Cage Combinations Cheat Sheet — Killer Sudoku Technique
Every (cage size, cage sum) pair has a finite list of legal digit combinations. Look it up — anything outside the set is ruled out.
Killer Sudoku sudoku technique
What it is
Killer cages carry two constraints: the cage sum must equal the printed total, AND no digit repeats inside a cage. For each combination of (cage size N, cage sum S), only certain digit sets {d1, d2, ..., dN} satisfy both — and the list is short. Some (N, S) pairs have a UNIQUE combination: those cages are effectively pre-filled the moment you read them. The canonical examples are size-2 cages summing to 3 ({1, 2}), 4 ({1, 3}), 16 ({7, 9}), 17 ({8, 9}); size-3 cages summing to 6 ({1, 2, 3}), 7 ({1, 2, 4}), 23 ({6, 8, 9}), 24 ({7, 8, 9}). Larger cages have more combinations, but the cheat sheet still narrows candidates dramatically — and intersecting the cage's combinations with the cage cells' shared row/column/box constraints cuts further.
When to use it
On every cage, at the START of the solve. Crossing out impossible candidates inside each cage triggers naked singles and cascading deductions immediately. Revisit the cheat sheet whenever a placement removes candidates from a cage cell.
Worked example
A 2-cell cage summing to 4 must be {1, 3} — {2, 2} is illegal because no digit repeats in a cage. Drop 2, 4, 5, 6, 7, 8, 9 from both cells before placing anything. If the two cells share a row, the entire row also loses 1 and 3 from every other cell. The cage's digit set is locked before any cell receives a value.
Try it
The Sudoku247Online solver walks you through every move of any puzzle one logical step at a time, naming the technique that justifies each placement. Paste a puzzle to see this technique applied in real time.