\documentclass{article}
    % Document metadata. I don't really want to have an author or
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    \title{CSE 311: \LaTeX{} Workshop; practice problems}
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\begin{document}

\maketitle

% Try experimenting with using \section{...} vs \section*{...}!

\section*{Question 1: Celebration?}

This year is the 311st anniversary of CSE 311. We have decided to buy a cake
for the celebration. Nicole ate a \textbf{quarter} of the slices, Jefferson 
ate \textbf{half} of them, and Andrew crashed the party and stole a
\textbf{sixth} of the total slices. After these three TAs took their slices,
there were only \textbf{three} slices left for the other TAs.

How many slices was the cake originally divided into? Be sure to show your 
work.

\section*{Question 2: Propositional Logic}

\begin{enumerate}[label=(\alph*)]
    \item Consider the following sentence:

        \begin{center}
            ``If I know \LaTeX{}, then I can write fancy papers or homework 
            assignments."
        \end{center}

        Define propositional variables for each atomic clause and translate
        the sentence into logical notation.

    \item Write out a truth table for your proposition from part (a).

    \item Draw your propositional statement from part (a) as a circuit.
        You should use the Law of Implication to convert all implications
        into disjunctions first.

        \LaTeX{} hint! Since typesetting circuits can be difficult,
        try a different program to draw the circuit visually! (You can
        find free websites online that let you do this, use MS paint, etc). 
        Once you're done, save the circuit as an image, and embed the image 
        within your document.

        Alternatively, if you want a challenge and use \LaTeX{} for 
        everything, try using the Circuitikz package.

    \item Write a Java method that accepts true/false values for $p$, $q$, 
        and $r$ as parameters, and returns the result of evaluating the
        proposition from part (a).

    \item \textbf{Challenge question:} Prove that your proposition is 
        equivalent to $\neg q \rightarrow (p \rightarrow r)$ using the rules 
        from today's lecture handout (e.g. associativity, commutivity, 
        absorption, domination, law of implication, etc).

        If you're not sure how to do this, we'll be covering this on
        Friday and Monday!
\end{enumerate}

\section*{Question 3: Simplification}

Simplify the equation $6(3p - 2) - (5p + 1)(2p + 2)$. Take small steps, and
briefly justify each step you take.

\section*{Question 4: Sneak Peek}

If $n$ is a positive integer (that is, if $n \in \N$), explain why dividing
$n(n + 1)(n + 2)$ by $6$ will always produce a positive integer.
You should attempt to explain why in English as rigorously as you can.

\section*{Question 5: Ymmy}

In honor of its new location, Dozen's Cupcakes is holding a party, where the
owners will give out lots of free cupcakes! A day before the party, they
notice that an employee was eating some of their cupcakes and fired him
on the spot.

As revenge for being fired, the former employee tainted one of the 30 batches
of cupcakes for the party with an undetectable poison. Eating even a piece
of the tainted cupcake would kill any living being in precisely 23 hours.
Several days ago, the owners caught five mice trying to get into their
kitchen, and they are willing to feed pieces of a single cupcake from each
batch to the mice to hopefully find the tainted one. 

Is it possible for them to find the tainted tray in time for the part in
24 hours? If so, how?

\end{document}
