From the rulebook
How to Solve Killer Sudoku
Killer Sudoku, also called sum Sudoku, keeps every rule of standard Sudoku but starts with no given digits. Instead the grid is split into dotted cages, and the digits in each cage must add up to its printed total without repeating. Those cage sums replace the starting clues, and once you know how to read them they give you more to work with, not less. This guide takes you from the rules to the techniques that crack hard cage grids.
The rules of Killer Sudoku
A Killer Sudoku is a 9 by 9 grid split into nine 3 by 3 boxes, exactly like standard Sudoku. Your job is to fill every cell so that each row, each column and each 3 by 3 box contains the digits 1 through 9 exactly once.
On top of that, the grid is divided into cages marked by dotted outlines, each printed with a small total. The digits inside a cage must add up to that total, and no digit may repeat within a single cage. Unlike standard Sudoku there are usually no given digits, so the cage sums are your only starting information.
Start with the extreme cages
The fastest opening move is finding cages whose sum can only be made one way. A two-cell cage totalling 3 must be 1 and 2. A two-cell cage totalling 4 must be 1 and 3, since 2 and 2 would repeat. At the top end a two-cell cage totalling 17 must be 8 and 9, and one totalling 16 must be 7 and 9. A three-cell cage totalling 6 must be 1, 2 and 3.
These locked combinations do not tell you the order of the digits yet, but they do tell you exactly which digits live in the cage. That lets you eliminate those digits from the rest of the row, column or box the cage touches, which is often enough to start placing numbers.
Use the rule of 45
Every row, every column and every 3 by 3 box contains 1 through 9, so each one sums to 45. This rule of 45 is the signature Killer Sudoku technique. Add up the cage totals that sit fully inside a single row, column or box, and the difference from 45 tells you the sum of the cells left over.
When a single cell pokes out of a box, the rule of 45 pins it exactly. Total the cages inside the box, subtract from 45, and the remainder is the value of that one stray cell. Extending the trick across two or three lines at once is how you break into the toughest grids.
Track cage combinations as candidates
When the obvious moves run out, write candidate pencil marks driven by the cage maths. For each cage, list the digit combinations that reach its total without repeating, then cross off any combination blocked by digits already placed in the cells the cage shares with its rows, columns and boxes.
A cell sitting at the crossing of a tight cage and a busy row often has only one surviving candidate. Cells where a small cage meets a nearly full box are the best place to look for these forced placements.
Combine cage logic with ordinary Sudoku
Killer Sudoku is still Sudoku underneath. Once cage sums let you place a few digits, switch on the standard tools: scanning a digit across rows, columns and boxes, naked pairs, hidden pairs and pointing pairs. Each placement you make from cage arithmetic feeds the ordinary eliminations, and each ordinary elimination narrows the cage combinations in turn.
Apply the techniques in order: lock the extreme cages first, then the rule of 45, then cage combinations as candidates, then standard Sudoku logic, looping back as the grid fills. On Puzzle Lair every Killer Sudoku is guaranteed solvable by logic alone, so if you are stuck there is always a deduction waiting, never a guess.
Frequently asked questions
- What is Killer Sudoku?
- Killer Sudoku, also called sum Sudoku, is Sudoku with cage sum clues instead of given digits. Each row, column and 3 by 3 box still holds 1 through 9 once, but the grid is also split into dotted cages, and the digits in each cage must add up to its printed total without any digit repeating inside the cage.
- What is the rule of 45 in Killer Sudoku?
- Every row, column and 3 by 3 box contains 1 through 9, so each one sums to 45. Adding the totals of the cages that sit inside a single line and subtracting from 45 gives the sum of the remaining cells. When only one cell is left over, the rule of 45 fixes its exact value.
- How do you start a Killer Sudoku?
- Begin with cages whose total can only be made one way. A two-cell cage of 3 is 1 and 2, a two-cell cage of 17 is 8 and 9, and a three-cell cage of 6 is 1, 2 and 3. These locked combinations tell you which digits live in the cage, letting you eliminate them from the rest of that row, column and box.
- Can a digit repeat inside a Killer Sudoku cage?
- No. A digit can never repeat within a single cage, on top of the normal Sudoku rule that it cannot repeat in a row, column or box. This is why a two-cell cage of 4 must be 1 and 3 rather than 2 and 2, and it is central to working out which combinations a cage allows.
- Does solving Killer Sudoku ever require guessing?
- No. A well-made Killer Sudoku has exactly one solution reachable by pure logic. Every Puzzle Lair Killer Sudoku is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet, often a cage sum or rule-of-45 check you have not run.