Tuesday, October 14, 2014

A Special Order 13 Magic Square

A Special Order 13 Magic Square:
This is an order 13 magic square with the normal “magic square properties”, but it also has some special additions. 
157
13
23
147
109
31
111
138
36
66
102
100
72
145
25
17
153
61
139
59
32
134
104
68
98
70
16
154
144
26
57
56
30
112
136
99
105
60
110
22
148
156
14
113
114
140
58
34
65
71
133
37
97
73
94
76
151
18
21
89
146
135
35
29
141
79
91
78
92
27
82
150
155
11
63
107
33
137
74
96
75
95
143
159
15
20
88
115
55
101
69
90
80
93
77
19
24
81
149
152
54
116
103
67
164
6
3
167
85
142
158
12
28
64
106
108
62
7
163
168
86
1
132
44
39
125
50
48
118
124
162
8
84
2
169
38
126
131
45
120
122
52
46
5
83
161
10
166
129
43
40
128
123
117
49
51
87
165
9
160
4
41
127
130
42
47
53
121
119
The square has 169 spaces for number, and contains all of the numbers from 1 to 169 (13 squared) one time each.  All of the rows have the same sum (1105), all of the columns have the same sum (1105), and both of the main diagonals have the same sum. 
What makes it special?  It also contains 12 smaller magic squares (well, one of them is only semi-magic because only one of its diagonals adds up to the magic constant for that square) ranging in size from 3 x 3 to 11 x 11.  So this magic square is really a total of 13 magic squares.
A 3 x3 semi-magic square with 3 in the upper left corner.  All rows and columns, but only 1 main diagonal have a magic constant of 255.
Four 4 x 4 magic squares with 157, 97, 132 or 50 in the upper left corner of each square.  All rows, columns and the two main diagonals sum to 340.
Two 5 x 5 magic squares with 164 or 151 in the upper left corner.  All rows, columns and the two main diagonals sum to 425.
Two 7 x 7 magic squares with 94 or 57 in the upper left corner.  All rows, columns, and the two main diagonals sum to 595.
Two 9 x 9 magic squares with 109 and 97 in the upper left corner.  Their magic constant is 765.
An 11 x 11 magic square with 23 in the upper left corner.  Its magic constant is 935.
And finally, a 13 x 13 magic square with 157 in the upper left corner (the entire array).  Its magic constant is 1105.
My daughter was born on the 13th of the month, turned 13 (became a teenager) on a Friday the 13th (with 12 friends attending a sleepover, all 13 dressed in black).  The last time I warned her about a Friday the 13th coming up (so that she could avoid hospital duty that nigh) she said "Why?  That's when all the fun stuff happens."  What can I say - she has a thing for the number 13.
David

1 comment:

  1. Hi,

    Question is how many 13x13 tables exist? Any information is greatly appreciated.

    Thank you,

    RFR

    ReplyDelete