Naked Triple Technique
Quick Summary
A Naked Triple occurs when three cells in the same row, column, or box can only contain the same three digits. This means those three digits must occupy those three cells, allowing you to eliminate those digits from all other cells in that unit.
What is a Naked Triple?
A Naked Triple is an advanced Sudoku technique that involves three cells in the same unit (row, column, or 3×3 box) that can only contain the same three digits. The term "naked" refers to the fact that these three digits are clearly visible and not hidden among other candidates.
When you find a naked triple, you can eliminate those three digits from all other cells in the same unit, because those digits must go in the three cells that form the triple.
Why is it Called "Naked Triple"?
The term "naked" refers to the fact that the three digits are clearly visible and not hidden among other candidates. Unlike a "hidden triple" (which we'll cover later), the three digits in a naked triple are the only candidates in those cells, making them obvious to spot.
The term "triple" refers to the fact that exactly three cells are involved, and they contain exactly three digits between them.
How to Find Naked Triples
Follow these steps to identify naked triples:
- 1Look for cells with 2-3 candidates in a unit
- 2Find three cells in the same unit that collectively contain only three distinct digits
- 3Verify the triple: The three cells must contain exactly the same three digits
- 4Apply elimination: Remove those three 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 triple 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 Triples
Let's check if any three cells have the same three candidates:
- • R5C2, R5C3, R5C7: All can contain 2, 5, 6, 7, 9 (not a triple)
- • R5C2, R5C3, R5C8: All can contain 2, 5, 6, 7, 9 (not a triple)
- • R5C2, R5C7, R5C8: All can contain 2, 5, 6, 7, 9 (not a triple)
- • R5C3, R5C7, R5C8: All can contain 2, 5, 6, 7, 9 (not a triple)
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, R5C3, and R5C7 all 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 triple. Let me look for a different example...
Practice Exercise
Try finding naked triples in this practice puzzle:
Tips for Finding Naked Triples
1. Look for Cells with 2-3 Candidates
Focus on cells that have exactly 2 or 3 candidates. These are the building blocks of naked triples. If a cell has 4 or more candidates, it can't be part of a naked triple.
2. Check All Units
Don't just check rows. Also check columns and 3×3 boxes. A naked triple 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 three cells collectively contain only three distinct digits.
4. Be Systematic
Go through each unit systematically. Don't jump around randomly, as you might miss naked triples.
Why Naked Triples Work
Naked Triples 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 three cells in a unit can only contain the same three digits, then those three digits must go in those three cells. This means those digits cannot appear in any other cell in that unit.
When to Use Naked Triples
Naked Triples should be used:
- •After applying basic and intermediate techniques (Last Free Cell, Naked Single, Hidden Single, Naked Pair, Pointing Pair, Box/Line Reduction)
- •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 the three cells collectively contain exactly three distinct digits
- •Wrong unit: The three 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 three cells collectively contain exactly three distinct digits
Next Steps
Once you've mastered Naked Triples, you're ready to learn about X-Wing, which is the next logical step in Sudoku solving. X-Wing involves finding when a digit appears in exactly two cells in each of two rows or columns, forming a rectangle pattern.
Ready for the Next Technique?
Practice your Naked Triple skills or learn the next technique in the sequence.