Composite 12x12 magic square (1)

 

It is possible to use a 3x3 magic square and a 4x4 magic square to construct a 12x12 magic square.

 

Use as first grid 4x4 the same 3x3 magic square and as second grid 3x3 the same 4x4 magic square. Take a digit from a cell of the first grid and add (digit -/- 1) x 9 from the same cell of the second grid.

 

 

1x digit

2 9 4 2 9 4 2 9 4 2 9 4
7 5 3 7 5 3 7 5 3 7 5 3
6 1 8 6 1 8 6 1 8 6 1 8
2 9 4 2 9 4 2 9 4 2 9 4
7 5 3 7 5 3 7 5 3 7 5 3
6 1 8 6 1 8 6 1 8 6 1 8
2 9 4 2 9 4 2 9 4 2 9 4
7 5 3 7 5 3 7 5 3 7 5 3
6 1 8 6 1 8 6 1 8 6 1 8
2 9 4 2 9 4 2 9 4 2 9 4
7 5 3 7 5 3 7 5 3 7 5 3
6 1 8 6 1 8 6 1 8 6 1 8

 

 

+ (digit -/- 1) x 9

1 8 13 12 1 8 13 12 1 8 13 12
15 10 3 6 15 10 3 6 15 10 3 6
4 5 16 9 4 5 16 9 4 5 16 9
14 11 2 7 14 11 2 7 14 11 2 7
1 8 13 12 1 8 13 12 1 8 13 12
15 10 3 6 15 10 3 6 15 10 3 6
4 5 16 9 4 5 16 9 4 5 16 9
14 11 2 7 14 11 2 7 14 11 2 7
1 8 13 12 1 8 13 12 1 8 13 12
15 10 3 6 15 10 3 6 15 10 3 6
4 5 16 9 4 5 16 9 4 5 16 9
14 11 2 7 14 11 2 7 14 11 2 7

 

 

= composite magic 12x12 square

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

 

 

This composite magic 12x12 square has as extra feature that each random chosen 3x4 or 4x3 rectangle inside the square gives the magic sum of 870.

 

Download
12x12, composite (1).xls
Microsoft Excel werkblad 53.0 KB