Basic pattern method (2) - Magisch vierkant

8x8 magic square

Basic pattern method (2)

Use a 4x4 panmagic square to construct a 8x8 Franklin panmagic square.

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

Choose a 4x4 panmagic square and split it as follows:

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

Fill in the empty cells crosswise with the same numbers in the 4x4 sub-square:

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

Combine the 2 squares and put the same 2 squares below to complete the first grid of the 8x8 magic square:

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

Replace the numbers using the table above:

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

In total there are 6 ways to split the panmagic 4x4 square to construct the basic grid:

1 split the panmagic 4x4 Complete grid and replace numbers = 8x8 Franklin panmagic square

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

2 split the panmagic 4x4 Complete grid and replace numbers = 8x8 Franklin panmagic square

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

3 split the panmagic 4x4 Complete grid and replace numbers = 8x8 Franklin panmagic square

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

4 split panmagic 4x4 Complete grid and replace numbers = 8x8 Franklin panmagic square

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

5 split panmagic 4x4 Complete grid and replace numbers = 8x8 Franklin panmagic square

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

6 split panmagic 4x4 Complete grid and replace numbers = 8x8 Franklin panmagic square

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

Use the basic pattern method (2) also to construct a most perfect 16x16 magic square.

8x8, Basic pattern method (2).xls

Microsoft Excel werkblad 135.5 KB

8x8 magic square