messages listlengths 3 3 |
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[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "130 trees are planted in a circle: birches and lindens (both types are present). Each tree has a sign that reads: \"Two different ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "3-5. The distance from \\(A\\) to \\(B\\) is 999 km. Along the road, there are kilometer markers indicating the distances to \\(A\... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "$\\underline{\\text { Folklore }}$Among the actors of Karabas Barabas theater, a chess tournament was held. Each participant playe... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Task Condition\n\nFind the derivative.\n\n$y=2 x-\\ln \\left(1+\\sqrt{1-e^{4 x}}\\right)-e^{-2 x} \\cdot \\arcsin \\left(e^{2 x... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "5. Given $n!=n \\times(n-1) \\times(n-2) \\times \\cdots \\times 2 \\times 1$, then $10!\\div(5!\\times 2!)=$",
"role": "user"... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In cube \\(ABCD - A_1B_1C_1D_1\\), find the measure of the acute dihedral angle between plane \\(AB_1D_1\\) and plane \\(A_1BD\\).... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "5. Given $f(x)=\\sum_{i=1}^{2009}|x+i|+\\sum_{i=1}^{2009}|x-i|$ $(x \\in \\mathbf{R})$, and $f\\left(a^{2}-3 a+2\\right)=f(a-1)$. ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "36. Find the prime number $p$, given that the number $13 p+1$ is a perfect cube.",
"role": "user"
},
{
"content": "<th... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The integers $1, 2, \\dots, n$ are written in order on a long slip of paper. The slip is then cut into five pieces, so that each... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "8. Find the smallest positive integer $k$ such that the equation $2 x y-3 x-5 y=k$ has an odd number of positive integral solution... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In right triangle \\( \\triangle ABC \\), \\( AD \\) is the altitude on hypotenuse \\( BC \\). The line connecting the incenters o... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Problem Statement\n\nCalculate the limit of the function:\n\n$$\n\\lim _{x \\rightarrow 0} \\frac{\\sqrt[3]{8+3 x-x^{2}}-2}{\\s... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "\nDetermine the type of the equation\n\n\\[ u_{xx} - 2u_{xy} + u_{yy} + u_{x} - u_{y} + u = xy \\]\n\nand transform it to its cano... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "We draw $n$ convex quadrilaterals in the plane. They divide the plane into regions (one of the regions is infinite). Determine the... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "9. Buratino the Statistician (from 7th grade, 2 points). Every month, Buratino plays in the \"6 out of 45\" lottery organized by K... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "7.3. Three eleventh-graders played tic-tac-toe against two ninth-graders (in each match, an eleventh-grader played against a ninth... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "3. At the mathematics olympiad in two rounds, it is necessary to solve 14 problems. For each correctly solved problem, 7 points ar... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The polynomial \\(12x^3 + ax^2 + bx + c\\) has three distinct real roots, but \\((x^2 + x + 2001)^3 + a(x^2 + x + 2001)^2 + b(x^2 ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "$8 \\cdot 1$ Arrange all powers of 3 and the sums of any finite number of distinct powers of 3 in an increasing sequence:\n$$\n1,3... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "6. (8 points) By expanding the expression $(1+\\sqrt{13})^{210}$ using the binomial theorem, we obtain terms of the form $C_{210}^... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $\\Gamma_1, \\Gamma_2, \\Gamma_3$ be three pairwise externally tangent circles with radii $1,2,3,$ respectively. A circle pass... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Two congruent right circular cones each with base radius $3$ and height $8$ have the axes of symmetry that intersect at right angl... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "33rd Eötvös 1929 Problem 1 Coins denomination 1, 2, 10, 20 and 50 are available. How many ways are there of paying 100?",
"rol... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Consider the ellipse given by the equation \\(\\frac{x^{2}}{3}+\\frac{y^{2}}{2}=1\\). From the right focus \\( F \\) of the ellips... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "10. A class has 48 students, of which 24 are interested in calligraphy, and 30 are interested in music. The number of students int... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 5. Find the singular solutions of the differential equation\n\n$$\n\\left(y^{\\prime}\\right)^{2}(2-3 y)^{2}=4(1-y)\n$$",
... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 31 (2002 Australian National Mathematics Olympiad) Given the polynomial $p(n)=n^{3}-n^{2}-5 n+2$, find all integers $n$ su... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "There are 195 different cards with the numbers \\(1, 5, 7, 5^{2}, 7^{2}, \\ldots, 5^{97}, 7^{97}\\) (each card has exactly one num... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. The two roots of the equation $x^{2}-3|x|-4=0$ are $x_{1}$, $x_{2}$, then $x_{1}+x_{2}=$ $\\qquad$",
"role": "user"
},
... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "How many ordered sequences of 36 digits have the property that summing the digits to get a number and taking the last digit of the... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "6.073. $\\left\\{\\begin{array}{l}y^{2}-x y=-12, \\\\ x^{2}-x y=28\\end{array}\\right.$",
"role": "user"
},
{
"content... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Example 6 Find the range of the function $y=3 x^{2}-12 x+18 \\sqrt{4 x-x^{2}}-23$.\n\n",
"role": "user"
},
{
"content"... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $BCX$ be an acute-angled triangle. The tangents to its circumcircle at $B$ and $C$ intersect at $A$. The line $(AX)$ intersect... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. There is a sequence of numbers, starting from the 3rd number, each number is the sum of all the numbers before it. If the 1st n... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. On the board, three quadratic equations are written:\n\n$$\n\\begin{gathered}\n2020 x^{2}+b x+2021=0 \\\\\n2019 x^{2}+b x+2020=... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. Let $z=m+n \\mathrm{i}$ be a complex root of the equation\n$$\na z^{4}+\\mathrm{i} b z^{3}+c z^{2}+\\mathrm{i} d z+e=0\n$$\n\nw... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Call a positive integer one-full if it satisfies the following criteria:\n\n(a) Every digit is either 0, 1, or 2.\n\n(b) Out of ev... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "\n2. Two circles $k_{a}$ and $k_{b}$ are given, whose centers lie on the legs of lengths a and b, respectively, of a right triangl... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. A father has five sons, all of different ages. The father has a certain amount of money that he wants to divide among his five ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "93. A small train puzzle. The express from Basltown to Ironchester travels at a speed of 60 km/h, and the express from Ironchester... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 2. (a) Calculate\n\n$$\n\\int_{0}^{1} x \\sin \\left(\\pi x^{2}\\right) \\mathrm{d} x\n$$\n\n(b) Calculate\n\n$$\n\\lim _{... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "87. Bobo has 640 points, Guagua has 1000 points. Now both of them exchange their points for the same watch. As a result, the point... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Given positive numbers \\( x, y, z \\) such that \\( x + y + z = a \\) and \\( x^2 + y^2 + z^2 = \\frac{a^2}{2} \\) (where \\( a >... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. (3 points) The left figure below is the recently discovered Archimedes' \"Stomachion\" puzzle, dividing a square into 14 polygo... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "7.2. On his birthday, Nikita decided to treat his classmates and took 4 bags of candies to school, each containing the same number... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "For how many positive integers $n$ less than or equal to $1000$ is \\[(\\sin t + i \\cos t)^n=\\sin nt + i \\cos nt\\] true for al... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "An equilateral triangle is tiled with $n^2$ smaller congruent equilateral triangles such that there are $n$ smaller triangles alon... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "(a) Calculate the sum:\n\n$$\n\\frac{1}{2}+\\frac{1}{3}+\\frac{1}{6}\n$$\n\n(b) Calculate the sum:\n\n$$\n\\frac{1}{12}+\\frac{1}{... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Task Condition\n\nCalculate the volumes of solids formed by rotating figures bounded by the graphs of functions. The axis of ro... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "5. In $\\triangle A B C$, $\\angle B A C=90^{\\circ}, A C=A B=4$, point $D$ is inside $\\triangle A B C$, and $A D=\\sqrt{2}$. The... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 6.4. Misha made himself a homemade dartboard during the summer at the cottage. The round board is divided by circles into ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 11.4. A positive integer $a$ whose decimal representation has 2006 digits is called \"bad\" if 3 does not divide any integ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1.043. $\\frac{0.125 X}{\\left(\\frac{19}{24}-\\frac{21}{40}\\right) \\cdot 8 \\frac{7}{16}}=\\frac{\\left(1 \\frac{28}{63}-\\frac... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "19. (2006 Zhejiang Province High School Mathematics Party Competition Training Test) Given $a, b, c \\in \\mathbf{R}^{+}$, and sat... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Abdul goes to the market, where he exchanges goat's milk for honey. He can exchange 5 cans of goat's milk for 3 cans of honey. As ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "$\\begin{aligned} \\text { 8. } 1+\\frac{1}{1+2}+\\cdots+\\frac{1}{1+2+\\cdots+2010} \\\\ =\\end{aligned}$",
"role": "user"
... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "# 6. Problem 6\n\nIn triangle $A B C$, points $M$ and $N$ are chosen on sides $A B$ and $B C$ respectively, such that $A M=2 M B$ ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "60. A store purchased a batch of oranges. On the first day, it sold $40 \\%$, on the second day, it sold $50 \\%$ of the remaining... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 5. From point $O$ in rectangle $A B C D$, lines are drawn parallel to the sides of the rectangle, dividing it into four sm... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let $\\tau(n)$ denote the number of positive integer divisors of $n$. Find the sum of the six least positive integers $n$ that are... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "One, (20 points) Renovate a pedestrian path, changing the ground originally paved with $n^{2}-96$ identical square tiles to be pav... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Solve the inequality $(\\lg 20)^{2 \\cos x} > 1$ for $x \\in (0, \\pi)$.",
"role": "user"
},
{
"content": "<think>\nOk... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "# Problem 1. (2 points)\n\nLet $p_{1}, p_{2}, \\ldots, p_{97}$ be prime numbers (not necessarily distinct). What is the largest in... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "From a point \\(M\\) inside a regular tetrahedron, perpendiculars \\(M A_{i} (i=1,2,3,4)\\) are dropped to its faces. Prove that \... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "2. Given points\n$$\nA\\left(x-\\frac{3-\\sqrt{5}}{2} \\cdot y, 1\\right) 、 B\\left(x-\\frac{3+\\sqrt{5}}{2} \\cdot y,-1\\right)\n... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "12. Given a positive integer $m$ that satisfies $m^{2}+5 m+30$ is a perfect square. Then the value of $m$ is $\\qquad$ .",
"ro... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "16. (15 points) Uncle Li contracted 12 mu of paddy fields, with a yield of 660 kilograms per mu. Aunt Lin contracted 2 mu less of ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "12. (15th American Mathematical Invitation Contest) Given that $a, b, c, d$ are non-zero real numbers, $f(x)=\\frac{a x+b}{c x+d} ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In a sequence of numbers, a term is called golden if it is divisible by the term immediately before it. What is the maximum possib... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "5. Given $\\odot O: x^{2}+y^{2}=1$ with a moving chord $A B=\\sqrt{3}$, and a moving point $P$ on $\\odot C:(x-2)^{2}+(y-3)^{2}=2$... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. The diagonal $\\overline{A C}$ of trapezoid $A B C D$ has a length of $13 \\mathrm{~cm}$. For the measurement numbers of the ot... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "A ball was floating in the water of a lake, forgotten. With the arrival of winter, the lake froze over completely, the ball was re... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 2. Masha wrote the numbers $4,5,6, \\ldots, 16$ on the board, and then erased one or several of them. It turned out that t... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Problem 6.7. The Amur and Bengal tigers started running in a circle at 12:00, each at their own constant speed. By 14:00, the Amur... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "3. The number n is the product of three different prime numbers. If we increase the two smaller ones by 1 and leave the largest on... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Task 2. (10 points) Calculate $\\left(\\frac{2}{3}-\\frac{4}{9}+\\frac{8}{27}-\\frac{16}{81}+\\ldots\\right) \\cdot\\left(\\frac{3... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let \\( n \\geq 5 \\) be an integer. There are \\( n \\) points in the plane, no three of them collinear. Each day, Tom erases one... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1.45. In a circle of radius $R$, two parallel chords are drawn on opposite sides of the center, one of which subtends an arc of $6... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The small animals in the forest are going on an outing. They form a line 40 meters long and move forward at a speed of 3 meters pe... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "C1. We consider sequences of integers $a_{1}, a_{2}, \\ldots, a_{n}$ consisting of $n$ integers. For a given $k \\leqslant n$, we ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In a triangle with side lengths \\(a\\), \\(b\\), and \\(c\\), if the angle opposite the side of length \\(a\\) is \\(60^\\circ\\)... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "9.5. Let $M$ - be a finite set of numbers (distinct). It is known that among any three of its elements, there will be two whose su... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In the quadrilateral \\(ABCD\\), it is known that \\(AB = BC\\) and \\(\\angle ABC = \\angle ADC = 90^\\circ\\). A perpendicular \... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "## Task Condition\n\nWrite the decomposition of vector $x$ in terms of vectors $p, q, r$:\n\n$x=\\{-19 ;-1 ; 7\\}$\n\n$p=\\{0 ; 1 ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "$[$ Classical combinatorics (miscellaneous).]\n\nIn a dark room, on a shelf, there are four pairs of socks of two different sizes ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "11.3. How many points are there on the hyperbola $y=\\frac{2013}{x}$ such that the tangent at these points intersects both coordin... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "3. Given two sets of numbers, set $A$ is: $1,2, \\cdots, 100$; set $B$ is: $1^{2}, 2^{2}, \\cdots, 100^{2}$. For a number $x$ in s... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "The base of a rectangular parallelepiped is a square with a side length of \\(2 \\sqrt{3}\\). The diagonal of a lateral face forms... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let \\( F(x) = |f(x) \\cdot g(x)| \\), where \\( f(x) = a x^{2} + b x + c \\) and \\( g(x) = c x^{2} + b x + a \\), with \\( x \\i... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "A computer program evaluates expressions without parentheses in the following way:\n\n1) First, it performs the multiplications an... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "6. In the Cartesian coordinate system $x O y$, the ellipse $\\Gamma: \\frac{x^{2}}{4}+y^{2}=1$, point $L$ is in the third quadrant... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "20. Let $\\lfloor x\\rfloor$ be the greatest integer not exceeding $x$. For instance, $\\lfloor 3.4\\rfloor=3,\\lfloor 2\\rfloor=2... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "**假设我们有一个神秘的岛屿，岛屿上的居民遵循一定的规则。这些规则是：**\n\n**规则1：** 岛上只有两类居民，诚实者和骗子。诚实者总是说实话，骗子总是说谎话。 \n**规则2：** 诚实者知道自己是诚实者，骗子也知道自己是骗子。 \n**规则3：*... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "4. Every day, from Monday to Friday, the old man went to the blue sea and cast his net into the water. Each day, the net caught no... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "1. Given real numbers $a>0, b>0$, satisfying $a+\\sqrt{a}=2008, b^{2}+b=2008$. Then the value of $a+b$ is $\\qquad$",
"role": ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "In the room, there are 12 people; some of them are honest, meaning they always tell the truth, while the rest always lie. \"There ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "8. (3 points) The digits of a non-zero unit integer, when rearranged from right to left, form a new integer called the reverse num... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "Let \\( O \\), \\( A \\), and \\( B \\) be points in the plane. Show that\n\n\\[\n\\|\\overrightarrow{O A}\\|+\\|\\overrightarrow{... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "6. Let the side length of a regular $n$-sided polygon be $a$, and the longest and shortest diagonals be $b$ and $c$ respectively. ... |
[
{
"content": "You are a friendly assistant. When given a question, think step by step and reason about it before providing an answer.",
"role": "system"
},
{
"content": "观察字母。\n观察B、C、D、P、X这几个字母，你觉得哪一个字母与其它字母不同？",
"role": "user"
},
{
"content": "<think>\n嗯，用户问的是观察B、C、D、P、X这几个字母，找出哪一个与其他不同... |
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