are the nine integers from one to nine (not necessarily in order). They satisfy the following constraints:

What values are taken by each of `A`

to `I`

?

Answer below:

Since and sum to 40, must be 5.

If `E`

is 5, subtracting equation 1 with equation 2, `A - 5 - F = 0`

; subtracting equation 3 with equation 4, `D +5 - I = 0`

. So, any combinations that satified these two equations can be the answer. For example, `A=9`

, `F=4`

, `D=2`

, `I=7`

.

With this, only `B`

, `C`

, `G`

, `H`

are left. Subtracting equation 2 with equation 3, `B + C = G + H`

. There are again many combinations depending on what you chose for `A`

, `F`

, `D`

, `I`

. If we used the above numbers, what’s left is `1, 3, 6, 8`

. So, one answer can be `B=1`

, `C=8`

, `G=6`

, `H=3`

.