Shift method

You can use this method to construct magic squares of odd order which are no multiple of 3 (= 5x5, 7x7, 11x11, 13x13, 17x17, ... magic squares). Construct the first row of the 7x7 magic square with the numbers 0-a-b-c-d-e-f (fill in the numbers 1 up to 6 in random order instead of a up to f; that gives 6x5x4x3x2 = 720 different combinations).

1x number from shift 2 to the left + 7x number from shift 2 to the right+1 = Panmagic 7x7 square

0	1	2	3	4	5	6	0	1	2	3	4	5	6	1	9	17	25	33	41	49
2	3	4	5	6	0	1	5	6	0	1	2	3	4	38	46	5	13	21	22	30
4	5	6	0	1	2	3	3	4	5	6	0	1	2	26	34	42	43	2	10	18
6	0	1	2	3	4	5	1	2	3	4	5	6	0	14	15	23	31	39	47	6
1	2	3	4	5	6	0	6	0	1	2	3	4	5	44	3	11	19	27	35	36
3	4	5	6	0	1	2	4	5	6	0	1	2	3	32	40	48	7	8	16	24
5	6	0	1	2	3	4	2	3	4	5	6	0	1	20	28	29	37	45	4	12

It is also possible to shift the numbers of the first row 3 (instead of 2) places to right/left, and you get more 7x7 panmagic squares (see website: www.grogono.com/magic/7x7.php ). There are 6 possibilities to shift the first row in the first grid / second grid:

2 to the left / 2 to the right
2 to the left / 3 to the right
2 to the left / 3 to the left
3 to the left / 2 to the right
3 to the left / 3 to the right
3 to the left / 2 to the left

Construct all 6 (above mentioned shift possibilities) x 720 (combinations first grid) x 720 (combinations second grid) x 49 (shifted version on the 2x2 carpet) x 8 (by rotating and/or mirroring) / 4 (because of duplications) is 304.819.200 panmagic 7x7 squares.

Use the shift method to construct magic squares of odd order from 5x5 to infinity.

See 5x5, 7x7, 9x9 (1), 9x9 (2), 11x11, 13x13, 15x15 (1), 15x15 (2), 17x17, 19x19, 21x21 (1), 21x21 (2), 23x23, 25x25, 27x27 (1), 27x27 (2), 29x29 and 31x31

7x7, shift method.xls

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7x7, shift method, shift possibilities.x

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7x7 magic square