--- a/cws/cw01.tex	Wed Aug 12 00:56:20 2020 +0100
+++ b/cws/cw01.tex	Sun Aug 23 14:39:58 2020 +0100
@@ -64,12 +64,12 @@
 \newpage
 \subsection*{Preliminary Part (3 Marks, file collatz.scala)}
 
-This part is about recursion. You are asked to implement a Scala program
-that tests examples of the \emph{$3n + 1$-conjecture}, also called
-\emph{Collatz
-conjecture}.\video{https://www.youtube.com./watch?v=LqKpkdRRLZw} This
-conjecture can be described as follows: Start with any positive number
-$n$ greater than $0$:
+This part is about function definitions and recursion. You are asked
+to implement a Scala program that tests examples of the
+\emph{$3n + 1$-conjecture}, also called \emph{Collatz
+  conjecture}.\video{https://www.youtube.com./watch?v=LqKpkdRRLZw}
+This conjecture can be described as follows: Start with any positive
+number $n$ greater than $0$:
 
 \begin{itemize}
 \item If $n$ is even, divide it by $2$ to obtain $n / 2$.
@@ -134,7 +134,7 @@
   power of two is reached.  For this, implement an
   \textit{is-power-of-two} function which tests whether a number is a
   power of two. The easiest way to implement this is by using the
-  bit-operator $\&$. For a power of two, say $n$ with $n > 0$, it
+  bit-operator $\&$ of Scala. For a power of two, say $n$ with $n > 0$, it
   holds that $n \;\&\; (n - 1)$ is equal to zero. I let you think why
   this is the case. The function \textit{is-hard} calculates whether
   $3n + 1$ is a power of two.  Finally the \textit{last-odd} function
@@ -151,7 +151,7 @@
 \end{itemize}
 
 \noindent
-\textbf{Test Data:} Some test ranges are:
+\textbf{Test Data:} Some test ranges and cases are:
 
 \begin{itemize}
 \item 1 to 10 where $9$ takes 19 steps 
@@ -162,6 +162,9 @@
 \item 1 to 1 Million where $837,799$ takes 524 steps
   %% runs out of stack space
   %% \item[$\bullet$] $1 - 10$ million where $8,400,511$ takes 685 steps
+\item 21 is the last odd number for 84
+\item 341 is the last odd number for 201, 604, 605 and 8600
+  
 \end{itemize}