Sudoku Naked Pair Explained (Step-by-Step)

Naked singles and hidden singles get you through Easy and Medium. The naked pair is the technique that opens up Hard difficulty — and once you understand it, you'll see it everywhere. Here's exactly how it works.

The One-Line Definition

A naked pair is when exactly two cells in the same row, column, or 3×3 box each contain only the same two candidates. Because those two digits are "locked" to those two cells, they can be eliminated from every other cell in that row, column, or box.

You can't solve either cell individually — you don't know which digit goes in which cell yet. But you know the two digits must occupy those two cells. That certainty lets you clean up candidates everywhere else in the unit.

A Concrete Example

Let's work through a row example. Consider row 7 of a puzzle. After filling in what's known and doing pencil marks, the candidates look like this:

In row 7: columns 4 and 6 each contain only the candidates {2, 4}. That's a naked pair. Neither cell has any other possibility.

The logical consequence: digits 2 and 4 are fully accounted for within this pair. They cannot appear in any other cell in row 7. So we can eliminate 2 and 4 from columns 2, 5, and 8 — cutting those cells' candidate lists down significantly.

The Logic in Plain English

Here's why the elimination is valid. One of these two scenarios must be true:

• Scenario A: Cell (row 7, col 4) = 2, Cell (row 7, col 6) = 4
• Scenario B: Cell (row 7, col 4) = 4, Cell (row 7, col 6) = 2

In either scenario, digits 2 and 4 are placed in columns 4 and 6. They are unavailable to any other cell in row 7. So any other cell in row 7 that currently has 2 or 4 as a candidate? Those candidates are invalid — cross them out.

Step-by-Step: How to Find a Naked Pair

1. 1
   Fill in pencil marks (candidates) for the whole puzzle. Naked pairs only become visible when you can see which candidates each cell holds. Without pencil marks you're flying blind.
2. 2
   Scan each row, column, and box for cells with exactly two candidates. Cells with only two possible digits are your naked pair candidates.
3. 3
   Check if any two such cells share the same two candidates within the same unit. If cell A has {3, 7} and cell B in the same row also has {3, 7}, you have a naked pair.
4. 4
   Eliminate those two digits from all other cells in that unit. Scan every other cell in the row (or column or box) and cross out those two candidates wherever they appear.
5. 5
   Check if any eliminations created naked or hidden singles. Reducing candidates often cascades — newly isolated candidates become singles. Rescan the board.

Naked Pairs in Columns and Boxes

The technique works identically in all three unit types:

In a Column

Two cells in the same column both containing only {5, 8} means 5 and 8 are reserved for those two cells. Every other cell in that column cannot contain 5 or 8 — eliminate them.

In a 3×3 Box

Two cells in the same box containing only {1, 6} means 1 and 6 are locked into those two box positions. Eliminate 1 and 6 from every other empty cell in the box. This is often the most impactful version because box eliminations can interact with row and column constraints simultaneously.

Why "Naked"?

The word "naked" in sudoku strategy means the candidates are explicitly visible in the cell — they're out in the open. A naked pair's candidates are right there in the cell, plain as day: {2, 4}. Compare this to a hidden pair, where two cells in a unit are the only two cells that can hold two specific digits — but those cells might have other candidates cluttering them. The constraint is hidden beneath the noise.

Naked pairs are easier to spot than hidden pairs for exactly this reason. When you see two cells with only two identical candidates in the same unit, you've found your naked pair without having to reason about what other cells can't hold.

Naked Pairs vs. Hidden Pairs

Both techniques ultimately let you eliminate candidates from a unit — but they work in opposite directions:

• Naked pair: Two cells with only {X, Y}. Eliminate X and Y from all other cells in the unit.
• Hidden pair: Digits X and Y only appear in two cells within a unit (even if those cells have other candidates). Eliminate all other candidates from those two cells, reducing them to just {X, Y}.

Both result in the same solved state. Naked pairs are the forward approach; hidden pairs are the reverse.

Extending the Pattern: Naked Triples and Quads

Once you understand naked pairs, the extension is intuitive:

• Naked triple: Three cells in a unit that together contain only three specific candidates (e.g., {1,5}, {1,7}, {5,7} — collectively {1, 5, 7}). Eliminate those three digits from all other cells in the unit.
• Naked quad: Four cells containing only four candidates between them. Same elimination logic, harder to spot visually.

In practice, naked pairs are by far the most common — and the most impactful. If you can spot naked pairs reliably, you've unlocked the majority of Hard puzzles.

What Makes Naked Pairs Hard to Spot

The difficulty isn't the logic — it's the visual search. In a partially filled Hard puzzle, you might have 30+ cells with pencil marks. Finding two cells with matching two-candidate sets in the same unit requires systematic scanning, not casual glancing.

Strategies to spot naked pairs faster:

• Prioritize cells with exactly two candidates. Two-candidate cells are your naked pair candidates. Scan for them first.
• Compare cells within the same unit. Once you find a two-candidate cell, immediately look at other cells in its row, column, and box for a matching pair.
• Look in units with more filled cells. A row with 7 filled cells and 2 empty ones is much more likely to yield naked pairs than a row with 4 filled cells.
• Let the app do the work. Sudoku Coach identifies naked pairs automatically and explains the elimination — so you learn while solving, not just after the fact.

Putting It All Together

Here's where naked pairs fit in the progression of sudoku techniques:

1. Naked singles — One cell, one candidate. Easiest. Essential.
2. Hidden singles — One digit, one cell in a unit. One level up.
3. Naked pairs — Two cells, two candidates. Eliminates from the rest of the unit. This is where you are now.
4. Pointing pairs / box-line reduction — When a digit in a box is confined to one row or column.
5. X-Wing — Four cells in a rectangle pattern, across two rows and two columns.

Each technique builds directly on the last. If you understand why a naked pair works — two cells own two digits, therefore no other cell in the unit can have them — X-Wing and beyond will make sense when you get there. They're all just variations of the same question: "Where can this digit go? Where must it go? What can I eliminate?"