Obvious Triples: The Next Level of Candidate Locking

Obvious Triples, also called Naked Triples, extends the logic of Obvious Pairs from two cells to three. When three cells within a single row, column, or 3×3 box collectively contain only three candidate numbers among them (even if not every cell contains all three), those three numbers are locked into those three cells. You can then confidently eliminate those three candidates from every other cell in the same unit.

How Obvious Triples Work

The key insight is that Obvious Triples don't require each cell to contain all three candidates. A Triple is valid if the three cells, combined, use exactly three distinct numbers. Here's how to identify and apply them:

• Step 1: Scan a unit for three cells whose combined candidate set contains exactly three distinct numbers. For example, cells with candidates 5, 7, and 7 form a triple — between them, they only use 2, 5, and 7.
• Step 2: Verify that no fourth number appears as a candidate in any of these three cells. If even one cell in the trio contains a fourth candidate (like 8), it's not a clean triple.
• Step 3: Eliminate those three numbers (2, 5, and 7 in our example) from every other cell in that unit. They are reserved for the triple's cells.

Important: Not Every Cell Needs All Candidates

This is the most common misunderstanding about Obvious Triples. Consider these three cells:

• Cell A: 5
• Cell B: 7
• Cell C: 7

None of these cells contains all three numbers, and each cell only has two candidates. But together, they form a valid Naked Triple because the union of their candidates is exactly 7 — three distinct numbers. Cell A must be 2 or 5. Cell B must be 2 or 7. Cell C must be 5 or 7. Whatever the actual assignment, these three cells will consume 2, 5, and 7 in some order. Therefore, 2, 5, and 7 cannot appear in any other cell in this unit.

This also works when one cell has all three candidates and the others have subsets:

• Cell X: 8
• Cell Y: 4
• Cell Z: 8

The union is still 8 — three numbers. This is a valid Naked Triple.

How Triples Relate to Pairs

Obvious Triples are the natural progression from Obvious Pairs. Both use the same underlying logic of "naked subsets": if N cells in a unit collectively contain only N candidate numbers, those N numbers are locked into those N cells. Pairs (N=2) are the simplest case. Triples (N=3) are harder to spot because the three cells might be spread across the unit and might not all contain the same candidates. Quads (N=4) exist in theory but are rarely needed in practice — most puzzles that require advanced techniques are solved with Pairs and Triples.

When to Use Obvious Triples

Obvious Triples appear most frequently in Hard and Expert puzzles. After you've exhausted Obvious Singles and Obvious Pairs, systematically scan each unit for triples. The payoff is significant: a single triple can eliminate candidates from up to 6 other cells in a row or column, or from up to 6 other cells in a box. These eliminations often cascade into new Obvious Singles or reveal Hidden Singles, breaking open sections of the puzzle that seemed impenetrable.

A practical tip: when scanning for triples, look for units with multiple two-candidate cells. If a row has cells with 4, 8, and 8, you've found a triple. The pattern of two-candidate cells that form an interlocking web is the telltale sign of a Naked Triple.

On Extreme puzzles, you may need to combine Obvious Triples with advanced techniques like Pointing Pairs and Hidden Singles. Triples are particularly powerful because they often reveal Hidden Singles — once you eliminate the triple's numbers from surrounding cells, a Hidden Single may emerge that was previously obscured.