\documentclass[11pt,
% twoside,
logo = {example-image},
% logo height = 1cm, % logo width = 2cm,
title in boldface,
% title in sffamily,
theorem in new line,
% remove qed,
colored solution,
]{homework}
%% For highlighting the code in this document
\usepackage{newverbs}
\newverbcommand{\cverb}{\color{red!50!orange}}{}
%% Below is the main document
\title{The Subject, Week 1}
\author{Author NAME}
% \date{\today, Location}
% \date{\today[only-year-month], Location}
\date{\TheDate{2024-01-01}, Location}
\begin{document}
\textcolor{gray!55}{(If you wish to write the answer directly...)}
\begin{problem}
Here lies the solution / proof.
\end{problem}
\bigskip\textcolor{gray!55}{(If you wish to state the problem and then write your answer...)}
\begin{problem}[Brief description]
You may also state the problem here...
\end{problem}
\begin{solution}
... and write the solution here...
\end{solution}
\bigskip\textcolor{gray!55}{(If you prefer \textquote{Proof} instead of \textquote{Solution}...)}
\begin{solution}[Proof]
... or a proof like this one...
\begin{lemma}[You may write some description here]\label{lem}
Some auxiliary result.
\end{lemma}
\begin{proof}
The proof of \cref{lem}, where we use the following formula (note the use of \cverb|\qedhere|):
\[
\infty = \infty + 1.
\qedhere % To place the Q.E.D. symbol in the right place.
\]
\end{proof}
\begin{fact}[This statement requires no proof]
\proofless
Use \cverb|\proofless| to change the hollow box marking the end of a theorem-type environment into a solid one.
\end{fact}
... and the rest steps...
\end{solution}
\bigskip\textcolor{gray!55}{(You may also write \texttt{answer} instead of \texttt{solution} if you wish...)}
\begin{answer}
The usage of the \verb|answer| environment is exactly the same as \verb|solution|.
\end{answer}
\bigskip\textcolor{gray!55}{(If you prefer the classical proof style...)}
\begin{proof}
The usual \verb|proof| environment also works.
\end{proof}
\bigskip\textcolor{gray!55}{(If you wish to answer each sub-question of a problem separately...)}
\begin{problem}[A problem with many sub-questions]
\begin{enumerate}
\item First question.
\begin{solution}
The solution of the first question.
\end{solution}
\item Second question.
\begin{enumerate}
\item First sub-question.
\begin{solution}
The solution of the first sub-question.
\end{solution}
\item Second sub-question.
\begin{solution}
The solution of the second sub-question.
\end{solution}
\end{enumerate}
\item Third question.
\begin{solution}
The solution of the third question.
\end{solution}
\end{enumerate}
Use \cverb|\noqed| (or \cverb|\noQED|) at the end to suppress the Q.E.D. symbol that marks the end of the current problem.
\noQED
\end{problem}
\bigskip\textcolor{gray!55}{(If you wish to number the exercise manually...)}
\ManualNumbering{exercise}{A.1.1}
\begin{exercise}[An exercise with custom numbering]
Use \cverb|\ManualNumbering| to manually set the numbering. This number will only be applied to the next specified environment.
\end{exercise}
\begin{exercise}
Back to normal numbering.
\end{exercise}
\bigskip\textcolor{gray!55}{(If there is a question that you can't figure out how to solve at the moment...)}
\DNF
\end{document}