A $4 \times 4$ grid is filled with digits $d$, $0 \le d \le 9$.
It can be seen that in the grid $$\begin{matrix} 6 & 3 & 3 & 0\\ 5 & 0 & 4 & 3\\ 0 & 7 & 1 & 4\\ 1 & 2 & 4 & 5 \end{matrix}$$ the sum of each row and each column has the value $12$. Moreover the sum of each diagonal is also $12$.
In how many ways can you fill a $4 \times 4$ grid with the digits $d$, $0 \le d \le 9$ so that each row, each column, and both diagonals have the same sum?
Solution
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