Naked Pairs in Sudoku

What is a Naked Pair?

A Naked Pair is two cells in the same row, column, or 3x3 box that both contain exactly the same two candidates — and nothing else. The word "naked" means nothing is hidden: those two candidates are written plainly in the pencil marks.

When you spot a Naked Pair, you don't learn which digit goes in which cell yet — but you learn something just as valuable: those two digits are locked into those two cells, and nowhere else in that unit. Every other cell in the same row, column, or box can have those two candidates erased.

Why it works (the logic)

Imagine two cells in a row, both marked with only the candidates {3, 7}. You don't know which cell holds 3 and which holds 7 — but you know one of them is 3, and the other is 7. There's no third option.

Now look at any other cell in that row. Could it be 3? No — one of the two paired cells must hold the 3. Could it be 7? No — the other paired cell holds the 7. So every other cell in that row can safely have 3 and 7 removed from its pencil marks.

This is what makes the Naked Pair powerful: you erase candidates from cells you haven't solved yet, often triggering a cascade of Naked Singles and Hidden Singles in their place.

Example 1: A Naked Pair in a 3x3 box

In the top-left box below, suppose you have completed enough scanning to know that two specific cells can only contain 2 or 3 — nothing else.

Because {2, 3} are locked into those two cells, the other cells in the same box (rows 2 and 3 of the box) can have 2 and 3 eliminated from their candidates. Often this immediately reveals a Hidden Single or Naked Single elsewhere in the box.

Example 2: Naked Pair in a row, cascading eliminations

Naked Pairs are most powerful when they sit in a row or column that crosses multiple unsolved boxes — the elimination ripples across all of them.

If cells (R4, C7) and (R4, C8) both have candidates {2, 4}, the seven other empty cells in row 4 can all drop those digits. With Row 4 partially solved or already containing 5, 6, 7, 8, 9, 1, this elimination alone might leave cell (R4, C1) with only one candidate left — a Naked Single, ready to fill in.

How to spot Naked Pairs

One catch: pencil marks are required. Naked Pairs are invisible without candidate notes. Once you have pencil marks filled in:

1. Scan each row, column, and box. Look for any cell with exactly two candidates.
2. When you find one, scan the rest of that unit for another cell with the same exact two candidates.
3. If you find a match — you have a Naked Pair. Erase those two candidates from every other cell in that unit.

The biggest hurdle for beginners is "exactly the same two". A cell with {3, 7} and a cell with {3, 7, 9} are not a Naked Pair — the second cell has an extra option, breaking the lock.

Naked Pair vs. Hidden Pair (don't confuse them)

Both techniques involve two digits and two cells, but they look opposite:

• Naked Pair: two cells where the only candidates are exactly {X, Y}. The lock is visible.
• Hidden Pair: two digits X and Y that can only appear in the same two cells in a unit — but those cells also have other candidates that look distracting. The lock is buried.

If your pencil marks are accurate, a Naked Pair is easy to spot at a glance. Hidden Pairs require scanning by digit instead of by cell — same mindset shift as Hidden Singles.

Common beginner mistakes

• Skipping pencil marks. Without candidate notes, Naked Pairs are invisible. Fill in every cell's candidates before hunting.
• Confusing "subset of" with "equal to". A cell with {3, 7} and a cell with {3, 7, 4} are not a pair — the second cell has more options.
• Forgetting to erase. Finding a Naked Pair only matters if you actually use it to erase candidates from the other cells in the unit. The elimination is the whole point.
• Only checking boxes. Naked Pairs appear in rows and columns too. Scan all three unit types.

The thinking process, summed up

Naked Pairs teach a critical Sudoku habit: you don't have to solve a cell to make progress. Eliminating candidates is just as valuable as placing digits. Most Hard puzzles aren't solved by "finding the next answer" — they're solved by chaining careful eliminations until a hidden answer reveals itself.

Try it on a real puzzle

Head back to the play page and start a Medium or Hard puzzle. Turn on Notes mode and fill in candidates wherever you have two or three options. Then press the 💡 Hint button when stuck — if a Naked Pair is available, SudokuHint will highlight both cells and explain which candidates to eliminate where, using the same logic shown in this article.