9x9 bimagic square

See On the website of Harvey Heinz a bimagic 9x9 square of John Hendricks:

http://www.magic-squares.net/multimagic.htm

A bimagic square is a simple magic square, but also if you fill in the squares of the numbers (= number x number), you get a valid (impure) magic square.

The bimagic 9x9 square of John Hendricks consist of 4 regular ternary grids. You can put the grids in random order and you can swap the numbers 0, 1 and 2 in each grid to get more possibilities:

0	2	0	0	0	1	0	2
1	0	1	2	1	2	1	1
2	1	2	1	2	0	2	0

*1x number +1 1x number +1*
0	2	1	2	1	0	1	0	2	0	0	0	1	1	1	2	2	2
1	0	2	0	2	1	2	1	0	2	2	2	0	0	0	1	1	1
2	1	0	1	0	2	0	2	1	1	1	1	2	2	2	0	0	0
0	2	1	2	1	0	1	0	2	1	1	1	2	2	2	0	0	0
1	0	2	0	2	1	2	1	0	0	0	0	1	1	1	2	2	2
2	1	0	1	0	2	0	2	1	2	2	2	0	0	0	1	1	1
0	2	1	2	1	0	1	0	2	2	2	2	0	0	0	1	1	1
1	0	2	0	2	1	2	1	0	1	1	1	2	2	2	0	0	0
2	1	0	1	0	2	0	2	1	0	0	0	1	1	1	2	2	2


*+ 3x number + 3x number*
2	1	0	0	2	1	1	0	2	0	1	2	1	2	0	2	0	1
2	1	0	0	2	1	1	0	2	2	0	1	0	1	2	1	2	0
2	1	0	0	2	1	1	0	2	1	2	0	2	0	1	0	1	2
1	0	2	2	1	0	0	2	1	0	1	2	1	2	0	2	0	1
1	0	2	2	1	0	0	2	1	2	0	1	0	1	2	1	2	0
1	0	2	2	1	0	0	2	1	1	2	0	2	0	1	0	1	2
0	2	1	1	0	2	2	1	0	0	1	2	1	2	0	2	0	1
0	2	1	1	0	2	2	1	0	2	0	1	0	1	2	1	2	0
0	2	1	1	0	2	2	1	0	1	2	0	2	0	1	0	1	2


*+ 9x number + 9x number*
1	2	0	1	2	0	1	2	0	2	0	1	2	0	1	2	0	1
2	0	1	2	0	1	2	0	1	0	1	2	0	1	2	0	1	2
0	1	2	0	1	2	0	1	2	1	2	0	1	2	0	1	2	0
2	0	1	2	0	1	2	0	1	0	1	2	0	1	2	0	1	2
0	1	2	0	1	2	0	1	2	1	2	0	1	2	0	1	2	0
1	2	0	1	2	0	1	2	0	2	0	1	2	0	1	2	0	1
0	1	2	0	1	2	0	1	2	1	2	0	1	2	0	1	2	0
1	2	0	1	2	0	1	2	0	2	0	1	2	0	1	2	0	1
2	0	1	2	0	1	2	0	1	0	1	2	0	1	2	0	1	2


*+ 27x number + 27x number*
1	1	1	2	2	2	0	0	0	0	1	2	2	0	1	1	2	0
0	0	0	1	1	1	2	2	2	0	1	2	2	0	1	1	2	0
2	2	2	0	0	0	1	1	1	0	1	2	2	0	1	1	2	0
2	2	2	0	0	0	1	1	1	1	2	0	0	1	2	2	0	1
1	1	1	2	2	2	0	0	0	1	2	0	0	1	2	2	0	1
0	0	0	1	1	1	2	2	2	1	2	0	0	1	2	2	0	1
0	0	0	1	1	1	2	2	2	2	0	1	1	2	0	0	1	2
2	2	2	0	0	0	1	1	1	2	0	1	1	2	0	0	1	2
1	1	1	2	2	2	0	0	0	2	0	1	1	2	0	0	1	2


*= bimagic 9x9 square = bimagic 9x9 square*
43	51	29	66	80	58	14	19	9	19	31	70	77	8	38	54	57	15
26	4	12	46	36	41	78	56	70	9	39	78	55	13	52	32	71	20
63	68	73	2	16	24	31	39	53	14	53	56	72	21	33	37	76	7
76	57	71	27	5	10	47	34	42	29	68	26	6	45	75	61	10	49
32	37	54	61	69	74	3	17	22	43	73	4	11	50	62	69	27	30
15	20	7	44	49	30	64	81	59	51	63	12	25	28	67	74	5	44
1	18	23	33	38	52	62	67	75	66	24	36	40	79	1	17	47	59
65	79	60	13	21	8	45	50	28	80	2	41	48	60	18	22	34	64
48	35	40	77	55	72	25	6	11	58	16	46	35	65	23	3	42	81

Putting the grids in random order gives (4 x 3 x 2 x 1 = ) 24 possibilities. Swapping the numbers 0, 1 and 2 within each grid gives ([3x2x1]x[3x2x1]x[3x2x1]x[3x2x1] = ) 1296 possibilities. In total you can construct (24 x 1296 = ) 31104 different 9x9 bimagic squares.

9x9, Bimagic 9x9 square.xls

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9x9 magic square