Eight of the nine numbers \(2, 3, 4, 5, 7, 10, 11, 12, 13\) are to be placed in the empty cells of the \(3 \times 4\) array (with \(1, 9, 14, 15\) already placed) so that the arithmetic average of the numbers in each row and each column is the same integer. Which one number must be left out?
