Denote the squares with letters A to I.
We have . To have an equal sum of each row, we divide 45 by 3 and obtain 15. So the sum of each row, column and diagonal is 15.
We then consider the parity of the numbers at corners.
Consider the case if A is odd.
(1) If B is also odd:
Then since , C is odd as well. As and , G is also odd. By similar idea, D, I and H are also odd. But now we have 6 odd numbers, which is impossible. So B is not odd if A is odd.
(2) If B is even:
Since , C is even. Similarly, H is even. Then means that I is odd. This further gives F and G are even. Now we have 5 even numbers, which is impossible. So B is not odd if A is odd.
Since the above two cases are impossible, A must not be odd. It is even.
Similarly, C, G and I cannot be odd. They are even.
Fill in the 4 even numbers, 2, 4, 6 and 8, in the 4 corners and find the corresponding the values of B, D, F and H.
Here shows one of the solutions:
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