From 929a60898caa5213106430bcfc0401cab3c9d9f0 Mon Sep 17 00:00:00 2001
From: problsolv <stchung4@gmail.com>
Date: Sat, 22 Nov 2025 22:41:59 -0600
Subject: [PATCH] Update exam/packet.tex

---
 exam/packet.tex | 70 ++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 60 insertions(+), 10 deletions(-)

diff --git a/exam/packet.tex b/exam/packet.tex
index c141eee..b519ec9 100644
--- a/exam/packet.tex
+++ b/exam/packet.tex
@@ -6,7 +6,7 @@
 \usepackage{listings}
 \usepackage{xcolor}
 \usepackage{enumitem}
-\usepackage{comment}
+
 % Page layout
 \geometry{margin=1in}
 \pagestyle{fancy}
@@ -54,7 +54,7 @@
     \item For each problem, write a function or program according to the specified input/output format.
     \item Clearly comment your code if necessary.
 \end{enumerate}
-\begin{comment}
+
 % ========================= Problem 1 =========================
 \problem{Problem 1: Two Sum}
 \textit{Difficulty: Easy}
@@ -140,13 +140,13 @@ Output:
 8 10
 15 18
 \end{verbatim}
-\end{comment}
-% ========================= Problem 6 =========================
-\problem{Problem 6(.7): Six Seven}
-\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:
 
+% ========================= Problem 4 =========================
+\problem{Problem 4: Six Seven}
+\textit{Difficulty: Easy}
+
+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:
+\begin{itemize}
 \item 6 - add a 6 to the end of the sequence
 \item 7 - if the sequence is non-empty and its last chracter is ‘6', remove that last ‘6', otherwise, add ‘7' to the end of the sequence
 \item A - reverse the sequence
@@ -155,7 +155,7 @@ You are given a string S composed of only the characters ‘6', ‘7’, ‘A',
 \end{itemize}
 \inputformat
 \begin{itemize}
-    \item The first line consists of the string S. The string consists only of the characters 6, 7, A, B, and \#.
+    \item The first line consists of the string S ($1 \leq |S| \leq 2 * 10^5$). The string consists only of the characters 6, 7, A, B, and \#.
 \end{itemize}
 
 \outputformat
@@ -184,5 +184,55 @@ Output 3:
 EMPTY
 \end{verbatim}
 
-\end{document}
+% ========================= Problem 5 =========================
+\problem{Problem 5: Limited Jumps}
+\textit{Difficulty: Medium}
 
+You are given a grid of size N x M, where each cell contains either 6 or 7. You start at the top-left corner (1,1) and want to reach the bottom-right corner (N,M). You can move right, down, or jump diagonally (right+down). The maze has these rules:
+\begin{itemize}
+\item You can step on a 6 any number of times
+\item You can step on a 7 at most once in your path
+\item You can make at most one diagonal move in your path
+\end{itemize}
+
+Your task is to determine if there exists any valid path from (1,1) to (N,M) obeying the rules.
+
+\inputformat
+\begin{itemize}
+    \item The first line consists 2 integers N and M ($1 \leq N, M \leq 10^9$), the number of rows and columns, respectively
+    \item The next N lines will consist of strings of length M, containing 6 or 7
+\end{itemize}
+
+\outputformat
+\begin{itemize}
+    \item Output a single line. If there exists a valid path, print ``Sixxx sevennn" (without the quotations). If there does not exist a valid path, print ``Six was afraid of seven after all" (without the quotations).
+\end{itemize}
+
+\examples
+\begin{verbatim}
+Input 1:
+2 2
+66
+67
+
+Output 1:
+Sixxx sevennn
+
+Input 2:
+2 2
+77
+77
+
+Output 2:
+Six was afraid of seven after all
+
+Input 3:
+3 3
+666
+676
+666
+
+Output 3:
+Sixxx sevennn
+\end{verbatim}
+\end{document}
\ No newline at end of file