MULTIMAGIE.COM - Bimagic squares, 9th-order

Bimagic squares, 9th-order

Only 6 months after publication of his first 8th-order bimagic square, G. Pfeffermann published in Les Tablettes du Chercheur, on July 15 1891, the first 9th-order bimagic square, or rather a part of it, the reader having to complete it.

Here is exactly how it was published. You must fill the 32 empty cells, knowing that the magic sum is 369, and that the bimagic sum is 20,049 for the 9 rows + 9 columns + 2 diagonals. Pfeffermann adds that his square is partially trimagic: the 4 lines going through the central cell (row + column + 2 diagonals) have a sum of 1,225,449 when each number is cubed.

1891: First odd-order bimagic square
(9th-order, of Pfeffermann)
	3	81	42		47	17	59
37		15	71		57	32		7
33	38		55		77		13	21
68	73	43				63	51	29
				41
53	31	19				39	9	14
61	69		5		27		44	49
75		50	25		11	67		45
	23	65	35		40	1	79

Pfeffermann published the solution of this square a fortnight later. Les Tablettes later published other 9th-order bimagic squares constructed by Pfeffermann.

See the link between Sudokus and 9th-order bimagic squares.

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	3	81	42		47	17	59
37		15	71		57	32		7
33	38		55		77		13	21
68	73	43				63	51	29
				41
53	31	19				39	9	14
61	69		5		27		44	49
75		50	25		11	67		45
	23	65	35		40	1	79

	3	81	42		47	17	59
37		15	71		57	32		7
33	38		55		77		13	21
68	73	43				63	51	29
				41
53	31	19				39	9	14
61	69		5		27		44	49
75		50	25		11	67		45
	23	65	35		40	1	79

	3	81	42		47	17	59
37		15	71		57	32		7
33	38		55		77		13	21
68	73	43				63	51	29
				41
53	31	19				39	9	14
61	69		5		27		44	49
75		50	25		11	67		45
	23	65	35		40	1	79