# Not your average table of operations

Consider the 10-digit integer

$$N=\overline { ABCDEFGHIJ}$$

(where $$A,B,C,D..J$$ are the digits of $$N$$). Each digit of $$N$$ is a number between $$0$$ and $$9$$ inclusive and all digits of $$N$$ are different from each other.

What must be the value of $$N$$ so that the three vertical and three horizontal operations in the table below are correct?

$$\begin{matrix} \overline { EDJH } & \div & \overline { JF } & = & \overline { AA } \\ - & \quad & + & \quad & + \\ \overline { EDB } & \times & \overline { I } & = & \overline { EHCG } \\ \quad = & \quad & = & \quad & = \\ \overline { EEID } & - & \overline { DJ } & = & \overline { EEAE } \end{matrix}$$

Details and assumptions

You may assue that only one value of $$N$$ satisfies the constraints above.

×