The Magnificent Magic Cube

If you are fascinated by magic squares, you will be more astonished that magic cubes also exist, one of which is shown in the first figure.

Magic Cubes are cubical arrangements of numbers from to such that the sums of the rows and the sum of he columns are equal. In the magic cube above, the numbers from to are arranged in a cube and the sum of the numbers on each column and each row is .

The second figure shows the disassembled magic cube. As you can see, the sum of the rows and columns is indeed .

 

In the third figure, we can also see that the sum of all the space diagonals is also . Use the second  figure to check the other sums.

For those who are interested in Magic Cubes, read Magic Cube with Durer’s square.