Solving Tips
Naked Pairs Technique: Eliminate Candidates Using Number Pairs
Naked Pairs is one of the most commonly used intermediate Sudoku techniques. The core idea is: when two cells in the same row, column, or box have exactly the same two candidates, those two numbers must go in those two cells, so you can eliminate these candidates from other cells in that unit.
Core Principle:
If two cells in a row, column, or box both have the same two candidates (e.g., both have only 4 and 8), then these two numbers must belong to these two cells. If one cell gets 4, the other must get 8, and vice versa. Therefore, no other cell in that unit can contain these two numbers.
If two cells in a row, column, or box both have the same two candidates (e.g., both have only 4 and 8), then these two numbers must belong to these two cells. If one cell gets 4, the other must get 8, and vice versa. Therefore, no other cell in that unit can contain these two numbers.
Before reading this article, we recommend understanding Sudoku naming conventions to help you follow the examples.
Example 1: Naked Pair in a Row
Let's look at the first example, finding a pair of cells with identical candidates in Row 7.
Figure 1: E7 and F7 form a Naked Pair {4,8} in Row 7
Analysis Process
1
Identify the Pair: Looking at Row 7, both E7 and F7 have candidates {4, 8}. They form a Naked Pair.
2
Understand the Logic: Since E7 and F7 can only contain 4 or 8, and these two cells must have these two numbers (one gets 4, the other gets 8), no other cell in Row 7 can have 4 or 8.
3
Eliminate Candidates: Check other cells in Row 7 and remove 4 and 8 from their candidates.
Conclusion:
In Row 7, E7 and F7 form a Naked Pair {4, 8}. Therefore, candidates 4 and 8 must be removed from all other cells in Row 7.
In Row 7, E7 and F7 form a Naked Pair {4, 8}. Therefore, candidates 4 and 8 must be removed from all other cells in Row 7.
Example 2: Naked Pair in a Box
Now let's look at another example, finding a Naked Pair in Box 9.
Figure 2: G9 and I9 form a Naked Pair {3,4} in Box 9
Analysis Process
1
Identify the Pair: Looking at Box 9 (bottom-right 3×3 region), both G9 and I9 have candidates {3, 4}. They form a Naked Pair.
2
Understand the Logic: Since G9 and I9 can only contain 3 or 4, these two numbers must belong to these two cells, so no other cell in Box 9 can have 3 or 4.
3
Eliminate Candidates: Check other cells in Box 9 and remove 3 and 4 from their candidates.
Conclusion:
In Box 9, G9 and I9 form a Naked Pair {3, 4}. Therefore, candidates 3 and 4 must be removed from all other cells in Box 9.
In Box 9, G9 and I9 form a Naked Pair {3, 4}. Therefore, candidates 3 and 4 must be removed from all other cells in Box 9.
Comparison with Other Techniques
| Aspect | Naked Single | Hidden Single | Naked Pairs |
|---|---|---|---|
| Focus | Single cell | Single number | Two cells + two numbers |
| Condition | Cell has 1 candidate | Number has 1 position | Two cells share same 2 candidates |
| Result | Direct answer | Direct answer | Eliminate candidates |
| Difficulty | Beginner | Beginner | Intermediate |
Common Mistakes:
- The two cells must be in the same unit (row/column/box) to form a pair
- You can only eliminate from the unit where the pair exists
- If candidates are {4,8} and {4,7,8}, they do NOT form a Naked Pair
Practice Now:
Start a Sudoku game and try using the Naked Pairs technique!
Start a Sudoku game and try using the Naked Pairs technique!