Choose how many white squares a run has and its clue, and see every set of different digits that can fill it. Cross out a digit you have ruled out, and only the combinations still possible stay. The full kakuro combinations chart, a cheat sheet for runs of two to nine squares, is below.
Squares in the run
Cross out digits the run 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 run.
How to use the calculator
A run is a line of white squares across or down, ended by a black square or the edge. Count its squares and choose that number, then choose its clue, the sum printed in the black square at its start. The list shows every set of different digits that adds up to it. A digit can appear only once in a run, so 5 + 5 never makes 10: a run 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 run that crosses one of its squares rules out a digit, or a digit is already written elsewhere in the run, cross it out: every combination with that digit goes, and the line under the list says which digits the run must still hold and which it cannot. When one combination is left, you know the run’s digits, though not yet their order.
Kakuro combinations chart
Every sum for runs 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 runs are the best places to start, and the ones worth learning by heart: a two-square 17 is always 8 and 9, a three-square 6 is always 1, 2 and 3.
The ends are sure. For every length, 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 run of three adding up to 22 is 589 or 679: it holds a 9 either way, so one of its squares is 9.
Long runs are about what is missing. A run of nine always adds up to 45. A run of eight leaves out one digit: 45 minus its clue. A run of seven leaves out two digits that add up to 45 minus its clue.
Cross it with the other run. Each white square sits in one run across and one down, and its digit has to suit both. Where a two-square 17 across (8 and 9) meets a two-square 16 down (7 and 9), the square can only be 9.