How to Solve Killer Sudoku Cages
A two-cell cage marked 3 can hold exactly one pair of distinct digits: 1 and 2. A two-cell cage marked 17 can only be 8 and 9. Killer Sudoku is built entirely out of small certainties like these. The grid starts with no given numbers at all — just cages, the dotted outlines grouping cells, each printed with a target sum. Your job is to turn those sums into digits.
A cage is a short list of digit sets
The first habit to build is reading a cage not as a sum to add up, but as the small set of digit combinations that can reach it. A cage holds distinct digits, so the options are tightly limited. A 3-cell cage summing to 7 can only be {1,2,4}. A 3-cell cage summing to 24 can only be {7,8,9}. Many cages have just one or two possible sets — those are where you start.
The extreme sums are the most valuable: they are the ones with a single combination. The smallest and largest sums for each cage size are forced, and from there each step toward the middle adds one more option. A complete cage calculator lists every sum and its sets, but you will quickly memorise the forced ones — the 3s, 4s, 16s and 17s — because they appear constantly.
A worked opening
Suppose the top-left box has a two-cell cage of 4 running down the first column, and a two-cell cage of 16 beside it. The 4 is either {1,3} (a cage cannot repeat a digit, so 2+2 is out), and the 16 is forced to {7,9}. You have not placed a digit yet, but you have already removed 1, 3, 7 and 9 from being anywhere else those cages touch — and the moment a crossing cage or the box rule rules out the 1 in that first cell, the 3 drops in and the cascade begins.
The 45 rule
Every row, column, and 3×3 box in a 9×9 grid contains the digits 1 through 9 exactly once, so each one sums to 45. That single fact is the most powerful tool in Killer Sudoku. If the cages inside a box account for 40 across their sums, the remaining cell must be 5. If a set of cages covers a box except for one cell that pokes out into the next box — an "innie" or "outie" — the 45 rule pins its value exactly.
Used across whole rows and columns, the 45 rule lets you solve regions that no single cage could. Add the cage targets fully inside the region, compare to 45 (or a multiple of 45 for several rows), and the difference is the sum of the cells that cross the boundary — often a single forced digit.
Overlap: when a digit cannot hide
Cages combine with boxes in a second useful way. If every combination a cage can take includes a particular digit, that digit must appear somewhere in the cage — even before you know which cell. A 3-cell cage of 23 can only be {6,8,9} or {7,8,9}; either way it contains both 8 and 9, so neither 8 nor 9 can sit anywhere else in a box, row, or column that the cage fully occupies. Shared digits like these quietly eliminate candidates across the grid.
The opposite is just as useful. If a cage can never contain a digit — a 2-cell cage of 4 is {1,3}, so it holds neither 2 nor any digit above 3 — then a crossing unit that needs that digit must place it in one of its other cells. Reading both what a cage must hold and what it cannot hold turns each sum into eliminations in every direction.
Then it is just Sudoku
Once cages and the 45 rule have placed a handful of digits, the ordinary Sudoku techniques take over: naked singles, hidden singles, and pointing pairs finish the job. Cage logic is the way in; standard logic is the way through. Keep pencil marks for the candidates a cage still allows in each empty cell, and let them shrink as crossings rule digits out. Whenever progress stalls, return to a fresh cage: re-read its sum as a set of combinations, intersect that set with the digits its cells can still take, and a new forced placement usually appears.
A common mistake is to start adding cages together too early, hunting for a clever 45-rule deduction before the easy forced cages are placed. Resist it. The fastest solves come from clearing every single-combination cage first, taking the placements that follow, and only then reaching for innies and outies when the simple supply runs dry.
Practice it now
Start on a 6×6 Killer, where the short cages make forced combinations appear early, and do nothing at first but place every single-combination cage. Follow the 45 rule around one box, then let the singles finish it. When the forced cages and innies feel automatic, step up to the full 9×9 board — and keep a cage calculator open until the combinations are second nature.