Naked Pairs Technique: Identifying and Using Candidate Pairs
Naked Pairs is one of the most commonly used intermediate Sudoku techniques. The core concept is: when two cells in the same row, column, or box have exactly the same two candidates, these two numbers must be placed in these two cells, so they can be eliminated from other cells in that unit.
If two cells in a row, column, or box both have the same two candidates (e.g., both have 2 and 3), then these two numbers must belong to these two cells. Because if one cell contains 2, the other must contain 3; and vice versa. Therefore, no other cells in that unit can contain these two numbers.
Before reading this article, we recommend understanding Sudoku naming conventions, which will help you understand the analysis examples below.
Example 1: Naked Pairs in a Column
Let's look at the first example, where we find a pair of cells with identical candidates in Column 5.
Analysis Process
- R2C5 has candidates {1,2,3,4}, remove 2 and 3
- R7C5 has candidates {1,2,3,4,7}, remove 2 and 3
- R9C5 has candidates {1,2,3,4,6,7}, remove 2 and 3
In Column 5, R3C5 and R5C5 form a Naked Pair {2, 3}.
Action: Remove candidates 2, 3 from R2C5, R7C5 and R9C5.
Example 2: Naked Pairs in a Box
Now let's look at another example, finding a Naked Pair in Box 3 (the top-right 3×3 region).
Analysis Process
- R1C7 has candidates {2,7,8,9}, remove 7 and 9
- R1C9 has candidates {2,3,7,8}, remove 7
- R2C8 has candidates {4,6,7,9}, remove 7 and 9
- R2C9 has candidates {3,4,6,7}, remove 7
- R3C9 has candidates {3,4,7}, remove 7
In Box 3, R1C8 and R2C7 form a Naked Pair {7, 9}.
Action: Remove candidates 7, 9 from R1C7 and R2C8; remove candidate 7 from R1C9, R2C9 and R3C9.
Naked Pairs vs Other Techniques
Let's compare Naked Pairs with beginner techniques:
| Comparison | Naked Single | Hidden Single | Naked Pairs |
|---|---|---|---|
| Focus | Single cell | Single number | Two cells + two numbers |
| Condition | Cell has only 1 candidate | Number has only 1 position in unit | Two cells have same 2 candidates |
| Result | Directly determines answer | Directly determines answer | Eliminates candidates from other cells |
| Difficulty | Beginner | Beginner | Intermediate |
In Sudoku terminology, "Naked" means the candidates are "exposed" and visible—both cells clearly show only these two numbers as candidates. In contrast, there's also "Hidden Pairs", where two numbers only appear in two cells within a unit, but those cells may have other candidates as well.
Technique Summary
Key points for applying Naked Pairs:
- Search condition: Two cells must be in the same row, column, or box
- Candidate requirement: Both cells must have exactly the same candidates, with only two numbers
- Elimination scope: Can only eliminate these two candidates from other cells in the same unit
- Note: Naked Pairs don't directly give answers, but simplify the puzzle by eliminating candidates
- Both cells must be in the same unit (row/column/box) to form a pair
- Can only eliminate candidates from the unit where the pair exists, cannot eliminate across units
- If two cells have candidates {2,3} and {2,3,7}, they do not form a Naked Pair (candidates are not exactly the same)
Advanced: Naked Triples
Naked Pairs can be extended to Naked Triples: When three cells in the same unit have candidates that are subsets of the same three numbers, those three numbers can be eliminated from other cells. For example, if three cells have candidates {1,2}, {2,3}, and {1,3}, they collectively use digits 1, 2, 3, forming a triple.
Start a Sudoku game and try using Naked Pairs to find candidates you can eliminate!