Added passing warmup

Misc/Warm-Ups/passing.tex

@@ -0,0 +1,47 @@
+\documentclass[
+	solutions,
+	singlenumbering,
+	nopagenumber
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+
+\usepackage{graphicx}
+
+\title{Warm-Up: Passing balls}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today}
+
+\begin{document}
+
+	\maketitle
+
+	\problem{}
+
+	Twelve people are standing in a circle. Each is assigned a number between 1 and 12. \par
+	Participants numbered 1, 2, 3, and 4 hold red, green, yellow, and black balls, respectively. \par
+	Everyone else is empty-handed.
+
+	\vspace{2mm}
+
+	Each participant can pass their ball to any student that is exactly 5 positions away. \par
+	Balls cannot be passed to someone who has one in hand.
+
+	\vspace{2mm}
+
+	After a number of passes, the first four participants again hold all the balls. \par
+	Participant 1 has a black ball. Which balls are held by participants 2, 3, and 4?
+
+	\begin{solution}
+		\begin{itemize}
+			\item the graph of possible moves is isomorphic to a circle (since 5 and 12 are coprime),
+			\item but the balls get passed around, so swapping the place of any two balls is not allowed. \\
+			Therefore, the balls will stay in their initial (cyclic) order:
+		\end{itemize}
+
+		\begin{center}
+			\includegraphics[width=\textwidth]{pass-sol.png}
+		\end{center}
+	\end{solution}
+
+
+\end{document}