The rules
The grid has black squares and white squares. A run is a line of two or more white squares, across or down, between black squares or the edge. Each run has a clue, a number printed in the black square just before it: the number above the diagonal belongs to the run going across to its right, the number below the diagonal to the run going down beneath it.
- Write one digit from 1 to 9 in every white square.
- The digits in each run add up to its clue.
- No digit appears twice in the same run. (It may appear again in another run.)
That is all. Every white square belongs to exactly two runs, one across and one down, so every digit has to suit two sums at once.
A small puzzle, step by step
Here is the smallest kind of kakuro: four white squares, two runs across and two down.
Two different digits that make 4 can only be 1 and 3: 2 + 2 is not allowed, because a digit cannot repeat in a run. Two that make 3 can only be 1 and 2. Now look at the top left square. Going across it is part of the 4, so it is 1 or 3. Going down it is part of the 3, so it is 1 or 2. Only 1 is in both.
The rest follows from the sums. The top run is 4, so its other square is 4 − 1 = 3. The left run is 3, so the square below the 1 is 2. The bottom run is 3, so its last square is 1, and the right-hand run checks out: 3 + 1 = 4.
Techniques
Start with the sums that have one answer
Most sums can be made several ways: three different digits adding up to 12 can be 1 + 2 + 9, 1 + 3 + 8, 1 + 4 + 7, 1 + 5 + 6, 2 + 3 + 7, 2 + 4 + 6, 3 + 4 + 5. But some can be made only one way, and they are where every puzzle starts. A three-square 6 is always 1, 2, 3; a three-square 24 is always 7, 8, 9. In general the smallest and largest sums for a length, and the next one in from each end, have one answer. The kakuro calculator lists them all, and the full chart.
Cross the runs
A square’s digit must be in the possible digits of its run across and its run down. When the two lists share only one digit, that is the square’s digit, exactly as in the small puzzle above. Look hardest where a run with one answer crosses another run with one answer.
Mind the big and small digits
A run of two adding up to 15 or more needs a 6 or more in both squares; a run of three adding up to 6 or 7 always holds a 1 and a 2. So a square where a large sum crosses a small one often has very few choices. Write those choices in as notes.
Finish the run
When all but one square of a run is filled, the last one is the clue minus the others. And when a run must contain a digit (every way to make the sum uses it) and only one of its squares can take that digit, it goes there.
Use notes, then cross them off
On harder puzzles, note the possible digits in each square of a long run. Each time you fill a square, the game takes that digit out of the notes in its two runs, and a square left with a single note is settled.
A whole puzzle
This is an Easy puzzle as the game deals it, seven squares on a side counting the clue row and column. Every Easy puzzle can be finished with the first two techniques alone.
Try it on the board: play this puzzle.
Tips for beginners
- Learn a few sure sums. 3 and 4 in two squares, 16 and 17 in two, 6, 7, 23 and 24 in three. They come up all the time.
- Work from the corners. Short runs in corners cross each other, so their squares settle first.
- Count down. If a run of three adds up to 9 and one square is 1, the other two add up to 8 without a 1: 2 + 6 or 3 + 5.
- Check early. One wrong digit spoils both of its runs. Press Check if a sum stops making sense.