Question 116
$$
\begin{array}{|c|c|c|c|}
\hline
a_1 & a_2 & a_3 & a_4 \\
\hline
a_5 & a_6 & a_7 & a_8 \\
\hline
a_9 & a_{10} & a_{11} & a_{12} \\
\hline
a_{13} & a_{14} & a_{15} & a_{16} \\
\hline
\end{array}
$$
**Fig. 7**
A $4 \times 4$ table has positive integers in its cells so that the sum of any two cells that share a side is a factorial of some positive integer. Show that there are at least 4 equal numbers in this table.
(Arsenii Nikolaiev)
\begin{array}{|c|c|c|c|}
\hline
a_1 & a_2 & a_3 & a_4 \\
\hline
a_5 & a_6 & a_7 & a_8 \\
\hline
a_9 & a_{10} & a_{11} & a_{12} \\
\hline
a_{13} & a_{14} & a_{15} & a_{16} \\
\hline
\end{array}
$$
**Fig. 7**
A $4 \times 4$ table has positive integers in its cells so that the sum of any two cells that share a side is a factorial of some positive integer. Show that there are at least 4 equal numbers in this table.
(Arsenii Nikolaiev)