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# Problem 166

## Criss Cross

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?

## 纵横交错

$$\begin{matrix} 6 & 3 & 3 & 0 \\ 5 & 0 & 4 & 3 \\ 0 & 7 & 1 & 4 \\ 1 & 2 & 4 & 5 \\ \end{matrix}$$