messages listlengths 3 3 |
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[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "How do you kill a god?\nA: theyre immortal\nB: being\nC: assassination\nD: be\nE: vidar",
"r... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A convex polyhedron is bounded by 4 regular hexagonal faces and 4 regular triangular faces. At e... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "What is $4+10\\div2-2\\cdot3$?",
"role": "user"
},
{
"content": "<think>\nTo solve $... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Each side and each segment \\(A_{i}B_{j} (i, j = 1, 2, \\cdots, 5)\\) of a polygon is either col... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "If for any real number \\( x \\), the function\n\\[ f(x)=x^{2}-2x-|x-1-a|-|x-2|+4 \\]\nalways yi... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "The sum of three terms of a geometric progression is 105. If 15 is subtracted from the third ter... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "When Scott completes the square on the quadratic $x^2 + 8x - 1 = 0$, he obtains an equation of t... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Given that $f(x), g(x)$, and $h(x)$ are real-coefficient polynomials and $f^2(x) = x g^2(x) + x ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose $z$ is an imaginary number, $\\omega = z + \\frac{1}{z}$ is a real number, and $-1 < \\o... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Kelvin the Frog is hopping on a number line (extending to infinity in both directions). Kelvin s... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Evaluate $\\lfloor -4 -.5 \\rfloor \\cdot \\lceil 4 +.5 \\rceil \\cdot \\lfloor -3 -.5 \\rfloor ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A solid wooden rectangular prism measures \\(3 \\times 5 \\times 12\\). The prism is cut in half... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Each cell of an $n \\times n$ chessboard, where $n \\geq 3$ is an integer, contains a lamp. Init... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "At each of the sixteen circles in the network below stands a student. A total of $3360$ coins ar... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Prove that there exists a nonzero complex number \\( c \\) and a real number \\( d \\) such that... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A chemistry student needs to identify an unknown compound using mass spectrometry. The compound ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A regular 12-gon is inscribed in a circle of radius 12. The sum of the lengths of all sides and ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "If the equation $m x^{2}-2(m+2) x+m+5=0$ has no real roots, then how many real roots does the eq... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "How does the gravitational pull of a black hole affect the orbit of a star located in its vicini... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "If the digit represented by $\\triangle$ satisfies the following addition problem $$ \\begin{arr... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In a geometric sequence of real numbers, the sum of the first $2$ terms is $7$, and the sum of t... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In triangle $ABC$ , $AD$ is angle bisector ( $D$ is on $BC$ ) if $AB+AD=CD$ and $AC+AD=B... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Simplify\n\\[\\tan x + 2 \\tan 2x + 4 \\tan 4x + 8 \\cot 8x.\\]The answer will be a trigonometri... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Can the sum of a finite number of terms of a geometric progression equal zero?",
"role": "us... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, $\\angle ABC=45^\\circ$. Point $D$ is on $\\overline{BC}$ so that $2\\cdot ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "For which positive integer values of \\( x \\) and \\( y \\) does the following equation hold?\n... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In this figure $\\angle RFS=\\angle FDR$, $FD=4$ inches, $DR=6$ inches, $FR=5$ inches, $FS=7\\df... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In a certain condominium, there are 29 families, each of which owns either one, three, or five c... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A pyramid \\( S A B C D \\) has a trapezoid \\( A B C D \\) as its base, with bases \\( B C \\) ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer. Prove that\n\\[\\sum_{i=1}^nx_i(1-x_i)^2\\le\\left(1-\\frac{1}{... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A line passing through vertex $A$ of triangle $ABC$ intersects side $BC$ at point $M$. Here, $BM... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Find all values of the parameter \\( a \\), for which the common solutions of the inequalities \... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "The positive numbers \\(A\\), \\(B\\), \\(C\\), and \\(D\\) are such that the system of equation... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "What is the Hall conductivity in a two-dimensional electron gas under the influence of a magneti... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "\nTetrahedron \\(ABCD\\) has base \\( \\triangle ABC \\). Point \\( E \\) is the midpoint of \\(... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "What is the diameter of the circle inscribed in triangle $ABC$ if $AB = 11,$ $AC=6,$ and $BC=7$?... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Find the solution set to the equation \\(\\left( x^{2} - 5x + 5 \\right)^{x^{2} - 9x + 20} = 1\\... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Find the number of integers $c$ such that the equation \\[\\left||20|x|-x^2|-c\\right|=21\\]has ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "How many positive integers less than 10,000 have at most two different digits?\n",
"role": "... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A goat eats 1 cartload of hay in 6 weeks, a sheep in 8 weeks, and a cow in 3 weeks. How many wee... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Solve for t: $3 \\cdot 3^t + \\sqrt{9 \\cdot 9^t} = 18$.",
"role": "user"
},
{
"cont... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A right triangle has an area of 120 square units, and a leg length of 24 units. What is the peri... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "The products by four and by five of an integer, when considered together, use each digit from 1 ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $ABCD$ be a trapezoid with the measure of base $AB$ twice that of base $DC$ , and let ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Given a positive integer \\( N \\), let \\( a_1, a_2, \\ldots, a_n \\) be \\( n \\) distinct pos... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "For four non-coplanar points, an equalizer plane is a plane such that the respective distances f... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Given \\( p_{1}, p_{2}, \\cdots, p_{25} \\) as 25 distinct prime numbers, each not exceeding 200... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let \\(a, b, c\\) be positive real numbers. Prove that \\(a^{2a} b^{2b} c^{2c} \\geqslant a^{b+c... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $\\theta$ be the angle between the line\n\\[\\frac{x + 1}{2} = \\frac{y}{3} = \\frac{z - 3}{... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a secon... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "\nContinue each row of the following table in both directions such that the sum of any 3 consecu... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "The circle $2x^2 = -2y^2 + 12x - 4y + 20$ is inscribed inside a square which has a pair of sides... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Which statement is correct?\n$\\mathrm{(A)\\ } \\text{If } x<0, \\text{then } x^2>x. \\qquad \\m... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Leibniz's theorem. Let $M$ be an arbitrary point in the plane, and $G$ be the centroid of triang... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $f(x)=x^4+14x^3+52x^2+56x+16$. Let $z_1,z_2,z_3,z_4$ be the four roots of $f$. Find the sm... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "The RSA Factoring Challenge, which ended in 2007, involved factoring extremely large numbers tha... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Given \\(\\tan \\alpha = \\sqrt{2} - 1\\), and the function \\(f(x) = x^2 \\tan 2\\alpha + x \\s... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Prove that \\(\\log _{a}\\left(x_{1} x_{2}\\right) = \\log _{a} x_{1} + \\log _{a} x_{2}\\).",
... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "One integer was removed from the set $S=\\left \\{ 1,2,3,...,n \\right \\}$ of the integers fr... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let lines \\( l_{1}: y=\\sqrt{3} x \\) and \\( l_{2}: y=-\\sqrt{3} x \\). Points \\( A \\) and \... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Given the sequence \\( a_1, a_2, a_3, \\cdots \\) where \\( a_1 = 1 \\) and \\( a_{n} = a_{n-1} ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking spa... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Calculate the area of the parallelogram formed by vectors $a$ and $b$.\n\n$$\n\\begin{aligned}\n... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "For which $n \\in \\mathbf{N}^{*}$ is $n \\times 2^{n+1} + 1$ a square?",
"role": "user"
}... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Find all numbers in the range of\n\\[f(x) = \\arctan x + \\arctan \\frac{1 - x}{1 + x},\\]expres... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A solid right prism $ABCDEF$ has a height of $16,$ as shown. Also, its bases are equilateral tri... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "An ellipse has foci $(2, 2)$ and $(2, 6)$, and it passes through the point $(14, -3).$ Given thi... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Triangle $ABC$ is isosceles with angle $B$ congruent to angle $C$. The measure of angle $C$ is f... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Segments \\(AD\\), \\(BD\\), and \\(CD\\) are pairwise perpendicular. It is known that the area ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In a certain set, an operation * is defined, which, for any two elements $a$ and $b$ in this set... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $U$ be a set consisting of $m$ triangles. Prove that there exists a subset $W$ of $U$ such t... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A six place number is formed by repeating a three place number; for example, $256256$ or $678678... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In the tetrahedron \\(A_{1} A_{2} A_{3} A_{4}\\), the circumradius is \\(R\\), and the volume is... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "On the blackboard, all natural numbers from 1 to 1988 are written. These numbers are alternately... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Two congruent cylinders each have radius 8 inches and height 3 inches. The radius of one cylinde... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let \\( m \\) be the smallest integer greater than \\( (\\sqrt{3} + 1)^{2n} \\). Show that \\( m... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "The set \\( A = \\left\\{ x \\left\\lvert\\, x = \\left\\lfloor \\frac{5k}{6} \\right\\rfloor \\... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "For each natural number \\( n \\), let \\( p(n) \\) denote the number of partitions of \\( n \\)... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Prove that when \\( m \\) is any natural number, \\( 1978^{m}-1 \\) cannot be divisible by \\( 1... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Generate an executable Python function generated from the given prompt. The function should take... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "In a non-obtuse triangle \\(ABC\\), prove the inequality:\n\n\\[\n\\frac{(1-\\cos 2A)(1-\\cos 2B... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A teacher writes five different possible values for \\((5^2 - 4^2)^3\\) on the board and asks he... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "The sum of the first $20$ positive even integers is also the sum of four consecutive even intege... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let's introduce the notations: \\( AB = 2c \\), \\( AC = 2b \\), and \\(\\angle BAC = \\alpha\\)... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $S$ be a set of $6$ integers taken from $\\{1,2,\\dots,12\\}$ with the property that if $a$ ... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "A finite number of red and blue lines are taken on the plane, none of which are parallel, so tha... |
[
{
"content": "You are a precise, helpful assistant. Always reason step by step inside <think></think> tags, then write your final answer inside <answer></answer> tags.",
"role": "system"
},
{
"content": "Triangle $ABC$ has sides of $6$ units, $8$ units, and $10$ units. The width of a rectangle, whos... |
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