CageDoku3-cell cage with sum 9 in Killer Sudoku: possible combinations
By Andrew Boyko, developer of CageDoku · Updated
A 3-cell Killer Sudoku cage that adds up to 9 has 3 possible digit sets: 1-2-6, 1-3-5, 2-3-4.
Digits in this cage
| Combinations | 1 2 61 3 52 3 4 |
|---|---|
| Always in the cage | none |
| Never in the cage | 7, 8, 9 |
| Candidates for every cell | 1, 2, 3, 4, 5, 6 |
How to use it
Write the candidates 1, 2, 3, 4, 5, 6 in every cell of the cage and cross out everything else. If the cage lies inside a single row, column or box, any digit that must be in the cage can be removed from the rest of that region. Also watch rows, columns and boxes that already contain some of these digits: a cell that sees a digit cannot hold it, and a combination that needs it can be ruled out.
If you know one digit
Once you place or deduce a digit in the cage, only the combinations containing it remain:
| Digit | Remaining combinations | # |
|---|---|---|
| 1 | 1 2 61 3 5 | 2 |
| 2 | 1 2 62 3 4 | 2 |
| 3 | 1 3 52 3 4 | 2 |
| 4 | 2 3 4 | 1 |
| 5 | 1 3 5 | 1 |
| 6 | 1 2 6 | 1 |
Neighbouring sums
Sum 8 (2 combinations) · Sum 10 (4 combinations). See the full 3-cell chart or use the calculator to add must-have or excluded digits.
Frequently asked questions
Which digits can a 3-cell cage with sum 9 contain?
Only 1, 2, 3, 4, 5, 6. The digits 7, 8, 9 never appear in this cage.
How many combinations make 9 with 3 different digits?
3: 1-2-6, 1-3-5, 2-3-4.
Which digits are always in a 3-cell cage that sums to 9?
No single digit is in every combination, so you have to narrow it down with the row, column or box.
Practice it in CageDoku
Free, ad-free Killer Sudoku and seven more variants. Hints name the technique and highlight the cells, so you learn why a digit goes where it goes.