system stringclasses 1
value | conversations listlengths 2 2 | problem stringlengths 67 28.8k ⌀ | reasoning stringlengths 1.08k 118k ⌀ | deepseek_solution stringlengths 4 15.6k ⌀ | id stringclasses 230
values | ground_truth_solution stringclasses 177
values | source stringclasses 1
value | code null | correct bool 1
class | judge_reasoning stringclasses 230
values | __original_row_idx int64 6 2.26k ⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|
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{}. Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the ... | null | null | null | null | null | null | null | 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 ABC, prove:\n$$\nx^{2} + y^{2} + z^{2} \\geq 2yz \\sin A + 2zx \\sin B - 2xy \\cos C.\n$$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to prove this inequality in triangle ABC: x²... | null | null | null | null | null | null | null | 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{}. Prove that the sum of the 2009th powers of the first 2009 positive integers is divisible by 2009."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to prove that the sum of the 2009th powers of th... | null | null | null | null | null | null | null | 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 the quadrilateral pyramid \\(PABCD\\), the lateral face \\(P A D\\) is an equilateral triangle and is perpendicular to the base \\(ABCD\\). The base \\(ABCD\\) is a rhombus with side length 2, and \\(\\angle B A D = 60^\\circ\\). Le... | null | null | null | null | null | null | null | 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{}. For \\( x \\in \\mathbf{R}, n \\in \\mathbf{N}^{*} \\), define \\( C_{x}^{n}=\\frac{x(x-1) \\cdots(x-n+1)}{n!} \\). Let \\( P(x) \\) be a 6th-degree polynomial that satisfies \\( P(0)=1 \\) and \\( P(k)=2^{k-1} \\) for \\( k=1,2, \\cdo... | null | null | null | null | null | null | null | 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{}. For a positive integer \\( n \\), let \\( \\mathrm{I}_{\\mathrm{n}}=\\{1,2, \\ldots, \\mathrm{n}\\} \\) and \\( \\mathrm{P}_{\\mathrm{n}}=\\left\\{\\left.\\frac{\\mathrm{m}}{\\sqrt{k}} \\right| \\mathrm{m} \\in \\mathrm{I}_{\\mathrm{n}... | null | null | null | null | null | null | null | 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 ordered pairs of integers $(m,n)$ are there such that $m$ and $n$ are the legs of a right triangle with an area equal to a prime number not exceeding $80$ ?"
},
{
"from": "assistant",
"value": "<|begin_of_th... | null | null | null | null | null | null | null | 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 \\(C, B, E\\) be three points on a straight line \\(l\\) in that order. Suppose that \\(A\\) and \\(D\\) are two points on the same side of \\(l\\) such that\n(i) \\(\\angle ACE = \\angle CDE = 90^{\\circ}\\) and\n(ii) \\(CA = CB =... | null | null | null | null | null | null | null | 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 line with slope equal to 1 and a line with slope equal to 2 intersect at the point \\( P(1,6) \\). The area of \\(\\triangle P Q R\\) is:\n(A) 6\n(B) 9\n(C) 12\n(D) 15\n(E) 18"
},
{
"from": "assistant",
"value": "<|begin_... | null | null | null | null | null | null | null | 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.Little girl Margarita is a big fan of competitive programming. She especially loves problems about a... | null | null | null | null | null | null | null | 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{}. Internal angles of triangle are $(5x+3y)^{\\circ}$ , $(3x+20)^{\\circ}$ and $(10y+30)^{\\circ}$ where $x$ and $y$ are positive integers. Which values can $x+y$ get ?"
},
{
"from": "assistant",
"value": "<|begin_o... | null | null | null | null | null | null | null | 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{}. On the coordinate plane, consider the family of all concentric circles with the center at the point \\( M(\\sqrt{2} ; \\sqrt{3}) \\). Prove that there exists a circle in this family that contains exactly 2019 points with integer coordi... | null | null | null | null | null | null | null | 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 temperature \\( T \\) of an object throughout the day is a function of time \\( t \\): \\( T(t) = a t^3 + b t^2 + c t + d \\) (\\(a \\neq 0\\)). The temperature is measured in \\(^\\circ \\text{C}\\), and time is measure... | null | null | null | null | null | null | null | 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 set of points on the coordinate plane where coordinates \\(x\\) and \\(y\\) satisfy the conditions:\n1) \\(y^{2}-y x^{2}=0\\)\n2) \\(x^{5}+x^{4}=0\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOk... | null | null | null | null | null | null | null | 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 real numbers \\( a \\), \\( b \\), \\( c \\), and \\( d \\) satisfying \\( ad + bc = 1 \\), determine the minimum value of \n\\[ \nu = a^2 + b^2 + c^2 + d^2 + (a+c)^2 + (b-d)^2.\n\\]"
},
{
"from": "assistant",
"value"... | null | null | null | null | null | null | null | 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 the coordinates of the vertices of a pyramid \\( A_{1}(4, 2, 5) \\), \\( A_{2}(0, 7, 2) \\), \\( A_{3}(0, 2, 7) \\), \\( A_{4}(1, 5, 0) \\). Find:\n1. The equations of the planes \\( A_{1} A_{2} A_{3} \\) and \\( A_{1} A_{2} A_{4... | null | null | null | null | null | null | null | 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 $ABC$ be an equilateral triangle inscribed in circle $O$. $M$ is a point on arc $BC$. \nLines $\\overline{AM}$, $\\overline{BM}$, and $\\overline{CM}$ are drawn. Then $AM$ is: \n\n$\\textbf{(A)}\\ \\text{equal to }{BM + CM}\\qquad ... | null | null | null | null | null | null | null | 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 side lengths of squares \\( A, B, C, \\) and \\( D \\) are \\( 15, b, 10, d \\) respectively (\\( b \\) and \\( d \\) are natural numbers). If their areas satisfy \\( S_A = S_B + S_C + S_D \\), then \\( b + d = \\) ______."
},
... | null | null | null | null | null | null | null | 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 bank teller has some stacks of bills. The total value of the bills in each stack is $1000. Every stack contains at least one $20 bill, at least one $50 bill, and no other types of bills. If no two stacks have the same number of $20 b... | null | null | null | null | null | null | null | 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 function $f(x)$ satisfies\n\\[f(x + f(x)) = 4f(x)\\]for all $x,$ and $f(1) = 4.$ Find $f(21).$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's try to tackle this problem. The function f(x) sati... | null | null | null | null | null | null | null | 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{}. Each third-grade classroom at Pearl Creek Elementary has $18$ students and $2$ pet rabbits. How many more students than rabbits are there in all $4$ of the third-grade classrooms?\n$\\textbf{(A)}\\ 48\\qquad\\textbf{(B)}\\ 56\\qquad\\t... | null | null | null | null | null | null | null | 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 following two schemes illustrate multiplications where the letters replace illegible digits. In the first scheme, the calculator shortened the work with a simple trick and then verified the result in the second scheme by swapping t... | null | null | null | null | null | null | null | 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{}. It is known that the difference between the variables \\( y \\) and \\( z \\) is proportional to the variable \\( x \\), and the difference between the variables \\( z \\) and \\( x \\) is proportional to the variable \\( y \\). The co... | null | null | null | null | null | null | null | 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{}. Show that \\(\\frac{2}{b(a+b)} + \\frac{2}{c(b+c)} + \\frac{2}{a(c+a)} \\geq \\frac{27}{(a+b+c)^2}\\) for positive reals \\(a, b, c\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to prove t... | null | null | null | null | null | null | null | 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{}. Which set of rectangles with integer sides has more members: those with a perimeter of 1996 or those with a perimeter of 1998?\n\n(Note: Rectangles \\(a \\times b\\) and \\(b \\times a\\) are considered identical.)"
},
{
"from"... | null | null | null | null | null | null | null | 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{}. Point \\( M \\) is the midpoint of side \\( AC \\) of triangle \\( ABC \\). Points \\( P \\) and \\( Q \\) are chosen on segments \\( AM \\) and \\( CM \\), respectively, such that \\( PQ = \\frac{AC}{2} \\). The circumcircle of triang... | null | null | null | null | null | null | null | 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 \\( n \\) be a natural number, \\( a \\) and \\( b \\) be positive real numbers, and satisfy \\( a + b = 2 \\). What is the minimum value of \\(\\frac{1}{1+a^n} + \\frac{1}{1+b^n} \\)?"
},
{
"from": "assistant",
"value"... | null | null | null | null | null | null | null | 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 Patisserie AtCoder sells cakes with number-shaped candles. There are X, Y and Z kinds of cakes w... | null | null | null | null | null | null | null | 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{}. \nKnown that the real number sequence \\( a_{0}, a_{1}, a_{2}, \\cdots \\) satisfies\n\\[ \na_{i-1} + a_{i+1} = 2 a_{i} \\quad (i = 1, 2, 3, \\cdots) . \n\\]\n\nProve: for any natural number \\( n \\),\n\\[ \nP(x) = a_{0} \\binom{n}{0}... | null | null | null | null | null | null | null | 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.There are n computers in a row, all originally off, and Phoenix wants to turn all of them on. He wil... | null | null | null | null | null | null | null | 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.Idol --- It's the eternal longing of girls. However, only a handful stand at the top. You have decid... | null | null | null | null | null | null | null | 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{}. Yesterday, Nikita bought several pens: black pens for 9 rubles each and blue pens for 4 rubles each. Today, he found out that the prices have changed: black pens now cost 4 rubles each and blue pens cost 9 rubles each. Nikita remarked:... | null | null | null | null | null | null | null | 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{}. 1. Is it possible to label the edges of a cube with the values \\(1, 2, \\cdots, 12\\) so that the sum of the labels of the edges emanating from each vertex is the same?\n2. If one of the labels is replaced by 13, is it still possible ... | null | null | null | null | null | null | null | 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 five-digit positive integers have the product of their digits equal to 1000? \n\nA) 10\nB) 20\nC) 28\nD) 32\nE) 40"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's try to figure out how many... | null | null | null | null | null | null | null | 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": "You're writing a program for a new automated roulette croupier to be installed in a major casino. Unfortunately, the last guy bailed out on the company and published buggy software. You're stuck with a thousand burned flash chips with only a few kilobytes of space to store a work... | You're writing a program for a new automated roulette croupier to be installed in a major casino. Unfortunately, the last guy bailed out on the company and published buggy software. You're stuck with a thousand burned flash chips with only a few kilobytes of space to store a working program. Can you do it?
The task is ... | Okay, I need to write a Python program for this automated roulette croupier. The main challenge is to handle various types of bets and compute the payouts correctly, keeping the code as small as possible. Let's start by breaking down the problem.
First, the input comes in two phases: the bets and then the result. The ... | To solve this problem, we need to develop a program that accurately handles bets, wins, and losses for a roulette game. The program must process bets placed by players, determine the payouts based on where the ball lands, and calculate the casino's net gain or loss. The solution must be efficient and concise due to spa... | null | null | null | null | 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.There is an infinite set generated as follows:\n\n * 1 is in this set. \n * If x is in this set, x... | null | null | null | null | null | null | null | 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 $\\triangle ABC$, $C=\\frac{\\pi}{2}$, $P$ is a point on the altitude $CD$, $PE \\parallel BC$ and intersects $AB$ at $E$ and $AC$ at $H$; $PF \\parallel AB$ and intersects $CB$ at $F$ and $CA$ at $I$; $PG \\parallel CA$ and interse... | null | null | null | null | null | null | null | 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{}. Six people, a mix of knights (who always tell the truth) and liars (who always lie), sat around a round table. Each of them was given a coin. Then, each person passed their coin to one of their two neighbors. After that, 3 people said,... | null | null | null | null | null | null | null | 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{}. \nGiven that \\( a \\neq b \\), a polynomial \\( f(x) \\) leaves remainders \\( c \\) and \\( d \\) when divided by \\( x-a \\) and \\( x-b \\) respectively. Find the remainder of \\( f(x) \\) when divided by \\((x-a)(x-b)\\)."
},
... | null | null | null | null | null | null | null | 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 point \\( M^{\\prime} \\) that is symmetric to the point \\( M \\) with respect to the line.\n\n$$\n\\begin{aligned}\n& M(0, -3, -2) \\\\\n& \\frac{x-1}{1} = \\frac{y+1.5}{-1} = \\frac{z}{1}\n\\end{aligned}\n$$"
},
{
"... | null | null | null | null | null | null | null | 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{}. From the set $\\{1,2,3, \\cdots, 10\\}$, 6 different integers are randomly selected. What is the probability that the second smallest number among the selected integers is 3?\nA. $\\frac{1}{60}$\nB. $\\frac{1}{6}$\nC. $\\frac{1}{3}$\nD... | null | null | null | null | null | null | null | 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.Read problem statements in [Mandarin Chinese], [Russian], and [Vietnamese] as well.\n\nCodechef chal... | null | null | null | null | null | null | null | 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 value of \\((2014-2013) \\times (2013-2012)\\) is\n(A) 0\n(B) 1\n(C) 2\n(D) 2014\n(E) -1"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. The problem is asking for the value of (2014 - 2013)... | null | null | null | null | null | null | null | 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{}. Prove that the inequality $\\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c} \\geq \\frac{9}{a+b+c}$ holds for any positive $a, b, c$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to prove that for ... | null | null | null | null | null | null | null | 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 \\((R x^{2} - x + 1)^{1999} \\equiv a_{0} + a_{1} x + a_{2} x^{2} + \\ldots + a_{3998} x^{3998}\\). If \\( S = a_{0} + a_{1} + a_{2} + \\ldots + a_{3997} \\), find the value of \\( S \\)."
},
{
"from": "assistant",
... | null | null | null | null | null | null | null | 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{}. Three distinct numbers are drawn at random from the set \\(\\{1, 2, \\cdots, 10\\}\\). Find the probability that the sample variance \\(s^2 \\leq 1\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I... | null | null | null | null | null | null | null | 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. Return the function body without invoking it at the final solution.You have to create a function,named `insertMissingLetters`, that takes in a `string` and outputs the same string processed in a particular wa... | null | null | null | null | null | null | null | 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.You are given an integer N. Find the number of strings of length N that satisfy the following condit... | null | null | null | null | null | null | null | 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": "Because we can't get enough of esoteric language golfs, can we?\n///—pronounced slashes—is a fun little language based on the s/// regex-replacement function of Perl fame. It contains only two special characters, slash / and backslash \\. You can find a full article on it at the ... | Because we can't get enough of esoteric language golfs, can we?
///—pronounced slashes—is a fun little language based on the s/// regex-replacement function of Perl fame. It contains only two special characters, slash / and backslash \. You can find a full article on it at the esolangs wiki, but I will reproduce a desc... | Okay, I need to write an interpreter for the /// language. Let's think about how this works.
First, the language has states: print, pattern, replacement, substitution. The states cycle in that order. The substitution mode is a bit different. So the interpreter needs to track the current state, the current pattern and... | To solve this problem, we need to create an interpreter for the esoteric language /// (slashes), which processes a string based on a series of substitutions defined by patterns and replacements. The language uses four states: print, pattern, replacement, and substitution, cycling through them in order. The challenge is... | null | null | null | null | 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": "\"How can the purity level of a chemical be increased from 80% to 99% through the development of a purification process in chemical engineering?\""
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how to increase the purity of ... | null | null | null | null | null | null | null | 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 point moves along a straight line with constant acceleration. Find the law of motion of the point."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the law of motion for a point moving ... | null | null | null | null | null | null | null | 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 many identical rectangular cardboard pieces of size \\(a \\times b\\) cm, where \\(a\\) and \\(b\\) are integers, and \\(a<b\\). It is known that from such cardboard pieces, you can form both a \\(49 \\times 51\\) cm rectangl... | null | null | null | null | null | null | null | 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 smallest positive integer $n$ such that \\[2^{1989}\\; \\vert \\; m^{n}-1\\] for all odd positive integers $m>1$ ."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's try to figure out the s... | null | null | null | null | null | null | null | 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.Little Timofey likes integers a lot. Unfortunately, he is very young and can't work with very big in... | null | null | null | null | null | null | null | 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 trapezoid, the smaller base is 1 decimeter, and the angles adjacent to it are $135^{\\circ}$. The angle between the diagonals, opposite to the base, is $150^{\\circ}$. Find the area of the trapezoid."
},
{
"from": "assista... | null | null | null | null | null | null | null | 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{}. Prove that if\n$$\n\\sin \\alpha+\\sin \\beta+\\sin \\gamma=\\cos \\alpha+\\cos \\beta+\\cos \\gamma=0 \\text{, }\n$$\nthen\n$$\n\\begin{array}{l}\n\\cos 3 \\alpha+\\cos 3 \\beta+\\cos 3 \\gamma=3 \\cos (\\alpha+\\beta+\\gamma) \\\\\n\... | null | null | null | null | null | null | null | 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{}. For each positive integer $n$ larger than $1$ with prime factorization $p_1^{\\alpha_1}p_2^{\\alpha_2}\\cdots p_k^{\\alpha_k}$ , its *signature* is defined as the sum $\\alpha_1+\\alpha_2+\\cdots+\\alpha_k$ . Does there exist $2... | null | null | null | null | null | null | null | 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 all functions \\( f: \\mathbb{N} \\rightarrow \\mathbb{N} \\) satisfying\n\n\\[ \n\\forall x, y \\in \\mathbb{N}, \\quad f(x+y)=f(x)+f(y) \n\\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I ne... | null | null | null | null | null | null | null | 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 100 people in a room with ages 1, 2, ..., 100. A pair of people is called cute if each of them is at least seven years older than half the age of the other person in the pair. At most how many pairwise disjoint cute pairs can... | null | null | null | null | null | null | null | 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{}. Fill in the empty boxes with numbers so that each box in the middle of the marked lines contains the sum of the numbers from its end boxes and that the sums of the numbers from the boxes on both diagonals are the same."
},
{
"f... | null | null | null | null | null | null | null | 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.After the piece of a devilish mirror hit the Kay's eye, he is no longer interested in the beauty of ... | null | null | null | null | null | null | null | 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 grid of n*m consisting of O's and X's. The task is to find the number of 'X' total shapes.\... | null | null | null | null | null | null | null | 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 \\( SABC D \\) be a regular quadrilateral pyramid with base \\(ABCD\\). On the segment \\(AC\\), there is a point \\(M\\) such that \\(SM = MB\\) and the planes \\(SBM\\) and \\(SAB\\) are perpendicular. Find the ratio \\(AM : AC\\... | null | null | null | null | null | null | null | 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 remainder when \\(2^{2018} + 2019\\) is divided by 5."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out how to solve this problem: Find the remainder when \\(2^{2018} + 201... | null | null | null | null | null | null | null | 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 random number generator will always output 7. Sam uses this random number generator once. What is the expected value of the output?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle this prob... | null | null | null | null | null | null | null | 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{}. Solve the equations:\n\na) \\(x^{4} + x^{3} - 3a^{2} x^{2} - 2a^{2} x + 2a^{4} = 0\\)\n\nb) \\(x^{3} - 3x = a^{3} + a^{-3}\\)"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to solve these two e... | null | null | null | null | null | null | null | 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": "What is the most accurate method to measure the mass of a top quark, and what are the potential sources of systematic errors in this measurement?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out the most accurate method to mea... | null | null | null | null | null | null | null | 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{}. \nThe cells of a $15 \\times 15$ square table are colored in red, blue, and green. \n\nProve that there exist at least two rows in which the number of cells of at least one color is the same."
},
{
"from": "assistant",
"val... | null | null | null | null | null | null | null | 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.Chef found N magical cards in his drawer. Each card has a number written on each of its faces. He pl... | null | null | null | null | null | null | null | 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": "This challenge is simply to return a list of lists of integers, similar to the Python range function, except that each successive number must be that deep in lists.\nRules:\n\nCreate a program or a non-anonymous function\nIt should return or print the result\nThe result should be... | This challenge is simply to return a list of lists of integers, similar to the Python range function, except that each successive number must be that deep in lists.
Rules:
Create a program or a non-anonymous function
It should return or print the result
The result should be returned in a list (of lists) or array (of a... | Okay, I need to solve this problem where I have to generate a nested list structure based on a given integer n. The example given is for n=6, the output is [0, [1, [2, [3, [4, [5]]]]]]. So, each successive number is nested one level deeper. Let me think about how to approach this.
First, the problem says that for n=0,... | To solve this problem, we need to generate a nested list structure based on a given integer `n`, where each successive number is nested one level deeper. The structure should be returned as a list of lists, with each integer `i` (from 0 to `n-1`) at a depth corresponding to its value.
### Approach
The approach to solv... | null | null | null | null | 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.You are given two integers $l$ and $r$ ($l \\le r$). Your task is to calculate the sum of numbers fr... | null | null | null | null | null | null | null | 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 sequence consists of 20 different natural numbers. The product of each pair of consecutive numbers is a perfect square of a natural number. The first number is 42. Prove that at least one of the numbers is greater than 16000."
},
... | null | null | null | null | null | null | null | 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.A string t is called nice if a string \"2017\" occurs in t as a subsequence but a string \"2016\" do... | null | null | null | null | null | null | null | 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 \\(ABCD\\) be a rectangle with \\(AB = 10\\). Draw circles \\(C_1\\) and \\(C_2\\) with diameters \\(AB\\) and \\(CD\\) respectively. Let \\(P\\) and \\(Q\\) be the intersection points of \\(C_1\\) and \\(C_2\\). If the circle with... | null | null | null | null | null | null | null | 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 \\(O_1\\) be the center of the inscribed circle in triangle \\(ABC\\) with radius \\(R\\), and \\(O_2\\) be the center of the inscribed circle in triangle \\(ADE\\) with radius \\(r\\). Let \\(p_1\\) be the semiperimeter of triangl... | null | null | null | null | null | null | null | 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 a quadrilateral with two parallel sides and two other equal sides a parallelogram?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out if a quadrilateral that has two parallel side... | null | null | null | null | null | null | null | 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 line separates two circles if and only if the circles do not have any common points with the line and the circles are on opposite sides of the line. Suppose three circles, each pair of which are disjoint, have the following property:... | null | null | null | null | null | null | null | 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 \\(ABC\\) and \\(A'B'C'\\) be two triangles such that \\(\\angle BAC = \\angle B'A'C', \\angle ACB = \\angle A'C'B'\\), and \\(\\angle CBA = \\angle C'B'A'\\). Show that \\[\\frac{AB}{AC} = \\frac{A'B'}{A'C'}.\\]"
},
{
"fro... | null | null | null | null | null | null | null | 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{}. 1. Suppose \\( A=\\left\\{x \\mid x^{2}<\\log _{a} x\\right\\} \\) and \\( B=\\left\\{y \\mid y=2^{x}, x \\in(-\\infty,-1)\\right\\} \\).\n\nIf \\( A \\varsubsetneqq B \\), then the range of \\( a \\) is"
},
{
"from": "assistan... | null | null | null | null | null | null | null | 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 lateral edge lengths of a regular pyramid (with a regular polygon as its base, and all lateral edges being equal) together equal the perimeter of the base. Calculate the angle between the adjacent lateral faces of the pyramid."
}... | null | null | null | null | null | null | null | 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.Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as we... | null | null | null | null | null | null | null | 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 the inequality\n$$\n\\sqrt{2}(2 a+3) \\cos \\left(\\theta-\\frac{\\pi}{4}\\right)+\\frac{6}{\\sin \\theta+\\cos \\theta}-2 \\sin 2 \\theta<3 a+6\n$$\n\nfor \\(\\theta \\in\\left[0, \\frac{\\pi}{2}\\right]\\) to always hold, deter... | null | null | null | null | null | null | null | 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 sequence \\( s_{0}, s_{1}, s_{2}, s_{3}, \\ldots \\) is defined by \\( s_{0}=s_{1}=1 \\) and, for every positive integer \\( n \\), \\( s_{2n}=s_{n} \\), \\( s_{4n+1}=s_{2n+1} \\), and \\( s_{4n-1}=s_{2n-1} + \\frac{s_{2n-1}^2}{s_{n-... | null | null | null | null | null | null | null | 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{}. Show that \\( \\frac{5^{125} - 1}{5^{25} - 1} \\) is composite."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to show that the number \\(\\frac{5^{125} - 1}{5^{25} - 1}\\) is composite. Hmm, l... | null | null | null | null | null | null | null | 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$ and $b$ be positive integers. When $a^{2}+b^{2}$ is divided by $a+b,$ the quotient is $q$ and the remainder is $r.$ Find all pairs $(a,b)$ such that $q^{2}+r=1977$ ."
},
{
"from": "assistant",
"value"... | null | null | null | null | null | null | null | 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{}. During a math test, Oleg was supposed to divide a given number by 2, and then add 6 to the result. However, he hurried and instead multiplied the given number by 2, and then subtracted 6 from the result. Nevertheless, he got the correc... | null | null | null | null | null | null | null | 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 all positive integers $n$ for which both $837 + n$ and $837 - n$ are cubes of positive integers."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. I need to find all positive integers ... | null | null | null | null | null | null | null | 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 side lengths of a triangle are consecutive integers. Find these lengths, given that one of the medians is perpendicular to one of the angle bisectors."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, s... | null | null | null | null | null | null | null | 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{}. Through a point inside a triangle, three lines are drawn from the vertices to the opposite sides forming six triangular sections. Then: \n$\\textbf{(A)}\\ \\text{the triangles are similar in opposite pairs}\\qquad\\textbf{(B)}\\ \\text... | null | null | null | null | null | null | null | 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.Consider an array A consisting of N positive elements. The *frequency array* of A is the array B of ... | null | null | null | null | null | null | null | 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 all polynomials $W$ with integer coefficients satisfying the following condition: For every natural number $n, 2^n - 1$ is divisible by $W(n).$ "
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, s... | null | null | null | null | null | null | null | 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 polynom of degree $n \\geq 5$ with integer coefficients given by $P(x)=a_{n}x^n+a_{n-1}x^{n-1}+\\cdots+a_0 \\quad$ with $a_i \\in \\mathbb{Z}$ , $a_n \\neq 0$ .\r\n\r\nSuppose that $P$ has $n$ different integer... | null | null | null | null | null | null | null | 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 all the continuous bounded functions $f: \\mathbb R \\to \\mathbb R$ such that \n\\[(f(x))^2 -(f(y))^2 = f(x + y)f(x - y) \\text{ for all } x, y \\in \\mathbb R.\\]"
},
{
"from": "assistant",
"value": "<|begin_of_t... | null | null | null | null | null | null | null | 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 collects coins: he has exactly one coin for every year from 1 to n. Naturally, Vasya keeps all... | null | null | null | null | null | null | null | 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 \\( x \\) and \\( y \\) be real numbers between 0 and 1. Prove that\n\n\\[ x^{3} + x y^{2} + 2 x y \\leq 2 x^{2} y + x^{2} + x + y \\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to prov... | null | null | null | null | null | null | null | 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 all $(n,x,y,z,p)$ of positive integers with $p$ prime and $$ (x^2 + 4y^2)(y^2 + 4z^2)(z^2 + 4x^2) = p^n $$ "
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I have this problem here: Find al... | null | null | null | null | null | null | null | 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 non-parallel sides of a trapezoid are extended until they intersect, and a line parallel to the bases of the trapezoid is drawn through this point of intersection. Find the length of the segment of this line that is limited by the ... | null | null | null | null | null | null | null | 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{}. Can the range of a real-coefficient bivariate polynomial be the open interval \\((0, +\\infty)\\)?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so the question is: Can the range of a real-coefficient b... | null | null | null | null | null | null | null | 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{}. Suppose that \\( f(x) = a(x - b)(x - c) \\) is a quadratic function where \\( a, b \\) and \\( c \\) are distinct positive integers less than 10. For each choice of \\( a, b \\) and \\( c \\), the function \\( f(x) \\) has a minimum va... | null | null | null | null | null | null | null | 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{}. Systems of linear equations"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how to solve systems of linear equations. Let me start by recalling what I know. A system of linear equa... | null | null | null | null | null | null | null | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.