\section{Bonus problems}


\problem{}
Make sense of the document on the next page. \par
What does it describe, and how does it work?


\problem{}
Given a table with a marked point, $O$, and with $2013$ properly working watches put down on the table, prove that there exists a moment in time when the sum of the distances from $O$ to the watches' centers is less than the sum of the distances from $O$ to the tips of the watches' minute hands.

\vfill


\problem{A Minor Inconvenience}
A group of eight friends goes out to dinner. Each drives his own car, checking it in with valet upon arrival.
Unfortunately, the valet attendant forgot to tag the friends' keys. Thus, when the group leaves the restaurant,
each friend is handed a random key.
\begin{itemize}
	\item What is the probability that everyone gets the correct set of keys?
	\item What is the probability that each friend gets the wrong set?
\end{itemize}

\vfill


\problem{Bimmer Parking}
A parking lot has a row of 16 spaces, of which a random 12 are taken. \par
Ivan drives a BMW, and thus needs two adjacent spaces to park. \par
What is the probability he'll find a spot?

\vfill
\pagebreak

\includepdf[
	pages=1,
	fitpaper=true
]{parts/qoi-specification.pdf}

\pagebreak