Lozenge method of John Horton Conway

With the Lozenge method of John Horton Conway you get a magic square of odd order and you find all odd numbers in the (white) 'diamond' and all even numbers outside the diamond (in the dark area). See for detailed explanation: Lozenge 5x5 magic square.

Take 1x number from row grid +1

6	7	8	9	10	11	12	0	1	2	3	4	5
5	6	7	8	9	10	11	12	0	1	2	3	4
4	5	6	7	8	9	10	11	12	0	1	2	3
3	4	5	6	7	8	9	10	11	12	0	1	2
2	3	4	5	6	7	8	9	10	11	12	0	1
1	2	3	4	5	6	7	8	9	10	11	12	0
0	1	2	3	4	5	6	7	8	9	10	11	12
12	0	1	2	3	4	5	6	7	8	9	10	11
11	12	0	1	2	3	4	5	6	7	8	9	10
10	11	12	0	1	2	3	4	5	6	7	8	9
9	10	11	12	0	1	2	3	4	5	6	7	8
8	9	10	11	12	0	1	2	3	4	5	6	7
7	8	9	10	11	12	0	1	2	3	4	5	6

+ 13x number from column grid

7	8	9	10	11	12	0	1	2	3	4	5	6
8	9	10	11	12	0	1	2	3	4	5	6	7
9	10	11	12	0	1	2	3	4	5	6	7	8
10	11	12	0	1	2	3	4	5	6	7	8	9
11	12	0	1	2	3	4	5	6	7	8	9	10
12	0	1	2	3	4	5	6	7	8	9	10	11
0	1	2	3	4	5	6	7	8	9	10	11	12
1	2	3	4	5	6	7	8	9	10	11	12	0
2	3	4	5	6	7	8	9	10	11	12	0	1
3	4	5	6	7	8	9	10	11	12	0	1	2
4	5	6	7	8	9	10	11	12	0	1	2	3
5	6	7	8	9	10	11	12	0	1	2	3	4
6	7	8	9	10	11	12	0	1	2	3	4	5

= 13x13 Lozenge magic square

98	112	126	140	154	168	13	14	28	42	56	70	84
110	124	138	152	166	11	25	39	40	54	68	82	96
122	136	150	164	9	23	37	51	65	66	80	94	108
134	148	162	7	21	35	49	63	77	91	92	106	120
146	160	5	19	33	47	61	75	89	103	117	118	132
158	3	17	31	45	59	73	87	101	115	129	143	144
1	15	29	43	57	71	85	99	113	127	141	155	169
26	27	41	55	69	83	97	111	125	139	153	167	12
38	52	53	67	81	95	109	123	137	151	165	10	24
50	64	78	79	93	107	121	135	149	163	8	22	36
62	76	90	104	105	119	133	147	161	6	20	34	48
74	88	102	116	130	131	145	159	4	18	32	46	60
86	100	114	128	142	156	157	2	16	30	44	58	72

Use this method to construct magic squares of odd order (= 3x3, 5x5, 7x7, ... magic square).

See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 and 31x31

13x13, Lozenge method.xls

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13x13 magic square