Franklin’s Construction Method
Part 4

 

 
Unknown author's 8x8
260
 
 
               
B
1
8
58
63
9
16
50
55
260
0
0
7
7
1
1
6
6
 
0
7
1
6
0
7
1
6
62
59
5
4
54
51
13
12
260
7
7
0
0
6
6
1
1
 
5
2
4
3
5
2
4
3
7
2
64
57
15
10
56
49
260
0
0
7
7
1
1
6
6
 
6
1
7
0
6
1
7
0
60
61
3
6
52
53
11
14
260
7
7
0
0
6
6
1
1
 
3
4
2
5
3
4
2
5
17
24
42
47
25
32
34
39
260
2
2
5
5
3
3
4
4
 
0
7
1
6
0
7
1
6
46
43
21
20
38
35
29
28
260
5
5
2
2
4
4
3
3
 
5
2
4
3
5
2
4
3
23
18
48
41
31
26
40
33
260
2
2
5
5
3
3
4
4
 
6
1
7
0
6
1
7
0
44
45
19
22
36
37
27
30
260
5
5
2
2
4
4
3
3
 
3
4
2
5
3
4
2
5
260
260
260
260
260
260
260
260
260
 

 

This square was found among Franklin’s papers written in a hand other than his own. It must have been important for him to have kept it. It’s a pandiagonal magic square with Franklin’s bent diagonals and half columns and half rows that total half row total. However, some of the 2x2s in rows four and five and rows eight and row one wrap around don’t have the proper total. It appears to have been constructed by merging two squares, which I feel is a Franklin technique.

Both square A and B can be broken into four 4x4s, one in each quadrant. Row one in the upper left 4x4 of square A has two pairs of a complimentary pair, two zeros and two sevens. Rows two, three, and four are filled by complimentary construction, also a Franklin technique. The other three quadrants are filled with the same pattern using the other three complimentary pairs in order-ones in the upper right, twos in the lower left, and threes in the lower right. All four quadrants of square B are identical. Rows one and two contain the four complimentary pairs. Rows three and four are rows one and two reversed. This construction matches all the numbers in square A with all the numbers in square B.

 
 
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