Question 72
We take a $6 \times 6$ chessboard, which has six rows and columns, and indicate its squares by $(i, j)$ for $1 \leq i, j \leq 6$. The $k$th northeast diagonal consists of the six squares satisfying $i-j \equiv k \pmod{6}$ (and so there are six such diagonals); hence there are six such diagonals.
Determine if it is possible to fill the entire chessboard with the numbers $1,2, \ldots, 36$ (each exactly once) such that each row, each column, and each of the six northeast diagonals has the same sum.
Determine if it is possible to fill the entire chessboard with the numbers $1,2, \ldots, 36$ (each exactly once) such that each row, each column, and each of the six northeast diagonals has the same sum.