👯 Naked Pair

Naked Pair is the first technique that moves beyond filling in confirmed cells — it is a pure elimination technique. Rather than directly placing a digit, a Naked Pair removes candidates from cells, paving the way for Naked Singles and Hidden Singles to fire. It is the gateway to the world of advanced Sudoku solving and the technique that first requires systematic pencil-mark management.

What is a Naked Pair?

A Naked Pair exists when exactly two cells in the same unit (row, column, or box) each contain exactly the same two candidates — and only those two candidates. Because one of those two digits must go in cell A and the other in cell B (we do not know which yet), both digits are "claimed" by this pair and cannot appear anywhere else in the unit.

The word naked means the pair is visible directly in the cells' candidate lists, with no extra candidates present.

Step-by-step guide

Activate pencil mode and fill in all candidates for every empty cell. Naked Pairs are most efficiently found with a complete candidate list.
Scan a unit (row, column, or box) for any cell with exactly two candidates.
Look for a matching cell. If another cell in the same unit has the exact same two candidates, you have a Naked Pair.
Eliminate the pair's digits from all other cells in that unit. If cells A and B both show {3, 7}, remove candidate 3 and candidate 7 from every other empty cell in the same unit.
Check for new deductions. Eliminations often create Naked Singles or Hidden Singles in the affected cells. Always re-scan the unit after applying a Naked Pair.

Indigo cells: Naked Pair {3,7} — one holds 3, the other holds 7; green cells show only {5,9} after {3,7} were eliminated

Why does it work?

If two cells in a unit each have exactly two candidates {X, Y} and no others, the only possibilities are:

Cell A = X and Cell B = Y
Cell A = Y and Cell B = X

In every possible scenario, X and Y are both "used up" by these two cells. No other cell in the unit can contain X (because cell A or B will hold it) and no other cell can contain Y. Therefore, eliminating X and Y from all other cells in the unit is completely safe and logically required.

Note that we do not yet know which cell gets X and which gets Y. That will be determined later by other constraints. The Naked Pair only tells us where X and Y cannot go — not where they must go.

Naked Triple and beyond

The Naked Pair concept extends naturally to larger groups:

Naked Triple: Three cells in a unit collectively containing only three distinct candidates {X, Y, Z}. Each cell does not need all three — one might have {X, Y}, another {Y, Z}, another {X, Z}. Any combination where no cell has candidates outside {X, Y, Z} counts. Eliminate X, Y, and Z from all other cells in the unit.
Naked Quad: Four cells with collectively only four candidates. Rare but powerful. Eliminate those four candidates from the remaining cells in the unit.

Naked Triples appear occasionally on Hard puzzles. Naked Quads are very rare and usually signal that a simpler technique has been overlooked.

Naked Pair vs Hidden Pair

There is a complementary technique called a Hidden Pair. A Hidden Pair occurs when two digits each appear in exactly two cells within a unit — but those cells also have other candidates besides the pair digits. The two digits form a pair, and all other candidates in those two cells can be eliminated.

Interestingly, every Naked Pair implies a Hidden Pair in the same unit, and vice versa — they are two descriptions of the same logical constraint, viewed from different angles (cell-first vs digit-first).

When does it apply?

Naked Pairs are typically first needed on Hard difficulty in SudokuStreak.
On Expert and Evil, Naked Pairs (and Triples) are essential and appear frequently.
Always exhaust Naked Singles and Hidden Singles first — Naked Pairs are unnecessary if simpler techniques still have moves available.

Common mistakes

Applying elimination across the wrong unit. The two pair cells must share a row, column, OR box. You only eliminate from that shared unit — each unit independently warrants its own elimination if the cells share it.
Requiring both cells to have the exact same candidates. Both cells must have exactly and only the same two candidates. If one cell has {3, 7, 9}, it does not form a Naked Pair with a cell showing {3, 7}.
Forgetting to cascade. After eliminating candidates with a Naked Pair, immediately scan for new Naked Singles and Hidden Singles. These often appear right away in the affected unit.