AMC 8 1996 Problem 14

Six different digits from the set $$\{ 1,2,3,4,5,6,7,8,9\}$$ are placed in the squares in the figure shown so that the sum of the entries in the vertical column is 23 and the sum of the entries in the horizontal row is 12. The sum of the six digits used is

$\text{(A)}\ 27 \text{(B)}\ 29 \text{(C)}\ 31 \text{(D)}\ 33 \text{(E)}\ 35$