Lesson:Naked Pairs
If two cells in a unit (row, col, or box) contain exactly the same two candidates...
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Naked Pairs is one of the foundational candidate-elimination techniques in intermediate Sudoku solving. A Naked Pair occurs when two cells in the same unit (a row, column, or 3×3 box) each contain exactly the same two candidates — and no other candidates. Because one of those two cells must ultimately hold one digit and the other cell must hold the other, no other cell in the unit can contain either of those digits. This allows you to safely eliminate both candidates from every other cell in the shared unit.
The term "naked" reflects the fact that the pair is clearly visible: the two cells openly advertise that they hold exactly two candidates. This is in contrast to Hidden Pairs, where the pair is concealed among other candidates. Naked Pairs are easier to spot than Hidden Pairs but require the same prerequisite: you must be tracking pencil-mark candidates for every empty cell.
Naked Pairs unlock eliminations that frequently lead to cascades of Naked Singles and Hidden Singles. A single Naked Pair discovery can sometimes break open a puzzle that appeared completely stuck, making it one of the most rewarding techniques to master.
How It Works — Step by Step
Step 1 — Identify cells with exactly two candidates
Scan all empty cells in your pencil-mark grid and locate any cell that has exactly two remaining candidates. These cells are candidates for forming a Naked Pair. Make a mental or written note of each bi-value cell and what two digits it contains.
Step 2 — Look for a matching cell in the same unit
For each bi-value cell you found, check whether any other empty cell in the same row, column, or box contains exactly the same two candidates. If you find such a matching cell, you have found a Naked Pair.
Step 3 — Eliminate from the rest of the unit
Once you have confirmed a Naked Pair, neither of the two digits can appear in any other cell of that shared unit. Remove both digits from the candidate lists of all other empty cells in that row, column, or box. Do not remove them from cells outside the shared unit.
Step 4 — Check for new simplifications
After the elimination, check whether any cells in the unit now have only one candidate left (Naked Single) or whether a digit is now confined to only one cell in the unit (Hidden Single). It is common for a Naked Pair to trigger a chain of straightforward placements.
When to Use This Technique
Use Naked Pairs after exhausting Naked Singles and Hidden Singles. They are the natural next step when you have a fully-marked candidate grid and the simpler techniques no longer produce placements. Always scan your bi-value cells first — two identical bi-value cells in the same unit are the quickest Naked Pairs to find.
Worked Examples
Suppose you are looking at Row 5 of a puzzle. After tracking all candidates, you notice that the cell in Column 2 contains only {3, 7} and the cell in Column 8 also contains only {3, 7}. These two cells form a Naked Pair. You immediately know that the digit 3 and the digit 7 will be distributed between those two cells in some order. Therefore, every other empty cell in Row 5 cannot contain a 3 or a 7 — remove those digits from their candidate lists.
A box-based Naked Pair: In the bottom-right 3×3 box, three cells are empty. Two of them each contain {1, 6} as their only candidates. The third empty cell had candidates {1, 4, 6}. The Naked Pair of {1, 6} in the first two cells means you can remove 1 and 6 from the third cell, leaving it with only {4} — a Naked Single that you can immediately place.
Frequently Asked Questions
Can a Naked Pair eliminate candidates from multiple units at once?
Yes, if the two Naked Pair cells share more than one unit. For example, if both cells are in the same row AND the same 3×3 box, you can eliminate both digits from the entire row and from the entire box (excluding the pair cells themselves). This is particularly powerful when the pair sits along a box-row intersection.
What if a bi-value cell has the same candidates as three different cells?
That is unusual and warrants careful checking. If three cells all contain exactly the same two candidates, something is wrong with your candidate tracking — two of the three must be in the same unit, and the third might be a coincidence in a different unit. Re-verify your candidate lists and confirm which cells share a unit.
Is a Naked Pair also a Hidden Pair?
Naked Pairs and Hidden Pairs describe different logical structures. However, in some specific board configurations, the same pair of cells and digits satisfies both definitions simultaneously. In practice, if you spot a Naked Pair, apply it as a Naked Pair — the resulting eliminations are the same regardless of which perspective you take.
How do Naked Triples differ from Naked Pairs?
A Naked Triple extends the same logic to three cells and three (or sometimes just two or three shared) candidates. Three cells in a unit that collectively contain only three candidate digits form a Naked Triple — all three digits can be eliminated from every other cell in that unit. Naked Triples are rarer and harder to spot than Naked Pairs.
Ready to test your knowledge? Try applying this technique in our Intermediate Sudoku lessons, Medium Sudoku puzzles or explore Hard Sudoku challenges. Keep training to improve your solve times and master the grid!
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