16 What numbers can form a fourth-order magic square? Four groups of arbitrary numbers, as long as the difference between the four numbers in each group is the same, can form a fourth-order magic square with Latin square. The following is the mathematical model of the fourth-order Latin square:

For example:

Fourth-order perfect magic square

If the array satisfies a+b=c and x+y=z,

That is, a=c-b, x=z-y, that is, 1, 2-row difference = 3,4-row difference, 1, 2-column difference = 3,4-column difference, and such an array can form a perfect Rubik's cube. Here is an example:

Perfect magic square means that not only the sum of rows, columns and two diagonals is equal to the magic sum, but also the sum of pan-diagonals parallel to the diagonal is equal to the magic sum. Imagine tiling the Rubik's cube like a tile, and then taking any 4×4 square is a Rubik's cube.

1- 16 is a special case of the above array, that is, 16 is an arithmetic number, which is different from 1.

Arrays that can form a fourth-order perfect magic square can be arranged in sequence, and the magic square can be completed by symmetrically exchanging numbers at the center point. As shown in the figure below: