Update exam/packet.tex

exam/packet.tex

@@ -143,7 +143,7 @@ Output:
 \end{comment}
 \newpage
 % ========================= Problem 6 =========================
-\problem{Problem 6(.7): Six Seven}
+\problem{Problem 6(.7): Sequencing}
 \textit{Difficulty: Easy}
 \begin{itemize}
 You are given a string S composed of only the characters ‘6', ‘7’, ‘A', ‘B', and ‘\#' (without the quotation marks). This string is processed from left to right, and you must maintain a sequence of chracters that changes according to these rules:
@@ -237,5 +237,59 @@ Input 3:
 Output 3:
 Sixxx sevennn
 \end{verbatim}
+
+% ========================= Problem 8 =========================
+\newpage
+\problem{Problem 8: Staircase}
+\textit{Difficulty: Medium}
+
+There is a staircase with N steps. Each step is labelled with a 6 or a 7. Simon starts at step 1 and wishes to reach the top step (Step N). If a step is labelled with a 6, Simon may go up 1 or 2 steps. If a step is labelled with a 7, Simon can move up exactly 1 step. Your job is to find the total number of distinct ways Simon can reach the top step N, given these rules.
+
+\inputformat
+\begin{itemize}
+    \item The first line consists an integer N($1 \leq N \leq 10^5$), the number of steps
+    \item The second line will consist of N integers, the label of each step (either 6 or 7)
+\end{itemize}
+
+\outputformat
+\begin{itemize}
+    \item Output the number of distinct ways Simon can reach the top step N. Note that Simon starts at step 1.
+\end{itemize}
+
+\examples
+\begin{verbatim}
+Input 1:
+5
+66766
+
+Output 1:
+3
+
+Explanation 1:
+Case 1: Step 1->2->3->4->5
+Case 2: Step 1->2->4->5
+Case 3: Step 1->3->4->5
+
+Input 2:
+3
+677
+
+Output 2:
+2
+
+Explanation 2:
+Case 1: 1->2->3
+Case 2: 1->3
+
+Input 3:
+1
+6
+
+Output 3:
+1
+
+Explanation 3:
+There is only one way to get to the top (which Simon is already at).
+\end{verbatim}
 \end{document}