What are the rules of Killer Sudoku?

Fill a 9×9 grid so that every row, column, and 3×3 box contains the digits 1–9 exactly once (standard Sudoku rules). Additionally, the grid is divided into dotted-line cages, each with a small sum clue. The digits in each cage must add up to that sum, and no digit may repeat within a cage.

How is Killer Sudoku different from regular Sudoku?

In regular Sudoku, some digits are pre-filled as clues. In Killer Sudoku, no digits are given. Instead, cells are grouped into cages with sum clues. You must use both the sum constraints and standard Sudoku elimination to deduce every digit.

What are cage combinations in Killer Sudoku?

A cage combination is a set of distinct digits that add up to the cage's sum. For example, a 2-cell cage with sum 4 can only be {1,3} since {2,2} would repeat. Knowing all possible combinations for a cage is a key solving technique.

What is the 45-rule in Killer Sudoku?

Every row, column, and 3×3 box in Sudoku contains digits 1–9, which always sum to 45. In Killer Sudoku, if you know the cage sums for all but one group of cells within a row, column, or box, you can calculate the missing value. This is called the Rule of 45 (or innies and outies) and is one of the most powerful Killer Sudoku strategies.

Play Killer Sudoku Online

Q: Can Killer Sudoku be solved without guessing?

Yes. Well-constructed Killer Sudoku puzzles can always be solved using logic alone, combining Sudoku elimination techniques with cage-sum arithmetic. Our generator ensures every puzzle has a unique solution solvable without trial and error.

Sudoku meets Kakuro — fill the 9×9 grid using cage sum clues with 4 difficulty levels. Notes, undo & error checking — all free.

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What Is Killer Sudoku?

Killer Sudoku (also called Sum Sudoku or Samunamupure) is a popular number-placement puzzle that blends the logic of standard Sudoku with the arithmetic of Kakuro. Like regular Sudoku, you must fill a 9×9 grid so that every row, column, and 3×3 box (also called a nonet) contains the digits 1 through 9 exactly once.

The twist? Instead of pre-filled numbers, the grid is divided into groups of cells called cages, outlined with dashed borders. Each cage shows a sum clue — the digits inside must add up to that number, and no digit may repeat within a cage. This extra constraint is what makes Killer Sudoku so engaging: you combine Sudoku elimination techniques with cage-sum arithmetic to crack every cell.

History of Killer Sudoku

Killer Sudoku first appeared in Japan in 2004, published by the puzzle company Nikoli in their magazine. It was quickly picked up by The Times of London in 2005, which branded it “Killer Sudoku” — the name that stuck worldwide. Before that, similar sum-based Sudoku variants existed in Japanese puzzle magazines under names like Samunamupure (a portmanteau of “sum” and “number place”).

The puzzle rapidly gained popularity alongside the global Sudoku craze of 2005–2006. Today, Killer Sudoku appears in newspapers, puzzle books, and dedicated apps. It is a staple of the World Puzzle Championship and is considered a natural next step for Sudoku enthusiasts looking for a greater challenge.

Rules of Killer Sudoku

Standard Sudoku rules apply: Each row, column, and 3×3 box must contain the digits 1–9 exactly once.
Cage sums: Cells are grouped into cages (shown with dashed borders). A small number in the top-left corner of each cage is its target sum.
No repeats in cages: Digits within a single cage must all be different — even if the cage spans multiple rows, columns, or boxes.
No given digits: Unlike standard Sudoku, Killer Sudoku typically starts with an empty grid. All information comes from the cage sums.

How to Play

Choose a difficulty level. Easy uses larger cages with more constrained sums; Expert has trickier cage layouts requiring advanced techniques.
Tap a cell to select it. Then tap a number on the pad to fill it in.
Use Notes mode (pencil icon) to write small candidate numbers in cells when you’re not yet sure of the answer.
Check your work with the Check button — errors are highlighted in red.
Undo any move, or Erase the selected cell.

Difficulty Levels Explained

Easy: Small cage sizes (mostly 2–3 cells), many cages with forced combinations. Great for beginners learning cage arithmetic.
Medium: Larger cages and more possible combinations. Requires combining cage analysis with standard Sudoku elimination.
Hard: Complex cage layouts that span multiple boxes. Needs the Rule of 45 (innies/outies) and intersection analysis.
Expert: Minimal constraint hints, large cage sizes, and layouts that demand advanced strategies like X-Wing, cage splitting, and multi-step deduction chains.

Killer Sudoku Strategy & Tips

1. Learn the Cage Combinations

The foundation of Killer Sudoku solving is knowing which digit combinations produce a given sum. For example, a 2-cell cage summing to 3 can only be {1, 2}. A 2-cell cage summing to 17 can only be {8, 9}. These forced combinations give you immediate candidate restrictions. Memorising the extremes (very low and very high sums for each cage size) is the fastest way to improve.

2. The Rule of 45 (Innies & Outies)

Every row, column, and 3×3 box contains digits 1–9, which always sum to 45. If all cages within a region are entirely contained in that region, you can calculate any unknown. When a cage extends outside the region, the cells inside are called innies and the cells outside are outies. The difference between cage sums and 45 reveals the innie/outie values — one of the most powerful techniques in Killer Sudoku.

3. Naked & Hidden Singles

Just like standard Sudoku, if only one digit remains possible for a cell (a naked single) or only one cell in a unit can hold a particular digit (a hidden single), you can fill it in immediately. Use pencil notes to track candidates after applying cage constraints.

4. Cage-Line Interaction

When a cage lies entirely within a single row or column, its digits are restricted both by the cage sum and the row/column uniqueness rule. This cage-line interaction often eliminates candidates that cage analysis alone would not.

5. Naked Pairs & Triples in Cages

If two cells in a cage can only contain the same two digits, those digits are locked to those cells and can be eliminated from other cells in the same row/column/box. This extends naturally to triples and quads.

6. Cross-hatching with Cage Constraints

Combine standard Sudoku cross-hatching (scanning rows and columns to find where a digit can go in a box) with cage-sum restrictions. A digit might be possible in a box by Sudoku rules but impossible in a cage because it would violate the sum or the no-repeat rule.

Killer Sudoku Cage Combination Reference

Here are key forced combinations for 2-cell and 3-cell cages:

2 cells, sum 3: {1, 2}
2 cells, sum 4: {1, 3}
2 cells, sum 16: {7, 9}
2 cells, sum 17: {8, 9}
3 cells, sum 6: {1, 2, 3}
3 cells, sum 7: {1, 2, 4}
3 cells, sum 23: {6, 8, 9}
3 cells, sum 24: {7, 8, 9}

Killer Sudoku vs Other Puzzles

vs Sudoku: Standard Sudoku gives you pre-filled digits; Killer Sudoku gives you cage sums instead. Killer requires arithmetic alongside logic.
vs Kakuro: Both use sum clues, but Kakuro has a crossword-style grid with black cells, while Killer Sudoku uses the full 9×9 Sudoku grid with row/column/box constraints.
vs KenKen: KenKen uses all four arithmetic operations (+, −, ×, ÷) on variable-sized grids. Killer Sudoku uses only addition on the standard 9×9 grid.

Frequently Asked Questions

Fill the 9×9 grid so every row, column, and 3×3 box contains digits 1–9 exactly once. Cells are grouped into cages with a sum clue — the digits in each cage must add up to that sum with no repeats.

In regular Sudoku, some digits are pre-filled. In Killer Sudoku, the grid starts empty and you get cage-sum clues instead. You need both arithmetic and Sudoku elimination to solve it.

Yes. Every puzzle on this page has a unique solution that can be reached by logic alone. Techniques include cage combination analysis, the Rule of 45, naked/hidden singles, and cross-hatching.

Every row, column, and 3×3 box sums to 45 (1+2+…+9). If you know the cage sums for most cells in a unit, you can calculate the unknown values. This technique, also called innies and outies, is essential for harder puzzles.

The sets of distinct digits that add up to a cage’s target sum. For example, a 2-cell cage with sum 4 can only be {1, 3}. Knowing these narrows candidates immediately. Low and high sums for each cage size are most restrictive.

More Puzzle & Strategy Games

If you enjoy Killer Sudoku, try these other free games on our site:

Sudoku

The classic 9×9 number puzzle with 6 difficulty levels from Easy to Extreme.

Kakuro

Cross-sum puzzle — fill digits so segments add up to the given clues.