Naked Triples in Sudoku: How to Find & Use Them

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Published April 14, 2026 · 11 min read

You’ve mastered Naked Pairs. You can spot two cells with two matching candidates almost instantly. But what happens when the pattern involves three cells and three digits? The grid looks more complex, the cells don’t always contain the same candidates, and it’s easy to miss what’s right in front of you.

This is where Naked Triples come in — a slightly trickier extension of the same subset logic that can eliminate candidates from up to six cells in one move. Once you understand they work exactly like pairs but with one extra cell and one extra digit, they become surprisingly easy to find.

In this guide we’ll explain exactly what Naked Triples are, why the logic is airtight, and walk through a real example with before-and-after diagrams. We’ll also cover common mistakes, how to spot them quickly, and where they sit in the solving hierarchy.

✅ What Are Naked Triples in Sudoku?

A Naked Triple is an intermediate candidate-elimination technique and the three-cell extension of the Naked Pair. The word “naked” means the cells contain only digits from the triple’s set — no extra candidates are hiding alongside them.

The crucial detail that trips up many solvers: not every cell needs all three candidates. A cell with {1, 3} is a perfectly valid member of a Naked Triple for digits {1, 3, 9}. As long as every candidate in the cell is part of the triple’s three digits, it counts.

🧠 How Naked Triples Work (The Logic)

Imagine you’re examining Row 4 of a sudoku grid. Three cells stand out:

• R4C4 has candidates: {1, 3, 9}
• R4C8 has candidates: {1, 3}
• R4C9 has candidates: {1, 3}

Every candidate in each cell is drawn from the same set: {1, 3, 9}. Think about what this means:

• There are three digits (1, 3, 9) and three cells.
• Each cell must ultimately hold one of those three digits.
• No matter how you assign 1, 3, and 9 to these three cells, all three digits are accounted for.

Because 1, 3, and 9 are fully consumed by R4C4, R4C8, and R4C9, no other cell in Row 4 can contain a 1, 3, or 9. You can safely remove those candidates from every other cell in the row.

🔎 Step-by-Step Example

Let’s walk through a concrete Naked Triple on a real grid. We’re looking at Row 4 with the triple digits {1, 3, 9}.

Step 1: Identify the Triple

Scan Row 4 for cells whose candidates are subsets of a three-digit set. In this grid:

• R4C4 contains candidates {1, 3, 9} — all three triple digits.
• R4C8 contains candidates {1, 3} — a subset of {1, 3, 9}.
• R4C9 contains candidates {1, 3} — same subset.

All three cells contain only digits from {1, 3, 9}. That’s a Naked Triple!

Step 2: Make the Eliminations

The triple locks digits 1, 3, and 9 into R4C4, R4C8, and R4C9. We can remove candidates 1, 3, and 9 from every other cell in Row 4:

• R4C1: remove 1 and 9 — {1, 6, 7, 8, 9} → {6, 7, 8}
• R4C2: remove 1, 3, and 9 — {1, 3, 4, 6, 7, 8, 9} → {4, 6, 7, 8}
• R4C3: remove 1, 3, and 9 — {1, 3, 6, 7, 8, 9} → {6, 7, 8}
• R4C5: remove 1, 3, and 9 — {1, 3, 4, 9} → {4}

Step 3: Continue Solving

Look at the result — R4C5 has been reduced to a single candidate {4}, meaning it’s now a naked single! One Naked Triple elimination just solved a cell directly and removed 11 candidates in total. The remaining cells in Row 4 have significantly fewer candidates, which can trigger further deductions across the grid.

🕵️ How to Spot Naked Triples in Your Grid

Naked Triples are trickier to spot than Naked Pairs because the three cells don’t need identical candidates. Here’s a practical method:

The key visual cue: look for clusters of cells with small candidate counts (2 or 3). When three of them share the same three digits — even in different combinations — that’s your triple.

🔄 Naked Triples in Rows, Columns & Boxes

Naked Triples work identically in all three types of sudoku unit:

• Row: Three cells in the same row share three candidates → eliminate from other cells in that row.
• Column: Three cells in the same column share three candidates → eliminate from other cells in that column.
• Box: Three cells in the same 3×3 box share three candidates → eliminate from other cells in that box.

Box-based Naked Triples are especially powerful because eliminations affect cells across multiple rows and columns, potentially triggering cascading deductions.

⚠️ Common Mistakes to Avoid

Naked Triples are conceptually simple but easy to get wrong in practice. Watch out for these common errors:

1. Requiring All Three Candidates in Every Cell

This is the most common mistake. A Naked Triple does not require each cell to contain all three digits. Cells with {1, 3}, {1, 9}, and {3, 9} form a perfectly valid triple for {1, 3, 9} — none of them has all three candidates.

2. Including Cells With Extra Candidates

Every candidate in a triple cell must be one of the three triple digits. If a cell has {1, 3, 5}, it cannot be part of a Naked Triple for {1, 3, 9} because 5 is not in the set. That cell might be part of a Hidden Triple instead.

3. Eliminating from the Triple Cells

Never remove candidates from the triple cells themselves! Eliminations apply only to the other cells in the unit. The triple cells keep their candidates — they define the pattern.

4. Confusing Naked Triples with Hidden Triples

In a Naked Triple, the cells contain only the triple digits. In a Hidden Triple, three digits appear in only three cells of a unit, but those cells may also have other candidates. Different technique, different eliminations.

📅 When to Look for Naked Triples

Naked Triples sit in the intermediate tier of sudoku strategies, slightly above Naked Pairs:

1. Basic techniques: Naked singles, hidden singles, full-house.
2. Intermediate techniques: Naked Pairs, Naked Triples, hidden pairs, hidden triples, pointing pairs, box/line reduction.
3. Advanced techniques: X-Wing, Swordfish, XY-Wing.
4. Expert techniques: Jellyfish, chains, almost locked sets.

Exhaust Naked Pairs before hunting for Naked Triples. If you can’t find any pairs, start looking for triples — they’re often the key to cracking medium and hard puzzles that seem impossible with simpler techniques.

🚀 Naked Pairs vs Triples vs Quads

Naked Triples belong to the naked subsets family. The logic scales up and down:

The pattern is always the same: N cells in a unit together contain exactly N candidates. Those N digits can be removed from all other cells in the unit. Master Naked Pairs first, then triples become intuitive, and quads are just one more step up.

🎯 Practice Naked Triples

The best way to master Naked Triples is to practise on real puzzles. Here are some tips:

• Use pencil marks: Fill in all candidates before looking for intermediate patterns. Our pencil-mark mode makes this easy.
• Start with medium puzzles: Medium grids regularly feature Naked Triples without requiring expert techniques on top.
• Build on Naked Pairs: When you find a pair, check nearby cells for a possible third member. Pairs often extend to triples.
• Verify with the solver: Use our sudoku solver to confirm your eliminations are correct.