Sudoku solution 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 vertical and horizontal line. Also, they cannot be repeated in small squares (3x3 cells). At the very beginning of the game there are already numbers (depending on the difficulty of the level, the number of initially given numbers may differ).

Rules for playing Sudoku:

• Select a row, column or square with the maximum number of given numbers. Fill in what is 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 into each cell. You can write down options on a separate piece of paper.
• When also looking at lines and squares, eliminate numbers that are repeated.
• As you fill the puzzle with numbers, it will become easier to solve.

Start playing Sudoku with easy tasks, because the ability to solve the 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 simply 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 prototype of the puzzle is considered to be the Latin squares of Leonhard Euler, a famous mathematician who lived in the 18th century. However, in the form in which it is known today, it was invented by Howard Garnes. Being an architect by training, Garnes simultaneously invented puzzles for magazines and newspapers. In 1979, an American publication called “Dell Pencil Puzzles and Word Games” first published 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, a Japanese publication published the puzzle for the first time. It immediately became widespread. It was then that the puzzle got its name - Sudoku. In Japanese, “su” means “number” and “doku” means “standing alone.” Some time later, this rebus appeared in many printed publications in Japan. In addition, separate collections of Sudoku were published. In 2004, the puzzle began to be published in UK newspapers, which marked the beginning of the game's spread outside Japan.

The puzzle is a square field with a side of 9 cells, divided in turn into squares measuring 3 by 3. Thus, the large square is divided into 9 small ones, the total number of cells of which is 81. Some cells initially contain clue numbers. The essence of the rebus is to fill empty cells with numbers so that they are not repeated in rows, columns, or squares. Sudoku only uses numbers from 1 to 9. The difficulty 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 continues in our time, and successfully. The game is becoming an increasingly common puzzle game, largely due to the fact that it can now be found not only on the pages of the newspaper, but also on your phone or computer. In addition, various variations of this rebus have appeared - letters are used instead of numbers, the number of cells and the shape change.

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Sumdoku

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

How to solve sumdoku?

Consider sumdoku (in the picture 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 = 55. For sumdoku 9x9 it would be 45.

Let's 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 the numbers 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 numbers in the marked blocks is 100. But if we take the two lower rectangles completely, then the sum of the numbers in them should be 55 + 55 = 110. This means that in the only unmarked cell the number is 10.

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

Let us now consider the blocks highlighted in the figure on the right. They cover one penultimate horizontal line of the Sudoku and two “extra” cells. Let's calculate the sum of numbers in blocks: 13 + 8 + 15 + 13 + 10 + 14 = (13+13+14) + (10+15) + 8 = 40 + 25 + 8 = 73. But we know that the sum of numbers in horizontal line is 55, which means you can find out the sum of the numbers in 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 - eliminated, since the cells are located on the same horizontal line, leaving 10+8 and 8+10. But if you put 8 in the first “extra” cell, then in the penultimate horizontal line you will get two fives, and the numbers in the horizontal lines should not be repeated. Thus, we find that the first “extra” cell can only contain 10. We immediately arrange the remaining obvious numbers.

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

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

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

The rules for playing Sudoku are not complicated; they are found on the pages of newspapers or can be found quite easily on the Internet.

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

Today we offer you several versions of the Sudoku-4tune electronic game, including more than a million built-in puzzle options in each game player.

For clarity and a better understanding of the process of solving the riddle, let's consider one of the simple options, the first difficulty level of Sudoku-4tune, 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 measuring 3x3 cells. (Fig.1.)

Do not be confused by the further mention of an electronic game. You can find the game on the pages of newspapers or magazines, the basic principle remains the same.

The electronic version of the game provides great opportunities to choose the difficulty level of the puzzle, 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 changed. You can choose the option that is more suitable for the solution, in your opinion. Reasoning logically, starting from the given numbers, 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. It is necessary to decide where to start the solution. Typically, you need to determine the row, column, or mini square that has the minimum number of empty cells. In the version we have presented, we can immediately select two lines, top and bottom. These lines are missing just one digit. Thus, a simple decision is made, having determined the missing numbers -7 for the first line and 4 for the last, we enter them into the free cells of Fig. 3.

The resulting result: two completed lines with numbers from 1 to 9 without repetitions.

Next move. Column number 5 (from left to right) has only two free cells. After some 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: column, row and 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. It is impossible to 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. Likewise with the number 5 for the second cell (bottom) and the second lower mini-square in Fig. 4 (wrong location).

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

Accordingly, for the correct solution, you need to enter 5 in the second (top) cell, and 8 in the second (bottom) cell. This decision fully complies with the rules.

For the correct option, see Figure 5.

Further solution to a seemingly simple task requires careful consideration of the playing field and the use 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). There were three cells left unfilled. 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 filling out 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 this conclusion based on?

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

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

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

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

As free cells are filled, their number decreases, and we are gradually getting closer to solving our puzzle. But at the same time, solving a problem can be both simplified and complicated. And the first method of filling 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 decreases. (Example: the third column we left). In this case, you need to use the method of searching for individual cells, setting numbers that do not raise any doubts.

In electronic games Sudoku-4tune, 6** series, it is possible to use a hint. Four times per game you can use this function and the computer itself will set the correct number in the cell you have chosen. In the 8** series models there is no such function, and the use of the second method becomes the most relevant.

Let's look at the second method in the example we're using.

For clarity, let's take the fourth column. The empty 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. You can reduce the number of options by taking as a basis the average mini-square, which has a fairly large number of specific numbers and only two free cells in a given column. Comparing them with the numbers we need, we can see that 1,6, and 4 can be excluded. They should not be in this mini-square to avoid repetition. That leaves 7,8 and 9. Please note that in the row (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 left for this cell is number 9, Fig. 8. There is no doubt about the correctness of this solution option and the fact that all the numbers we considered and excluded were originally given in the task. That is, they are not subject to any change or transfer, confirming the uniqueness of the number we have chosen for installation in this particular cell.

Using two methods simultaneously depending on the situation, analyzing and thinking logically, you will fill in all the empty cells and come to the correct solution to any Sudoku puzzle, and this riddle in particular. Try to complete the solution to 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 lovers and fans of this game. Good luck.

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

The Sudoku puzzle has only one rule. It is necessary to fill in the empty cells so that in each row, in each column and in each small square 3 x 3 each digit from 1 to 9 would appear only once.

Program Cross+A knows how 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 ("Sudoku X"). To solve these tasks you need to check the box 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 numbers.

The puzzle may contain free-form regions; these are called sudoku geometric or curly ("Jigsaw Sudoku", "Geometry Sudoku", "Irregular Sudoku", "Kikagaku Nanpure").

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

Sudoku-asterisk ("Asterisk") is a variation of Sudoku that contains an additional area of ​​9 squares. 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 (a girandole is a fountain of several jets in the form of fireworks, a “fire wheel”).

Sudoku with center points ("Center Dot") is a variant of Sudoku, where the central cells of each region 3 x 3 form an additional area.

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

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

Sudoku puzzle ("Offset Sudoku", "Sudoku-DG") contains 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 number from 1 to 9 should appear only once.

Not a horse's step ("Anti-Knight Sudoku") has an additional condition: identical numbers cannot “beat” each other with a knight’s move.

IN sudoku hermits ("Anti-King Sudoku", "Touchless Sudoku", "Sudoku without touching") identical numbers cannot be in adjacent cells (both diagonally, horizontally and vertically).

IN sudoku-antidiagonal ("Anti Diagonal Sudoku") each diagonal of the square contains no more than three different digits.

Killer Sudoku ("Killer Sudoku", "Sums Sudoku", "Sums Number Place", "Samunamupure", "Kikagaku Nampure"; another name - Sum-do-ku) is a variation of regular Sudoku. The only difference: additional numbers are specified - 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 whether the numbers in the cells are even or odd. 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 regular Sudoku. It marks the boundaries between adjacent cells that contain 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 a cell contains the number 3, adjacent cells should not contain the numbers 2 or 4.

Sudoku points ("Kropki Sudoku", Dots Sudoku, "Sudoku with dots") contains white and black dots at the boundaries 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 of size 9 x 9, containing 81 groups of numbers. It is necessary to leave only one number in each cell so that in each row, in each column and in each small square 3 x 3 each number from 1 to 9 would appear only once.

Sudoku chains ("Chain Sudoku", "Strimko", "Sudoku-convolutions") is a square consisting 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 4 x 4 before 9 x 9.

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

Skyscraper Sudoku ("Skyscraper Sudoku") contains key numbers along the sides of the grid. It is necessary to arrange the numbers in a grid; each number indicates the number of floors in the skyscraper. Key numbers outside the grid indicate exactly how many houses are visible in the corresponding row or column when viewed from that number.

Sudoku tripod (Tripod Sudoku) is a type of Sudoku in which the boundaries between regions are not indicated; instead, points are specified at the intersections of the lines. The dots indicate where regional boundaries intersect. Only three lines can extend from each point. It is necessary to restore the boundaries of the regions and fill the grid with numbers so that they are not repeated 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. You need 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 the cells of the grid with numbers from 1 to 9 so that the numbers are not repeated in each row, in each column and on each diagonal. Also, the same number cannot appear twice in each of the regions separated by thick lines.

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

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

• 16 x 16(size of regions 4 x 4).

Cross+A can solve and create variations of Sudoku consisting of several squares 9 x 9.

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

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

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

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

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

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

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

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

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

The program can solve double sudokus in which the regions have arbitrary shapes:

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

Sudoku twins ("Twin Corresponding Sudoku") is a pair of regular Sudoku puzzles, each of which contains several starting numbers. Both puzzles must be solved; in this case, 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, there is a 4 in the second grid.

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

Unlike Hoshi, in sudoku star ("Star Sudoku") a row on the outer edge 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 one contains nine small triangles. The 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 touching triangular cells must not contain the same numbers (even if the cells touch each other by only one point).

Online assistant for solving Sudoku.

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

Many people like to force themselves to think: some - to develop intelligence, others - to keep their brains in good shape (yes, not only the body needs exercise), and the best simulator for the mind are various logic games and puzzles. One of the options for such educational entertainment can be called Sudoku. However, some have never even heard of such a game, let alone knowing 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 solve, but always interesting and addictive to anyone who decides to play this game. The name comes from Japanese: “su” means “digit”, and “doku” means “standing alone”.

Not everyone knows how to solve Sudoku. Complex puzzles, for example, can be solved either by smart, well-thought-out beginners or by professionals who have been practicing the game for more than one day. It will not be possible for everyone to just take it and solve the problem in five minutes.

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, and strive to recreate the picture. You probably have to love numbers to solve Sudoku.

First, a 9 x 9 square is drawn. Then, with bolder 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 along the entire perimeter should not be repeated either in “regions” (3 x 3 squares) or in lines vertically and/or horizontally. In any Sudoku, there are initially some filled cells. Without this, the game is simply impossible, because otherwise the result will not be solving, but inventing. The complexity of the puzzle depends on the number of numbers. Complex sudokus contain a few numbers, often arranged in such a way that you have to rack your brain quite a bit before solving them. In the lungs, about half of the numbers are already in place, making it much easier to figure out.

Fully disassembled example

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

To begin with, you can look at the 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 5 and 9 are missing in the empty cells on the second and eighth lines. With the five, not everything is clear yet, it can be both here and there, but if you look at the nine, everything becomes clear. Since there is already a number 9 on the second line (in the seventh column), it means that in order to avoid repetitions, the nine must be placed down, on the 8th line. Using the elimination method, we add 5 to the 2nd row - and now we already have one filled column.

You can solve the entire Sudoku puzzle in a similar way, but in more complex versions, when one column, row or square is missing not just a couple of numbers, but much more, you will have to use a slightly different method. We will also analyze that now.

This time we will take as a basis the middle “region”, in which five numbers are missing: 3, 5, 6, 7, 8. We fill each cell not with large effective numbers, but with small, “draft” ones. We simply write in each square the numbers that are missing and that may be there due to their lack. In the top cell it is 5, 6, 7 (3 on this line is already in the “region” on the right, and 8 on the left); the cell on the left can contain 5, 6, 7; in the very middle - 5, 6, 7; right - 5, 7, 8; from below - 3, 5, 6.

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

Alternating these two methods, 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 him it will be extremely difficult.

By the way, when a middle seven is found in the upper “region”, it can be removed from the mini-digits 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

There are different types of Sudoku puzzles. In some cases, a prerequisite is the absence of identical numbers not only in rows, columns and mini-squares, but also diagonally. Some contain other figures instead of the usual “regions,” which makes solving the problem much more difficult. One way or another, you know how to solve Sudoku, at least the basic rule that applies to any kind. This will always help you 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 something to do for long hours, or even days, because Sudoku is unrealistically drawn out, especially when you have to actually figure out the principle of their solution. Practice, practice and practice again - and then you will crack 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, 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.

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, the rules of the game are very simple and eliminate multiple solutions. Each row or column contains numbers from 1 to 9. Also, the values ​​are not repeated within one small block.

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.

Rules for solving Sudoku

To get 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.

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

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.

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, whether there are standard methods and strategies. As in any logic puzzle there is. We looked at the simplest of them. To move to a higher 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. Essentially, hard Sudoku is like solving a 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 with possible options in order to make the decision as easy as possible and have the full picture before your eyes.

The answer to how to solve complex sudoku puzzles is different for everyone. Some people find it more convenient to use different colors to color cells or numbers, while others 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 with the rules of Sudoku and a careful look, you can see that in the top line of the middle small block there is the number 5, which appears only once in its line. In this regard, you can safely mark it and exclude it from the cells colored green. 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 out how to solve complex Sudoku puzzles, you need to arm yourself with several 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 complex Sudoku puzzles. Their combination suggests that these cells can only contain 4 or 9. This conclusion is made based on the rules of Sudoku.

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 appearance of other open pairs, for example 1 and 2 on the top line, which also make it possible to narrow down the range of 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 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.

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

Loner or the last hero.

So, where do you start solving Sudoku? It doesn't matter whether the difficulty level is easy or not. But always at the beginning there is a search for obvious cells to fill.

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

There are three ways to search for singles:

• Single player in a 3 by 3 square.
• Horizontally
• Vertically

Of course, you can randomly browse and identify singles. But it is better to stick to a specific system. The most obvious thing to do is start with number 1.

• 1.1 Check the squares where there is no unit, check the horizontal and vertical lines that intersect the given square. And if they already contain ones, then we eliminate the line completely. Thus, we are looking for the only possible place.
• 1.2 Next, we check the horizontal lines. In which there is a unit, and in which there is not. We check in small squares that include this horizontal line. And if they contain a 1, then we exclude the empty cells of this square from possible candidates for the desired number. We will also check all verticals and exclude those that also contain a single. If the only possible empty space remains, then put the required 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 Similar to the previous point, we check all horizontal lines.

"Hidden Units"

Another similar technique is called “who, if not me?!” Look at Figure 2. Let's work with the upper left small square. First, let's go through the first algorithm. After which we managed to find out that in cell 3 1 there is a single figure - 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 which we discover the following: in cell 2 3 there can only be one number 5. Of course, at the moment the 5 can also appear 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 appear, 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 due to their similarity and the only difference is in the number of numbers and cells involved.

So, let's figure it out. Look at Figure 3. Here we put all the possible options in fine print in the usual way. And let's take a closer look at the upper middle small square. Here in cells 4 1, 5 1, 6 1 we have a series of identical numbers - 1, 5, 7. This is a naked three in its true form! What does this give us? And the fact is that only in these cells will these three numbers 1, 5, 7 be located. 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 one; we should think further about four and six. But that's a different story.

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

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

hidden couple

This method of solving Sudoku will reduce the number of candidates and give life to other strategies. Look at Figure 4. The middle top 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 to us? Only these two cells contain candidates 4 and 9. This is our hidden pair. By and large, it is the same couple as in point three. Only in cells there are other candidates. These others can be safely crossed out from these cells.