All problems are text-only with mathematical notation in LaTeX. The following conventions are observed:
- \\(\\verb|amssymb|\\), \\(\\verb|amsmath|\\) and \\(\\verb|enumitem|\\) packages are used. No other package is assumed.
-  Variable names are given in math mode e.g. \\(a\\), \\(x\\), \\(y\\).
-  Integers such as 1, 2 can be outside of math mode or inside. Large integers such as \\(10^{50}\\) are in math mode.
-  \\(\\verb|itemize|\\) and \\(\\verb|enumerate|\\) environments may be used (with the latter using the conventions from the \\(\\verb|enumitem|\\) package).
-  Other environments such as \\(\\verb|\\begin{equation}|\\) are not used.
-  \\(\\mathtt{\\$}...\\mathtt{\\$}\\), \\(\\verb|\\ \(...\\ \)|\\), \\(\\verb|\\\[...\\\]|\\) may all be used for equations.
-  \\(\\verb|\\ldots|\\), \\(\\verb|\\cdots|\\), \\(\\verb|...|\\) can be used to continue a finite sequence or infinite.
-  Multiplication can be represented by simple adjacency \\(2x\\) or using LaTeX \\(\\verb|\\cdot|\\) command for \\(x \\cdot y\\) or LaTeX \\(\\verb|\\times|\\) command for \\(x \\times y\\).
-  \\(n!\\) for an integer represents the factorial function \\(n! = n\\cdot(n-1)\\cdot(n-2) \\cdots 2 \\cdot 1\\).
-  \\(\\log\\), \\(\\sin\\), \\(\\cos\\) are generally in math mode.
-  Fractions may be represented using \\(\\frac{a}{b}\\) or inline using \\(a/b\\).
-  \\(\\lvert x \\rvert\\) represents the absolute value of \\(x\\), eg, \\(\\lvert -2 \\rvert = 2\\).
-  Standard geometric notation is used such as the triangle \\(\\triangle ABC\\) with sides \\(AB\\), \\(BC\\), and \\(AC\\). Standard notation is also used for angles, eg, \\(\\angle ABC\\). Angles may be specified in degrees \\(\\angle ABC = 60^\\circ\\).
-  Standard trigonometric operators including \\(\\sin\\), \\(\\cos\\), \\(\\tan\\) may be used.
-  Sets are denoted using standard curly bracket notation, eg, \\(\\{1,2,3\\}\\).
-  \\(\\lfloor x \\rfloor\\) represents the integer part of the real number \\(x\\) ie the greatest integer less than or equal to \\(x\\). \\(\\lceil x \\rceil\\) represents the smallest integer greater than or equal to \\(x\\). \\(\\{x\\}\\) for a single value \\(x\\) refers to the fractional part of the real number \\(x\\) ie \\(x - \\lfloor x \\rfloor\\).
-  \\(\\verb|\\left|\\) and \\(\\verb|\\right|\\) may be used in conjunction with other LaTeX commands eg  \\(\\verb|\\left \\lceil \\frac{x}{2}\\right\\rceil|\\) producing \\(\\left \\lceil \\frac{x}{2}\\right\\rceil\\).
-  Overline notation \\(\\overline{abcd}\\) represents the integer formed by the digits \\(a\\),\\(b\\),\\(c\\),\\(d \\in \\{0, 1, \\ldots, 9\\}\\) with \\(a \\neq 0\\) eg with \\(a=1\\), \\(b=2\\): \\(\\overline{ab}=12\\)  and \\(\\overline{bab}=212\\).
-  \\(\\binom{a}{b}\\) is interpreted as the binomial coefficient, representing the number of ways of choosing \\(b\\) elements from a set of size \\(a\\).
-  \\(\\mathbb{N},\\mathbb{Z},\\mathbb{Q}\\), and \\(\\mathbb{R}\\) are used to denote the set of positive integers, integers, rational numbers, and real numbers, respectively (where positive means \\(>0\\)).
-  We allow informal probability language such as: a point is chosen uniformly at random in the interval \\([0, 1]\\).
-  The sum over the empty set is \\(0\\), and the product over the empty set is \\(1\\).
-  For integers \\(l\\), \\(m\\), and \\(n\\), \\(l^{m^n}\\) denotes \\(l^{\\left(m^n\\right)}\\).
-  British or American versions of English can be used. Thus ''highest common factor'' means the same as ''greatest common divisor''.
-  A prefix or subscript may be used to indicate features of a triangle associated with vertices. Thus triangle \\(ABC\\) has three altitudes, and the one dropped from \\(A\\) could be denoted the altitude through \\(A\\), the \\(A\\)-altitude or the altitude \\(h_a\\). Similarly, for median lines.
-  \\(:=\\) means 'is defined to be equal to'.
-  Note on taxonomy: An equilateral triangle is a specific type of isosceles triangle, a square is a specific type of rectangle, and a rectangle is a specific type of parallelogram, among other similar relationships.
-  The word *trapezium* can mean different things in different countries. For the purposes of this competition, a trapezium is a quadrilateral with at least one pair of parallel opposite sides.