Base techniques

Advanced techniques

Open Single

According to the rules of Sudoku in a single box, as well as in the row or column may not be the same figures.

In the simplest case, when in a square, row or column, filled with all the numbers except one, the missing figure is calculated by exclusion, as the figures should not be repeated.

This rule can be difficult to apply and in cases where the box is not filled in all the figures, but it is missing digits method exception.

 sudoku1

For example, the figure in the highlighted box lacks the following numbers: 2, 3, 4, 7, 9.

But at the top of the already allocated numbers are: 2 and 9. And in the last column of the highlighted numbers are 3 and 7. Consequently, the cell located in the upper right corner of the figure should be 4, she received the exception of numbers 2, 9, 3 and 7 of the first list of numbers.

sudoku2

Slice and dice

Consider the following rule. As we already mentioned, in one box, as well as in the row or column may not be the same figures.

Please note in red on the top box game board in the picture below. Try to determine what value should be placed in a cell, box green.

One can notice that the three top squares in row 2 and 3 are already present figure 2, which in the picture surrounded by red and strikethrough red lines. Therefore, missing the two should be present in the average square and on the top line, as a last square it was already there, in the middle and bottom lines

So, we have determined that, on average, the top box should be at number 2. Now determine the row and column in the box, it should be.

Figure 2 may not be the first and second columns of the upper middle square, which appear in blue, as in the first column at the top of the already figure 7, while the second column has a number 2 in the middle box (it is highlighted in red). But even if the figure 7 was not in the top row, it still would not be 2 because the number 2 is already in this column.   

Consequently, in the green box need to place the figure 2.

sudoku3

Hidden pairs

Consider a more complex rule. To begin with, in each empty cell tips, there are several options for possible values.

sudoku4

Pay attention to the highlighted red line in the bottom row of squares of the playing field. Try to determine what value should be placed in a cell, box green and blue.

One can notice that in the lower left square game board in the selected cells are hidden pairs, as in these cells the same range of possible values - 1 and 3.

In these cells may be only two options - 1 and 3. Consequently, if in a square in two cells there are only two options for the values, the remaining cells in this line, the values of options should be deleted. Therefore, the values 1 and 3 are excluded from the options in the green and blue box (in the green cell crossed figure 3, while the blue figure 1).

So, we have determined that in the green box should be number 7, as it had only two options for the values, one of which was deleted. Now we define a figure of a blue cell, in which there are three variants of possible values - 1, 5 and 7. As figure 1 was removed earlier, and the number 7 in the box already exists, therefore, in the blue box must be placed the number 5.

Lone ranger

Let's look at one rule. As we already mentioned, in each empty cell tips, there are several options for possible values.

sudoku5

Pay attention to the highlighted red line in the top row of squares of the playing field. Try to determine what value should be placed in a cell, box green.

 After reviewing all possible options at the top of the values, notice that the version 5 there is only one cell, which is highlighted in green. Consequently, the cell value is 5.

sudoku6

AI Sudoku Solver 2011