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Methods to solve Sudoku

Any number in a Sudoku can be logically deduced if you take into account Sudoku rules.

In case there is a row, column or region where only one number is missing, you just have to check the numbers you already have to deduce the missing one. If you re-count the numbers you have, you will obtain the number you need.

Examples of re-counting method for Sudoku partial solution

A number cannot be repeated in the row, column or region where it has been placed, so we can reject it as candidate for the empty cells in such row, column and region. In some cases, we can solve numbers that may seem complicated at first by scanning the Sudoku puzzle this way.

Example of scanning method for Sudoku partial solution

In the example we can see that in the upper right region there is only one possible cell for number 7 (highlighted with a red circle), since there are no more 7 possible in the two upper rows or in the two right columns.

Sometimes we can face a different situation when there is only one cell empty because the others have already been solved:

Example of situation that allows partial solution of Sudoku with scanning method Example of situation that allows partial solution of Sudoku with scanning method Example of situation that allows partial solution of Sudoku with scanning method
Example of situation that allows partial solution of Sudoku with scanning method     Example of situation that allows partial solution of Sudoku with scanning method     Example of situation that allows partial solution of Sudoku with scanning method


Writing down all the numbers that have not been rejected, i.e. that are possible candidates to be the correct number, can help to have a clearer view of the situation.

Example of Sudoku with candidates

In the example the possible candidates have been written down in each cell.

So the cells that only have one candidate indicate the only number possible. Once these cells are solved, the number has to be rejected as candidate from the corresponding row, column and region.

Example of Sudoku partial solution by writing candidates down Example of Sudoku partial solution by writing candidates down Example of Sudoku partial solution by writing candidates down

As you can see in the last step, every time we update the possible candidates new cells with only one possible number come up. So the same operation can be repeated until the whole Sudoku is solved or until it is not possible to deduce more numbers (this usually happens in the most difficult Sudoku puzzles).

Here you are a list of sites where you can get more information and explanations:

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