How to solve complex Sudoku?
Many people wonder how to solve Sudoku, are there standard methods and strategies. As in any logic puzzle there is. We have considered the simplest of them. To move to a higher level, you need to have a greater margin of time, perseverance, patience. To solve the puzzle, you will have to make assumptions and, possibly, get the wrong result, which will return you to the place of choice. Complex Sudoku is essentially how to solve a problem using an algorithm. Let's consider several popular techniques used by professional "sudokuvedov" in the following example.
First of all, it is necessary to fill in the empty cells with possible options in order to make the decision as easy as possible and have the complete picture before your eyes.
The answer to how to solve difficult Sudoku is different for everyone. It is more convenient for someone to use different colors for coloring cells or numbers, someone prefers a 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 singles in this task. Armed with the Sudoku rules and a close look, you can see that the top line of the middle small block contains the number 5, which occurs once in its line. In this regard, you can safely put it down and exclude it from the cells colored green. This action will entail the opportunity to put down the number 3 in the orange cell and boldly cross it out of the corresponding violet vertically and in the small block 3 * 3.
In the same way, we check the rest of the cells and put ones in the circled cells, since they are also the only ones in their rows.
To figure out how to solve complex Sudoku, you need to arm yourself with a few 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 lines. In the example, these pairs are 4 and 9 from the third line. They show you how to solve free Sudoku hard. Their combination indicates that only 4 or 9 can be entered in these cells. This conclusion is made based on the rules of Sudoku.
From the cells highlighted in green, you can remove the blue values and thereby reduce the number of options. In this case, the combination 1249 located in the first line is called by analogy the "open four". You can also find "open threes". Such actions entail the appearance of other open pairs, for example 1 and 2 in the top row, which also make it possible to narrow the range of combinations. In parallel, we put 7 in the circled cell of the first square, since the five in this row will in any case be located in the lower block.
Hidden Pairs / Threes / Fours Method
This method is the opposite of open combinations. Its essence lies in the fact that it is necessary to find cells in which numbers are repeated within a square / row that are not found in other cells. How does this help you solve Sudoku? The technique allows you to cross out the rest of the numbers, since they serve as a background and cannot be entered 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 that says that it is possible to put down a single number.
An example is blue-stained cells. The numbers 4 and 7 are found exclusively in these cells, so the rest can be safely removed.
The conjugation system operates 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.
The principle of how to solve Sudoku online is the ability to analyze and match. Another way to exclude variants is the presence of any number in two columns or lines that intersect with each other. In our example, a similar situation was not encountered, so we will consider another. The picture shows that the "two" occurs in the second and third middle blocks once, with a combination of which they are connected and 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 difficulty of visualizing and identifying connections.
As a result of each action, the number of options in the cells is reduced and the solution is reduced to the "Singleton" method. This process can be called abbreviation and separated into a separate method, since it involves a thorough analysis of all rows, columns and small squares with the successive elimination of options. As a result, we come to a single solution.