Sudoku examples. Hidden Pair Method. What is Sudoku

Sudoku solving is a creative process. The rules of the puzzle are very simple, although the logical reasoning during the search for a solution can be of varying degrees of complexity. Experience comes only with time, and each player develops his own strategy. And so that you can better navigate the ways of solving puzzles and get a taste, we present some recommendations.

Start the solution from one.

1. First, "look around" on the playing field, finding all the cells with the number "1".

2. Check successively each of the 3x3 blocks to see if it already contains one. If it does, consider the following.

3. If there is no one in the block yet, try to find all the cells inside this block that could have a one. Don't forget about the rule: each number can appear in each row, each column and each block only once. Exclude from consideration all cells of the block in which the number "1" cannot be located, because the column or row is already "occupied". It is likely that there will be such a block in which there will be only one cell, in which there can be a unit. Enter her.

4. If you are not sure about the uniqueness of the solution, it is better to leave this block and try with another one. A suitable block is sure to be found.

After you "pass" all the blocks with the number "1", repeat the search with a different number. For example with a double. Then three, and so on. Until you check all the numbers from 1 to 9. And you will see that you have already filled in a lot of cells. After that, we advise you to repeat the entire "procedure" again from the very beginning - again from 1 to 9. The second time, things will go easier, because many cells have already been filled. And where you doubted, you can confidently enter a number.

Using the recommendations, it will not be difficult to solve a simple puzzle. We know from experience that people who can easily solve simple Sudokus may have difficulty with complex ones. Therefore, let us consider in detail the solution of one of the problems.

For convenience of explanation, we will use the numbering of rows, columns and 3x3 blocks from 1 to 9. The numbering order is from left to right and from top to bottom.

Designations:

1. The gray block, row or column is the "zone" that we analyze in search of a solution;

2. Highlighted "bold" number (blue) - the desired number found during the analysis;

3. The lines show that the figure from which this line begins cannot be placed in this direction.

We find the number "1" in the 2nd block. The lines coming from the units of the 5th and 8th blocks cross out the rest of the empty cells.

We find the number "1" in the 4th block. For this sleep, we determine where in the 6th block there can be ones by drawing lines from the ones of the 5th and 9th blocks - two ones in the top row. Already from them we draw a line towards the 4th block and a line from the unit of the 5th block.

The search for possible twos was not successful, but you can find a three in the 9th block by drawing lines from threes in the 3rd and 6th blocks. There were no options for the numbers "4", "5", "6", "7". But the number "8" was found in the 8th square: lines from the eights of the 2nd, 5th and 7th blocks. Nine was also missing.

Let's start a new search for units. A unit was found in the first block: the lines from the units in the 2nd and 9th blocks determined the possible positions of the unit in the 3rd block, from which the lines stretched to the 1st block. The remaining lines are visible in the figure. The next unit was found in block 7.

The first two was found in block 4, after which the first five was also determined there. The numbers "3", "4", "6", "7" were not found.

The number "8" of block 1 is determined by the lines from the eights from blocks 4 and 7. Then we find the nine of the 9th row: since it cannot be in blocks 7 and 8 (see lines from the corresponding nines), then it is in the block nine.

The number "9" in the 1st line: it cannot be in block 2, so it is in block 3. In the remaining cell of the line, enter "5". Two digits "9" were found in blocks 5 and 6. We start again with the number "1".

The quarter of the 6th block was found first. Then the four of the 5th column - it cannot be in the 4th and in the 7th row. Three cannot be in the 7th line, so it is in the 4th. Then there is a six in the remaining cell.

In the next step, the queue is optional: first we find the eight, and then the one in block 6, or vice versa.

We continue to arrange the eights: first we find "8" in block 9, and from it we draw a line, defining the eight in block 3.

The next ones were the numbers "1" and "6" in block 3, the order of finding is not fundamental.

Then we will decide on the number "7" in the 9th column: it cannot be in block 6, then it is in the 2nd row. From the five in block 1 we draw a line - we find a place for the number "5" in the 3rd block. In the free cell we enter the last digit - "2".

In the second row we find the number "2", then "4" and finally "9".

Then we find the number "4" in block 8. In the remaining cell - "7". We lead a line from it up to block 5 - a new seven. In the empty cell of the 9th line - "7".

Let's find sequentially the numbers "5", "2", "6" in block 5 and the numbers "7", "3" in the 6th row. Then we get "5" and "6" in the 6th block. The last digit is "6" in the 4th block.

The next "7" and "3" in the 1st block; the numbers "7" and "2" in the 7th column and "5" in block 9. We analyze the 7th row, the 2nd column and place "9" first, then "3" and "2". The final touch is "4" and "6".

Solution completed.

In very complex problems, there is another trick. It is used when it is impossible to calculate a single move in any way. There are at least two cells for one digit in a block (row/column). It is extremely difficult to sort out in your mind all the consequences of a position chosen at random. Then you should enter the number at random, but with a pencil. In this case, the only options can be entered immediately with a ballpoint pen. If after a few moves an error is detected, for example, it is impossible to enter any number in the block - there is no suitable place, then the entire pencil version is erased and the second option is entered in the initial cells. You can also use the entry in the cells of all possible numbers on this moment, this helps to quickly navigate in the search for a solution. In any case, start with easy puzzles and good luck to you!

• tutorial

1. Basics

1.1 " Last Hero»

Consider the seventh square. Only four free cells, so something can be quickly filled.
"8 " on D3 blocks padding H3 and J3; similar " 8 " on G5 closes G1 and G2
With a clear conscience we put " 8 " on H1

1.2 "Last Hero" in a row

After viewing the squares for obvious solutions, move on to the columns and rows.
Consider " 4 " on the field. It is clear that it will be somewhere in the line A .
We have " 4 " on G3 that covers A3, eat " 4 " on F7, cleaning A7. And one more " 4 " in the second square prohibits its repetition on A4 and A6.
"The Last Hero" for our " 4 " it A2

1.3 "No Choice"

1.4 "And who, if not me?"

In jargon it is " naked loner". If you fill in the field with possible values ​​​​(candidates), then in the cell such a number will be the only possible one. Developing this technique, you can search for " hidden loners" - numbers unique for a particular row, column or square.

2. "Naked Mile"

2.1 Naked couples

2.2 "Threesome"

Candidate combinations for "naked trio" may be like this:

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

In this example, everything is pretty obvious. In the fifth square of the cell E4, E5, E6 contain [ 5,8,9 ], [5,8 ], [5,9 ] respectively. It turns out that in general these three cells have [ 5,8,9 ], and only these numbers can be there. This allows us to remove them from other block candidates. This trick gives us the solution " 3 " for cell E7.

2.3 "Fab Four"

In the above example, in the first square of the cell A1, B1, B2 and C1 generally contain [ 1,5,6,8 ], so these numbers will occupy only those cells and no others. We remove the candidates highlighted in yellow.

3. "Everything hidden becomes clear"

3.1 Hidden pairs

3.1 Hidden triplets

Second, in a column 9 . [4,7,8 ] are unique to cells B9, C9 and F9. Using the same logic, we remove candidates.

3.1 Hidden fours

4. "Non-rubber"

If any of the numbers appear twice or thrice in the same block (row, column, square), then we can remove that number from the conjugate block. There are four types of pairing:

1. Pair or Three in a square - if they are located in one line, then you can remove all other similar values ​​​​from the corresponding line.
2. Pair or Three in a square - if they are located in one column, then you can remove all other similar values ​​​​from the corresponding column.
3. Pair or Three in a row - if they are located in the same square, then you can remove all other similar values ​​​​from the corresponding square.
4. Pair or Three in a column - if they are located in the same square, then you can remove all other similar values ​​\u200b\u200bfrom the corresponding square.

4.1 Pointing pairs, triplets

Let me show you this puzzle as an example. In the third square 3 "is only in B7 and B9. Following the statement №1 , we remove candidates from B1, B2, B3. Likewise, " 2 " from the eighth square removes a possible value from G2.


Special puzzle. Very difficult to solve, but if you look closely, you can see a few pointing pairs. It is clear that it is not always necessary to find them all in order to advance in the solution, but each such find makes our task easier.

4.2 Reducing the irreducible

It often happens that you need something to occupy yourself, entertain yourself - while waiting, or on a trip, or simply when there is nothing to do. In such cases, a variety of crosswords and scanwords can come to the rescue, but their minus is that the questions are often repeated there and remembering the correct answers, and then entering them “on the machine” is not difficult for a person with a good memory. Therefore, there is an alternative version of crossword puzzles - this is Sudoku. How to solve them and what is it all about?

What is Sudoku?

Magic square, Latin square - Sudoku has a lot of different names. Whatever you call the game, its essence will not change from this - this is a numerical puzzle, the same crossword puzzle, only not with words, but with numbers, and compiled according to a certain pattern. AT recent times is a very popular way to brighten up your leisure time.

The history of the puzzle

It is generally accepted that Sudoku is a Japanese pleasure. This, however, is not entirely true. Three centuries ago, the Swiss mathematician Leonhard Euler developed the Latin Square game as a result of his research. It was on its basis that in the seventies of the last century in the United States they came up with numerical puzzle squares. From America, they came to Japan, where they received, firstly, their name, and secondly, unexpected wild popularity. It happened in the mid-eighties of the last century.

Already from Japan, the numerical problem went to travel the world and reached, among other things, Russia. Since 2004, British newspapers began to actively distribute Sudoku, and a year later, electronic versions of this sensational game appeared.

Terminology

Before talking in detail about how to solve Sudoku correctly, you should devote some time to studying the terminology of this game in order to be sure of the correct understanding of what is happening in the future. So, the main element of the puzzle is the cage (there are 81 of them in the game). Each of them is included in one row (consists of 9 cells horizontally), one column (9 cells vertically) and one area (square of 9 cells). A row may otherwise be called a row, a column a column, and an area a block. Another name for a cell is a cell.

A segment is three horizontal or vertical cells located in the same area. Accordingly, there are six of them in one area (three horizontally and three vertically). All those numbers that can be in a particular cell are called candidates (because they claim to be in this cell). There can be several candidates in the cell - from one to five. If there are two of them, they are called a pair, if there are three - a trio, if four - a quartet.

How to solve Sudoku: rules

So, first, you need to decide what Sudoku is. This is a large square of eighty-one cells (as mentioned earlier), which, in turn, are divided into blocks of nine cells. Thus, there are nine small blocks in total in this large Sudoku field. The player's task is to enter numbers from one to nine in all Sudoku cells so that they do not repeat either horizontally or vertically, or in a small area. Initially, some numbers are already in place. These are hints given to make it easier to solve Sudoku. According to experts, a correctly composed puzzle can only be solved in the only correct way.

Depending on how many numbers are already in Sudoku, the degrees of difficulty of this game vary. In the simplest, accessible even to a child, there are a lot of numbers, in the most complex there are practically none, but that makes it more interesting to solve.

Varieties of Sudoku

The classic type of puzzle is a large nine-by-nine square. However, in recent years, various versions of the game have become more and more common:

Basic solution algorithms: rules and secrets

How to solve Sudoku? There are two basic principles that can help solve almost any puzzle.

1. Remember that each cell contains a number from one to nine, and these numbers should not be repeated vertically, horizontally and in one small square. Let's try by elimination to find a cell, only in which it is possible to find any number. Consider an example - in the figure above, take the ninth block (lower right). Let's try to find a place for the unit in it. There are four free cells in the block, but one cannot be placed in the third in the top row - it is already in this column. It is forbidden to put a unit in both cells of the middle row - it also already has such a figure, in the area next door. Thus, for this block, it is permissible to find a unit in only one cell - the first in the last row. So, acting by the method of elimination, cutting off extra cells, you can find the only correct cells for certain numbers both in a specific area, and in a row or column. The main rule is that this number should not be in the neighborhood. The name of this method is "hidden loners".
2. Another way to solve Sudoku is to eliminate extra numbers. In the same figure, consider the central block, the cell in the middle. It cannot contain the numbers 1, 8, 7 and 9 - they are already in this column. The numbers 3, 6 and 2 are also not allowed for this cell - they are located in the area we need. And the number 4 is in this row. Therefore, the only possible number for this cell is five. It should be entered in the central cell. This method is called "loners".

Very often, the two methods described above are enough to quickly solve a Sudoku.

How to solve Sudoku: secrets and methods

It is recommended to adopt the following rule: write small in the corner of each cell those numbers that could be there. As new information is obtained, the extra numbers must be crossed out, and then in the end the correct solution will be seen. In addition, first of all, you need to pay attention to those columns, rows or areas where there are already numbers, and as much as possible - than fewer options remains, the easier it is to deal with. This method will help you quickly solve Sudoku. As experts recommend, before entering the answer into the cell, you need to double-check it again so as not to make a mistake, because because of one incorrectly entered number, the whole puzzle can “fly”, it will no longer be possible to solve it.

If there is such a situation that in one area, one row or one column in any three cells, it is permissible to find the numbers 4, 5; 4, 5 and 4, 6 - this means that in the third cell there will definitely be the number six. After all, if there were a four in it, then in the first two cells there could only be five, and this is impossible.

Below are other rules and secrets on how to solve Sudoku.

Locked Candidate Method

When you work with any one particular block, it may happen that a certain number in a given area can only be in one row or in one column. This means that in other rows/columns of this block there will be absolutely no such number. The method is called “locked candidate” because the number is, as it were, “locked” within one row or one column, and later, with the advent of new information, it already becomes clear exactly in which cell of this row or this column this number is located.

In the figure above, consider block number six - the center right. The number nine in it can only be in the middle column (in cells five or eight). This means that in other cells of this area there will definitely not be a nine.

Method "open pairs"

The next secret, how to solve Sudoku, says: if in one column / one row / one area in two cells there can be only two any identical numbers (for example, two and three), then they are in no other cells of this block / row / column will not. This often makes things a lot easier. The same rule applies to the situation with three identical numbers in any three cells of one row/block/column, and with four - respectively, in four.

Hidden Pair Method

It differs from the one described above in the following way: if in two cells of the same row/region/column, among all possible candidates, there are two identical numbers that do not occur in other cells, then they will be in these places. All other numbers from these cells can be excluded. For example, if there are five free cells in one block, but only two of them contain the numbers one and two, then they are exactly there. This method works for three and four numbers/cells as well.

x-wing method

If any specific figure(for example, five) can be located only in two cells of a certain row / column / area, which means that it is only there. At the same time, if in the adjacent row/column/area the placement of a five is permissible in the same cells, then this figure is not located in any other cell of the row/column/area.

Difficult Sudoku: Solving Methods

How to solve difficult sudoku? The secrets, in general, are the same, that is, all the methods described above work in these cases. The only thing is that in complex sudoku situations are not uncommon when you have to leave logic and act by the “poke method”. This method even has its own name - "Ariadne's Thread". We take some number and substitute it in the right cell, and then, like Ariadne, we unravel the ball of threads, checking whether the puzzle fits. There are two options here - either it worked or it didn't. If not, then you need to “wind up the ball”, return to the original one, take another number and try all over again. In order to avoid unnecessary scribbling, it is recommended to do all this on a draft.

Another way to solve complex sudoku is to analyze three blocks horizontally or vertically. You need to choose some number and see if you can substitute it in all three areas at once. In addition, in cases with solving complex Sudokus, it is not only recommended, but it is necessary to double-check all the cells, return to what you missed earlier - after all, it appears new information, which must be applied to the playing field.

Math Rules

Mathematicians do not remain aloof from this problem. Mathematical methods, how to solve Sudoku, are as follows:

1. The sum of all the numbers in one area/column/row is forty-five.
2. If three cells are not filled in some area / column / row, while it is known that two of them must contain certain numbers (for example, three and six), then the desired third digit is found using example 45 - (3 + 6 + S), where S is the sum of all filled cells in this area/column/row.

How to increase guessing speed?

The following rule will help you solve Sudoku faster. You need to take a number that is already in place in most blocks / rows / columns, and by eliminating extra cells, find cells for this number in the remaining blocks / rows / columns.

Game Versions

More recently, Sudoku remained only printed game published in magazines, newspapers and individual books. Recently, however, all sorts of versions of this game have appeared, such as board sudoku. In Russia, they are produced by the well-known company Astrel.

There are also computer variations Sudoku - and you can either download this game to your computer or solve the puzzle online. Sudoku comes out for completely different platforms, so it doesn't matter what exactly is on your personal computer.

And more recently, there have been mobile applications with the Sudoku game - for both Android and iPhones, the puzzle is now available for download. And I must say that this application is very popular among cell phone owners.

1. The minimum possible number of clues for a Sudoku puzzle is seventeen.
2. There is an important recommendation on how to solve Sudoku: take your time. This game is considered relaxing.
3. It is advised to solve the puzzle with a pencil, not a pen, so that you can erase the wrong number.

This puzzle is a truly addictive game. And if you know the methods of how to solve Sudoku, then everything becomes even more interesting. Time will fly by for the benefit of the mind and completely unnoticed!

When solving Sudoku, be consistent in your reasoning. Periodically check your actions, because if you make a mistake at the beginning of the solution, then it can eventually lead to an incorrect solution to the entire puzzle. It is easier to avoid mistakes at the beginning of a solution than when a contradiction is found in a solved puzzle.

The following ways to solve Sudoku are listed in order of difficulty and frequency of use in practice.

Selection of candidates

With this technique, they begin to solve any Sudoku, regardless of its complexity. In accordance with the proposed task, it is necessary to enter variants of numbers in empty cells, which can be determined by excluding the numbers already present in rows, columns or blocks.

For example, consider cell A2, it is marked in gray. "1" is in the block, "2" is in the row, "3" is in the block and row, "4" is in the row, "5" is in the column, "7" is in the block, "8" is in the row, "9" is in the column. Accordingly, the only option for this cell is the number "6".

But in most cases, for each cell there are several candidates at once. Fill in the grid with all possible candidates for each cell.

As you can see, there are only two cells in which there is only one candidate each - A2 and D9, they are called the only candidates. After finding the only candidates, it is also necessary to cross them out of the candidates for other cells (cells of this column, row, block). So, deleting the number "6" from line 2, column A and block 1, we will also get the only candidate in cell B1 - the number "2". We proceed in the same way.

However, there are also "hidden" single candidates. Let's take cell I7 as an example. This cell is in block 9. In this block, the number 5 can only be in cell I7, since columns G and H already have the number 5, it is also present in row 8. Accordingly, of the three candidates for cell I7, we leave only the number "5".

Exclusion of candidates

The methods described above allow you to unambiguously determine which number to enter in a particular cell, the following will reduce their number, which ultimately will lead to the only candidates.

During the solution process, a situation may arise when a certain number in a block can only be located in one row or column within this block. As a consequence, this number cannot be in other cells of this row or column outside the block.

Consider block 5. In this block, the number "4" can only be in cells D5 and F5, i.e. in line 5. Accordingly, no matter which of these two cells contains the number "4", it can no longer be in line 5 in other blocks, so it can be safely deleted from the candidates of cell G5.

There is also an alternative to the previous method. If a certain number in a row or column can only be located within one block, then the same number cannot be located in other cells of the block in question.

So in line 1, the number "4" can only be in cells D1 and F1, i.e. in block 2. Therefore, no matter which of these two cells contains the number "4", it cannot be in block 2 in other cells, so it can be safely deleted from the candidates of cells D3 and F3.

If two cells in a block, row, or column contain only a pair of identical candidates, then these candidates cannot be in other cells of this block, row, or column.

Cells G9 and H9 contain a pair of candidates "6" and "8". Accordingly, no matter which of these two cells contains the numbers "6" and "8" (if "6" in G9, then "8" in H9, and vice versa), in block 9 in other cells they can no longer be, as well as in line 9. Therefore, they can be safely deleted from the candidate cells H7, G8, B9, C9, F9.

Also, this method can be applied for three and four candidates, only cells in a block, row, column must be taken three and four, respectively.

From the cells highlighted in yellow - B7, E7, H7 and I7 we cross out the candidates contained in the cells highlighted in gray - A7, D7 and F7.

We do the same with fours. From the cells highlighted in yellow - C1 and C6 we cross out the candidates contained in the cells highlighted in gray - C4, C5, C8 and C9.

But there are often "hidden" pairs of candidates. If in two cells in a block, row or column, a pair of candidates occurs among the candidates that does not occur in any other cell of the block, row, or column, then no other cells of the block, row, or column can contain candidates from this pair. Therefore, all other candidates from these two cells can be crossed out.

So, for example, in column G, the pair of numbers "7" and "9" occurs only in cells G1 and G2. Therefore, all other candidates from these cells can be removed.

You can also look for "hidden" triples and fours.

There are more complex methods used in solving Sudoku. They are not so much difficult to understand as when to apply them. So, for example, if in one of the columns a candidate can only be in two cells and there is a column in which the same candidate can also be in only two cells, and all these four cells form a rectangle, then this candidate can be excluded from other cells of these lines.

By analogy, out of two rows, the excluded candidates would then be in columns.

In column A, the number "2" can only be in two cells A4 and A6, and in column E in E4 and E6. Accordingly, these pairs of cells are in the same rows - 4 and 6, forming a rectangle.

There is a certain dependency:

If the number "2" is in cell A4, then it will also be in cell E6 (it cannot be in cell E4, because the number "2" will already be in line 4, it will not be in cell A6, because j. the number "2" will already be in column A and block 4);

If the number "2" is in cell A6, then it will also be in cell E4 (it cannot be in cell E6, because the number "2" will already be in line 6, it will not be in cell A4, because since the number "2" will already be in column E and block 5).

Therefore, wherever the number "2" is located, in cells A4 and E6 or A6 and E4, from other cells of lines 4 and 6, you can safely cross out the number "2". In addition, this method can be applied to blocks. Since in block 4 the number "2" will necessarily be in cells A4 or A6, it can also be deleted from the candidate cells of block 4.

These are the main ways in which you can solve classic Sudoku. If the Sudoku is not difficult, then it can be solved using the first methods. Solving more challenging puzzles the latter methods are indispensable. But these methods are not stereotyped, in the process of guessing you will develop your own tactics and strategy. The more you solve Sudoku, the better you will get at it. And all the candidates will not need to be written down, and you can easily keep them “in your head”.

An example of a classic Sudoku solution

Now let's try to solve the following Sudoku in its entirety.

To begin with, we will write down all the candidates.

Now let's identify the only candidates (gray cells). And cross them out of the candidates for other cells in blocks, rows, columns (yellow cells).

At the same time, in some cells, we again have the only candidates (for example, in line 1, the number "2" is only in cell B1), we also cross them out of the candidates for other cells of blocks, rows, columns.

Now let's find the "hidden" single candidates (gray cells). And cross them out of the candidates for other cells in blocks, drains, columns (yellow cells).

At the same time, in some cells, we again have “hidden” unique candidates (for example, in row 1, the number “5” is only in cell C1), we also cross them out of the candidates for other cells of blocks, rows, columns.

Now we take cell H5. In line 5, the number "2" occurs only in this cell. We continue to solve our Sudoku regarding this cell.

After only the only candidates remain in some cells, we cross them out from other cells of rows, columns and blocks.

As a result, we get the following combination.

Having solved it, we come to the only correct solution:

This is one of the ways to solve this Sudoku. Of course, it was possible to start the solution from other cells and in other ways, but this solution shows that Sudoku has the only correct solution and it can be found in a logical way, and not by enumeration of numbers.

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 exciting game develop and train logical thinking, memory, perseverance.

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 options for electronic games, including more than a million built-in puzzle options 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, in the cells playing field key figures will be given. 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. 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, for yourself, determine 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.