Perfect magic squares - Transformation method

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How to transform a square with sequential digits to a most-perfect magic square!

Introduction

On the website of Harvey Heinz is shown on page www.magic-squares.net/most-perfect.htm that a 4x4 square with sequential
digits can be transformed to a panmagic 4x4 square.

Firstly I present step by step the transformation to the 3 basic squares of the panmagic 4x4 square (see page ‘panmagic 4x4
square’).

Secondly I present step by step the transformation of a 8x8, 12x12 and 16x16 square with sequential digits to a most-perfect
8x8, 12x12 and 16x16 square.

Transformation to the 3 basic squares of the panmagic 4x4 square

Transform a 4x4 square with sequential digits to a panmagic 4x4 square in 5 steps by swapping each time ‘yellow’ and ‘red’;
see below:

1	5	9	13	1	5	13	9	1	5	13	9	1	8	13	12	1	8	13	12	1	8	13	12
2	6	10	14	2	6	14	10	2	6	14	10	2	6	14	10	14	10	2	6	15	10	3	6
3	7	11	15	3	7	15	11	4	8	16	12	4	5	16	9	4	5	16	12	4	5	16	9
4	8	12	16	4	8	16	12	3	7	15	11	3	7	15	11	15	11	3	7	14	11	2	7


1	3	9	11	1	3	11	9	1	3	11	9	1	8	11	14	1	8	11	14	1	8	11	14
2	4	10	12	2	4	12	10	2	4	12	10	2	4	12	10	12	10	2	4	15	10	5	4
5	7	13	15	5	7	15	13	6	8	16	14	6	3	16	9	6	3	16	9	6	3	16	9
6	8	14	16	6	8	16	14	5	7	15	13	5	7	15	13	15	13	5	7	12	13	2	7


1	2	9	10	1	2	10	9	1	2	10	9	1	8	10	15	1	8	10	15	1	8	10	15
3	4	11	12	3	4	12	11	3	4	12	11	3	4	12	11	12	11	3	4	14	11	5	4
5	6	13	14	5	6	14	13	7	8	16	15	7	2	16	9	7	2	16	9	7	2	16	9
7	8	15	16	7	8	16	15	5	6	14	13	5	6	14	13	14	13	5	6	12	13	3	6

Transformation to a Franklin panmagic 8x8 square

Transform a 8x8 square with sequential digits to a Franklin panmagic 8x8 square in 5 steps by swapping each time ‘yellow’ and
‘red’; see below:

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


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

Transformation to a most-perfect 12x12 magic square

Transform a 12x12 square with sequential digits to a most-perfect 12x12 magic square in 5 steps by swapping each time ‘yellow’
and ‘red’; see below:

		#	*			@	@			*	#
1	13	25	37	49	61	73	85	97	109	121	133		1	13	133	121	49	61	85	73	97	109	37	25
2	14	26	38	50	62	74	86	98	110	122	134		2	14	134	122	50	62	86	74	98	110	38	26
3	15	27	39	51	63	75	87	99	111	123	135	#	3	15	135	123	51	63	87	75	99	111	39	27
4	16	28	40	52	64	76	88	100	112	124	136	*	4	16	136	124	52	64	88	76	100	112	40	28
5	17	29	41	53	65	77	89	101	113	125	137		5	17	137	125	53	65	89	77	101	113	41	29
6	18	30	42	54	66	78	90	102	114	126	138		6	18	138	126	54	66	90	78	102	114	42	30
7	19	31	43	55	67	79	91	103	115	127	139	@	7	19	139	127	55	67	91	79	103	115	43	31
8	20	32	44	56	68	80	92	104	116	128	140	@	8	20	140	128	56	68	92	80	104	116	44	32
9	21	33	45	57	69	81	93	105	117	129	141