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%%% file:      s1.tex                                                        %%%
%%% author:    Ján Komara                                                    %%%
%%% email:     komara@fmph.uniba.sk                                          %%%
%%% copyright: public domain                                                 %%%
%%% version:   2019/10/01                                                    %%%
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\begin{document}

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\title{1. domáca úloha z predmetu 1-AIN-121 Matematika (1) ZS 2019/20}

\author{Ján Komara}

%\date{}
\date{\today}

\maketitle

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\section*{1. príklad}

Rovnako ako na prvej prednáške uvažujme digitálne hodiny, ktoré sú nastavené
na európsky 24-hodinový cyklus. Tie ukazujú denný časový údaj vo formáte
\emph{hodiny:minúty:sekundy}.
Tak napr. 12:22:34 je čas, ktorý sa na takýchto hodinách môže vyskytnúť.

Spočítajte, koľkokrát za deň sa na hodinách vyskytne časový údaj
\begin{align*}
H_1H_2:M_1M_2:S_1S_2
\end{align*}
taký, že
\begin{align*}
H_1 < H_2 \leq M_1 \leq M_2 < S_1 < S_2
.
\end{align*}

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\subsection*{Riešenie 1. príkladu}

Táto časť obsahuje riešenie 1. príkladu.

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\section*{2. príklad}

Spočítajte, koľko celočíselných riešení má nasledujúci systém pozostávajúci 
z jednej rovnice a jednej nerovnice:
\begin{align}
x_1 + x_2 + x_3 & = 11
\label{eq}
\\
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 & < 71
,
\label{lt}
\end{align}
ak
$-2 \leq x_1$,
$3 \leq x_2$,
$-4 \leq x_3$,
$-5 \leq x_4 \leq 5$,
$6 \leq x_5$,
$7 \leq x_6$
a
$-8 \leq x_7 \leq 8$.

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\subsection*{Riešenie 2. príkladu}

Táto časť obsahuje riešenie 2. príkladu.

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