Naked Pairs in Sudoku: How to Spot & Use Them

A naked pair occurs when two cells in the same row, column, or box have exactly the same two candidates and no other candidates. Because those two numbers must go in those two cells (in some order), you can eliminate both numbers from all other cells in that shared group. Naked pairs are the first intermediate technique most solvers learn, and mastering them is the key to breaking through from easy to medium difficulty puzzles. They are surprisingly common, and once you learn to spot them, you will find them in nearly every medium-difficulty puzzle.

What Exactly Is a Naked Pair?

Let us define this precisely. A naked pair requires three conditions:

1. Two cells are in the same row, column, or 3x3 box.
2. Both cells have exactly two candidates.
3. Both cells have the same two candidates.

When these conditions are met, you know with certainty that those two numbers will be distributed between those two cells. You do not know which cell gets which number yet, but you do know that no other cell in that group can contain either number.

The word "naked" refers to the fact that these candidates are openly visible — the cells contain only those two numbers and nothing else. This distinguishes them from "hidden pairs," where the pair of numbers exists alongside other candidates in the cells.

Why Naked Pairs Work: The Logic

Consider a row where two cells both have candidates {3, 7}. Since only 3 and 7 can go in these cells, one cell will get 3 and the other will get 7. This accounts for both the 3 and the 7 for this row. Therefore, no other cell in that row can contain 3 or 7 — those numbers are "claimed" by the naked pair.

This elimination is what makes naked pairs powerful. Removing candidates from other cells may create new naked singles, trigger other patterns like pointing pairs, or even reveal additional naked pairs. The cascade potential is significant.

How to Spot Naked Pairs

Spotting naked pairs requires pencil marks. Without pencil marks, naked pairs are essentially invisible. Here is a systematic approach to finding them:

Step 1: Fill in Pencil Marks

Before looking for naked pairs, you need pencil marks in your cells. You do not need full notation everywhere — focus on areas where you have been unable to make progress with singles techniques. Any cell with exactly two candidates is a potential half of a naked pair.

Step 2: Look for Cells with Two Candidates

Scan your pencil marks for cells containing exactly two numbers. These are your "pair candidates." Cells with three or more candidates cannot form naked pairs (though they can be part of naked triples, which we will discuss later).

Step 3: Check for a Match in the Same Group

For each two-candidate cell, check the other cells in the same row, column, and box. If another cell in any of those groups has the exact same two candidates, you have found a naked pair.

Step 4: Eliminate from Other Cells

Once you identify a naked pair, remove both candidates from every other cell in the shared group. If the pair shares a row, eliminate from that row. If they share a column, eliminate from that column. If they share a box, eliminate from that box. If they share multiple groups (for example, both the same row and the same box), eliminate from all shared groups.

Detailed Example

Let us walk through a concrete example. Imagine Row 5 has the following pencil marks in its empty cells:

• Cell R5C2: candidates {2, 8}
• Cell R5C4: candidates {2, 5, 8}
• Cell R5C6: candidates {2, 8}
• Cell R5C8: candidates {5, 9}

Look at R5C2 and R5C6 — they both have exactly the candidates {2, 8}. This is a naked pair. The 2 and 8 in Row 5 must go in cells C2 and C6 (in some order). Therefore, we can eliminate 2 and 8 from all other cells in Row 5.

Applying this elimination to R5C4: we remove 2 and 8, leaving only {5}. That is now a naked single — the cell must be 5. The naked pair did not directly solve any cell in the pair itself, but it solved another cell by eliminating candidates.

This is the typical outcome of finding a naked pair. It rarely tells you which number goes in the pair cells, but it reduces candidates elsewhere, often creating singles or enabling other techniques.

Naked Pairs in Boxes

Naked pairs in boxes work identically to naked pairs in rows and columns, but they are sometimes easier to spot visually because boxes are compact 3x3 regions. Two cells within a box that share the same two candidates form a naked pair, and you can eliminate those candidates from the remaining cells in the box.

Box-based naked pairs are especially powerful when the pair cells are also in the same row or column. In that case, you get eliminations in both the box and the shared line, potentially clearing candidates in two directions at once.

Naked Pairs vs. Hidden Pairs

A related technique is the hidden pair. While a naked pair is two cells that each contain only two specific candidates, a hidden pair is two candidates that appear in only two cells within a group — even if those cells have additional candidates.

For example, if in a box, the numbers 4 and 6 only appear as candidates in two specific cells (say R1C1 has {1, 4, 6, 9} and R2C3 has {3, 4, 6}), then 4 and 6 must go in those two cells. You can eliminate all other candidates from those cells, reducing R1C1 to {4, 6} and R2C3 to {4, 6}.

Notice that after resolving a hidden pair, the two cells become a naked pair. Hidden pairs and naked pairs are two perspectives on the same underlying logic — hidden pairs are just harder to spot because the target candidates are "hidden" among other numbers.

Extending to Naked Triples and Quads

The naked pair concept generalizes to larger groups. A naked triple is three cells in the same group that collectively contain exactly three candidates (though each individual cell may contain two or three of those candidates). Similarly, a naked quad involves four cells and four candidates.

For example, three cells with candidates {2, 5}, {2, 7}, and {5, 7} form a naked triple for the numbers 2, 5, and 7. Notice that no single cell contains all three numbers — but the three cells collectively use only those three numbers, so 2, 5, and 7 can be eliminated from all other cells in the group.

Naked triples are less common than naked pairs and harder to spot, but the logic is identical. If you are comfortable with naked pairs, triples are a natural extension. They appear mainly in hard-level puzzles.

Common Mistakes with Naked Pairs

Confusing Naked Pairs with Simple Observation

Sometimes a solver sees two cells with the same candidates and gets excited, but the cells are not in the same group (not in the same row, column, or box). Naked pairs only produce eliminations when the cells share at least one group. Always verify that the pair shares a row, column, or box before eliminating candidates.

Forgetting to Eliminate from All Shared Groups

If two cells share both a box and a row, you can eliminate the pair's candidates from all other cells in both the box and the row. Some solvers only eliminate from one group and miss eliminations in the other. Always check how many groups the pair shares.

Incomplete Pencil Marks

If your pencil marks are incomplete, you might think a cell has only two candidates when it actually has three. This can lead to a false naked pair and incorrect eliminations, which will eventually cause a contradiction. Make sure your pencil marks are accurate before relying on them for pair detection.

Practice Strategy for Finding Naked Pairs

The best way to get comfortable with naked pairs is deliberate practice:

1. Solve medium puzzles with full pencil marks. After applying singles techniques as far as they go, carefully scan for cells with exactly two candidates.
2. Check every two-candidate cell against its groups. For each such cell, quickly scan the same row, column, and box for a matching pair.
3. Practice in a structured environment. Sudoku Royale's Practice mode gives you unlimited puzzles with pencil mark support, so you can practice finding pairs without time pressure.
4. After finding a pair, always check for cascading deductions. The eliminations from a naked pair frequently create new singles or other patterns. Train yourself to immediately exploit these cascades.

For a broader look at intermediate techniques that pair well with naked pairs, see our guides on pointing pairs and hidden singles. When you are ready for the next level, our X-Wing guide introduces the first truly advanced elimination technique.