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{}. Grogg’s favorite positive integer is $n\\ge2$ , and Grogg has a lucky coin that comes up heads with some fixed probability $p$ , where $0<p<1$ . Once each day, Grogg flips his coin, and if it comes up heads, he does two things:\n[li... | 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": "How can we improve the accuracy and speed of DNA sequencing technologies to better understand genetic mutations and variations that cause diseases in humans?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how to improve 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 a tetrahedron \\(ABCD\\), the lengths of edges \\(AB, AC, AD\\) are \\(a_1, a_2, a_3\\) respectively, and the lengths of their opposite edges are \\(b_1, b_2, b_3\\). The angles formed by these pairs of edges are \\(\\theta_1, \\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": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a text consisting of *n* lines. Each line contains some space-separated words, consist... | 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, b, c\\) be non-negative real numbers. Prove that:\n$$\n\\begin{aligned}\n\\frac{1}{3}\\left[(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\\right] & \\leq a^{2}+b^{2}+c^{2}-3 \\sqrt[3]{3 a^{2} b^{2} c^{2}} \\\\\n& \\leq (a-b)^{2}+(b-c)^{2}+(c... | 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 30 consecutive days, the daily high temperature was recorded. On each of the first 25 days, the temperature recorded was $21^{\\circ} \\mathrm{C}$. On each of the remaining 5 days, the temperature recorded was $15^{\\circ} \\mathrm... | 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 \\( N = 1 + 11 + 101 + 1001 + 10001 + \\ldots + 1\\overbrace{000 \\ldots 0000}^{50 \\text{ zeroes }} \\).\n\nWhen \\( N \\) is calculated and written as a single integer, the sum of its digits is:\n(A) 58\n(B) 99\n(C) 55\n(D) 5... | 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 triangle with a base of 80 and one base angle of $60^{\\circ}$, the sum of the lengths of the other two sides is 90. What is the length of the shortest side?\n(A) 45\n(B) 40\n(C) 36\n(D) 17\n(E) 12"
},
{
"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{}. Given distinct positive integers \\( a, b, c \\) that satisfy \\( abc = 72^3 \\), how many such ordered triplets \\( (a, b, c) \\) are there?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to 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": "Return your final response within \\boxed{}. If \\( f(x) \\) is a real-valued function of the real variable \\( x \\), and \\( f(x) \\) is not identically zero, and for all \\( a, b \\), \\( f(a+b) + f(a-b) = 2 f(a) + 2 f(b) \\), which of the following holds for all \\( x, y \\)?... | 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 \\( S_{n} = \\alpha^{n} + \\beta^{n} \\), where \\(\\alpha\\) and \\(\\beta\\) are the roots of the equation \\( a x^{2} + b x + c = 0 \\). Find the relationship between \\(S_{n}\\), \\(S_{n+1}\\), and \\(S_{n+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": "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 developing a robot that processes strings. When the robot is given a string t consisting 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{}. The teacher wrote a two-digit number on the board. Each of the three boys made two statements.\n\n- Andrey: \"This number ends in the digit 6\" and \"This number is divisible by 7.\"\n- Borya: \"This number is greater than 26\" and \"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.I and my flatmate ,Sayan, went to see the magnificient fountains in the Jubilee park on 3rd March.It... | 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 \\) be an acute angle. Find the maximum value of the function \\( y = \\sin x \\cdot \\sin 2x \\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the maximum value of the func... | 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 a triangle, \\( M \\) be the midpoint of \\( BC \\), and \\( N \\) be one-third of the way along \\( AC \\) starting from \\( C \\). The line \\( MN \\) intersects \\( AB \\) at \\( P \\). Determine the position 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": "What would be a good way to satisfy my curiosity?\nA: find truth\nB: see particular program\nC: go to market\nD: attend school\nE: pizza"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. The question is asking what would be a good way to sa... | 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 \\) is defined on the set of real numbers and satisfies the equations \\( f(2 - x) = f(2 + x) \\) and \\( f(7 - x) = f(7 + x) \\) for all real numbers \\( x \\). Given that \\( x = 0 \\) is a root of \\( f(x) = 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": "Return your final response within \\boxed{}. Let $ABCD$ be a cyclic quadrilateral, and suppose that $BC = CD = 2$ . Let $I$ be the incenter of triangle $ABD$ . If $AI = 2$ as well, find the minimum value of the length of diagonal $BD$ ."
},
{
"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{}. Quadrilateral \\(ABCD\\) is inscribed in a circle with center \\(O\\). Two circles \\(\\Omega_1\\) and \\(\\Omega_2\\) of equal radii with centers \\(O_1\\) and \\(O_2\\) are inscribed in angles \\(ABC\\) and \\(ADC\\) respectively, wi... | 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 trapezoid \\(ABCD\\), the diagonal \\(BD\\) is equal in length to the base \\(AD\\). Diagonals \\(AC\\) and \\(BD\\) intersect at point \\(E\\). Point \\(F\\) on segment \\(AD\\) is chosen such that \\(EF \\parallel CD\\). Prove tha... | 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 $x^4 + 2$ is divided by $(x - 2)^2.$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the remainder when the polynomial \\( x^4 + 2 \\) is divided by \\( (x - 2)^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{}. In the grid made up of $1 \\times 1$ squares, four digits of 2015 are written in the shaded areas. The edges are either horizontal or vertical line segments, line segments connecting the midpoints of adjacent sides of $1 \\times 1$ squ... | 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 \\geqslant 1\\) that satisfy the equation \\(a b c + 2 a^{2} + 2 b^{2} + 2 c^{2} + c a - c b - 4 a + 4 b - c = 28\\), find the maximum value of \\(a + b + c\\)."
},
{
"from": "assistant",
"valu... | 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 \\( e_{1} = (1,0,0) \\), \\( e_{2} = (0,1,0) \\), and \\( e_{3} = (0,0,1) \\) be three vectors in \\(\\mathbb{R}^{3}\\).\n\nShow that the vectors \\( e_{1} \\), \\( e_{2} \\), and \\( e_{3} \\) form a basis of \\(\\mathbb{R}^{3}\\)... | 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 as \\( n \\to \\infty \\), the values of the two functions \\( f(x) \\equiv 0 \\) and \\( g(x) = \\frac{1}{n} \\sin \\left(\\frac{\\pi}{6} + 2n^2 x \\right) \\) at the point \\( x = \\pi \\) become arbitrarily close to each 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{}. Prove that if \\( a^2 + b^2 = 7ab \\), then\n\n\\[ \\log_{k} \\frac{a+b}{3} = \\frac{1}{2} \\left( \\log_{k} a + \\log_{k} b \\right) \\]\n\nwhere\n\n\\[ a>0, b>0, k>0, k \\neq 1 \\]"
},
{
"from": "assistant",
"value": "<|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": "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.Asmany strings are strings of '0's and '1's that have as many 00 as 11. A string such as 00110001 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{}. A rectangular sheet of paper of dimensions \\( a \\times b \\) cm is cut into rectangular strips, each of which has one side of 1 cm. The cut lines are parallel to the sides of the original sheet. Prove that at least one of the numbers... | 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{}. \nBased on the definition of the derivative, find \\( f^{\\prime}(0) \\):\n\n\\[ f(x) = \n\\begin{cases} \n\\tan\\left(x^3 + x^2 \\sin\\left( \\frac{2}{x} \\right) \\right), & \\text{if } x \\neq 0 \\\\\n0, & \\text{if } x = 0 \n\\end{... | 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 Devil and the Man play a game. Initially, the Man pays some cash $s$ to the Devil. Then he lists some $97$ triples $\\{i,j,k\\}$ consisting of positive integers not exceeding $100$ . After that, the Devil draws some convex p... | 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{}. Two natural numbers, $p$ and $q$ , do not end in zero. The product of any pair, p and q, is a power of 10\n(that is, $10, 100, 1000, 10 000$ , ...). If $p >q$ , the last digit of $p – q$ cannot be $\\textbf{(A)}\\ 1 \\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": "What is the gravitational redshift effect and how does it differ from the Doppler shift in terms of the distortion of light frequency in gravitational fields?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, I need to figure out what the gravitationa... | 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 integer solutions \\((x, y)\\) does the equation \\(|x| + |y| = n\\) have?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how many integer solutions (x, y) there are 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{}. An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of tha... | 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 three quadratic polynomials with pairwise distinct leading coefficients, the graphs of any two of them intersect at exactly one common point. Prove that all three graphs intersect at exactly one common point."
},
{
"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{}. If $ x \\plus{} y \\equal{} 1$ , then the largest value of $ xy$ is:\r\n\r $ \\textbf{(A)}\\ 1\\qquad \r\n\\textbf{(B)}\\ 0.5\\qquad \r\n\\textbf{(C)}\\ \\text{an irrational number about }{0.4}\\qquad \r\n\\textbf{(D)}\\ 0.25\\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{}. 15 boxes are given. They all are initially empty. By one move it is allowed to choose some boxes and to put in them numbers of apricots which are pairwise distinct powers of 2. Find the least positive integer $k$ such that it is pos... | 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 be two distinct natural numbers $ k_1 $ and $ k_2 $ and a sequence $ \\left( x_n \\right)_{n\\ge 0} $ which satisfies $$ x_nx_m +k_1k_2\\le k_1x_n +k_2x_m,\\quad\\forall m,n\\in\\{ 0\\}\\cup\\mathbb{N}. $$ Calculate $ \\... | 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": "How do parasitic infections affect the physical and cognitive development of children?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how parasitic infections affect the physical and cognitive development of children. Let me... | 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, y \\) be integers such that \\( x, y > 1 \\) and \\( x + y - 1 \\) divides \\( x^2 + y^2 - 1 \\). Show that \\( x + y - 1 \\) is not a prime number."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAl... | 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 a manager of a prestigious soccer team in the JOI league.\n\nThe team has $N$ players number... | 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 tree is an undirected connected graph without cycles.\n\nLet's consider a rooted undirected tree 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{}. Each Friday, ten gentlemen come to the club and each gives his hat to the doorman. Each hat fits exactly to its owner, but no two hats are of the same size. The gentlemen leave one by one in a random order.\n\nWhen seeing off the next ... | 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{}. What is the largest number of natural numbers less than 50 that can be chosen so that any two of them are relatively prime?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so the problem is asking for 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{}. A piece can move one cell to the right, up, or down. How many ways are there to move from cell \\(a\\) to cell \\(b\\) on the grid shown in the picture, avoiding the shaded cells? (The piece cannot move to cells it has already visited.... | 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 pairs of numbers \\(a > 1\\), \\(b > 0\\) for which the equation \\(a^x = x^b\\) has exactly one positive solution. Indicate this solution for each found pair of values \\(a\\) and \\(b\\)."
},
{
"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{}. Triangle \\( ABC \\) has side lengths \\( AB = 14 \\), \\( AC = 13 \\), and \\( BC = 15 \\). Point \\( D \\) is chosen in the interior of \\( \\overline{AB} \\), and point \\( E \\) is selected uniformly at random from \\( \\overline{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{}. A line \\( l \\) with slope \\(\\frac{1}{3}\\) intersects the ellipse \\( C: \\frac{x^{2}}{36} + \\frac{y^{2}}{4} = 1\\) at points \\(A\\) and \\(B\\). Point \\(P(3\\sqrt{2}, \\sqrt{2})\\) is located to the upper left of line \\( 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{}. On the board is written the number 98. Every minute the number is erased and replaced with the product of its digits increased by 15. What number will be on the board in an hour?"
},
{
"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": "You should write a program or function that given an N by N equally spaced square grid and a solid inscribed circle outputs or returns the number of grid squares which are overlapped partially or fully by the solid circle.\n0-sized overlaps (i.e. when the circle only touches a li... | You should write a program or function that given an N by N equally spaced square grid and a solid inscribed circle outputs or returns the number of grid squares which are overlapped partially or fully by the solid circle.
0-sized overlaps (i.e. when the circle only touches a line) are not counted. (These overlaps occu... | Okay, I need to solve this problem where given an integer N, representing an N x N grid, I have to find the number of squares that are partially or fully covered by a solid inscribed circle. The circle is inscribed in the grid, so it's centered at (0.5*(N-1), 0.5*(N-1)) and has a radius of 0.5*(N-1). Wait, no. Wait, th... | To solve this problem, we need to determine the number of grid squares that are overlapped partially or fully by a solid inscribed circle within an N x N grid. The circle is centered at the midpoint of the grid and has a radius equal to half the grid's side length. Zero-sized overlaps (where the circle only touches a l... | 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{}. Xiaohui started from point $A$ and walked 15 meters west to point $B$, then walked 23 meters east from point $B$ to point $C$. What is the distance from point $C$ to point $A$ in meters?"
},
{
"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 real number sets \\( A_n = \\{ x \\mid n < x^n < n+1, n \\in \\mathbf{N} \\} \\), if the intersection \\( A_1 \\cap A_2 \\cap \\cdots \\cap A_n \\neq \\emptyset \\), determine the maximum value of \\( n \\)."
},
{
"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": "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 an integer array arr[] of size n which contains only 1 and 0. Your task is to make the array p... | 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{}. Arrange six distinct numbers in a circle such that each number is equal to the product of its two neighbors."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to arrange six distinct numbers in 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{}. Find all integer solutions to the equations:\n1. \\( mm + n = n \\cdot 12 \\)\n2. \\( n(m + n) = m \\cdot 3 \\)"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle these two equations step by ste... | 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{}. Zeljko travelled at 30 km/h for 20 minutes and then travelled at 20 km/h for 30 minutes. How far did he travel, in kilometres?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. Zeljko traveled at... | 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 employees of the R1 company often spend time together: they watch football, they go camping, 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{}. The positive integer 2018 is the product of two primes. What is the sum of these two primes?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I have this problem here: The positive integer 2018 is the p... | 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_1 < a_2 < \\cdots < a_k$ denote the sequence of all positive integers between $1$ and $91$ which are relatively prime to $91$ , and set $\\omega = e^{2\\pi i/91}$ . Define \\[S = \\prod_{1\\leq q < p\\leq k}\\left(\\omeg... | 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 equation in integers: \\( n^{4} + 2n^{2} + 2n^{2} + 2n + 1 = m^{2} \\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, let me try to solve this equation step by step. The equation given is \... | 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{}. Using a compass and straightedge, construct a point on the given line that is equidistant from two given points."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how to construct 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{}. One car covers a distance of 120 km 18 minutes faster than another car. If the first car reduced its speed by 12 km/h and the second car increased its speed by 10%, they would take the same amount of time to travel the same distance. 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. Return the function body without invoking it at the final solution.Write a function named setAlarm which receives two parameters. The first parameter, employed, is true whenever you are employed and the secon... | 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 4-digit numbers exist where the thousands digit is greater than the hundreds digit?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how many 4-digit numbers exist where 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{}. A factory produces no more than \\( a \\) units on its first day. Thereafter, the daily production increases every day, but the increase each time does not exceed \\( a \\) units.\n\nProve that when the daily production reaches \\( 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": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.We have N cards numbered 1, 2, ..., N. Card i (1 \\leq i \\leq N) has an integer A_i written in red ... | 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 $128 \\div x + 75 \\div x + 57 \\div x = 6.5$, find the value of $x$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. I need to find the value of x in this equation: 128 divided by 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{}. Two lines pass through the center of parallelogram $ABCD$. One of them intersects sides $AB$ and $CD$ at points $M$ and $K$ respectively, and the other intersects sides $BC$ and $AD$ at points $N$ and $L$ respectively. Prove that quadr... | 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 the numbers \\(x\\), \\(y\\), and \\(z\\) for certain values of \\(p\\) and \\(q\\) are solutions of the system\n\n$$\ny = x^n + px + q, \\quad z = y^n + py + q, \\quad x = z^n + pz + q,\n$$\n\nthen the inequality \\(x^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{}. Let \\( \\triangle ABC \\) be a triangle, and let \\( K, L, \\) and \\( M \\) be any distinct points on the segments \\([BC], [CA],\\) and \\([AB]\\) respectively. The circumcircles of \\(\\triangle BKM\\) and \\(\\triangle KCL\\) inte... | 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.Polycarpus has n friends in Tarasov city. Polycarpus knows phone numbers of all his friends: they ar... | 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 Valbonne, $n$ problems have been posted on a wall. Each of the $m$ trainees has solved at least $\\frac{n}{2}$ problems. Show that there exists a problem that has been solved by at least $\\frac{m}{2}$ trainees."
},
{
"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": "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 and B are preparing themselves for programming contests.\n\nTo train their logical thinking and so... | 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 such natural numbers whose product is 2020 and whose sum is 2020."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, let me try to figure out this problem. So, we need to find natural numbers (which ... | 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{}. Two teams of movers are lowering a piano from the window of a $10$ floor apartment building. The rope breaks\nwhen the piano is $30$ meters above the ground. The movers on the ground, alerted by the shouts of the movers\nabove, fir... | 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 none of 52 different positive integers is greater than 100, then it is possible to choose three of them such that the sum of two of them equals the third one."
},
{
"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{}. The production of ceramic items consists of 3 consecutive stages: shaping the ceramic item on a potter's wheel for 15 minutes, drying for 10 minutes, and firing for 30 minutes. It is required to produce 75 items. How should 13 workers ... | 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 $N$ bikers present in a city (shaped as a grid) having $\\mbox{M}$ bikes. All the bikers 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{}. The room temperature $T$ (in degrees Celsius) as a function of time $t$ (in hours) is given by: $T = a \\sin t + b \\cos t, \\ t \\in (0, +\\infty)$, where $a$ and $b$ are positive real numbers. If the maximum temperature difference 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{}. \nDefine a sequence of positive integers \\(\\{a_n\\}\\) such that \\(a_1 = 1\\), \\(a_2 = 2\\), and \\(a_{n+2} = 2a_{n+1} + a_{n}\\).\n\n(1) Find all positive real numbers \\(\\beta\\) for which there exist infinitely many pairs of po... | 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 a triangle \\( \\triangle ABC \\) inscribed in a circle \\( O \\). A tangent \\( PD \\) is drawn at point \\( A \\), with \\( D \\) lying on the ray \\( BC \\) and \\( P \\) on the ray \\( DA \\). A secant \\( PU \\) is then draw... | 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{}. m and n are fixed positive integers. X is a union of disjoint arcs on a circle with radius 1 and total length 2πh. X_i is the set obtained by rotating X_0 through an angle iπ/n. Y is a union of m disjoint arcs on the circle, each 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{}. A sphere of radius \\( r \\) touches all the lateral faces of a triangular pyramid at the midpoints of the sides of its base. The segment connecting the apex of the pyramid with the center of the sphere is divided into two equal parts ... | 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 occasion of the 47th Mathematical Olympiad 2016 the numbers 47 and 2016 are written on the blackboard. Alice and Bob play the following game: Alice begins and in turns they choose two numbers $a$ and $b$ with $a > b$ writt... | 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 points on an infinite plane. The i-th point has coordinates (x_i, y_i) such that x_i > 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": "Return your final response within \\boxed{}. Suppose two distinct integers are chosen from between 5 and 17, inclusive. What is the probability that their product is odd?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. I need to find 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{}. Find all pairs of positive integers \\((a, b)\\) such that \\(\\frac{a^{3} b - 1}{a + 1}\\) and \\(\\frac{b^{3} a + 1}{b - 1}\\) are integers."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's try to ... | 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 \\( f(x)=\\frac{x+1}{x-1} \\) (where \\( x \\in \\mathbf{R} \\) and \\( x \\neq \\pm 1 \\)), which of the following always holds?\n(A) \\( f(x) \\cdot f(-x)=1 \\)\n(B) \\( f(x)+f(-x)=0 \\)\n(C) \\( f(x) \\cdot f(-x)=-1 \\)\n(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{}. Given the polynomial \\( P(x)=1+2x+3x^{2}+4x^{3}+\\ldots+101x^{100} \\), is it possible to rearrange the coefficients to form a polynomial \\( Q(x)=q_{0}+q_{1}x+q_{2}x^{2}+q_{3}x^{3}+\\ldots+q_{100}x^{100} \\) such that for all natural... | 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 cyclic quadrilateral $ABCD$ inscribed in circle $\\odot O$, $AC$ is not the diameter of $\\odot O$. Point $E$ is on segment $AC$ such that $AC = 4AE$. From point $E$, a perpendicular is drawn to $OE$, intersecting $AB$ and $AD$ at... | 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 \\( f(x) = \\left\\{ \\begin{array}{ll} (3-a)x - a, & x < 1 \\\\ \\log_a x, & x \\geq 1 \\end{array} \\right. \\), and \\( f(x) \\) is monotonically increasing over \\((-\\infty, +\\infty)\\), determine the range of values 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 chess tournament is held with the participation of boys and girls. The girls are twice as many as boys. Each player plays against each other player exactly once. By the end of the tournament, there were no draws and the ratio of girl... | 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 $\\triangle ABC$, if $A > B$, then $\\cos 2B > \\cos 2A$ is a\nA. Sufficient but not necessary condition\nB. Necessary but not sufficient condition\nC. Sufficient and necessary condition\nD. Neither sufficient nor necessary conditio... | 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{}. If a natural number \\( n \\) can be uniquely represented as the sum \\( a_1 + a_2 + \\cdots + a_k \\) and the product \\( a_1 a_2 \\cdots a_k \\) of \\( k \\) natural numbers (\\( k \\geq 2 \\)), then this natural number is called 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{}. Evaluate the sum: $\\sum_{m=1}^{\\infty} \\sum_{n=1}^{\\infty} \\frac{m^{2} n}{3^{m}\\left(n \\cdot 3^{m}+m \\cdot 3^{n}\\right)}$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to evaluate 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{}. The center of the hyperbola \\( y = \\frac{1}{x} \\) is \\( O \\). Points \\( K \\) and \\( L \\) on the hyperbola are symmetric with respect to \\( O \\), and there is another point \\( M \\) on the hyperbola. Prove that the projectio... | 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{}. \\(ABCD\\) is a cyclic quadrilateral. The extension of side \\(AB\\) beyond point \\(B\\) and the extension of side \\(CD\\) beyond point \\(C\\) intersect at point \\(P\\). The extension of side \\(AD\\) beyond point \\(D\\) and the 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": "Return your final response within \\boxed{}. A pizza parlor has six different toppings. How many different one- and two-topping pizzas can you order?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how many different one- and... | 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{}. Two symmetrical coins are flipped. What is the probability that both coins show numbers on their upper sides?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out this probability prob... | 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.