Klsudoku traditional Sudoku game software user manual version 1.1

Handbook

Klsudoku traditional Sudoku game software user manual version 1.1

Statement

This manual can be obtained from the project wiki address to the latest version: http://code.google.com/p/klsudoku/wiki/HandBook

Authorization statement: without the authorization of ttylikl, all sections of this manual shall not be reproduced by any media or commercial organization. An individual can repost all or part of the chapters to the personal network media (such as a blog), but keep the source description of the manual for reprinting.

Directory

• Statement
• Directory
• Glossary
• Rule Description for Sudoku games
• Operation instructions on the klsudoku Interface
  • Normal mode operation instructions
    • Hot Spot count
    • Number of hot points
    • Methods for calculating the number of remaining operation hotspots
    • Tips for solving problems in Normal Mode
  • Operations on the candidate number Mode
    • Automatic Display of candidate quantity
    • Switching between common mode and candidate number Mode
    • How to Use the candidate number pattern to mark and solve problems
  • Klsudoku question format description
  • Copy and paste
  • Prompt and automatic Problem Solving
  • Undo and redo operations
• Klsudoku question generation and difficulty Division
• Common problem-solving skills
  • Basic skills in Normal Mode
    • Sole position Technique)
    • Basic Elimination Technique)
    • Block elimination technique)
    • Unique remainder (sole number Technique)
    • Combination Elimination Technique)
    • Rectangle elimination technique)
  • Problem-solving skills in the Candidate number Mode
    • Explicit unique number method (naked Single)
    • Implicit unique number method (hidden Single)
    • Intersection Removal)
    • Explicit number pair method (naked pair)
    • Implicit number pair method (hidden pair)
    • Explicit three-digit set method (naked triplet)
    • Implicit three-digit set method (hidden triplet)
    • Explicit four-digit set method (naked quad)
    • Implicit quartile set method (hidden quad)
    • Xy-wing)
    • XYZ-wing)
    • Rectangular diagonal line (X-Wing)
    • Sword fish)
    • Jelly fish)
    • Unique rectangle division unique rectangle (7 types)
    • X-chain)
    • Xy-chain)
    • Association deletion method (forcing-chain)
• Klsudoku appendix Information

Glossary

English	Chinese	Description
Cell	Lattice	Fill in (or fill in a small square with numbers)
Row	Line	The 9 numbers in the horizontal direction form a row, and the Sudoku is composed of 9 different rows.
Column	Column	The 9 numbers in the vertical direction of a Sudoku are a column, and the Sudoku is composed of 9 different rows.
Box	Block, Palace, Nine Palaces	A matrix composed of three numbers in the horizontal and vertical directions of a Sudoku is called a block. A Sudoku consists of nine different segments.
House, rcb	Row and column Blocks	A column or column block is collectively referred to as a block. It may represent a row or column or a block according to the context semantics.
Group	Group	For a cell, the Group is composed of all squares of its row, column, and block (excluding the cell). Therefore, the group has another English name peers20.
Candidate	Number of candidates	In a dag, the number 1-9 that has not been excluded is called the number of candidates. When only one candidate number is left in a grid, or only one number grid in a house has a certain number of candidates, this number of candidates is the only candidate number for this number grid.

Rule Description for Sudoku games

1. Each row in a Sudoku game has a number ranging from 1 to 9. Each number appears only once.
2. Each column in the sudoku game has a number ranging from 1 to 9. Each number appears only once.
3. Each box in a Sudoku game has a number ranging from 1 to 9. Each number appears only once.

In addition to the above three basic rules, the sudoku game also has several other rules:

1. Each Sudoku question must have a solution
2. Each Sudoku question can have at most one solution.

It has only one solution and is often used in some advanced solutions.

Operation instructions on the klsudoku Interface

The normal mode is the non-candidate number mode. In this mode, in the 9x9 integer, only the initial number and the number entered by the user will appear. You need to deduce the number that should be filled in for a certain number, and then enter it directly by pressing the key or mouse.

When playing a game in normal mode, you need to know the following questions:

1. How can I determine the number of operations to perform?
2. How do I enter the desired number?
3. How to mark the number of possible candidates?

In normal mode, klsudoku also provides an auxiliary method for prompting by the number of color tags and the number of candidates. When you encounter a difficult situation, you can use tips to continue the game.

Hot Spot count

In klsudoku, a hotspot number is used to identify the number of operations to be performed on. For example, if the A9 number is filled in orange, it indicates that it is the current hot number. The hotspot cell follows the mouse, but you can move it up, down, and left without the mouse.

Number of hot points

You can enter the number of hotspot cells by clicking the mouse or pressing the keyboard. It should be noted that if you want to fill in the number, and the number you fill in obviously violates the 1.2 game rules, your fill in operation is invalid, there may be no changes on the interface.

As shown in, you can change the default operation number by clicking the number of columns on the square matrix of 9x9, the current operation number is highlighted with a gray background and a black number.

When you click the left mouse button on the hot points, the default operation number is required for this number. However, if you hold down the ctrl key while clicking the left mouse button, the number of candidates that are the same as the default operation number will be added to the hotspot number. (in normal mode, the number of candidates is not automatically displayed, however, you can add or delete candidates by yourself ).

For example
If you do not use the mouse, you can use the keyboard to play the game. You can use the arrow keys to adjust the number of pods in 9 x
9. When moving to the boundary, if moving continues, the number of hot spots will appear in another direction.
When the hotspot number reaches the expected position, you can press the number on the keyboard to enter a number in the hotspot number. If you press the ctrl key while pressing the number
Add this number as the candidate number in the hotspot number, instead of entering this number.

Methods for calculating the number of remaining operation hotspots

Although you can use the mouse to quickly locate the number of hot points and perform the filling operation, you often have to select the default operand before filling in the number, which obviously affects the operation comfort. Therefore, a function is added to klsudoku. If you right-click a hot point, a shortcut label pop-up window is displayed, which allows you to perform quick operations.

The shortcut tag pop-up window contains two tabs: Enter number and set candidate number. Each tab has a number of 0-9, as shown in.

Mark
After the pop-up window appears, you can select a candidate or number of tags Based on the operation you want. The pop-up window will remember the selected tag for the last appearance. In many cases, this small feature can be quite convenient.
Operation.
After selecting the tag, you can click the corresponding number. If you click the number with the left mouse button, the pop-up window will immediately hide and disappear. You can also enter the number of hotspot cells or add candidates. Right-click
When a number or tag pop-up window appears, the pop-up window immediately hides and disappears without any operation on the hotspot number.

Tips for solving problems in Normal Mode

In
In normal mode, klsudoku can use color prompts for explicit and implicit unique number methods. For example, it shows the derivation process of an implicit unique number.
The derivation process of an explicit unique number is displayed. numbers 1-8 can be found in the row, column, and palace (Block) of H8. Therefore, H8 can only be filled with numbers 9, in the intuitive solution, this is also called the unique remainder.
Method.

In normal mode, klsudoku will display the number of candidates for some related numbers for some other advanced problem-solving skills to help you understand the reasoning process. Demonstrate the reasoning process of block exclusion:

It should be noted that, even in normal mode, if a prompt is used, the remaining candidates for the key number involved in the prompt will be displayed. For example, in addition to the number of candidates 7, the number of candidates for the numbers A8, A9, B8, C8, and C9 will also be displayed.

The operations in the Candidate quantity mode describe the automatic display principle of the candidate quantity.

In the candidate number mode, klsudoku automatically calculates the number of possible candidates in each unfilled number. The calculation principle is to exclude the numbers that appear in the row, column, and palace. In other words, if a cell is filled with a number, there will be no more candidates for all the other cells in the cell, row, and column.

The following figure provides a simple description:

For example, the E4 number is 7, so in Row E, column 4, and the ninth Palace where E4 is located, no number of candidates for all cells is 7. The automatic display of the number of candidates is based on the three basic game rules of the traditional standard Sudoku.

Switching between common mode and candidate number Mode

It also indicates that you can click the "number of candidates" button on the toolbar to display or hide the number of candidates for all numbers. In addition to this shortcut, you can click "edit"-> "option" in the menu, and then in the pop-up options window, click the check box before "show candidate quantity" to implement the same function. As shown in:

How to Use the candidate number pattern to mark and solve problems

There are three statuses for the number of candidates: not displayed, marked to be deleted, and normal.

Generally, the number of candidates that are not displayed is directly excluded due to the three basic rules of sudoku.

You can also right-click the number of candidates to mark them as deleted or normal.

When you use the get prompt or automatically solve the problem, if you have marked a candidate number as deleted in a certain number, klsudoku considers that this number does not exist.

Klsudoku question format description

Klsudoku supports the 9x9 numeric matrix format and 81-Character single-line question format. It can be replaced by 0 or. For countless words, klsudoku will automatically identify and process the question.

Klsudoku output question uses the 9x9 format. When loading a question, both the 9x9 format and the 81 character format are supported.

Examples of 9x9 format and 81 character format are as follows:

81 character format:

.216.784.7...1...39.......23.......82.......7.9.....6...4...7.....2.1.......8....

9x9 matrix format:

.216.784.
7...1...3
9.......2
3.......8
2.......7
.9.....6.
..4...7..
...2.1...
....8....

Klsudoku
You can generate a random question from lvl1.xml-
Lvl5.xml reads five levels of difficult questions for the game. When you install klsudoku, it has already carried more than 40 thousand simple questions by default. If you do not like it, you can attach the installation package
You can use klsudoku to instantly generate the latest question.

Copy and paste

You can copy and paste files from the menu or toolbar during the game.

1. You can copy the current situation of a game question to the clipboard.

The format of the copy is the same as that of the Number Matrix with nine columns in the current situation. The unfilled number is replaced by the dot. Note: The process of copying the current situation does not check whether the current situation is correct. That is to say, if there is an error in the manual problem solving process, the copied situation will keep this error,

1. You can also copy the starting scene of the current game to the clipboard.
2. You can also paste the sudoku questions to klsudoku from other software or websites for the game.

You can copy the problem-solving process to the clipboard during and after the problem-solving is completed.

Klsudoku will include the 9x9 format and 81 character format during the problem solving process. Then, the problem-solving process is gradually attached.

Prompt and automatic Problem Solving

Whether in normal mode or candidate number mode, you can choose either by pressing the CTRL-H or from the menu at any time, click the button in the toolbar to give klsudoku a simple problem-solving prompt.

Klsudoku colors the numbers and candidates associated with the prompts, and displays the reasoning process in text format in the status bar.

If you seek the klsudoku prompt and do not cancel the operation, but perform other problem-solving operations, the current prompt will be automatically executed. When you continuously obtain the prompt, it is equivalent to letting klsudoku perform an automatic one-step problem-solving operation.

You can also use the toolbar button to enable klsudoku to automatically solve the problem in one step or completely automatically, but note that, if there is an error in your manual problem solving process, the problem will be solved automatically and cannot be completed.

Undo and redo operations

Klsudoku automatically records the steps for solving your problem, and provides unlimitedly undo and redo functions based on this.

If you think there is a problem with the current error step, you can click the single-step Undo button on the toolbar to undo the previous step at any time. Similarly, you can click the "redo" button to undo the last Undo operation.

Klsudoku also verifies whether the problem-solving steps are correct and allows you to cancel all the wrong steps at a time to ensure that the current situation and the problem-solving steps are correct. When solving the problem, you can use the "cancel all errors" function to verify that your operation steps are correct and valid at any time.

Klsudoku question generation and difficulty Division

Klsudoku has five levels of difficulty: Easy, common, difficult, extremely difficult, ashes

• Easy: you only need to use the unique number method, block exclusion, and number pair exclusion to solve the problem.
• Common: in addition to the skills required for "easy" questions, you also need to use three-digit division, four-digit division, X-wing, xy-wing, and XYZ-wing to solve the problem.
• Difficulty: in addition to the skills required for the "common" question, you also need to use the unique rectangular division, swordfish? And jellyfish? Skills
• Extremely difficult: in addition to the skills required for "difficult" questions, you also need to use the X-chain, xy-chain, and forcing-chain skills to solve problems.
• Ashes: in addition to the skills required for "extremely difficult" questions, questions requiring other skills

Klsudoku can generate questions randomly and also support preset question libraries. the preset question library is lvl1.xml-lvl5.xml in the same directory.

Common problem-solving skills basic skills in Common Mode

Intuitive solution-solving skills are the most commonly used skills in general game mode. For complicated puzzles, you may need to enter the number of candidates and use advanced skills to solve problems.

Sole position Technique)

This should be the simplest method in the intuitive method. Basically, you only need to look at the puzzles and do not use reasoning and analysis. This is because the conditions needed to use them are very obvious. Likewise, it is because it is simple that it can only be used to deal with simple puzzles or later stages of complicated puzzles.

Let's take a look at the example. Row A shows that numbers exist in all cells except A5. According to the rule of the sudoku game, that is, each row, the column or block cannot contain repeated numbers. The numbers that can be entered in A5 can only be those that have not been shown in Row A, that is, number 7. Therefore, you can enter 7 in A5 without hesitation.

This is the application of the unit uniqueness method in the row. Unit, or group refers to rows, columns, or blocks. There are three situations:

• When a row has eight cells with numbers, or
• When a column has eight cells with numbers, or
• When a block has eight cells that contain numbers.

In either case, we can quickly enter a number that has not yet appeared in the row, column, or block space.

Similarly, we can also see the unique unit method in column and block (Palace) applications:

In Column 2nd, only B2 is not filled with numbers, and number 5 in this column has not yet appeared. So b2 = 5.

The same is true in blocks (palaces:

In the block starting from D1 (left jiugong), only F3 has not been filled with a number, and the number 9 in this block has not yet appeared, so you can enter 9 in F3 immediately.

The Unit uniqueness method has a low probability of application in the early stage of solving the problem. In the late stage of solving the problem, as more and more cells are filled with numbers, the conditions for applying this method are gradually met.

Basic Elimination Technique)

Unit Division is the most commonly used method in the intuitive method, and is also the most frequently used method for solving the sudoku puzzle. If used properly, you can even solve difficult puzzles separately.

The purpose of unit exclusion is to find the unique position in a unit (that is, a row, column, or block) that can be filled with a number. In other words, it is to exclude all other blank positions in the unit.

The Unit exclusion method corresponds to the implicit uniqueness method in the Candidate number method.

How can we exclude other spaces? Of course, you still cannot forget the game rules, that is, the row, column, or block cannot contain duplicate numbers. From another perspective

• If a number already exists in a row, the number cannot appear at any other position in the row.
• If a number already exists in a column, the number cannot appear at any other position in the column.
• If a number already exists in a block, it is impossible for other locations in the block to appear again.

Simply understanding the above rules is not enough to solve the problem, but in practice these rules can be used in combination. In the actual problem solving process, the most convenient and convenient application is the division of units in the block.

Let's take a look at the following example:

For blocks starting from A4 (the ninth Palace), we can use the relationship between rows, columns, and blocks, that is, a cell is on a row, it also solves this problem in a column and in a block.

1. Observe the position of number 5 in the puzzle and you can see it appears in A3, B8, D5, G6, and H5. Among these locations, only A3, B8, G6, and D5 are associated with the block starting with A4.
2. Because B8 = 5, it is impossible to see 5 in other cells on Row B, and B5 and B6 in the block are also on Row B, therefore, the possibility of entering 5 in these two cells is ruled out.
3. Similarly, because D5 = 5, it is impossible for other cells in the column 5th to enter 5, and B5 and C5 in the block are exactly in the column 5th. Therefore, B5, the possibility of entering 5 in C5 is also ruled out.
4. Let's look at the 6th columns again. Because G6 is 5, it is impossible to enter B6 and C6 in the column as 5, and these cells are also in the block starting from A4. Therefore, only C4 is left in the starting block of A4 (the ninth Palace) where the number 5 is entered, so that the answer is obtained by division, that is, C4 = 5.

Next, let's look at an example of unit exclusion in a row:

1. Observe number 5 and row G in the puzzle, and there are 6 empty cells in row G that cannot determine the number, however, the value 5 at the D5 position makes it impossible for other cells in the column 5th to appear 5, so G5 cannot be filled with 5.
2. 5 on H1 makes it impossible to enter 5 in the block (lower left 9th Palace). It helps Row g to exclude three cells G1, G2, and G3.
3. The number 5 in column B8 of column 8th makes the G8, which is also located in this column, exclude the possibility of entering 5. In this way, only G6 is left in the position of 5 in the row G.

You can also use unit exclusion in a column:

1. In column 4th, we try to determine the position where the number 1 can be entered. In row B, the number 1 already appears on B2, so B4 cannot be filled with the number 1.
2. The number 1 at D5 also makes D4, E4, and F4 exclude the possibility of entering the number 1, because they are located in the same block.
3. In row H, since the number of H7 is 1, H4 cannot be a number of 1. In this way, only I4 can be filled with the number 1 in column 4th.

The preceding example shows that to use unit division for a block, you need to observe the rows and columns that intersect the block. To use unit division for a row, observe the blocks and columns that intersection the row. To use unit division for a column, you need to observe the blocks and rows that intersection the column.

In
In the actual problem solving process, the relationship between rows, columns, and blocks is not as obvious as shown in the preceding figures. Therefore, we need to observe the relationship with eye and attention. Generally, the number that appears most frequently in the puzzle,
Start with a number, find the unit (row, column, or block) that has not been filled in the number, and use the relationship between the cell and the unit that has been filled in the number, check if you can exclude digits that cannot be filled with this number.
Until there is a unique position. If you are afraid of figuring out which numbers have been processed, you can check the blocks in the upper-left corner from Number 1 to the lower-right corner to see if you can
Division by units. Then test number 2, and so on.

Unit Division is the most intuitive method used. Although many chances of using this method are often missed due to carelessness in practice, it can be used freely as long as you work diligently.

Block elimination technique)

Block exclusion is an advanced technique in the intuitive method. Although it is not as widely used as unit division, it may be used to find solutions that cannot be found using unit division. Sometimes, when you encounter difficulties and cannot continue, you only need to use a block exclusion method to solve the problem.

Zone
Block exclusion is actually achieved by using the relationship between blocks and rows or columns, which is quite similar to unit exclusion. However, it is actually a fuzzy exclusion, that is, it is not like the unit exclusion
The current number in the puzzle is used to exclude rows, columns, or blocks, but not the specific position of the number. This sentence does not seem to be easy to understand. Let's start with an example,
Let's see how block exclusion is applied.

Let
Let's first look at number 1. We can see number 1 in C2, D5, and i8. How can we use block exclusion? (In this example, we can draw conclusions using other methods, but we will not consider other technologies first.
Coincidentally !)
Let's take a look at the lower left 9th Palace, which consists of C2 and i8 1. We excluded the possibility that G2, H2, i1, I2, I3, but there are still three numbers: G1, G3, and H3.
The grid can be number 1. As shown in:

For example
Why do we find the correct number 1 in G1, G3, and H3? We noticed that the number 1 in D5 ruled out the possibility of entering the number 1 in other cells in Row D. Because C2 excluded 2nd columns of other numbers
Enter the number 1, so we can draw a conclusion that in the left ninth Palace, only E3 and F3 can enter the number 1, and the Number 1 must also exist in E3, F3. So we can repeat
Some excluding inferences are as follows:

We can see that E3 and F3 must have numbers 1, so the other numbers in the 3rd Column cannot be numbers 1, that is, G3, H3 cannot be numbers 1.

So far, we can conclude that in the lower left 9th Palace, only G1 can enter the number 1.

The preceding solution is as follows:

In solving the problem, the division of unit units is actually applied in the blocks (Auxiliary blocks) that have an impact on the target block (main block, enable the secondary block to meet certain conditions and participate in the exclusion of the number of the primary block. In the preceding example, the lower left jiugong is the main block, and the lower left jiugong is the auxiliary block.

In practice, the following four situations may occur:

1. When a number can be filled in exactly the same row in a block, because the block must have this number, therefore, this number cannot appear on cells that are not in the block in this row.
2. When a number can be entered in a block in exactly the same column, because the block must have this number, therefore, this number cannot appear on cells in this block in this column.
3. When a number can be filled in exactly the same block in a row, because this number must exist in this row, therefore, this number cannot appear on cells that are not in this row in this block.
4. When a number can be entered in a column in exactly the same block, because the column must have this number, therefore, this number cannot appear on cells that are not in this column in this block.

Two of them are relatively common and easy to judge.

Block exclusion is also a very common advanced technique. Sometimes it takes multiple auxiliary blocks to get the final inference. However, you can quickly master this technique through a large number of exercises.

Unique remainder (sole number Technique)

The only remainder is not commonly used in the intuitive method. Although it is easy to understand, it is not necessary to explain this method. However, in practice, it is difficult to see whether the conditions for using this method can be met, this restricts the application of this method.

Compared with the unique unit method, the unique remainder distinct method is used to determine the number of cells that can be filled in. The unique unit method is used to determine the number of cells that can be filled in. In addition, the unique unit method is easy to understand.

Compared with the candidate number method, the unique remainder equals the explicit uniqueness method. Although the explicit uniqueness method is the simplest and easiest method to use in the Candidate number method, it is the opposite in the intuitive method.

For example, you can use the unique remainder of a G4 number to draw a conclusion. You can only enter the number 9. Because A4 = 1, G9 = 2, G2 = 3, D4 = 4, G3 = 5, F4 = 6, I5 = 7, G5 = 8, G4 = 9.

The inference process is well understood, but it is hard to notice this point during observation!

Combination Elimination Technique)

The combined exclusion method is the same as the block exclusion method. It is an advanced technique in the intuitive method, but its application scope is smaller. In general, there is basically no chance to use this method to solve problems, so it is also difficult to find the corresponding examples. Of course, if you want to give priority to this technique, you can still encounter many situations that can meet the conditions for using the combined exclusion.

Combination exclusion, as the name suggests, takes into account a combination. The combination includes both the combination of blocks and blocks, as well as the combination of cells and cells, and some exclusion by means of the Association and rejection of the combination. It is also a type of fuzzy exclusion. It is also excluded when you are not sure about the specific position of a number. The following is an example:

Can you determine the position of Number 6 in the block starting from G4 for the above puzzle?

It seems a little difficult to get the correct answer at first. Although there are already two 6 cells in G9 and H3, they can only be used to exclude the G4 and H6 cells in the block. It is still difficult to determine whether 6 is in I4 or I5. At this time, the combined exclusion method will be used.

Now, let's start with the G4 block. First, let's look at the two blocks above, that is, the blocks starting with A4 and D4. These blocks share the same number of columns, that is, 4th to 6th columns. Therefore, the numbers between these blocks affect each other directly.

For the block starting with A4, use the number 6 in A1 to exclude the row. We can see that there are only two places left in this block that may be filled with 6: B5 and C6. For the block starting with D4, use the number 6 in E7 to exclude the row. We can see that there are two places left in this block that may be filled with 6: F5 and F6.

At this time, we still cannot determine the exact location of 6 in the two blocks. However, you may wish to analyze the possible situations:

• Assume that in the block starting from A4, B5 = 6, C6 in the same block is not 6, and B5 also excluded F5, so that in the block starting from D4, only F6 = 6.
• Suppose that in the block starting from A4, C6 = 6, B5 in the same block is not 6, and C6 also removes column F6, so that in the block starting from D4, only F5 = 6.

Simplified
Simply put, there are only two possibilities: B5 = 6 and F6 = 6, or C6 = 6 and F5 = 6. There will never be any other situation. However, in either case, the 5th columns and 6th columns all have 6 definite results.
In these two blocks, that is to say, the number 6 cannot appear in other positions of the 5th column and the 6th column. In this way, the position of Block 6 starting from block G4 becomes uncertain at once.

Use blocks starting with A4 and D4 to exclude the blocks starting with G4, so that you can exclude I5. In this way, only I4 can be filled with 6.

To sum up, the conditions to be met for the combination exclusion are as follows:

• If a number may be filled in exactly the same two rows in two horizontally parallel blocks, these two rows can be used to exclude rows from another block in horizontal parallelism.
• If a number may be filled in exactly the same two columns in the vertical parallel blocks, these two columns can be used to exclude columns from another vertical Parallel Block.

Rectangle elimination technique)

Although rectangular division is easy to understand, it is rarely used in practical solutions. This is because it is difficult to see this method even if the puzzle is used. However, compared with the combined exclusion method, there are more opportunities to use the rectangular exclusion method in solving the problem. The following is an example:

Pair
In this puzzle, we cannot continue without rectangular division. We will explain this technique to find the number 8 starting from G1
. At first glance, it seems that there is nothing to do. Because 8 columns on B2 and E3 can only exclude G2 in the lower left corner of the block,
There are still two cells, G1 and H1, which cannot be determined.

Let's take a look at the 6th columns. This column does not contain 8 at the moment. Which cells may 8 be filled in? First, the 8 rows in B2 exclude B6, while the 8 rows in E3 and F4 exclude E6 and F6 respectively. In this way, only C6 and i6. See:

Similarly, for the 9th columns, F9 cannot be set to 8 due to the exclusion of F4. therefore, only C9 and I9 are left in this column.

Coincidentally, the positions of 8 in the two columns are on the same two rows, that is, Row C and row I. In this case, we have created a prerequisite for applying the rectangular division.

If column 6th contains C6 = 8, the numbers of I6 and C9 must not be 8. In this case, only I9 can be filled with 8 columns;

Alternatively, if I6 is 8 in column 6th, then C6 and I9 cannot be 8, while column 9th can only be 8 For C9.

No more than 3rd cases are possible. Therefore, either C6 = 8 and I9 = 8, I6 = 8 and C9 = 8. However, in either case, it is not difficult to find that row C and row I have been filled in with 8, so the other positions of the two rows cannot be filled in with 8. We can use this to exclude it.

Observe the block starting from G1. Now we know that only cells G1 and I1 are left uncertain. Through the above analysis, the i1 located on row I is excluded by the rectangular division, the number 8 must be on G1.

To sum up, the conditions for using rectangular exclusion are as follows:

• If a number can be filled in exactly the same two columns in one row, the number cannot appear in other cells of the two columns;
• If a number can be filled in exactly the same two rows in two columns, the number cannot appear in other cells of the two rows.

Rectangular division can be said to be the most difficult technique in the intuitive method, because the current puzzle is too difficult to discover even if it meets the conditions for applying this method. In general, try to use other relatively simple and intuitive methods first. If the last division of the connected rectangle still cannot be used, you may need to try the candidate number method.

Solutions in the Candidate number mode explicit unique number method (naked Single)

This is the simplest way to delete candidate numbers. It is to scan the grid table of candidate numbers. If only one candidate number is left in a cell, an explicit and unique method can be applied, enter this number in the cell and delete the number in the candidate numbers of the corresponding rows, columns, and blocks.

Cell A1 has a unique number of candidates 9, so it is undoubtedly possible to enter number 9 in the cell and scan its row, column, and block for the number of candidates 9:

If yes, delete 9 from the candidate numbers of these cells:

Although the explicit uniqueness method is simple, it is one of the most effective candidate number reduction methods. Especially when the puzzle is relatively simple, it can be solved simply by using the explicit uniqueness method.

In klsudoku, if you enter a number in a cell when playing a game in the Candidate number mode, then klsudoku will automatically exclude this candidate number from the other numbers in the row and column houses where the number is located.

Implicit unique number method (hidden Single)

As mentioned in the document, the implicit uniqueness method is also the only candidate number method, but it is certainly not as obvious as the explicit uniqueness method. We know that if there is only one candidate number in a cell, you can enter it without hesitation. But is there any such situation, even if there are more than one candidate number in a cell, we can also easily infer the correct answer to this cell?

Let's take a look at the above questions:

In Row A, although cell A7 contains multiple candidate numbers, we can find that only the number 3 in this cell is in the entire column. According to the rule of the sudoku game, each column must have all numbers from 1 to 9, while 3 can only appear in this cell at the same time, so obviously A7 = 3. Of course, do not forget to delete 3 from the column and block where A7 is located.

The example is the implicit unique number found in the row. Similarly, the implicit unique number can also appear in the column and palace. Because the implicit unique number is not easy to observe during the game, you can also find the implicit unique number by combining the unit exclusion method in the intuitive method during the game.