3. GAME SYSTEM

3.1 SOLVING METHODS

To solve sudokus is an exercise that develops our memory, logic, thinking dodginess and inventiveness. Besides, it improves the health of our mind and keeps it fit.

The rules of the game are very easy. The board is divided into cells. Only one symbol may be set for each cell. Our aim is to fill all the cells of the board by means of logical thinking, without guessing the numbers. Each grid of the board is divided into boxes, rows and columns that contain the same number of cells. Each box, row and column of sudoku should contain all symbols without their repeating. That is why sometimes we call boxes, rows and columns groups.


This program introduces the new notion in sudokus world: possibilities. The possibilities show symbols which can appear in a cell. In the beginning of the game all cells, which are not the initial data, possess all the possibilities. When there is one possibility in one cell it is considered to be the final value.

Remember that to delete the possibilities is not the sole means of finding the value. Taking into account all the rules you will be able to apply some basic logical norms:

3.1.1 ADD SYMBOLS OF THE GROUP

This norm is applied when you are short of only one cell without number in a definite group. Each box, row and column of sudoku should contain all symbols without their repeating. That is why the final value of the cell is the only symbol that is not even situated inside the group.

3.1.2 VISUALIZATION OF POSSIBILITIES IN INTERSECTION OF GROUPS

This is the expansion of the previous rule. It is applied in the situation when in spite of the existence of several empty cells only one certain symbol is possible in one of them. It happens because each cell belongs to 3 groups (at the minimum): 1 row, 1 box and 1 column.

For example, the X cell belongs to row 1 and column 5. Column 5 contains value 2, so there can be no another 2 in this cell. In such a way we can guess where value 2 from row 1 is situated.

3.1.3 SCANNING

It is applied when the existence of a symbol in several close groups leads to the existence of a cell with a possible symbol only in one group. It is based on the deletion of all group possibilities where the symbol is placed.

3.1.4 PAIRS

There are cases when there exist two cells in a group in which only two symbols are possible. That is why it is impossible that one of these symbols appears in another cell of the group that contains two of the above said cells.

For example, we see box 9 composed of 1 and 8 (green). We can delete 1 and 8 from the rest of the cells of row 9 where they both appear.

3.1.5 HIDDEN PAIRS

There are cases when two cells exist in one group where two or more symbols are possible. But in the above mentioned group these two cells may contain only two symbols (namely a pair of symbols hidden because of a great number of possible symbols in these cells). The application of this rule forces to delete possibilities in two cells which do not belong to the group.

Like in the previous example, we see a hidden pair composed of 4 and 5 (blue) in row 9. We can delete 1 from the cells of the group. Besides, we delete 4 and 5 from row 7 which also belong to the above mentioned pair.


3.1.6 TRIOS AND QUARTETS (HIDDEN AND NOT HIDDEN)

Trios and quartets are like pairs but in this case we work with groups of three and four symbols, though there may be cases when in any cell of a trio or of a quartet one value can not belong to this trio or to this quartet. Often these cases may be solved by applying rules of a lesser complexity. But if any trio is identified always remember about the deletion of all the possibilities that do not belong to the trio from all cells of the trio. Besides, you can delete the possibility of the trio from all group cells that are situated outside the above mentioned trio. The same happens during the identification of a quartet.

We recommend applying these rules not only in your mind, but also for providing help during the deletion of possibilities because in a great number of cases you can get the final value by means of applying some of these norms simultaneously within one cell. This system may seem to be very difficult intellectually but the usage of possibilities may make your life much easier.