9x9 magic square

9x9 concentric magic square

 

Start with a 3x3 magic square and put a border around the square again and again to get a 3x3 in 5x5 in 7x7 in 9x9 in ... magic square.

 

 

Number + 8       Number + 12                  Number + 16                               9x9 concentric magic square

                                          10 81 79 77 9 11 13 15 74
                        6 1 3 43 41 39 42     16 22 17 19 59 57 55 58 66
          22 18 3 2 20     48 34 30 15 14 32 2     14 64 50 46 31 30 48 18 68
2 9 4     7 10 17 12 19     46 19 22 29 24 31 4     12 62 35 38 45 40 47 20 70
7 5 3     5 15 13 11 21     45 17 27 25 23 33 5     75 61 33 43 41 39 49 21 7
6 1 8     25 14 9 16 1     10 37 26 21 28 13 40     76 26 53 42 37 44 29 56 6
          6 8 23 24 4     12 18 20 35 36 16 38     78 28 34 36 51 52 32 54 4
                        8 49 47 7 9 11 44     80 24 65 63 23 25 27 60 2
                                          8 1 3 5 73 71 69 67 72

 

 

Take the 7x7 concentric magic square, add 16 to all numbers and construct the border [see webpage pan 7x7 in 9x9 (1)]

 

See how the concentric magic square on this website is growing bigger and bigger: 

3x3, 4x4, 5x5, 6x6, 7x7, 8x8, 9x9, 10x10, 11x11, 12x12, 13x13, 14x14, 15x15, 16x16, 17x1718x18, 19x19, 20x20, 21x21, 22x22, 23x23, 24x24, 25x25, 26x26, 27x27, 28x28, 29x29,  30x30, 31x31 and 32x32

 

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9x9, 3x3 in 5x5 in 7x7 in 9x9 magic squa
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9x9 magic square