change numbers in 3x3 table - Portugal OPM 2000 p1
Source:
May 18, 2024
algebracombinatorics
Problem Statement
Consider the following table where initially all squares contain zeros:
\begin{tabular}{ | l | c | r| }
\hline
0 & 0 & 0 \\ \hline
0 & 0 & 0 \\ \hline
0 & 0 & 0 \\ \hline
\end{tabular}
To change the table, the following operation is allowed: a square formed by adjacent squares is chosen, and a unit is added to all its numbers. Complete the following table, knowing that it was obtained by a sequence of permitted operations
\begin{tabular}{ | l | c | r| }
\hline
14 & & \\ \hline
19 & 36 & \\ \hline
& 16 & \\ \hline
\end{tabular}