Hidden pairs
What it is
A hidden pair is two digits that, within one row, column or box, can only go in the same two cells. Those two cells may have other candidates noted too, which is what hides the pair. But since the two digits need homes and only these two cells are available, the cells must hold those two digits. Everything else in them can be removed.
A naked pair and a hidden pair are two views of the same idea:
- A naked pair starts from cells: two cells that can only hold two digits.
- A hidden pair starts from digits: two digits that can only go in two cells.
How to spot it
Hidden pairs are harder to see than naked ones because the cells look busy. The trick is to count digits rather than cells. Pick a row, column or box and, for each missing digit, count how many cells it could go in. If two different digits each have exactly two possible cells, and they are the same two cells, you have found a hidden pair.
Boxes with lots of empty cells are good places to look, because notes there tend to be cluttered and pairs are easy to miss.
A worked example
Look at box 9, which covers rows 7 to 9 and columns 7 to 9. Five of its cells are empty, and it is missing 1, 4, 5, 6 and 8.
Checking where each digit can go:
- 1 can go in row 7, column 9 or row 9, column 7. Nowhere else in the box.
- 6 can also only go in row 7, column 9 or row 9, column 7.
- 4, 5 and 8 each have several possible cells.
So the 1 and the 6 are a hidden pair in those two cells. One will be the 1, the other the 6.
Say your notes for row 7, column 9 were 1, 4, 6 and 8, and for row 9, column 7 they were 1, 5 and 6. You can now remove the 4 and 8 from the first cell, and the 5 from the second. Both cells are left with just 1 and 6.
That might not place a digit straight away. But clearing the 4, 5 and 8 from those two cells may leave one of those digits with only one place left in box 9, giving you a hidden single. And the newly clean pair might also help with eliminations in row 7 or column 7.
Why it works
Box 9 needs a 1 and a 6. Each has only two places to go, and they are the same two places. If either cell took a 4, 5 or 8, there would be only one cell left for both the 1 and the 6, which is impossible. So those other candidates cannot be right.
A common mistake
The most common mistake is removing the wrong digits. With a hidden pair, you clear other candidates from the two pair cells. You do not remove 1 or 6 from anywhere, because inside box 9 they already only appear in those two cells.
(Once the pair cells are cleaned down to just 1 and 6, it is now a naked pair. If the two cells also happened to share a row or column, you could remove 1 and 6 from the rest of that line. Here, row 7, column 9 and row 9, column 7 do not share a line, so that does not apply.)
Another trap is a digit with only one cell in the unit. That is a hidden single, not part of a pair. Place it first.
When you will need it
Hidden pairs are part of the Medium toolkit on sudoku.ie, with pointing, claiming and naked pairs. They show up on Tuesday, Wednesday and Sunday puzzles, and they are the stepping stone to hidden triples.