30 32 34 2 1 23 25 66 68 70
3 1 36 29 22 27 20 67 72 65
80 73 78 44 37 42 8 1 6
75 77 79 39 4 1 43 3 5 7
76 8 1 74 40 45 38 4 9 2
17 10 15 62 55 60 53 46 5 1
12 14 16 57 59 6 1 48 50 52
13 18 1 1 58 63 56 49 54 47
I met many friends who also like math problems and asked 9 square questions. I am here to make answers and solutions, hoping to give you some help.
Nine squares, twenty-five squares and even eighty-one squares, as long as they are odd squares, can be added with horizontal squares, real squares and diagonal squares to get the same number. There are only sixteen squares for even squares, and there are some rules.
Below are three squares, five squares, seven squares and nine squares.
Sangongge (and 15)
8 1 6
3 5 7
4 9 2
Five squares (and 65)
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
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
There is a unified solution to this kind of problem, which was discovered by a mathematician and can be used for all odd squares, or was learned in our primary school mathematics competition. Fill in the rules as follows
Fill 1 in the middle of the first line.
Fill in the numbers in order, like the upper right corner.
If it is above the square matrix, fill in the number in the bottom box of the column where it should be.
If it is on the right side of the square, fill the number in the leftmost box of the line where it should be.
If there are numbers in the upper right corner of the square or outward to the upper right corner (diagonal direction)
The number is filled in the next cell of the previous number.
Compare the answers I gave you, and you will fully understand that you can draw 9,49 palaces and 8 1 palaces, which is absolutely wonderful.
Seven squares (and 175)
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
Jiugongge (and 369)
47 58 69 80 1 12 23 34 45
57 68 79 9 1 1 22 33 44 46
67 78 8 10 2 1 32 43 54 56
77 7 18 20 3 1 42 53 55 66
6 17 19 30 4 1 52 63 65 76
16 27 29 40 5 1 62 64 75 5
26 28 39 50 6 1 72 74 4 15
36 38 49 60 7 1 73 3 14 25
37 48 59 70 8 1 2 13 24 35
This is the arrangement diagram of 8 1 square, from which we can find the rules.
Write 1 in the middle of the first line, then move down to the bottom, move one space to the right and write down 2, and finally write it to the upper right.
Then pan to the far left, move up one space and write in the upper right corner. When you meet a number, write down a space and continue to write to the right.
According to this rule, you can write any odd square grid.
Even the squares are irregular, except for the sixteenth house, nothing seems to be filled in. There is also a rule in the filling of the sixteenth house, which is called "orderly arrangement and shoulder exchange", that is, the first line writes 1, 2, 3, 4, the second line writes 5, 6, 7, 8, and the fourth line writes 13, 14,1.
Sixteen squares (and 34)
1 15 14 4
12 6 7 9
8 10 1 1 5
13 3 2 16