\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{2025-01-01}, 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<some description>


\end{document}
