system stringclasses 1
value | conversations listlengths 2 2 | extracted_instruction stringlengths 45 14.1k ⌀ | completion stringlengths 6 33k ⌀ | __original_row_idx int64 0 114k ⌀ |
|---|---|---|---|---|
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The farmer said: \"I have $N$ rabbits. Exactly 13 of them have long ears. Exactly 17 of them can jump far.\"\n\nThe traveler rightly noted: \"Therefore, among your rabbits, at least 3 rabbits both have long ears and can jump far.\"\n\n... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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 f(n)= [((1^2)x(nC1)^2) + ((2^2)x(nC2)^2) + ((3^2)x(nC3)^2) + ...... + ((n^2)x(nCn)^2)]%MOD.\n\... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Nikhil learnt two new commands pwd and cd on the first day of Operating Systems lab.\npwd - command ... | 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.Nikhil learnt two new commands pwd and cd on the first day of Operating Systems lab.
pwd - command displays the current working directory an... | Here is the executable Python function that meets the requirements of the prompt. The function processes commands to manage the current working directory and handles the special cases of changing to parent directories using "..".
```python
def manage_directory():
import sys
from pathlib import PurePath
... | 2,537 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "The rural general store is a staple of the great nation called what?\nA: towns\nB: salt\nC: canada\nD: america\nE: small town"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's try to figure out the answer to this question. The question is asking... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Macy could have?\n$\\textbf{(A) }1\\qq... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\(\\ell\\) be the line through \\((0,0)\\) and tangent to the curve \\(y=x^{3}+x+16\\). Find the slope of \\(\\ell\\)."
},
{
"from": "assistant",
"value": "To find the slope of the line \\(\\ell\\) that is tangent to t... | Return your final response within \boxed{}. Let \(\ell\) be the line through \((0,0)\) and tangent to the curve \(y=x^{3}+x+16\). Find the slope of \(\ell\). | To find the slope of the line \(\ell\) that is tangent to the curve given by \(y = x^3 + x + 16\) at the origin (0,0) or through the origin, we first need to find the derivative of the function to determine the slopes of the tangents.
1. **Find the derivative of the curve**:
\[
\frac{dy}{dx} = \frac{d}{dx}(x^3 +... | 51,396 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Determine all positive integers \\( n \\) such that:\n\n\\[ 5^{n-1} + 3^{n-1} \\mid 5^n + 3^n \\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find all positive integers n such that 5^{n-1... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Perform the following operation on a natural number \\( k \\):\n\n1. Decompose it into the product of prime numbers \\( k = p_{1} p_{2} \\cdots p_{n-1} p_{n} \\).\n2. Calculate the sum \\( p_{1} + p_{2} + \\cdots + p_{n-1} + p_{n} + 1 ... | Return your final response within \boxed{}. Perform the following operation on a natural number \( k \):
1. Decompose it into the product of prime numbers \( k = p_{1} p_{2} \cdots p_{n-1} p_{n} \).
2. Calculate the sum \( p_{1} + p_{2} + \cdots + p_{n-1} + p_{n} + 1 \).
Then, repeat the operation on the resulting su... | To follow the procedure specified, let's start with a natural number \( k \), break it down into its prime factors and then compute the sum as described.
#### Step 1: Decomposition into Prime Factors
Consider a natural number \( k \).
Assume \( k \) can be written as:
\[
k = p_{1}^{a_1} p_{2}^{a_2} \cdots p_{n}^{a... | 74,153 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A sequence of integers \\(\\left\\{a_{i}\\right\\}\\) is defined as follows: \\(a_{i}=i\\) for all \\(1 \\leq i \\leq 5\\), and \\(a_{i}=a_{1} a_{2} \\cdots a_{i-1}-1\\) for all \\(i>5\\). Evaluate \\(a_{1} a_{2} \\cdots a_{2011}-\\sum... | Return your final response within \boxed{}. A sequence of integers \(\left\{a_{i}\right\}\) is defined as follows: \(a_{i}=i\) for all \(1 \leq i \leq 5\), and \(a_{i}=a_{1} a_{2} \cdots a_{i-1}-1\) for all \(i>5\). Evaluate \(a_{1} a_{2} \cdots a_{2011}-\sum_{i=1}^{2011} a_{i}^{2}\). | To compute \(a_{1} a_{2} \cdots a_{2011} - \sum_{i=1}^{2011} a_{i}^{2}\), we begin by calculating the first few terms of the sequence \(a_i\).
For \(1 \leq i \leq 5\):
\[
\begin{align*}
a_1 &= 1, \\
a_2 &= 2, \\
a_3 &= 3, \\
a_4 &= 4, \\
a_5 &= 5.
\end{align*}
\]
Next, we need to find \(a_i\) for \(i > 5\):
\[
\begin... | 54,684 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. What is the smallest three-digit number \\( K \\) which can be written as \\( K = a^b + b^a \\), where both \\( a \\) and \\( b \\) are one-digit positive integers?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In triangle \\( \\triangle ABC \\), prove:\n\\[ 6r \\leq a \\cot A + b \\cot B + c \\cot C \\leq 3R. \\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to prove that in any triangle ABC, the ex... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a convex $n$-gon, a diagonal is selected. The selected diagonal is intersected by exactly 14 other diagonals of the $n$-gon. Find the sum of all possible values of $n$. A vertex of the $n$-gon is not considered an intersection."
}... | Return your final response within \boxed{}. In a convex $n$-gon, a diagonal is selected. The selected diagonal is intersected by exactly 14 other diagonals of the $n$-gon. Find the sum of all possible values of $n$. A vertex of the $n$-gon is not considered an intersection. | To solve this problem, we need to analyze the conditions under which a diagonal in a convex \( n \)-gon intersects with exactly 14 other diagonals.
Let’s denote the vertices of the convex \( n \)-gon as \( A_1, A_2, \ldots, A_n \) and consider a diagonal \( A_i A_j \). This diagonal will intersect with another diagona... | 63,415 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Calculate the limit of the function:\n$$\\lim _{x \\rightarrow 0}(\\cos \\pi x)^{\\frac{1}{x \\cdot \\sin \\pi x}}$$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle this limit problem: the li... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the range of values for the real number \\( a \\) such that for any real number \\( x \\) and any \\( \\theta \\in \\left[0, \\frac{\\pi}{2}\\right] \\), the following inequality always holds:\n\\[\n(x + 3 + 2 \\sin \\theta \\cos ... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $a,b,c,d$ be pairwise distinct positive integers such that $$ \\frac{a}{a+b}+\\frac{b}{b+c}+\\frac{c}{c+d}+\\frac{d}{d+a} $$ is an integer. Prove that $a+b+c+d$ is **not** a prime number."
},
{
"from": "assistant",
... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $AC$ be a diameter of a circle and $AB$ be tangent to the circle. The segment $BC$ intersects the circle again at $D$ . Show that if $AC = 1$ , $AB = a$ , and $CD = b$ , then $$ \\frac{1}{a^2+ \\frac12 }< \\frac{b}{a}< ... | Return your final response within \boxed{}. Let $AC$ be a diameter of a circle and $AB$ be tangent to the circle. The segment $BC$ intersects the circle again at $D$ . Show that if $AC = 1$ , $AB = a$ , and $CD = b$ , then $$ \frac{1}{a^2+ \frac12 }< \frac{b}{a}< \frac{1}{a^2} $$ | In the given problem, we have a circle with diameter \( AC = 1 \), where point \( B \) lies outside the circle such that \( AB \) is a tangent and \( BC \) intersects the circle again at point \( D \). The distances given are \( AB = a \) and \( CD = b \).
First, since \( A \) and \( C \) are the endpoints of the diam... | 103,333 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the ellipse $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1$ where $a > b > 0$, let $P$ be any point on the ellipse. The tangent line at $P$ intersects the tangents drawn from the endpoints $A_{1}$ and $A_{2}$ of the major axis of t... | Return your final response within \boxed{}. Given the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ where $a > b > 0$, let $P$ be any point on the ellipse. The tangent line at $P$ intersects the tangents drawn from the endpoints $A_{1}$ and $A_{2}$ of the major axis of the ellipse at points $Q_{1}$ and $Q_{2}$. P... | To begin, let \( A_1 = (-a, 0) \) and \( A_2 = (a, 0) \), the endpoints of the major axis of the ellipse given by the equation \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \).
### Step 1: Parameterizing the point on the ellipse
Let us parameterize a point \( P \) on the ellipse using the angle \( \theta \):
\[
P = (a \cos... | 75,502 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Consider the fraction, $a/b$, where $a$ and $b$ are positive integers. If $a < b$ and $GCD(a,b) = 1$... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The numbers \\( 2^{2021} \\) and \\( 5^{2021} \\) are written out one after the other. How many digits are written in total?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how man... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the polynomial of the form \\(x^{2} + ax + b\\) whose maximum modulus on the interval \\([-1, 1]\\) is minimal."
},
{
"from": "assistant",
"value": "To find the polynomial of the form \\(p(x) = x^2 + ax + b\\) that min... | Return your final response within \boxed{}. Find the polynomial of the form \(x^{2} + ax + b\) whose maximum modulus on the interval \([-1, 1]\) is minimal. | To find the polynomial of the form \(p(x) = x^2 + ax + b\) that minimizes its maximum modulus on the interval \([-1, 1]\), we will use the properties of Chebyshev polynomials.
The Chebyshev polynomial of degree 2 is given by:
\[
T_2(x) = 2x^2 - 1.
\]
This polynomial achieves its maximum absolute value of 1 on the in... | 45,817 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Suppose there are \\( n \\geq 3 \\) points on a plane. Prove that among them, there exist three points \\( A, B, \\) and \\( C \\) such that\n\\[ 1 \\leq \\frac{AB}{AC} < \\frac{n+1}{n-1}. \\]"
},
{
"from": "assistant",
"va... | Return your final response within \boxed{}. Suppose there are \( n \geq 3 \) points on a plane. Prove that among them, there exist three points \( A, B, \) and \( C \) such that
\[ 1 \leq \frac{AB}{AC} < \frac{n+1}{n-1}. \] | To prove that among \( n \geq 3 \) points in a plane, there exist three points \( A, B, \) and \( C \) such that
\[
1 \leq \frac{AB}{AC} < \frac{n+1}{n-1},
\]
we will utilize geometric configurations and properties.
**Step 1: Definition and setup**
Consider \( n \) points \( P_1, P_2, \ldots, P_n \) in the plane. F... | 85,218 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A group with 7 young men and 7 young women was divided into pairs randomly. Find the probability that at least one pair consists of two women. Round the answer to two decimal places."
},
{
"from": "assistant",
"value": "<|b... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Zane the wizard is going to perform a magic show shuffling the cups.\n\nThere are *n* cups, numbered... | 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.Zane the wizard is going to perform a magic show shuffling the cups.
There are *n* cups, numbered from 1 to *n*, placed along the *x*-axis ... | Here's the Python function based on your prompt to determine the final position of the bone after Zane the wizard performs his swaps:
```python
def final_bone_position():
import sys
input = sys.stdin.read
data = input().splitlines()
# Read n, m, k
n, m, k = map(int, data[0].split())
# Rea... | 18,962 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Bag $A$ contains 2 ten-yuan bills and 3 one-yuan bills, and bag $B$ contains 4 five-yuan bills and 3 one-yuan bills. Now, two bills are randomly drawn from each bag. What is the probability that the sum of the values of the bills remai... | Return your final response within \boxed{}. Bag $A$ contains 2 ten-yuan bills and 3 one-yuan bills, and bag $B$ contains 4 five-yuan bills and 3 one-yuan bills. Now, two bills are randomly drawn from each bag. What is the probability that the sum of the values of the bills remaining in bag $A$ is greater than the sum o... | To find the probability that the sum of the values of the bills remaining in bag \( A \) is greater than the sum of the values of the bills remaining in bag \( B \) after randomly drawing two bills from each bag, we need to evaluate the possible draws from both bags.
### Bag Compositions
- **Bag A**:
- 2 ten-yuan bi... | 46,424 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The radii of the four circles that are tangent to the lines of a triangle form a geometric progression. What is the largest angle of the triangle?"
},
{
"from": "assistant",
"value": "Let the radii of the four circles be \\... | Return your final response within \boxed{}. The radii of the four circles that are tangent to the lines of a triangle form a geometric progression. What is the largest angle of the triangle? | Let the radii of the four circles be \( r_1, r_2, r_3, r_4 \) such that they are in geometric progression. Since the circles are tangent to the lines of the triangle, these circles are the incircle and the excircles corresponding to the triangle.
For a triangle with angles \( A, B, C \), the radius \( r \) of the inci... | 44,098 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The Production Manager of a dance company has been tasked with determining the cost for the seasonal... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The Production Manager of a dance company has been tasked with determining the cost for the seasonal dance recital. Because of their excepti... | To tackle the problem, we will create a Python function that calculates the minimum number of quick changes needed for a dance recital. The function will read the number of routines and the dancers in each routine from standard input, calculate the required quick changes based on the combinations of consecutive routine... | 17,702 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the planar region $\\Omega=\\{(x, y) \\mid x+y \\leqslant 6, x \\geqslant 0, y \\geqslant 0\\}$, and another region $A=\\{(x, y) \\mid x \\leqslant 4, y \\geqslant 0, x-2 y \\geqslant 0\\}$, if a point $P$ is randomly chosen with... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. How many consecutive terms of the arithmetic progression \\(32, 28, 24, \\ldots\\), starting from the first term, must be added to obtain a sum equal to 132?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlri... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $p$ be a permutation of the set $S_n = \\{1, 2, \\dots, n\\}$ . An element $j \\in S_n$ is called a fixed point of $p$ if $p(j) = j$ . Let $f_n$ be the number of permutations having no fixed points, and $g_n$ be the n... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Iroha is very particular about numbers. There are K digits that she dislikes: D_1, D_2, ..., D_K.\nS... | 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.Iroha is very particular about numbers. There are K digits that she dislikes: D_1, D_2, ..., D_K.
She is shopping, and now paying at the cas... | Here is the executable Python function that meets the requirements of the given prompt. The function reads input from standard input (stdin) and prints the minimum amount of money Iroha will hand to the cashier:
```python
def minimum_hand_money():
import sys
input_data = sys.stdin.read().splitlines()
... | 11,276 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Which digits can be placed in the letters $A, B, C$ to make the following multiplication correct: $\\overline{A B B C} \\cdot \\overline{C C A} = \\overline{C C C C A C}$? - In which other base number systems can the problem still be s... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The Reuleaux triangle is a shape formed from an equilateral triangle by adding circular arcs with the centers at the vertices of the triangle and with radii equal to the side of the triangle.\n\nWhat is the area of a Reuleaux triangle ... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The bases $AB$ and $CD$ of the trapezoid $ABCD$ are equal to 101 and 20, respectively, and its diagonals are mutually perpendicular. Find the dot product of the vectors $\\overrightarrow{AD}$ and $\\overrightarrow{BC}$."
},
{
"... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The *Olimpia* country is formed by $n$ islands. The most populated one is called *Panacenter*, and every island has a different number of inhabitants. We want to build bridges between these islands, which we'll be able to travel in b... | Return your final response within \boxed{}. The *Olimpia* country is formed by $n$ islands. The most populated one is called *Panacenter*, and every island has a different number of inhabitants. We want to build bridges between these islands, which we'll be able to travel in both directions, under the following condi... | To solve the problem of determining the number of ways we can build the bridges between the islands in the *Olimpia* country, we must consider a few key points regarding the constraints:
1. **Tree Structure**: Since we want to connect all islands such that they can be reached from *Panacenter* without using any bridge... | 104,929 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A driver travels at a speed of 60 miles per hour for 2 hours. During this time, his car can travel 30 miles per gallon of gasoline, and he earns $0.5 per mile. The only expense is refueling the car at $2 per gallon. After deducting fue... | Return your final response within \boxed{}. A driver travels at a speed of 60 miles per hour for 2 hours. During this time, his car can travel 30 miles per gallon of gasoline, and he earns $0.5 per mile. The only expense is refueling the car at $2 per gallon. After deducting fuel costs, his hourly wage is ( ) dollars.
... | To calculate the driver's hourly wage after deducting fuel costs, let's break down the problem step by step.
1. **Distance traveled**: The driver travels for 2 hours at a speed of 60 miles per hour.
\[
\text{Distance} = \text{Speed} \times \text{Time} = 60 \text{ miles/hour} \times 2 \text{ hours} = 120 \text{ m... | 34,700 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \\(\\sin(180^{\\circ} - \\alpha) = \\sin \\alpha \\) (where \\( \\alpha \\) is an arbitrary angle). What does this statement assert?"
},
{
"from": "assistant",
"value": "The statement \\(\\sin(180^{\\circ} - \\alpha) = \\si... | Return your final response within \boxed{}. \(\sin(180^{\circ} - \alpha) = \sin \alpha \) (where \( \alpha \) is an arbitrary angle). What does this statement assert? | The statement \(\sin(180^{\circ} - \alpha) = \sin \alpha\) asserts that the sine function is symmetric with respect to the angle \(90^{\circ}\) (or in the unit circle, symmetric about the line \(x = 0\)).
To understand this more clearly, when you evaluate \(\sin(180^{\circ} - \alpha)\), you are effectively saying tha... | 82,169 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In the coordinate plane, does there exist a family of lines \\( l_{1}, l_{2}, \\cdots, l_{n}, \\cdots \\) containing infinitely many lines that satisfies the following conditions:\n1. The point \\((1,1)\\) lies on \\( l_{n} \\) for \\(... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Is it possible to color the points of the plane with two colors in such a way that there is no equilateral triangle with sides of unit length whose vertices are all the same color?"
},
{
"from": "assistant",
"value": "<|beg... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. There is a frog jumping on a $ 2k \\times 2k$ chessboard, composed of unit squares. The frog's jumps are $ \\sqrt{1 \\plus{} k^2}$ long and they carry the frog from the center of a square to the center of another square. Some $ m$... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that for any \\( n \\in \\mathbf{N}^{*} \\), \\( a_n > 0 \\) and \\( \\sum_{j=1}^{n} a_{j}^{3} = \\left( \\sum_{j=1}^{n} a_{j} \\right)^{2} \\), prove that \\( a_n = n \\)."
},
{
"from": "assistant",
"value": "To prov... | Return your final response within \boxed{}. Given that for any \( n \in \mathbf{N}^{*} \), \( a_n > 0 \) and \( \sum_{j=1}^{n} a_{j}^{3} = \left( \sum_{j=1}^{n} a_{j} \right)^{2} \), prove that \( a_n = n \). | To prove that \( a_n = n \) under the condition \( \sum_{j=1}^{n} a_j^3 = \left( \sum_{j=1}^{n} a_j \right)^2 \), let's define:
\[
S_n = \sum_{j=1}^{n} a_j
\]
and
\[
T_n = \sum_{j=1}^{n} a_j^3.
\]
According to the given condition, we can express it as:
\[
T_n = S_n^2.
\]
We can expand \( S_n \) and \( T_n \):
- **F... | 54,136 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given an equilateral triangle \\( \\triangle ABC \\) with side length 1, there are \\( n \\) equally spaced points on the side \\( BC \\). Let these points be \\( P_1, P_2, \\ldots, P_{n-1} \\) in the direction from point \\( B \\) to ... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Everyone is tired after searching for Mr. NU for hours after finally finding him in the Spiral Maze.... | 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.Everyone is tired after searching for Mr. NU for hours after finally finding him in the Spiral Maze.
The NU-Tech team has N members. The me... | Here is the Python function that implements the description you provided. The function reads input from standard input (stdin), processes the commands, and prints the results for Type-3 orders as specified.
```python
def manage_team():
import sys
from collections import defaultdict
input = sys.stdin.read
... | 15,833 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the functions \\( f(x)=a x^{2}+b x+c \\) and \\( g(x)=a x+b \\), where \\( a, b, \\) and \\( c \\) are real numbers with \\( a > 0 \\). When \\(|x| \\leqslant 1\\), \\(|f(x)| \\leqslant 1\\), and the maximum value of \\( g(x) \\)... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The surface area of the lateral surface of a right circular cylinder is in the ratio $5:3$ to the area of its base; the diagonal of the axial cross-section is $39 \\mathrm{~cm}$. What is the total surface area and volume of the cylinde... | Return your final response within \boxed{}. The surface area of the lateral surface of a right circular cylinder is in the ratio $5:3$ to the area of its base; the diagonal of the axial cross-section is $39 \mathrm{~cm}$. What is the total surface area and volume of the cylinder? | Let the radius of the base of the cylinder be denoted as \( r \) and the height as \( h \). The lateral surface area \( A_L \) of a right circular cylinder is given by
\[
A_L = 2\pi rh
\]
The area of the base \( A_B \) is given by
\[
A_B = \pi r^2
\]
According to the problem, the ratio of the lateral surface area... | 45,523 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The Little Elephant and his friends from the Zoo of Lviv were returning from the party. But suddenly... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The Little Elephant and his friends from the Zoo of Lviv were returning from the party. But suddenly they were stopped by the policeman Big ... | Here's a Python function that implements the given problem by taking input from stdin and printing the output. The function will evaluate the number of operations needed for each test case to ensure that no group of K consecutive elephants has at least M of them with the maximum test result.
```python
def minimum_oper... | 5,255 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A circle is called a separator for a set of five points in a plane if it passes through three of these points, contains a fourth point in its interior, and the fifth point is outside the circle.\nProve that every set of five points suc... | Return your final response within \boxed{}. A circle is called a separator for a set of five points in a plane if it passes through three of these points, contains a fourth point in its interior, and the fifth point is outside the circle.
Prove that every set of five points such that no three are collinear and no four ... | To prove that every set of five points in the plane, where no three points are collinear and no four points are concyclic, has exactly four separators, we will analyze the configurations of these points and how to construct the circles that serve as separators.
Let \( P_1, P_2, P_3, P_4, P_5 \) be the five points in g... | 75,649 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. On the sides \\( BC, CA \\), and \\( AB \\) of triangle \\( ABC \\), points \\( A_{1}, B_{1} \\), and \\( C_{1} \\) are taken such that \\( AC_{1} = AB_{1} \\), \\( BA_{1} = BC_{1} \\), and \\( CA_{1} = CB_{1} \\). Prove that \\( A_{1}... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The ultimate battle has begun in Tekken. \nEach fight has two players. Let the initial health of th... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The ultimate battle has begun in Tekken.
Each fight has two players. Let the initial health of the players be X and Y, then, after the fig... | Here's a Python function that implements the specified logic to determine if Anna can have positive health after all battles. This function takes input from standard input (stdin) and prints the output for multiple test cases as described in the prompt.
```python
def can_anna_survive():
import sys
input = sys.... | 13,777 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered fr... | 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.In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k ... | Here is an executable Python function that follows the description you provided. Let's define the function `find_fall_point`, which reads from standard input and computes the point where Grasshopper Bob will fall down. After the definition, we call the function.
```python
def find_fall_point():
import sys
inpu... | 6,245 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Among 18 coins, one is counterfeit. The real coins all weigh the same, but the counterfeit coin has a different weight. What is the minimum number of weighings on a balance scale (without additional weights) needed to determine whether... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Consider an $n \\times n$ matrix $\\left\\|\\xi_{i j}\\right\\|$ where all the (random) elements are independent and $\\mathrm{P}\\left(\\xi_{i j}= \\pm 1\\right)=1 / 2$. Show that the mean and variance of the determinant of this rando... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Vasya wants to buy himself a nice new car. Unfortunately, he lacks some money. Currently he has exac... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nThere are 12 shapes made from matches - 3 triangles, 4 squares, and 5 pentagons. The shapes do not share sides. Petya and Vasya take turns removing one match at a time. Vasya wants as few untouched shapes as possible to remain, while... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Luka is fooling around in chemistry class again! Instead of balancing equations he is writing coded ... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. There are two types of tables in a restaurant: a square table can seat 4 people, and a round table can seat 9 people. The restaurant manager calls a number a \"wealth number\" if the total number of diners can exactly fill a certain nu... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $a,b,c$ be positive real numbers such that $a+b+c=10$ and $ab+bc+ca=25$. Let $m=\\min\\{ab,bc,ca\\}$. Find the largest possible value of $m$."
},
{
"from": "assistant",
"value": "Let \\( a, b, c \\) be positive real n... | Return your final response within \boxed{}. Let $a,b,c$ be positive real numbers such that $a+b+c=10$ and $ab+bc+ca=25$. Let $m=\min\{ab,bc,ca\}$. Find the largest possible value of $m$. | Let \( a, b, c \) be positive real numbers such that \( a + b + c = 10 \) and \( ab + ac + bc = 25 \). We need to find the largest possible value of \( m = \min(ab, ac, bc) \).
Firstly, we denote the pairwise products as follows:
- Let \( x = ab \)
- Let \( y = ac \)
- Let \( z = bc \)
We seek to maximize \( m = \min... | 93,039 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The point \\( P(-1,4) \\) is reflected in the \\( y \\)-axis to become \\( Q \\). The point \\( Q \\) is reflected in the line \\( y=x \\) to become \\( R \\). The point \\( R \\) is reflected in the \\( x \\)-axis to become \\( S \\).... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Determine all functions $f : N_0 \\to R$ satisfying $f (x+y)+ f (x-y)= f (3x)$ for all $x,y$ ."
},
{
"from": "assistant",
"value": "To solve the functional equation \\( f(x+y) + f(x-y) = f(3x) \\) for all \\( x, y \\in... | Return your final response within \boxed{}. Determine all functions $f : N_0 \to R$ satisfying $f (x+y)+ f (x-y)= f (3x)$ for all $x,y$ . | To solve the functional equation \( f(x+y) + f(x-y) = f(3x) \) for all \( x, y \in \mathbb{N}_0 \), we'll start by analyzing the equation.
1. **Substituting \( y = 0 \)**:
\[
f(x + 0) + f(x - 0) = f(3x) \implies f(x) + f(x) = f(3x) \implies 2f(x) = f(3x).
\]
This tells us that \( f(3x) = 2f(x) \).
2. **S... | 103,565 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Determine whether there exists a set of points $M$ in three-dimensional space that contains a finite number of points, which do not all lie in the same plane, and has the following property:\n\nFor any two (distinct) points $A$ and $B$... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nProve that for any natural number \\(a\\), there exists a natural number \\(n\\) such that all the numbers \\(n+1, n^{n}+1, n^{n^{n}}+1, \\ldots\\) are divisible by \\(a\\)."
},
{
"from": "assistant",
"value": "<|begin_of... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( f(x) = x^2 - r_2 x + r_3 \\) for all real numbers \\( x \\), where \\( r_2 \\) and \\( r_3 \\) are some real numbers. Define a sequence \\( \\{ g_n \\} \\) for all nonnegative integers \\( n \\) by \\( g_0 = 0 \\) and \\( g_{n+... | Return your final response within \boxed{}. Let \( f(x) = x^2 - r_2 x + r_3 \) for all real numbers \( x \), where \( r_2 \) and \( r_3 \) are some real numbers. Define a sequence \( \{ g_n \} \) for all nonnegative integers \( n \) by \( g_0 = 0 \) and \( g_{n+1} = f(g_n) \). Assume that \( \{ g_n \} \) satisfies the ... | To analyze the function \( f(x) = x^2 - r_2 x + r_3 \) and the sequence \( \{ g_n \} \) defined by \( g_0 = 0 \) and \( g_{n+1} = f(g_n) \), we first note the behavior of \( f \).
We can determine the vertex of the parabola represented by the quadratic function \( f(x) \):
\[
x_v = \frac{r_2}{2}.
\]
The value of \( f ... | 21,935 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given real numbers \\(a, b, c\\) and a positive number \\(\\lambda\\) such that the function \\(f(x) = x^3 + a x^2 + b x + c\\) has three real roots \\(x_1, x_2, x_3\\), satisfying the conditions:\n(1) \\(x_2 - x_1 = \\lambda\\),\n(2) ... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The longer leg of a right triangle is $1$ foot shorter than twice the length of the shorter leg. The area of the triangle is $60$ square feet. What is the length of the hypotenuse, in feet?"
},
{
"from": "assistant",
"value... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. $ABCDEFGH$ shown below is a cube. Find $\\sin \\angle HAC$.\n\n[asy]\n\nimport three;\n\ntriple A,B,C,D,EE,F,G,H;\n\nA = (0,0,0);\n\nB = (1,0,0);\n\nC = (1,1,0);\n\nD= (0,1,0);\n\nEE = (0,0,1);\n\nF = B+EE;\n\nG = C + EE;\n\nH = D + EE... | Return your final response within \boxed{}. $ABCDEFGH$ shown below is a cube. Find $\sin \angle HAC$.
[asy]
import three;
triple A,B,C,D,EE,F,G,H;
A = (0,0,0);
B = (1,0,0);
C = (1,1,0);
D= (0,1,0);
EE = (0,0,1);
F = B+EE;
G = C + EE;
H = D + EE;
draw(B--C--D);
draw(B--A--D,dashed);
draw(EE--F--G--H--EE);
... | To find \(\sin \angle HAC\) in a cube, we need to identify the coordinates of points \(H\), \(A\), and \(C\).
1. **Assigning coordinates for the cube:**
- Let \(A = (0, 0, 0)\)
- Let \(B = (1, 0, 0)\)
- Let \(C = (1, 1, 0)\)
- Let \(D = (0, 1, 0)\)
- Let \(E = (0, 0, 1)\)
- Let \(F = (1, 0, 1)\)
-... | 91,258 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find all positive integers such that they have $6$ divisors (without $1$ and the number itself) and the sum of the divisors is $14133$ ."
},
{
"from": "assistant",
"value": "To find positive integers that have exactly ... | Return your final response within \boxed{}. Find all positive integers such that they have $6$ divisors (without $1$ and the number itself) and the sum of the divisors is $14133$ . | To find positive integers that have exactly 6 divisors excluding 1 and the number itself, we first consider the forms a number with 6 total divisors can take. The two possible forms are:
1. \( n = p^5 \), where \( p \) is a prime, giving divisors \( 1, p, p^2, p^3, p^4, p^5 \).
2. \( n = p^2 q \), where \( p \) and \(... | 104,624 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Decompose the function \\( y = e^{2x} \\) into a Fourier series over the interval \\((-\\infty, \\infty)\\) using the system of Hermite polynomials."
},
{
"from": "assistant",
"value": "To represent the function \\( y = e^{... | Return your final response within \boxed{}. Decompose the function \( y = e^{2x} \) into a Fourier series over the interval \((-\infty, \infty)\) using the system of Hermite polynomials. | To represent the function \( y = e^{2x} \) as a Fourier series using the Hermite polynomials over the interval \((-\infty, \infty)\), we start by recalling that the Hermite polynomials \( H_n(x) \) form a complete orthogonal set with respect to the weight function \( e^{-x^2} \) on the interval \((-\infty, \infty)\).
... | 28,564 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $b$ be a non-zero natural number. Show that for any natural number $n$, there exists a unique pair of natural numbers $(q, r)$ such that $r < b$ and $n = qb + r$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Max bought a new dirt bike and paid $10\\%$ of the cost upfront, which was $\\$150$. What was the price of the bike?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. Max bought a new dirt bike a... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Calculate the sum of the coefficients:\n1) in the expansion of $(a+b)^{n}$,\n2) in the expansion of $(a-b)^{n}$,\n3) of the terms occupying even positions in the expansion of $(a+b)^{n}$."
},
{
"from": "assistant",
"value":... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The parabolas with equations \\( y = x^2 - 2x - 3 \\) and \\( y = -x^2 + 4x + c \\) intersect at points \\( A \\) and \\( B \\). Determine the value of \\( c \\) so that the sum of the \\( x \\)-coordinate and \\( y \\)-coordinate of t... | Return your final response within \boxed{}. The parabolas with equations \( y = x^2 - 2x - 3 \) and \( y = -x^2 + 4x + c \) intersect at points \( A \) and \( B \). Determine the value of \( c \) so that the sum of the \( x \)-coordinate and \( y \)-coordinate of the midpoint of \( AB \) is 2017. | To find the value of \( c \) such that the sum of the \( x \)-coordinate and \( y \)-coordinate of the midpoint of points \( A \) and \( B \) is 2017, we start by finding the points of intersection of the two parabolas given by the equations:
\[
y = x^2 - 2x - 3
\]
and
\[
y = -x^2 + 4x + c.
\]
To find the points of... | 90,176 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The center of circle $\\omega_{2}$ lies on circle $\\omega_{1}$. From a point $X$ on circle $\\omega_{1}$, tangents $XP$ and $XQ$ are drawn to circle $\\omega_{2}$ ($P$ and $Q$ are the points of tangency), and they intersect $\\omega_{... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nIn an acute-angled triangle $\\triangle ABC$, $\\angle BAC \\neq 60^{\\circ}$. Tangents $BD$ and $CE$ are drawn from points $B$ and $C$ respectively to the circumcircle of $\\triangle ABC$ such that $BD = CE = BC$. Line $DE$ intersec... | Return your final response within \boxed{}.
In an acute-angled triangle $\triangle ABC$, $\angle BAC \neq 60^{\circ}$. Tangents $BD$ and $CE$ are drawn from points $B$ and $C$ respectively to the circumcircle of $\triangle ABC$ such that $BD = CE = BC$. Line $DE$ intersects the extensions of $AB$ and $AC$ at points $F... | To establish the desired equality \( AM = AN \) in triangle \( \triangle ABC \) with the points defined in the problem, we will utilize geometric properties related to angles and tangent lengths.
First, let's consider the points \( D \) and \( E \). Since \( BD \) and \( CE \) are tangents to the circumcircle of \( \... | 84,321 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. If a school bus leaves school with 48 students on board, and one-half of the students get off the bus at each of the first three stops, how many students remain on the bus after the third stop?"
},
{
"from": "assistant",
"v... | Return your final response within \boxed{}. If a school bus leaves school with 48 students on board, and one-half of the students get off the bus at each of the first three stops, how many students remain on the bus after the third stop? | To determine the number of students remaining on the bus after the third stop, we'll calculate the number of students that get off at each stop.
1. **Initial number of students:** 48 students.
2. **First stop:**
- Students getting off: \( \frac{1}{2} \times 48 = 24 \)
- Students remaining: \( 48 - 24 = 24 \)
3... | 95,449 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Prove that for any real numbers \\(a\\) and \\(b\\), the inequality \\(a^{2} + ab + b^{2} \\geq 3(a + b - 1)\\) holds."
},
{
"from": "assistant",
"value": "To prove the inequality \\(a^{2} + ab + b^{2} \\geq 3(a + b - 1)\\)... | Return your final response within \boxed{}. Prove that for any real numbers \(a\) and \(b\), the inequality \(a^{2} + ab + b^{2} \geq 3(a + b - 1)\) holds. | To prove the inequality \(a^{2} + ab + b^{2} \geq 3(a + b - 1)\) for any real numbers \(a\) and \(b\), we start by rearranging it:
\[
a^{2} + ab + b^{2} - 3a - 3b + 3 \geq 0.
\]
We can denote the left-hand side as \( f(a, b) \):
\[
f(a, b) = a^{2} + ab + b^{2} - 3a - 3b + 3.
\]
To analyze this expression, we can tr... | 38,866 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. How many positive whole numbers have cube roots that are less than $10$? For example, $20$ would count since $\\sqrt[3]{20}<10.$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so the question is asking h... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Pankhuri hates Algebra. Doesn't matter how hard she tries, she always fails to get good marks in her... | 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.Pankhuri hates Algebra. Doesn't matter how hard she tries, she always fails to get good marks in her assessments. One of her marked assessme... | To solve the problem of maximizing the value of a mathematical expression that consists of integers and + or - operations, we can utilize dynamic programming. The idea is to evaluate all possible ways to place parentheses to maximize the expression. The plan will be to compute the maximum values for different parts of ... | 13,812 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A quality control department checks 900 parts for standard compliance. The probability that a part is standard is 0.9. Find the bounds, with a probability of 0.95, within which the number $m$ of standard parts among those checked will ... | Return your final response within \boxed{}. A quality control department checks 900 parts for standard compliance. The probability that a part is standard is 0.9. Find the bounds, with a probability of 0.95, within which the number $m$ of standard parts among those checked will fall. | To find the bounds within which the number \( m \) of standard parts will fall with a probability of 0.95, we can use the normal approximation to the binomial distribution since \( n = 900 \) is large and the conditions for the approximation (both \( n \cdot p \) and \( n \cdot (1-p) \) should be greater than 5) are sa... | 74,217 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. What is the largest integer $n$ with no repeated digits that is relatively prime to $6$ ? Note that two numbers are considered relatively prime if they share no common factors besides $1$ .\n\n*Proposed by Jacob Stavrianos*"
},
... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Construct a circle passing through two given points and tangent to a given circle (or line)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how to construct a circle that passes t... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Density is defined as the ratio of an object's mass to its volume. There are two cubes. The second cube is made from a material with half the density of the first cube, and the side length of the second cube is 100% greater than that o... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given four lines \\(m_{1}, m_{2}, m_{3}, m_{4}\\) that intersect at a single point \\(O\\). From an arbitrary point \\(A_{1}\\) on line \\(m_{1}\\), draw a line parallel to \\(m_{4}\\) intersecting \\(m_{2}\\) at point \\(A_{2}\\). The... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Joisino is about to compete in the final round of a certain programming competition.\nIn this contes... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Today is Tom's Birthday. His Mom gifted him two sets of integers to play with, set Q and set R. R is... | 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.Today is Tom's Birthday. His Mom gifted him two sets of integers to play with, set Q and set R. R is the transformation of set Q. Both Q and... | Here's a Python function that meets the requirements of your prompt. This function reads from standard input, processes the two sets of integers to find the missing numbers, and prints the output in ascending order.
```python
def find_missing_numbers():
import sys
from collections import Counter
input... | 5,592 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Is there a non-constant function \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfies the inequality \n\n$$\n(f(x) - f(y))^2 \\leq |x-y|^3\n$$ \n\nfor all \\( x, y \\in \\mathbb{R} \\)?"
},
{
"from": "assistant",
... | Return your final response within \boxed{}. Is there a non-constant function \( f: \mathbb{R} \rightarrow \mathbb{R} \) that satisfies the inequality
$$
(f(x) - f(y))^2 \leq |x-y|^3
$$
for all \( x, y \in \mathbb{R} \)? | To analyze the given inequality
\[
(f(x) - f(y))^2 \leq |x-y|^3,
\]
we start by rewriting it in a more manageable form. Taking the square root on both sides gives us
\[
|f(x) - f(y)| \leq |x-y|^{3/2}.
\]
This inequality indicates that the difference in the function values \( |f(x) - f(y)| \) is controlled by the ... | 55,007 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. What is the minimum number of equilateral triangles, of side length 1 unit, needed to cover an equilateral triangle of side length 10 units?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to fi... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that the four vertices of the quadrilateral \\( P_{1} P_{2} P_{3} P_{4} \\) are located on the sides of triangle \\( \\triangle ABC \\), prove that among the four triangles \\( \\triangle P_{1} P_{2} P_{3} \\), \\( \\triangle P_{... | Return your final response within \boxed{}. Given that the four vertices of the quadrilateral \( P_{1} P_{2} P_{3} P_{4} \) are located on the sides of triangle \( \triangle ABC \), prove that among the four triangles \( \triangle P_{1} P_{2} P_{3} \), \( \triangle P_{1} P_{2} P_{4} \), \( \triangle P_{1} P_{3} P_{4} \... | To prove that at least one of the triangles \( \triangle P_{1} P_{2} P_{3} \), \( \triangle P_{1} P_{2} P_{4} \), \( \triangle P_{1} P_{3} P_{4} \), and \( \triangle P_{2} P_{3} P_{4} \) has an area not greater than one-fourth of the area of triangle \( \triangle ABC \), we can utilize the concept of affine transformat... | 41,003 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. $\\left(\\frac{1}{4}\\right)^{-\\tfrac{1}{4}}=$\n$\\text{(A) } -16\\quad \\text{(B) } -\\sqrt{2}\\quad \\text{(C) } -\\frac{1}{16}\\quad \\text{(D) } \\frac{1}{256}\\quad \\text{(E) } \\sqrt{2}$"
},
{
"from": "assistant",
"... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Two squares \\(ABCD\\) and \\(KLMN\\) are arranged so that the vertices \\(B, C, K,\\) and \\(N\\) lie on the same line, and the remaining four vertices are on opposite sides of \\(BC\\) and lie on the same circle. It is known that the... | Return your final response within \boxed{}. Two squares \(ABCD\) and \(KLMN\) are arranged so that the vertices \(B, C, K,\) and \(N\) lie on the same line, and the remaining four vertices are on opposite sides of \(BC\) and lie on the same circle. It is known that the side length of one square is 1 greater than the si... | Given two squares \(ABCD\) and \(KLMN\) where \(ABCD\) has a side length \(a\) and \(KLMN\) has a side length \(b\), and it is known that \(a = b + 1\).
First, we set the side lengths of the squares:
- Let \(b\) be the side length of square \(KLMN\).
- Thus, \(a = b + 1\).
Now let us position square \(ABCD\) and \(KL... | 64,053 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Through a certain point $Q$, taken inside the triangle $ABC$, three lines parallel to its sides are drawn. These lines divide the triangle into six parts, three of which are triangles with areas $S_{1}, S_{2}$, and $S_{3}$. Prove that ... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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 a string S that contains only digits (0-9) and an integer target, return all possible strings ... | 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 a string S that contains only digits (0-9) and an integer target, return all possible strings to insert the binary operator ' + ', ' -... | Here's a complete Python function that implements the behavior described in your prompt. The function generates all valid expressions by inserting operators between the digits of a string `S` and then evaluates those expressions to find those that match the target value. It handles leading zeros appropriately and retur... | 17,903 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.When Valera has got some free time, he goes to the library to read some books. Today he's got *t* fr... | 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.When Valera has got some free time, he goes to the library to read some books. Today he's got *t* free minutes to read. That's why Valera to... | Certainly! Below is an executable Python function that reads input from stdin, calculates the maximum number of books Valera can read, and then prints the output. The function works based on the given specifications and constraints.
```python
def max_books():
import sys
input = sys.stdin.read
data = input(... | 19,219 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nIs there a polyhedron (not necessarily convex) whose complete list of edges consists of the following: \\(AB, AC, BC, BD, CD, DE, EF, EG, FG, FH, GH, AH\\)?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOka... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A motorcyclist left city A for city B. If he travels at a speed of 50 km/h, he will arrive in city B one hour earlier than the scheduled time. If he travels at a speed of 35 km/h, he will be 2 hours late. Find the distance between citi... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. ABCD is a convex quadrilateral with AB not parallel to CD. A circle through A and B touches CD at X, and a circle through C and D touches AB at Y. The two circles meet at U and V. Show that UV bisects XY if and only if BC is parallel t... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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 the number n, find the smallest positive integer which has exactly n divisors. It is guarantee... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "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.Petya is a beginner programmer. He has already mastered the basics of the C++ language and moved on ... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nOn the base $AC$ of an isosceles triangle $ABC$ ($AB = BC$) there is a point $M$. It is known that $AM = 7$, $MB = 3$, and $\\angle BMC = 60^\\circ$. Find the length of the segment $AC$."
},
{
"from": "assistant",
"value"... | Return your final response within \boxed{}.
On the base $AC$ of an isosceles triangle $ABC$ ($AB = BC$) there is a point $M$. It is known that $AM = 7$, $MB = 3$, and $\angle BMC = 60^\circ$. Find the length of the segment $AC$. | To find the length of segment \( AC \) in the isosceles triangle \( ABC \) where \( AB = BC \), we will use the given values \( AM = 7 \), \( MB = 3 \), and \( \angle BMC = 60^\circ \).
1. We begin by finding the length \( BM \):
\[
BM = 3
\]
2. The total length \( AB \) can be expressed in terms of \( AM \)... | 74,033 |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( S \\) be a subset of \\( \\mathbb{N}^{*} \\). Show that one of the following two properties is satisfied:\n\n(i) There exist two distinct finite subsets \\( A \\) and \\( B \\) of \\( S \\) such that:\n\n\\[ \\sum_{x \\in A} \\... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let be $f: (0,+\\infty)\\rightarrow \\mathbb{R}$ monoton-decreasing . \n\nIf $f(2a^2+a+1)<f(3a^2-4a+1)$ find interval of $a$ .\n"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I have this probl... | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. There are 5 ping pong balls, among which 3 are new and 2 are old (i.e., used at least once). Each time a match occurs, 2 balls are selected and used, and then all balls are returned. Let $\\xi$ be the number of new balls picked in the ... | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.