Hidden pairs and hidden triples in Sudoku

1 September 2026 · 6 min read

A naked pair is two cells that can only hold two digits. A hidden pair is two digits that can only go in two cells. Same relationship as naked and hidden singles: one is a fact about cells, the other a fact about digits.

And as with singles, the hidden version is the one that hides in plain sight — because the cells involved look completely ordinary.

Hidden pairs

Pick a unit. For each digit it is still missing, note which cells could hold it. If two digits both come down to the same two cells, those two cells must be those two digits — so every other candidate in them can go.

In row 1 below, the digits 2 and 9 can each only go in two cells: column 1 and column 3.

Look at those two cells and there is nothing obviously interesting about them: one holds {1, 2, 4, 6, 9} and the other {1, 2, 6, 9}. Five candidates and four. Neither is close to being solved.

But row 1 needs a 2 somewhere and a 9 somewhere, and these are the only two cells that can take either. Two digits, two cells — so between them they are 2 and 9, in some order. Everything else in them is impossible:

Nine candidates became four. And note what the position turned into: a naked pair on {2, 9} in row 1, which now eliminates 2 and 9 from the rest of the row as well. A hidden pair very often unlocks a naked one.

Why this is easier to find than it looks

Finding a naked pair means comparing candidate sets between cells. Finding a hidden pair means counting how many times each digit appears among a unit’s marks — and counting is easier than comparing.

The routine, for one unit:

1. For each digit the unit is missing, count the cells whose marks include it.
2. Keep the digits with a count of exactly two.
3. Among those, look for two digits whose pair of cells is identical. Same two cells, not merely overlapping.

Step 3 is where errors creep in. Digit 2 in cells A and B, digit 9 in cells B and C, is not a hidden pair — the cell sets have to match exactly. Two digits sharing one cell tells you nothing.

Hidden triples

Three digits confined to the same three cells. Just as with naked triples, each digit does not need to be possible in all three cells — the requirement is that all three digits appear only within those three cells, and nowhere else in the unit.

So digit 3 in cells {A, B}, digit 5 in {B, C} and digit 7 in {A, C} is a valid hidden triple on cells A, B and C: three digits needing three homes, and only those three available. Every other candidate in A, B and C can be struck out.

Hidden triples are worth knowing but not worth hunting cold. They usually turn up because you were looking for a hidden pair and noticed a third digit confined to the same region.

The complement rule

In a unit with K empty cells, every naked subset of size N is paired with a hidden subset of size K − N. They describe the same situation from opposite ends and produce equivalent eliminations.

Which is useful, because it tells you which search to skip:

• 4 empty cells: naked pair ⟷ hidden pair. Same difficulty, do either.
• 5 empty cells: naked triple ⟷ hidden pair. Do the hidden pair — counting two digits beats checking ten cell-triples.
• 6 empty cells: naked triple ⟷ hidden triple. A coin toss; usually the naked one, since two-candidate cells jump out.
• 7+ empty cells: naked pairs and hidden pairs are the only ones cheap enough to be worth the look.

The general shape: in nearly-full units hunt naked subsets, in nearly-empty units hunt hidden ones.

A caution about incomplete marks

Hidden subsets are less forgiving of sloppy notation than naked ones, and it is worth being explicit about why. A naked pair reads two cells; if you missed a candidate in a third cell elsewhere, the pair is still valid. A hidden pair is a claim about the entire unit — “2 appears nowhere else in this row”. One unmarked candidate anywhere in the row and that claim is false, along with every elimination you based on it.

So hidden subsets need complete marks for the unit you are working in. Keeping notation honest is what makes them safe to use.

Once the eliminations are in, go back and sweep for singles — and if that finds nothing, the next rung up is normally the box/line intersections.

Every diagram on this page is a real position from a generated puzzle, and every elimination shown is checked against that puzzle’s unique solution as part of the test suite. Want a move explained on your own board? Play a puzzle.