9, 10, 1 1, 15, 16, 17, 2 1, 22, 23 are three symmetrical arithmetic arrays, which can form a third order. The two most commonly used methods, formula method and mathematical method, are as follows:

The prefix can be placed in the middle of both sides, or it can be filled diagonally.

Magic sum =3× 16=48. That is, the sum of the three numbers of rows, columns and diagonal lines is equal, all of which are 48.

The third-order magic square has one and only one basic solution and eight forms. Among them, seven forms are obtained by the rotation and mirror image (flip) of the basic solution, which is the isomorphism of the basic solution.

10, 1 1, 15, 16,17,21,22,23, the sum of these 9 numbers is 144.

There are two groups of numbers where the maximum number of 23 adds up to 48: 9, 16 and 10, 15, so the maximum number of 23 can only be within the margin.

Similarly, there are two groups that add up to 48, the smallest numbers are 9:16,23 and17,22, and the smallest number 9 can only be in the side grid.

There must be three sets of numbers in the corner grid, which add up to a magical sum. )

Therefore, 9, 16 and 23 must be filled in the middle row (or column), 10 and 15 in the two corners adjacent to 23.

Every row, every column and two diagonal lines know that the sum is 48 and two numbers, and then the third number can be found in turn.