8 1 6

3 5 7

4 9 2

where the numbers are arranged such that the sum of the numbers in any horizontal, vertical, or main diagonal line is always the same number

8 + 1 + 6 = 8 + 3 + 4 = 8 + 5 + 2 = 15

For normal magic squares of order n = 3, 4, 5, ..., the magic constants are: n(n^2+1)/2

Now, let's consider a magic square where the numbers 1 to 9 in a 3x3 array so that the numbers surrounding each number add to a multiple of that number.

2 6 5

7 3 1

9 8 4

Notice that

7 + 3 + 6 = 16 (a multiple of 2)

6 + 3 + 1 = 10 (a multiple of 5)

8 + 3 + 1 = 12 (a multiple of 4)

8 + 3 + 7 = 18 (a multiple of 9)

Similarly in the following squares

2 7 9

6 3 8

5 1 4

4 1 5

8 3 6

9 7 2

4 8 9

1 3 7

5 6 2

5 1 4

6 3 8

2 7 9

5 6 2

1 3 7

4 8 9

9 7 2

8 3 6

4 1 5

9 8 4

7 3 1

2 6 5

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