Two digits, two cells
A naked pair starts from the cells: two cells with the same two notes. A hidden pair starts from the digits. You notice that, in one unit, the digit 2 can go in only two cells, and the digit 3 can go in only the same two.
The unit needs a 2 and a 3. Both have to come from those two cells, so one cell is the 2 and the other is the 3. There is no room in either cell for anything else, and their other candidates can go.
A worked example
Row 5 of this position has six empty cells. Look for the digit 2 in their notes. It appears in column 5 and in column 9 and nowhere else. Now look for 3: columns 5 and 9 again, and nowhere else.
So the cells in columns 5 and 9 are a hidden pair on 2 and 3. The cell in column 5 has the notes 2, 3 and 8, and the 8 can be erased. The cell in column 9 has 2, 3 and 9, and the 9 can be erased.
Both cells now show 2 and 3 only. The hidden pair has become a naked pair, which is always what happens.
Two views of the same thing
Look at the other four empty cells in that row. Between them they hold only 4, 6, 8 and 9: four cells and four digits. That is a naked quad, and it leads to exactly the same eliminations.
This is true in general. Every hidden pair has a naked group sitting in the rest of its unit. You only ever need to find the smaller of the two, and with six empty cells the hidden pair is much easier to see than the quad.
With few empty cells in a unit, look for naked pairs. With many, look for hidden pairs.
How to spot them
- Take one unit and go through the digits it is missing. For each, count the cells that can hold it.
- Note every digit with exactly two possible cells. If two digits share the same two cells, that is a hidden pair.
- Boxes are the easiest place to look, because all the cells are close together.
- Solvers who use Snyder notation find these quickly: two digits noted in the same two cells of a box are a hidden pair already.
Common mistakes
- One of the digits has a third possible cell. Both digits must be confined to the same two cells, with no exceptions.
- Erasing the wrong thing. A hidden pair clears the other notes from its own two cells. A naked pair clears its two digits from the other cells.
- Working from incomplete notes. A digit that seems to fit in two cells may fit in a third you haven’t filled in.
When a digit’s two possible cells in a box line up in one row or column, there is another deduction to make. See pointing pairs.