Killer Sudoku: Rules, Combinations & Strategies

The complete guide to the world's most popular Sudoku variant - rules, a full combinations table, and 6 strategies to solve any puzzle.

Killer Sudoku takes the familiar 9×9 grid and replaces the given numbers with something more interesting: cages with target sums. Instead of starting with a handful of filled-in digits, you start with dotted outlines and small numbers that tell you what the digits inside must add up to.

The result is a puzzle that blends classic Sudoku elimination with arithmetic reasoning. You still can't repeat a digit in any row, column, or 3×3 box. But now you also can't repeat a digit within a cage, and every cage must hit its target sum. Two constraint systems, one grid - and solving requires both.

This guide covers everything you need: the rules, the complete combinations reference table for cage sizes 2 through 5, and 6 strategies that will take you from your first Killer puzzle to confident solving.

Quick links: Rules · Combinations Table · Strategies · All Sudoku Variants · Standard Sudoku Strategies

What Is Killer Sudoku?

The Standard Sudoku Rules Still Apply

Every row, column, and 3×3 box must contain the digits 1–9, each exactly once. This never changes. If you know standard Sudoku rules, you already know half of Killer Sudoku.

The Killer Rules (What's New)

1. Cages: The grid is divided into groups of cells called "cages," outlined by dotted lines. Each cage contains 2–5 cells (occasionally more in harder puzzles).
2. Cage sums: Each cage has a small number in its corner - the target sum. The digits inside the cage must add up to exactly that number.
3. No repeats in cages: You cannot use the same digit twice within a single cage. Combined with the row/column/box rule, this is your most powerful constraint.
4. No given digits: Unlike standard Sudoku, Killer puzzles typically start with an empty grid. All information comes from the cage sums.

A Quick Example

Imagine a 2-cell cage in a row with a target sum of 4. The only way to make 4 from two different digits (1–9) is 1+3. So this cage must contain 1 and 3 - you just don't know which cell gets which number yet. That's where standard Sudoku logic comes in: check the row, column, and box to figure out the placement.

Killer Sudoku Combinations Table

This is the reference you'll use constantly. For each cage size (2–5 cells) and each possible sum, the table lists every valid combination of digits. Bookmark this page - you'll come back to it.

How to read the table: Find your cage size, then find the sum. The "Combinations" column shows every possible set of digits. The "Count" column tells you how many options you have - fewer options means more information.

2-Cell Cages (Sums 3–17)

Key insight: Sums of 3, 4, 16, and 17 have only one possible combination each. These are your freebies - the digits are locked in, you just need to determine which cell gets which number.

3-Cell Cages (Sums 6–24)

Key insight: The extremes are powerful. A 3-cell cage summing to 6 or 7 (or 23 or 24) has only one combination, immediately locking in which three digits go there.

4-Cell Cages (Sums 10–30)

5-Cell Cages (Sums 15–35)

Quick-Reference: Unique Combinations (Only 1 Possibility)

These cage sums have exactly one valid combination - they're the first things to fill in:

6 Strategies for Solving Killer Sudoku

1. Start with Unique Combinations

Before anything else, scan the grid for cages that have only one possible combination. A 2-cell cage summing to 3? That's 1 and 2, guaranteed. A 3-cell cage summing to 24? Must be 7, 8, and 9. Use the quick-reference table above - these are free information.

Even when the exact placement isn't clear yet, knowing which digits belong in a cage eliminates candidates from the rest of the row, column, and box.

2. Use the "Rule of 45"

Every row, column, and 3×3 box sums to exactly 45 (because 1+2+3+4+5+6+7+8+9 = 45). This is one of the most powerful tools in Killer Sudoku.

How it works: If all but one cage in a row are fully contained within that row, you can calculate the value of the remaining cell(s) by subtracting the known cage sums from 45.

Example: A row contains three complete cages summing to 12, 15, and 9 - that's 36. The remaining cells must sum to 45 − 36 = 9. If there's just one remaining cell, it must be 9. If there are two remaining cells, they must sum to 9.

This technique is especially useful for "innies" (cells inside a region but outside all cages that are fully in that region) and "outies" (cells in a cage that extends outside a region).

3. Cross-Reference Cages with Rows, Columns, and Boxes

A digit that appears in every possible combination for a cage is guaranteed to be in that cage. Use this to eliminate that digit from other cells in the same row, column, or box.

Example: A 3-cell cage sums to 7. The only combination is {1,2,4}. If this cage sits entirely within one 3×3 box, then 1, 2, and 4 are taken - no other cell in that box can contain those numbers.

Work the other direction too: if a row already contains a 5, you can eliminate every combination that includes 5 from any cage in that row.

4. Look for Naked and Hidden Sets

The same techniques from standard Sudoku - naked pairs, hidden pairs, triples, and quads - work in Killer Sudoku. They're especially effective when cage constraints have narrowed candidates down.

If two cells in a row can only contain {3,7}, those digits are locked. Remove 3 and 7 from every other cell in that row. This cascading elimination often unlocks cells that arithmetic alone couldn't resolve.

5. Eliminate from Overlapping Constraints

Every cell in a Killer Sudoku grid belongs to four constraint groups: a row, a column, a 3×3 box, and a cage. When a cage spans two boxes, the digits in each box-portion of the cage are constrained by both the cage sum and the box.

Look for cells that sit at the intersection of a tightly constrained cage and a mostly-filled row or column. These intersections are where digits get forced into place.

6. Work the Extremes of Cage Ranges

For every cage, you can calculate the minimum and maximum possible value for any single cell. In a 3-cell cage summing to 20, the three digits must be distinct and from 1–9. The smallest possible trio is {3,8,9} (min digit: 3), and the largest is {5,7,8} (max digit: 8). So no cell in this cage can be 1 or 2, and no cell can be 9.

This "range narrowing" is most useful for mid-range sums where the combinations table shows many options but the extreme digits are consistent across all of them.

Frequently Asked Questions

Is Killer Sudoku harder than regular Sudoku?

Generally, yes. Killer Sudoku requires both standard elimination and arithmetic reasoning. Most players who are comfortable with medium-to-hard standard Sudoku find Killer Sudoku challenging but learnable. The combinations table makes the arithmetic manageable - the real skill is combining cage constraints with row/column/box logic.

Do I need to be good at math?

Not really. You need basic addition with single digits (sums up to 45). The combinations table does the heavy lifting. Once you've memorized the common sums (like "two cells summing to 3 must be 1+2"), the arithmetic becomes second nature.

Where can I find Killer Sudoku puzzles?

Killer Sudoku appears in many newspaper puzzle sections and dedicated puzzle apps. For standard Sudoku practice with a clean, distraction-free interface, try the Sudoku a Day app - it's a great way to build the elimination skills that transfer directly to Killer Sudoku.

What's the difference between Killer Sudoku and Kakuro?

Both use cage sums, but they're different puzzles. Kakuro uses a crossword-style grid where you fill runs of cells with digits that sum to a clue - there are no 3×3 box constraints. Killer Sudoku uses the full 9×9 Sudoku grid with all the standard row/column/box rules plus cages. Think of Killer Sudoku as "Sudoku with cage sums" and Kakuro as "crossword with digit sums."

Keep Exploring

• All Sudoku Variants - Diagonal, Samurai, Jigsaw, and more.
• Sudoku Rules - The fundamentals behind every Sudoku variant.
• Sudoku Strategies - Standard techniques that apply in Killer Sudoku too.
• Printable Sudoku Puzzles - Free weekly PDF packs to practice elimination skills.