Solving Tips
Naked Triples Technique: Eliminate Candidates Using Number Triplets
Naked Triples is an extension of the Naked Pairs technique and an important intermediate Sudoku strategy. The core principle is: when three cells in the same row, column, or box contain candidates that are subsets of the same three numbers, those three numbers must go in those three cells, so they can be eliminated from other cells in that unit.
Core Principle:
If three cells in a row, column, or box contain only candidates from the same set of three numbers (each cell may have 2 or 3 of these numbers), then those three numbers must belong to those three cells. Therefore, other cells in that unit cannot contain these three numbers.
Important: A Naked Triple doesn't require each cell to have exactly three candidates. For example, cells with candidates {1,9}, {1,5,9}, and {1,5,9} still form a Naked Triple because together they use only the numbers {1,5,9}.
If three cells in a row, column, or box contain only candidates from the same set of three numbers (each cell may have 2 or 3 of these numbers), then those three numbers must belong to those three cells. Therefore, other cells in that unit cannot contain these three numbers.
Important: A Naked Triple doesn't require each cell to have exactly three candidates. For example, cells with candidates {1,9}, {1,5,9}, and {1,5,9} still form a Naked Triple because together they use only the numbers {1,5,9}.
Before reading this article, we recommend understanding Sudoku naming conventions and Naked Pairs first.
Example 1: Naked Triple in a Box
Let's look at the first example, finding a Naked Triple in Box 2.
Figure 1: D3, E3, and E2 in Box 2 form a Naked Triple {2,7,9}
Analysis Process
1
Find the Triple: In Box 2 (top-center 3×3 region), D3, E3, and E2 all have candidates {2, 7, 9}, forming a Naked Triple.
2
Understand the Logic: Since D3, E3, and E2 can only contain 2, 7, or 9, and these three numbers must go in these three cells, no other cell in Box 2 can contain 2, 7, or 9.
3
Eliminate Candidates: Check other cells in Box 2 and remove 2, 7, and 9 from their candidates (shown in yellow).
Conclusion:
In Box 2, D3, E3, and E2 form a Naked Triple {2, 7, 9}. Therefore, candidates 2, 7, and 9 must be removed from all other cells in Box 2.
In Box 2, D3, E3, and E2 form a Naked Triple {2, 7, 9}. Therefore, candidates 2, 7, and 9 must be removed from all other cells in Box 2.
Example 2: Naked Triple in a Row
Now let's look at another example, finding a Naked Triple in Row 8.
Figure 2: G8, H8, and I8 in Row 8 form a Naked Triple {1,5,9}
Analysis Process
1
Find the Triple: In Row 8, G8 has candidates {1, 9}, H8 has {1, 5, 9}, and I8 has {1, 5, 9}. All candidates are subsets of {1, 5, 9}, forming a Naked Triple.
2
Understand the Logic: Although G8 only has two candidates {1, 9}, together with H8 and I8, they occupy the numbers 1, 5, and 9. These three numbers must go in G8, H8, and I8, so no other cell in Row 8 can contain 1, 5, or 9.
3
Eliminate Candidates: Check other cells in Row 8 and remove 1, 5, and 9 from their candidates (shown in yellow).
Conclusion:
In Row 8, G8, H8, and I8 form a Naked Triple {1, 5, 9}. Therefore, candidates 1, 5, and 9 must be removed from all other cells in Row 8.
In Row 8, G8, H8, and I8 form a Naked Triple {1, 5, 9}. Therefore, candidates 1, 5, and 9 must be removed from all other cells in Row 8.
Variations of Naked Triples
Naked Triples can appear in several variations. The key is that three cells share three numbers:
| Variation Type | Candidates in Three Cells | Description |
|---|---|---|
| Complete | {1,2,3}, {1,2,3}, {1,2,3} | All three cells have all three candidates |
| 2-3-3 Type | {1,9}, {1,5,9}, {1,5,9} | One cell has 2 candidates, two have 3 |
| 2-2-3 Type | {1,2}, {2,3}, {1,2,3} | Two cells have 2 candidates, one has 3 |
| 2-2-2 Type | {1,2}, {2,3}, {1,3} | All three cells have only 2 candidates (hardest to spot) |
Key Recognition Tip:
To identify a Naked Triple: combine all candidates from three cells. If the union contains exactly three different numbers, it's a Naked Triple. For example: {1,9} ∪ {1,5,9} ∪ {1,5,9} = {1,5,9} — only 3 numbers, so it's a Naked Triple.
To identify a Naked Triple: combine all candidates from three cells. If the union contains exactly three different numbers, it's a Naked Triple. For example: {1,9} ∪ {1,5,9} ∪ {1,5,9} = {1,5,9} — only 3 numbers, so it's a Naked Triple.
Naked Pairs vs Naked Triples
| Comparison | Naked Pairs | Naked Triples |
|---|---|---|
| Number of Cells | 2 cells | 3 cells |
| Number of Digits | 2 digits | 3 digits |
| Candidate Requirement | Both cells have identical candidates | Candidates are subsets of 3 numbers |
| Recognition Difficulty | Easier | Harder (more variations) |
| Elimination Power | Eliminates 2 numbers | Eliminates 3 numbers |
Summary
- Location: Three cells must be in the same row, column, or box
- Candidate Requirement: Combined candidates must have exactly three numbers
- Variation Recognition: Not every cell needs three candidates; {1,2}, {2,3}, {1,3} is also a Naked Triple
- Elimination Scope: Only eliminate from other cells in the same unit
- Note: Naked Triples don't directly solve cells; they simplify by eliminating candidates
Common Mistakes:
- Three cells must be in the same unit (row/column/box)
- Only eliminate from cells within that unit, not across units
- If combined candidates exceed 3 numbers (e.g., {1,2}, {2,3}, {3,4} = {1,2,3,4}), it's not a Naked Triple
- The 2-2-2 type (all cells with only 2 candidates) is often overlooked
Practice Now:
Start a Sudoku game and try finding Naked Triples to eliminate candidates!
Start a Sudoku game and try finding Naked Triples to eliminate candidates!