Step 3 · Beginner
What is Cage Combinations? How to Solve Killer Sudoku
Narrows down which numbers can go in a cage from its total and number of cells; a number that appears in none of the possible combinations can't go in the cage.
What it is
Numbers in a cage (the dotted outline) never repeat, and they add up to the small number in its corner. So only a few combinations of different numbers can make that total.
Example: 2 cells totaling 3 can only be 1+2, 2 cells totaling 17 can only be 8+9, and 3 cells totaling 7 can only be 1+2+4.
A number that appears in none of the combinations can't go in the cage. When only one cell of a cage is left, it is the total minus the numbers already in it.
How to spot it
Start with cages whose total is very small or very large (2 cells: 3, 4, 16, 17; 3 cells: 6, 7, 23, 24). They have only one combination, so they narrow things down right away.
Example
Dotted outlines are cages, with their total in the top-left corner. Yellow cells are where to look, orange cells are the reason, red digits are candidates you can remove, and the green digit is the answer.
In the 4-cage at R8C5, the 2 cells (R8C5 and R9C5) add up to 4. Numbers in a cage never repeat, so look for 2 different numbers that make 4. The only possibilities are 1+3. Numbers in none of them (2, 4, 5, 6, 7, 8, and 9) can't go in R8C5 and R9C5. Also, with R8C5=3, the rest of the cage could not be filled from its candidates, so that number is removed too.
→ Killer Sudoku Cage Combinations Chart (2–9 Cells, All 502)