conversations listlengths 3 3 |
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[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Twenty-five coins are being separated into piles in the following manner. First, they are... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The first term of a sequence is 934. Each following term is equal to the sum of the digit... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given the function \\( y = \\frac{\\sqrt{4 - x^2}}{\\lg (|x| + x)} \\), determine its dom... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find all extrema of the function \\( y = \\frac{2}{3} \\cos \\left(3x - \\frac{\\pi}{6}\\... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let $A=\\{1,2,3,\\ldots,40\\}$ . Find the least positive integer $k$ for which it is p... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given \\( x, y, z \\in \\mathbf{R}_{+} \\) and \\( n \\in \\mathbf{N}^{*} \\), prove that... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Xiaohu uses 6 equilateral triangles with side lengths of 1 to form shapes on a table with... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "\nUsing Abel's transformation, compute the following sums:\n\na) \\(\\sum_{k=1}^{n} k^{2}... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "A sequence of two distinct numbers is extended in two ways: one to form a geometric progr... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Two people, A and B, are collaborating to type a document. Initially, A types 100 charact... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "For all \\(a, b, c \\in \\mathbf{R}^{+}\\), find the minimum value of \\(\\frac{a}{\\sqrt... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The sum \\( A = \\left\\lfloor \\frac{8}{9} \\right\\rfloor + \\left\\lfloor \\frac{8^2}{... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Say that a 4-digit positive integer is *mixed* if it has 4 distinct digits, its leftmost ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Evaluate $\\sqrt{12 +\\!\\sqrt{12 + \\!\\sqrt{12 + \\!\\sqrt{12 + \\cdots}}}}$."
},
{... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In a sequence, each term after the first two terms is the mean of all the terms which com... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let $m$ and $n$ be two odd integers with $m, n \\geqslant 3$. In an $m \\times n$ grid, e... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let \\( a \\) and \\( b \\) be integers such that\n\n\\[ |a + b| > |1 + ab|. \\]\n\nProve... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let \\( a, b, c, \\) and \\( d \\) be four distinct positive real numbers that satisfy th... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The product \\( 29 \\cdot 28 \\) when \\( P \\) is divided by \\( D \\), the quotient is ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given a regular $n$-gon $A_{1} A_{2} \\ldots A_{n}$ on a plane:\n\na) Prove that if $n$ i... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In trapezoid \\(A B C D\\), the bases \\(A D\\) and \\(B C\\) are 8 and 18, respectively.... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The time on a digital clock is 5:55. How many minutes will pass before the clock next sho... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$. Find all ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let \\( A A_1 \\) be the median of triangle \\( ABC \\). Prove that angle \\( A \\) is ac... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find all monotonic and invertible functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find all strictly increasing functions \\( f: \\mathbb{N}^{*} \\rightarrow \\mathbb{N}^{*... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let $ABCD$ be a trapezoid and a tangential quadrilateral such that $AD || BC$ and $|... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let \\( O \\) be the point \\( (0,0) \\). Let \\( A, B, C \\) be three points in the plan... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "There are 100 points on a circle that are about to be colored in two colors: red or blue.... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "\nLet $\\Gamma_{1}$ and $\\Gamma_{2}$ be two circles such that $\\Gamma_{1}$ is tangent i... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Suppose that $a$ varies inversely with $b^2$. If $a=9$ when $b=2$, find the value of $a$ ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "A train passes a bystander in $t_{1}$ seconds, and at the same speed it crosses a bridge ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "A finite sequence of positive integers $ m_i$ for $ i\\equal{}1,2,...,2006$ are defin... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The first 9 positive odd integers are placed in the magic square so that the sum of the n... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find the point \\( M^{\\prime} \\) that is symmetric to the point \\( M \\) with respect ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "From five number cards $0, 2, 4, 6, 8$, three different cards are chosen to form a three-... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "On the sides \\(AB\\) and \\(BC\\) of triangle \\(ABC\\), equal segments \\(AE\\) and \\(... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Determine the number of solutions to\n\\[2\\sin^3 x - 5 \\sin^2 x + 2 \\sin x = 0\\]in th... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "On a checkered board of size 2016 by 2017 which is painted alternately with gold and silv... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given a pentagonal prism \\(P\\) with the upper base being the pentagon \\(A_1 A_2 A_3 A_... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "We consider \\( n \\) numbers each being 1 or -1 on a board. We take two of them and repl... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "A kilogram of one type of candy costs 80 kopecks more than another. Andrey and Yura bough... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The first three terms of an arithmetic progression are $x - 1, x + 1, 2x + 3$, in the ord... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let $\\Gamma$ be a circle with center $O$ and $P$ a point outside the circle. Let $A \\in... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "A rectangle can be divided into $n$ equal squares. The same rectangle can also be divid... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The magician Magimático calls three people from the audience: Ana, Beto, and Caio, to hel... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In how many ways can the number 1500 be represented as the product of three natural numbe... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given that \\( x, y, z \\) are distinct real numbers, and \\( x + \\frac{1}{y} = y + \\fr... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given \\( 2014 + y = 2015 + x = 2016 + z \\) and \\( y \\times x \\times z = 504 \\), fin... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Methanol can be gently oxidized with hot copper metal. What is(are) the product(s) of thi... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Define points on the plane with both coordinates as integers as lattice points. How many ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "If \\((x+y)^{2}-(x-y)^{2}=20\\), then \\(xy\\) is equal to:\n(a) 0\n(b) 1\n(c) 2\n(d) 5\n... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The numbers from 1 to 6 are to be placed at the intersections of three circles, one numbe... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "David, when submitting a problem for CMIMC, wrote his answer as $100\\tfrac xy$ , where ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The circle graph shown illustrates the results of a survey taken by the Fermat H.S. Stude... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "\nAre the vectors \\( c_{1} \\) and \\( c_{2} \\), constructed from the vectors \\( a \\)... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In \\(\\triangle ABC\\), \\(AB = 9\\), \\(BC = 8\\), and \\(AC = 7\\). The bisector of \\... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "For which \\( k \\in \\mathbb{N} \\) do there exist non-negative integers \\( a \\) and \... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "There are 2022 points marked on a line such that each two neighboring points are at the s... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let \\( x, y, z \\geq 0 \\) and \\( yz + zx + xy = 1 \\). Show that:\n\\[ x(1 - y)^2(1 - ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find the largest positive integer $N$ so that the number of integers in the set $\\{1,... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find the solutions of the system of equations\n\n$$\n\\begin{aligned}\na^{3}+3 a b^{2}+3 ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given $a_{1}, a_{2}, \\ldots, a_{n}$ as strictly positive real numbers, prove the geometr... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let \\( a, b, c \\) represent the lengths of the sides \\( BC, CA, AB \\) respectively in... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find a one-to-one correspondence between the open interval \\((0, 1)\\) and the closed in... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Seven friends have picked a total of one hundred mushrooms, each having picked a differen... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Prove that if the feet of the perpendiculars dropped from a point \\(M\\) in the plane of... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "176. \\(C\\) is a sufficient condition for \\(B\\), and \\(B\\) is a necessary condition ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In a grid rectangle of size \\(49 \\times 69\\), all \\(50 \\cdot 70\\) vertices of the c... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Ostap Bender, in an interview for a chess magazine about a simultaneous exhibition in Vas... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let \\( a_{n}=1-\\frac{1}{3}+\\frac{1}{5}-\\frac{1}{7}+\\ldots+(-1)^{n} \\frac{1}{2 n+1} ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Vasya has an unlimited supply of $1 \\times 1 \\times 3$ bars and corners made from three... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "\nGiven that \\( k \\) and \\( m \\) are real numbers, the inequality\n$$\n\\left|x^{2}-k... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find all positive integers \\( m \\) and \\( n \\) so that for any \\( x \\) and \\( y \\... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Scientists gathered at a congress, some of whom are friends. It turned out that any two o... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In an isosceles triangle, the length of each leg is $b$. The distance between the bases o... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Prove that if the real numbers \\( a, b, c \\) are each at least 2, then\n\n$$\n\\log _{b... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In a strange city called \"Impossibility City,\" people must include the word \"impossibl... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let the set \\( M = \\{x_1, x_2, \\cdots, x_{30}\\} \\) be composed of 30 distinct elemen... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Let $N$ be a positive integer. Kingdom Wierdo has $N$ castles, with at most one road ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "A shop sells the same type of pastries in two sizes of gift boxes: a large box costing 85... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In a large square room, two square carpets were brought in, with the side of one carpet b... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Compute the multiplicative inverse of $201$ modulo $299$. Express your answer as an integ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The positions of cyclists in the race are determined by the total time across all stages:... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find all real solutions to\n\\[\\frac{1}{(x - 1)(x - 2)} + \\frac{1}{(x - 2)(x - 3)} + \\... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given \\( a, b, c \\in \\mathbb{R}^{+} \\) and \\( abc = 1 \\) with \\( k \\geqslant 3 \\... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The edge length of cube \\( A B C D A_{1} B_{1} C_{1} D_{1} \\) is \\( a \\). Points \\( ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Given the acute angles $\\alpha, \\beta, \\gamma$ that satisfy $\\cos^2 \\alpha + \\cos^2... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Since \\( 24 = 3 + 5 + 7 + 9 \\), the number 24 can be written as the sum of at least two... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find the sum of all values of $x$ such that $2^{x^2-3x-2} = 4^{x - 4}$."
},
{
"ro... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "In the USA, standard letter-size paper is 8.5 inches wide and 11 inches long. What is th... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The feet of perpendiculars from the intersection point of the diagonals of cyclic quadril... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Petya colored one cell of a rectangle. Sasha can color other cells of this rectangle acco... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The distance between the roots of the quadratic polynomial \\(x^2 + px + q\\) is 1. Find ... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Prove that the product of two even or two odd functions is an even function."
},
{
... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "The decreasing sequence $a, b, c$ is a geometric progression, and the sequence $19a, \\fr... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "There are 60 people sitting at a large round table; each person is either a knight or a l... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Of the following sets, the one that includes all values of $x$ which will satisfy $2x - 3... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "Find the point \\( c \\) mentioned in Lagrange's theorem for the function \\( y = x^{2} +... |
[
{
"role": "system",
"value": "You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer."
},
{
"role": "user",
"value": "A circle $ \\Gamma$ is inscribed in a quadrilateral $ ABCD$ . If $ \\angle A\\equal{}... |
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