Nine palace map knew it, that is, the nine numbers 1~9 were filled into 3×3, so that the sum of the slopes of each level was equal, as follows:
4 9 2
3 5 7
8 1 6
Later, it has been expanded into digital art, which can be expanded indefinitely (because there are rules to be found, it is said that someone has done it 1999X 1999, or is it bigger than this? )
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Say 5*5 first.
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
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4*4 is here.
16 2 3 13
5 1 1 10 8
9 7 6 12
4 14 15 1
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There are two dazzling pearls in the ancient temple of China culture-Hutuluo, which has attracted the research enthusiasm of many scholars so far. People are extremely surprised by the mythical legend, profound meaning, rich content and concise form of Hutuluo, and even more puzzled by the close relationship between Hutuluo and China's ideological culture, social science and natural science. Various expositions show that Hutuluo is the general source of China culture, which has a far-reaching impact on the development of China and the world culture. However, to everyone's surprise and confusion, the book Hutuluo is just two simple numbers.
The dragon and horse carry the river map and the tortoise carries the letter.
Hutuluo was created by our ancestors. Looking through all kinds of classic works of the motherland, I can't find the founder at all. The appearance of Hutuluo can be traced back to at least 4500 years ago. At that time, mankind was still in an era without words, and the level of human understanding was still very low. It is hard to imagine that at that time, someone could create such an inscrutable book. Among all kinds of ancient books in China, there are only two legends about the origin of River Book. The tortoise carries the legend of River Book.
First, the dragon and horse carrying the river map
According to legend, in the ancient Jinmeng River, one day the river suddenly rose and the waves went straight into the sky. There is a huge beast in the water, like a dragon and a horse, flying in the waves. At that time, officials such as Fuxi Huangdi heard a report and immediately went to the river to watch it. They saw the huge waves in the flood. In the waves, a behemoth stepped on the water like a flat ground, but it was roughly like a scaly horse, eight or nine feet high and with wings. It is like a camel, with a pattern made up of spots. The Yellow Emperor ordered people to walk to the river and record the pattern. Hardly had I written it down when the monster disappeared. After studying this picture carefully, Emperor Fuxi found that it was composed of ten kinds of flower points, representing the number 1- 10 respectively. The two kinds of flower points form a group, which are arranged in five positions: east, west, north and south, and the difference between the numbers represented by each group is 5. This harmonious, unified and symmetrical feature makes Huang Diyue feel more and more wonderful in his research. Because this painting was found in Jinmeng River, it is called a river map.
Second, the tortoise is carrying a letter.
In the 23rd century BC, when Dayu was harnessing water, one day a turtle suddenly floated out of the Luoshui River, a tributary of the Yellow River. At that time, Dayu and the soldiers who were in charge of water conservancy were checking the water situation in Luohe and discussing the plan to control the Yellow River. It's strange to meet a turtle tossing up and down in the river. I saw this turtle walking around on the water, swimming around, with a huge figure and a flat back. A closer look reveals that there are nine patterns of mottling on the armor. Dayu asked the soldiers to write down the layout of the mottled pattern and take it back for in-depth study. He was surprised to find that the nine patterns of the spot were the nine numbers 1-9, and the positions of the numbers were quite clever. The sum of three numbers on six vertical and horizontal lines and two diagonal lines is 15, which is both balanced and symmetrical, profound and interesting. Inspired, Dayu divided rain into nine categories with reference to nine numbers, and also divided general political affairs into nine Olympics. According to Records of the Historian Xia Benji, Yu Xia once said: "Zuo Yuntong adjusted his tune to the right, and decided it at four o'clock, making Kyushu open, nine roads open, and nine rivers evil ..." Dayu's water control was based on nine palaces and was applied to surveying, mapping, meteorology, geography and transportation, thus governing the Yellow River, which achieved great success and won the support of people on both sides of the Yellow River. Because the picture on the turtle's back was found in Luoshui, a tributary of the Yellow River, and the content in the picture is profound, people call it Luoshu.
structured approach
There is a mathematical method for this odd number problem, and a solution can be constructed. It's more troublesome to describe.
How to construct the solution:
First, set 1 at the center of the bottom row of the whole matrix.
Then fill in 2, 3, 4, 5, 6, 7, ...
Pay attention to turn the number to the top when touching the bottom, and turn to the left when touching the right.
For example, in a 5*5 Rubik's Cube, if 1 is filled with (5,3), 2 is filled with (1 4) and 4 is filled with (3,0/). ...
In addition, when there is a number below the original number, the number to be filled in should be filled right above the original number.
Let's take the 5*5 Rubik's Cube as an example. When 5 is filled with (4,2), its lower right is 1. You can't fill in 6 there, you have to fill in (3,2), which means more than 5.
Finally, a special point, the lower right corner, should also fill in the new number above the lower right corner.