THE CONSTRAINT THAT CHANGES EVERYTHING
Standard Sudoku gives you digits and asks you to fill the grid. Killer Sudoku gives you cages: irregular groups of cells with a required sum. The rules from standard Sudoku still apply — every row, column, and 3×3 box must contain digits 1 through 9 exactly once. But each cage also has its own uniqueness rule: no digit may repeat within a cage.
This is the constraint most beginners underweight. A cage of three cells summing to 6 could be {1, 2, 3} in any order — but it cannot be {1, 1, 4} or {2, 2, 2}. The no-repeat rule is what makes Killer solvable without the given digits. Without it, the cages alone wouldn't constrain the puzzle enough.
FORCED COMBINATIONS — WHERE TO START
The most powerful entry point into any Killer Sudoku puzzle is finding cages where the target sum and cell count together force a specific set of digits. With only one valid digit set, you know exactly which digits are in the cage — even if you don't yet know their order.
The clearest examples: a 2-cell cage summing to 3 can only be {1, 2}. A 2-cell cage summing to 17 can only be {8, 9}. A 3-cell cage summing to 6 can only be {1, 2, 3}. A 3-cell cage summing to 23 can only be {6, 8, 9}. Any cell in such a cage narrows the possible digits for its entire row, column, and box — the same elimination logic as a given digit in standard Sudoku.
Scan all cages at the start of the puzzle. Mark forced combinations first — they give you the most information for the least work.
SINGLE-CELL CAGES AND NEAR-FORCED CAGES
When a cage contains only one cell, the sum is the digit. Place it immediately — it's a free given that Killer Sudoku rarely offers but always rewards.
Near-forced cages are almost as useful. A 2-cell cage with a sum between 3 and 17 has multiple possible combinations, but a cage summing to 16 can only be {7, 9} — just two options. A cage summing to 4 can only be {1, 3}. Even when you don't know the order, eliminating all other digits from those cells simplifies the surrounding rows and columns substantially.
Once you've placed all forced and near-forced cages, standard Sudoku elimination applies to the digits you've locked in. The two techniques work together — Killer entry, standard follow-through.
THE RULE OF 45
Every row, column, and 3×3 box in Killer Sudoku must contain the digits 1 through 9 — which always sum to exactly 45. That fixed total is the basis for the Rule of 45, one of Killer Sudoku's most powerful deductions.
If you can identify all the cages that lie entirely within a row (or column, or box), their sums must add up to 45. Any cage that crosses the boundary — part inside, part outside — can be used to derive what the boundary cell or cells must equal.
Example: a row contains four complete cages summing to 38. The remaining cell (which belongs to a cage that exits the row) must hold the digit that makes the row total 45, so it must be 7. You've placed a digit without touching the cage that contains it.
The Rule of 45 is deep enough to deserve its own treatment — see the linked post for worked examples and harder applications.
CAGE OVERLAP ELIMINATION
When two cages share a row, column, or box, their digit sets interact. If cage A in a row uses {3, 6} and cage B in the same row uses {1, 4, 8}, then neither 3, 6, 1, 4, nor 8 can appear in any other cage in that row. This is exactly the same elimination logic as standard Sudoku pairs and triples — the cage sum tells you the digit set, and the digit set excludes those values from the shared unit.
The harder version: when a cage spans two boxes, the digits in the cage are excluded from both boxes in the overlapping cells' rows and columns. Learning to track these cross-box interactions is the difference between solving medium Killer puzzles and stalling on hard ones.
SOLVE ORDER IN PRACTICE
Start with forced and near-forced cages — any cage where the sum and cell count together limit possible digit sets to one or two options. Place single-cell cages immediately. Apply standard Sudoku elimination to what you've locked in.
When that stalls, scan for Rule of 45 deductions — rows, columns, or boxes where the boundary cell can be calculated directly. Then look for cage overlap eliminations: cages whose digit sets rule out values from shared rows or columns.
Pencil marks become essential at medium difficulty. Mark candidate digit sets per cage, not just per cell, and update them as the surrounding grid fills in. The discipline is the same as standard Sudoku — eliminate first, place second, never guess.