Problem. Magic Square (click here to see the problem statement)

My Solution (21 in Center).

 

If 21 is to be the number in the center square, we can assume that the sum of each row, column, and diagonal is the product of 21 and 3: That is the AVERAGE value of the squares is 21. This establishes a target sum of 63. The sum of the remaining pairs must equat 63 - 21 = 42.

I make a list of 20 pairs:

 1, 41

2, 40

3, 39

4, 38

5, 37

6, 36

7, 35

8, 34

9, 33

10, 32

11, 31

12, 30

13, 29

14, 28

15, 27

16, 26

17, 25

18, 24

19, 23

20, 22

Here are several solutions I found. {I have no doubt there are many others. A good question would be - How solutions are there? But this will have to wait for another day}: