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.
A cage is the core mechanic of Killer Sudoku. It's a contiguous group of cells outlined with a dotted line, and a small printed number in the cage's top-left corner is the sum the digits inside the cage must add up to. Cages cover every cell on the grid, with no overlaps and no gaps — a Killer Sudoku puzzle is a partition of the 81 cells into cages, each with its own sum.
How it replaces the given
Classic Sudoku gives you starting digits and asks you to fill in the rest. Killer Sudoku gives you no starting digits at all — the cage sums are the constraint that takes their place. Every cage-sum-with-its-cell-count narrows the possible digit sets considerably. A cage of two cells summing to 3 must be {1, 2} — there's no other option. A cage of three cells summing to 7 must be {1, 2, 4}. A cage of four cells summing to 30 must be {6, 7, 8, 9}. The smaller and the more extreme the sum, the more digit sets the cage rules out — and small extreme cages are the entry points solvers look for first.
Cage shapes
Cages are usually 2 to 5 cells in size and can be any contiguous shape — straight line, L-shape, T-shape, square, irregular blob. A 1-cell cage is a degenerate case where the cage sum equals the cell's digit (used in puzzle generation but rare in publishable puzzles, because it gives away a free digit).
Why the constraint matters
A cage's sum and cell count together rule out most possible digit sets via simple arithmetic. This is what techniques like the killer pair exploit. The 45 rule — every row, column, and box sums to 45 because 1 + 2 + ... + 9 = 45 — is another tool that uses cage sums against the standard unit constraint. The basic cage techniques, the cage single and the cage completion, pick up where the cage definition ends.
For an introduction to the variant as a whole, see Meet Killer Sudoku.
See also
- 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.
- 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.
- 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.
- The 45 rule— In Killer Sudoku, the fact that every row, column, and 3×3 box must sum to 45 — because 1+2+…+9 = 45. The foundational arithmetic identity behind most killer techniques.
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.