The four magic cubes of order 3

There is only one magic square of order 3, excluding rotations and symmetries:

4	3	8
9	5	1
2	7	6

But there are four different magic cubes of order 3, again excluding rotations and symmetries:

Cube 1				Cube 2				Cube 3				Cube 4
1	17	24		2	18	22		10	26	6		12	26	4
15	19	8		24	1	17		24	1	17		23	1	18
26	6	10		16	23	3		8	15	19		7	15	20
23	3	16		15	19	8		23	3	16		22	3	17
7	14	21		7	14	21		7	14	21		9	14	19
12	25	5		20	9	13		12	25	5		11	25	6
18	22	2		25	5	12		9	13	20		8	13	21
20	9	13		11	27	4		11	27	4		10	27	5
4	11	27		6	10	26		22	2	18		24	2	16

In the four cubes:

• The magic sum is 42
• The center cell is the medium number 14 of the used numbers, from 1 to 27
• The 9 rows, 9 columns, 9 pillars and 4 triagonals (=space diagonals) of each cube are magic. But the small diagonals, for example 1+19+10 in Cube 1, are not always magic : it is impossible to construct a perfect magic cube of order 3.

Download these four existing standard magic cubes of order 3 (Excel file of 18Kb)

Return to the home page http://www.multimagie.com