SuuudokuuuHidden Pair Sudoku Technique
Updated
A hidden pair is two digits that can only go in the same two cells of a row, column or box, which reserves both cells for those digits and removes every other candidate from them.
When a hidden pair applies
Hidden subsets are read digit-first. Take a unit, pick two digits it still needs, and list the cells where each digit is possible. If both lists are the same two cells, the two digits will fill those cells between them. Nothing else fits, so every unrelated candidate inside the pair comes off.
The eliminations therefore land inside the pattern rather than around it, which is the exact opposite of a naked pair. That is the single most useful thing to remember about hidden subsets: naked subsets clean the neighbours, hidden subsets clean themselves.
Hidden pairs are common on hard puzzles and easy to walk past, because the two cells often carry four or five candidates each and look unremarkable. They usually surface right after a run of intersection eliminations has thinned a unit out.
Worked example
Column 4 has seven empty cells. Follow the digit 1: it is possible only in r1c4 and r3c4. Follow the digit 5: also only r1c4 and r3c4. Two digits, the same two homes, so those two cells will take 1 and 5 in some order.
r1c4 was carrying 1, 2, 5, 6 and 8, and loses the 2, the 6 and the 8. r3c4 was carrying 1, 2, 5 and 8, and loses the 2 and the 8. Both cells now read 1 and 5, and the pattern has converted itself into a naked pair that will clear those digits from the rest of the column on the next pass.
How to spot a hidden pair
- List the digits a unit still needsWork unit by unit. Write down which digits are missing before you look at any individual cell.
- Count homes for each missing digitFor every missing digit, note the cells in the unit that can still hold it. Digits with exactly two homes are your candidates.
- Match two digits to the same two cellsIf two of those digits share the identical pair of homes, you have found a hidden pair.
- Strip the two cells down to the pairDelete every other candidate from both cells. The result is a naked pair, so immediately clear those two digits from the rest of the unit as well.
Common mistakes
- Eliminating from the wrong cells. A hidden pair removes candidates inside the pair, not from its neighbours.
- Requiring the two digits to be the only candidates in the cells. If they were, the pattern would already be a naked pair; the hidden version is precisely the case where they are buried among others.
- Accepting a digit that has three homes. Both digits must be restricted to exactly the same two cells for the deduction to hold.
- Stopping after the strip. The pair becomes a naked pair, and that second step often does the real damage.
Hidden pair FAQ
How do I tell a hidden pair from a naked pair?
Look at what you counted. If you counted candidates inside two cells, it is naked. If you counted cells available to two digits, it is hidden. The eliminations then land in opposite places.
Does a hidden pair place any digits?
No. It reduces two cells to two candidates each. The placement comes later, usually from the naked pair it creates or from a hidden single elsewhere in the unit.
Why is a hidden pair harder to see than a naked pair?
Because nothing about the two cells looks special. They can be the widest cells in the unit. The pattern is only visible once you count homes per digit rather than candidates per cell.
Can a hidden pair span a row and a box?
The deduction is made within one unit, but if both cells also share a second unit, the naked pair it produces can be applied to that unit too, which doubles the payoff.