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%%% file:      s3.tex                                                        %%%
%%% author:    Ján Komara                                                    %%%
%%% email:     komara@fmph.uniba.sk                                          %%%
%%% copyright: public domain                                                 %%%
%%% version:   2020/10/14                                                    %%%
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\begin{document}

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\title{3. domáca úloha z predmetu 1-AIN-121 Matematika (1) ZS 2020/21}

\author{Ján Komara}

%\date{}
\date{\today}

\maketitle

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\section*{1. príklad}

Spočítajte, koľko celočíselných riešení má nasledujúca rovnica:
\begin{align*}
x_1 + x_2 + x_3 + x_4 + x_5 = 16
,
\end{align*}
kde
$-1 \leq x_1 \leq 1$,
$-2 \leq x_2 \leq 2$,
$-3 \leq x_3 \leq 3$,
$-4 \leq x_4 \leq 4$
a
$-5 \leq x_5$.

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\subsection*{Riešenie 1. príkladu}

Táto časť obsahuje riešenie 1. príkladu.

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\section*{2. príklad}

Na kolotoči sa vozí $6$ manželských párov.
Koľkými spôsobmi ich možno usadiť tak,
aby žiaden manžel nesedel bezprostredne za svojou manželkou?

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\subsection*{Riešenie 2. príkladu}

Táto časť obsahuje riešenie 2. príkladu.

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\end{document}

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