given eight integers S_1,S_2,\\dots, and S_8,\r\nprint Yes if they satisfy all of the following three conditions, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 227 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if a given sequence of eight integers meets three specific conditions. The conditions are:
1. The sequence is monotonically non-decreasing, meaning each element is less than or equal to the next.
2. Each element must be between 100 and 675, inclusive.
3. Each element must be... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 23 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum possible length of a string after repeatedly removing occurrences of the substrings "AB" or "CD". The key challenge is that after each removal, new "AB" or "CD" substrings might be formed, so we need to process the string iteratively until no more removals can be ... |
[
{
"content": "Problem: The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? [asy]\ndraw((-.3,-3)--(.1,1)--(-1,0)--(3,0)--cycle);\nlabel(\"$A$\",(.1,1),N);\nlabel(\"$B$\",(-1,0),W);\nlabel(\"$C... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 222 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem, we need to find the area of triangle \( \triangle CDE \) given that the area of \( \triangle ABC \) is 6 square centimeters, \( \overline{AB} \parallel \overline{DE} \), and \( BD = 4BC \).
First, let's analyze the given information. Since \( \overline{AB} \parallel \overline{DE} \), triangles \(... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: We have a large ensemble of 10.000 (ten thousand) identical systems. Each system has a particle that are the same and under the same conditions. Each particle can move a... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 38 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the value of 'a' in the given wave function, we need to consider the properties of wave functions and the fact that particles are only found between x=1 and x=3. The wave function must be normalized, meaning the total probability over all space is 1. However, since the particles are only found between x=1 ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $l_{1}, l_{2}, \\ldots, l_{100}$ be consecutive terms of a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 381 | JEEBench | {
"expected_answer": "18900",
"problem_id": "6",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve the problem, we start by understanding the given information. The lengths \( l_1, l_2, \ldots, l_{100} \) form an arithmetic progression (AP) with common difference \( d_1 \). Similarly, the widths \( w_1, w_2, \ldots, w_{100} \) form another AP with common difference \( d_2 \), and it is given that \( d_1 d_2... |
[
{
"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 sticks with several balls stuck onto them. Each ball has a lowercase English letter written on it.\nFor ea... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 240 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of distinct sticks among the given N sticks. Each stick is defined by a string of lowercase letters, and two sticks are considered the same if one is the reverse of the other. The challenge is to efficiently compare these strings to count the unique ones, consideri... |
[
{
"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 | 376 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to calculate the sum of Manhattan distances each person moves when the person at position (r, c) leaves. The key is to determine for each person j (where j > i) their initial position and their new position after the movement, then compute the Manhattan distance between these positions.
... |
[
{
"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 | 65 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Turtle and Piggy are playing a game. The goal is to find the maximum possible score Piggy can get by breaking down the chosen x into factors. Let's think through the problem step by step.
First, let's understand the problem. Turtle picks x in the range [l, r], inclusive... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N cities in a certain country.\nYou will travel from your office in city 1 to a destination in city N, via z... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 309 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the minimum time to travel from city 1 to city N using either company cars or trains. The key challenge is to determine the optimal points to switch from a company car to a train to minimize the total travel time.
### Approach
1. **Dynamic Programming (DP) Setup**: We use a DP ar... |
[
{
"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 colloids is(are)\n(A) The process ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 321 | JEEBench | {
"expected_answer": "BC",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine the correct statements regarding colloids, let's analyze each option step by step.
**Option (A): The process of precipitating colloidal sol by an electrolyte is called peptization.**
- **Analysis**: Peptization is the process where colloidal particles become stabilized by adsorbing electrolyte ions onto ... |
[
{
"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_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where I have to construct a permutation of numbers from 1 to n such that when I perform the given operations (bitwise AND for odd steps and OR for even steps), the final k is maximized. Let's think about how to approach this.
First, let's understand the process. For each posi... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Find KE of product particles in,\nPi(+) = mu(+) + nu\nhere Pi(+) is stationary.\nRest mass of Pi(+) & mu(+) is 139.6 MeV & 105.7 MeV respectively.\nOptions: A) 7.2 MeV,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 11 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the kinetic energy of the product particles when a stationary π+ meson decays into a μ+ (muon) and a ν (neutrino). Let's break down the steps:
1. **Identify Given Information:**
- Rest mass of π+ (M_π) = 139.6 MeV
- Rest mass of μ+ (M_μ) = 105.7 MeV
- The π+ is stat... |
[
{
"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 compound(s) which generate(s) $\\mathrm{N}_{2}$ gas upon thermal d... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 128 | JEEBench | {
"expected_answer": "BC",
"problem_id": "19",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine which compounds generate nitrogen gas (\(\mathrm{N}_2\)) upon thermal decomposition below \(300^{\circ}\mathrm{C}\), we need to analyze the decomposition reactions of each given compound and check if they produce \(\mathrm{N}_2\).
Let's examine each option step by step:
**Option (A): \(\mathrm{NH}_4\math... |
[
{
"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: The solubility of a salt of weak acid (AB) at $\\mathrm{pH} 3$... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 136 | JEEBench | {
"expected_answer": "4.47",
"problem_id": "31",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the solubility of the salt AB in mol L\(^{-1}\) at pH 3, given the solubility product constant (\(K_{sp}\)) and the acid dissociation constant (\(K_a\)) of the conjugated acid HB. The goal is to find the value of Y such that the solubility is \(Y \times 10^{-3}\) mol L\(^{-1}... |
[
{
"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": 2,
"temperature": 0.7
} | 2 | 126 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum number of swaps required between elements of nums1 and nums2 at the same indices to ensure that the last elements of both arrays are the maximum in their respective arrays. If it's impossible to achieve this, we return -1.
### Approach
1. **Identify Potential Can... |
[
{
"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: Sometimes it is convenient to construct a system of units so that all ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 245 | JEEBench | {
"expected_answer": "AB",
"problem_id": "9",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the relationships between the exponents \(\alpha\), \(\beta\), \(p\), \(q\), and \(r\) given the dimensions of different physical quantities in a system where all are expressed in terms of a single physical quantity \(X\).
### Step-by-Step Solution:
1. **Understanding the P... |
[
{
"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 | 286 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about maximizing the deck size after buying up to k new cards. The key constraints are that each deck must have all unique numbers, and all decks must be the same size. So the goal is to find the maximum possible m (deck size) such that we can partition all the cards into m-sized... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Among the following, the correct statement(s) about polymers is(are)\n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 446 | JEEBench | {
"expected_answer": "BC",
"problem_id": "50",
"reference_solution": null,
"subject": "chem",
"type": "MCQ(multiple)"
} | To determine the correct statements about polymers, let's analyze each option step by step.
**Option (A): The polymerization of chloroprene gives natural rubber.**
- Chloroprene (2-chlorobutadiene) is the monomer used to produce chloroprene rubber (CR), which is synthetic, not natural. Natural rubber comes from the l... |
[
{
"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 a playlist with N songs.\nSong i (1 \\leq i \\leq N) lasts T_i seconds.\nTakahashi has started random pl... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 298 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the probability that Takahashi is listening to song 1 exactly (X + 0.5) seconds after starting the random playlist. The solution involves dynamic programming (DP) to track the state of the playlist, considering the current song and the remaining time until the next switch.
#... |
[
{
"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 $a_{1}, a_{2}, a_{3}, \\ldots$ be an arithmetic progression with $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 385 | JEEBench | {
"expected_answer": "BC",
"problem_id": "10",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given sequences and determine which of the provided statements are true. Let's break down the problem step by step.
### Step 1: Understand the Arithmetic Progression (AP)
Given:
- The arithmetic progression \(a_1, a_2, a_3, \ldots\) with \(a_1 = 7\) and common difference \... |
[
{
"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 length n and a positive integer k.\nA subarray of nums is called good if the absolute difference between its first and last elem... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 171 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the maximum sum of a good subarray in the given array where a good subarray is defined by the absolute difference between the first and last element being exactly k. The challenge is to efficiently determine this maximum sum, especially given the potential size of the array (up to... |
[
{
"content": "Problem: For how many ordered pairs $(a,b)$ of integers does the polynomial $x^3+ax^2+bx+6$ have $3$ distinct integer roots?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 4,
"temperature": 0.7
} | 4 | 27 | AMC23 | {
"expected_answer": "5",
"problem_id": "30",
"reference_solution": "",
"subject": null,
"type": null
} | To solve the problem of finding the number of ordered pairs \((a, b)\) such that the polynomial \(x^3 + ax^2 + bx + 6\) has three distinct integer roots, we need to consider the factorization of the polynomial into three linear factors. Let's denote the roots by \(r, s, t\), where \(r, s, t\) are distinct integers. The... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a string word, compress it using the following algorithm:\n\nBegin with an empty string comp. While word is not empty, use the following operation:\n\n\t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 505 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compress a given string using a specific algorithm. The algorithm involves repeatedly removing the longest possible prefix of single characters (repeating at most 9 times) and appending the length followed by the character to the result string.
### Approach
1. **Initialize an empty r... |
[
{
"content": "Problem: Rows 1, 2, 3, 4, and 5 of a triangular array of integers are shown below.\n1\n1 1\n1 3 1\n1 5 5 1\n1 7 11 7 1\nEach row after the first row is formed by placing a 1 at each end of the row, and each interior entry is 1 greater than the sum of the two numbers diagonally above it in the prev... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 10 | AMC23 | {
"expected_answer": "5",
"problem_id": "12",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the units digit of the sum of the 2023rd row in a triangular array of integers. The array starts with the first row as \(1\), the second row as \(1 1\), the third row as \(1 3 1\), and so on, with each subsequent row formed by placing a 1 at each end and each interior entry b... |
[
{
"content": "Problem: A line is parameterized by\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} 8 \\\\ -1 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ 3 \\end{pmatrix}.\\]The equation of the line can be expressed in the form $y = mx + b.$ Enter the ordered pair $(m,b).$\nMark your solution with... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 206 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the equation of the line in the form \( y = mx + b \) from the parameterized form \(\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \end{pmatrix}\), we need to determine the slope \( m \) and the y-intercept \( b \).
First, recall that the parameterized l... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a positive integer N.\nFind the maximum value of a palindromic cube number not greater than N.\nHere, a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 397 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the maximum palindromic cube number not greater than a given integer N. A palindromic cube number is a number that is both a cube (x^3 for some integer x) and a palindrome (reads the same forwards and backwards).
### Approach
1. **Understanding Palindromes**: A palindrome number ... |
[
{
"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 $P_{1}$ and $P_{2}$ be two planes given by\n\\[\n\\begin{aligned}\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 386 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "11",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To determine which lines can be edges of a tetrahedron where two faces are the given planes \(P_1\) and \(P_2\), we need to check if the line is parallel to the intersection of the two planes. The edge of the tetrahedron must lie in both planes, so it must be parallel to the line of intersection of \(P_1\) and \(P_2\).... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 193 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where Slavic has to replace the '?' in his string s such that t becomes a subsequence of s. Let's see. So a subsequence doesn't have to be contiguous, right? It just needs the characters of t to appear in order, but not necessarily consecutively in s.
First, I need to process... |
[
{
"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 likes full moons.\nLet today be day 1. The first day on or after today on which he can see a full moon is da... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 270 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the number of days between day 1 and day N (inclusive) on which Takahashi can see a full moon. The full moons occur starting from day M, every P days. Given the constraints, we need an efficient way to calculate this without iterating through each day up to N, which could be ... |
[
{
"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: In modern societies, social status is typically measured by a person's:\nOptions: A. physical strength, B. height, C. musical ability, D. knowledge o... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 128 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the correct answer to this question, I need to think about how modern societies typically measure social status. Let me eliminate options one by one.
First, options like physical strength (A) and height (B) are less common in modern times compared to historical periods. While they might still matter in so... |
[
{
"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: Put a uniform meter scale horizontally on your extended index ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 246 | JEEBench | {
"expected_answer": "25.6",
"problem_id": "13",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | To solve this problem, we need to analyze the forces acting on the left and right fingers as they are moved towards the center of the meter scale. The key is to determine the point at which each finger starts slipping due to the maximum static friction force, and then find the position \( x_R \) where the right finger ... |
[
{
"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 $G$ be a circle of radius $R>0$. Let $G_{1}, G_{2}, \\ldots, G_{n}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 423 | JEEBench | {
"expected_answer": "CD",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the geometric configuration of the circles. Each of the \( n \) smaller circles \( G_1, G_2, \ldots, G_n \) touches the larger circle \( G \) externally and also touches its adjacent smaller circles, forming a regular polygonal arrangement around \( G \).
### Step-by-Step Solu... |
[
{
"content": "Problem: Janet rolls a standard $6$-sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal $3$? The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive inte... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 18 | AMC23 | {
"expected_answer": "265",
"problem_id": "20",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the probability that Janet's running total equals 3 at some point during her 4 rolls, we need to analyze the possible sequences of dice rolls and identify those that reach a sum of 3 before the fourth roll. This problem can be approached using the concept of states in probability, where each state represen... |
[
{
"content": "Problem: Simplify the following expression to a simplified fraction: $$\\sqrt{\\dfrac{\\dfrac{5}{\\sqrt{80}}+\\dfrac{\\sqrt{845}}{9}+\\sqrt{45}}{\\sqrt5}}.$$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 331 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To simplify the given expression \(\sqrt{\dfrac{\dfrac{5}{\sqrt{80}}+\dfrac{\sqrt{845}}{9}+\sqrt{45}}{\sqrt5}}\), we will proceed step by step.
First, simplify the numerator inside the square root. The numerator is \(\dfrac{5}{\sqrt{80}} + \dfrac{\sqrt{845}}{9} + \sqrt{45}\).
Start by simplifying each term individual... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A string consisting of 0 and 1 is called a good string if two consecutive characters in the string are always differen... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 388 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to efficiently handle two types of queries on a binary string. The challenges are to process the queries quickly, especially given the potential size of the input (up to 500,000 elements). The key is to use a segment tree with lazy propagation to keep track of the flips in specific ranges... |
[
{
"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 | 313 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Tree of Life problem. Let's read the problem carefully.
So the problem is about a tree where each node is a magical source connected by channels (edges). The sages need to perform rituals along paths to block all magical resonance vibrations. The key point is that for every pair of 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 0-indexed array nums consisting of positive integers.\nYou can do the following operation on the array any number of times:\n\nChoose an intege... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 57 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the largest possible element that can be obtained by repeatedly applying the given operation to the array. The operation allows us to choose an integer i (where 0 <= i < nums.length - 1) such that nums[i] <= nums[i+1], replace nums[i+1] with nums[i] + nums[i+1], and delete nu... |
[
{
"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 | 208 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem. Let's read the problem statement carefully.
So the task is to find the number of different deterministic max-heaps formed by applying the add operation exactly k times. The answer should be modulo p.
First, let's understand the problem. The add operation is: choose a vert... |
[
{
"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": 0,
"temperature": 0.7
} | 0 | 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 mass of the boson and the masses of the possible fermion pairs it can decay into. The key point is that the sum of the masses of the decay products must be less than or equal to the mass of the boson X. Given that the mass of X is 6 G... |
[
{
"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 | 184 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to generate k distinct integer-coordinate points centered at (x_c, y_c). The points must have integer coordinates, and when averaged, they equal the center. Also, the points need to be distinct. Hmm. Let's think about how to approach this.
The problem says the center is ... |
[
{
"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: If $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ is a differentiable funct... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 115 | JEEBench | {
"expected_answer": "AC",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the given conditions and determine which of the provided options are correct. Let's start by understanding the problem statement.
Given:
- \( f: \mathbb{R} \rightarrow \mathbb{R} \) is a differentiable function.
- \( f'(x) > 2f(x) \) for all \( x \in \mathbb{R} \).
- \( f(0) =... |
[
{
"content": "Problem: In how many ways can 5 students be selected from a group of 6 students?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 455 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the number of ways to select 5 students from a group of 6, we can use the concept of combinations. Combinations are used when the order of selection does not matter, which is the case here since selecting student A and B is the same as B and A.
The formula for combinations is given by:
\[
C(n, k) = \frac{... |
[
{
"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 positive integer array nums.\nPartition nums into two arrays, nums1 and nums2, such that:\n\nEach element of the array nums belongs to either t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 43 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to partition the given array into two non-empty parts such that the absolute difference between the maximum of one part and the minimum of the other part is minimized.
### Approach
The key insight here is that the optimal partition will split the array such that the maximum element in t... |
[
{
"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: Among $[\\mathrm{Ni(CO)}_{4}]$, $[\\mathrm{NiCl}_{4}]^{2-}$, $[\\mathrm{C... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 14 | JEEBench | {
"expected_answer": "B",
"problem_id": "22",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To determine the number of paramagnetic compounds among the given options, we need to analyze each compound's electronic configuration and check if it has unpaired electrons. Paramagnetic substances are those that have one or more unpaired electrons in their ground state, meaning the electron's spins are not paired.
L... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence A=(A_1,\\ldots,A_N) of length N. The elements of A are distinct.\nProcess Q queries in the or... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 404 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to efficiently handle dynamic insertions and deletions on a sequence of elements. The challenge is to maintain the sequence while allowing these operations in a way that is both time and space efficient.
### Approach
The problem requires handling two types of queries efficiently:
1. Ins... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the amount of water produced (in g) in the oxidation o... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 227 | JEEBench | {
"expected_answer": "288",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the amount of water produced when 1 mole of rhombic sulfur (S8) is oxidized by concentrated nitric acid (HNO3) to a compound with the highest oxidation state of sulfur. Let's break down the solution step by step.
### Step 1: Determine the Oxidation State of Sulfur in the Pro... |
[
{
"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: Consider the functions $f, g: \\mathbb{R} \\rightarrow \\mathbb{R}$ defined by\n\\[\nf(x)=x^{2}+\\frac{5}{12} ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 419 | JEEBench | {
"expected_answer": "6",
"problem_id": "8",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | To find the area \(\alpha\) of the region defined by \( \{(x, y) \in \mathbb{R} \times \mathbb{R}: |x| \leq \frac{3}{4}, 0 \leq y \leq \min \{f(x), g(x)\}\} \), we need to determine the points where the functions \(f(x)\) and \(g(x)\) intersect and then compute the area under the minimum of these two functions between ... |
[
{
"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 ball is thrown at an angle of $45^{\\circ}$ to the ground. If the ball lands $90 \\mathrm{~m}$ away, what was the initial speed of the ball?\n\nOpt... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 395 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the initial speed of a ball thrown at a \(45^\circ\) angle that lands 90 meters away. Let's break down the solution step by step.
First, recall that when a ball is thrown at an angle, its motion can be analyzed in both horizontal and vertical components. Given the angle is \... |
[
{
"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: Which statement about protein digestion and absorption is most correct?\n\nOptions: A. The products of protein digestion may be absorbed as free amin... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 97 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Let's approach this step by step. The question is asking which statement about protein digestion and absorption is most correct. Let's go through each option one by one.
Option A: The products can be absorbed as free amino acids or di/tripeptides. I remember that the small intestine can absorb both, so this seems plau... |
[
{
"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 | 211 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about determining if a person can move from the starting point to the target without ever getting too close to any of the circles. The circles start with radius zero and increase at 1 unit per second. The person's speed is 1 unit per second, so they can move along a path, and we ... |
[
{
"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 | 134 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this Grid Puzzle problem. Let's see. The problem is about transforming an n x n grid where each row has the first a_i cells black and the rest white. The goal is to make all cells white using the minimum number of operations. The allowed operations are dyeing a 2x2 subgrid white or dyeing ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given an integer N and strings R and C of length N consisting of A, B, and C. Solve the following problem.\nTh... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 314 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if we can fill an N x N grid with characters A, B, and C such that each row and column contains exactly one of each character. Additionally, the first character of each row must match the corresponding character in the R string, and the first character of each column must mat... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 218 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "5",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the adiabatic compression of a mixture of ideal gases. Let's break down the problem step by step.
### Step 1: Understand the Initial Conditions
The initial state of the gas mixture is:
- Pressure: \( P_0 \)
- Volume: \( V_0 \)
- Temperature: \( T_0 \)
- Contains 5 moles of mon... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a positive integer N. Print a string of length (N+1), s_0s_1\\ldots s_N, defined as follows.\n\nFor each... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 275 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where given a positive integer N, I have to generate a string of length N+1 based on some rules. Let's see. The rules are for each index i from 0 to N, check if there's a divisor j of N (so j divides N) between 1 and 9 (inclusive) such that i is divisible by N/j. Then, among a... |
[
{
"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 frame house, located in a Class A town, insured for $24,000, or the sameframe house, located in a Class B town, insured for thesame $24,000? How mu... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 317 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand the difference in insurance premiums between a frame house located in a Class A town versus a Class B town, both insured for $24,000. Let's break down the information step by step.
First, recall that insurance companies typically charge higher premiums for properties in are... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: A flat plate is moving normal to its plane through a gas under the act... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 68 | JEEBench | {
"expected_answer": "ABD",
"problem_id": "1",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | To solve this problem, we need to analyze the motion of a flat plate moving through a gas under the action of a constant force \( F \). The gas is at very low pressure, and the plate's speed \( v \) is much less than the average speed \( u \) of the gas molecules. Let's evaluate each option step by step.
### Option [A... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.The imbalance number of a 0-indexed integer array arr of length n is defined as the number of indices in sarr = sorted(arr) such that:\n\n0 <= i < n - 1, and\n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 46 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compute the sum of imbalance numbers for all possible subarrays of the given array. The imbalance number of a subarray is defined based on the sorted version of the subarray. Let's break down the approach to solve this problem.
### Approach
1. **Understanding Imbalance Number**: The i... |
[
{
"content": "Problem: There exist real numbers $x$ and $y$ , both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$ . Find $xy$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | AIME24 | {
"expected_answer": "25",
"problem_id": "aime24-16",
"reference_solution": "By properties of logarithms, we can simplify the given equation to $x\\log_xy=4y\\log_yx=10$ . Let us break this into two separate equations: \\[x\\log_xy=10\\] \n \\[4y\\log_yx=10.\\] \nWe multiply the two equations to get: \n \\[4xy\\... | To solve the problem, we start by analyzing the given equations:
\[
\log_x(y^x) = 10 \quad \text{and} \quad \log_y(x^{4y}) = 10
\]
First, we simplify each logarithmic equation using the properties of logarithms.
For the first equation, \(\log_x(y^x) = 10\), we can use the power rule of logarithms, which states \(\l... |
[
{
"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 | 364 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out this problem. So, the problem is about a circuit with n lights and 2n switches. Each light is connected to exactly two switches, and each switch is connected to exactly one light. The question is, given the states of all switches, what's the minimum and maximum number of lights that can be... |
[
{
"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 key feature is that parallel cross-sections perpendicular to the base are isosceles right triangles with their hypotenuse lying along the base.
First, let's visualize the solid. The base is a circle of radius ... |
[
{
"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 positive integers n and m.\nDefine two integers, num1 and num2, as follows:\n\nnum1: The sum of all integers in the range [1, n] that are not div... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 120 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compute the difference between the sum of integers in the range [1, n] that are not divisible by m and those that are divisible by m.
### Approach
1. **Identify Divisible and Non-divisible Numbers**:
- The sum of all integers from 1 to n can be calculated using the formula for th... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 248 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, I need to solve this problem where there's an array and multiple operations that either add or subtract 1 to elements within a certain range. After each operation, I have to find the maximum value in the array. Hmm. Let's think about how to approach this efficiently because the constraints are up to 1e5 e... |
[
{
"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 molar constant volume heat capacity for $\\mathrm{I}_2(\\mathrm{~g})$ is $28.6 \\mathrm{~J} \\mathrm{~mol}^{-1} \\mathrm{~K}^{-1}$. What is the v... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 114 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the vibrational contribution to the heat capacity of \(\mathrm{I}_2(\mathrm{g})\), we need to consider the degrees of freedom available to the molecule. The problem states that the electronic contribution is negligible, so we'll focus on translational, rotational, and vibrational modes.
First, let's recal... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: From laboratory measurements we know that a particular spectral line formed by hydrogen appears at a wavelength of 486.1 nanometers (nm). The spectru... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 335 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to understand the relationship between the wavelength of a spectral line and the motion of the source. This is a classic example of the Doppler effect as applied to light.
When a source of light is moving relative to an observer, the wavelength of the light changes. If the source is movi... |
[
{
"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 | 130 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about a matrix where each cell has a color restriction after each query. We need to compute the minimum cost to paint the matrix according to all current restrictions. The cost depends on whether we paint rows or columns, and when multiple actions are done at once, the cost is th... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.We have an undirected graph with (N_1+N_2) vertices and M edges. For i=1,2,\\ldots,M, the i-th edge connects vertex a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 236 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum possible minimum path length (d) between vertex 1 and vertex (N_1 + N_2 + 1) after adding a single edge between a vertex in the first group (1 to N_1) and a vertex in the second group (N_1+1 to N_1+N_2). The key insight is that the existing structure of the graph ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given two grids, A and B, each with H rows and W columns.\nFor each pair of integers (i, j) satisfying 1 \\leq... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 345 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if we can transform grid A into grid B using the minimum number of row and column swaps. The operations allowed are swapping adjacent rows in grid A and swapping adjacent columns in grid A.
### Approach
1. **Check Feasibility**: First, we need to check if the grids can be m... |
[
{
"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: Investment demand most likely increases when\nOptions: A. the stock market experiences a downturn., B. inflation rates rise., C. the real rate of int... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 195 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine which factor most likely increases investment demand, let's analyze each option step by step:
A. **Stock Market Downturn**: When the stock market performs poorly, investors might lose confidence, leading them to reduce risk-taking. This could decrease investment demand as they prefer safer assets. So A is... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 85 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine if a given integer \( x \) can be expressed as the sum of two large positive integers with the same number of digits. A large integer is one where all digits are between 5 and 9, inclusive.
### Approach
1. **Understanding the Problem**: For \( x \) to be the sum of two large... |
[
{
"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 representing a 12-hour format time where some of the digits (possibly none) are replaced with a \"?\".\n12-hour times are formatted as... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 475 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to replace all '?' characters in a given 12-hour time string such that the resulting time is the latest possible valid time. The approach involves strategically replacing each '?' to maximize the time value while adhering to the 12-hour format constraints.
### Approach
1. **Maximize Hour... |
[
{
"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 order of the oxidation state of the phosphorus atom in $\\mathrm{H}_{... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 102 | JEEBench | {
"expected_answer": "C",
"problem_id": "23",
"reference_solution": null,
"subject": "chem",
"type": "MCQ"
} | To determine the order of the oxidation states of the phosphorus atoms in the given compounds, we need to calculate the oxidation state of phosphorus (P) in each molecule. The oxidation state of hydrogen (H) is typically +1, and oxygen (O) is -2, except in peroxides. Let's go through each compound step by step.
### St... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 343 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. The problem is about Alice cutting a cake into m+1 pieces so that each of the m creatures gets a piece with at least v taste, and Alice wants to maximize her own piece. If it's impossible, return -1.
Hmm. So first, I need to process each test case by looking at the array of a's, and find the m... |
[
{
"content": "Problem: Find the remainder when $(5x + 9)^{611} + (x + 5)^{11} + (x - 1)^{11} + 3x^2 + 1$ is divided by $x + 2.$\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 203 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To find the remainder when the polynomial \( P(x) = (5x + 9)^{611} + (x + 5)^{11} + (x - 1)^{11} + 3x^2 + 1 \) is divided by \( x + 2 \), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial \( P(x) \) by \( x - c \) is \( P(c) \). In this case, since we are ... |
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