Question 130
Each cell $(i, j)$ of a $2n \times 2n$ grid is filled with the number $2n(i-1)+j$.
A total of $2n^2$ cells are selected such that exactly $n$ cells are chosen from each row and exactly $n$ cells from each column. Prove that the sum of the numbers in the selected cells is equal to the sum of the numbers in the unselected cells.
(Nursoltan Khavalbolot)
A total of $2n^2$ cells are selected such that exactly $n$ cells are chosen from each row and exactly $n$ cells from each column. Prove that the sum of the numbers in the selected cells is equal to the sum of the numbers in the unselected cells.
(Nursoltan Khavalbolot)