Office Applications and Entertainment, Magic Squares of Subtraction

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Construction of Magic Squares of Subtraction (12 x 12)
Associated, Res12 = 24, Pair Sum = 145


With square B Simple Magic and square A Associated, the resulting square C will be an Associated Magic Square of Subtraction, as illustrated below:

A, Res4 = 8
16 7 14 13
11 12 9 2
15 8 5 6
4 3 10 1
C, Res12 = 24, Pair Sum = 145
64 55 62 61
59 60 57 50
63 56 53 54
52 51 58 49
144 135 142 141
139 140 137 130
143 136 133 134
132 131 138 129
32 23 30 29
27 28 25 18
31 24 21 22
20 19 26 17
48 39 46 45
43 44 41 34
47 40 37 38
36 35 42 33
80 71 78 77
75 76 73 66
79 72 69 70
68 67 74 65
112 103 110 109
107 108 105 98
111 104 101 102
100 99 106 97
128 119 126 125
123 124 121 114
127 120 117 118
116 115 122 113
16 7 14 13
11 12 9 2
15 8 5 6
4 3 10 1
96 87 94 93
91 92 89 82
95 88 85 86
84 83 90 81
B, s3 = 15
4 9 2
3 5 7
8 1 6

With 8 possible squares for B and n4 for Cj (j = 1 ... 9), the resulting number of 12th order Associated Squares of Subtraction with Res12 = 24 will be 8 * n49 with n4 = 8 * 8 (ref. Attachment 4.1).


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