How to play Sudoku: step by step solving the puzzle

Sudoku is a very interesting puzzle. It is necessary to arrange the numbers from 1 to 9 in the field in such a way that each row, column and block of 3 x 3 cells contain all the digits, and they should not be repeated. Consider step by step instructions on how to play Sudoku, basic methods and strategy solutions.

Algorithm for solving: from simple to complex

The algorithm for solving the game of the mind of Sudoku is quite simple: it is necessary to repeat the following steps until the problem is completely solved. Gradually move from the simplest steps to more complex ones, when the first ones do not allow you to open the cell or exclude the candidate.

Single Candidates

First of all, for a more vivid explanation of how to play Sudoku, we introduce a numbering system for blocks and cells of the field. Both cells and blocks are numbered from top to bottom and from left to right. Let's start our field. First, you need to find single candidates for a place in the cell. They can be hidden or explicit. Let's consider the possible candidates of the sixth block: we see that only in one of the five free cells there is a unique figure, therefore, the four can be safely entered into the fourth cell. Considering this block further, we can conclude: in the second cell there should be a figure of 8, since after excluding the quadruple the eight in the block is not found anywhere else. With the same justification, we put the number 5.

Next, we consider each row, column, or block for hidden or explicit single candidates, given the numbers previously assigned, and put them in the field.

Carefully look through all the possible options. Looking at the central cell of the fifth block, we find that in addition to the number 9 there can not be any more options - it's an obvious single candidate for this cell. Nine can be deleted from the remaining cells of this block, after which the other figures are easily displayed. By the same method we go through the cells of other blocks.

How to discover hidden and explicit "naked pairs"

Putting the necessary numbers in the fourth block, we return to the empty cells of the sixth block: it is obvious that the number 6 should be in the third cell, and 9 in the ninth.

The concept of "naked pair" is only present in Sudoku. The rules for detecting them are as follows: if there is an identical pair of candidates in two cells of the same block, row or column (and only this pair!), Then the remaining cells of the group can not have them. We will explain this with the example of the eighth block. Putting in each cell of possible candidates, we find out an obvious "bare pair". Figures 1 and 3 are present in the second and fifth cells of this block, and there are only two candidates present there and hence from other cells they can be safely excluded.

Completion of the puzzle solving

If you have learned the lesson of how to play Sudoku, and step by step to follow the above instructions, then you should get about the same picture as this field:

Here you can find single candidates: a unit in the seventh cell of the ninth block and a deuce in the fourth cell of the third block. Try to solve the puzzle to the end. Now compare the result with the correct solution.

Happened? Congratulations, because it means that you have successfully learned the lessons of how to play Sudoku, and have learned to solve the simplest puzzles. There are many varieties of this game: Sudoku of different sizes, Sudoku with additional areas and additional conditions. The playing field can vary from 4 x 4 to 25 x 25 cells. You can find a puzzle in which the numbers can not be repeated in an additional area, for example, diagonally.

Begin with simple options and gradually move on to more complex ones, because with training comes experience.