Killer Sudoku: The Complete Guide

Mastering the perfect blend of logic and arithmetic — from cage rules to the Rule of 45.

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If standard Sudoku has started to feel like "autopilot" for you, it's time to face the Killer. While the grid may look daunting with its dotted "cages" and missing starting digits, Killer Sudoku follows the same fundamental rules as the classic game — with one powerful addition: The Sum Rule. You aren't just looking for where numbers can go; you're calculating where they must go based on the total value of each cage.

Rule of 45
14 11 9 6 8 Sum of all cages = 45
Every 3×3 box contains digits 1–9, which always sum to 45. If all cages within a box are known, their total must equal 45. Any cage that crosses the box boundary can reveal the value of its cell outside the box.

This is the most powerful Killer Sudoku technique. Master it and most medium puzzles become straightforward.

What is Killer Sudoku?

Killer Sudoku combines two classic puzzle types: the logical structure of Sudoku and the arithmetic of Kakuro (cross-sums). The grid is divided into "cages" — groups of cells outlined by dotted lines with a small target sum in the corner.

Killer Sudoku — Cage Sums
9 15 8 7
Each coloured group is a "cage" with a target sum in its corner. The digits inside must add up to that sum — with no repeats allowed within the cage.
Cage = 9 (2 cells)
{1+8} {2+7} {3+6} {4+5}
Cage = 15 (3 cells)
{1+5+9} {1+6+8} {2+4+9} {2+5+8} {2+6+7} {3+4+8} {3+5+7} {4+5+6}

The full sum combination chart is below. Memorising the most common 2-cell and 3-cell cage sums dramatically speeds up your solving.

The Rules

Standard Sudoku rules apply: Every row, column, and 3x3 block must contain the digits 1–9 exactly once.

The Sum Rule: The digits within each cage must add up exactly to the cage's target number.

The No-Repeat Rule: No digit may repeat within a single cage — even if the standard Sudoku rules would otherwise allow it. This is crucial: a sum of 4 in two cells cannot be 2 + 2; it must be 1 + 3.

💡 Key Insight: Unlike classic Sudoku, Killer puzzles typically start with no given digits at all. Every number you place must be deduced entirely from the cage sums and the standard Sudoku constraints. This sounds harder — but the cage arithmetic actually gives you more information than a typical set of givens.

Key Strategies for Your First Killer Puzzle

1

Hunt for Unique Partitions First

Some cage sums have only ONE possible set of digits (called "unique partitions"). Start by identifying all cages with unique partitions — these give you immediate, certain information. 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}. Use the Sum Chart below to find them instantly.

2

Apply the No-Repeat Rule Aggressively

Always remember: a digit cannot appear twice in the same cage. This eliminates many apparently valid combinations. A cage summing to 10 in two cells could be {1,9}, {2,8}, {3,7}, or {4,6} — but never {5,5}.

3

Master the "Innies and Outies" (Rule of 45)

This is the secret weapon that separates Killer masters from beginners. Since every row, column, and block must sum to exactly 45, you can calculate the value of any cells that "stick out" of or into a region. See the full explanation below.

4

Use Standard Sudoku Logic Too

Don't forget you're still playing Sudoku! Once you've placed some digits using cage arithmetic, use Cross-Hatching, Naked Singles, and Pointing Pairs to fill in more cells — these techniques work exactly as they do in the classic game.

⚡ The Rule of 45: Killer Sudoku's Secret Weapon

Because every row, column, and 3x3 block must contain the numbers 1 through 9, the sum of any complete "house" is always 1+2+3+4+5+6+7+8+9 = 45. This fact is immensely powerful.

How to use it: Look at a 3x3 block where most cages are fully contained within the block. Add up the target sums of all those cages. If one cell of a cage "pokes out" into a different block (called an "outie"), the difference between your total and 45 tells you exactly what that protruding cell must be.

📐 Example: The cages inside a block sum to 41. One cell of one cage extends outside the block. That outside cell must equal 45 - 41 = 4. You've just solved a cell without looking at a single number on the board!

🔢 The Killer Sudoku Sum Chart

The rows highlighted in yellow are Unique Partitions — cages with only one possible combination. These are the most valuable starting points in any Killer puzzle.

2-Cell Cages

SumPossible CombinationsNotes
3{1, 2}UNIQUE Only one way
4{1, 3}(2+2 is illegal — no repeats)
5{1, 4} or {2, 3}2 combinations
6{1, 5} or {2, 4}2 combinations (3+3 illegal)
7{1, 6} or {2, 5} or {3, 4}3 combinations
10{1,9} or {2,8} or {3,7} or {4,6}Most common — 4 combinations
16{7, 9}UNIQUE Only one way
17{8, 9}UNIQUE Only one way

3-Cell Cages

SumPossible CombinationsNotes
6{1, 2, 3}UNIQUE Minimum 3-cell sum
7{1, 2, 4}UNIQUE
8{1, 2, 5} or {1, 3, 4}2 combinations
9{1, 2, 6} or {1, 3, 5} or {2, 3, 4}3 combinations
15{1,5,9} or {1,6,8} or {2,4,9} or {2,5,8} or {2,6,7} or {3,4,8} or {3,5,7} or {4,5,6}Most common — 8 combinations
23{6, 8, 9}UNIQUE
24{7, 8, 9}UNIQUE Maximum 3-cell sum

4-Cell Cages

SumPossible CombinationsNotes
10{1, 2, 3, 4}UNIQUE Minimum 4-cell sum
11{1, 2, 3, 5}UNIQUE
12{1,2,3,6} or {1,2,4,5}2 combinations
29{5, 7, 8, 9}UNIQUE
30{6, 7, 8, 9}UNIQUE Maximum 4-cell sum
💡 Pro-Tips for Using the Sum Chart:
  • The "High/Low" Strategy: If you see a 2-cell cage summing to 17, it must be 8 and 9. If you then spot an 8 elsewhere in the intersecting row, you've instantly solved both cells of that cage.
  • The "Rule of 1": The digit 1 can never appear in a 2-cell cage that sums to more than 10 (since 1's partner would have to be 9 max).
  • The "Rule of 9": The digit 9 can never appear in a 2-cell cage that sums to less than 11 (since 9's partner would have to be 1 minimum).

Ready to Try Killer Sudoku?

Find the best Killer Sudoku apps and books on our Resources page, or return to the Variants overview.

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