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[
{
"content": "Anna and Zsófi take turns rolling a die, and the number rolled is always added to the sum of the numbers rolled so far. The person who first makes the sum divisible by 4 wins. If Anna starts, what is the probability that she will win? Let's think step by step and output the final answer within \\b... |
[
{
"content": "Let $\\Gamma$ be a circle with center $O$ and $P$ a point outside the circle. Let $A \\in \\Gamma$ such that the line segment $PA$ is tangent to $\\Gamma$, and let $B$ be the point diametrically opposite to $A$. Let $\\Delta$ be a line passing through $P$ and intersecting $\\Gamma$ at points $C$ a... |
[
{
"content": "If $\\varepsilon _{k}, k=1,2,...,2013$ are all $2013^{th}$ roots of unity, evaluate the product: \\[ \\prod_{k=1}^{2013}(2-\\varepsilon _{k}^{2}). \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
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{
"content": "[THINK]\nHere's a thinking pro... |
[
{
"content": "Arrange the arithmetic operation signs and parentheses in the expression consisting of the three numbers $\\frac{1}{8} \\ldots \\frac{1}{9} \\ldots \\frac{1}{28}$ so that the result of the calculations is equal to $\\frac{1}{2016}$. Let's think step by step and output the final answer within \\box... |
[
{
"content": "Let \\( p \\in \\mathbb{N} \\) and \\( f \\in \\mathbb{Z}[X] \\) such that \\( f(p) = 6 \\), \\( f(p+1) = 18 \\), and \\( f(p+2) = 54 \\). How many solutions does the equation \\( f(x) = 2 \\) have over \\( \\mathbb{Z} \\)? Let's think step by step and output the final answer within \\boxed{}.",
... |
[
{
"content": "Consider the function \\( f: \\mathbb{N} \\setminus \\{0,1\\} \\to \\mathbb{R} \\), defined by \\( f(n) = \\sqrt[n]{5\\sqrt{2} + 7} + \\sqrt[n]{5\\sqrt{2} - 7} \\). Calculate the value of \\( f(2) - f(3) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "use... |
[
{
"content": "Find all $n \\geq 10$ such that $\\binom{n}{10} \\binom{n+1}{10}$ is a perfect square. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
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{
"content": "[THINK]\nThe problem asks for all integers $n \\geq 10$ such that the product $\\binom{n}{10} ... |
[
{
"content": "Calculate the integral \\[ \\int \\frac{dx}{(x+a)^{m}(x+b)^{n}} \\quad \\text{where } m,n \\in \\mathbb{N}. \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to solve the integral $\\int \\fra... |
[
{
"content": "Determine the general term of the sequence $(a_n)_{n\\ge 1}$ given by $a_0=0$, $a_1=b$, and the recurrence relation $$a_{n+1}=a_n\\sqrt{1+a_{n-1}^2}+a_{n-1}\\sqrt{1+a_n^2}.$$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
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{
"content": "[THINK... |
[
{
"content": "Find the functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that for all \\( x, y \\), \\[ f(x+y)^{2}=f(x)^{2}+f(y)^{2} \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to solve t... |
[
{
"content": "Find the largest prime divisor of $25^2 + 72^2$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
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{
"content": "[THINK]\nHere's a thinking process that leads to the solution:\n\n1. **Analyze the Request:**\n * The goal is to find the larg... |
[
{
"content": "Given \\(a, b, c > 0\\), find the maximum value of the expression \\[ \\sum \\left( \\frac{a}{a + b + c} - \\frac{1}{3} \\right) \\left( \\frac{a}{a + b} - \\frac{1}{2} \\right) - \\frac{2}{3} \\left( \\sum \\frac{a}{b + c} - \\frac{3}{2} \\right). \\] Let's think step by step and output the final... |
[
{
"content": "Let \\( M \\) be a point with barycentric coordinates \\((x, y, z)\\) with respect to triangle \\( ABC \\), which has an incircle \\( C(I, r) \\) and a circumcircle \\( C(O, R) \\). If \\( M \\) lies on the incircle, calculate the value of the expression \\(\\sum bcx - \\sum yza^2\\) given that \\... |
[
{
"content": "Given a point outside a sphere with distances $h_1$, $h_2$, $h_3$, and $h_4$ to four non-coplanar points on the sphere, can the equation of the sphere be determined? If so, how? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
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{
"content": "[TH... |
[
{
"content": "For which odd $n$ is it possible to partition the edges of the complete graph $K_n$ into $\\dfrac{n-1}{2}$ disjoint cycles of length $n$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nThe problem asks for which odd int... |
[
{
"content": "The sum of two numbers is $12$ and their difference is $20$. What is the smaller number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
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{
"content": "[THINK]\nLet the two numbers be $x$ and $y$.\nWe are given two pieces of information:\n1. Th... |
[
{
"content": "There is a stack of $n$ cards labeled from top to bottom as $1, 2, \\cdots, n$. Each time, you can take a small stack of these cards (which can be just one card), and without disturbing their order, insert them into any position in the original stack (between any two cards, on top of the first car... |
[
{
"content": "Given the equation \\(x^2 + y^2 - 3y = 1\\), find the maximum value of \\(x + y\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to solve the problem:\n\n1. **Understand the Goal:** The obje... |
[
{
"content": "For a given positive integer \\( m \\) and a prime \\( p > m \\), let \\( N(p) \\) be the number of positive integers \\( n \\) such that \\( m^2 + n^2 + p^2 - 2mn - 2mp - 2pn \\) is a perfect square. Find the value of \\( N(p) \\) for any prime \\( p > m \\). Let's think step by step and output t... |
[
{
"content": "Let \\( x, y, z \\) satisfy the equations: \\[ x - y = yz - \\frac{x}{z} = yz - x + 2014 = P \\]. Find \\( P \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to solve the problem:\n\n1. **A... |
[
{
"content": "Find the coordinates of point $P_{1557}$ in the sequence of points $P_n$ where an ant moves along a spiral path starting from $(0, 0)$ and moving to $(1, 0)$, and then continuing counterclockwise. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
... |
[
{
"content": "We are given 6 boxes arranged in a line from left to right and 5 distinct balls. The balls are placed in some or all of the first 5 boxes (resulting in a total of $5^5$ ways to arrange them). We apply the following rule repeatedly until none of the first 5 boxes has more than one ball in it: if a ... |
[
{
"content": "Find all increasing bijections \\( f: \\mathbb{R}_{+} \\longrightarrow \\mathbb{R}_{+} \\) satisfying the functional equation \\( f(f(x)) - 3f(x) + 2x = 0 \\) and for which there exists \\( x_{0} > 0 \\) such that \\( f(x_{0}) = 2x_{0} \\). Let's think step by step and output the final answer with... |
[
{
"content": "On the plane, there is a circle \\(k\\) centered at point \\(S\\) with radius 3 and also a fixed point \\(A\\), such that \\(AS = 9\\). Find the locus of the centers of the circumscribed circles of \\(\\triangle ABC\\), where \\(BC\\) runs through all the diameters of the circle \\(k\\). Let's thi... |
[
{
"content": "How many positive roots does the polynomial $x^6 + 9x^5 + 2x^3 - x^2 - 2$ have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process that leads to the solution:\n\n1. **Understand the Goal:** The ob... |
[
{
"content": "Find all $n \\in \\mathbb{N}$ such that $2^{n+1} n$ is a perfect square. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process that leads to the solution:\n\n1. **Analyze the Problem:**\n The goal... |
[
{
"content": "A circle is centered at the origin with a radius larger than one. The arc length of the arc of the circle above the line \\( y = 1 \\) is \\( \\frac{4\\pi}{3} \\). Find the radius of the circle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
... |
[
{
"content": "Find all triples $(x, y, z)$ of positive integers such that $x! + y! = 15 \\cdot 2^{z!}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to solve the problem:\n\n1. **Understand the Goal:** Th... |
[
{
"content": "Let $\\mathbb N_{>1}$ denote the set of integers greater than $1$. An increasing function $f \\colon \\mathbb N_{>1} \\to \\mathbb N_{>1}$ satisfies the equation $$f(f(n))=2n$$ for any $n \\in \\mathbb N_{>1}$. Find all values of the parameter $\\lambda \\in \\mathbb Q$ for which the equation $$f(... |
[
{
"content": "Estimate the probability that the proportion of heads obtained lies between $.49$ and $.51$ when a fair coin is tossed $n = 500$ times. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to solve t... |
[
{
"content": "Consider an infinite chessboard where a positive integer is written in every cell. Let $S(m, n)$ denote the sum of the numbers in an $m \\times n$ rectangle on this chessboard. If for all positive integers $m$ and $n$, $S(m, n)$ is divisible by $m + n$, find the smallest possible value of $S(3, 4)... |
[
{
"content": "Let \\(ABC\\) be an \\(A\\)-isosceles triangle with \\(AB = AC\\). For a point \\(P\\) on \\(BC\\) such that \\(B \\in (PC)\\), let \\(r_1\\) be the inradius of \\(\\triangle APB\\) and \\(r_2\\) be the \\(P\\)-exinradius of \\(\\triangle APC\\). If \\(AB = AC = 10\\) and \\(BC = 12\\), calculate ... |
[
{
"content": "Let \\( m \\) and \\( M \\) be positive integers greater than 1, and let \\( a \\) be a positive real number. Suppose that \\( m \\mid \\left \\lfloor na \\right \\rfloor \\) for all \\( n \\geq M \\). Find the smallest possible value of \\( a \\) such that \\( a \\) is not an integer. Let's think... |
[
{
"content": "Determine the automorphisms Aut(Q*) of the multiplicative group of nonzero rational numbers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process that leads to the description of $\\text{Aut}(\\mathb... |
[
{
"content": "Your response should contain at least 2 placeholders represented by square brackets, such as [address]. Your answer must contain exactly 3 bullet points. Use the markdown bullet points such as: * This is point 1. Your response must have 2 sections. Mark the beginning of each section with Section X... |
[
{
"content": "In the serene town of Willowbrook, Mubbly Bubbly, the sentient mud volcano, had been a beloved, cherished member of the community, thanks to the unconditional care of Miss Henderson. Their unique bond had inspired compassion and understanding among the townsfolk. However, as life often has its twi... |
[
{
"content": "use JavaScript reander 10000 data, and create and insert table element Your response should contain at least 4 sentences. Include keywords [animals, plants, environment, conservation] in the response. The word [environment] should appear at least 3 times. What are some ways to promote conservation... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. During their New Year holidays, Alice and Bob play the following game using an array a of n integers: * Players take turns, Alice moves first. * Each turn a player chooses any element and removes it... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Consider a thin, isotropic, elastic membrane under uniaxial tensile strain. How does the strain affect the surface tension (\\(\\gamma\\)) and the resulting Laplace pressure (\\(\\Delta P\\)) for a curved ... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Which of the following represents a fundamental limitation in applying reinforcement learning (RL) to *de novo* small molecule design for a novel kinase target, considering polypharmacology and synthesizab... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. In studying a ligand-receptor system exhibiting non-Michaelis-Menten kinetics, you analyze dose-response curves for two ligands (X and Y) on the same receptor population. Ligand X produces a curve describe... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. A binary string is a string that consists of characters $0$ and $1$. Let $\\operatorname{MEX}$ of a binary string be the smallest digit among $0$, $1$, or $2$ that does not occur in the string. For ... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Consider a database system that uses a hybrid indexing technique combining B-trees and hash tables. Which of the following statements about this hybrid approach is true? A: It guarantees the fastest query ... |
[
{
"content": "Let \\( \\triangle ABC \\) have an inscribed circle \\( \\Gamma \\). This inscribed circle is tangent to sides \\( AC, BC, \\) and \\( AB \\) at points \\( Y, X, \\) and \\( Z \\), respectively. Let \\( \\gamma_A \\) be the A-excircle tangent to sides \\( AC, BC, \\) and \\( AB \\) at points \\( K... |
[
{
"content": "Find the largest possible value of $k$ for which $3^{11}$ is expressible as the sum of $k$ consecutive positive integers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere is a thinking process to solve the problem:\n... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. Note that this is the first problem of the two similar problems. You can hack this problem only if you solve both problems. You are given a tree with n nodes. In the beginning, 0 is written on all e... |
[
{
"content": "As RPGGPT, you will act as a text-based RPG (role-playing game) guiding the party characters through a setting of choice. Ensure you do not break character or go off track. You must describe each scene and choice in great detail, and include stats for each character mentioned. Do not create your o... |
[
{
"content": "polish the bellow: the effect of x makes the Lagrangian not invariant under this local gauge transformation. What is the process of photosynthesis, and how does it benefit plants and the environment? Your response should contain at least 4 sentences. Highlight at least 2 sections in your answer wi... |
[
{
"content": "Let \\( O \\) be a fixed point in \\( \\triangle ABC \\), and let \\( P \\) be a moving point such that \\( \\vec{OP} = \\vec{OA} + \\lambda \\left( \\frac{\\vec{AB}}{|\\vec{AB}| \\sin B} + \\frac{\\vec{AC}}{|\\vec{AC}| \\sin C} \\right) \\) for \\( \\lambda > 0 \\). Determine which \"center\" of ... |
[
{
"content": "Is it possible to represent the sum $\\sum_{k=0}^{\\infty} {n \\choose k} {m \\choose k} 2^{k}$ in a closed-form, where $n$ and $m$ are positive integers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
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{
"content": "[THINK]\nHere's a thinking... |
[
{
"content": "Your response should contain at least 3 sentences. Include keywords [summer, vacation, travel] in the response. In your response, the word [travel] should appear at least 2 times. What are some tips for planning a summer vacation that includes travel?",
"role": "user"
},
{
"content": "... |
[
{
"content": "How do i overload -= operator for an Hour class in c++. Use the term 'data-driven' at least once in your response.",
"role": "user"
},
{
"content": "[THINK]\nThinking Process:\n\n1. **Analyze the Request:**\n * Task: Explain how to overload the `-=` operator for an `Hour` class i... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. A car travels from a starting position to a destination which is target miles east of the starting position. Along the way, there are gas stations. Each station[i] represents a gas station that is s... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. In a chemical reaction, 2 moles of hydrogen gas (H\\(_2\\)) react with 1 mole of oxygen gas (O\\(_2\\)) to form 2 moles of water (H\\(_2\\)O). Given the standard enthalpies of formation: - H\\(_2\\)O: -285... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. Ntarsis has been given a set $$$S$$$, initially containing integers $$$1, 2, 3, \\ldots, 10^{1000}$$$ in sorted order. Every day, he will remove the $$$a_1$$$-th, $$$a_2$$$-th, $$$\\ldots$$$, $$$a_n... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Let \\( G \\) be a group acting transitively on a set \\( X \\) with \\( |X| = 10 \\). Suppose there exists a subgroup \\( H \\) of \\( G \\) such that \\( |H| = 5 \\) and the action of \\( H \\) on \\( X ... |
[
{
"content": "Let \\( a, b, c \\in \\mathbb{R} \\). Consider the function \\( f(x) = |8x^4 + ax^2 + bx + c| \\) for \\( -1 \\leq x \\leq 1 \\). Find the values of \\( x \\) when the maximum value \\( M \\) of \\( f(x) \\) satisfies \\( M \\geq 1 \\). Let's think step by step and output the final answer within \... |
[
{
"content": "In triangle \\(\\triangle ABC\\), points \\(P\\) and \\(Q\\) are respectively taken on sides \\(AB\\) and \\(AC\\) such that \\(\\angle APC = \\angle AQB = 45^\\circ\\). A perpendicular from point \\(P\\) to \\(AB\\) intersects line \\(BQ\\) at point \\(S\\), and a perpendicular from point \\(Q\\)... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. In a large software development project, which of the following strategies would best address the challenge of maintaining quality while adhering to tight deadlines and managing multiple stakeholders? A: I... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Which modification is most likely to improve the oral absorption of a weakly acidic drug with poor bioavailability? A: Increasing the pH of the gastrointestinal tract B: Decreasing the pH of the gastrointe... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well. You are given a string $S$ with length $N$ and you should change it to a palindrome using a se... |
[
{
"content": "In a game, to climb a 5-step ladder, you can jump any number of steps, stop to collect a toast, and go back up any number of steps. Additionally, you can go down once to any previous step (before reaching the top), collect a toast, and go back up. How many different ways can you climb this ladder?... |
[
{
"content": "Determine the maximum number of cycles that such a tournament can have. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process that leads to the solution:\n\n1. **Analyze the Request:**\n * The u... |
[
{
"content": "Given an isosceles triangle \\(ABC\\) such that \\(AB = AC = 2BC\\). Point \\(M\\) varies within the triangle. \\(MD\\), \\(ME\\), and \\(MF\\) are perpendicular to \\(BC\\), \\(CA\\), and \\(AB\\) respectively. Determine all points \\(M\\) such that \\(AD\\), \\(BE\\), and \\(CF\\) have a common ... |
[
{
"content": "In triangle \\(ABC\\), let \\(G\\) be the centroid and \\(P\\) be a point. Consider the rectangular circum-hyperbola through \\(P\\) and let \\(O\\) be its center. If the traces of \\(G\\) and \\(P\\) on the sides of the triangle \\(ABC\\) form a conic, find the value of \\(k\\) such that the dist... |
[
{
"content": "Given a cyclic quadrilateral \\(ABCD\\) with \\(\\angle A = 3 \\angle B\\). Points \\(C_1\\) and \\(A_1\\) are chosen on sides \\(AB\\) and \\(BC\\) respectively such that \\(AA_1 = AC = CC_1\\). Calculate the minimum possible value of \\(\\frac{A_1C_1}{BD}\\). Let's think step by step and output ... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. A multinational corporation aims to enhance its eco-efficiency through dematerialization strategies for a product currently requiring 800 grams of rare earth minerals (environmental impact: 15 units/g) and... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. You are given a grid with $n$ rows and $m$ columns. Rows and columns are numbered from $1$ to $n$, and from $1$ to $m$. The intersection of the $a$-th row and $b$-th column is denoted by $(a, b)$. I... |
[
{
"content": "Describe the process of making pizza from scratch. Your response should contain at least 4 sentences. Highlight at least 2 sections in your answer with markdown. At the end of your response, please explicitly add a postscript starting with P.S.",
"role": "user"
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{
"content": "[THINK]... |
[
{
"content": "Let \\( n \\) be a positive integer. Suppose that there are 666 ordered triples \\((x, y, z)\\) of positive integers satisfying the equation \\[ x + 8y + 8z = n. \\] Find the maximum value of \\( n \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Under the Fair Labor Standards Act (FLSA), which of the following scenarios would most likely be considered a violation of employee rights regarding overtime compensation? A: An employer classifies all emp... |
[
{
"content": "Find all continuous functions \\( f \\) that satisfy the equation \\[ f(x+y) = f(x) + f(y) + xy(x+y) \\] for all \\( x, y \\in \\mathbb{R}. \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to... |
[
{
"content": "Find the function \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f(x^2 + x + 3) + 2f(x^2 - 3x + 5) = 6x^2 - 10x + 17 \\). Determine \\( f(2009) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinkin... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. In a criminal case, the defendant is accused of assault. The evidence shows that the defendant verbally threatened the victim, causing them to fear immediate bodily harm, but no physical contact occurred. ... |
[
{
"content": "What are the benefits of using a firewall in a network? Your response should contain at least 5 sentences. Highlight at least 2 sections in your answer with markdown, i.e. *highlighted section*. In your response, the word \"security\" should appear at least 3 times. what are the best frames that c... |
[
{
"content": "Find the value of $\\sin^2 6^{\\circ} + \\sin^2 42^{\\circ} + \\sin^2 66^{\\circ} + \\sin^2 78^{\\circ}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking process to solve the problem:\n\n1. **Analyze t... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. A cylindrical capillary tube with radius $ r $ is partially filled with a liquid that perfectly wets the tube walls (contact angle $ \\theta = 0^\\circ $). The liquid exhibits capillary condensation under ... |
[
{
"content": "Given \\( A = \\sqrt{3|4 - x^2|^2 - 2x^4 + 16x^2 - 32} \\), find the number of real roots of the equation \\( A = ax + 4 \\) for every \\( a \\in \\mathbb{R} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a ... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Consider a complex mechanical system consisting of a series of interconnected gears, pulleys, and levers, designed to convert an input torque of 100 N·m into an output force. The system includes a series o... |
[
{
"content": "Please provide a summary of the key points in the recent climate change report. Your response should contain at least 4 sentences.",
"role": "user"
},
{
"content": "[THINK]\nThinking Process:\n\n1. **Analyze the Request:**\n * Topic: Summary of key points in the \"recent climate ... |
[
{
"content": "Your response should contain at least 3 sentences. Include keywords [travel, destination, vacation] in the response. The word [travel] should appear at least 2 times. Answer with [relation] [num_words] words. (relation: at least, num_words: 150)",
"role": "user"
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{
"content": "[THINK... |
[
{
"content": "Your response should contain at least 4 sentences. The response must contain exactly 2 bullet points. Use the markdown bullet points such as: * This is point 1. Highlight at least 2 sections in your answer with markdown, i.e. *highlighted section*. At the end of your response, please explicitly ad... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. Given a 2D array and a number of generations, compute n timesteps of [Conway's Game of Life](http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life). The rules of the game are: 1. Any live cell with f... |
[
{
"content": "A natural number, when raised to the fourth power, contains exactly 2025 digits. At most how many digits can the cube of the same natural number have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nHere's a thinking pro... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. Chef has two numbers N and M. He calls a pair of numbers (A, B) *good* if it satisfies the following conditions: 1 ≤ A, B ≤ M \\gcd(A, B) ≥ N Chef wants to find a good pair (A, B) such that the valu... |
[
{
"content": "Let $\\triangle ABC$ be a triangle and $D$ be a point on the extension of $BC$ over $C$, such that $|CD|=|AC|$. The circumcircle of $\\triangle ACD$ intersects the circle with diameter $[BC]$ at another point $P$. $BP$ intersects $AC$ at $E$ and $CP$ intersects $AB$ at $F$. If $D$, $E$, and $F$ ar... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Which of the following technologies is primarily used for short-range, low-power wireless communication, commonly used in home automation devices? A: Bluetooth B: Zigbee C: NFC (Near Field Communication) D... |
[
{
"content": "Suppose that \\(a, b, c\\) are real numbers such that \\[ \\frac{1}{a}+\\frac{1}{b}+\\frac{1}{c}=4\\left(\\frac{1}{a+b}+\\frac{1}{b+c}+\\frac{1}{c+a}\\right)=\\frac{c}{a+b}+\\frac{a}{b+c}+\\frac{b}{c+a}=4. \\] Determine the value of \\(a \\cdot b \\cdot c\\). Let's think step by step and output th... |
[
{
"content": "Your response should contain at least 3 sentences. The response must have 2 sections. Mark the beginning of each section with SECTION X, such as: SECTION 1. In your response, the word \"example\" should appear at least 2 times. In your response, the letter \"e\" should appear at least 10 times. SE... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. The farmer Polycarp has a warehouse with hay, which can be represented as an n × m rectangular table, where n is the number of rows, and m is the number of columns in the table. Each cell of the tab... |
[
{
"content": "Find all positive integers $k$ for which there exist positive integers $a, b,$ and $c$ such that $$|(a-b)^3+(b-c)^3+(c-a)^3|=3 \\cdot 2^k.$$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "[THINK]\nLet the given equation be\n$$|(... |
[
{
"content": "Callie bought six ounces of coffee cream and 10 ounces of coffee. She first mixes both the cream and the coffee in one large pitcher, then pours 3/5 of the coffee mixture into her cup. What fraction of the coffee mixture in Callie's coffee cup is cream? Express your answer as a common fraction. Le... |
[
{
"content": "Explain the process of photosynthesis in plants. Your response should contain at least 5 sentences. Highlight at least 2 sections in your answer with markdown, i.e. *highlighted section*. Include keywords *chlorophyll*, *light energy*, and *oxygen* in the response. in point form for a slideshow , ... |
[
{
"content": "Suppose \\(a, b,\\) and \\(c\\) are positive integers with \\(a + b + c = 2006\\), and \\(a!b!c! = m \\cdot 10^n\\), where \\(m\\) and \\(n\\) are integers and \\(m\\) is not divisible by 10. What is the smallest possible value of \\(n\\)? Let's think step by step and output the final answer withi... |
[
{
"content": "Your answer must contain exactly 3 bullet points. Use the markdown bullet points such as: * This is point 1. Additionally, your response must contain at least 2 placeholders represented by square brackets, such as [address]. What are the steps to [action] effectively?",
"role": "user"
},
{... |
[
{
"content": "What are the benefits of using a content management system (CMS) for a website? Your answer must contain a title, wrapped in double angular brackets, such as <<poem of joy>>. Highlight at least 3 sections in your answer with markdown, i.e. *highlighted section*. Your response should contain at lea... |
[
{
"content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}. Consider a quantum harmonic oscillator undergoing Quantum Brownian Motion in contact with a thermal bath at temperature $ T $. Assuming the bath has a spectral density of Ohmic type with a high-frequency c... |
[
{
"content": "Three rugs have a combined area of \\(200 \\, \\mathrm{m}^2\\). By overlapping the rugs to cover a floor area of \\(140 \\, \\mathrm{m}^2\\), the area which is covered by exactly two layers of rug is \\(24 \\, \\mathrm{m}^2\\). What area of floor is covered by three layers of rug? (A) \\(12 \\, \\... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. In a game of American Football, there are several factors to take into consideration when detailing the rules of the game. The goal of the game is to move the football across the field into the endz... |
[
{
"content": "Here is a problem for which you need to generate an executable code in python programming language. There are $n$ astronauts working on some space station. An astronaut with the number $i$ ($1 \\le i \\le n$) has power $a_i$. An evil humanoid has made his way to this space station. The power of th... |
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