Franklin Squares
Part 2

My Construction Method

16x16 Square B
0
15
0
15
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15
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15
0
15
0
15
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15
0
15
1
14
1
14
1
14
1
14
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1
14
1
14
1
14
15
0
15
0
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0
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0
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0
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0
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0
15
0
14
1
14
1
14
1
14
1
14
1
14
1
14
1
14
1
2
13
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16x16 Square A
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Magic Square
1
242
16
255
3
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14
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5
246
12
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10
249
32
239
17
226
30
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241
2
256
15
243
4
254
13
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252
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8
250
9
240
31
225
18
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29
227
20
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234
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33
210
48
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35
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128
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127
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114
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135
120

 

The simplest and most obvious is to produce a square with imbedded squares. Using column one square B as the sequence in row one square A will do that. All the features in square B will be in square A 90 degrees out of phase. All of the main Franklin features will remain as well as most if not all of the lesser features. In fact some features that were horizontal only in his original 8x8 and 16x16 will become horizontal and vertical.

Review the square with imbedded squares on My Squares Part 2. The wraparound of the bent diagonals can be explained by examining the component squares. In square B all the numbers in the wraparound are the same when started in any odd column. In square A there are two complimentary pairs, one pair in rows four and five, the other in rows three and six. Those pairs will always be complimentary pairs no matter where they are placed. Any pair of cells in a column will be a complimentary pair if one element is in an odd row and the other in an even row. The wraparound will always produce the proper total if wrapped around into any odd column.

This construction is general for all multiples of eight.

 
Some materials on this site are Copyright © Donald Morris 2005 all rights reserved