Naked Triple sudoku technique

Intermediate level Appears in puzzles rated SE 2.0 – 2.5

Three cells in a unit form a naked triple when, between them, they hold only three distinct candidates. The cells do not need to show all three digits each — lists like 1-4, 4-9 and 1-9 qualify just as well as three full 1-4-9 cells. However the digits distribute, those three cells will consume those three digits, so the rest of the unit can be swept clean of them.

How to find a naked triple

  1. Pencil-mark a stubborn unit completely.
  2. Hunt for three cells whose combined candidates form a set of exactly three digits.
  3. Remove those three digits from every other cell in the unit.
  4. Re-examine the unit — triples usually break the logjam that pairs could not.
From the table: The broken form trips people up: 1-4, 4-9, 1-9 is a perfectly good triple even though no cell shows all three digits. Count distinct candidates across the trio; three cells, three digits total, is all the definition there is.

The pattern on the grid

14449919

r3c2, r3c5 and r3c9 share the digit set {1,4,9} — those digits vanish from the rest of row 3.

Worked example

Row 3 shows r3c2 with 1-4, r3c5 with 4-9 and r3c9 with 1-9. Three cells, and their combined candidates are just {1, 4, 9} — a naked triple in its broken form, no cell holding all three. The trio will absorb those digits however they fall, so the 4 pencilled at r3c4 and the 9 at r3c7 are removed from the rest of the row.

When it fails

Four distinct digits across the three cells means no triple, full stop. And remember the count is over the union: 1-4, 4-9, 1-9 works precisely because the union stays at three.

Puzzles that need it

These grids come from rated games on this site — our solver confirmed that naked triple was part of the shortest solving path for each one.

1985412938244536675937861991
Expert SE 3.0 28 clues
21975231473978426134837982627
Expert SE 3.0 29 clues
69285182571582637538945837
Expert SE 3.0 26 clues

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