Franklin Squares Primer


Part 2

Franklin square features

 

Franklin's original 8x8
 
#3
260
 
 
 
260
 
 
292
 
 
#3A
 
 
 
 
 
130
 
 
52
61
4
13
20
29
36
45
260
 
130
52
61
4
13
20
29
36
 45 
 
14
3
62
51
46
35
30
19
260
 
 
14
3
62
51
46
35
30
19
 
53
60
5
12
21
28
37
44
260
 
 
53
60
5
12
21
28
37
44
 
11
6
59
54
43
38
27
22
260
 
 
11
6
59
54
43
38
27
22
 
55
58
7
10
23
26
39
42
260
 
 
55
58
7
10
23
26
39
42
 
9
8
57
56
41
40
25
24
260
 
 
9
8
57
56
41
40
25
24
 
50
63
2
15
18
31
34
47
260
 
 
50
63
2
15
18
31
34
47
 
16
1
64
49
48
33
32
17
260
 
 
16
1
64
49
48
33
32
17
 
260
260
260
260
260
260
260
260
228
 
130
 
 
 
 
 
 
 
#4 Franklin's original 16x16
2168
 
2040
199
216
231
248
7
24
39
56
71
88
103
120
135
152
167
184
2040
 
 
57
38
25
6
249
230
217
198
185
166
153
134
121
102
89
70
2040
 
 
197
218
229
250
5
26
37
58
69
90
101
122
133
154
165
186
2040
 
 
59
36
27
4
251
228
219
196
187
164
155
132
123
100
91
68
2040
 
 
200
215
232
247
8
23
40
55
72
87
104
119
136
151
168
183
2040
 
 
54
41
22
9
246
233
214
201
182
169
150
137
118
105
86
73
2040
 
 
202
213
234
245
10
21
42
53
74
85
106
117
138
149
170
181
2040
 
 
52
43
20
11
244
235
212
203
180
171
148
139
116
107
84
75
2040
 
 
204
211
236
243
12
19
44
51
76
83
108
115
140
147
172
179
2040
 
 
50
45
18
13
242
237
210
205
178
173
146
141
114
109
82
77
2040
 
 
206
209
238
241
14
17
46
49
78
81
110
113
142
145
174
177
2040
 
2040
48
47
16
15
240
239
208
207
176
175
144
143
112
111
80
79
2040
 
 
195
220
227
252
3
28
35
60
67
92
99
124
131
156
163
188
2040
 
 
61
34
29
2
253
226
221
194
189
162
157
130
125
98
93
66
2040
 
 
193
222
225
254
1
30
33
62
65
94
97
126
129
158
161
190
2040
 
 
63
32
31
0
255
224
223
192
191
160
159
128
127
96
95
64
2040
 
 
2040
2040
2040
2040
2040
2040
2040
2040
2040
2040
2040
2040
2040
2040
2040
2040
1912
 
 


In squares #3 and #4, Franklin’s original 8x8 and 16x16, diagonals have the wrong totals. These squares are not true magic squares. However they have many features that make them interesting. I think three of them are necessary in a Franklin type square.

What we call “bent diagonals” he called “bent rows”. In square #4 the highlighted feature from 57 to 70 is a bent diagonal and totals 2040, the same as the rows. The wrapped around bent diagonal from 195 to 188 totals the same. Square #3 shows bent diagonals that also have proper totals. All bent diagonals in these two squares, V up, V down, V right, and V left, have the same totals as the rows. This is Franklin’s trademark feature.

Two other features are shown in #3a. Every half row and half column starting at an outside edge totals half a row total. In each square every 2x2, wherever placed, totals the same.
 
 
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