Naked Triples in Sudoku: The Complete Guide

What is a Naked Triple?

A naked triple occurs when three cells in the same unit (row, column, or box) collectively contain only three candidate numbers between them. These three numbers are "locked" into those three cells, which means you can eliminate them from all other cells in that unit.

The cells don't need to have identical candidates—they just need to use exactly three distinct numbers between them.

Example:

In Row 4, you have three cells:

Cell A: {2, 5}
Cell B: {2, 7}
Cell C: {5, 7}

Together, these three cells use only three distinct candidates: 2, 5, and 7. This is a naked triple. Since 2, 5, and 7 must go in these three cells (in some arrangement), you can eliminate 2, 5, and 7 from all other cells in Row 4.

Why Naked Triples Matter

They unlock progress when pairs and singles fail.
They eliminate candidates from multiple cells simultaneously.
They often trigger chain reactions, revealing hidden singles.
They're essential for intermediate to advanced puzzles.
They demonstrate pattern recognition skills that apply to quads and larger sets.

How to Spot a Naked Triple

Look for three cells in the same unit.
Scan one row, column, or box at a time.
Check if they share exactly three candidates.
Count the distinct numbers across all three cells. If there are only three unique numbers, you might have a triple.
Verify the pattern.
Common patterns include {A,B}, {B,C}, {A,C} or {A,B,C}, {A,B}, {B,C} or even {A,B,C}, {A,B,C}, {A,B,C}.
Eliminate from other cells.
Remove all three candidates from every other cell in that unit.

Naked Triple vs Naked Pair

These techniques follow the same logic but different scales:

Naked pair: Two cells contain exactly two candidates between them. Eliminate those two numbers from other cells in the unit.
Naked triple: Three cells contain exactly three candidates between them. Eliminate those three numbers from other cells in the unit.

Think of naked triples as the next step up from naked pairs. Both eliminate outward from the group to other cells.

Step-by-Step Example

Let's examine Box 6 (middle-right box):

Box 6 cells (rows 4-6, columns 7-9):

Row 4, Col 7: {1, 4, 6}
Row 4, Col 8: {1, 4}
Row 4, Col 9: {2, 8, 9}
Row 5, Col 7: [filled with 5]
Row 5, Col 8: {2, 8, 9, 7}
Row 5, Col 9: {1, 4, 6}
Row 6, Col 7: {2, 8, 9, 7}
Row 6, Col 8: {1, 6}
Row 6, Col 9: [filled with 3]

Analysis: Look at rows 4 and 5-6 cells in columns 7-9:

Row 4, Col 7: {1, 4, 6}
Row 4, Col 8: {1, 4}
Row 5, Col 9: {1, 4, 6}

Check candidates: These three cells collectively use 1, 4, and 6—exactly three numbers!

Naked triple found: {1, 4, 6} across these three cells.

Elimination: Remove 1, 4, and 6 from all other cells in Box 6:

Row 6, Col 8 has {1, 6}—wait, this is part of the triple actually. Let me reconsider...

Corrected Analysis: Let me use a clearer example.

Clearer Example - Column 5:

Column 5 candidates:

Row 1: [filled]
Row 2: {3, 7, 8}
Row 3: {3, 8}
Row 4: {1, 2, 5}
Row 5: {3, 7}
Row 6: [filled]
Row 7: {1, 2, 5, 6}
Row 8: {1, 2, 5, 6, 9}
Row 9: [filled]

Identify the triple:

Row 2: {3, 7, 8}
Row 3: {3, 8}
Row 5: {3, 7}

Check: These three cells use candidates 3, 7, and 8 only—a naked triple!

Action: Eliminate 3, 7, and 8 from all other cells in Column 5. In this case, Row 8 has candidates {1, 2, 5, 6, 9}, so no eliminations there (none of the triple numbers present). The triple has locked those three numbers to those three cells.

Visual Example: The {1,2,3} Triple

Scenario: In Row 6, you find:
Cell A: {1, 2, 3}
Cell B: {1, 2}
Cell C: {2, 3}
Pattern: All three cells use only the numbers 1, 2, and 3.
Naked triple confirmed: These three numbers are locked to these three cells.
Elimination: Remove 1, 2, and 3 from all other cells in Row 6.
Result: Other cells with candidates like {1, 4, 5, 7} would become {4, 5, 7}, simplifying the grid.

Strategies for Spotting Naked Triples Quickly

Look for cells with 2-3 candidates
Naked triples rarely involve cells with 4+ candidates. Focus on simpler cells first.
Scan for repeating numbers
If you see the same 2-3 numbers appearing across multiple cells in a unit, investigate further.
Use systematic unit checking
Go through each row, column, and box methodically rather than jumping around.
Look for "almost" patterns
Patterns like {A,B}, {B,C}, and {A,C} are easier to spot than three cells with {A,B,C} each.
Practice with pairs first
Master naked pairs before focusing heavily on triples—the logic is identical.

Common Pitfalls

Counting wrong: Make sure there are exactly three distinct candidates across the three cells, not four or more.
Missing non-identical patterns: The cells don't all need to be {1,2,3}. Patterns like {1,2}, {2,3}, {1,3} also form naked triples.
Looking in multiple units: All three cells must be in the same row, column, OR box—not spread across different units.
Forgetting to eliminate: After finding a triple, make sure you actually remove those candidates from other cells.
Not checking for smaller patterns first: Always look for naked singles and pairs before searching for triples.

Practice: Find the Naked Triple

Try this Row 3 scenario:

Row 3 candidates:

Col 1: [filled with 7]
Col 2: {4, 6, 9}
Col 3: {4, 6}
Col 4: {1, 2, 3, 5, 8}
Col 5: {1, 2, 3, 5}
Col 6: {4, 9}
Col 7: {1, 2, 3, 5, 8}
Col 8: [filled with 6]
Col 9: {1, 2, 5, 8}

Question: Can you find a naked triple?

Solution: Look at columns 2, 3, and 6:

Col 2: {4, 6, 9}
Col 3: {4, 6}
Col 6: {4, 9}

Check: These three cells collectively use 4, 6, and 9 only—exactly three candidates!

Naked triple found: {4, 6, 9}

Action: Eliminate 4, 6, and 9 from all other cells in Row 3. Wait—Col 8 is already filled, so we check the remaining cells. None of the other cells (4, 5, 7, 9) have 4, 6, or 9 as candidates in this example, so the triple is confirmed but doesn't create eliminations here. In a real puzzle, this would often clean up other cells.

Why Naked Triples Set the Stage

Naked triples extend the logic of naked pairs and prepare you for even more advanced techniques:

They introduce thinking about multiple cells as a locked group
They naturally lead to naked quads (four cells with four candidates)
They improve pattern recognition skills needed for X-Wing and Swordfish
They help you recognize when to scale up your search from pairs to larger groups
They're often the breakthrough technique for challenging intermediate puzzles

Quick Recap

Technique	Cells	Candidates	Elimination	Difficulty
Naked Pair	2	2	Other cells in unit	Intermediate
Naked Triple	3	3	Other cells in unit	Intermediate
Naked Quad	4	4	Other cells in unit	Advanced
Hidden Pair	2	2	Within the pair cells	Intermediate

Final Thought

When pairs don't crack the puzzle, ask yourself: are there three cells sharing just three candidates? Naked triples might be your next breakthrough.

Frequently Asked Questions

What is a Naked Triple in Sudoku?

A naked triple occurs when three cells in the same unit (row, column, or box) collectively contain only three candidate numbers between them. These three numbers are "locked" into those three cells, so you can eliminate them from all other cells in that unit. Each cell may have 2-3 candidates, but together they use exactly three distinct numbers.

How do I spot a Naked Triple?

To spot naked triples: 1) Look for three cells in the same unit, 2) Check if they collectively contain only three distinct candidate numbers (like {1,2}, {2,3}, {1,3} or {1,2,3} patterns), 3) Verify each cell has 2-3 candidates from this set, 4) Eliminate those three numbers from all other cells in the unit.

What's the difference between Naked Triples and Naked Pairs?

Naked pairs involve two cells with two candidates; naked triples involve three cells with three candidates. Both eliminate outward from the group. Naked triples are rarer but more powerful, often eliminating candidates from multiple cells. The logic is identical—just scaled from 2 cells to 3 cells.

Why are Naked Triples important?

Naked triples are important because they unlock progress when pairs and singles fail, they eliminate candidates from multiple cells simultaneously, they often trigger chain reactions revealing hidden singles, and they're essential for intermediate to advanced puzzles.

When should I look for Naked Triples?

Look for naked triples after exhausting naked singles, hidden singles, and naked pairs. They appear in units where cells have 2-3 candidates each. Systematically scan rows, columns, and boxes looking for three cells that share only three distinct candidates between them.

Ready to advance? Check out our complete strategy guide for more techniques.

Related Strategies

Once you've mastered naked triples, these techniques build naturally:

Naked Pairs - The foundation technique for naked triples
Hidden Triples - The complementary technique (coming soon)
Naked Quads - Four-cell extension of this logic (coming soon)
Hidden Pairs - Another intermediate elimination technique
X-Wing - Advanced pattern using different logic

Practice Naked Triples

Next up: Try Hidden Triples to complete your triple techniques toolkit (coming soon).

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