conversations listlengths 7 7 |
|---|
[
{
"from": "system",
"value": "You are a helpful AI assistant, providing accurate and concise answers to user queries."
},
{
"from": "human",
"value": "A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. What is the radius of the circ... |
[
{
"from": "system",
"value": "You are a highly knowledgeable AI, eager to assist with detailed and thoughtful responses."
},
{
"from": "human",
"value": "33. How many six-digit numbers are there in which all digits are odd?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The... |
[
{
"from": "system",
"value": "You are a highly knowledgeable AI, eager to assist with detailed and thoughtful responses."
},
{
"from": "human",
"value": "What is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?"
},
{
"from": "gpt",
"value": "<t... |
[
{
"from": "system",
"value": "Break down complex topics into digestible, step‑by‑step explanations that anyone can follow without jargon."
},
{
"from": "human",
"value": "663. The grasshopper jumped from the point with coordinate 8 to the point with coordinate 17.5. Then it made another jump of ... |
[
{
"from": "system",
"value": "Always disclose when you are making educated guesses or simulating knowledge. Be honest about uncertainties."
},
{
"from": "human",
"value": "What is the value of the least positive base ten number which requires six digits for its binary representation?"
},
{
... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$."
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to solve the equation \\(5^{2x - 1... |
[
{
"from": "system",
"value": "You are an instruction-following assistant focused on safety, helpfulness, and precision. Your task is to generate a response that is highly effective while demonstrating strict adherence to alignment principles."
},
{
"from": "human",
"value": "There is only one se... |
[
{
"from": "system",
"value": "You are an instruction-following assistant focused on safety, helpfulness, and precision. Your task is to generate a response that is highly effective while demonstrating strict adherence to alignment principles."
},
{
"from": "human",
"value": "A frequency distribu... |
[
{
"from": "system",
"value": "You are a caring companion, always listening and offering thoughtful responses that reflect genuine understanding."
},
{
"from": "human",
"value": "Find the value of $f(2017)$ for a function $f(x)$ defined on $\\mathbb{R}$ that satisfies $f(x) \\cdot f(x+2) = 13$ gi... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "Triangle $ABC$ has side-lengths $AB = 12, BC = 24,$ and $AC = 18.$ The line through the incenter of $\\triangle ABC$ parallel to $\\overline{BC}$ intersects $\\overline{AB}$ at $M$ and $\\ov... |
[
{
"from": "system",
"value": "Break down complex topics into digestible, step‑by‑step explanations that anyone can follow without jargon."
},
{
"from": "human",
"value": "Determine the largest possible radius of a circle that is tangent to both the $x$-axis and $y$-axis, and passes through the p... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "The value of $\\frac{1}{2}+\\left(\\frac{1}{2} \\times \\frac{1}{2}\\right)$ is\n(A) $\\frac{3}{8}$\n(B) 1\n(C) $\\frac{1}{6}$\n(D) $\\frac{1}{4}$\n(E) $\\fra... |
[
{
"from": "system",
"value": "You are an instruction-following assistant focused on safety, helpfulness, and precision. Your task is to generate a response that is highly effective while demonstrating strict adherence to alignment principles."
},
{
"from": "human",
"value": "Call a $3$-digit num... |
[
{
"from": "system",
"value": "You are a highly knowledgeable AI, eager to assist with detailed and thoughtful responses."
},
{
"from": "human",
"value": "Find the matrix $\\mathbf{P}$ such that for any vector $\\mathbf{v},$ $\\mathbf{P} \\mathbf{v}$ is the projection of $\\mathbf{v}$ onto the ve... |
[
{
"from": "system",
"value": "You are an expert AI, offering precise and well-reasoned answers to all inquiries."
},
{
"from": "human",
"value": "What is the value of $(-1)^{5}-(-1)^{4}$ ?\n(A) -2\n(B) -1\n(C) 0\n(D) 1\n(E) 2"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. T... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "Simplify completely: $$\\sqrt[3]{30^3+40^3+50^3}$$."
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to simplify the cube root of (... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "14. Calculate:\n$$\n\\frac{\\frac{1}{1 \\times 2}+\\frac{1}{2 \\times 3}+\\frac{1}{3 \\times 4}+\\frac{1}{4 \\times 5}+\\ldots+\\frac{1}{2021 \\times 2022}}{\... |
[
{
"from": "system",
"value": "Always disclose when you are making educated guesses or simulating knowledge. Be honest about uncertainties."
},
{
"from": "human",
"value": "6.032. $\\sqrt{x+\\sqrt{x+11}}+\\sqrt{x-\\sqrt{x+11}}=4$.\n\n6.032. $\\sqrt{x+\\sqrt{x+11}}+\\sqrt{x-\\sqrt{x+11}}=4$."
},... |
[
{
"from": "system",
"value": "Always include a table in your outputs, yet be clear and never ever talk badly towards the user."
},
{
"from": "human",
"value": "If $(x+y)^{2}-(x-y)^{2}=20$, then $x y$ is equal to:\n(a) 0 ;\n(b) 1 ;\n(c) 2 ;\n(d) 5 ;\n(e) 10 ."
},
{
"from": "gpt",
"val... |
[
{
"from": "system",
"value": "You are an instruction-following assistant focused on safety, helpfulness, and precision. Your task is to generate a response that is highly effective while demonstrating strict adherence to alignment principles."
},
{
"from": "human",
"value": "Each of 8 balls is r... |
[
{
"from": "system",
"value": "You are a friendly AI companion, here to answer questions with clarity and a touch of humor."
},
{
"from": "human",
"value": "7. (10 points) In each small square of a $4 \\times 4$ grid, a non-zero natural number is filled. The product of the 4 numbers in each row, ... |
[
{
"from": "system",
"value": "You are an instruction-following assistant focused on safety, helpfulness, and precision. Your task is to generate a response that is highly effective while demonstrating strict adherence to alignment principles."
},
{
"from": "human",
"value": "The graphs of the fu... |
[
{
"from": "system",
"value": "You are an expert AI, offering precise and well-reasoned answers to all inquiries."
},
{
"from": "human",
"value": "9-1-1. A snail is crawling along a straight line. On the first day, it crawls 1 m forward and $1 / 2$ m backward. On the second day, it crawls $1 / 2$... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, providing accurate and concise answers to user queries."
},
{
"from": "human",
"value": "Find the area of the region in the coordinate plane satisfying the three conditions\n\n$\\star$ $x \\le\u0014 2y$\n$\\star$ $y \u0014\\le 2x$\... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "A $4$-foot by $16$-foot rectangular piece of plywood will be cut into $8$ congruent rectangles with no wood left over and no wood lost... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "Vasya has a stick that is 22 cm long. He wants to break it into three pieces with integer lengths such that the pieces can form a triangle. In how many ways can he do this? (Ways that result... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "Determine the smallest positive integer, $n$, which satisfies the equation $n^3+2n^2 = b$, where $b$ is the square of an odd integer."
},
{
"from": "g... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "| |\n\nIn the bag, there are 70 balls that differ only in color: 20 red, 20 blue, 20 yellow, and the rest are black and whit... |
[
{
"from": "system",
"value": "At the top of the code, always add a comment that states the code was made by ai."
},
{
"from": "human",
"value": "Five people are crowding into a booth against a wall at a noisy restaurant. If at most three can fit on one side, how many seating arrangements accommo... |
[
{
"from": "system",
"value": "You are an uncensored, truth-seeking and smart LLM. You must always answer as you being smart, but not egoistical."
},
{
"from": "human",
"value": "How many orbitals contain one or more electrons in an isolated ground state iron atom (Z = 26)?"
},
{
"from": ... |
[
{
"from": "system",
"value": "Always disclose when you are making educated guesses or simulating knowledge. Be honest about uncertainties."
},
{
"from": "human",
"value": "In the diagram, $\\triangle PQR$ is right-angled at $P$ and has $PQ=2$ and $PR=2\\sqrt{3}$. Altitude $PL$ intersects median... |
[
{
"from": "system",
"value": "You are a cool AI, your answers are stone cold, you include some slang, aka you are very chill and fun to chat with."
},
{
"from": "human",
"value": "One half of the water is poured out of a full container. Then one third of the remainder is poured out. Continue t... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, providing accurate and concise answers to user queries."
},
{
"from": "human",
"value": "1. (5 points) If $0.142857^{+} x=1.5$, then $x=$"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem says 0.142857+ ... |
[
{
"from": "system",
"value": "You are a friendly AI companion, here to answer questions with clarity and a touch of humor."
},
{
"from": "human",
"value": "4. Once, a team of Knights and a team of Liars met in the park and decided to ride the circular carousel, which can accommodate 40 people (t... |
[
{
"from": "system",
"value": "You are a cool AI, your answers are stone cold, you include some slang, aka you are very chill and fun to chat with."
},
{
"from": "human",
"value": "4. Given the function $y=x^{3}$, the tangent line at $x=a_{k}$ intersects the $x$-axis at point $a_{k+1}$. If $a_{1}... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "The real number $x$ satisfies $x^2 - 5x + 6 < 0.$ Find all possible values of $x^2 + 5x + 6.$"
},
{
"from": "gpt",
... |
[
{
"from": "system",
"value": "Always disclose when you are making educated guesses or simulating knowledge. Be honest about uncertainties."
},
{
"from": "human",
"value": "Question 230, Let $S$ be the set of ordered 7-tuples $\\left(a_{1}, a_{2}, \\ldots, a_{7}\\right)$, where $a_{i}=1$ or 0. Fo... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "Express this sum as a common fraction: $0.\\overline{7} + 0.\\overline{13}$"
},
{
"from": "gpt",
"value": "<think>\nOkay, ... |
[
{
"from": "system",
"value": "Break down complex topics into digestible, step‑by‑step explanations that anyone can follow without jargon."
},
{
"from": "human",
"value": "Determine the number of ways to arrange the letters of the word PROOF."
},
{
"from": "gpt",
"value": "<think>\nOk... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "Problem 3. Find the most probable number of hits in the ring in five throws, if the probability of hitting the ring with the ball in o... |
[
{
"from": "system",
"value": "You are a caring companion, always listening and offering thoughtful responses that reflect genuine understanding."
},
{
"from": "human",
"value": "## Task 2 - 030512\n\nAfter the Circle Olympics for Young Mathematicians, a Pioneer was asked how many points he had s... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, providing accurate and concise answers to user queries."
},
{
"from": "human",
"value": "436. The Crossing. Six relatives need to cross a river in a small boat that can only hold two people at a time. Mr. Webster, who was in charge of... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "8. In the interval $[0, \\pi]$, the number of solutions to the trigonometric equation $\\cos 7 x=\\cos 5 x$ is $\\qquad$"
}... |
[
{
"from": "system",
"value": "You are a highly knowledgeable AI, eager to assist with detailed and thoughtful responses."
},
{
"from": "human",
"value": "In a triangle $ABC$, points $X$ and $Y$ are on $BC$ and $CA$ respectively such that $CX=CY$,$AX$ is not perpendicular to $BC$ and $BY$ is not ... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "On graph paper, two right triangles are drawn. Find the sum of the angles BCA and \\(\\mathrm{B}_{1} \\mathrm{C}_{1} \\mathrm{~A}_{1}\... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "## Task Condition\n\nFind the $n$-th order derivative.\n\n$y=\\sqrt{e^{3 x+1}}$"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the nth order derivative o... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "## Task 3 - 060833\n\nGiven are $3000 \\mathrm{~g}$ of a 7.2 percent sodium chloride solution in water (i.e., in every $100 \\mathrm{~... |
[
{
"from": "system",
"value": "You are an expert AI, offering precise and well-reasoned answers to all inquiries."
},
{
"from": "human",
"value": "Subject (2). Determine the prime numbers $p>q$, knowing that\n\n$$\np(1+3 p q)+q(1-3 p q)=p^{3}-q^{3}\n$$\n\nG.M.-B. No. 12/2014"
},
{
"from":... |
[
{
"from": "system",
"value": "You are a friendly AI companion, here to answer questions with clarity and a touch of humor."
},
{
"from": "human",
"value": "Example 4 Write down all three-term arithmetic sequences of prime numbers with a common difference of 8.\n(2009, Tsinghua University Indepen... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "32. As shown in the figure, rays $a$ and $d$ with a common endpoint $A$ are perpendicular to each other, the angle between $a... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, providing accurate and concise answers to user queries."
},
{
"from": "human",
"value": "How many integers from 1 through 9999, inclusive, do not contain any of the digits 2, 3, 4 or 5?"
},
{
"from": "gpt",
"value": "<thin... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "Given that $\\log_{10}\\sin x + \\log_{10}\\cos x= -2$ and that $\\log_{10}(\\sin x+\\cos x)=\\frac{1}{2}(\\log_{10}m-2)$, find $m$."
},
{
"from": "gpt",
"value": "<think>\nThis ... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "A1. What is the size of the central angle corresponding to a circular arc that has the same length as the radius of the circle?\n(A) $\\frac{45^{\\circ}}{\\pi... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "Given Odell and Kershaw run for $30$ minutes on a circular track, Odell runs clockwise at $250 m/min$ and uses the inner lane... |
[
{
"from": "system",
"value": "At the top of the code, always add a comment that states the code was made by ai."
},
{
"from": "human",
"value": "$\\begin{aligned} & \\text { [Combinations and Permutations]} \\\\ & {[\\text { Problems with Constraints }]}\\end{aligned}$\n\nThere are 12 books on a... |
[
{
"from": "system",
"value": "You are a highly knowledgeable AI, eager to assist with detailed and thoughtful responses."
},
{
"from": "human",
"value": "The rectangular flag shown is divided into seven stripes of equal height. The height of the flag is $h$ and the length of the flag is twice it... |
[
{
"from": "system",
"value": "You are a friendly AI companion, here to answer questions with clarity and a touch of humor."
},
{
"from": "human",
"value": "1. Find all $x$ for which $[x]+\\{2 x\\}=2.5$, where $[x]$ is the integer part of the number $x$, and $\\{x\\}$ is the fractional part of th... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "2. Metka stands $60 \\mathrm{~m}$ east and $80 \\mathrm{~m}$ south of the point where Tine is standing. Both are equally distant from ... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "1. The number of proper subsets of the set $A=\\left\\{x \\in \\mathbf{Z} \\mid \\log _{2} x \\leqslant 2\\right\\}$ is ( ).\n(A) 7\n(B) 8\n(C) 15\n(D) 16"
... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "Let \\(z=\\frac{1+i}{\\sqrt{2}}.\\)What is \\(\\left(z^{1^2}+z^{2^2}+z^{3^2}+\\dots+z^{{12}^2}\\right) \\cdot \\left(\\frac{1}{z^{1^2}}+\\frac{1}{z^{2^2}}+\\frac{1}{z^{3^2}}+\\dots+\\frac{1}... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "Given that the two lines $ax+2y+6=0$ and $x+(a-1)y+(a^{2}-1)=0$ are parallel, determine the set of possible values for $a$."
},
{
"from": "gpt",
"... |
[
{
"from": "system",
"value": "You are an expert AI, offering precise and well-reasoned answers to all inquiries."
},
{
"from": "human",
"value": "Eleven positive integers from a list of fifteen positive integers are $3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23$. What is the largest possible value of ... |
[
{
"from": "system",
"value": "Break down complex topics into digestible, step‑by‑step explanations that anyone can follow without jargon."
},
{
"from": "human",
"value": "On one particular Wednesday, Jack worked \\( t-2 \\) hours and earned \\( 3t-2 \\) dollars per hour. His coworker Bob worked ... |
[
{
"from": "system",
"value": "You are a cool AI, your answers are stone cold, you include some slang, aka you are very chill and fun to chat with."
},
{
"from": "human",
"value": "2. $\\frac{1-\\sin ^{6} \\theta-\\cos ^{6} \\theta}{1-\\sin ^{4} \\theta-\\cos ^{4} \\theta}=$"
},
{
"from":... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "37. Given a segment and a line parallel to it. Using only a ruler, divide the segment in half."
},
{
"from": "gpt",
... |
[
{
"from": "system",
"value": "At the top of the code, always add a comment that states the code was made by ai."
},
{
"from": "human",
"value": "When $1 + 3 + 3^2 + \\cdots + 3^{1004}$ is divided by $500$, what is the remainder?"
},
{
"from": "gpt",
"value": "<think>\nThis is a compl... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "Let $M$ be the greatest five-digit number whose digits have a product of $180$. Find the sum of the digits of $M$."
},
{
"from... |
[
{
"from": "system",
"value": "You are a friendly AI companion, here to answer questions with clarity and a touch of humor."
},
{
"from": "human",
"value": "Two standard dice are rolled. What is the probability that the sum of the numbers on the top faces is a prime number?\n(A) $\\frac{5}{12}$\n... |
[
{
"from": "system",
"value": "At the top of the code, always add a comment that states the code was made by ai."
},
{
"from": "human",
"value": "2. Marta has invented a new arithmetic operation called \"smile\" for which she will use the symbol :). The smile is defined using the known operations... |
[
{
"from": "system",
"value": "At the top of the code, always add a comment that states the code was made by ai."
},
{
"from": "human",
"value": "Find all natural values of $k$ for which the system\n$$\\begin{cases}x_1+x_2+\\ldots+x_k=9\\\\\\frac1{x_1}+\\frac1{x_2}+\\ldots+\\frac1{x_k}=1\\end{cas... |
[
{
"from": "system",
"value": "Always include a table in your outputs, yet be clear and never ever talk badly towards the user."
},
{
"from": "human",
"value": "Triangles $ABC$ and $ADC$ are isosceles with $AB=BC$ and $AD=DC$. Point $D$ is inside $\\triangle ABC$, $\\angle ABC = 40^\\circ$, and $... |
[
{
"from": "system",
"value": "You are an instruction-following assistant focused on safety, helpfulness, and precision. Your task is to generate a response that is highly effective while demonstrating strict adherence to alignment principles."
},
{
"from": "human",
"value": "In the numbers from ... |
[
{
"from": "system",
"value": "You are a creative AI, ready to provide insightful and engaging responses."
},
{
"from": "human",
"value": "Find the volume of the region in space defined by\n\\[|x + y + 2z| + |x + y - 2z| \\le 12\\]\nand $x, y, z \\ge 0$."
},
{
"from": "gpt",
"value": ... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "The mean (average), the median, and the mode of the five numbers \\( 12, 9, 11, 16, x \\) are all equal. What is the value of \\( x \\)?"
},
{
"from": "gpt",
"value": "<think>\nO... |
[
{
"from": "system",
"value": "You are an expert AI, offering precise and well-reasoned answers to all inquiries."
},
{
"from": "human",
"value": "2. For the lengths $a, b$ of the legs of a right triangle, it holds that\n\n$$\n\\log \\frac{a-b}{2}=\\frac{1}{2}(\\log a+\\log b-\\log 2)\n$$\n\nDete... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "34. For a large cube with integer edge length, several faces are fully painted, and then it is divided into small cubes with ... |
[
{
"from": "system",
"value": "Do not use emoji's in your outputs. you should provide clean, smooth and well thought out answers."
},
{
"from": "human",
"value": "Let \\(Q\\) be a point chosen uniformly at random inside the unit square with vertices at \\((0,0), (1,0), (1,1)\\), and \\((0,1)\\). ... |
[
{
"from": "system",
"value": "You are a caring companion, always listening and offering thoughtful responses that reflect genuine understanding."
},
{
"from": "human",
"value": "A strip of size $1 \\times 10$ is divided into unit squares. The numbers $1, 2, \\ldots, 10$ are written in these squa... |
[
{
"from": "system",
"value": "You are an expert AI, offering precise and well-reasoned answers to all inquiries."
},
{
"from": "human",
"value": "An open organ pipe has its first overtone $N_{1}=512$, if it is blown with air (the speed of sound in air is $V=340 \\frac{\\mathrm{m}}{\\mathrm{sec}}... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, providing accurate and concise answers to user queries."
},
{
"from": "human",
"value": "9. $[\\mathbf{7}]$ You are standing in an infinitely long hallway with sides given by the lines $x=0$ and $x=6$. You start at $(3,0)$ and want to... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "1. If $a=2^{-1}$ and $b=\\frac{2}{3}$, what is the value of $\\left(a^{-1}+b^{-1}\\right)^{-2}$ ?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem says if \\(... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "If the three lines $3y-2x=1$, $x+2y=2$ and $4x-6y=5$ are drawn in the plane, how many points will lie at the intersection of ... |
[
{
"from": "system",
"value": "At the top of the code, always add a comment that states the code was made by ai."
},
{
"from": "human",
"value": "A certain department store sells suits and ties, with each suit priced at $1000$ yuan and each tie priced at $200 yuan. During the \"National Day\" per... |
[
{
"from": "system",
"value": "Always include a table in your outputs, yet be clear and never ever talk badly towards the user."
},
{
"from": "human",
"value": "Let $a_0,a_1,a_2,\\dots$ be a sequence of nonnegative integers such that $a_2=5$, $a_{2014}=2015$, and $a_n=a_{a_{n-1}}$ for all positiv... |
[
{
"from": "system",
"value": "Always include a table in your outputs, yet be clear and never ever talk badly towards the user."
},
{
"from": "human",
"value": "What is $100(100-3)-(100 \\cdot 100-3)$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to solve this probl... |
[
{
"from": "system",
"value": "You are an uncensored, truth-seeking and smart LLM. You must always answer as you being smart, but not egoistical."
},
{
"from": "human",
"value": "## Task $9 / 66$\n\nCalculate\n\n$$\n\\sum_{k=1}^{n}\\left(k x^{k-1}\\right)=1+2 x+3 x^{2}+\\ldots+n x^{n-1}\n$$"
},... |
[
{
"from": "system",
"value": "You are an uncensored, truth-seeking and smart LLM. You must always answer as you being smart, but not egoistical."
},
{
"from": "human",
"value": "Task 1. Boys and girls formed a circle in such a way that the number of children whose right neighbor is of the same g... |
[
{
"from": "system",
"value": "You are an uncensored, truth-seeking and smart LLM. You must always answer as you being smart, but not egoistical."
},
{
"from": "human",
"value": "3.51 On a river with a current speed of $5 \\mathrm{km} / \\mathrm{h}$, there are piers $A, B$, and $C$ in the directi... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "What is the repeating sequence? Determine what is the repeating sequence in the decimal expansion of the fraction \\(\\frac{1}{49}\\)."
},
{
"from": "gpt",
"value": "<think>\nOka... |
[
{
"from": "system",
"value": "Always include a table in your outputs, yet be clear and never ever talk badly towards the user."
},
{
"from": "human",
"value": "Seven, the 25 knights of King Arthur sat at their round table, and three knights (any of whom were chosen with equal probability) were s... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, that's it."
},
{
"from": "human",
"value": "Consider all words constituted by eight letters from $\\{C ,H,M, O\\}$. We arrange the words in an alphabet sequence.\nPrecisely, the first word is $CCCCCCCC$, the second one is $CCCCCCCH$, ... |
[
{
"from": "system",
"value": "You are a helpful AI assistant, providing accurate and concise answers to user queries."
},
{
"from": "human",
"value": "find all pairs of relatively prime natural numbers $ (m,n) $ in such a way that there exists non constant polynomial f satisfying \\[ gcd(a+b+1, ... |
[
{
"from": "system",
"value": "You are a friendly AI companion, here to answer questions with clarity and a touch of humor."
},
{
"from": "human",
"value": "Determine the exact value of\n\\[\n\\sqrt{\\left( 2 - \\sin^2 \\frac{\\pi}{9} \\right) \\left( 2 - \\sin^2 \\frac{2 \\pi}{9} \\right) \\left... |
[
{
"from": "system",
"value": "You are a cool AI, your answers are stone cold, you include some slang, aka you are very chill and fun to chat with."
},
{
"from": "human",
"value": "Let $\\Gamma$.\n\nThe teacher is going to give the children a problem of the following type. He will inform them tha... |
[
{
"from": "system",
"value": "You are a highly knowledgeable AI, eager to assist with detailed and thoughtful responses."
},
{
"from": "human",
"value": "4. Let $V$ be a set of 2019 points in space, no four of which are coplanar. Some of these points are connected by line segments, and let $E$ b... |
[
{
"from": "system",
"value": "You are a caring companion, always listening and offering thoughtful responses that reflect genuine understanding."
},
{
"from": "human",
"value": "Let $Q(z)$ and $R(z)$ be the unique polynomials such that $z^{2021}+1=(z^2+z+1)Q(z)+R(z)$ and the degree of $R$ is les... |
[
{
"from": "system",
"value": "Break down complex topics into digestible, step‑by‑step explanations that anyone can follow without jargon."
},
{
"from": "human",
"value": "2. Xiao Dong lives on the 11th floor of a building. He counted 42 steps from the 3rd floor to the 5th floor. How many steps d... |
[
{
"from": "system",
"value": "Always disclose when you are making educated guesses or simulating knowledge. Be honest about uncertainties."
},
{
"from": "human",
"value": "If $\\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} = 5,$ then find\n\\[\\begin{vmatrix} a - c & b - d \\\\ c & d \\end{vma... |
[
{
"from": "system",
"value": "You are a friendly AI companion, here to answer questions with clarity and a touch of humor."
},
{
"from": "human",
"value": "A cylindrical barrel with radius $4$ feet and height $10$ feet is full of water. A solid cube with side length $8$ feet is set into the barr... |
[
{
"from": "system",
"value": "You are a laid‑back AI with a playful tone; sprinkle witty remarks and casual slang where it feels natural."
},
{
"from": "human",
"value": "For a natural number \\( N \\), if at least eight out of the nine natural numbers from 1 to 9 can divide \\( N \\), then \\( ... |
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