Solution

We should first find out the central number. Let this be a.

The sum of the 3 lines is , is divisible by 3.

Since  mod, we have  (mod 3).

Only 1, 4 and 7 satisfy this.

When , since , the sum of two numbers on the same line is 9, i.e. (2, 7), (3, 6) and (4, 5).

When , since , the sum of two numbers on the same line is 8, i.e. (1, 7), (2, 6) and (3, 5).

When , since , the sum of two numbers on the same line is 7, i.e. (1, 6), (2, 5) and (3, 4).

So we have the 3 solutions: