Added stick section

Advanced/Knots/main.tex

@@ -38,6 +38,7 @@
 	\input{parts/0 intro.tex}
 	\input{parts/1 composition.tex}
 	\input{parts/2 links.tex}
+	\input{parts/3 sticks.tex}
 
 
 	% Make sure the knot table is on an odd page

Advanced/Knots/parts/2 links.tex

@@ -66,6 +66,7 @@ Find a Brunnian link with four components.
 Find a Brunnian link with $n$ components.
 
 \begin{solution}
+	One of many possible solutions:
 	\begin{center}
 		\includegraphics[width=40mm]{images/brunnian.png}
 	\end{center}

Advanced/Knots/parts/3 sticks.tex

@@ -0,0 +1,62 @@
+\section{Knots and Sticks}
+
+\definition{}
+The \textit{stick number} of a knot is the smallest number of \say{sticks} you must glue together to make the knot. An example of this is below.
+
+\begin{center}
+	\includegraphics[width=30mm]{images/sticks.png}
+\end{center}
+
+\problem{}
+Make the trefoil knot with sticks. \par
+How many do you need?
+
+\begin{solution}
+	\begin{center}
+		\includegraphics[width=20mm]{images/stick trefoil.png}
+	\end{center}
+\end{solution}
+
+\vfill
+
+\problem{}
+How many sticks will you need to make a figure-eight knot?
+
+\begin{solution}
+	The figure-eight knot has stick number 7. \par
+	In fact, this is the \textit{only} knot with stick number 7.
+\end{solution}
+
+\vfill
+\pagebreak
+
+\problem{}
+Make the knot $5_1$ (refer to the knot table) with eight sticks.
+
+\vfill
+
+\problem{}
+Show that the only nontrivial knot you can make with six sticks is the trefoil.
+
+\vfill
+
+\problem{}
+Let $S(k)$ be the stick number of a knot $k$. \par
+Show that $S(j \boxplus k) \leq s(j) + s(k) - 1$
+
+
+\vfill
+
+\problem{}
+What is the stick number of $(\text{trefoil} \boxplus \text{trefoil})$?
+
+\begin{solution}
+	You can make $(\text{trefoil} \boxplus \text{trefoil})$ with 8 sticks.
+
+	\begin{center}
+		\includegraphics[angle=90, width=40mm]{images/stick trefoil composition.png}
+	\end{center}
+\end{solution}
+
+\vfill
+\pagebreak