Cage completion
In Killer Sudoku, placing the last digit of a cage by subtracting the digits already in it from the cage's sum. The cage's leftover arithmetic does the work.
Cage completion is the killer-Sudoku move where a cage has all but one of its digits already placed, and you fill in the last one by simple subtraction. The cage's sum minus the digits already in it equals the digit that goes in the empty cell.
How it works
Worked example: a four-cell cage with sum 22 already contains 9, 6, and 4. The remaining cell must be 22 − 9 − 6 − 4 = 3. Place a 3. Done.
The arithmetic is trivial — what makes the move worth a technique label is that it cascades. Every cage completion produces a placement, every placement tightens the constraints on neighbouring cells, and the next cage often becomes completable as a result. On easy and medium killer puzzles, cage completions chain through the grid the same way naked singles do in Classic.
How it differs from a naked single
A naked single places a digit because every other digit is ruled out by the cell's row, column, and box. A cage completion places a digit because the cage's arithmetic leaves only one possible value. The two often agree — a cage-completable cell is usually also a naked single by then — but the cage path reaches the conclusion faster, with simpler reasoning.
When you'll see it
Cage completion is the second-most-common deduction on easy killer puzzles, after the cage single. On harder killer puzzles it surfaces later in the solve, as cages fill up via deeper techniques and reach the one-empty-cell state.
For an introduction to Killer Sudoku and where cage completion fits in the broader technique set, see Meet Killer Sudoku.
See also
- 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.
- Cage single— In Killer Sudoku, when a one-cell cage's sum directly forces the cell's digit. The simplest possible killer deduction — the cage's sum is the cell's value.
- 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.
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.