Hidden Pair Sudoku Technique
The mirror image of a naked pair, and much easier to miss: the two cells can be carrying four or five candidates each and still be locked.
Also called: hidden double.
What a hidden pair is
Two digits within a unit have only two cells left between them where either can go. Those two cells must therefore take those two digits, so every other candidate in them is wrong.
The pair is hidden because the cells look busy. A cell showing {2,4,6,8} is not obviously resolved, but if 4 and 8 fit nowhere else in the box, that cell is a 4 or an 8 and the 2 and 6 can go.
A naked pair tells you about the cells and clears the unit. A hidden pair tells you about the unit and clears the cells. Both end up in the same place.
How to spot one
- Count occurrences per digit within a unit rather than reading cells. Any digit appearing in exactly two cells is a candidate for the pattern.
- When two different digits produce the same two cells, you have a hidden pair.
- Hidden pairs are worth hunting in boxes that are nearly full, where most digits are already placed and the survivors have few homes left.
Worked example
| Column 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|
| Row 3 | 1245 | 2345 | 123 | 13 | 23 | 6 | 7 | 8 | 9 |
Solid digits are already placed. Small digits are the candidates still available in that cell.
- Count homes per digit. The 4 appears only in cells one and two. The 5 appears only in cells one and two.
- Two digits, two cells: those cells must take 4 and 5 between them, so 1, 2 and 3 are struck from both.
- Cell one becomes {4, 5} and cell two becomes {4, 5} — now an ordinary naked pair, and the remaining three cells are free to take 1, 2 and 3.
What it eliminates
Every candidate other than the two paired digits, inside the two cells that form the pair.
When you need it
Around the same point as naked pairs, and often on the same grid — a hidden pair is frequently the faster route to the same elimination.
Difficulty here is set by how many clues are left in the grid: Easy starts from 46, Medium 40 and Hard 34, with Extreme and Insane stripped further still. Fewer clues is what makes the techniques below necessary — the fewer digits you start with, the deeper you have to reason.
Worth being straight about: Betty Bee’s technique solver implements naked pairs but never applies hidden pairs, so no puzzle here is graded on your ability to find one. It remains one of the most useful things to know, because it often resolves a unit several moves before the naked pair does.