How to solve Sudoku of any complexity

Many people like to force themselves to think: someone - to develop intelligence, someone - to keep their brains in good shape (yes, not only the body needs charging), and the best simulator for the mind are various games on logic and puzzles. One of the options for such developmental entertainment can be called Sudoku. However, some did not hear about such a game, what can we say about knowledge of the rules or other interesting moments. Through the article you will learn all the necessary information, for example, how to solve Sudoku, as well as their rules and views.

General information

Sudoku is a puzzle. Sometimes difficult, difficult to disclose, but always interesting and addictive to any person who decided on this game. The name came from Japanese: "su" means "figure", and "doc" means "standing alone".

Not everyone knows how to solve Sudoku. Complex puzzles, for example, can either be clever, well-thought-out beginners, or professionals in their field, who practice the game for more than a day. It's just that it is not possible for everyone to solve the task in five minutes.

rules

So, how to solve Sudoku. The rules are very simple and understandable, remember them easily. However, do not think that simple rules promise a "painless" solution; Think a lot, use logical and strategic thinking, try to recreate the picture. Perhaps you need to love the numbers to solve Sudoku.

First a squared 9 x 9 cells are drawn. Then, with thicker lines, it is divided into so-called "regions" of three squares in each. As a result, we get 81 cells, which in the end must be completely filled with numbers. This is the difficulty: the numbers placed around the perimeter from 1 to 9 should not be repeated in the "regions" (3 x 3 squares), nor in the vertical and / or horizontal lines. In any Sudoku, initially there are some filled cells. Without this, the game is simply impossible, because otherwise it will not be a guessing, but an invention. The complexity of the puzzle depends on the number of digits. Complex sudoku contain a few numbers, often arranged so that you will have to seriously shatter your head before deciding them. In the lungs - about half the figures are already in place, making it easier to unravel at times.

Completely parsed example

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

For a start, you can look at the lines or squares where there are especially many numbers. For example, the second column on the left is perfect, there are only two numbers missing. If you look at those that already exist, 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 on the second line there is already a number 9 (in the seventh column), so that there are no repetitions, the nine should be put down, on the 8th line. Use the exception method to add 5 to the 2nd line - and now we already have one filled column.

In a similar way, you can solve the whole Sudoku puzzle, but in more complex cases, when there is not a couple of digits missing in one column, row or square, but much more, you need to apply a slightly different method. We'll take care of it, too.

This time, let's take as a basis the middle "region", in which five digits are missing: 3, 5, 6, 7, 8. Each cell is filled with not small effective numbers, but small "rough" ones. We simply write in each box those figures that are missing and which can be there because of their shortage. In the upper cell this is 5, 6, 7 (3 on this line already exists in the "region" on the right, and 8 on the left); In the cell to the left can be 5, 6, 7; In the very middle - 5, 6, 7; On the right - 5, 7, 8; From the bottom - 3, 5, 6. So, now we look, what mini-numbers contain other numbers. 3: there is only one place, the others do not. Hence, it can be corrected for a large. 5, 6 and 7 are in at least two cells, so we leave them alone. 8 is only in one, then the remaining figures are dropped and you can leave the eight.

Alternating these two methods, we continue to solve Sudoku. In our example, we will apply 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" was found in the upper "region", it can be removed from the mini-digits of the middle square. If you do this, you can see that there is only 7 left in that region, so you can only leave it.

That's all; Finished result:

Kinds

Sudoku's puzzles are different. In some compulsory condition is the absence of identical numbers not only in rows, columns and mini-squares, but also diagonally. In some, instead of the usual "regions" contain other figures, because of what to solve the problem becomes many times more difficult. Anyway, how to solve Sudoku, at least, the basic rule that acts on any kind, you know. This will always help to cope with a puzzle of any complexity, the main thing is to try our best to achieve the goal.

Conclusion

Now you know how to solve Sudoku, but because you can download such puzzles from various sites, solve them online or buy paper versions from newspaper kiosks. In any case, now you will have an occupation for long hours, or even days, because they delay Sudoku unrealistically, especially when you have to actually understand the principle of their solution. Practice, practice and practice again - and then you will click this puzzle as nuts.