'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.