Can't solve Sudoku. How to solve Sudoku - methods, methods and strategy. Loner or the last hero
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Game history
The numerical structure was invented in Switzerland back in the 18th century; on its basis, a numerical crossword was developed in the 20th century. However, in the USA, where the game itself was invented, it did not become widespread, unlike Japan, where the puzzle not only took root, but also gained great popularity. It was in Japan that it acquired the familiar name “Sudoku”, and then spread throughout the world.
Negative raster steps
The best place to start is by rowing the number fields in the empty help windows that are already listed on that line. After this you will also cross this through all the vertical columns, but there are already overlaps in nine blocks also check the numbers that are listed there from the beginning - in most cases there are only a few left. In the diagram below, these intersections were made for the first three horizontal rows, the first three vertical columns, and the first nine blocks.
From this it can be seen that this method significantly reduces the difficulty of the puzzle and also prevents possible "thinking errors" during careful work. Basically, this schematic approach does not save the actual thinking and combination, but also enables beginners to quickly learn the principle and partly give up the misfortunes. For example, in the example above, the first column in fields 5 and 6 could only contain the numbers 1 or 2.
Rules of the game
The crossword has simple structure: A matrix of 9 squares called sectors is specified. These squares are arranged three in a row and have a size of 3x3 cells. The Sudoku matrix looks like a square consisting of 3 rows and 3 columns, which divide it into 9 sectors containing 9 cells each. Some of the cells are filled with numbers - the more numbers you know, the simpler the puzzle.
In the case of easy sudokus with numerous numbers, even after these first three systematic runs, individual numbers are recorded that can be entered correctly immediately. In the fourth step, new numbers must be “systematically” eliminated for the remaining fields using crosses in the rows, columns, and nine-block blocks. The result is a snowball system.
In complex Sudokus - especially those where there are several intermediate ones - there are, of course, less often “automatic” solutions, but control points help in any case to avoid mistakes. In theory, sure bets often require more than ten solution steps, which also means that some "experts" are overextended, so they might as well use systematic testing. Here it helps you make two or more copies of each game and continue these fights systematically until the puzzle is solved or you realize there would have been a different way.
Purpose of the game
You need to fill in all the empty cells, and there is only 1 rule: the numbers should not be repeated. Each sector, row and column must contain numbers from 1 to 9 without repetition. It is better to fill in the empty cells with a pencil: this will make it easier to make changes in case of an error or start over.
Solution methods
Let's look at a simple version of Sudoku. For example, in a sector or line there is only 1 empty cell left - it is logical that you need to enter into it the number that is not in the number series.
Example of the negative method: The first three steps of the negative method have been performed as an example in the diagram on the left. This systematic reduction already produces, for example, the first useful number in the ninth block. In the middle block, the result is 5, from which the middle column can be executed immediately, since the position in FIG. 3 and fig. 4 also results from the introduction of FIG. Of course, you must complete the first three steps for each number you enter, and other solutions also appear in easy to medium difficulty puzzles.
Next, you should examine the rows and columns that contain same numbers in 2 sectors. Since numbers should not be repeated, you can check which cells can contain the same number in sector 3. Often there is only 1 cell left, in which you just need to enter a number.
Thus, part of the crossword puzzle field will be filled. Then you can start studying the strings. Let’s say there are 3 free cells in a line, you understand what numbers should be entered there, but you don’t know where exactly. You need to try substitution. There are often options when a number cannot be located in the other 2 cells, because either it is in the corresponding column or in the sector.
The relevant literature often recommends testing positive possibilities. Since the "negative method" is not based on a symbolic numerical value, but on an abstract numerical space that is gradually reduced for each field, it also promotes a more "tangible" experience. Thanks to this method difficult relationships between the three fundamental planes can be easily recognized and written in the appropriate form. Such methods support the learning process and subsequently lead to "automatic" recognition of Sudoku, so that in simple puzzles these tools can be overridden again.
Challenging Sudoku
In complex Sudoku, these methods only work halfway; there comes a time when it is completely impossible to determine which cell to enter the number in. Then you need to make an assumption and test it. If there are 2 cells in a row, column or sector in which it is equally possible to enter a number, then you need to enter it in pencil and follow the logic of filling in further. If your assumption is incorrect, then at some point the crossword will show an error and a repetition of numbers will occur. Then it becomes obvious that the number should be in the second cell, you need to go back and correct the error. In this case, it is better to use a colored pencil to make it easier to find the point at which you need to solve the crossword puzzle again.
In particular, the solution method proposed here allows us to sequentially explore those partially complex inferences that are necessary to solve a difficult Sudoku. The charm of Sudokus lies not only in the solving of individual puzzles, but also in particular in the implementation of the solving principles that accompany the sudden experience of aha. Therefore, these rules will not be disclosed here, especially since they are displayed on many pages on the Internet in any case.
Key Notes on Labeling and Dissolution Methods
A researcher from the University of Valencia had 84 young men dissolved in the presence strange man and very attractive woman. If the woman left the men alone, the stress hormone cortisol did not change in the test subject's blood.
Little secret
It is easier and faster to solve Sudoku if you first mark with a pencil what numbers can be in each cell. Then you won’t have to check all the sectors every time, and during the filling process, those cells in which only 1 variant of a valid number remains will be immediately obvious.
Sudoku is not only exciting game, which allows you to pass the time, it is a puzzle that develops logical thinking, ability to retain a large amount of information and attention to detail.
Optimists are people who solve Sukoda using ballpoint pen. Some days, unfortunately, bad luck in these free offers. We apologize for any incidents and will return to one of the above. The Sudoku grid consists of 81 boxes, divided into nine rows and 9 columns.
Fly in two directions
Flight - quick method, which is usually enough to solve simple puzzles. However, this method has proven itself also for serious puzzles, but only to the point where more complex solution methods are needed. Here are some of the flyover techniques. When we look at boxes 1 and 2, we see that both contain 9 in rows 2 and 3, which eliminates those two rows in box 2. 
This method can be extended to look at rows and columns at the same time. Let's see where we can put 1 in Box 3.
Sudoku is a popular leisure activity that is a number puzzle also called the magic square. Its solution allows you to develop logical thinking, attention, and an analytical approach. The benefits of Sudoku lie not only in the benefits for the brain, but also in the ability to escape from problems and fully concentrate on the task.
In this example, lines 1 and 2 already contain 1, resulting in two possible fields in block 3. 
It often happens that only one number fits into a field because the other eight already appear in key columns, rows, or the field. 
This method can be especially useful when rows and columns are almost complete.
Sudoku rules
This puzzle takes up little space, unlike scanwords, crosswords, and so on. The playing field consists of 81 squares, the cells are divided into small blocks, 3*3 in size. It can easily fit on a piece of paper. The task looks like selectively filled cells that need to be supplemented with values and fill out the entire table. IN sudoku game rules are very simple and eliminate multiple decisions. Each row or column contains numbers from 1 to 9. Also, the values are not repeated within one small block.
If Sudoku becomes more complex, the methods described are no longer sufficient and more complex methods must be used. Hard puzzles require deeper logical analysis, which can be done using pencil markers. In this method, small numbers are written in fields to record what numbers may be possible. Once the puzzle has been provided with these small numbers, the results must be analyzed, special combinations of numbers must be identified and obtained from which the numbers must be placed.
Sudokus vary in difficulty level, which depends on the number of cells filled with numbers and solution methods. Usually there are about 5 levels, where only real masters can solve the most difficult one.
The game of Sudoku has its own rules and secrets. The simplest puzzles can be solved in a few minutes using deduction, as there is always at least one cell for which only one number fits. Complex Sudoku puzzles can take hours to solve. A correctly constructed puzzle has only one solution.
Exclude fields in cells in “naked pairs”
Here are some forms of analysis. We don't yet know exactly which number is correct, but we do know that both boxes are busy. Such a case where the same pair can only be placed in two blocks is called a "disjunctive subset", and when these "disjunctive subsets" are easily recognizable, they are called "naked pairs". 
Exclude fields in rows and columns with "naked pairs"
The previous solution method is useful for eliminating a number within a row or column. Again, we don't know who exactly is, but we do know that both fields are occupied.Rules for solving Sudoku
To obtain the right decision, you need to consider a few simple rules:
- A number can be written in a cell only if it is not in the horizontal and vertical lines, as well as in the small square 3*3.
- If it can be written exclusively in one cell.
If both points are taken into account, then you can be sure that the cell is filled out correctly.
Exclude fields based on “hidden pairs” in rows and columns
"Disjunctive partial quantities" are not always recognizable at first glance, so we call them " hidden pairs" in this case. 
It should be noted that a solution cannot be reached without a clear list of possible values or candidates for the empty field. If you don't have program support, you will systematically analyze every empty field. This way you get a list of candidates for each empty field. 
This value can be assigned to each field for which there is only one candidate.
How to solve simple Sudoku?
Let's look at a specific example of how to solve Sudoku. The playing field in the picture is a relatively simple version of the game. Sudoku game rules for simple ones boil down to identifying dependencies in the horizontal and vertical planes and in individual squares.
Very often there is only one candidate for a certain group, but he is hidden among others
It is very important to remove it as a candidate in all other fields in the same group whenever a value is entered into the field. Hidden individual candidates. Since the number 6 must appear in every field, this must be the field. The above two steps lead directly to the value; you can only solve the simplest puzzles. This is good, because otherwise Sudokus would not be so popular today. The following steps will help reduce the number of candidates in the empty fields until sooner or later there is only one candidate or a hidden individual candidate left.
For example, in the central vertical there are not enough numbers 3, 4, 5. Four cannot be in the lower square, since it is already present in it. We can also eliminate the empty center square, since we see 4 in a horizontal line. From this we conclude that it is located in the upper square. We can similarly put 3 and 5 and get the following result.
Fixed Candidates 1. Sometimes a candidate in a box is limited to a row or column. Since one of these fields must contain this candidate, it can be removed from other fields in that row or column. In the example below, in the right window, number 2 is only on the bottom line. Because one of these fields must be the number 2, it cannot appear in any field on the same line outside of that field. Therefore, the number 2 can be eliminated as a candidate in the marked boxes.
Sometimes a candidate appears in a row or column only in a field. Since one of these fields must contain this candidate, it can be removed from the other fields in this field. In the example on the right, the number 9 for the left column may only appear in the middle field. Since one of these fields must be the number 9, it can be removed from all fields in this middle field except the left column.
By drawing lines in the upper middle small square 3*3, you can exclude cells that cannot contain the number 3.
Solve Continuing in this way, you need to fill in the remaining cells. The result is the only correct solution.
Some people call this method “The Last Hero” or “Loner”. It is also used as one of several in master levels. The average time spent on the easy difficulty level hovers around 20 minutes.
How to solve difficult Sudoku?
Many people wonder how to solve sudoku, are there standard methods and strategy. As in any logic puzzle There is. We looked at the simplest of them. To go to more high level, you need to have more time, perseverance, and patience. To solve the puzzle, you will have to make assumptions and possibly get an incorrect result, returning you to the place of choice. In fact difficult sudoku - how to solve it problem using an algorithm. Let's look at several popular techniques used by professional sudoku experts using the following example.
First of all, you need to fill in the empty cells possible options, in order to make the decision as easy as possible and have the full picture before your eyes.
Answer, how to solve difficult sudoku for each one. It is more convenient for someone to use different colors for coloring cells or numbers, some people prefer the black and white version. The figure shows that there is not a single cell in which there would be a single digit, however, this does not mean that there are no single digits in this task. Armed Sudoku rules and with a close look, you can see that in the top line of the middle small block there is the number 5, which appears once in its line. In this regard, you can safely mark it and exclude it from the cells colored in green color. This action will entail the opportunity to put the number 3 in the orange cell and boldly cross it out from the corresponding purple ones vertically and in the small block 3 * 3.
In the same way, we check the remaining cells and put units in the circled cells, since they are also the only ones in their lines.
To figure it out how to solve difficult sudoku, you need to arm yourself with a few simple methods.
Open Pairs Method
To clear the field further, you need to find open pairs that allow you to exclude the numbers in them from other cells in the block and rows. In the example, such pairs are 4 and 9 from the third line. They clearly show how to solve difficult sudoku. Their combination suggests that these cells can only contain 4 or 9. This conclusion is made on the basis Sudoku rules.
You can remove blue values from cells highlighted in green, thereby reducing the number of options. In this case, the combination 1249 located in the first line is called by analogy “open four”. You can also find “open threes”. Such actions entail the emergence of other open pairs, such as 1 and 2 on the top line, which also provide an opportunity to narrow down the combinations. At the same time, we put 7 in the circled cell of the first square, since the five in this line will in any case be located in the lower block.
Hidden pairs/triples/fours method
This method is the opposite of open combinations. Its essence is that you need to find cells in which numbers are repeated within a square/row that are not found in other cells. How will this help you solve Sudoku?? This technique allows you to cross out the remaining numbers, since they serve as background and cannot be placed in the selected cells. This strategy has several other names, for example “The cell is not rubber”, “The secret becomes apparent”. The names themselves explain the essence of the method and compliance with the rule indicating the possibility of putting down a single number.
An example would be blue-colored cells. The numbers 4 and 7 are found exclusively in these cells, so the rest can be safely deleted.
The conjugation system works in a similar way, when you can exclude from the cells of a block/row/column values that appear several times in an adjacent or conjugate one.
Cross exclusion
The principle of how to solve sudoku, lies in the ability to analyze and compare. Another way to exclude options is the presence of any number in two columns or rows that intersect with each other. In our example, such a situation did not occur, so let’s consider another one. The picture shows that the “two” occurs only once in the second and third middle blocks, and when combined, they are connected and are mutually exclusive. Based on this data, the number 2 can be removed from other cells in the specified columns.
Can also be used for three and four lines. The complexity of the method lies in the difficulties of visualization and identifying connections.
Reduction method
As a result of each action, the number of options in the cells is reduced and the solution is reduced to the “Single” method. This process can be called reduction and isolated as a separate method, since it involves a thorough analysis of all rows, columns and small squares with the sequential elimination of options. As a result, we come to a single solution.
Color method
This strategy differs little from the one described, and consists of color indication of cells or numbers. The method helps to visualize the entire course of the solution, however, it is not suitable for everyone. For some, the colors are confusing and make it difficult to concentrate. To use the gamut correctly, you need to choose two or three colors and paint the same options in different blocks/lines, as well as controversial cells.
To figure it out how to solve sudoku, it is better to arm yourself with a pen and paper. This approach will allow you to train your head, as opposed to using electronic algorithms with hints. The BrainApps team has reviewed several of the most popular, understandable and effective techniques, however, there are many other algorithms. For example, the “Trial and Error” method, when a trial option is selected from two or three possible ones and the entire chain is checked. The disadvantage of this technique is the need to use a computer, since it is not so easy to return to the original version on a piece of paper.