How to Solve Killer Sudoku: Rules, Tips and Strategies for Beginners
Killer sudoku takes ordinary sudoku and adds arithmetic: the 9 × 9 grid is split into dashed cages, and the small number in each cage's corner tells you what its digits must add up to. Every row, column and box still needs the digits 1 to 9 exactly once — but now you also have to make the sums work, with no digit repeated inside a cage. It sounds like two puzzles at once, yet a handful of techniques crack it nearly every time. Here's how to play and how to get good fast.
The rules in one minute
Fill every cell with a digit from 1 to 9. Every row, every column and every 3 × 3 box must contain 1 to 9 exactly once — that's ordinary sudoku. On top of that, the digits inside each dashed cage must add up to the small number in the cage's corner, and no digit may repeat within a cage. A killer sudoku has exactly one solution, reachable by logic and simple arithmetic.
How to read a cage
Each dashed outline is a cage, and the little number in one corner is the sum of all the digits inside it. A two-cell cage marked 3 must contain 1 and 2 in some order; a three-cell cage marked 6 must be 1, 2 and 3. The size of the cage is just as important as the sum — a two-cell cage of 10 is 1+9, 2+8, 3+7 or 4+6, while a three-cell cage of 10 has different options entirely. On our killer sudoku generator the cages and sums are drawn exactly this way, so you can practice on a printed puzzle.
1. Start with the smallest cages
Short cages with small sums are the killer sudoku equivalent of a free clue. A two-cell cage of 3 can only be 1 + 2, a two-cell cage of 4 can only be 1 + 3, and a two-cell cage of 17 can only be 8 + 9. Whenever you place one digit of a two-cell cage, the other is forced — and the sudoku rules then tell you which digit can sit where.
2. Learn the unique cage combinations
A surprising number of cages have exactly one possible combination, and recognizing them fills cells instantly. For two-cell cages: 3 is 1+2, 4 is 1+3, 16 is 7+9 and 17 is 8+9. For three-cell cages: 6 is 1+2+3, 7 is 1+2+4, 23 is 6+8+9 and 24 is 7+8+9. When a cage's sum matches one of these, you know exactly which digits it holds — then use the crossing row, column and box to place them.
3. Use sudoku elimination inside the cages
Every cage lives inside the normal sudoku rules, so once a cage's combination is down to two options, the rest of the grid decides. If a two-cell cage of 4 (1 + 3) sits in a row that already contains a 1, the cage must be 3 + 1 in that order — or the other way around if the row has a 3. Scan the row, column and 3 × 3 box for digits you already know, and the cage places itself.
4. Apply the rule of 45
This is the signature killer sudoku technique. Every row, every column and every 3 × 3 box adds up to 45 — the sum of 1 through 9. If a set of cages fills most of a row, add their sums and subtract from 45 to find the leftover cell. For example, if three cages cover eight cells of a row and their sums total 39, the ninth cell must be 45 − 39 = 6. The same trick works on columns and boxes, and it's the fastest way to unlock the middle of the grid.
5. Look for cages that nearly fill a house
Any time cages cover all but one or two cells of a row, column or box, do the subtraction: 45 minus the cage sums leaves the uncovered cells, and their total is often small enough to pin down exactly. If two cells are left and their sum is 3, they're 1 and 2; if their sum is 17, they're 8 and 9. This "innie" logic is the same idea as the rule of 45, just applied cell by cell.
6. Use minimum and maximum limits
Cages can't hold digits below 1 or above 9, and that alone forces answers. A three-cell cage of 24 must be 7 + 8 + 9 — there's no other way to reach 24 with three digits from 1 to 9. A four-cell cage of 6 must be 1 + 1 + 1 + 3, 1 + 1 + 2 + 2 or 1 + 2 + 1 + 2 — except no digit repeats inside a cage, which leaves 1 + 2 + 1 + 2 out and leaves only combinations built from 1s and 2s. Whenever a cage's sum is very high or very low for its size, its digits are nearly forced.
7. Jot down candidate digits
In the corner of each cell, pencil in the digits the cage sum still allows. Cross digits off as the row, column and box rule them out. Killer sudoku grids get busy, and tidy pencil marks are what turn a wall of cages into a workable chart — on screen, our killer sudoku maker lets you type digits directly and check your work as you go.
8. Avoid the classic mistakes
Two errors trip up almost every beginner. First, repeating a digit inside a cage: 1 + 1 + 5 makes 7, but a cage can never hold two of the same number. Second, forgetting the ordinary sudoku rules: the cage sums are only half the puzzle, and a correct-looking cage can still break a row, column or box. Check every completed cage for both its sum and its digits, and double-check every house for repeats. If you're stuck, revealing the answer key is a great way to see the pattern you missed.
Practice with a printable killer sudoku
Killer sudoku improves with practice, and the fastest way to practice is a fresh puzzle. Generate one in seconds on the killer sudoku generator — pick a difficulty, then print the blank puzzle with its cages and sums or solve on screen with instant checking. Start on easy, where the cages are small and numerous — plenty of tight sums to crack — and work up to hard, where cages grow larger and the combinations get trickier. If you enjoy the number logic, kakuro is a natural companion puzzle — and if you want the pure sudoku rules first, our sudoku guide has you covered.