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How to fill in 36 squares?
Do you think it is possible to have more Rubik's Cube for the answer I am looking for? What is this? If the picture on the right is a Rubik's cube, that is, n * n (n >; =3) Put the numbers into the grid of n*n, so that the numbers in each row, column and diagonal of the grid are equal.

I have been interested in this for a long time, and I have gained something.

Odd order magic square

When n is odd, we call the magic square an odd magic square. It can be realized by Merzirac method and loubere method. According to my research, it is found that a more magical Rubik's Cube can also be constructed through chess posture, so it is named Mafa.

Even order magic square

When n is even, we call the magic square an even magic square. When n is divisible by 4, we call the even magic square a dichotomy magic square. When n is not divisible by 4, we call this even magic square simple even magic square. It can be realized by Hire method, Strachey and YinMagic. Strachey is a single couple model. I modified the double couple (4m order) and made another feasible mathematical model, called spring. YinMagic is a model I designed in 2002. It can generate any even magic square.

Before filling in the magic square, we make the following agreement: if the number is beyond the scope of the magic square, then the magic square is regarded as a graph that can be stretched indefinitely, as shown in the following figure:

Merzirac method for generating magic square

Put 1 in the square in the middle of the first line, and fill in 2, 3, 4… in the upper left. If there is a number in the upper left corner, move down one space to continue filling. The fifth-order magic square generated by Merziral method is as follows:

17 24 1 8 15

23 5 7 14 16

4 6 13 20 22

10 12 19 2 1 3

1 1 18 25 2 9

Generating odd-order magic squares by loubere method

Put 1 in the middle box, and fill in 2, 3, 4 in the upper right … If there are numbers in the upper right corner, move up two boxes to continue filling. The seventh-order magic square generated by Louberel method is as follows:

30 39 48 1 10 19 28

38 47 7 9 18 27 29

46 6 8 17 26 35 37

5 14 16 25 34 36 45

13 15 24 33 42 44 4

2 1 23 32 4 1 43 3 12

22 3 1 40 49 2 1 1 20

Generating odd-order magic squares by horse method

First, put 1 in any box. Go left 1 step, go down two steps to put 2 (called "horse stance just look"), go left 1 step, go down two steps to put 3, and so on. Put n+ 1 (called skip) under n, then put it under 2n according to the above method, and put 2n+ 1 under 2n. The fifth-order magic square generated by Ma method is as follows:

77 58 39 20 1 72 53 34 15

6 68 49 30 1 1 73 63 44 25

16 78 59 40 2 1 2 64 54 35

26 7 69 50 3 1 12 74 55 45

36 17 79 60 4 1 22 3 65 46

37 27 8 70 5 1 32 13 75 56

47 28 18 80 6 1 42 23 4 66

57 38 19 9 7 1 52 33 14 76

67 48 29 10 8 1 62 43 24 5

Generally let the matrix take a step to the left. The horse stance just look can be expressed as 2X+Y, {x ∈ {,}, y ∈ {[0, 1], [0, 1]} {y ∈ {,}, and the corresponding jump of X∈{[2X+Y can The above is an x jump. The Rubik's Cube generated by Mafa is the Devil's Cube.

Generating even-order magic squares by Hire method

Consider the magic square of order n as a matrix, and write it as a, and the numbers in the grid of row I and column J are written as a(i, j). Fill in 1, 2,3, ..., n on the two diagonal lines of A, and then fill in 1, 2,3, ..., n, so that the sum of the numbers in each row and column is n*(n+ 1)/2. The filling method is: line 1 is filled from n to 1, and line 2 to n/2 is filled from 1 (line 2, line 1, line 2, column n 1), and line 2, line n/2+/kloc. The following is the sixth-order filling method:

1 5 4 3 2 6

6 2 3 4 5 1

1 2 3 4 5 6

6 5 3 4 2 1

6 2 4 3 5 1

1 5 4 3 2 6

The following is the eighth-order filling method (after transposition):

1 8 1 1 8 8 8 1

7 2 2 2 7 7 2 7

6 3 3 3 6 3 6 6

5 4 4 4 4 5 5 5

4 5 5 5 5 4 4 4

3 6 6 6 3 6 3 3

2 7 7 7 2 2 7 2

8 1 8 8 1 1 1 8