1993 AJHSME Problems/Problem 14

Problem

The nine squares in the table shown are to be filled so that every row and every column contains each of the numbers $1,2,3$ . Then $A+B=$

\[\begin{tabular}{|c|c|c|} \hline 1 & & \\ \hline

& 2 & A \\ \hline
& & B \\ \hline

\end{tabular}\]

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 6$