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Killer Sudoku Combinations - Complete Cheat Sheet

Use this interactive Killer Sudoku combinations chart to quickly look up every valid digit combination for any cage size and sum. Whether you're a beginner learning the ropes or an expert looking for a quick reference, this cheat sheet covers all possible cage combinations from 2 to 9 cells.

2 cells · Sum 3–17

SumCombinationsCount
3Unique
1 2
1
4Unique
1 3
1
5
1 42 3
2
6
1 52 4
2
7
1 62 53 4
3
8
1 72 63 5
3
9
1 82 73 64 5
4
10
1 92 83 74 6
4
11
2 93 84 75 6
4
12
3 94 85 7
3
13
4 95 86 7
3
14
5 96 8
2
15
6 97 8
2
16Unique
7 9
1
17Unique
8 9
1

The 45 Rule Explained

The 45 Rule is the most powerful technique in Killer Sudoku. Since each row, column, and 3×3 box in a standard Sudoku must contain the digits 1 through 9 exactly once, the sum of any complete row, column, or box is always 45 (1+2+3+4+5+6+7+8+9 = 45).

This means if you know the sums of all cages in a row except one, you can calculate the missing cage's contribution by subtracting the known sums from 45. This technique is especially useful when a cage spans multiple rows or boxes.

For example, if a row contains cages summing to 12, 15, and 10, the remaining cells in that row must sum to 45 − 12 − 15 − 10 = 8.

How to Use This Cheat Sheet

Select a cage size using the toggle buttons above the table. The chart will display every valid sum for that cage size, along with all digit combinations that produce it.

Combinations marked as "Unique" have only one valid set of digits - these are solved immediately once you identify the cage. When playing, cross-reference this table with the digits already placed in the same row, column, or box to narrow down possibilities.

Tip: Memorize the forced combinations for 2-cell cages (sums of 3, 4, 16, and 17) - they appear constantly and speed up your solving.

Common Cage Sums - Quick Reference

These are the must-know Killer Sudoku cage combinations. When only one set of digits can form the sum, the cage is immediately solved.

Cage SizeSumCombinationNote
231 + 2Smallest 2-cell cage
241 + 3Low 2-cell cage
2167 + 9High 2-cell cage
2178 + 9Largest 2-cell cage
361 + 2 + 3Smallest 3-cell cage
3247 + 8 + 9Largest 3-cell cage
4101 + 2 + 3 + 4Smallest 4-cell cage
4306 + 7 + 8 + 9Largest 4-cell cage

FAQ

What is the 45 rule in Killer Sudoku?
The 45 Rule states that every row, column, and 3×3 box in Sudoku sums to exactly 45 (1+2+3+...+9). In Killer Sudoku, you can use this to calculate unknown cage values by subtracting the known cage sums in a row, column, or box from 45.
What are the possible combinations for a Killer Sudoku cage?
The possible combinations depend on the cage size and target sum. For example, a 2-cell cage with sum 10 can be 1+9, 2+8, 3+7, or 4+6. A 3-cell cage with sum 10 can be 1+2+7, 1+3+6, 1+4+5, or 2+3+5. Use the interactive chart above to look up any combination.
What is the trick to Killer Sudoku?
The key trick is combining the 45 Rule with cage combination logic. Start with cages that have only one possible combination (forced cages), then use elimination within rows, columns, and boxes. Memorizing common 2-cell and 3-cell combinations speeds up solving significantly.
Can digits repeat in a Killer Sudoku cage?
No. Digits cannot repeat within a single cage, just like they cannot repeat in a row, column, or 3×3 box. This constraint is what makes cage combination analysis so powerful - it drastically limits the possible digit sets for each cage.

Printable Killer Sudoku Combinations Chart

Use your browser's print function (Ctrl+P / Cmd+P) to save this cheat sheet as a PDF for offline reference.

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