Problem

Source: Baltic Way 2001

Tags: combinatorics proposed, combinatorics



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 $A = B$?