Sudoku technique
Hidden Pair
Within a zone, two digits can only go in two cells. Those two cells monopolize those digits, even if they still carry other candidates — which get eliminated. The flip side of the naked pair: you hunt for digits, not cells.
A puzzle that requires it
Level Hard — the puzzle is shown twice: right below, and again in the demo that follows.
| 6 | 5 | 2 | 1 | 4 | ||||
| 5 | 6 | 1 | 2 | |||||
| 1 | 3 | |||||||
| 4 | 3 | 9 | ||||||
| 4 | ||||||||
| 2 | 5 | 7 | ||||||
| 1 | 7 | |||||||
| 9 | 8 | 1 | 2 | |||||
| 7 | 9 | 1 | 8 | 6 |
Demonstration
State of the grid right when the technique applies, after 17 earlier deductions.
Demo — watch first, you'll play right after.
- Technique's pattern
- Candidates removed
- Solved earlier
- Given (clue)
| 6 | 5 | 2 | 1 | 4 | ||||
| 5 | 3 | 6 | 1 | 2 | ||||
| 1 | 2 | 3 | ||||||
| 1 | 4 | 3 | 2 | 9 | ||||
| 2 | 4 | 6 | 1 | |||||
| 2 | 6 | 1 | 5 | 7 | 4 | |||
| 6 | 2 | 5 | 1 | 9 | 7 | |||
| 9 | 8 | 1 | 2 | 4 | ||||
| 7 | 5 | 9 | 1 | 2 | 8 | 6 |
Paire cachée
Dans cette zone, les chiffres 6, 7 ne peuvent occuper que ces 2 cases. Ils les monopolisent : tout autre candidat y est éliminé.
Candidates removed:
- the 8 from cell L4C5
- the 8 from cell L4C6
The Hidden Pair is the flip side of the Naked Pair: you no longer hunt for cells, you hunt for digits. When, in a zone, two digits can only go in the same two cells, those cells belong to them, even if they carry other candidates. Those other candidates disappear: the Hidden Pair cleans its own cells.
The principle
A zone is a row, a column or a box. Suppose that, in one zone, 3 and 8 each have only two possible places, and they are the same two cells. The 3 and the 8 must go somewhere in the zone: they will go in those two cells, one in each.
Those two cells are therefore entirely taken by the 3 and the 8, whatever their other candidates. Remove those others from their notes: only the 3 and the 8 remain in each. The other cells of the zone do not change. The pair is “hidden” because the two cells still look open to other digits, when they no longer are.
How to spot it
You need candidate notes. In a zone, take the digits one by one and note the cells where each remains possible. Look for two digits that appear only in the same two cells, and nowhere else in the zone.
When you find them, open those two cells and erase all their other candidates. Only the pair of digits remains. Do not touch the other cells of the zone.
Then check whether the cleanup has consequences: a neighboring cell, in another zone, may gain a Naked Single, or a digit may be left with one place.
A worked example
In a box, 1 is only possible in two cells, and so is 6, the same two. One of those cells has 1, 4, 6 and 9 as candidates, the other 1, 2, 6 and 7. Around them, other cells still accept 4 or 9, but none accepts 1 or 6.
The two digits have only those two places: the cells are theirs. So erase the 4 and the 9 from the first cell, the 2 and the 7 from the second. Only 1 and 6 remain in each: a Naked Pair has appeared, and the freed 4 and 9 are only possible in the other cells of the box.
Common mistakes
Confusion number one is with the Naked Pair. The Naked Pair eliminates its digits outside its cells. The Hidden Pair does the opposite: it eliminates the other candidates of its cells, and does not touch the neighboring cells. If you erase digits in the neighboring cells, you are applying the Naked Pair, which the reasoning does not support here.
Another mistake is to take for a Hidden Pair two digits that appear in two cells, but also in a third. Both digits must be confined to the same two cells. A digit that appears elsewhere in the zone cannot form a Hidden Pair. Finally, incomplete notes lead to false pairs.
When to use it
The Hidden Pair is expected at the Hard level, with the three other pairs of the catalog. It is slower to spot than the Naked Pair, because the pair’s digits are buried among other candidates. It is often the last pair you try.
It leads to the Hidden Triple, which follows the same reasoning with three digits confined to three cells.
- Hard sudoku
- Technique: the Naked Pair
- Technique: the Claiming Pair
- How to solve a sudoku
- Learn the techniques
Frequently asked questions
What is the difference between a Hidden Pair and a Naked Pair?
The Naked Pair eliminates elsewhere: two cells have only the same two candidates, and you erase those digits from the other cells of the zone. The Hidden Pair cleans its own cells: two digits fit in only two cells, and you erase the other candidates from those two cells. The first is spotted by its cells, the second by its digits.
Why is it called a “hidden” pair?
Because the two cells still carry other candidates: the pair is concealed among them. In a Naked Pair, on the contrary, the two cells show only the two digits of the pair.
Does a Hidden Pair place a digit?
No, it removes candidates inside its two cells. Those eliminations can then make a Naked or Hidden Single appear, or a Naked Pair.
Does the Hidden Pair work on rows, columns and boxes?
Yes, on all three types of zone. The reasoning is the same: you look for two digits that can only go in the same two cells of the zone.
Practice
Every technique helps remove candidates ; once a cell has only one left, you place it.
Three puzzles where Hidden Pair is the key move, served right before the step, with a coach.
Puzzle 1
Hard
The technique is used once in this puzzle
Puzzle 2
Hard
The technique is used once in this puzzle
Puzzle 3
Hard
The technique is used twice in this puzzle
Puzzles change every day.