CageDoku3-cell cage with sum 22 in Killer Sudoku: possible combinations
By Andrew Boyko, developer of CageDoku · Updated
A 3-cell Killer Sudoku cage that adds up to 22 has 2 possible digit sets: 5-8-9, 6-7-9.
Digits in this cage
| Combinations | 5 8 96 7 9 |
|---|---|
| Always in the cage | 9 |
| Never in the cage | 1, 2, 3, 4 |
| Candidates for every cell | 5, 6, 7, 8, 9 |
How to use it
Write the candidates 5, 6, 7, 8, 9 in every cell of the cage and cross out everything else. Because 9 is in every combination, that digit is certain to sit somewhere in the cage. 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 | # |
|---|---|---|
| 5 | 5 8 9 | 1 |
| 6 | 6 7 9 | 1 |
| 7 | 6 7 9 | 1 |
| 8 | 5 8 9 | 1 |
| 9 | 5 8 96 7 9 | 2 |
Neighbouring sums
Sum 21 (3 combinations) · Sum 23 (1 combination). 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 22 contain?
Only 5, 6, 7, 8, 9. The digits 1, 2, 3, 4 never appear in this cage.
How many combinations make 22 with 3 different digits?
2: 5-8-9, 6-7-9.
Which digits are always in a 3-cell cage that sums to 22?
9 appears in every combination.
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.