Mathematical_Recreations-Kraitchik-2e

17~ Mathematical Recreations
which that magic constant was derived. The result is an
m X n composite square (Figure 51).
The same procedure can be applied to the fundamental
square of order 15. It is to be noted that the magic constants
816
357
492
1 12 7 14
8 13 2 11
10 3 16 5
15 6 9 4
8 1
3 5
4 9
6 107 100 105
7 102 104 106
2 103 108 101
62
57
58
55 60 125 118 123
59 61 120 122 124
63 56 121 126 119
71 64
69 116 109 114
17
10 15 98 91 96
66 68
67 72
70 111 113 115
65 112 117 110
12
13
14 16 93 95 97
18 11 94 99 92
89 82
84 86
85 90
134 127
129 131
130 135
87 26 19 24
88 21 23 25
83 22 27 20
132 53 46 51
133 48 50 52
128 49 54 47
143 136 141 44 37 42
138 140 142 39 41 43
139 144 137 40 45 38
80 73 78 35 28 33
75 77 79 30 32 34
76 81 74 31 36 29
FIGURE 49.
determined by the squares of order 5 into which the fundamental
square is decomposed form three arithmetic progressions
with the same common difference and having their first
terms in arithmetic progression, so that a magic square of
order 3 can be formed from them. These progressions are:
165, 190, 215; 540, 565, 590; 915, 940, 965. When this magic