\begin{frame}
    \frametitle{\problemtitle}
    \begin{block}{Problem}
        \begin{itemize}
            \item Find the area of a hidden arbitrarily rotated square.
            \item Ask two query directions and receive the distances from square center to edge.
        \end{itemize}
    \end{block}

    \begin{block}{Solution}
        \begin{itemize}
            \item Query two directions $45$ degrees apart, i.e. $(1, 0)$ and $(1, 1)$.
            \item Assume the two points in those directions lie on one side of the square.
            \item Calculate minimum distance $d$ to that side (line), the answer is $(2d)^2$.
            \item Why is this correct?
        \end{itemize}
        \vspace{-1cm}
        \center
        \includegraphics[height=3cm]{figure1.pdf}
    \end{block}
    % \solvestats
\end{frame}

\begin{frame}
    \frametitle{\problemtitle}
    \begin{block}{Solution}
        \begin{itemize}
            \item Why is this correct?
            \item Note that a square has $90$ degree rotation symmetry.
            \item Specifically, direction $(-1, 1)$ gives the same distance as $(1, 1)$.
            \item Notice that either $(0, 0)$ and $(1, 1)$ lie on the same side, or $(0, 0)$ and $(-1, 1)$.
            \item So assuming $(0, 0)$ and $(1, 1)$ on same side results in correct area.
        \end{itemize}
        \center
        \includegraphics[height=4cm]{figure2.pdf}
    \end{block}
\end{frame}

\begin{frame}
    \frametitle{\problemtitle}
    \begin{block}{Wrong Solution}
        \begin{itemize}
            \item Just using two very close directions does not work, with given constraints, there can always be a corner in between.
        \end{itemize}
    \end{block}
    % \solvestats
\end{frame}
