Hidden pairs and triples
A hidden pair is two digits that, within one row, column or box, are candidates in the same two cells and nowhere else. Those two cells must hold those two digits, so every other candidate in them can be removed. A hidden triple works the same way with three digits confined to three cells. After the removal the cells show a naked pair or triple. The Bare Sudoku hint labels the resulting placement "Pair or triple".
When to use it
When a unit has cells with many candidates and singles are gone. Hidden pairs hide inside busy cells, which is why they are worth looking for exactly where naked pairs are not visible. Hidden triples are rare; Bare Sudoku checks for them, but most Hard puzzles are solved without.
How to spot it
Work by digit, not by cell. In a unit, note the cells where each missing digit can go. If two digits each have only two possible cells and they are the same two cells, you have a hidden pair. In the game, tap a digit key to highlight its candidates; if two digits light up the same two cells of a unit and nothing else in it, that is the pattern.
Example
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 6 | 3 | 4589 | 58 | 578 | 1 | 4579 | 2 | 45 |
| r2 | 25 | 24 | 1 | 6 | 9 | 2357 | 3457 | 457 | 8 |
| r3 | 2589 | 7 | 2589 | 2358 | 358 | 4 | 1 | 59 | 1 |
| r4 | 128 | 5 | 2368 | 3489 | 1368 | 389 | 23469 | 49 | 7 |
| r5 | 78 | 9 | 3678 | 3458 | 2 | 3578 | 3456 | 1 | 3456 |
| r6 | 4 | 126 | 2367 | 359 | 13567 | 3579 | 23569 | 8 | 2356 |
| r7 | 2579 | 246 | 245679 | 1 | 58 | 2589 | 2457 | 3 | 245 |
| r8 | 3 | 12 | 2579 | 259 | 4 | 6 | 8 | 57 | 125 |
| r9 | 125 | 8 | 245 | 7 | 35 | 235 | 1245 | 6 | 9 |
Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.
- In row 3, digits 1 and 6 each have only two possible cells, and they are the same two: r3c7, r3c9.
- Those two cells must hold 1 and 6, so their other candidates are impossible.
- Remove 3 from r3c7, 5 from r3c7, 9 from r3c7, 3 from r3c9, 5 from r3c9. Now the two cells show a naked pair, which may unlock more.
Common mistakes
- Removing the two pair digits from the pair cells. It is the other candidates of those cells that go; the pair digits stay.
- Accepting a digit that has a third possible cell in the unit. Both digits must be limited to exactly the two cells.
- Looking only in boxes. Hidden pairs occur just as often in rows and columns.
In Bare Sudoku
Needed from level: Hard
In the game, the hint says: Pair or triple
Frequently asked questions
What is a hidden pair in Sudoku?
Two digits that can go in only the same two cells of a unit. Those cells must take those digits, so their other candidates are removed.
How is a hidden pair different from a naked pair?
A naked pair is visible: two cells that show only the same two candidates. A hidden pair is covered by extra candidates in the two cells. Removing those extras turns a hidden pair into a naked pair.
What is a hidden triple?
Three digits confined to three cells of a unit. Each digit need not appear in all three cells; what matters is that none of the three digits has a candidate outside those cells.
Does the hint distinguish hidden and naked pairs?
No. Bare Sudoku finds both and labels the resulting placement "Pair or triple". The pages here separate them because they are found in different ways.
Previous technique: Naked pairs and triplesAll techniquesNext technique: X-Wing