Franklin (panmagic) 8x8 transformation - Magisch vierkant

8x8 magic square

Franklin (panmagic) 8x8 transformation

It is also possible to swap a 8x8 square with consecutive numbers into (a version of) the famous 8x8 Franklin magic square in the following 4 steps:

Swap column 3&4 and 7&8 rearrange the rows (1-8, 2-7, 3-6, 4-5) swap colours and bold & not bold

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

Swap row 2 and 3 and 6 and 7 8x8 Franklin magic square

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

Take two extra steps to transform the 8x8 Franklin magic square into an 8x8 Franklin panmagic square:

Swap column 1 and 2 and column 5 and 6

			130	130	130	130	130	130	130	130
			130	130	130	130	130	130	130	130
		146									114
130	130		16	1	64	49	48	33	32	17
130	130		50	63	2	15	18	31	34	47
130	130		9	8	57	56	41	40	25	24
130	130		55	58	7	10	23	26	39	42
130	130		14	3	62	51	46	35	30	19
130	130		52	61	4	13	20	29	36	45
130	130		11	6	59	54	43	38	27	22
130	130		53	60	5	12	21	28	37	44
		114									146
			130	130	130	130	130	130	130
			130	130	130	130	130	130	130
			130	130	130	130	130	130	130
			130	130	130	130	130	130	130
			130	130	130	130	130	130	130
			130	130	130	130	130	130	130
			130	130	130	130	130	130	130

Swap in each 4x4 sub-square yellow and red

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

Franklin panmagic 8x8 square:

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

8

9

64

49

40

41

32

17

130

130

58

55

2

15

26

23

34

47

260

260

130

130

1

16

57

56

33

48

25

24

260

260

130

130

63

50

7

10

31

18

39

42

260

260

130

130

6

11

62

51

38

43

30

19

260

260

130

130

60

53

4

13

28

21

36

45

260

260

130

130

3

14

59

54

35

46

27

22

260

260

130

130

61

52

5

12

29

20

37

44

260

260

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

130

8x8, Franklin transformation.xls

Microsoft Excel werkblad 56.0 KB

8x8 magic square