Obvious Triples

A conspiracy of three. You will walk past it more than once.

Obvious Triples — also called Naked Triples — extends the logic of Obvious Pairs from two cells to three. It occurs when three cells in the same row, column, or 3×3 box collectively contain exactly three distinct candidate digits between them, even if no single cell lists all three — configurations like {A,B}, {A,C}, {B,C} qualify just as much as three identical {A,B,C} cells.

Because those three digits have to be distributed across exactly those three cells, and nowhere else in the region has room for them, all three digits can be eliminated from every other cell in that row, column, or box. Obvious triples are harder to spot than pairs, since the three candidate sets rarely match exactly and a scan has to check combined membership rather than an identical pattern. Regions that resist an obvious triple are worth checking for a hidden triple or a pointing triple instead.

How It Works

Three cells in the same row, column, or box form an obvious triple if together they contain exactly three distinct candidate digits and no others. Common configurations include:

  • {A, B}, {A, C}, {B, C}
  • {A, B}, {A, B, C}, {B, C}
  • {A, B, C}, {A, B, C}, {A, B, C}

In every case, digits A, B, and C must be distributed among those three cells. They cannot appear anywhere else in the region.

  1. Find three cells in the same region whose combined candidates total exactly three distinct digits.
  2. Remove those three digits from all other cells in that region.
  3. Recheck for naked singles and pairs.

Example

Below board presents an example of an obvious triple on digits 2, 5, and 8, spread across three cells.

the obvious triple {2, 5, 8}
eliminated by the triple

These three cells hold nothing but 2, 5, and 8 between them — no single cell has all three, but no digit outside the set appears in any of them either. Whichever arrangement resolves the triple, 2, 5, and 8 are spoken for. Any other cell in the box holding one of those digits as a candidate loses it.

On Evil Boards

The naked triple is harder to spot than the naked pair — three cells instead of two, and the configurations are varied enough to evade casual scanning. They do not appear often, and they often do not give much. If the region resists, check it for a hidden triple — the same three digits, hiding among other candidates instead of standing alone — or a pointing triple if a box is involved.