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Hidden triple in Sudoku

  • Advanced
  • Needed from Fiendish puzzles
  • 5 points in Duel

Three digits, three cells.

When three digits can only go in the same three cells of a unit, those cells are reserved for them, and every other candidate in the three cells can be removed.

How it works

A unit needs each of the three digits once. If the only cells that can take any of them are the same three cells, then those cells will hold the three digits and nothing else. Other notes in those cells are removed.

As with a naked triple, each digit does not have to appear in all three cells. One digit might fit in only two of them. What matters is that none of the three digits can go anywhere outside the three cells.

  1. Choose a unit with many empty cells.
  2. For each missing digit, note which cells it can go in.
  3. Find three digits whose possible cells, combined, are exactly three cells.
  4. Erase every other note from those cells.

A real example

112233445566778899213145656798134738948912496345345619548989324127348916891689271693451913458348952389389197613483891678916789368945231291385826873646134595967967934618345345214359592876
Hidden triple. In row 4, 3, 4 and 5 fit only in R4C1, R4C7 and R4C9, so those cells can hold nothing else.Blue: the pattern. Red: candidates that are removed. R3C7 means row 3, column 7.

The blue candidates are the three digits of the triple. In the highlighted unit they appear only in these three cells. The red candidates sharing those cells are removed.

How to spot them

This is one of the hardest basic patterns to see, because the three cells are crowded with other notes. Scan by digit instead of by cell: look for digits that appear only two or three times in a unit, and see whether three such digits keep to the same three cells. Units with six or more empty cells are where to look.

How often you need one

Rarely. Most of the time an easier move is available somewhere else on the board, and a hidden triple in a unit can often be read as a naked group among the unit's other cells. When a puzzle does need one, it is usually the single hardest step of the whole solve.

Questions

What is a hidden triple in Sudoku?

Three digits that can only go in the same three cells of a row, column or box. Those three cells must hold them, so their other candidates are removed.

How rare are hidden triples?

Rare. Many solvers go dozens of puzzles without needing one, because a simpler step is usually available.

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