Alternative method of Strachey

With the alternative method of Strachey we make 4 as proportional as possible 5x5 magic squares (shift) to construct the 10x10 magic square, and than we swap numbers to get the magic square valid.

To construct the 4 panmagic 5x5 squares, take the numbers 0 up to 4 as row coordinates and take the numbers 0 up to (5 x 4 -/- 1 = ) 19 as column coordinates.

5x column coordinate + 1x row coordinate + 1 = panmagic 5x5 square

											250	250	250	250	250
										250						250
0	5	10	15	17	0	1	2	3	4		1	27	53	79	90		250
10	15	17	0	5	3	4	0	1	2		54	80	86	2	28		250
17	0	5	10	15	1	2	3	4	0		87	3	29	55	76		250
5	10	15	17	0	4	0	1	2	3		30	51	77	88	4		250
15	17	0	5	10	2	3	4	0	1		78	89	5	26	52		250

											250	250	250	250	250
										250						250
1	4	9	14	19	0	1	2	3	4		6	22	48	74	100		250
9	14	19	1	4	3	4	0	1	2		49	75	96	7	23		250
19	1	4	9	14	1	2	3	4	0		97	8	24	50	71		250
4	9	14	19	1	4	0	1	2	3		25	46	72	98	9		250
14	19	1	4	9	2	3	4	0	1		73	99	10	21	47		250

											255	255	255	255	255
										255						255
2	6	11	13	16	0	1	2	3	4		11	32	58	69	85		255
11	13	16	2	6	3	4	0	1	2		59	70	81	12	33		255
16	2	6	11	13	1	2	3	4	0		82	13	34	60	66		255
6	11	13	16	2	4	0	1	2	3		35	56	67	83	14		255
13	16	2	6	11	2	3	4	0	1		68	84	15	31	57		255

											255	255	255	255	255
										255						255
3	7	8	12	18	0	1	2	3	4		16	37	43	64	95		255
8	12	18	3	7	3	4	0	1	2		44	65	91	17	38		255
18	3	7	8	12	1	2	3	4	0		92	18	39	45	61		255
7	8	12	18	3	4	0	1	2	3		40	41	62	93	19		255
12	18	3	7	8	2	3	4	0	1		63	94	20	36	42		255

Combine the 4 panmagic 5x5 squares.

(Semi) Magic 10x10 square to be corrected

		505	505	505	505	505	505	505	505	505	505
	500											510
505		1	27	53	79	90	11	32	58	69	85
505		54	80	86	2	28	59	70	81	12	33
505		87	3	29	55	76	82	13	34	60	66
505		30	51	77	88	4	35	56	67	83	14
505		78	89	5	26	52	68	84	15	31	57
505		16	37	43	64	95	6	22	48	74	100
505		44	65	91	17	38	49	75	96	7	23
505		92	18	39	45	61	97	8	24	50	71
505		40	41	62	93	19	25	46	72	98	9
505		63	94	20	36	42	73	99	10	21	47

Swap 2x two numbers to get a valid 10x10 magic square.

10x10 magic square

		505	505	505	505	505	505	505	505	505	505
	505											505
505		1	27	53	79	90	11	32	58	69	85
505		54	80	81	2	28	59	70	86	12	33
505		87	3	34	55	76	82	13	29	60	66
505		30	51	77	88	4	35	56	67	83	14
505		78	89	5	26	52	68	84	15	31	57
505		16	37	43	64	95	6	22	48	74	100
505		44	65	91	17	38	49	75	96	7	23
505		92	18	39	45	61	97	8	24	50	71
505		40	41	62	93	19	25	46	72	98	9
505		63	94	20	36	42	73	99	10	21	47

Use the alternative method of Strachey to construct magic squares of order is double odd. See 6x6, 10x10, 14x14, 18x18, 22x22, 26x26 en 30x30

10x10, Alternative method of Strachey.xl

Microsoft Excel werkblad 47.0 KB

Download

10x10 magic square