Sudoku solving scheme. Ways to solve classic Sudoku

How to play Sudoku?

Sudoku is a very popular number puzzle. Once you understand how to play Sudoku, you won't be able to put it down!

The essence of the game:

The cells of the playing field must be filled with numbers from 1 to 9. There should not be repeated numbers in each line vertically and horizontally. Also, they cannot be repeated in small squares (3x3 cells). At the very beginning of the game, there are already numbers (depending on the complexity of the level, the number of initially set numbers may differ).

Sudoku rules:

• Choose the row, column or square with the maximum number of given numbers. Add the missing (it is better to use a pencil). In almost all cases, there is a place where only 1 number fits.
• Next, look through each column in turn, compare which numbers can fit in each cell. On a separate piece of paper, you can write out options.
• Looking also at lines and squares, exclude numbers that are repeated.
• As the puzzle is filled with numbers, it will become easier to solve it.

Start playing Sudoku with easy tasks, because the ability to solve a puzzle comes with experience. Or play Sudoku online - incorrect numbers will be highlighted in a different color. This will help you get used to the game. During this lesson, logic develops, so you can gradually complicate the level. Also watch the video attached to the article.

Feb 27, 2015 —

Sudoku is a number puzzle. Today it is so popular that most people are familiar with it or have just seen it in print. In our article, we will tell you where this game came from, as well as who invented Sudoku.

Despite the Japanese name, the history of Sudoku does not begin in Japan. The Latin squares of Leonhard Euler, the famous mathematician who lived in the 18th century, are considered the prototype of the puzzle. However, in the form in which it is known today, it was invented by Howard Garnes. Being an architect by training, Garnes simultaneously came up with puzzles for magazines and newspapers. In 1979, an American publication called "Dell Pencil Puzzles and Word Games" first printed Sudoku on its pages. However, then the puzzle did not arouse interest among readers.

It was the Japanese who were the first to appreciate the rebus. In 1984, one of the Japanese publications published the puzzle for the first time. It immediately became widespread. At the same time, the puzzle got its name - Sudoku. In Japanese, "su" means "number", "doku" - "standing apart". Some time later, this rebus appeared in many publications in Japan. In addition, they released separate Sudoku collections. In 2004, newspapers in the UK began to print the puzzle, which marked the beginning of the spread of the game outside of Japan.

The puzzle is a square field with a side of 9 cells, divided in turn into 3 by 3 squares. Thus, the large square is divided into 9 small ones, the total number of cells of which is 81. Some cells initially contain hint numbers. The essence of the rebus is to fill empty cells with numbers so that they do not repeat in rows, columns, or squares. In Sudoku, only numbers from 1 to 9 are used. The complexity of the puzzle depends on the location of the clue numbers. The most difficult, of course, is the one that has only one solution.

The history of Sudoku in our time continues, and successfully. The game is becoming an increasingly common puzzle game, largely due to the fact that now it can be found not only in the pages of the newspaper, but also on the phone or computer. In addition, various variations of this rebus appeared - letters are used instead of numbers, the number of cells and the shape change.

Choose the topic you are interested in:

Sumdoku

Sumdoku is also known as killer sudoku or killer sudoku. In this type of puzzle, the numbers are arranged in the same way as in the classic Sudoku. But on the field there are additionally colored blocks, for each of which the sum of the numbers is indicated. Please note that sometimes numbers can be repeated in these blocks!

How to solve sumdoku?

Consider the sumdoku (in the figure on the right). To solve it, remember that the sum of the numbers in any row, any column and any small rectangle is the same. For our case, this is 1 + 2 + 3 + ... + 9 + 10 \u003d 55. For a 9x9 sumdoku, it would be 45.

Pay attention to the blocks highlighted in gray. They almost completely (except for one number) cover the two lower rectangles. Let's calculate the sum of digits in all marked blocks: 13 + 8 + 13 + 15 + 13 + 7 + 14 + 12 + 5 = (13+13+14) + (13+7) + (12+8) + (15+5 ) = 40 + 20 + 20 + 20 = 100. So, the sum of the digits in the marked blocks is 100. But if we take the two lower rectangles completely, then the sum of the digits in them should be 55 + 55 = 110. So, in the only unmarked cell worth the number 10.

As you can see, by constantly solving sumdoku, you will master arithmetic masterfully. You can, of course, use a calculator, but this dark and slippery path is not for real samurai

Consider now the blocks highlighted in the figure on the right. They cover one penultimate Sudoku horizontal and two "extra" cells. Let's calculate the sum of the digits in the blocks: 13 + 8 + 15 + 13 + 10 + 14 = (13+13+14) + (10+15) + 8 = 40 + 25 + 8 = 73. But we know that the sum of the digits in there are 55 horizontal lines, which means that you can find out the sum of the numbers in the two “extra” cells: 73 - 55 = 18.

Let's write down all possible combinations of numbers in these "extra" cells: 10+8, 9+9, 8+10.

History of Sudoku

9 + 9 - we exclude, since the cells are located on the same horizontal line, 10 + 8 and 8 + 10 remain. But if you put 8 in the first “extra” cell, then two fives will be obtained in the penultimate horizontal, and the numbers in the horizontals should not be repeated. Thus, we get that in the first "extra" cell there can be only 10. We immediately place the rest of the obvious numbers.

06/15/2013 How to solve Sudoku, rules with an example.

I would like to say that Sudoku is a really interesting and exciting task, a riddle, a puzzle, a puzzle, a digital crossword puzzle, you can call it whatever you like. The solution of which will not only bring real pleasure to thinking people, but will also allow developing and training logical thinking, memory, and perseverance in the process of an exciting game.

For those who are already familiar with the game in all its manifestations, the rules are known and understood. And for those who are just thinking of starting, our information may be useful.

The rules of Sudoku are not complicated, they are found on the pages of newspapers or they can be easily found on the Internet.

The main points fit into two lines: the main task of the player is to fill in all the cells with numbers from 1 to 9. This must be done in such a way that none of the numbers is repeated twice in the column line and the 3x3 mini-square.

Today we bring you several variations of the Sudoku-4tune electronic game, including more than a million built-in puzzle variations in every game player.

For clarity and a better understanding of the process of solving the riddle, consider one of the simple options, the first level of Sudoku-4tune difficulty, 6 ** series.

And so, a playing field is given, consisting of 81 cells, which in turn make up: 9 rows, 9 columns and 9 mini-squares 3x3 cells in size. (Fig.1.)

Don't let the mention of the electronic game bother you in the future. You can meet the game in the pages of newspapers or magazines, the basic principle is preserved.

The electronic version of the game provides great opportunities for choosing the level of difficulty of the puzzle, the options for the puzzle itself and their number, at the request of the player, depending on his preparation.

When you turn on the electronic toy, key numbers will be given in the cells of the playing field. which cannot be transferred or modified. You can choose the option that is more suitable for the solution, in your opinion. Reasoning logically, starting from the figures given, it is necessary to gradually fill the entire playing field with numbers from 1 to 9.

An example of the initial arrangement of numbers is shown in Fig. 2. Key numbers, as a rule, in the electronic version of the game are marked with an underscore or a dot in the cell. In order not to confuse them in the future with the numbers that will be set by you.

Looking at the playing field. You need to decide what to start with. Typically, you want to define a row, column, or mini-square that has the minimum number of empty cells. In our version, we can immediately select two lines, upper and lower. In these lines, only one digit is missing. Thus, a simple decision is made, having determined the missing numbers -7 for the first line and 4 for the last, we enter them in the free cells of Fig.3.

The resulting result: two filled lines with numbers from 1 to 9 without repetition.

Next move. Column number 5 (from left to right) has only two free cells. After not much thought, we determine the missing numbers - 5 and 8.

To achieve a successful result in the game, you need to understand that you need to navigate in three main directions - a column, a row and a mini-square.

In this example, it is difficult to navigate only by rows or columns, but if you pay attention to the mini-squares, it becomes clear. You cannot enter the number 8 in the second (from the top) cell of the column in question, otherwise there will be two eights in the second mine-square. Similarly, with the number 5 for the second cell (bottom) and the second lower mini-square in Fig. 4 (not the correct location).

Although the solution seems to be correct for a column, nine digits in a column, without repetition, it contradicts the main rules. In mini-squares, numbers should also not be repeated.

Accordingly, for the correct solution, it is necessary to enter 5 in the second (top) cell, and 8 in the second (bottom). This decision is in full compliance with the rules.

See Figure 5 for the correct option.

Further solution, seemingly simple task, requires careful consideration of the playing field and the connection of logical thinking.

How to Solve Sudoku - Ways, Methods and Strategy

You can again use the principle of the minimum number of free cells and pay attention to the third and seventh columns (from left to right). They left three cells empty. Having counted the missing numbers, we determine their values ​​- these are 2.3 and 9 for the third column and 1.3 and 6 for the seventh. Let's leave the filling of the third column for now, since there is no certain clarity with it, unlike the seventh. In the seventh column, you can immediately determine the location of the number 6 - this is the second free cell from the bottom. What is the conclusion?

When considering the mini-square, which includes the second cell, it becomes clear that it already contains the numbers 1 and 3. From the digital combination we need 1,3 and 6, there is no other alternative. Filling in the remaining two free cells of the seventh column is also not difficult. Since the third row, in its composition, already has a filled 1, 3 is entered into the third cell from the top of the seventh column, and 1 into the only remaining free second cell. For an example, see Figure 6.

Let's leave the third column for a clearer understanding of the moment. Although, if you wish, you can make a note for yourself and enter the proposed version of the numbers necessary for installation in these cells, which can be corrected if the situation is clarified. Electronic games Sudoku-4tune, 6** series allow you to enter more than one number in the cells, for a reminder.

We, having analyzed the situation, turn to the ninth (lower right) mini-square, in which, after our decision, there are three free cells left.

After analyzing the situation, you can notice (an example of filling a mini-square) that the following numbers 2.5 and 8 are not enough to completely fill it. Having considered the middle, free cell, you can see that only 5 of the required numbers fit here. Since 2 is present in the upper cell column, and 8 in the row in the composition, which, in addition to the mini-square, includes this cell. Accordingly, in the middle cell of the last mini-square, enter the number 2 (it is not included in either the row or column), and enter 8 in the upper cell of this square. Thus, we have completely filled the lower right (9th) mini- square with numbers from 1 to 9, while the numbers are not repeated in the columns or in the rows, Fig.7.

As the free cells are filled, their number decreases, and we are gradually approaching the solution of our puzzle. But at the same time, the solution of the problem can both be simplified and complicated. And the first way to fill the minimum number of cells in rows, columns or mini-squares ceases to be effective. Because the number of explicitly defined digits in a particular row, column, or mini-square is reduced. (Example: third column left by us). In this case, it is necessary to use the method of searching for individual cells, setting numbers in which there is no doubt.

In electronic games Sudoku-4tune, 6 ** series, the possibility of using hints is provided. Four times per game, you can use this function and the computer itself will set the correct number in the cell you have chosen. The 8** series models do not have this function, and the use of the second method becomes the most relevant.

Consider the second method in our example.

For clarity, let's take the fourth column. The unfilled number of cells in it is quite large, six. Having calculated the missing numbers, we determine them - these are 1,4,6,7,8 and 9. To reduce the number of options, you can take as a basis the average mini-square, which has a fairly large number of certain numbers and only two free cells in this column. Comparing them with the numbers we need, it can be seen that 1,6, and 4 can be excluded. They should not be in this mini-square to avoid repetition. It remains 7,8 and 9. Note that in the line (fourth from the top), which includes the cell we need, there are already numbers 7 and 8 from the three remaining ones that we need. Thus, the only option for this cell remains is the number 9, Fig. 8. The fact that all the numbers considered and excluded by us were originally given in the task does not cause doubts about the correctness of this solution. That is, they are not subject to any change or transfer, confirming the uniqueness of the number we have chosen to install in this particular cell.

Using two methods at the same time, depending on the situation, analyzing and thinking logically, you will fill in all the free cells and come to the correct solution of any Sudoku puzzle, and this riddle in particular. Try to complete the solution of our example in Fig. 9 yourself and compare it with the final answer shown in Fig. 10.

Perhaps you will determine for yourself any additional key points in solving puzzles, and develop your own system. Or take our advice, and they will be useful for you, and will allow you to join a large number of fans and fans of this game. Good luck.

Sudoku (Sudoku) is a number puzzle. Translated from Japanese, “su” means “number”, and “doku” means “standing apart”. In a traditional Sudoku puzzle, the grid is a square of size 9x9, divided into smaller squares with a side of 3 cells ("regions"). Thus, the entire field has 81 cells. Some of them already have numbers (from 1 to 9). Depending on how many cells are already filled, the puzzle task can be classified as easy or difficult.

Sudoku has only one rule. It is necessary to fill in the free cells so that in each row, in each column and in each small square 3x3 each digit from 1 to 9 would occur only once.

Program Cross+A able to solve a large number of varieties of sudoku.

The task can be complicated: the main diagonals of the square must also contain numbers from 1 to 9. This puzzle is called sudoku diagonals (SudokuX). To solve these tasks, you must put a "tick" in the paragraph Diagonals.

Sudoku Argyle (Argyle Sudoku) contains a pattern of lines arranged diagonally.

Sudoku rules

The argyle pattern, consisting of multi-colored diamonds of the same size, was present on the kilts of one of the Scottish clans. Each of the marked diagonals must contain non-repeating digits.

The puzzle may contain regions of arbitrary shape; such sudoku are called geometric or curly (Jigsaw Sudoku, Geometry Sudoku, Irregular Sudoku, "Kikagaku Nanpure").

Letters can be used instead of numbers in Sudoku; these puzzles are called Godoku ("Wordoku", Alphabet Sudoku). After solving in any row or column, you can read the keyword.

Sudoku asterisk (Asterisk) is a type of Sudoku that contains an additional area of ​​9 cells. These cells must also contain numbers from 1 to 9.

Sudoku Girandole ("Girandola") also contains an additional area of ​​9 cells, with numbers from 1 to 9 (girandol is a fountain of several jets in the form of fireworks, a "fiery wheel").

Sudoku with center dots ("Center Dot") is a variant of Sudoku where the central cells of each region 3x3 form an additional region.

The cells of this additional area must contain numbers from 1 to 9.

Sudoku can contain four additional regions 3x3. This type of puzzle is called sudoku window (Windoku, Four-Box Sudoku, Hyper Sudoku).

Sudoku Mosaic (Offset Sudoku, Sudoku-DG) contains an additional 9 groups of 9 cells. Cells within a group do not touch each other and are highlighted in the same color. In each group, each digit from 1 to 9 must occur only once.

Not a horse step (Anti-Knight Sudoku) has an additional condition: the same numbers cannot "hit" each other with the knight's move.

IN hermit sudoku ("Anti-King Sudoku", "Touchless Sudoku", "Sudoku without touches") the same numbers cannot be in adjacent cells (both diagonally and horizontally and vertically).

IN sudoku antidiagonal (Anti Diagonal Sudoku) each diagonal of the square contains at most three different digits.

Sudoku killer (Killer Sudoku, "Sums Sudoku", Sums Number Place, "Samunamupure", "Kikagaku Nampure"; another name - Sum-do-ku) is a variation of the regular Sudoku. The only difference is that additional numbers are given - the sums of values ​​in groups of cells. Numbers contained in a group cannot be repeated.

Sudoku more less (Greater Than Sudoku) contains comparison signs (">" and "<«), которые показывают, как соотносятся между собой числа в соседних ячейках. Еще одно название — Compdoku.

Sudoku even-odd ("Even Odd Sudoku") contains information about the even or odd numbers in the cells. Cells containing even numbers are marked in gray, cells containing odd numbers are marked in white.

Sudoku neighbors ("Consecutive Sudoku", "Sudoku with partitions") is a variation of the regular Sudoku. It marks the boundaries between adjacent cells in which there are consecutive numbers (that is, numbers that differ from each other by one).

IN Non-Consecutive Sudoku numbers in adjacent cells (horizontally and vertically) must differ by more than one. For example, if the cell contains the number 3, adjacent cells should not contain the numbers 2 or 4.

Sudoku dots (Kropki Sudoku, Dots Sudoku, "Sudoku with dots") contains white and black dots on the borders between cells. If the numbers in neighboring cells differ by one, then there is a white dot between them. If in neighboring cells one number is twice as large as the other, then the cells are separated by a black dot. Between 1 and 2 there can be a dot of any of these colors.

Sukaku (Sukaku, "Suuji Kakure", Pencilmark Sudoku) is a square 9x9, containing 81 groups of digits. It is necessary to leave only one number in each cell so that in each row, in each column and in each small square 3x3 each number from 1 to 9 would occur only once.

Sudoku chains (Chain Sudoku, "Strimco", "Sudoku meanders") is a square made up of circles.

It is necessary to arrange the numbers in the circles so that in each horizontal and each vertical all the numbers are different. In the links of one chain, all numbers must also be different.

The program can solve and create puzzles ranging in size from 4x4 before 9x9.

Sudoku Rama (Frame Sudoku, Outside Sum Sudoku, "Sudoku - sums on the side", "Sudoku with sums") is an empty square sized. Numbers outside the playing field indicate the sums of the nearest three digits in a row or column.

skyscraper sudoku (Skyscraper Sudoku) contains the key numbers along the sides of the grid. It is necessary to arrange the numbers in the grid; each number represents the number of floors in the skyscraper. Key numbers outside the grid show exactly how many houses are visible in the corresponding row or column, when viewed from this number.

Tripod Sudoku (Tripod Sudoku) - a type of Sudoku in which the boundaries between regions are not indicated; instead, points are given at the intersections of the lines. The dots represent where the borders of the regions cross. Only three lines can depart from each point. It is necessary to restore the boundaries of the regions and fill the grid with numbers so that they do not repeat in each row, each column and each region.

Sudoku Mines (Sudoku Mine) combines the features of Sudoku and Minesweeper puzzles.

The task is a square in size, divided into smaller squares with a side of 3 cells. It is necessary to place the mines in the grid so that there are three mines in each row, each column and each small square. The numbers show how many mines are in neighboring cells.

Sudoku half ("Sujiken") was invented by the American George Heineman. The puzzle is a triangular grid containing 45 cells. Some cells contain numbers. It is necessary to fill in all cells of the grid with numbers from 1 to 9 so that in each row, in each column and on each diagonal the numbers do not repeat. Also, the same number cannot appear twice in each of the regions separated by thick lines.

Sudoku XV (Sudoku XV) is a variation of the regular Sudoku. If the boundary between adjacent cells is marked with a Roman numeral "X", the sum of the values ​​in these two cells is 10, if with a Roman numeral "V" the sum is 5. If the boundary between two cells is not marked, the sum of the values ​​in these cells cannot be 5 or 10.

Sudoku-edge (Outside Sudoku) is a variation of the regular Sudoku puzzle. Outside the grid are the numbers that must be present in the first three cells of the corresponding row or column.);

• 16x16(size of regions 4x4).

Cross+A can solve and create variations of Sudoku consisting of multiple squares 9x9.

These puzzles are called "Gattai"(translated from Japanese: "connected", "connected"). Depending on the number of squares, puzzles denote "Gattai-3", "Gattai-4", "Gattai-5" and so on.

Sudoku Samurai (Samurai Sudoku, "Gattai-5") is a type of Sudoku puzzle. The playing field consists of five squares of size 9x9. The numbers from 1 to 9 must be placed correctly in all five squares.

flower sudoku (Flower Sudoku, Musketry Sudoku) is similar to Samurai Sudoku. The playing field consists of five squares of size 9x9; the central square is entirely covered by four others. The numbers from 1 to 9 must be placed correctly in all five squares.

Sudoku sohei (Sohei Sudoku) is named after warrior monks in medieval Japan. The playing field contains four squares of size 9x9

Sudoku windmill ("Kazaguruma", windmill sudoku) consists of five squares of size 9x9: one in the center, four other squares almost completely cover the central square. The numbers from 1 to 9 must be placed correctly in all five squares.

Butterfly Sudoku (Butterfly Sudoku) contains four intersecting squares of size 9x9, which form a single square of size 12x12. The numbers from 1 to 9 must be placed correctly in all four squares.

Sudoku Cross (Cross Sudoku) consists of five squares. The numbers from 1 to 9 must be placed correctly in all five squares.

Sudoku three ("Gattai-3") consists of three squares of size 9x9.

Double Sudoku ("Twodoku", Sensei Sudoku, "DoubleDoku") consist of two squares of size 9x9. The numbers from 1 to 9 must be placed correctly in both squares.

The program can solve double sudoku, in which the regions have an arbitrary shape:

Triple Sudoku ("Triple Doku") is a puzzle of three squares of size 9x9. The numbers from 1 to 9 must be placed correctly in all squares.

Sudoku twins ("Twin Corresponding Sudoku") is a pair of regular Sudoku puzzles, each with multiple leading digits. Both puzzles must be solved; at the same time, each type of numbers in the first grid corresponds to the same type of numbers in the second grid. For example, if the number 9 is in the upper left corner of the first Sudoku puzzle, and the number 4 is in the upper left corner of the second puzzle, then in all cells where there is a 9 in the first grid, the number 4 is in the second grid.

Hoshi (Hoshi) consists of six large triangles; numbers from 1 to 9 must be placed in the triangular cells of each large triangle. Each line (of any length, even broken lines) contains non-repeating digits.

Unlike hoshi, sudoku star (Star Sudoku) a row on the outer face of the grid includes a cell located at the nearest sharp end of the figure.

Tridoku (Tridoku) was invented by Japheth Light from the USA. The puzzle consists of nine large triangles; each of them contains nine small triangles. Numbers from 1 to 9 must be placed in the cells of each large triangle. The field contains additional lines, the cells of which must also contain non-repeating numbers. Two adjoining triangular cells must not contain the same numbers (even if the cells touch each other with only one point).

Sudoku solver online.

If you can't solve a difficult Sudoku, try this with a helper. It will highlight your options.

Many people like to force themselves to think: for someone - for the development of intellect, for someone - to keep their brains in good shape (yes, not only the body needs exercise), and the best simulator for the mind are various games of logic and puzzles. One of the options for such educational entertainment can be called Sudoku. However, some have not heard about such a game, let alone knowledge of the rules or other interesting points. Thanks to the article, you will learn all the necessary information, for example, how to solve Sudoku, as well as their rules and types.

General

Sudoku is a puzzle. Sometimes complex, difficult to reveal, but always interesting and addictive for any person who decides to play this game. The name comes from Japanese: "su" means "number", and "doku" is "standing apart".

Not everyone knows how to solve Sudoku. Complex puzzles, for example, are within the power of either smart, well-thinking beginners, or professionals in their field who have been practicing the game for more than one day. Just take it and solve the task in five minutes will not be possible for everyone.

Rules

So, how to solve Sudoku. The rules are very simple and clear, easy to remember. However, do not think that simple rules promise a "painless" solution; you will have to think a lot, apply logical and strategic thinking, strive to recreate the picture. You probably need to love numbers to solve Sudoku.

First, a 9 x 9 square is drawn. Then, with thicker lines, it is divided into so-called "regions" of three squares each. The result is 81 cells, which should eventually be completely filled with numbers. This is where the difficulty lies: the numbers from 1 to 9 placed around the entire perimeter should not be repeated either in the “regions” (3 x 3 squares), or in the lines vertically and / or horizontally. In any Sudoku, there are initially some filled cells. Without this, the game is simply impossible, because otherwise it will turn out not to solve, but to invent. The difficulty of the puzzle depends on the number of digits. Complex Sudokus contain few numbers, often arranged in such a way that you have to rack your brains before solving them. In the lungs - about half of the numbers are already in place, making it much easier to unravel.

Completely disassembled example

It is difficult to understand how to solve Sudoku if there is no specific sample showing step by step how, where and what to insert. The provided picture is considered to be uncomplicated, since many of the mini-squares are already filled with the necessary numbers. By the way, it is on them that we will rely for a solution.

For starters, you can look at lines or squares, where there are especially many numbers. For example, the second column from the left fits perfectly, there are only two numbers missing. If you look at those that are already there, it becomes obvious that there are not enough 5 and 9 in the empty cells on the second and eighth lines. With the five, not everything is clear yet, it can be both there and there, but if you look at the nine, everything becomes clear. Since the second line already has the number 9 (in the seventh column), it means that in order to avoid repetitions, the nine must be put down, on the 8th line. Using the elimination method, we add 5 to the 2nd row - and now we already have one filled column.

In a similar way, you can solve the entire Sudoku puzzle, however, in more complex cases, when one column, row or square lacks not a couple of numbers, but much more, you will have to use a slightly different method. We will also analyze it now.

This time we will take as a basis the average “region”, which lacks five digits: 3, 5, 6, 7, 8. We fill each cell not with large effective numbers, but with small, “rough” ones. We just write in each box those numbers that are missing and that may be there due to their lack. In the upper cell, these are 5, 6, 7 (3 on this line is already in the “region” on the right, and 8 on the left); in the cell on the left there can be 5, 6, 7; in the very middle - 5, 6, 7; right - 5, 7, 8; bottom - 3, 5, 6.

So, now we look at which mini-digits contain numbers different from others. 3: there is only in one place, in the rest it is not. So, it can be corrected for a large one. 5, 6 and 7 are in at least two cells, so we leave them alone. 8 is only in one, which means that the remaining numbers disappear and you can leave the eight.

Alternating these two ways, we continue to solve Sudoku. In our example, we will use the first method, but it should be recalled that in complex variations the second is necessary. Without it, it will be extremely difficult.

By the way, when the middle seven is found in the upper “region”, it can be removed from the mini-numbers of the middle square. If you do this, you will notice that there is only one 7 left in that region, so you can only leave it.

That's all; finished result:

Kinds

Sudoku puzzles are different. In some, a prerequisite is the absence of identical numbers not only in rows, columns and mini-squares, but also diagonally. Some instead of the usual "regions" contain other figures, which makes it much more difficult to solve the problem. One way or another, how to solve Sudoku is at least the basic rule that applies to any kind, you know. This will always help to cope with a puzzle of any complexity, the main thing is to try your best to achieve your goal.

Conclusion

Now you know how to solve Sudoku, and therefore you can download similar puzzles from various sites, solve them online or buy paper versions at newsstands. In any case, now you will have an occupation for long hours, or even days, because it is unrealistic to drag out Sudoku, especially when you have to actually figure out the principle of their solution. Practice, practice and more practice - and then you will click this puzzle like nuts.

- This is a popular form of leisure, which is a puzzle with numbers, which is also called a magic square. Its solution allows you to develop logical thinking, attention, analytical approach. The benefits of Sudoku lie not only in the benefits for the brain, but also in the ability to distract from problems, to fully concentrate on the task.

Sudoku rules

This puzzle takes up little space, unlike scanwords, crosswords and so on. The playing field, consisting 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, which must be supplemented with values ​​and fill the entire table. In Sudoku, the rules of the game are very simple and allow you to eliminate multiple solutions. Each row or column contains numbers from 1 to 9. Also, the values ​​​​are not repeated within one small block.

Sudokus differ in the level of difficulty, which depends on the number of cells filled with numbers and the methods of solving. 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 with the help of deduction, as there is always at least one cell for which only one number fits. Complex Sudoku can be solved for hours. A correctly composed puzzle has only one way to solve it.

Rules for solving Sudoku

To get the right decision, you need to consider a few simple rules:

• A number can be written into a cell only if it is not in the horizontal and vertical lines, as well as in the small 3*3 square.
• 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.

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. The rules of the Sudoku game for simple ones come down to identifying dependencies in the horizontal and vertical planes and in individual squares.

For example, the numbers 3, 4, 5 are missing in the central vertical. The four cannot be in the lower square, since it is already present in it. It is also possible to exclude the empty center cell, since we see 4 in the horizontal line. From this we conclude that it is located in the upper square. Similarly, we can put down 3 and 5 and get the following result.

By drawing lines in the upper middle small square 3 * 3, you can exclude cells in which the number 3 cannot be located.

Solve Continuing in this way, it is necessary to fill in the remaining cells. The result is the only correct solution.

Some call this method "The Last Hero" or "Singleman". It is also used as one of several at master levels. The average time spent on the easy difficulty level fluctuates around 20 minutes.

How to solve difficult sudoku?

Many people wonder how to solve Sudoku, if there are standard methods and strategy. As in any logic puzzle there is. We have considered the simplest of them. To move to a higher level, you need to have more time, perseverance, patience. To solve the puzzle, you will have to make assumptions and, possibly, get the wrong result, returning to the place of choice. In essence, Sudoku is difficult - it's like solving a problem using an algorithm. Let's consider several popular techniques used by professional "Sudokuveds" in the following example.

First of all, it is necessary to fill in the empty cells with possible options in order to make the decision as easy as possible and have the full picture before your eyes.

The answer, how to solve Sudoku is difficult for everyone. It is more convenient for someone to use different colors for coloring cells or numbers, someone prefers a 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 singles in this task. Armed with Sudoku rules and a careful look, you can see that the top line of the middle small block is the number 5, which occurs once in its line. In this regard, you can safely put it down and exclude it from the cells colored green. This action will entail the ability to put down the number 3 in the orange cell and boldly cross it out of the corresponding purple vertically and in a small 3*3 block.

In the same way, we check the remaining cells and put down units in the circled cells, since they are also the only ones in their lines.

To figure out how to solve complex Sudokus, you need to arm yourself with a few simple methods.

Method "Open Pairs"

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, these pairs are 4 and 9 from the third row. They clearly show how to solve complex Sudoku. Their combination suggests that only 4 or 9 can be entered in these cells. This conclusion is made on the basis of Sudoku rules.

You can remove the blue values ​​from the cells highlighted in green and thereby reduce the number of options. At the same time, the combination 1249 located in the first line is called by analogy an “open four”. You can also find "open triplets". Such actions entail the appearance of other open pairs, such as 1 and 2 in the top line, which also provide an opportunity to narrow the circle of combinations. In parallel, 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/Threes/Fours Method

This method is opposite to open combinations. Its essence lies in the fact that it is necessary to find cells in which numbers are repeated within a square / line that are not found in other cells. How does this help solve Sudoku? The technique allows you to cross out the rest of the numbers, since they serve as a background and cannot be entered in the selected cells. This strategy has several other names, for example, "The cell is not rubber", "The secret becomes clear." The names themselves explain the essence of the method and compliance with the rule, which speaks of the possibility of putting down a single digit.

An example is blue-stained 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 it is possible to exclude from the cells of a block / row / column values ​​that occur several times in an adjacent or conjugated one.

Cross exclusion

The principle of how to solve Sudoku is the ability to analyze and compare. Another way to exclude options is to have a number in two columns or lines that intersect. In our example, this situation did not occur, so let's consider another one. The picture shows that the "two" occurs in the second and third middle block once, with a combination of which they are connected and mutually exclude each other. 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 identification of relationships.

Reduction method

As a result of each action, the number of options in the cells is reduced and the solution is reduced to the "Singleman" method. This process can be called a reduction and separated into a separate method, since it involves a thorough analysis of all rows, columns and small squares with the successive elimination of options. As a result, we come to a single solution.

color method

This strategy differs little from the one described, and consists in the color indication of cells or numbers. The method helps to visualize the entire course of the solution, however, it is not suitable for everyone. Some coloring knocks down and makes it difficult to concentrate. To correctly use the gamut, you need to choose two or three colors and paint the same options in different blocks / lines, as well as controversial cells.

To figure 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, in contrast to the use of electronic algorithms with hints. The BrainApps team has reviewed some of the most popular, clear 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 options 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.

Good day to you, dear lovers of logic games. In this article, I want to outline the main methods, methods and principles for solving Sudoku. There are many types of this puzzle on our site, and in the future, even more will undoubtedly be presented! But here we will consider only the classic version of Sudoku, as the main one for all the others. And all the tricks outlined in this article will also be applicable to all other types of Sudoku.

A loner or the last hero.

So, where does the Sudoku solution begin? It doesn't matter if it's easy or not. But always at the beginning there is a search for obvious cells to fill.

The figure shows an example of a loner - this is the number 4, which can be safely placed on cell 2 8. Since the sixth and eighth horizontals, as well as the first and third verticals, are already occupied by four. They are shown with green arrows. And in the lower left small square, we have only one unoccupied position left. The figure is marked in green in the picture. The rest of the loners are also placed, but without arrows. They are colored blue. There can be quite a lot of such singles, especially if there are a lot of digits in the initial condition.

There are three ways to search for singles:

• A loner in a 3 by 3 square.
• Horizontally
• Vertically

Of course, you can randomly view and identify singles. But it is better to stick to any particular system. The most obvious would be to start with the number 1.

• 1.1 Check the squares where there is no one, check the horizontals and verticals that intersect this square. And if there are already ones in them, then we completely exclude the line. Thus, we are looking for the only possible place.
• 1.2 Next, check the horizontal lines. In which there is a unity, and where not. We check in small squares, which include this horizontal line. And if there is a one in them, then we exclude the empty cells of this square from possible candidates for the desired number. We will also check all the verticals and exclude those in which there is also a unity. If the only possible empty space remains, then we put the desired number. If there are two or more empty candidates left, then we leave this horizontal line and move on to the next one.
• 1.3 Similarly to the previous paragraph, we check all horizontal lines.

"Hidden Units"

Another similar technique is called "and who, if not me ?!" Look at figure 2. Let's work with the upper left small square. Let's go through the first algorithm first. After that, we managed to find out that in cell 3 1 there is a loner - the number six. We put it, And in all the other empty cells we put in small print all the possible options, in relation to the small square.

After that, we find the following, in cell 2 3 there can be only one number 5. Of course, at the moment, five can also be on other cells - nothing contradicts this. These are three cells 2 1, 1 2, 2 2. But in cell 2 3 the numbers 2,4,7, 8, 9 cannot stand, since they are present in the third row or in the second column. Based on this, we rightfully put the number five on this cell.

naked couple

Under this concept, I combined several types of sudoku solutions: naked pair, three and four. This was done in connection with their uniformity and differences only in the number of numbers and cells involved.

And so, let's take a look. Look at Figure 3. Here we put down all the possible options in the usual way in small print. And let's take a closer look at the upper middle small square. Here in cells 4 1, 5 1, 6 1 we got a series of identical numbers - 1, 5, 7. This is a naked triple in its true form! What does it give us? And the fact that these three numbers 1, 5, 7 will be located only in these cells. Thus, we can exclude these numbers in the middle upper square on the second and third horizontal lines. Also in cell 1 1 we will exclude the seven and immediately put four. Since there are no other candidates. And in cell 8 1 we will exclude the unit, we should think further about the four and six. But that's another story.

It should be said that only a particular case of a bare triple has been considered above. In fact, there can be many combinations of numbers

• // three numbers in three cells.
• // any combinations.
• // any combinations.

hidden couple

This way of solving Sudoku will reduce the number of candidates and give life to other strategies. Look at Figure 4. The top middle square is filled with candidates as usual. The numbers are written in small print. Two cells are highlighted in green - 4 1 and 7 1. Why are they remarkable for us? Only in these two cells are candidates 4 and 9. This is our hidden pair. By and large, it is the same pair as in paragraph three. Only in cells are there other candidates. These others can be safely deleted from these cells.