The 12x12 Magic Squares
Technique 2: The Composite Approach
The Composite Approach creates a magic square derived from combining an order-3 with an order-4 magic square. The order-3 square is used as a template for a 12x12 component with 4x4 blocks of numbers based on the original square. Each cell in this square is multiplied by 16.
The order-4 square is repeated three times in each axis to create the second 12x12 component.
Original 3x3 | Original 4x4 |
7 | 7 | 7 | 7 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 7 | 7 | 7 | 7 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 7 | 7 | 7 | 7 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 7 | 7 | 7 | 7 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 0 | 0 | 0 | 0 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 0 | 0 | 0 | 0 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 0 | 0 | 0 | 0 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 6 | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 6 | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 6 | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 6 | 1 | 1 | 1 | 1 | 16 x | 0 | 7 | 12 | 11 | 0 | 7 | 12 | 11 | 0 | 7 | 12 | 11 | 13 | 10 | 1 | 6 | 13 | 10 | 1 | 6 | 13 | 10 | 1 | 6 | 3 | 4 | 15 | 8 | 3 | 4 | 15 | 8 | 3 | 4 | 15 | 8 | 14 | 9 | 2 | 5 | 14 | 9 | 2 | 5 | 14 | 9 | 2 | 5 | 0 | 7 | 12 | 11 | 0 | 7 | 12 | 11 | 0 | 7 | 12 | 11 | 13 | 10 | 1 | 6 | 13 | 10 | 1 | 6 | 13 | 10 | 1 | 6 | 3 | 4 | 15 | 8 | 3 | 4 | 15 | 8 | 3 | 4 | 15 | 8 | 14 | 9 | 2 | 5 | 14 | 9 | 2 | 5 | 14 | 9 | 2 | 5 | 0 | 7 | 12 | 11 | 0 | 7 | 12 | 11 | 0 | 7 | 12 | 11 | 13 | 10 | 1 | 6 | 13 | 10 | 1 | 6 | 13 | 10 | 1 | 6 | 3 | 4 | 15 | 8 | 3 | 4 | 15 | 8 | 3 | 4 | 15 | 8 | 14 | 9 | 2 | 5 | 14 | 9 | 2 | 5 | 14 | 9 | 2 | 5 | + 1 x |
112 | 119 | 124 | 123 | 32 | 39 | 44 | 43 | 48 | 55 | 60 | 59 |
125 | 122 | 113 | 118 | 45 | 42 | 33 | 38 | 61 | 58 | 49 | 54 |
115 | 116 | 127 | 120 | 35 | 36 | 47 | 40 | 51 | 52 | 63 | 56 |
126 | 121 | 114 | 117 | 46 | 41 | 34 | 37 | 62 | 57 | 50 | 53 |
0 | 7 | 12 | 11 | 64 | 71 | 76 | 75 | 128 | 135 | 140 | 139 |
13 | 10 | 1 | 6 | 77 | 74 | 65 | 70 | 141 | 138 | 129 | 134 |
3 | 4 | 15 | 8 | 67 | 68 | 79 | 72 | 131 | 132 | 143 | 136 |
14 | 9 | 2 | 5 | 78 | 73 | 66 | 69 | 142 | 137 | 130 | 133 |
80 | 87 | 92 | 91 | 96 | 103 | 108 | 107 | 16 | 23 | 28 | 27 |
93 | 90 | 81 | 86 | 109 | 106 | 97 | 102 | 29 | 26 | 17 | 22 |
83 | 84 | 95 | 88 | 99 | 100 | 111 | 104 | 19 | 20 | 31 | 24 |
94 | 89 | 82 | 85 | 110 | 105 | 98 | 101 | 30 | 25 | 18 | 21 |
Total Order 12 magic Square
Resulting Magic Square
Using this technique, the final square cannot be Pan-Magic because the original 3x3 square is not Pan-Magic. This technique is included here to illusrate the use of the composite technique.
Copyright © Mar 2010 |
Magic Squares Website |
Updated
Mar 6, 2010
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