Naked Pairs
What's a Naked Pair?
A naked pair happens when any two cells in the same row, column, or 3×3 block (a "unit") have exactly the same two candidates—and no others. Despite not knowing which number goes where, you do know those two numbers must occupy those two cells—so you can eliminate them everywhere else in that unit.
This is different from a Naked Single, where the cell itself only has one possible candidate left. Learn more about Naked Singles.
Why It Matters
It's a super-practical technique for cleaning up "busy" puzzles. Once you spot and eliminate those candidates from other cells, you often open the way to naked or hidden singles next. It's like clearing the path for more obvious moves.
How to Spot and Use a Naked Pair (Step-by-Step)
- Scan your puzzle systematically — pick a row, column, or box after penciling in candidates.
- Look for exactly two matching candidates in two cells (e.g., both are {2, 5}).
- Confirm no other cells in that unit have both 2 and 5. If so, you've got your naked pair.
- Eliminate both of those numbers from all other cells in that unit.
- Check for new singles or progress—you may have just unlocked easy placements!
Illustrative Example
Imagine Row 7 has these candidate sets:
{1, 6} {3, 4, 5} {2, 5} {1, 2, 5} {4, 7} {1, 6} {8, 9} {3, 5} {2, 9}
Suppose the two cells in that row both show exactly {4, 7} — that's a naked pair. You can now remove 4 and 7 from all other cells in that row, potentially simplifying others to singles or revealing hidden pairs or chains. That cleanup is satisfying, trust me.
Common Slip-ups to Avoid
- Mixing it up with hidden pairs—those are when two numbers only appear as candidates in two cells, but those cells may have extras. Naked pairs, by contrast, have only the two numbers.
- Ignoring pencil marks—it's much harder to spot naked pairs without a full candidate grid.
- Forgetting that elimination might reveal further opportunities—you'll often find naked or hidden singles right after removing clutter.
Bonus: Locked Pairs (A Neat Variation)
Sometimes those two cells are aligned in both a row and a block (or column and block). In that case, they're called a locked pair, and you can remove the pair's numbers from both houses—not just one unit. It's like doubling down on your elimination power.
Why Naked Pairs Are a Solver's Go-to Move
They're high-leverage: one little discovery can unclog a puzzle. You don't need complex chains or fish patterns—just clear logic that makes the puzzle breathe again. Fast games, deep puzzles—they both benefit hugely.
Practice Routine
After every placement (especially singles), pause and do a quick naked-pairs sweep across all units. With regular pencil work, you'll start spotting them at a glance.
Wrap-Up
Naked pairs might not feel glamorous, but mastering them is like unlocking a secret toolkit that makes tougher puzzles click into place more naturally. Once you can spot them fluidly, your solving flow will get that satisfying "snap" feeling more often.
Frequently Asked Questions
What's a Naked Pair in Sudoku?
A naked pair happens when any two cells in the same row, column, or 3×3 block (a "unit") have exactly the same two candidates—and no others. Despite not knowing which number goes where, you do know those two numbers must occupy those two cells—so you can eliminate them everywhere else in that unit.
How do I spot and use a Naked Pair?
To spot and use a Naked Pair: 1) Scan your puzzle systematically - pick a row, column, or box after penciling in candidates, 2) Look for exactly two matching candidates in two cells (e.g., both are {2, 5}), 3) Confirm no other cells in that unit have both numbers, 4) Eliminate both numbers from all other cells in that unit, 5) Check for new singles or progress.
What's the difference between Naked Pairs and Hidden Pairs?
Naked pairs have exactly the same two candidates in two cells with no extras. Hidden pairs are when two numbers only appear as candidates in two cells, but those cells may have additional candidates. Naked pairs are more obvious to spot and provide cleaner eliminations.
Why are Naked Pairs important?
Naked Pairs are important because they're high-leverage - one discovery can unclog a puzzle. They help clean up "busy" puzzles by eliminating misleading candidates and often open the way to naked or hidden singles. They're super-practical for intermediate to advanced players.
How often should I look for Naked Pairs?
After every placement (especially singles), pause and do a quick naked-pairs sweep across all units. With regular pencil work, you'll start spotting them at a glance. They're a go-to move that helps maintain solving momentum throughout the puzzle.
Practice Naked Pairs
Next strategy: Check out X-Wing — it's like magic once you see it.