Merzirac's formula for generating odd-numbered magic squares: (applicable to all odd-numbered magic squares, 3×3, 5×5, etc. )

1? In the middle of the rising line, don't forget to fill it diagonally in turn. Write down the boundaries of the upper and lower boxes, and put the left box on the left. If it is repeated, fill in the box below and repeat it at the corner.

The third-order magic square is an odd-order magic square, which is filled in according to the formula, as shown in the following figure:

There is more than one solution to the third-order magic square. There are seven forms, * * * eight forms. Turn the third-order Rubik's Cube (Jiugongge) and mirror it (turn it over).

The sum of the third-order magic square is equal, and this sum is called magic square sum = 15.

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, 3 as the left, 7 as the right, 9 as the shoe and 5 as the heart.

Second-and fourth-order magic squares

The formula of generating double even magic square by spring method;

Fill in the numbers in turn and exchange them symmetrically around the center point.

The fourth-order magic square is the simplest dichotomy magic square, and its method is as follows:

Step 1: Fill in the numbers in sequence. First, put 1 on any of the four corners of the fourth-order Rubik's cube, and fill the rest of the numbers in the same direction in turn.

The second step is to exchange numbers symmetrically with the center point. (There are two methods of symmetric exchange)

Method 1: Symmetrically exchange the numbers on the diagonal with the central point (i.e. 1- 16, 4- 13, 6- 1 1 7- 10 exchange) to complete the magic square and magic sum 34.

Method 2: Symmetrically exchange off-diagonal numbers with the central point (i.e. 2- 15, 3- 14, 5- 12, 8-9 exchange) to complete the magic square and magic sum 34.

There are 880 methods for the fourth-order magic square.

Details/Math/x-huanfeng10.htm

Third-and fifth-order magic squares

There are many ways to fill in the fifth-order Rubik's cube. I'll give you a few, hoping to help you.

1, one of the stair methods (step back stair method):

Put the smallest number 1 into the five yellow squares as shown in the figure, and fill in 2, 3, 4 ... from the upper right in turn. If it appears above the Rubik's cube, fill the number in the lowest square in the column that should be filled; If it reaches the right side of the Rubik's cube, fill the number in the leftmost box of the line that should be filled in; If there is a Rubik's cube in the upper right corner (that is, diagonally)? Fill in the numbers in the lower left corner of the Rubik's Cube. If there are numbers in the upper right, move down one space and continue to fill in, and complete the magic square, with magic sum =65.

2, the second staircase method (two steps back staircase method):

As above, put the smallest number 1 into the five yellow squares as shown in the figure, and fill in 2, 3, 4 ... to the upper right in turn. If there are numbers in the upper right corner, move down two squares and continue to fill in.

3. The third step-by-step stair method, namely loubere method:

Put the smallest number 1 in the middle box, and fill in 2, 3, 4 at the upper right in turn ... If there is a number at the upper right, move it up to the second box to continue filling in.

4. A storage method (backward):

As the saying goes: Take a step back and broaden the horizon. The following fifth-order magic square completed by vault is an example.

Put the smallest number 1 in any box, take 1 step to the right, take two vault steps up, and fill in 2, 3 and 4 in turn. If there are numbers in the box, step back and continue to fill in, and the Rubik's Cube can be completed. The magic square completed in this way is called the perfect magic square.

5. The second insurance storage method (further):

Put the smallest number 1 into the five yellow squares as shown in the figure, take 1 step to the right, take two vault steps up, and fill in 2, 3, 4 in turn ... If there are numbers in the step-down box, continue to fill in a box up, and the Rubik's Cube can also be completed.

6, vault method 3 (two steps back):

Put the smallest number 1 into the five yellow squares as shown in the figure, walk 1 step to the right, take two vault steps up, and fill in 2, 3, 4 in turn ... If the number in the step-down box already exists, step back two squares to continue filling in, and the Rubik's Cube can also be completed.

I haven't counted how many forms there are in the Fifth Order Rubik's Cube. However, after each completion of the above method, there are seven ways to turn this one over and mirror it (turn it over).

If you are interested in Rubik's Cube, you can visit my Baidu space.