Anti-magic square - Magisch vierkant

Anti-magic square

Why using the same sum for each row/column/diagonal? In the anti-magic square each row/column/diagonal has a different (sequencial) magic sum.

3x3 anti-magic square


	1	8	7		16
	9	5	4		18
	3	2	6		11
15				12
	13	15	17

Magic sum = 11 up to 18 (14 missing & 15 double)

4x4 anti-magic square


	11	14	1	4		30
	5	2	16	10		33
	15	3	8	9		35
	6	12	7	13		38
29					34
	37	31	32	36

Magic sum = 29 up to 38

5x5 anti-magic square


	21	18	6	17	4		66
	7	3	13	16	24		63
	5	20	23	11	1		60
	15	8	19	2	25		69
	14	12	9	22	10		67
65						59
	62	61	70	68	64

Magic sum = 59 up to 70

6x6 anti-magic square


	10	25	32	13	16	9		105
	22	7	3	24	21	30		107
	20	27	18	26	11	6		108
	1	31	23	33	17	8		113
	19	5	36	12	15	29		116
	34	14	2	4	35	28		117
118							111
	106	109	114	112	115	110

Magic sum = 105 up to 118

7x7 anti-magic square


	14	3	34	21	47	29	22		170
	43	16	13	25	6	26	44		173
	30	48	24	8	12	9	45		176
	10	5	11	38	49	46	19		178
	4	41	37	36	33	27	1		179
	39	17	40	20	7	35	23		181
	31	42	18	32	28	2	15		168
183								175
	171	172	177	180	182	174	169

Magic sum = 168 up to 183

8x8 anti-magic square


	49	16	50	10	19	28	24	56		252
	42	43	11	15	44	38	55	5		253
	25	21	48	46	9	37	6	63		255
	29	47	8	40	51	30	52	1		258
	45	22	54	23	20	34	2	62		262
	14	59	18	33	41	26	61	13		265
	36	12	58	32	27	64	3	35		267
	17	39	7	57	53	4	60	31		268
269									260
	257	259	254	256	264	261	263	266

Magic sum = 252 up to 269

9x9 anti-magic square


	52	19	81	22	29	15	42	31	76		367
	61	10	67	23	54	79	25	33	16		368
	57	9	71	24	38	1	51	47	75		373
	26	78	7	69	66	77	13	27	12		375
	39	21	74	20	37	17	49	55	64		376
	8	65	4	62	50	34	73	41	40		377
	56	68	2	63	14	72	35	44	6		360
	53	30	60	32	36	3	46	43	58		361
	11	70	5	59	48	80	28	45	18		364
379										369
	363	370	371	374	372	378	362	366	365

Magic sum = 360 up to 379

Source: J.A. Lindon, Ant-magic squares, Recreational mathematic magazine, no. 7, feb. 1962, p. 16-19

Specials, Anti-magic square.xls

Microsoft Excel werkblad 74.0 KB