In Killer Sudoku, cages outline groups of cells with a target sum. Because digits cannot repeat within a cage, certain sums can only be formed by exactly one combination of numbers. Recognizing these unique combinations instantly speeds up your solves.
What are the most important Killer Sudoku combinations?
The most important Killer Sudoku combinations are the unique "extreme sums": for 2 cells, sum 3 ([1,2]), 4 ([1,3]), 16 ([7,9]), and 17 ([8,9]); for 3 cells, sum 6 ([1,2,3]), 7 ([1,2,4]), 23 ([6,8,9]), and 24 ([7,8,9]). Memorizing unique sums immediately eliminates impossible candidates from overlapping rows and boxes.
You can test any custom cage sum and filter by included/excluded digits with our Killer Sudoku Combination Calculator.
Unique Killer Sudoku cage sums table
| Cage Size | Unique Minimum Sum | Digits Required | Unique Maximum Sum | Digits Required |
|---|---|---|---|---|
| 2 Cells | 3 | [1, 2] |
17 | [8, 9] |
| 2 Cells | 4 | [1, 3] |
16 | [7, 9] |
| 3 Cells | 6 | [1, 2, 3] |
24 | [7, 8, 9] |
| 3 Cells | 7 | [1, 2, 4] |
23 | [6, 8, 9] |
| 4 Cells | 10 | [1, 2, 3, 4] |
30 | [6, 7, 8, 9] |
| 4 Cells | 11 | [1, 2, 3, 5] |
29 | [5, 7, 8, 9] |
| 5 Cells | 15 | [1, 2, 3, 4, 5] |
35 | [5, 6, 7, 8, 9] |
All 2-cell cage combinations
| Sum | Combinations | Sum | Combinations |
|---|---|---|---|
| 3 | [1, 2] (Unique) |
11 | [2, 9], [3, 8], [4, 7], [5, 6] |
| 4 | [1, 3] (Unique) |
12 | [3, 9], [4, 8], [5, 7] |
| 5 | [1, 4], [2, 3] |
13 | [4, 9], [5, 8], [6, 7] |
| 6 | [1, 5], [2, 4] |
14 | [5, 9], [6, 8] |
| 7 | [1, 6], [2, 5], [3, 4] |
15 | [6, 9], [7, 8] |
| 8 | [1, 7], [2, 6], [3, 5] |
16 | [7, 9] (Unique) |
| 9 | [1, 8], [2, 7], [3, 6], [4, 5] |
17 | [8, 9] (Unique) |
| 10 | [1, 9], [2, 8], [3, 7], [4, 6] |
Key 3-cell cage combinations
- Sum 6: `[1, 2, 3]` (Unique)
- Sum 7: `[1, 2, 4]` (Unique)
- Sum 8: `[1, 2, 5]`, `[1, 3, 4]`
- Sum 9: `[1, 2, 6]`, `[1, 3, 5]`, `[2, 3, 4]`
- Sum 10: `[1, 2, 7]`, `[1, 3, 6]`, `[1, 4, 5]`, `[2, 3, 5]`
- Sum 21: `[4, 8, 9]`, `[5, 7, 9]`, `[6, 7, 8]`
- Sum 22: `[5, 8, 9]`, `[6, 7, 9]`
- Sum 23: `[6, 8, 9]` (Unique)
- Sum 24: `[7, 8, 9]` (Unique)
Tired of arithmetic cages?
Play pure constraint deduction without sums
If you love Latin square logic and constraint elimination but want a refreshing break from adding numbers, try Detective Sudoku on iOS. Replace math cages with suspects and floor plans.
See how Detective Sudoku works →How to use the "Rule of 45" (Innie / Outie technique)
Every complete row, column, and 3×3 box in Sudoku sums to exactly 45 ($1+2+3+4+5+6+7+8+9 = 45$). When several cages lie almost entirely inside one 3×3 box:
- Sum all cages fully contained in the box.
- Subtract from 45. The difference reveals the exact value of the remaining empty cell inside the box ("innie").
- If a cage pokes one cell outside the box ("outie"), the excess over 45 gives the exact value of the external cell.
For more solving strategies, read our Killer Sudoku Strategies Guide and check out Games Like Sudoku.
Frequently asked questions about Killer Sudoku combinations
Can digits repeat in a Killer Sudoku cage?
No. A fundamental rule of Killer Sudoku is that no digit may appear more than once inside any single dashed cage, even if the cage bends across multiple rows or columns.
What is the minimum sum for a 4-cell cage?
The minimum sum is 10, formed uniquely by `[1, 2, 3, 4]`.
What is the maximum sum for a 4-cell cage?
The maximum sum is 30, formed uniquely by `[6, 7, 8, 9]`.
How do I calculate combinations with missing digits?
Use our free Killer Sudoku Combination Calculator to toggle specific digits on or off.