Killer pair

A killer pair is the cage-flavoured cousin of the naked pair. It's two cells in the same unit whose cage arithmetic forces both cells to hold the same two-digit set. Once spotted, those two digits can be eliminated from every other cell in the shared unit.

How to spot one

The trigger is usually a small cage with very few possible digit sets. A two-cell cage summing to 4 must be {1, 3} (since {2, 2} is illegal). A two-cell cage summing to 17 must be {8, 9}. When such a cage sits entirely within a single row, column, or box, those two digits are locked to those two cells inside the unit — and ruled out from the unit's other cells.

Worked example: row 3 contains a two-cell cage with sum 17. The cage must be {8, 9}. Both cells of the cage sit in row 3. So 8 and 9 must occupy those two cells, and every other cell in row 3 can have 8 and 9 ruled out.

When the cage doesn't sit entirely in a unit

If the two-cell cage spans two units (say it crosses a box boundary), the killer-pair logic still applies inside each unit individually — the digit pair appears in two cells of one unit and one cell of another. Sudoku Mountain's solver handles both shapes; the technique label is the same.

Why it works

Killer pairs reduce to the standard naked-pair argument once the cage has narrowed the cells' candidates. The difference is that a naked pair is spotted from pencil marks; a killer pair is spotted from cage arithmetic — usually before the pencil marks would have made the same claim visible. On killer puzzles you'll often place 80% of your eliminations before drawing pencil marks at all, because cage logic gets there faster.

For an introduction to Killer Sudoku and where killer pairs fit in the broader technique set, see Meet Killer Sudoku. The next-step extension — three cells, three digits, same logic — is the killer triple.