Added mario kart warmup

Misc/Warm-Ups/mario.tex

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+\documentclass[
+	solutions,
+	hidewarning,
+	singlenumbering,
+	nopagenumber
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+
+
+\title{Warm-Up: Mario Kart}
+\subtitle{Prepared by \githref{Mark} on \today}
+
+
+\begin{document}
+
+	\maketitle
+
+	\problem{}
+	A standard Mario Kart cup consists of 12 players and four races. \par
+	Each race is scored as follows:
+	\begin{itemize}
+		\item 15 points are awarded for first place;
+		\item 12 for second;
+		\item and $(13 - \text{place})$ otherwise.
+	\end{itemize}
+	In any one race, no players may tie.
+	A player's score at the end of a cup is the sum of their scores for each of the four races.
+
+	\vspace{2mm}
+
+	An $n$-way tie occurs when the top $n$ players have the same score at the end of a round. \par
+	What is the largest possible $n$, and how is it achieved?
+
+	\begin{solution}
+		A 12-way tie is impossible, since the total number of point is not divisible by 12.
+
+		\vspace{2mm}
+
+		A 11-way tie is possible, with a top score of 28:
+		\begin{itemize}
+			\item Four players finish $1^\text{st}$, $3^\text{ed}$, $11^\text{th}$, and $12^\text{th}$;
+			\item Four players finish $2^\text{nd}$, $4^\text{th}$, $9^\text{th}$, and $10^\text{th}$;
+			\item Two players finish fifth twice and seventh twice,
+			\item One player finishes sixth in each race.
+		\end{itemize}
+		The final player always finishes eighth, with a non-tie score of 20.
+	\end{solution}
+
+\end{document}