Other orders

Nowadays, we know that there can be no bimagic square, whose order is less than 8 (take a look at the multimagic pages of Christian Boyer). All bimagic squares with a lower order are not composed of consecutive numbers beginning with 1, such as the following pandiagonal bimagic square sixth order of David M. Collison. (left fig.)

Other squares are indeed composed of the numbers from 1 to 36, but not all rows, columns and diagonals have the same sum. Although the following magic square, created by Pfeffermann in 1894, possesses magical columns, rows and diagonals fail. (right fig.)

15134745921
124320164910
48198141744
5412935373
3414038730
3633623142
1309262322
2918312274
17512243221
16341325320
3310356198
15141128736

There are several methods to construct bimagic squares of orders 8, 9 and 16, where each of them generates a great variety of different squares. But for different orders only a few squares are known and some of them are listed in the gallery.

For orders 8, 9 and 16 bimagic squares can be created that have additional properties. The following bimagic square of Brutus Portier for example, is symmetric and self-complementary. Additionally, you can also split the square into two Euler squares.

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17241395232677463
40473671785512255
61687521822333753
61026344148567276
29454960648071421
77577027411463542
19815503043815865
54313873626923316