Killer triple
In Killer Sudoku, when three cells in the same unit are confined to the same three-digit set by their cage's arithmetic — eliminating those digits from elsewhere in the unit.
A killer triple is the three-cell version of the killer pair. It's three cells in the same unit whose cage arithmetic forces them collectively to hold the same three-digit set. The three digits can be eliminated from every other cell in the unit.
How to spot one
The classic trigger: a three-cell cage with very few possible digit combinations, sitting entirely within one unit. A three-cell cage summing to 7 must be {1, 2, 4} — there's no other set of three distinct digits 1-9 that sums to 7. A three-cell cage summing to 24 must be {7, 8, 9}. When such a cage lives inside a single row, column, or box, those three digits are locked to those three cells, and ruled out from the unit's other cells.
A subtler trigger: two cages whose union covers three cells in one unit, and whose combined arithmetic narrows them to a three-digit set. The solver handles this; spotting it manually takes practice.
Worked example: column 5 contains a three-cell cage with sum 24. The cage must be {7, 8, 9}. All three cells sit in column 5. So 7, 8, and 9 occupy those three cells; every other cell in column 5 can have 7, 8, and 9 ruled out.
How it relates to the naked triple
A naked triple is spotted from pencil marks: three cells whose candidate union is three digits. A killer triple is spotted from cage arithmetic: three cells whose cage sum forces a three-digit set. They reach the same elimination by different routes. On killer puzzles, the cage path usually fires earlier in the solve.
For an introduction to Killer Sudoku and where killer triples fit in the broader technique set, see Meet Killer Sudoku.
See also
- Killer pair— In Killer Sudoku, when two cells in the same unit are confined to the same two-digit pair by their cage's arithmetic — eliminating those digits from elsewhere in the unit.
- Naked triple— Three cells in the same unit whose candidates collectively use only three digits. Together they claim those digits across the unit and rule them out elsewhere.
- Cage— In Killer Sudoku, a contiguous group of cells outlined by a dotted line, with a printed sum the digits inside must add up to. Replaces the classic Sudoku given.
- Unique combinations— In Killer Sudoku, cage sums whose cell count and total leave only one possible digit set. The arithmetic shortcut behind most killer pair and triple deductions.
Read more
- Meet Killer Sudoku
An introduction to Killer Sudoku for someone who knows the classic version — what changes, how the experience differs, and where to start.