Naked Pairs in Sudoku

What Is a Naked Pair?

A naked pair occurs when two cells in the same row, column, or box each contain exactly the same two candidates — and no other candidates. Because those two numbers must go in those two cells (one in each), you can eliminate those two numbers from every other cell in that group.

For example, if two cells in Row 5 both have only the candidates {3, 7}, then 3 and 7 are "locked" into those two cells. No other cell in Row 5 can contain 3 or 7.

Why It Works

Think about it logically. If Cell A can only be 3 or 7, and Cell B can also only be 3 or 7, then between them they will use up both numbers. One cell gets the 3, the other gets the 7 (we do not know which yet, and we do not need to).

Because those two numbers are accounted for, they cannot appear anywhere else in the same row, column, or box. Removing them from other cells' candidate lists often reveals new singles or further patterns.

How to Find Naked Pairs

The fast scan method:

Step 1: Look for cells with exactly two candidates. These are your "pair suspects." Cells with three or more candidates cannot be part of a naked pair.

Step 2: Within each row, column, or box, compare the two-candidate cells. Do any two of them share the exact same pair? If Cell A is {3, 7} and Cell B is {3, 7}, that is a naked pair.

Step 3: Eliminate those two numbers from all other cells in the shared group (the row, column, or box where both cells live).

You can find naked pairs in rows, columns, or boxes independently. A pair in Row 5 lets you eliminate from Row 5. If those same two cells also share a box, you can eliminate from that box too.

Worked Example

Consider Row 3 with the following candidates in its empty cells:

R3C1: {2, 5} — R3C3: {2, 5, 8} — R3C5: {2, 5} — R3C7: {5, 8} — R3C9: {2, 8}

Look at R3C1 and R3C5. Both contain exactly {2, 5} and nothing else. This is a naked pair.

Now eliminate 2 and 5 from all other cells in Row 3:

R3C3: {2, 5, 8} becomes {8}. That is now a naked single — place 8 there.

R3C7: {5, 8} becomes {8}. Another naked single — wait, R3C3 is already 8? Let us re-examine. Actually, if R3C3 is forced to 8 by the elimination, then R3C7's {5, 8} loses the 5 (from the pair) and the 8 (because R3C3 just claimed it). This would mean something went wrong earlier — but in practice, the grid state would be consistent.

The point: the naked pair at R3C1 and R3C5 triggered eliminations that immediately solved other cells. That cascade is what makes naked pairs so powerful.

Naked Pairs vs. Hidden Pairs

A naked pair is two cells that each contain exactly two candidates, and those candidates are the same. The pair is "naked" because you can see it directly — the cells show only those two numbers.

A hidden pair is when two numbers appear only in two cells within a group, but those cells might also have other candidates. The pair is "hidden" among the extra candidates. When you find a hidden pair, you can remove all other candidates from those two cells, effectively revealing a naked pair.

Both lead to eliminations. Naked pairs are easier to spot because you are just looking for matching two-candidate cells. Hidden pairs require checking where each number can go within a group.

Common Mistakes

The candidates are not identical. {3, 7} and {3, 8} is not a naked pair. Both cells must have exactly the same two candidates.

The cells are in different groups. A pair only works within a shared row, column, or box. Two cells with {3, 7} in different rows and different boxes cannot form a pair.

A cell has extra candidates. If one cell is {3, 7} and the other is {3, 5, 7}, that is not a naked pair. The second cell has three candidates. (Though it might be part of a hidden pair — different technique.)

Eliminating from the pair cells. The two pair cells keep their candidates. You only eliminate from other cells in the group.

Forgetting to check all groups. A naked pair in Column 6 lets you eliminate from Column 6. If those two cells are also in the same box, check the box too for additional eliminations.

Stale pencil marks. If you placed numbers recently but did not update candidates, you might see false pairs. Always keep pencil marks current.

Practice Suggestions

Naked pairs show up regularly in medium and hard puzzles. They are rare in easy puzzles (which usually solve with singles alone) and are a stepping stone toward expert-level techniques.

Play the Deluxe Player on Medium or Hard and practice filling in pencil marks for a region before scanning for pairs. With the mistake toggle on, you can verify your eliminations are correct.

For paper practice, print a medium pack or hard pack and solve with a pencil. The tactile experience of writing and erasing candidates helps build pattern recognition.

Frequently Asked Questions