The third-order magic square is a three-row and three-column matrix composed of nine numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9, and its diagonal, horizontal and vertical sums are all 15, which is called the simplest magic square. The third-order Rubik's Cube is also called Jiugongge.
The third-order magic square rule includes:
1, the relationship between magic sum and central number;
The sum of the Rubik's cube is the sum of the numbers on each row, column and diagonal, and the center number is the middle number of the Rubik's cube. The magic sum is equal to three times the central number.
2, the relationship between the number on the corner and other numbers:
The number on any corner is equal to half of the sum of two numbers that are not on the same line, column or diagonal with this number.
3, the relationship between the number of centers and the number of edges:
There are four magic sums passing through the center number, which just covers all the squares, and the center amount is calculated three times. Therefore, the number of centers is equal to one third of the magic sum.
4, the relationship between the number of edges:
By observing the numbers on both sides, we can draw some relationships, such as the sum of the numbers on both sides is equal to twice the middle number.
Complete solution of third-order magic square;
You can use the above law to solve it. Firstly, the sum of magic numbers is determined, then the center number is determined, and then the blank of the magic square is gradually filled according to the relationship between the number on the corner and other numbers and the relationship between the numbers on the side until a complete magic square is obtained.
The third-order magic square has many applications in mathematical research;
1, magic square is an important research topic in combinatorial mathematics. Studying the magic square can help us understand the laws and properties of number arrangement and explore the symmetry and combination methods in mathematics.
2. Magic Square is widely used in experimental design. By designing a proper magic square, the experimental factors can be evenly distributed under different conditions, thus reducing errors and improving the reliability of the experiment.
3. The Rubik's Cube can be regarded as a special graph structure, in which each number represents a node and the relationship between each number represents an edge. By studying the graph theory properties of magic square, we can reveal the relationship and connection between numbers.