Detailed explanation of the solution of Luoshu Jiugong: odd and even numbers staggered

When Dayu was controlling the water, the turtle came out of Luoshui, and the patterns on the turtle's back were arranged in nine positions from one to nine, also known as Luoshu. There is a formula: "Wear nine shoes as one, the left three as seven, two as four shoulders, six as eight, five as the center, and the image of the turtle's back is also right." Five, as the middle of nine natural number sequences, it is located in the middle of Luoshu, with even numbers two, four, six and eight as yin, which is the way to the earth, marked by black dots, located in four corners (also called four dimensions, northeast, southeast, southwest and northwest), odd numbers one, three, seven and nine are the way to heaven, marked by white dots, which are located in four positive directions (due east, northwest)

Luoshu pattern is arranged by the number of black and white dots. On this basis, it later evolved into a nine-palace eight-door diagram commonly used in the related branches of the Book of Changes, referred to as Nine palace map.

The arrangement and distribution of Nine palace map follows strict mathematical algorithm and the law of sequence. It looks like nine simple numbers, but its hidden order changes endlessly. In addition to the ever-changing arithmetic, Nine palace map is also used to study the running laws of the nine planets. Nine palace map's thinking mode of enterprise management and the optimized layout of environment are of great significance for us to broaden our thinking and formulate the future development strategy of enterprises. The characteristic of Luo Shu Nine palace map is that the natural numbers of 1~9 are arranged in nine squares. In arithmetic, the sum of all the diagonal numbers is equal to 15. The arrangement of numbers in Jiugongge must follow the formula mentioned above, and there is no other answer. Odd and even numbers are staggered, the four corners are even, and the middle and four are odd.

Nine palace map numbers vary endlessly, among which four groups of arithmetic progression: [4, 5, 6], [3, 5, 7], [2, 5, 8], [1, 5, 9] all rotate counterclockwise around 5, and the tolerances of each series are 1, 2, 3, 4 respectively. If the even number of four corners rotates clockwise to four positive positions, the difference between odd and even numbers is equal to 5. It is not surprising that these laws can be found in ordinary primary and secondary school students. Nine palace map is even more magical: except that the sum of the numbers on the horizontal, vertical and diagonal lines is equal to 15, no matter which line or diagonal line is combined into three groups of numbers in a positive and negative cycle, they are all equal. Let's take [4,9,2] in the first row, [3,5,7] in the second row, and [8, 1 6] in the third row as examples.

(1) When these three numbers are combined in pairs to form the addition of three two-digit numbers, the sum of the values is still equal. The specific operation is as follows:

Forward circulation

49+92+24=35+57+73=8 1+ 16+68= 165

backcycling

29+94+42=75+53+37=6 1+ 18+86= 165

(2) When these three numbers are combined into three three-digit additions through three cycles, the sum of the values is still equal. The specific operation is as follows:

Forward circulation

492+924+249=357+573+735=8 16+ 168+68 1= 1665