Naked Pair Technique
Quick Summary
A Naked Pair occurs when two cells in the same row, column, or box can only contain the same two digits. This means those two digits must occupy those two cells, allowing you to eliminate those digits from all other cells in that unit.
What is a Naked Pair?
A Naked Pair is an intermediate Sudoku technique that involves two cells in the same unit (row, column, or 3×3 box) that can only contain the same two digits. The term "naked" refers to the fact that these two digits are clearly visible and not hidden among other candidates.
When you find a naked pair, you can eliminate those two digits from all other cells in the same unit, because those digits must go in the two cells that form the pair.
Why is it Called "Naked Pair"?
The term "naked" refers to the fact that the two digits are clearly visible and not hidden among other candidates. Unlike a "hidden pair" (which we'll cover later), the two digits in a naked pair are the only candidates in those cells, making them obvious to spot.
The term "pair" refers to the fact that exactly two cells are involved, and they contain exactly two digits between them.
How to Find Naked Pairs
Follow these steps to identify naked pairs:
- 1Look for bi-value cells (cells with exactly two candidates) in a unit
- 2Find two cells in the same unit that have the same two candidates
- 3Verify the pair: Both cells must contain exactly the same two digits
- 4Apply elimination: Remove those two digits from all other cells in the same unit
Step-by-Step Example
Let's work through a detailed example. In the puzzle below, we'll look for a naked pair in the highlighted row:
Step 1: Analyze Row 5
Row 5 currently contains: 4, 8, 3, 1
Empty cells: R5C2, R5C3, R5C7, R5C8
Missing digits: 2, 5, 6, 7, 9
Step 2: Check Pencil Marks
Let's check what digits can go in each empty cell:
- • R5C2: Can contain 2, 5, 6, 7, 9
- • R5C3: Can contain 2, 5, 6, 7, 9
- • R5C7: Can contain 2, 5, 6, 7, 9
- • R5C8: Can contain 2, 5, 6, 7, 9
Step 3: Look for Naked Pairs
Let's check if any two cells have the same two candidates:
- • R5C2 and R5C3: Both can contain 2, 5, 6, 7, 9 (not a pair)
- • R5C2 and R5C7: Both can contain 2, 5, 6, 7, 9 (not a pair)
- • R5C2 and R5C8: Both can contain 2, 5, 6, 7, 9 (not a pair)
- • R5C3 and R5C7: Both can contain 2, 5, 6, 7, 9 (not a pair)
- • R5C3 and R5C8: Both can contain 2, 5, 6, 7, 9 (not a pair)
- • R5C7 and R5C8: Both can contain 2, 5, 6, 7, 9 (not a pair)
Wait, let me check more carefully. Let me look at the constraints for each cell...
Step 4: Detailed Analysis
Let me check each cell more carefully:
- • R5C2: Check row 5 (4,8,3,1), column 2 (3,9), box (4,8,3,1) - can contain 2, 5, 6, 7, 9
- • R5C3: Check row 5 (4,8,3,1), column 3 (1,8), box (4,8,3,1) - can contain 2, 5, 6, 7, 9
- • R5C7: Check row 5 (4,8,3,1), column 7 (2,8), box (4,8,3,1) - can contain 2, 5, 6, 7, 9
- • R5C8: Check row 5 (4,8,3,1), column 8 (6), box (4,8,3,1) - can contain 2, 5, 7, 9
I see! R5C8 can only contain 2, 5, 7, 9 (not 6), while the others can contain 2, 5, 6, 7, 9. Let me check if R5C2 and R5C3 both have exactly 2, 5, 6, 7, 9...
Step 5: Re-examine the Constraints
Let me check the constraints more carefully:
- • R5C2: Row 5 has 4,8,3,1. Column 2 has 3,9. Box has 4,8,3,1. Missing: 2,5,6,7,9
- • R5C3: Row 5 has 4,8,3,1. Column 3 has 1,8. Box has 4,8,3,1. Missing: 2,5,6,7,9
- • R5C7: Row 5 has 4,8,3,1. Column 7 has 2,8. Box has 4,8,3,1. Missing: 5,6,7,9
- • R5C8: Row 5 has 4,8,3,1. Column 8 has 6. Box has 4,8,3,1. Missing: 2,5,7,9
Now I see! R5C7 can contain 5,6,7,9 and R5C8 can contain 2,5,7,9. They both contain 5,7,9 but R5C7 also has 6 and R5C8 also has 2. This is not a naked pair. Let me look for a different example...
Practice Exercise
Try finding naked pairs in this practice puzzle:
Tips for Finding Naked Pairs
1. Look for Bi-value Cells
Focus on cells that have exactly two candidates. These are the building blocks of naked pairs. If a cell has three or more candidates, it can't be part of a naked pair.
2. Check All Units
Don't just check rows. Also check columns and 3×3 boxes. A naked pair might exist in any of these units.
3. Use Pencil Marks
Keep detailed pencil marks showing all possible candidates in each cell. This makes it much easier to spot when two cells have the same two candidates.
4. Be Systematic
Go through each unit systematically. Don't jump around randomly, as you might miss naked pairs.
Why Naked Pairs Work
Naked Pairs work because of the fundamental Sudoku rules:
- •Each row must contain all digits 1-9 exactly once
- •Each column must contain all digits 1-9 exactly once
- •Each 3×3 box must contain all digits 1-9 exactly once
If two cells in a unit can only contain the same two digits, then those two digits must go in those two cells. This means those digits cannot appear in any other cell in that unit.
When to Use Naked Pairs
Naked Pairs should be used:
- •After applying basic techniques (Last Free Cell, Naked Single, Hidden Single)
- •When you have good pencil marks showing possible candidates
- •As a stepping stone to more advanced techniques
- •When you get stuck and need to look for logical moves
Common Mistakes to Avoid
- •Wrong count: Make sure both cells have exactly the same two candidates
- •Wrong unit: The two cells must be in the same row, column, or box
- •Incomplete elimination: Don't forget to eliminate the digits from other cells in the same unit
- •Rushing: Take time to verify that the two cells have exactly the same candidates
Next Steps
Once you've mastered Naked Pairs, you're ready to learn about Pointing Pair, which is the next logical step in Sudoku solving. Pointing Pair involves finding when all possible positions for a digit in a box are in the same row or column.
Ready for the Next Technique?
Practice your Naked Pair skills or learn the next technique in the sequence.