What are the rules of Jiugongge?

"Jiugongge" is an ancient structural scheme in China. Ou Yangxun introduced it into calligraphy practice to gain a sense of stability and order in its structure. Zhu Gekongming combined the thoughts of gossip and Jiugong, and evolved Jiugong Bagua Array by using the interdependence between the structures of Jiugong Bagua Array. China's metaphysics introduced it into the magic art of Taoism and applied it. "Jiugongge" criss-crosses, forming nine independent and interdependent units, with regular and interdependent combinations inside. The design inspiration of designer quot comes from the structure of "nine squares" and takes "nine songs"; Based on this design concept, the plane of Ling Xing International Center was designed separately. The middle compartment is designed for elevator shaft, tube shaft and stairs, and eight office units of different sizes are arranged around it in turn. Eight independent small modular units, which are flat inside and open outside, are combined with each other.

Form a larger combined open space, thus making the overall spatial structure layout more regular and providing greater freedom for the free combination of spaces. The founder of Jiugongge is Ou Yangxun.

Basic elements of Sudoku

Cell: the smallest unit in Sudoku, with 81in standard Sudoku;

Row: a group of 9 horizontal cells;

Column: a collection of 9 vertical cells;

Palace: the area divided by thick black lines is a collection of 9 cells in standard Sudoku;

Known number: the number given by the initial disk of Sudoku;

Candidate number: the number that can be filled in each empty cell.

Basic rules of Sudoku

The rule of standard Sudoku is to fill in the number 1-9 in each row, column and house of Sudoku, and it cannot be repeated.

Basic solution example

Sudoku solutions are all derived from rules, and the basic solutions are divided into two ways, one is the exclusion method and the other is the unique method. More complex solutions will eventually fall into these two categories. Let's briefly introduce several solutions with charts. As long as you take a few minutes to look at them, you can start Sudoku right away.

Basic exclusion method

The basic elimination method is a method to solve problems by using the rule that the number 1 ~ 9 can only appear once in each row, column and room. Basic exclusion methods can be divided into row exclusion method, column exclusion method and nine-square exclusion method.

The actual process of finding a solution is:

Find the solution of nine squares: find the situation that there is only one number left in the position where a nine squares can be filled; That is, I found the filling position of the number in the nine squares.

Find the column exclusion solution: find the case where only one number can fill a column; This means that the filling position of the number in this column has been found.

Looking for exclusive solutions: looking for a situation where only one number can be filled in a row; This means that the filling position of this line of numbers has been found.

The lifting method of foundation exclusion method is block exclusion method, which is one of the most commonly used methods in intuitive method.

Unique solution

When eight cells in a row are filled with numbers, the only number that can be filled in the remaining cells of the row is the number that has not yet appeared. Become a unique solution.

When a column has eight cells filled with numbers, the only number that can be filled in the remaining cells of the column is the number that has not yet appeared. Become a unique solution for chromatographic columns.

When the number of squares in a nine-square grid has reached eight, then the number that can be filled in the remaining squares of this nine-square grid is only the number that has not yet appeared. Become the only solution of Jiugongge.

Congruence solution

The congruence solution is that the number that can be added to a cell has been excluded, so the number of this cell can only be added to the number that does not appear.

Block exclusion method

Block exclusion method is a generalization of basic exclusion method and one of the most commonly used methods in intuitive method.

Residual test method

The so-called remainder test method is a problem-solving method of adding the values of the remaining cells when there are more numbers in a row or a column and there are two or three remaining cells.

Implicit unique candidate number method

When a number appears only once in the candidate numbers of each grid of a column, it is the only candidate number of the column. The value of this grid can be determined as this number. At this time, because according to the rules of Sudoku, each column should contain the number 1 ~ 9, and the candidate numbers in other grids do not contain this number, so it cannot appear in other grids, so it can only appear in this grid. ..

Triple chain number deletion method

The method of finding out no more than three different numbers in a column, a row or a nine-grid candidate, and then deleting these three numbers from the candidates in other grids is called the three-chain number deletion method.

Implicit triple chain number deletion method

In a row, there are three numbers in the same cell, but none of the other cells in the row contain them. We call this number pair the invisible triple chain number. Then all other numbers in the candidates of these three cells can be excluded.

When the invisible triple chain number appears in the column and nine squares, the treatment method is exactly the same.

Rectangular vertex deletion method

The rectangular vertex deletion method is the same as the rectangular exclusion method mentioned in the intuitive method. Rectangular vertex deletion method is not easy to find in recognition, so it is better to use other methods first.

Triple chain deletion method

The triple chain deletion method is an extension of the rectangular vertex deletion method. If you are not clear about the rectangular vertex deletion method, you can refer to the rectangular vertex deletion method to make it easier to understand the contents of this section. Find out the situation that a number only appears in the same three rows of a certain three columns, and then delete the number from the candidates of other squares in these three rows; Or the method of "finding a number that only appears in three columns with the same three rows, and then deleting this number from other candidates of these three columns" is called triple-chain column deletion method.

Key number deletion method

In the later stage of solving problems, when the above-mentioned unique candidate number method, hidden unique candidate number method, block deletion method, number pair deletion method, hidden number pair deletion method, triple chain number deletion method, hidden triple chain number deletion method, rectangular vertex deletion method and triple chain column deletion method can not make progress, the key number deletion method can be considered. The key number deletion method is to find a number that only appears twice in the row (or column, nine squares) in the later stage. Suppose this number is in one of the lattice classes, continue to solve it, and if there is an error, determine our hypothetical error. If it is still difficult to continue solving, let's assume that this number is in another cell and see if we can get an error. This is the key number reduction method.