How to solve sudoku

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Four easy ways to do it fast and fun.

What is Sudoku

Sudoku, or magic square, is a digital puzzle that must be solved on a special playing field.

The classic field is a lined square with dimensions of 9 by 9 cells. The large figure, in turn, consists of nine small, 3 by 3 cells each.

In each row and column, only a few cells are filled with numbers. The player's task is to find out which numbers are missing and place them correctly in all empty cells of the square.

Experts say that there are 6 670 903 752 021 072 936 960 numerals. Thus, new and new Sudoku can be played endlessly.

What rules of Sudoku should be taken into account

There are only two of them:

1. The playing field can only be filled with numbers from 1 to 9. There are types of Sudoku that can be solved with letters or symbols, but these are completely separate games with their own rules and strategy.
2. The number can be written only if it will not be repeated in the row, column and small square 3 x 3, in which the empty cell is located.

Also remember that Sudoku is a relaxing game that helps you not only train your brain, but also relieve stress. So take your time and try to have fun.

How to solve Sudoku in the classic brute-force way

It is suitable for solving Sudoku of any difficulty. But still it works best on simple playing fields, where initially at least half of the cells are filled with numbers. For example, on this:

First, select the small square filled with numbers as much as possible. In this case, this one:

Other fields may contain multiple options. Among the equivalents, stop at the one that you like best.

Now select the cell located at the intersection of the most digit-filled row and column.

To figure out the answer, you need to do a simple analysis. In theory, the number can be any - from 1 to 9. But we know that it should not be repeated within a small square.

In total, out of the possible nine options, we cross out those that are already present in the small square: 7, 2, 8, 1, 6, 4. This means that the desired number is 3, 5 or 9.

Now we parse the row in which our empty cell is located. It contains, among others, the number 3. This means that we can delete this option.

Thus, there are only two numbers that can be entered into the cell - this is 9 or 5. But if we enter 9, then the number 5 will only have space in the column, which already has its own five:

Since this contradicts the rules, we come to an unambiguous conclusion: only the number 5 can be in the analyzed cell:

Now we need to find out which numbers are located in the two remaining empty cells. It’s quite simple. We know that there are only two options - these are 3 and 9.

The triple cannot be in the middle row of the small square, since it is already in the same row of the large square. For the same reason, the bottom line of the small square cannot contain a nine. This means that only such an arrangement of numbers is possible:

Having filled in the first small square, move on to the next. We select it according to the same scheme - so that there are as many filled cells as possible in it and the rows and columns of the large square that cross it. In this case, it's the bottom right square.

We start filling it in from the top left cell, since it is located at the intersection of the most filled rows and columns.

Since four numbers are already known in the small square, only 1, 2, 6, 7, or 9 can be the desired one.

But 1, 7 and 6 are already in the common line. This means that there are only two options left: 2 and 9. However, 2 is present in the general column, so the result of the search looks like this:

We pass to the next empty cell, located at the intersection of the most filled lines and columns - this is the middle cell in the bottom row. We immediately find out that the number in this cell cannot be 1, 2, 3, 4 (since they are in the corresponding column), as well as 5, 7, 8 and 9 indicated in the corresponding row. Total option one:

Continue filling in empty cells using the same algorithm until you solve the puzzle.

How to solve Sudoku in a sequential way

The scheme for solving the puzzle is the same in this case. Only instead of a mental selection of suitable numbers, a documentary is used.

In each blank cell, write in all the numbers from 1 to 9, and then just cross out the unsuitable ones. Move from one cell to another.

Already at the first pass of the large square, you will find at least one cell with an unambiguous solution. Enter the found number in the box.

Example - number 3:

It is impossible to enter any other number in a specific cell, this will be a violation of the rules.

Next, analyze the remaining empty cells in the same small square, crossing out the number just inscribed from the possible options. Most likely, you will immediately find at least one more unambiguous solution for an unfilled cell.

Continue to cross out unsuitable options in the same way. The process will go like an avalanche.

How to solve Sudoku by elimination

This method allows you to fill in empty cells very quickly, but is suitable only for the most attentive. It consists in the fact that we scan several small squares located in one column or row at once.

In this example, it's easy to see that the middle and bottom squares already have the number 3, and in different columns. And in the square on the left, the three is in the middle row. This means that there is only one cell in the upper right square where you can insert 3 - the right one in the bottom row:

By the same principle, you can quickly enter the number 6 into the cell of another small square:

Continue to analyze other adjacent figures: there are many more cells that can be filled in just a couple of seconds, without going through the options.

How to Solve Sudoku Using Small Squares Analysis

Look at each small square and write down all the numbers that are missing next to it.

Select one of the shapes that has the fewest empty spaces. Let's put the left center square. There are no numbers 1, 2 and 8.

It is immediately noticeable that 2 cannot be in any of the empty cells in the top row: after all, there is already a two there. This means that the location of this figure is unambiguous.

There are only two cells left in the top row of the small square. But 1 cannot be in the right cell, since it is already in the entire column. Therefore, we put there 8. It turns out that only one place is available for a unit:

Consider the following figure. For example, the bottom left, where three digits are missing - 7, 8 and 9. Now we place the digits in the cells allowed for them.

Take 7: it should not be in either the first or the second column, since each of them already contains a seven. This means that this figure can be entered only in the third column.

Move on to 8. It cannot be in the second column, because it is already in it. Accordingly, the only space allowed for this digit is the first column.

According to the residual principle, we put the number 9 in the only free cell - in the central, second column:

Then switch to the next small square with a few empty cells.