### A self-complement magic square of order 8

The next self-complement inlaid magic square of order n=8 was found on the magic pages of Harvey Heinz. It is not symmetrical, but symmetric across the vertical center, so produces a horizontally reflected version of itself.

 17 23 9 53 12 56 42 48 5 50 22 46 19 43 15 60 13 64 38 36 29 27 1 52 47 3 35 31 34 30 62 18 7 4 25 37 28 40 61 58 63 59 32 26 39 33 6 2 57 16 44 20 45 21 49 8 51 41 55 11 54 10 24 14
 48 42 56 12 53 9 23 17 60 15 43 19 46 22 50 5 52 1 27 29 36 38 64 13 18 62 30 34 31 35 3 47 58 61 40 28 37 25 4 7 2 6 33 39 26 32 59 63 8 49 21 45 20 44 16 57 14 24 10 54 11 55 41 51

But more than this: you will get a new self-complement magic square, if you replace the integers of the inlaid magic square of order n=4 with their complementary numbers.

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 48 42 56 12 53 9 23 17 60 15 43 19 46 22 50 5 52 1 38 36 29 27 64 13 18 62 35 31 34 30 3 47 58 61 25 37 28 40 4 7 2 6 32 26 39 33 59 63 8 49 21 45 20 44 16 57 14 24 10 54 11 55 41 51

And even more: you will also get another self-complement magic square, if you replace the integers in the frame with their complementary numbers.

 48 42 56 12 53 9 23 17 60 15 43 19 46 22 50 5 52 1 38 36 29 27 64 13 18 62 35 31 34 30 3 47 58 61 25 37 28 40 4 7 2 6 32 26 39 33 59 63 8 49 21 45 20 44 16 57 14 24 10 54 11 55 41 51
 17 23 9 53 12 56 42 48 5 50 22 46 19 43 15 60 13 64 27 29 36 38 1 52 47 3 30 34 31 35 62 18 7 4 40 28 37 25 61 58 63 59 33 39 26 32 6 2 57 16 44 20 45 21 49 8 51 41 55 11 54 10 24 14