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Sudoku solving techniques

Basic techniques
Before starting on the techniques, make sure that you are familiar with how to play Sudoku, click here to learn the rules of Sudoku.

If you are familiar with basic sudoku solving techniques, then please have a look at our Advanced Techniques.

1.1 - Naked Single (Sole Candidate)
One of the simplest techniques used, the naked single is simply an empty cell where its value can be deduced from looking at the contents of its row, column and 3x3 block. If 8 numbers have already been assigned to these neighbouring cells then its logical that the empty cell must house the last remaining number.

example A
The shadowed cell in our puzzle must be a 7 because all other values have been placed in neighbouring valid positions.

1.2 - Hidden Single (Unique Candidate)
One of the simplest techniques used, the naked single is simply an empty cell where its value can be deduced from looking at the contents of its row, column and 3x3 block. If 8 numbers have already been assigned to these neighbouring cells then its logical that the empty cell must house the last remaining number.

example B
We can see that the two 4's eliminate two rows and two blocks, leaving a possible three cells in the middle for our final 4, two of the middle cells have been taken up by a 3 and 2 two, so its logical that the final place must be our final 4.

1.3 - Block and Column/Row Interactions
Sometimes a good technique doesn’t always reveal an answer for an empty cell, but it can whittle down the possible values. A single value in a row can sometimes predetermine a possible value in a block and this in turn can remove possible candidates from a column.

example C
The number 9 here has forced block 1 to either house a 9 in cell A or B, this in turn allows the shadowed column to remove all candidate 9's from each cell.

1.4 - Block/Block Interactions
This technique also removes candidates from empty cells, if two neighbouring blocks have some of their rows and columns blocked by a value, then the position for that value in the block can be whittled down. If this happens correctly you can also eliminate candidates from the adjoining 3rd block.

example D
Our 7's have blocked two rows, so our final two 7's must be in either cells A or cells B. this in turn allows the shadowed column to remove all candidate 7's from each cell.

1.5 - Naked Subset (Naked Pair, Disjoint Subset)
Depending on the number of candidates used this technique can also be called ‘Naked Triplet’ or ‘Naked Quad’. This is another technique used for removing candidates from a row, column or block, if two cells on a row have the same candidates then it is logical that any other cell on that row cannot possibly house those values, and therefore can remove the values from their candidate list.

example E
Our pencilling in here shows us that we have two cells that house the possible candidates 6 and 7. This in turn means that the shadowed cell cannot be a 7 and must be a 9.


1.6 - Hidden Subset (Hidden pair, Unique Subset)

Once again depending on the amount of candidates used this technique can also be called ‘Hidden Triplet’ or ‘Hidden Quad’. Similar to ‘Naked Subset’ this technique whittles down candidates from the empty cells we are interested in, not from the rest of the row, column or block. If three separate cells on a row house many candidates, but there are three common numbers that occupy at least one of the cells each then we can remove any other candidates from these three cells, leaving the three values as the only candidates.

example F
We have three cells here that house the numbers 1, 3 or 7, we can simply remove all the other candidates from those cells and we are left with our shadowed cell being a 1.

View Advanced Techniques


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