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values | __original_row_idx int64 1 7.5k ⌀ | solution stringlengths 335 3.59k ⌀ | r1_distill_70b_response listlengths 3 3 ⌀ | _majority_responses listlengths 1 1 ⌀ | verified_r1_distill_70b_response stringlengths 598 92.9k ⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and 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 acute-angled non-isosceles triangle $ABC$ is drawn, a circumscribed circle and its center $O$ are drawn. The midpoint of side $AB$ is also marked. Using only a ruler (no divisions), construct the triangle's orthocenter by draw... | null | null | null | null | 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 $M\\left(f_{n}\\right)$ be the minimum number of lines in a program that computes $f_{n}$, where each line computes either a disjunction or a conjunction. Prove that $M\\left(f_{n}\\right) \\geqslant M\\left(f_{n-2}\\right)+3$ for ... | null | null | null | null | 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 circles intersect at points \\( A \\) and \\( B \\) on the plane. Let \\( P Q \\) be one of their common tangents, with \\( P \\) and \\( Q \\) as the points of tangency. \\( S \\) is the intersection point of the tangents to the c... | null | null | null | null | 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.Nian is a monster which lives deep in the oceans. Once a year, it shows up on the land, devouring li... | null | null | null | null | 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 four points \\( A, B, C, \\) and \\( D \\) in space that are not coplanar, each pair of points is connected by an edge with a probability of \\( \\frac{1}{2} \\). The events of whether any two pairs of points are connected are mu... | null | null | null | null | 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 an $n \\times n$ grid, fill it with integers from 1 to $n^2$ according to the following rule: Place 1 in any cell, the row of 2 should match the column of 1, the row of 3 should match the column of 2, and so on. What is the diffe... | null | null | null | null | 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 \\(ABCD\\), \\(AB = 2\\), \\(BC = 4\\), \\(CD = 5\\). Find its area given that it is both circumscribed and inscribed."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to fin... | null | null | null | null | 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 string *s* consisting of *n* lowercase Latin letters. You have to type this string u... | null | null | null | null | 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 | 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": "In a religious sense where would a lemur be found?\nA: heaven\nB: cage\nC: russia\nD: field\nE: tree"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle this question. The user is asking where a lemur would be found in a religious sense, wi... | null | null | null | null | 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.Polycarp is working on the implementation of displaying likes on the Codehorses social network. The ... | null | null | null | null | 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.problem\n\nThere are many $ N $ colored balls of different weights in the queue. The queue is in asc... | null | null | null | null | 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{}. \nFor non-zero integers \\( x \\) and \\( y \\) we define \\( x \\nabla y = x^{y} + 4x \\). For example, \\( 2 \\nabla 3 = 2^{3} + 4(2) = 16 \\). Determine all real numbers \\( x \\) such that \\( x \\nabla 2 = 12 \\)."
},
{
"f... | null | null | null | null | 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{}. Trapezoid $ABCD$ has $AD||BC$, $BD = 1$, $\\angle DBA = 23^{\\circ}$, and $\\angle BDC = 46^{\\circ}$. The ratio $BC: AD$ is $9: 5$. What is $CD$?\n\n$\\mathrm{(A)}\\ \\frac 79\\qquad \\mathrm{(B)}\\ \\frac 45\\qquad \\mathrm{(C)}\\ ... | null | null | null | null | 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 a board, the numbers from 1 to 2009 are written. A couple of them are erased and instead of them, on the board is written the remainder of the sum of the erased numbers divided by 13. After a couple of repetition of this erasing, on... | null | null | null | null | 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 number $S$ is called the mean of two numbers $R_1$ and $R_2$ if $S$ is equal to $(R_1+R_2)/2$. M... | null | null | null | null | 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{}. Apprentices A and B are discussing who should cooperate with their master to process a batch of parts. A says, \"If I cooperate with the master, I will complete 20% of all the work.\" B says, \"That's not a big deal. If I cooperate wit... | null | null | null | null | 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{}. \"Modulo $m$ graph paper\" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\\le x<m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congru... | null | null | null | null | 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 circles $S_{1}$ and $S_{2}$ intersect at points $P$ and $Q$, let $A_{1}$ and $B_{1}$ be two points on circle $S_{1}$ other than $P$ and $Q$. The lines $A_{1}P$ and $B_{1}P$ intersect circle $S_{2}$ at points $A_{2}$ and $B_{2}$, ... | null | null | null | null | 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 integer solutions \\((x, y, z, n)\\) to the equation \\(x^{2n+1} - y^{2n+1} = xyz + 2^{2n+1}\\), where \\(n \\geq 2\\) and \\(z \\leq 5 \\cdot 2^{2n}\\)."
},
{
"from": "assistant",
"value": "<|begin_of_tho... | null | null | null | null | 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 a value of \\( n \\) such that the number \\( 10^n - 1 \\) is divisible by a) 7; b) 13; c) 91; d) 819."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. I need to find values of n such that ... | null | null | null | null | 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 any positive integer $m\\ge2$ define $A_m=\\{m+1, 3m+2, 5m+3, 7m+4, \\ldots, (2k-1)m + k, \\ldots\\}$ .\n\n(1) For every $m\\ge2$ , prove that there exists a positive integer $a$ that satisfies $1\\le a<m$ and $2^a\\in A_... | null | null | null | null | 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 watermelons brought to the base are intended for two stores. The first store immediately started transporting the watermelons and transported them daily in portions of equal mass. The second store began transporting the watermelons... | null | null | null | null | 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 side \\( AC \\) of an acute-angled triangle \\( ABC \\), point \\( D \\) is chosen. The median \\( AM \\) intersects the altitude \\( CH \\) and segment \\( BD \\) at points \\( N \\) and \\( K \\) respectively. Prove that if \\( AK... | null | null | null | null | 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 16 ones, 20 twos, and 31 threes written on a board. We can erase any two different digits and write the third digit once on the board. Prove that by repeating this procedure, we can reach a state where only one type of number... | null | null | null | null | 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 pedestrians simultaneously departed from point A to point B and from point B to point A. When the first pedestrian had covered half the distance, the second pedestrian had 24 kilometers remaining. When the second pedestrian had cov... | null | null | null | null | 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 the equation \\( x^{2} - 2 = 0 \\) has no solution in \\( \\mathbb{Q}_{5} \\). Deduce from this that \\( \\sqrt{2} \\) is irrational."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to... | null | null | null | null | 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 does temperature affect the solubility of a solute in a solvent? Using experimental data, compare the solubility of sodium chloride in water at 25°C and 50°C, and explain the underlying physical principles that govern solvation and solubility phenomena at different temperatur... | null | null | null | null | 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{}. 20 chess players participated in a chess tournament. Each pair of participants played exactly one game with each other. A win earned 1 point, a draw earned $1 / 2$ point, and a loss earned 0 points. In the end, all players had differen... | null | null | null | null | 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 number 392 was divided by a natural number \\( a \\) and then \\( a \\) was subtracted from the quotient. The same operation was performed with the resulting difference, and then again with the new result. The final result was equa... | null | null | null | null | 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 least common multiple of 3, 4, 6 and 15?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the least common multiple (LCM) of the numbers 3, 4, 6, and 15. Hmm, let me remember ... | null | null | null | null | 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 three-digit perfect cubes are divisible by $9?$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, let's try to figure out how many three-digit perfect cubes are divisible by 9. Hmm, okay. First,... | null | null | null | null | 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.#Find the missing letter\n\nWrite a method that takes an array of consecutive (increasing) letters as input and that returns the missing lett... | null | null | null | null | 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 is an infinite arithmetic progression of natural numbers with a non-zero difference. From each of its members, the square root is taken and, if the result is not an integer, it is rounded to the nearest integer. Can it be that al... | null | null | null | null | 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 values of parameter \\( a \\) for which the equation\n\n\\[ 5|x-4a|+\\left|x-a^{2}\\right|+4x-4a=0 \\]\n\nhas no solutions."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I have this equation... | null | null | null | null | 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.JJ has an array A of size N. He can perform the following operations on the array at most K times:\n... | null | null | null | null | 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{}. We have a rectangle \\(ABCD\\), as shown in the picture. The side lengths \\(AB\\) and \\(BC\\) are in the ratio 7:5. Inside the rectangle \\(ABCD\\) lie points \\(X\\) and \\(Y\\) such that triangles \\(ABX\\) and \\(CDY\\) are right-... | null | null | null | null | 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.Bob is a dance teacher and he started dance classes recently. He observes a strange attendance patte... | null | null | null | null | 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 map of Berland is a rectangle of the size n × m, which consists of cells of size 1 × 1. Each cel... | null | null | null | null | 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 natural numbers that satisfy the equation:\na) \\(x^{2}-y^{2}=105\\)\nb) \\(2x^{2}+5xy-12y^{2}=28\\)"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to solve these two equation... | null | null | null | null | 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 theater box office sells $2n$ tickets at 5 cents each, with each person limited to buying one ticket. Initially, the box office has no money, and among the first $2n$ people in line, half have 5 cent coins while the other half only h... | null | null | null | null | 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{}. \nLet \\( n \\) be a fixed integer, \\( n \\geq 2 \\).\n\n1. Determine the smallest constant \\( c \\) such that the inequality \\[\n\\sum_{1 \\leq i < j \\leq n} x_i x_j (x_i^2 + x_j^2) \\leq c \\left( \\sum_{i=1}^n x_i \\right)^4 \n\... | null | null | null | null | 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": "Why would a person stay in a relationship with a man?\nA: acknowledgment\nB: good lover\nC: mercy\nD: make others happy\nE: low crime"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so the question is asking why a person would stay in a relationshi... | null | null | null | null | 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 which natural value of \\( a \\) will the number \\( a^2 + a + 1589 \\) be a perfect square?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find a natural number \\( a \\) such that \\( ... | null | null | null | null | 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{}. ABC is a triangle. R is the circumradius, r is the inradius, a is the longest side and h is the shortest altitude. Show that \\( R / r > a / h \\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, so I ... | null | null | null | null | 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{}. Define the sequence \\(\\{a_{n}\\}\\) by \\(a_0 = a\\), \\(a_{n+1} = 2a_n - n^2\\) (for \\(n \\geq 0\\)). Determine all real numbers \\(a\\) such that \\(a_n \\geq 0\\) for any non-negative real number \\(n\\)."
},
{
"from": "a... | null | null | null | null | 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 array A of integers of size N. You will be given Q queries where each query is repr... | null | null | null | null | 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 tree consisting of n nodes numbered from 1 to n. The weights of edges of the tree ca... | null | null | null | null | 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{}. \nPoints A and B are 999 km apart, with 1000 milestones along the way. Each milestone indicates the distance to points A and B in the format (distance to A, distance to B), such as (0, 999), (1, 998), (2, 997), ..., (997, 2), (998, 1),... | null | null | null | null | 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 remainder when $x^2+7x-5$ divides $2x^4+11x^3-42x^2-60x+47$?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the remainder when the polynomial \\( x^2 + 7x - 5 \\) divides \\... | null | null | null | null | 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{}. Determine the greatest common divisor (gcd) of all the numbers of the form \\((a-b)(a-c)(a-d)(b-c)(b-d)(c-d)\\) where \\(a, b, c, d\\) range over the integers."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAl... | null | null | null | null | 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 binary string S consisting of 0s and 1s. The task is to find the maximum difference of the n... | null | null | null | null | 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 system of equations for positive numbers \\( x, y, z \\):\n\n\\[\n\\begin{cases}\nx^2 + xy + y^2 = 27 \\\\\ny^2 + yz + z^2 = 9 \\\\\nz^2 + xz + x^2 = 36\n\\end{cases}\n\\]\n\nfind the value of the expression \\( xy + yz + xz ... | null | null | null | null | 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 number \\(\\left(x^{2} + x + 1\\right)^{2} + \\left(y^{2} + y + 1\\right)^{2}\\) be a perfect square for some integers \\(x\\) and \\(y\\)?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so the q... | null | null | null | null | 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 circles $\\mathcal{C}_{1}$ and $\\mathcal{C}_{2}$ intersect at two distinct points $A$ and $B$. Let $I$ be the midpoint of the segment $[A B]$.\n\na) Is it possible to draw distinct lines concurrent at $I$ such that these lines and... | null | null | null | null | 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 any month with five Mondays, a school declares the fifth Monday a Marvelous Monday. School begins on Monday, September 4. What is the date of the first Marvelous Monday after school starts? (If you abbreviate, do not use a dot in th... | null | null | null | null | 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 the following 10 cardboard pieces on a $10 \\times 10$ grid paper: one $1 \\times 4$ piece, two $1 \\times 3$ pieces, three $1 \\times 2$ pieces, and four $1 \\times 1$ pieces. After placing them, the pieces must not share any ... | null | null | null | null | 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.Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are t... | null | null | null | null | 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{}. Every third student in the sixth grade is a member of the math club, every fourth student is a member of the history club, and every sixth student is a member of the chemistry club. The rest of the students are members of the literatur... | null | null | null | null | 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 positive integer and $a,b$ be invertible integers modulo $n$ such that $a\\equiv b^{-1}\\pmod n$. What is the remainder when $ab$ is divided by $n$?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\n... | null | null | null | null | 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 1978 sets, each containing 40 elements, and knowing that any two sets have exactly one common element, prove that there exists an element that belongs to all 1978 sets."
},
{
"from": "assistant",
"value": "<|begin_of_... | null | null | null | null | 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 trapezoid \\(ABCD\\) with bases \\(AD \\parallel BC\\), the diagonals intersect at point \\(E\\). Given the areas \\(S(\\triangle ADE) = 12\\) and \\(S(\\triangle BCE) = 3\\), find the area of the trapezoid."
},
{
"from"... | null | null | null | null | 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 cone and a hemisphere share a common base with a radius of $R$. Find the lateral surface area of the cone if its volume is equal to the volume of the hemisphere."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n... | null | null | null | null | 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 circle with a radius of \\( r \\) is touched by four other circles, each also with a radius of \\( r \\), and no two of these circles have interior points in common. What is the radius of the smallest circle that can contain all of t... | null | null | null | null | 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 $k$ satisfying: there is only a finite number of positive integers $n$ , such that the positive integer solution $x$ of $xn+1\\mid n^2+kn+1$ is not unique."
},
{
"from": "assistant",
"value... | null | null | null | null | 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{}. Circles \\(K_{1}\\) and \\(K_{2}\\) share a common point \\(A\\). Through point \\(A\\), three lines are drawn: two pass through the centers of the circles and intersect them at points \\(B\\) and \\(C\\), and the third is parallel to ... | null | null | null | null | 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.Two children are playing tag on a number line. (In the game of tag, the child called \"it\" tries to... | null | null | null | null | 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 regular $n$-sided polygon $A_{1} A_{2} \\cdots A_{n}$ inscribed in a unit circle and a point $P$ on the circumference, prove that:\n$$\n\\sum_{k=1}^{n}\\left|P A_{k}\\right|^{2}=2 n .\n$$"
},
{
"from": "assistant",
... | null | null | null | null | 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{}. \n57. Does there exist a polynomial \\(p(x)\\) with integer coefficients such that:\na) \\(p(1) = 19\\) and \\(p(19) = 99\\);\nb) \\(p(0) = 19\\), \\(p(1) = 99\\), and \\(p(2) = 1999\\)?\n\n58. Prove that the sum of all the coefficient... | null | null | null | null | 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 constant \\( a \\in \\mathbf{R} \\) and the function\n\\[ f(x) = (a - x)|x| \\]\n\nhave an inverse function \\( f^{-1}(x) \\). If the inequality\n\\[ f^{-1}\\left(x^{2} + m\\right) < f(x) \\]\n\nholds for all \\( x \\in [-2,2] \\... | null | null | null | null | 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 four-digit number whose last digit is not 0, if the first two digits can divide 2014, and the product of the first two digits and the last two digits can be divided by 2014, then what is the largest four-digit number?"
},
{
"... | null | null | null | null | 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": "(Better known as 3D Tic Tac Toe; I just made up a name that sounded catchy ;-) )\nLet two people play this game against each other.\nSpecifications:\n\nOutput\n\nthe easiest way of explaining this will be with an example:\n+-+-+-+-+\n|X| | | |\n+-+-+-+-+\n| |O| | |\n+-+-+-+-+\n| ... | (Better known as 3D Tic Tac Toe; I just made up a name that sounded catchy ;-) )
Let two people play this game against each other.
Specifications:
Output
the easiest way of explaining this will be with an example:
+-+-+-+-+
|X| | | |
+-+-+-+-+
| |O| | |
+-+-+-+-+
| | | | |
+-+-+-+-+
|O| | | |
+-+-+-+-+
+-+-+-+-+
| |... | Okay, I need to create a 3D Tic Tac Toe game according to the given specifications. Let's start by understanding the problem.
The game is played on four 4x4 grids (layers), making it a 3D game. Players alternate turns, starting with X. After each move, I have to check if the player has won by getting four in a row, co... | To solve this problem, we need to create a 3D Tic Tac Toe game where two players alternate turns, starting with X. The game is played on a 4x4x4 grid, and the goal is to get four symbols in a row, column, diagonal, or any of the 3D lines. The solution involves generating all possible winning lines, validating input, up... | null | 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.Raju is very fond of strings.Once he was playing a game with his friend.His friend gave him a strin... | null | null | null | null | 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 two bottles containing a mixture of liquids with equal total weight. The weight ratio of water, oil, and vinegar in bottle (1) is $1 : 2 : 3$, and in bottle (2) it is $3 : 4 : 5$. After thoroughly mixing the contents of both ... | null | null | null | null | 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 convex polygon has a minimum interior angle of $\\frac{2}{3} \\pi$, and each interior angle in radians forms an arithmetic sequence with a common difference of $\\frac{\\pi}{36}$. How many sides does this convex polygon have?\nA. 9\n... | null | null | null | null | 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{}. \nWith inspiration drawn from the rectilinear network of streets in New York, the Manhattan distance between two points \\((a, b)\\) and \\((c, d)\\) in the plane is defined to be \n\n\\[ \n|a-c| + |b-d| \\text{.}\n\\]\n\nSuppose only ... | null | null | null | null | 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 positive integers A and B.\nIf A is a divisor of B, print A + B; otherwise, print B - ... | null | null | null | null | 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 largest integer $T$ such that any positive integer not greater than $T$ can be expressed as a sum of distinct positive divisors of $(p_{1} p_{2} \\cdots p_{25})^{2004}$, including sums with a single term, where $p_{1}, p_{2}, ... | null | null | null | null | 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{}. Assume that I am either a knight or a liar and I make the following two statements:\n\n1) I love Linda.\n2) If I love Linda, then I love Katie.\n\nWho am I: a knight or a liar?"
},
{
"from": "assistant",
"value": "<|begin_o... | null | null | null | null | 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 exist integers $a,$ $b,$ and $c$ such that\n\\[(x - a)(x - 10) + 1 = (x + b)(x + c).\\]Enter all possible values of $a,$ separated by commas."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I nee... | null | null | null | null | 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 ancient and mysterious Apaxian civilization, which we most certainly did not make up, continues ... | null | null | null | null | 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 $k$ and $n$ be given integers with $n > k \\geq 2$. For any set $P$ consisting of $n$ elements, form all $k$-element subsets of $P$ and compute the sums of the elements in each subset. Denote the set of these sums as $Q$. Let $C_{Q... | null | null | null | null | 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 is a tree with N weighted vertices and N-1 weighted edges. The i-th vertex has a weight of A_{... | null | null | null | null | 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.C: Canisal cryptography\n\nproblem\n\nEbi-chan was given the string C obtained by encrypting a non-n... | null | null | null | null | 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 cyclic quadrilateral \\(ABCD\\) with \\(\\angle A = 2 \\angle B\\), the angle bisector of \\(\\angle C\\) intersects side \\(AB\\) at point \\(E\\). Prove that \\(AD + AE = BE\\)."
},
{
"from": "assistant",
"value":... | null | null | null | null | 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{}. This questions comprises two independent parts.\n\n(i) Let \\(g:\\mathbb{R}\\to\\mathbb{R}\\) be continuous and such that \\(g(0)=0\\) and \\(g(x)g(-x)>0\\) for any \\(x > 0\\). Find all solutions \\(f : \\mathbb{R}\\to\\mathbb{R}\\) ... | null | null | null | null | 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\\), the altitudes \\(AH\\) and \\(CP\\) are drawn. Find the measure of angle \\(B\\) if it is known that \\(|AC| = 2|PH|\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I have th... | null | null | null | null | 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 does the lymphatic system help in removing excess fluid and waste products from tissues, and what is the role of lymph nodes in detecting and combating infections?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how the l... | null | null | null | null | 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 solution to the equation \\(\\sqrt{3x + 1} + \\sqrt{3x + 6} = \\sqrt{4x - 2} + \\sqrt{4x + 3}\\) is \\(a\\), find the value of \\(a\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's... | null | null | null | null | 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 greatest integer less than 100 for which the greatest common factor of that integer and 18 is 3?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle this problem: Find the greatest in... | null | null | null | null | 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 \\( m \\) is a real number, and the sequence \\(\\left\\{a_{n}\\right\\}\\) has a sum of the first \\( n \\) terms \\( S_{n} \\) that satisfies: \\( S_{n}=\\frac{9}{8} a_{n}-\\frac{4}{3} \\times 3^{n}+m \\), with \\( a_{n} \\geqs... | null | null | null | null | 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.Each of you probably has your personal experience of riding public transportation and buying tickets... | null | null | null | null | 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 \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) be a function that satisfies the functional equation\n\\[ f(x-y)=2009 f(x) f(y) \\]\nfor all \\( x, y \\in \\mathbb{R} \\). If \\( f(x) \\) is never zero, what is \\( f(\\sqrt{2009}) ... | null | null | null | null | 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{}. All whole numbers are written in sequence, starting from one. What digit is located in the 206,788th position?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle this problem: \"All whole number... | null | null | null | null | 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 ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coord... | null | null | null | null | 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 $ABC$ is scalene. Points $P$ and $Q$ are on segment $BC$ with $P$ between $B$ and $Q$ such that $BP=21$ , $PQ=35$ , and $QC=100$ . If $AP$ and $AQ$ trisect $\\angle A$ , then $\\tfrac{AB}{AC}$ can be ... | null | null | null | null | 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{}. Consider the parabola consisting of the points \\((x, y)\\) in the real plane satisfying\n\\[\n(y + x) = (y - x)^2 + 3(y - x) + 3.\n\\]\nFind the minimum possible value of \\(y\\)."
},
{
"from": "assistant",
"value": "<|beg... | null | null | null | null | 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": "The goal of this challenge is to complete a list of consecutive nested header numbers when given a start and an end. When given 1.1.1 and 1.1.5 you should generate 1.1.1, 1.1.2, 1.1.3, 1.1.4, 1.1.5\nSpecific Rules\n\nYour entry must take in a start, end, and multiple optional ra... | The goal of this challenge is to complete a list of consecutive nested header numbers when given a start and an end. When given 1.1.1 and 1.1.5 you should generate 1.1.1, 1.1.2, 1.1.3, 1.1.4, 1.1.5
Specific Rules
Your entry must take in a start, end, and multiple optional range parameters. Parameters can be taken fo... | Okay, let's try to solve this problem. Hmm. The task is to generate a list of consecutive nested header numbers between a start and end value, following specific rules. Let me start by understanding the problem thoroughly.
First, the input is a start and end string, along with a range parameter. The start and end are ... | To solve this problem, we need to generate a list of consecutive nested header numbers between a given start and end value, following specific rules. The solution involves identifying the iterator segment, generating all possible combinations for the trailing segments according to provided ranges, and ensuring the corr... | null | 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{}. $m,n$ are positive intergers and $x,y,z$ positive real numbers such that $0 \\leq x,y,z \\leq 1$ . Let $m+n=p$ . Prove that: $0 \\leq x^p+y^p+z^p-x^m*y^n-y^m*z^n-z^m*x^n \\leq 1$ "
},
{
"from": "assistant",
"value": "... | null | null | null | null | 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 quadrilateral \\(ABCD\\) inscribed in circle \\(\\odot O\\), diagonals \\(AC\\) and \\(BD\\) are perpendicular, and \\(OE\\) is perpendicular to \\(AB\\) at \\(E\\). Prove that \\(OE = \\frac{1}{2} CD\\)."
},
{
"from": "assi... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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