Choose how many squares a cage has and the sum in its corner, and see every set of digits that can fill it. Cross out a digit you have ruled out, and only the combinations still possible stay. The full chart for cages of two to nine squares is below.
Squares in the cage
Cross out digits the cage cannot hold
8 combinations of 3 digits add up to 15.
1 5 9
1 6 8
2 4 9
2 5 8
2 6 7
3 4 8
3 5 7
4 5 6
Any digit from 1 to 9 could still be in the cage.
How to use the calculator
Count the squares inside the dotted outline of a cage and choose that number, then choose the sum printed in its corner. The list shows every set of different digits that adds up to it. A digit can appear only once in a cage, so 5 + 5 never makes 10; a cage of two adding up to 10 is 1 + 9, 2 + 8, 3 + 7, 4 + 6.
Then use what the grid already tells you. If the row, column or box the cage sits in already has a 4, cross out 4: every combination with a 4 goes, and the line under the list says which digits the cage must still hold and which it cannot. When only one combination is left, you know the cage’s digits, though not yet their order.
Killer sudoku combinations chart
Every sum for cages of two to nine squares, with each combination written as its digits, smallest first: 159 means 1, 5 and 9. A sum that can be made only one way is in bold; those cages are the best places to start a puzzle.
The ends are sure. For every size, the smallest and the largest sums can be made only one way, and so can the next one in from each end.
Look for a digit in every combination. A cage of three adding up to 22 is 589 or 679: it holds a 9 either way. If the cage lies within one box, no other square in that box can be 9.
Big cages are about what is missing. A cage of eight squares leaves out one digit: 45 minus its sum. A cage of seven leaves out two digits that add up to 45 minus its sum, so read the row for two squares instead.