Which cage totals have only one possible combination?
Forced cages are cages with a total achievable in only one way using unique digits. They are the first thing to identify in any Killer Sudoku puzzle because they give you free candidate information with no calculation required.
2-Cell Forced Cages
| Cage Sum | Only Combination | Why |
|---|---|---|
| 3 | {1, 2} | Minimum possible sum |
| 4 | {1, 3} | {2,2} repeats - Invalid |
| 16 | {7, 9} | {8,8} repeats - Invalid |
| 17 | {8, 9} | Maximum possible sum |
3-Cell Forced Cages
| Cage Sum | Only Combination |
|---|---|
| 6 | {1, 2, 3} |
| 7 | {1, 2, 4} |
| 23 | {6, 8, 9} |
| 24 | {7, 8, 9} |
4-Cell Forced Cage
| Cage Sum | Only Combination |
|---|---|
| 10 | {1, 2, 3, 4} |
How to Use Forced Cages
When you identify a forced cage, immediately write the combination candidates for each cell. A 2-cell {1,2} cage: both cells get candidates {1,2}. This pair also forms a naked pair within its unit - Remove 1 and 2 from all other cells in the shared row, column, or box. Forced cages give you candidate information and naked pairs simultaneously.
Related Questions
Spot Forced Cages in a Killer Puzzle