What is a Naked Pair?
A Naked Pair is one of the most fundamental intermediate Sudoku techniques. It occurs when two cells in the same house (row, column, or box) contain exactly the same two candidates and no other candidates.
Because these two cells must contain these two numbers (one in each cell), you can eliminate those two candidates from all other cells in the same house. It's called "naked" because the pair is clearly visible – not hidden among other candidates.
The Core Principle
The logic behind Naked Pairs is straightforward: if two cells in a house can only contain two specific numbers, then those two numbers must go in those two cells. This means no other cell in that house can contain either of those numbers.
For example, if cells R1C2 and R1C5 both contain only candidates {3, 7}, then:
- One cell will be 3, the other will be 7
- We don't know which is which yet
- But we know 3 and 7 cannot appear anywhere else in Row 1
How to Identify a Naked Pair
Step-by-Step Process:
- Scan for bi-value cells – Look for cells with exactly two candidates
- Find matching pairs – Look for another cell in the same house with the identical two candidates
- Verify the match – Both cells must have exactly the same two candidates, nothing more
- Eliminate – Remove both candidates from all other cells in that house
- Check all houses – The pair might affect a row, column, AND box simultaneously
Analysing the Example
Reading the Diagram
In the example image, you can see a Naked Pair highlighted:
- The pair cells: Two cells containing exactly the same two candidates
- The candidates: The two numbers that form the naked pair
- Eliminations: Other cells in the same house where these candidates are removed
Notice how the two cells "claim" their candidates, preventing them from appearing elsewhere in the house.
Worked Example
Finding a Naked Pair in a Box
Setup: In Box 5 (centre box), we have:
- Cell R4C4: {2, 8}
- Cell R4C5: {1, 3, 5}
- Cell R4C6: {2, 8}
- Cell R5C4: {1, 5, 9}
- Cell R5C5: {3, 5, 8}
- Cell R5C6: {1, 9}
- Cell R6C4: {3, 5}
- Cell R6C5: {3, 5, 8}
- Cell R6C6: {1, 3}
Analysis: Cells R4C4 and R4C6 both contain exactly {2, 8} – a Naked Pair!
Elimination: Remove 8 from R5C5 and R6C5 (the only other cells in Box 5 containing 8).
Result: R5C5 becomes {3, 5} and R6C5 becomes {3, 5}. This might create another Naked Pair!
Naked Pair vs Hidden Pair
It's important to understand the difference between Naked and Hidden Pairs:
Naked Pair
- Two cells contain ONLY two candidates
- Easy to spot – the cells stand out
- Eliminates from OTHER cells in the house
Hidden Pair
- Two candidates appear in ONLY two cells
- Harder to spot – hidden among other candidates
- Eliminates OTHER candidates from those two cells
Multiple House Eliminations
A Naked Pair can sometimes eliminate candidates from multiple houses simultaneously:
Box-Row Intersection
If a Naked Pair in a box also shares a row, you can eliminate from:
- Other cells in the same box
- Other cells in the same row (outside the box)
Always check all houses that contain both cells of the pair!
Common Mistakes to Avoid
- Extra candidates: Both cells must have EXACTLY two candidates – no more
- Different candidates: The two cells must have the SAME two candidates
- Wrong house: Only eliminate from cells in the SAME house as the pair
- Eliminating the pair: Never eliminate candidates from the pair cells themselves
- Missing houses: Check if the pair affects multiple houses
The Subset Family
Naked Pair is part of a family of "naked subset" techniques:
- Naked Single: One cell with one candidate (simplest)
- Naked Pair: Two cells with two candidates
- Naked Triple: Three cells with three candidates
- Naked Quad: Four cells with four candidates (rare)
The principle is the same: N cells with N candidates "claim" those candidates for themselves.
When to Look for Naked Pairs
Optimal Conditions:
- After finding all Naked and Hidden Singles
- When you see cells with only two candidates
- In houses with many solved cells (fewer candidates to check)
- When progress has stalled with basic techniques
Practice Tips
Building Recognition Skills:
- Mark bi-value cells: Mentally note cells with exactly two candidates
- Scan systematically: Check each house for matching pairs
- Use pencil marks: Good notation makes pairs easier to spot
- Check after eliminations: New pairs often appear after other techniques
- Practice regularly: Naked Pairs appear in most medium+ puzzles