Question 22
The numbers $1, 2, \ldots, 49$ are placed in a $7 \times 7$ array, and the sum of the numbers in each row and in each column is computed. Some of these 14 sums are odd while others are even. Let $A$ denote the sum of all the odd sums and $B$ the sum of all even sums. Is it possible that the numbers were placed in the array in such a way that $A = B$?