Naked Pairs in Sudoku

A naked pair is when exactly two cells in the same row, column, or 3×3 box each contain exactly the same two candidate numbers — and nothing else. Because those two numbers must occupy those two cells (in some order), you can safely eliminate both candidates from every other cell in that unit. It is one of the most reliable techniques for breaking through intermediate puzzles without guessing.

Jump to: When to use · How to spot · Worked examples · Naked vs. hidden pairs · What to learn next

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When to Use Naked Pairs

Naked pairs are the natural next step after you have exhausted naked singles and hidden singles. Reach for this technique when:

• No cell has been reduced to a single candidate.
• No number is forced into exactly one cell within any row, column, or box.
• The puzzle still has many cells with two or three candidates.

Prerequisites

• Complete candidate grid — every empty cell must have all remaining possibilities pencilled in. Without this, you will miss pairs or create false eliminations.
• Naked singles mastered — cells with one candidate should already be filled. Naked singles are always resolved first.
• Hidden singles mastered — a number forced into one cell per unit should already be placed. Hidden singles come before pairs in the solving order.

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How to Spot and Use a Naked Pair (Step-by-Step)

1. Pencil in all candidates — make sure every empty cell shows its full list of possible numbers.
2. Scan for bi-value cells — look for cells that contain exactly two candidates. These are your pair candidates.
3. Check the same unit — for each bi-value cell, look at every other cell in the same row, column, and box. Is there another cell with the exact same two candidates?
4. Confirm the pair — if two cells in the same unit both show {X, Y} and only {X, Y}, you have a naked pair.
5. Eliminate from the rest of the unit — remove both X and Y as candidates from every other cell in that row, column, or box.
6. Check for new progress — eliminations often reduce other cells to singles or reveal new pairs. Restart your singles sweep.

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Worked Examples

Example 1 — Naked Pair in a Row

Consider Row 4 after pencilling candidates. The full candidate state of all nine cells is:

R4C1: {1,3,7}    R4C2: {2,5}    R4C3: {1,3,6}    R4C4: {3,6,8}    R4C5: {2,5}    R4C6: {1,6,8}    R4C7: {4,7}    R4C8: {1,3,8}    R4C9: {3,9}

Observation: R4C2 and R4C5 both contain exactly {2, 5} — nothing else.

Conclusion: One of them holds 2, the other holds 5. Either way, no other cell in Row 4 can contain 2 or 5.

Eliminations: Remove 2 and 5 from R4C1, R4C3, R4C4, R4C6, R4C7, R4C8, R4C9.

Result: After removing candidates, any cell that previously held 2 or 5 alongside other numbers is narrowed. Depending on the rest of the grid, these reductions may cascade into hidden singles or new naked pairs elsewhere in the row or in the boxes those cells belong to.

Example 2 — Naked Pair in a 3×3 Box

Focus on the top-right 3×3 box (rows 1–3, columns 7–9). Candidate state:

R1C7: {1,4,6}    R1C8: {3,8}    R1C9: {1,6,9}
R2C7: {4,6,9}    R2C8: {4,6}      R2C9: {3,8}
R3C7: {1,4}      R3C8: {4,6,9}    R3C9: {1,6}

Observation: R1C8 and R2C9 both contain exactly {3, 8} — nothing else.

Conclusion: 3 and 8 are confined to those two cells within this box.

Eliminations: Remove 3 and 8 from all other cells in the box: R1C7, R1C9, R2C7, R2C8, R3C7, R3C8, R3C9.

Result: R2C8 already has {4, 6} so no change there. R1C7 becomes {1, 4, 6} → remove any 3 or 8 (none present, no change). R3C7 stays {1, 4}. R1C9 becomes {1, 6, 9} → no 3 or 8 to remove. However, any cell in the box that did carry 3 or 8 as an extra candidate now loses it, potentially revealing a single or another pair. Always check the full box after each elimination pass.

Note on scope: Eliminations from a box-based naked pair apply only within that box — unless the two cells happen to share a row or column, in which case you also get eliminations along that row or column (a locked pair).

Example 3 — Naked Pair in a Column, Leading to a Cascade

Column 6 candidate state after an earlier singles pass:

R1C6: {2,7,9}    R2C6: {4,9}    R3C6: {2,7}    R4C6: {2,7,9}
R5C6: {4,9}    R6C6: 5 (placed)    R7C6: {2,7}    R8C6: {2,3,7}    R9C6: {3,7}

Observation: R2C6 and R5C6 both contain exactly {4, 9}.

Eliminations: Remove 4 and 9 from every other cell in Column 6.

Step-by-step cascade:

1. R1C6: {2, 7, 9} → remove 9 → {2, 7}.
2. R4C6: {2, 7, 9} → remove 9 → {2, 7}.
3. R3C6 already {2, 7} — no change. R7C6 already {2, 7} — no change.
4. R8C6: {2, 3, 7} — 4 and 9 not present, no change.
5. R9C6: {3, 7} — already narrow, no change.
6. Now Column 6 has four cells each containing only values from {2, 7}: R1C6, R3C6, R4C6, R7C6. That is a naked quad worth investigating. Meanwhile, the column is significantly cleaner for further analysis.

Result: The {4, 9} naked pair tightened Column 6 in two cells and revealed a follow-on pattern. This cascade — one naked pair opening the door to the next technique — is exactly why the technique is so valuable.

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Locked Pairs (A Neat Variation)

When a naked pair sits in two cells that share both a 3×3 box and the same row (or column), it becomes a locked pair. You can then eliminate the pair's candidates from:

• All other cells in the box, and
• All other cells in that row (or column) outside the box.

Locked pairs are also known as pointing pairs when the focus is on extending eliminations from the box out into the rest of the row or column. The reverse scenario — a candidate inside a box restricted to one row or column — is covered by box-line reduction. Either way, cross-unit eliminations effectively double your reach.

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Naked Pairs vs. Hidden Pairs

These two techniques are mirror images and easy to confuse.

Feature	Naked Pair	Hidden Pair
What you see	Two cells each showing only {X, Y}	Two cells where X and Y appear only in those two cells within the unit — but the cells may have extra candidates
What you eliminate	X and Y from all other cells in the unit	All candidates except X and Y from those two cells
How to spot it	Look at the cells — both show {X, Y} only	Look at where X and Y can go in the unit — they are restricted to just two cells
Difficulty	Easy to moderate	Moderate

Common Mistakes to Avoid

• Confusing naked pairs with hidden pairs — always check whether the two target cells contain only the two candidates (naked) or whether the candidates are simply restricted to those two cells (hidden).
• Skipping the candidate grid — naked pairs are invisible without complete pencil marks.
• Forgetting to check all three unit types — a pair in a box does not automatically eliminate from the row or column unless it is also a locked or pointing pair.
• Stopping after one elimination — the chain of reductions often continues. Always re-sweep after applying a naked pair.

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What to Study Next

Naked Pairs are your entry into pair-based elimination. Here are the clearest paths forward:

• Natural next step: Hidden Pairs — the direct next step; the same two-cell logic, but the pair is hidden behind extra candidates. Learning both together sharpens your candidate scanning significantly.
• Also worth learning now: Pointing Pairs — when a naked pair inside a box aligns in one row or column, you can extend eliminations outside the box.
• Extend the pattern: Naked Triples — three cells sharing exactly three candidates; the direct expansion of naked pairs.
• Advanced path from here: X-Wing — a more advanced elimination pattern using candidate positions across two rows and two columns; a rewarding next step once pairs feel automatic.
• Go back if needed: Hidden Singles — revisit this if candidate tracking still feels uncertain before moving on.
• Naked Pairs and Triples in Sudoku — a blog post with additional examples and common pattern variations

The natural next step is Hidden Pairs — once naked pairs feel automatic, hidden pairs complete your two-cell elimination toolkit.

Practice Naked Pairs

• Daily Sudoku puzzle — intermediate and hard grids updated daily, the best way to encounter real naked pair patterns
• Printable Sudoku puzzles — ideal for pencil-and-paper candidate work where you need to write out all marks
• Sudoku a Day app — ad-free, with hint support to confirm when you have found a pair

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Frequently Asked Questions

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