Nine of the numbers 4,5,6,7,8,12,13,16,18,19 are going to be inputted to the empty cells in the following table:
\begin{array} {|c|c|c|} \cline{1-3}
10 & & \\ \cline{1-3}
& & 9 \\ \cline{1-3}
& 3 & \\ \cline{1-3}
11 & & 17 \\ \cline{1-3}
& 20 & \\ \cline{1-3}
\end{array}
such that each row sums to the same number, and each column sums to the same number. Determine all possible arrangements. modular arithmeticalgebra unsolvedalgebra