Concentric 12x12 magic square

 

To construct a concentric magic square you can put each time a new border around the square to make it larger and larger and so you can construct a 4x4 in 6x6 in 8x8 in 10x10 in ... magic square.

 

 

Number + 10     Number + 14                Number + 18

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

 

 

Number + 22                                =   Concentric 12x12 magic square

                        134 143 3 141 5 1 22 124 20 126 18 133
92 2 98 4 14 18 84 16 86 91     16 114 24 120 26 36 40 106 38 108 113 129
88 75 30 70 32 19 21 81 76 13     15 110 97 52 92 54 41 43 103 98 35 130
12 28 33 38 41 66 64 61 73 89     131 34 50 55 60 63 88 86 83 95 111 14
90 27 67 43 50 55 54 34 74 11     132 112 49 89 65 72 77 76 56 96 33 13
5 22 65 57 52 45 48 36 79 96     139 27 44 87 79 74 67 70 58 101 118 6
100 72 59 46 47 58 51 42 29 1     128 122 94 81 68 69 80 73 64 51 23 17
8 77 39 56 53 44 49 62 24 93     10 30 99 61 78 75 66 71 84 46 115 135
94 78 40 63 60 35 37 68 23 7     9 116 100 62 85 82 57 59 90 45 29 136
6 25 71 31 69 82 80 20 26 95     137 28 47 93 53 91 104 102 42 48 117 8
10 99 3 97 87 83 17 85 15 9     7 32 121 25 119 109 105 39 107 37 31 138
                        12 2 142 4 140 144 123 21 125 19 127 11

 

 

 

Take the 10x10 concentric magic square, add 22 to all numbers and construct the border [see webpage 10x10 in 12x12 (1)]

 

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

3x34x45x56x67x78x89x910x1011x1112x1213x1314x1415x1516x1617x1718x1819x1920x2021x2122x2223x2324x2425x2526x2627x2728x2829x29,  30x3031x31 and 32x32

 

Download
12x12, Concentric.xls
Microsoft Excel werkblad 72.0 KB