The sum of each row and column must be 15, because the sum of nine numbers should be the sum of three rows, and their sum is 45, which is three times the number of single rows.

For the number 1, the sum of the other two numbers should be 14. Obviously it can only be 9, 5 or 8, 6 (two kinds).

For the number 2, the sum of the other two numbers should be 13, obviously it can only be 9, 4 or 8, 5 or 7, 6 (three kinds).

For the number 3, the sum of the other two numbers should be 12, obviously it can only be 8,4 or 7,5 (two kinds).

For the number 4, the sum of the other two numbers should be 1 1, obviously it can only be 9, 2 or 8, 3 or 6, 5 (three kinds).

For the number 5, the sum of the other two numbers should be 10, which can obviously be 9 1 or 8,2 or 7,3 or 6,4 (four kinds).

For the number 6, the sum of the other two numbers should be 9, obviously it can only be 8, 1 or 7,2 or 5,4 (three kinds).

For the number 7, the sum of the other two numbers should be 8, obviously it can only be 6, 2 or 5, 3 (two kinds)

For the number 8, the sum of the other two numbers should be 7, obviously it can only be 6, 1 or 5,2 or 4,3 (three kinds).

For the number 9, the sum of the other two numbers should be 6, obviously it can only be 5, 1 or 4,2.

So the middle can only be 5, and the numbers on the four corners must be equal to 15 in all three ways. Only the numbers 2, 4, 6 and 8 are not unique, but they must be 2 relative to 8 and 4 relative to 6.

Next, we can determine the positions of 1, 3, 7 and 9.