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Information for whiz kids: How to produce a Franklin panmagic square from a 4x4 panmagic square
FRANKLIN PANMAGIC 24x24 SQUARE:
On page Basic pattern method (1) you can see how to use the patterns of a 4x4 panmagic square to produce a
Franklin panmagic 8x8, 16x16 or 32x32 square. It is also possible to produce the missing multiple of 8, a Franklin pan
magic 24x24 square. You need the 2 sub-squares (= basic pattern) of a 4x4 panmagic square [see page Basic
pattern method (1) ] and a fixed (36x16) ‘column pattern’.
1x digit from basic pattern
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
16
|
4
|
9
|
5
|
15
|
3
|
10
|
6
|
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
1
|
13
|
8
|
12
|
2
|
14
|
7
|
11
|
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
8
|
12
|
1
|
13
|
7
|
11
|
2
|
14
|
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
9
|
5
|
16
|
4
|
10
|
6
|
15
|
3
|
16x digit from (36x16) fixed column pattern
|
20
|
15
|
20
|
15
|
18
|
17
|
18
|
17
|
19
|
16
|
19
|
16
|
19
|
16
|
19
|
16
|
18
|
17
|
18
|
17
|
20
|
15
|
20
|
15
|
|
18
|
17
|
18
|
17
|
20
|
15
|
20
|
15
|
19
|
16
|
19
|
16
|
19
|
16
|
19
|
16
|
20
|
15
|
20
|
15
|
18
|
17
|
18
|
17
|
|
17
|
18
|
17
|
18
|
15
|
20
|
15
|
20
|
16
|
19
|
16
|
19
|
16
|
19
|
16
|
19
|
15
|
20
|
15
|
20
|
17
|
18
|
17
|
18
|
|
15
|
20
|
15
|
20
|
17
|
18
|
17
|
18
|
16
|
19
|
16
|
19
|
16
|
19
|
16
|
19
|
17
|
18
|
17
|
18
|
15
|
20
|
15
|
20
|
|
23
|
12
|
23
|
12
|
21
|
14
|
21
|
14
|
22
|
13
|
22
|
13
|
22
|
13
|
22
|
13
|
21
|
14
|
21
|
14
|
23
|
12
|
23
|
12
|
|
21
|
14
|
21
|
14
|
23
|
12
|
23
|
12
|
22
|
13
|
22
|
13
|
22
|
13
|
22
|
13
|
23
|
12
|
23
|
12
|
21
|
14
|
21
|
14
|
|
14
|
21
|
14
|
21
|
12
|
23
|
12
|
23
|
13
|
22
|
13
|
22
|
13
|
22
|
13
|
22
|
12
|
23
|
12
|
23
|
14
|
21
|
14
|
21
|
|
12
|
23
|
12
|
23
|
14
|
21
|
14
|
21
|
13
|
22
|
13
|
22
|
13
|
22
|
13
|
22
|
14
|
21
|
14
|
21
|
12
|
23
|
12
|
23
|
|
26
|
9
|
26
|
9
|
24
|
11
|
24
|
11
|
25
|
10
|
25
|
10
|
25
|
10
|
25
|
10
|
24
|
11
|
24
|
11
|
26
|
9
|
26
|
9
|
|
24
|
11
|
24
|
11
|
26
|
9
|
26
|
9
|
25
|
10
|
25
|
10
|
25
|
10
|
25
|
10
|
26
|
9
|
26
|
9
|
24
|
11
|
24
|
11
|
|
11
|
24
|
11
|
24
|
9
|
26
|
9
|
26
|
10
|
25
|
10
|
25
|
10
|
25
|
10
|
25
|
9
|
26
|
9
|
26
|
11
|
24
|
11
|
24
|
|
9
|
26
|
9
|
26
|
11
|
24
|
11
|
24
|
10
|
25
|
10
|
25
|
10
|
25
|
10
|
25
|
11
|
24
|
11
|
24
|
9
|
26
|
9
|
26
|
|
29
|
6
|
29
|
6
|
27
|
8
|
27
|
8
|
28
|
7
|
28
|
7
|
28
|
7
|
28
|
7
|
27
|
8
|
27
|
8
|
29
|
6
|
29
|
6
|
|
27
|
8
|
27
|
8
|
29
|
6
|
29
|
6
|
28
|
7
|
28
|
7
|
28
|
7
|
28
|
7
|
29
|
6
|
29
|
6
|
27
|
8
|
27
|
8
|
|
8
|
27
|
8
|
27
|
6
|
29
|
6
|
29
|
7
|
28
|
7
|
28
|
7
|
28
|
7
|
28
|
6
|
29
|
6
|
29
|
8
|
27
|
8
|
27
|
|
6
|
29
|
6
|
29
|
8
|
27
|
8
|
27
|
7
|
28
|
7
|
28
|
7
|
28
|
7
|
28
|
8
|
27
|
8
|
27
|
6
|
29
|
6
|
29
|
|
32
|
3
|
32
|
3
|
30
|
5
|
30
|
5
|
31
|
4
|
31
|
4
|
31
|
4
|
31
|
4
|
30
|
5
|
30
|
5
|
32
|
3
|
32
|
3
|
|
30
|
5
|
30
|
5
|
32
|
3
|
32
|
3
|
31
|
4
|
31
|
4
|
31
|
4
|
31
|
4
|
32
|
3
|
32
|
3
|
30
|
5
|
30
|
5
|
|
5
|
30
|
5
|
30
|
3
|
32
|
3
|
32
|
4
|
31
|
4
|
31
|
4
|
31
|
4
|
31
|
3
|
32
|
3
|
32
|
5
|
30
|
5
|
30
|
|
3
|
32
|
3
|
32
|
5
|
30
|
5
|
30
|
4
|
31
|
4
|
31
|
4
|
31
|
4
|
31
|
5
|
30
|
5
|
30
|
3
|
32
|
3
|
32
|
|
35
|
0
|
35
|
0
|
33
|
2
|
33
|
2
|
34
|
1
|
34
|
1
|
34
|
1
|
34
|
1
|
33
|
2
|
33
|
2
|
35
|
0
|
35
|
0
|
|
33
|
2
|
33
|
2
|
35
|
0
|
35
|
0
|
34
|
1
|
34
|
1
|
34
|
1
|
34
|
1
|
35
|
0
|
35
|
0
|
33
|
2
|
33
|
2
|
|
2
|
33
|
2
|
33
|
0
|
35
|
0
|
35
|
1
|
34
|
1
|
34
|
1
|
34
|
1
|
34
|
0
|
35
|
0
|
35
|
2
|
33
|
2
|
33
|
|
0
|
35
|
0
|
35
|
2
|
33
|
2
|
33
|
1
|
34
|
1
|
34
|
1
|
34
|
1
|
34
|
2
|
33
|
2
|
33
|
0
|
35
|
0
|
35
|
Franklin panmagic 24x24 square
|
336
|
244
|
329
|
245
|
303
|
275
|
298
|
278
|
320
|
260
|
313
|
261
|
319
|
259
|
314
|
262
|
304
|
276
|
297
|
277
|
335
|
243
|
330
|
246
|
|
289
|
285
|
296
|
284
|
322
|
254
|
327
|
251
|
305
|
269
|
312
|
268
|
306
|
270
|
311
|
267
|
321
|
253
|
328
|
252
|
290
|
286
|
295
|
283
|
|
280
|
300
|
273
|
301
|
247
|
331
|
242
|
334
|
264
|
316
|
257
|
317
|
263
|
315
|
258
|
318
|
248
|
332
|
241
|
333
|
279
|
299
|
274
|
302
|
|
249
|
325
|
256
|
324
|
282
|
294
|
287
|
291
|
265
|
309
|
272
|
308
|
| |