Sudoku method (3)

How to construct a most perfect (Franklin pan)magic 1024x1024 square in 9 steps by using only one 4x4 Sudoku

4x4 Sudoku

2	1	3	0
1	2	0	3
0	3	1	2
3	0	2	1

Step 1

Use the 4x4 Sudoku and a shifted version of the 4x4 Sudoku on a 2x2 carpet to construct a 4x4 panmagic square.

4x4 Sudoku shifted on 2x2 carpet

2	1	3	0	2	1	3	0
1	2	0	3	1	2	0	3
0	3	1	2	0	3	1	2
3	0	2	1	3	0	2	1
2	1	3	0	2	1	3	0
1	2	0	3	1	2	0	3
0	3	1	2	0	3	1	2
3	0	2	1	3	0	2	1

4x number + 1x number = +1 = 4x4 panmagic square

2	1	3	0	2	0	3	1	10	4	15	1	11	5	16	2
1	2	0	3	3	1	2	0	7	9	2	12	8	10	3	13
0	3	1	2	0	2	1	3	0	14	5	11	1	15	6	12
3	0	2	1	1	3	0	2	13	3	8	6	14	4	9	7

Step 2

Use a grid with 2x2 the 4x4 panmagic square and a grid with 2x2 the shifted versions of the 4x4 Sudoku to construct an 8x8 most perfect (Franklin pan)magic square.

Construct the grid with 2x2 the shifted versions of the 4x4 Sudoku as follows:


	+



+		+


	+

1x number + 16x number = 8x8 Franklin panmagic square

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

Step 3

Use a grid with 2x2 the 8x8 most perfect (Franklin pan)magic square and a grid with 2x2 the shifted versions of 8x8 Sudoku grid to construct an 16x16 most perfect (Franklin pan)magic square. See step 2 to construct the Sudoku grid

1x number

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

64x number

2	1	3	0	3	0	2	1	3	0	2	1	2	1	3	0
1	2	0	3	0	3	1	2	0	3	1	2	1	2	0	3
0	3	1	2	1	2	0	3	1	2	0	3	0	3	1	2
3	0	2	1	2	1	3	0	2	1	3	0	3	0	2	1
0	3	1	2	1	2	0	3	1	2	0	3	0	3	1	2
3	0	2	1	2	1	3	0	2	1	3	0	3	0	2	1
2	1	3	0	3	0	2	1	3	0	2	1	2	1	3	0
1	2	0	3	0	3	1	2	0	3	1	2	1	2	0	3
0	3	1	2	1	2	0	3	1	2	0	3	0	3	1	2
3	0	2	1	2	1	3	0	2	1	3	0	3	0	2	1
2	1	3	0	3	0	2	1	3	0	2	1	2	1	3	0
1	2	0	3	0	3	1	2	0	3	1	2	1	2	0	3
2	1	3	0	3	0	2	1	3	0	2	1	2	1	3	0
1	2	0	3	0	3	1	2	0	3	1	2	1	2	0	3
0	3	1	2	1	2	0	3	1	2	0	3	0	3	1	2
3	0	2	1	2	1	3	0	2	1	3	0	3	0	2	1

Most perfect 16x16 (Franklin pan)magic square

171	85	256	2	251	5	176	82	235	21	192	66	187	69	240	18
88	170	3	253	8	250	83	173	24	234	67	189	72	186	19	237
1	255	86	172	81	175	6	252	65	191	22	236	17	239	70	188
254	4	169	87	174	84