Naked Pairs

Naked pairs are the first intermediate technique most solvers pick up, and they tend to unlock Medium puzzles that refuse to yield to scanning alone. The idea is simple: two cells, one region, two matching candidates. Once you spot that pattern, you can remove those two digits from every other cell in the region.

It's called "naked" because the two candidates are visible — nothing is hidden behind other numbers, which is what distinguishes a naked pair from a hidden pair.

The Rule in Plain Terms

Suppose two cells in the same row each have exactly the candidates {3, 7}. We don't know yet which cell holds the 3 and which holds the 7 — but between them they definitely use both digits. That means 3 and 7 are locked to those two cells within the row. Every other cell in the row must therefore not contain 3 or 7 as a candidate, so we can strike 3 and 7 out of every other cell's candidate list.

The same reasoning works for columns and for 3×3 boxes. The key is that the two cells sit in the same unit and have exactly the same two candidates.

Worked Example

Consider this slice of a row, with the candidate lists shown in braces:

Cell A: {2, 5, 8}
Cell B: {3, 7}
Cell C: {3, 7}
Cell D: {1, 3, 5}
Cell E: {2, 7, 9}

Cells B and C form a naked pair on {3, 7}. The 3 and the 7 are locked inside B and C — we don't know which goes where, but neither can appear anywhere else in this row. So:

Cell D loses its 3 → candidates become {1, 5}.
Cell E loses its 7 → candidates become {2, 9}.

That one deduction might turn cell D into a naked single if {1, 5} collapses further elsewhere, which is how pair-based moves chain into placements.

How to Spot Naked Pairs

Pencil-mark a unit. Write candidates into every empty cell in one row, column, or box.
Scan for cells with exactly two candidates. Cells with three or more won't form a pair on their own.
Match. Two cells with identical two-candidate lists form a naked pair. Two cells with different two-candidate lists (say {3, 7} and {3, 4}) do not.
Eliminate. Strike those two digits from every other cell in the same unit.
Recheck. After eliminations, the grid may offer new naked singles, hidden singles, or further pairs.

Cross-Unit Pairs

Sometimes a naked pair sits in two cells that share more than one unit — for example, two cells in the same box and the same row. When that happens, the eliminations apply to both units simultaneously. A pair inside a box that also happens to sit in the same row lets you remove candidates from the rest of the box and the rest of the row.

This is where naked pairs start to feel powerful: one small observation eliminates candidates in two regions at once.

Common Mistakes

Accepting similar pairs as naked pairs. {3, 7} and {3, 4} share a 3 but do not form a naked pair. Both cells must have exactly the same two candidates.
Forgetting to check the unit. Two cells in different rows but the same column would form a pair in the column, not the row. Always note which unit the pair lives in.
Over-eliminating. When you remove 3 and 7 from other cells in the unit, don't remove them from the pair cells themselves. The pair cells are the only places those digits can live.
Ignoring the chain. A pair deduction that doesn't produce an obvious placement still matters — it simplifies other cells' candidates, which often leads to placements a few moves later.

Where Naked Pairs Come From

Naked pairs rarely appear out of nowhere. They usually show up after a round of scanning and a round of hidden-single placements, once enough digits are in the grid to narrow several cells' candidates down to two. In Medium puzzles they appear almost every game; in Hard puzzles they are one of the default tools you reach for; in Expert puzzles they often form part of a longer chain of deductions.

Bigger Brothers: Naked Triples and Quads

The same idea extends to three or four cells. Three cells in a unit whose combined candidate list is exactly three digits form a naked triple. Four cells whose combined list is four digits form a naked quad. The eliminations work the same way: those digits are locked to those cells, and every other cell in the unit loses them as candidates.

Quads are rare enough that you don't need to hunt for them actively. Triples show up more often than people expect — it's worth a second look at three-candidate cells in a tight unit.

Related Techniques

Hidden Pairs — the same idea from the other direction, focused on where two digits can go rather than which candidates a cell has.
Locked Candidates — when a digit is confined to one line inside a box, the whole box-line overlap becomes a mini pair.
Naked Singles — the simpler cousin. A naked pair eliminations often create a naked single later in the solve.

Practice

Naked pairs rarely show up in Easy puzzles, because scanning takes care of most placements. Try a Medium or Hard puzzle instead:

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Last reviewed on April 23, 2026.