Do you have to use the numbers 1 to 16 for the fourth order magic square?

All magic squares start at 1.

The fourth-order magic square is composed of 1-64. （4*4*4）

Generally fourth-order magic square].

What kind of 16 numbers can make up 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, you can use the Latin square to form a fourth-order magic square. The following is the number guess of the fourth-order Latin square of this model:

Example: <>

Fourth-order perfect magic square].

If the array satisfies a+b=c, x+y=z, i.e., a=c-b, x=z-y, that is, the difference between the rows, the difference between the rows, the difference between the columns, the difference between the columns, the array of which can form a perfect spike magic square. As shown in the following figure, it is an example

A perfect magic square is that not only the sum of rows, columns, and two diagonals is equal to the magic sum, but also the sum of the pan-diagonals parallel to the diagonal is equal to the magic sum. Imagine tiling the magic square like a tile, and then taking any 4 or 4 squares is a magic square.

1-16 is a special case of the above array, i.e. 16 numbers are equally different numbers with a difference of 1 starting from 1.

Arrays that can form a perfect magic square of the 4th order can be completed by the method of [sequential numbering, symmetrical exchange of numbers at the center point]. As shown below:

Summary. In this question, the number 1 to 16 is filled in with the fourth-order magic square to get 34, not 25, because adding the number from 1 to 16 is 136, 136 4=34, 1 so 1 to. The number 16 fills in the fourth-order magic square and is 34

In this problem, the number 1 to 16 is 34, not 25, and the number is 136 because the number is added from 1 to 16, and 136 = 34, 1 so 1 to the sail group. The number of 16 is 34

There are 1, 2, 3, three**. 1 and 3, or 1 and 2 can be achieved.

Because: 1+9=2+8=3+7=4+6=10;

According to the above conditions, fill in and adjust the backup file to obtain a third-order magic square filial piety rolling stove, and its magic sum is 15.

Any of the eight third-order magic squares can be appropriately reversed and rotated to get the other seven.

The third-order magic square is the simplest magic square, also known as the nine-square grid, which is a matrix of three rows and three columns composed of nine numbers (as shown on the right) of nine numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, and its diagonal, horizontal, and vertical sum is 15, and the magic sum of this simplest magic square is 15. The number of centers is 5.

Odd-order magic square general construction method formula:

1 on the top of the line **, in turn oblique fill do not forget, on the frame boundary to write down, right out of the frame when the left side, repeat in the lower grid to fill, out of the corner repeat a sample.

The explanation is as follows: 1. Put 1 in the square in the center of the first row, and fill in ...;

2. If the grid to be placed in this number has exceeded the top row, then put it in the bottom row, and still put it in the right column;

3. If the grid to be placed in this number has exceeded the rightmost column, then put it in the leftmost column, and still put it in the previous row;

4. If there are numbers and diagonal lines in the upper right, move down one square to continue filling.

5. You can also fill in the corresponding number in the magic square in the corresponding position in the magic square.

For example, if 1 is the middle of the first row, fill in the corresponding 9 in the middle of the last row. 2 and so on.

In this way, if you do mirror or rotational symmetry, you can get the same other filling method: just place 1 in the middle of the four declensions, and fill in the rest of the numbers diagonally to the outside of the magic square; If it is out of the side, turn the number to the other side; If there are already numbers or corners in the target grid, fill in the numbers in one step, and then continue to fill in the remaining numbers diagonally in the same direction at the beginning.