40 lines
1.2 KiB
TeX
40 lines
1.2 KiB
TeX
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\section{Bonus problems}
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\problem{}
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Make sense of the document on the next page. \par
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What does it describe, and how does it work?
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\problem{}
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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.
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\vfill
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\problem{A Minor Inconvenience}
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A group of eight friends goes out to dinner. Each drives his own car, checking it in with valet upon arrival.
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Unfortunately, the valet attendant forgot to tag the friends' keys. Thus, when the group leaves the restaurant,
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each friend is handed a random key.
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\begin{itemize}
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\item What is the probability that everyone gets the correct set of keys?
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\item What is the probability that each friend gets the wrong set?
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\end{itemize}
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\vfill
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\problem{Bimmer Parking}
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A parking lot has a row of 16 spaces, of which a random 12 are taken. \par
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Ivan drives a BMW, and thus needs two adjacent spaces to park. \par
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What is the probability he'll find a spot?
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\vfill
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\pagebreak
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\includepdf[
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pages=1,
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fitpaper=true
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]{parts/qoi-specification.pdf}
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\pagebreak
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