Working out which digits can fill a cage slows down every killer sudoku. This calculator lists every combination for a cage size and total, and the digits all of them share. No account needed.
Cage calculator
2 combinations for 3 cells adding up to 8.
125
134
Must contain: 1
Never in this cage: 6, 7, 8, 9
Killer sudoku cheat sheet
Every total for cages of two to five cells. Bold totals have only one combination. The last column shows digits that every combination of that total contains.
Cage combinations for 2 to 5 cells. Bold: only one combination. "In all": digits every combination contains. owlpuzzles.com/killer-sudoku/combinations
Start with the cages that have only one combination. Two cells adding up to 3 are always 1 and 2, and three cells adding up to 24 are always 7, 8 and 9. You don't know the order yet, but when the cage sits inside one row, column or box, those digits can't go anywhere else in it.
Next, look for digits that every combination shares. Three cells adding up to 8 are either 1, 2, 5 or 1, 3, 4, so the cage always holds a 1. Then cross out combinations that use a digit the row, column or box already has. Add that digit to the "must not include" list and the options shrink.
The 45 rule
Every row, column and 3×3 box holds 1 to 9 once, so its digits add up to 45. Add up the cages that sit fully inside a box and take that from 45. What's left is the total of the cells outside those cages. When the cages inside a box add up to 38 and one cell is left over, that cell is a 7. The same works across two or three rows, columns or boxes at once.
Cages of six cells or more
A big cage is the digits a small cage leaves out. Seven cells adding up to 40 leave out two digits that add up to 5, so the cage is missing 1 and 4, or 2 and 3. That's why the cheat sheet stops at five cells. The calculator works out cages of six to nine cells directly.
Common questions
What is the 45 rule in killer sudoku?
Every row, column and box adds up to 45, because it holds each digit from 1 to 9 once. Take the cage totals inside a box away from 45 and you have the total of the cells that are left.
How do you crack a killer sudoku?
Start with the cages that have only one combination, such as 3 in two cells or 24 in three. Then use the 45 rule on each box, and cross out combinations that clash with digits already in place.
Which killer sudoku cages have only one combination?
Two cells: 3, 4, 16 and 17. Three cells: 6, 7, 23 and 24. Four cells: 10, 11, 29 and 30. Five cells: 15, 16, 34 and 35. Every eight-cell cage has only one, since it leaves out a single digit.
Is there a printable killer sudoku combinations chart?
Yes. The print button above prints every combination for cages of two to five cells on one or two pages, in black and white. Choose Save as PDF in the print dialog to keep a file.
