Sudoku Assistant - The Sudoku Trainer and Solver

'N'-Possible

Also known as Naked Subset

When a two possible values are the only possible values on two cells in a particular row, column or subgrid, then those cells are the only place that can hold those values... so those two values can be removed from all pencil-marks the other cells in that region. This rule also applies to sets of 3 values on three cells, four on four etc; hence our describing this technique as 'N'-possible.

OK - this is probably easier to see from an example. Look at the cells highlighted in green in the top-right subgrid. The small markings represent the possible values for the cell, and in this case we see exactly two possible values {5,6} in exactly two cells in this subgrid. If one cell is 5, the other has to be 6. And so, no other cell in the subgrid can be 5 or 6. We've highlighted the cells that can have values removed from the pencil-marks in red:

2       3   156 7 56
9       1   2356 8 56
5       6   9 123 4
6 5 3 8 7 1 4 9 2
4 8 9 3 2 5 7 6 1
7 2 1 4 9 6     58
    5   8       679
  6     4       5789
  9     5       3

Exercise: You may notice that we've also shown the pencil-marks on the column - you may note that the key cells on which we found this 'Two-possible' / Naked-subset were also on the rightmost column... which means that there are some cells that can have values removed from pencil-marks.

If you are unsure of any of the terminology we use, you may find it helpful to refer to our Glossary.

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