Properties
inlaid

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

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

example 1

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

example 2

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

example 3

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Example 3

This magic square of order n=8 with magic sum S₈=260 has four inlaid magic squares with different magic sums.

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

The magic sums are:

	left	right
top:	87	111
bottom:	84	108

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

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

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