Composite 9x9 magic square (2)

Use 9 proportional (semi)magic 3x3 squares to construct a 9x9 magic square. Proportional means that all 9 (semi)magic 3x3 squares have the same magic sum of (1/3 x 369 = ) 123. Use the row and column coordinates of the 3x3 magic square. Don't use as row coordinates the numbers 0 up to 2, but use the numbers 1 up to (9x3 = ) 27 instead. To get the numbers proportional divided, use the following table:

1	18	23	42
2	16	24	42
3	17	22	42
4	12	26	42
5	10	27	42
6	11	25	42
7	15	20	42
8	13	21	42
9	14	19	42

Construct the 9 (semi)magic 3x3 squares.

Row coordinate +27x column coordinate = (semi)magic 3x3 square

18	1	23	0	2	1	18	55	50
23	18	1	2	1	0	77	45	1
1	23	18	1	0	2	28	23	72

16	2	24	0	2	1	16	56	51
24	16	2	2	1	0	78	43	2
2	24	16	1	0	2	29	24	70

17	3	22	0	2	1	17	57	49
22	17	3	2	1	0	76	44	3
3	22	17	1	0	2	30	22	71

12	4	26	0	2	1	12	58	53
26	12	4	2	1	0	80	39	4
4	26	12	1	0	2	31	26	66

10	5	27	0	2	1	10	59	54
27	10	5	2	1	0	81	37	5
5	27	10	1	0	2	32	27	64

11	6	25	0	2	1	11	60	52
25	11	6	2	1	0	79	38	6
6	25	11	1	0	2	33	25	65

15	7	20	0	2	1	15	61	47
20	15	7	2	1	0	74	42	7
7	20	15	1	0	2	34	20	69

13	8	21	0	2	1	13	62	48
21	13	8	2	1	0	75	40	8
8	21	13	1	0	2	35	21	67

14	9	19	0	2	1	14	63	46
19	14	9	2	1	0	73	41	9
9	19	14	1	0	2	36	19	68

Put the 9 (semi)magic 3x3 squares together.

9x9 magic square

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

Each 1/3 row/column gives 1/3 of the magic square and the 9x9 magic square is 3x3 compact, but not panmagic.

9x9, Composite (2a).xls

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Use a 3x9 magic rectangle to get a symmetric result:

1	25	16	42
2	23	17	42
15	21	6	42
20	18	4	42
19	14	9	42
24	10	8	42
22	7	13	42
11	5	26	42
12	3	27	42

Row coordinate +27x column coordinate = (semi)magic 3x3 square

25	1	16	0	2	1	25	55	43
16	25	1	2	1	0	70	52	1
1	16	25	1	0	2	28	16	79

23	2	17	0	2	1	23	56	44
17	23	2	2	1	0	71	50	2
2	17	23	1	0	2	29	17	77

21	15	6	0	2	1	21	69	33
6	21	15	2	1	0	60	48	15
15	6	21	1	0	2	42	6	75

18	20	4	0	2	1	18	74	31
4	18	20	2	1	0	58	45	20
20	4	18	1	0	2	47	4	72

14	19	9	0	2	1	14	73	36
9	14	19	2	1	0	63	41	19
19	9	14	1	0	2	46	9	68

10	24	8	0	2	1	10	78	35
8	10	24	2	1	0	62	37	24
24	8	10	1	0	2	51	8	64

7	22	13	0	2	1	7	76	40
13	7	22	2	1	0	67	34	22
22	13	7	1	0	2	49	13	61

5	11	26	0	2	1	5	65	53
26	5	11	2	1	0	80	32	11
11	26	5	1	0	2	38	26	59

3	12	27	0	2	1	3	66	54
27	3	12	2	1	0	81	30	12
12	27	3	1	0	2	39	27	57

9x9 magic square

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

Each 1/3 row/column gives 1/3 of the magic square and the 9x9 magic square is symmetric (but is not [fully] 3x3 compact and not panmagic).

9x9, Composite (2b).xls

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9x9 magic square