Volodymyr Sakhan  ·  April 11, 2026

Naked Triples (also called Obvious Triples) extend the logic of Naked Pairs to groups of three cells. When three cells in the same row, column, or box collectively contain only three distinct candidate digits — and no others — those three digits must fill exactly those three cells. Everything else in that unit can safely lose those candidates.

This technique is used in medium and hard sudoku puzzles. If you are new to candidates, start with Notes & Pencil Marks first, then come back here.

What Is a Naked Triple?

A naked triple is a set of exactly three cells within the same unit (row, column, or box) whose combined candidate list contains exactly three distinct digits. Each individual cell may hold two or three of those digits — not necessarily all three. The key is that the union of all candidates across the three cells is exactly {X, Y, Z}.

For example, cells with candidates {1,5}, {5,9}, and {1,9} form a valid naked triple for digits 1, 5, and 9 — even though no single cell holds all three. A cell with {1,5,9} by itself is not a triple; it only becomes one when two other cells cover exactly the same set. Once you spot the pattern, the elimination logic is identical regardless of how many candidates each cell carries.

When to Use Naked Triples

Naked Triples appear in medium and hard puzzles once you have written pencil marks for every empty cell. Look for this technique when:

• You have already applied Naked Pairs and are still stuck.
• Several cells in a unit have only two or three candidates remaining.
• No naked singles or hidden singles are visible — you need to reduce candidates before the next digit can be placed.

Step-by-Step Examples

Naked Triples work the same way in a box, a row, or a column. The three examples below show all three unit types.

Naked Triple in a Box

In box 5 (the centre box), cells D4, E4, and F4 sit in the top row of the box. Their candidates are D4 = {1,5}, E4 = {5,9}, F4 = {1,9}. Together they cover exactly three digits: 1, 5, and 9.

1. Write pencil marks for all empty cells in box 5.
2. Look for cells with only two or three candidates.
3. Spot D4 = {1,5}, E4 = {5,9}, F4 = {1,9}. The union of these three sets is {1,5,9} — exactly three distinct digits across three cells.
4. Conclude: digits 1, 5, and 9 must fill D4, E4, and F4 in some order. No other arrangement is possible.
5. Those three digits are now reserved for D4, E4, and F4 within box 5.
6. Scan the remaining empty cells in box 5 and remove 1, 5, and 9 from their candidate lists.
7. D5 loses candidate 5: {2,5,6} → {2,6}.

When three cells in a box collectively hold only three candidates, lock those digits in and clear them from every other empty cell in the box.

Naked Triple in a Row — the Chain Form

Row 6 contains three empty cells whose candidates form the union {2,6,8}: A6 = {2,8}, C6 = {2,6}, H6 = {6,8}. Notice that no single cell holds all three digits — this is called the chain form and is the hardest variant to spot.

1. Scan row 6 for empty cells with two or three candidates.
2. Find A6 = {2,8}, C6 = {2,6}, H6 = {6,8}.
3. Check the union: {2,8} ∪ {2,6} ∪ {6,8} = {2,6,8} — exactly three digits across three cells.
4. Digits 2, 6, and 8 are locked into A6, C6, and H6 in some order.
5. Eliminate 2, 6, and 8 from all other empty cells in row 6.
6. B6: {1,2,6} → {1}; E6: {1,6,8} → {1}; G6: {2,3,6} → {3}.
7. B6 and E6 both become naked singles — the naked triple unlocked two immediate placements.

The chain form — where no single cell holds all three candidates — works by exactly the same logic. The union of candidates across the three cells is all that matters.

Naked Triple in a Column

In column E, three empty cells E2, E5, and E8 form a naked triple for digits {4,7,9}: E2 = {4,7}, E5 = {7,9}, E8 = {4,9}. The remaining empty cells in the column — E3 and E6 — carry some of those digits and will have them eliminated.

1. Scan column E for cells with two or three candidates.
2. Find E2 = {4,7}, E5 = {7,9}, E8 = {4,9}.
3. Union = {4,7,9} — three distinct digits in three cells.
4. Digits 4, 7, and 9 are locked into E2, E5, and E8 within column E.
5. Eliminate 4, 7, and 9 from all other empty cells in column E.
6. E3: {2,4,7} → {2}; E6: {3,7,9} → {3}.
7. Both E3 and E6 become naked singles — place them immediately.

Naked Triples work identically in columns. Once the triple is identified, clean up the rest of the column in one pass.

How to Spot Naked Triples

Naked Triples can be tricky to see at first, especially the chain form. These tips will help you find them faster. Make sure you have a full set of pencil marks written before you start scanning.

• Start with cells that have only two candidates. Two-candidate cells often form chains: {XY} + {YZ} + {XZ} is a valid triple even though no cell holds all three digits.
• If you have found all naked pairs and are still stuck, widen your scan to groups of three cells within each unit.
• A triple that spans the top or bottom row of a box also eliminates candidates from the rest of that row outside the box — apply both eliminations at once.
• Sudoku apps and pencil mark tools often highlight naked triples automatically — use them to train your eye before finding them by hand.

The same logic that makes naked triples work extends naturally to Naked Quads — four cells sharing exactly four candidates. Once you are comfortable with triples, quads follow immediately. You can also look for the complementary Hidden Triples technique in our full solving guide.

Practice Naked Triples Online

Naked Triples appear most often in hard puzzles where naked pairs alone are not enough to advance. Play hard sudoku on OnSudoku with pencil marks enabled and scan each unit for groups of three cells whose combined candidates form exactly three distinct digits.

For a complete overview of solving strategies from beginner to advanced, visit our How to Solve Sudoku guide.