A three-row and three-column matrix composed of nine numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9, whose diagonal, horizontal and vertical sums are all 15, is called 15. This is the simplest third-order magic square.

Fill in by hand, the method is simple, you can fill in at will, but the disadvantage is that it needs reasoning and is not fast enough:

1+9= 10,2+8= 10,3+7= 10,4+6= 10。 If the sum of each logarithm plus 5 equals 15, it can be determined that the center grid should be filled with 5, and these four groups of numbers should be filled in the horizontal, vertical and diagonal positions respectively. Fill in four corners first. If you fill in two odd pairs, then you may get an odd number, because the sum of three odd numbers. You can't fill in any odd numbers in the four squares. No If all four corners are a pair of even numbers and an odd number, that won't do either. Therefore, it is decided that two even pairs must be filled in the four corners. After the numbers on the diagonal are filled in, the odd numbers in the remaining boxes are easy to fill in.

Formula method, the fastest, need to remember:

Yang Hui, a mathematician in the Southern Song Dynasty, summarized the construction method as follows:

"Nine oblique row. It's easy to go up and down, but it's more important to be left and right. All four dimensions are outstanding. "

The filling formula of Jiugongge in ancient China is:

In the sense of the Nine Palaces, Buddhism takes Gui Ling as the shoulder, 24 as the shoulder, 68 as the foot, 7 as the left, 3 as the right, 9 as the shoe and 5 as the heart.

There is also a combination of the two:

Nine sons are arranged obliquely, which is changeable up and down.

The left and right sides are more similar, and the four dimensions are prominent.

Wear nine, walk one, left seven, right three,

Two or four are shoulders, and six or eight are feet.