Kakuro Solver,
cross sums in, digits out.

Field guide

How the Kakuro Solver works.

Kakuro looks like a crossword that was filled with arithmetic. The grid mixes white entry cells with black clue cells, and a black cell can hold two small numbers separated by a diagonal. The number at the upper right is the total for the run of white cells to its right, and the number at the lower left is the total for the run below it. Each white cell takes a digit from 1 to 9, the digits of a run must add up to its total, and no digit may repeat within a run. Because every white cell belongs to one across run and one down run, the two directions keep checking each other.

Entering your puzzle

Work in three steps. First set the number of rows and columns, counting the black clue row and column along the top and left, then tap cells to turn them black or white until the pattern matches your puzzle. Second, switch to Enter totals, tap each black cell and type its across and down numbers; the tool shows the range a run of that length can reach and the digit sets that fit. Third, if your puzzle prints a few starting digits, add them under Start digits. The Example button loads a practice puzzle written for this tool.

Kakuro combinations

Every run is a small puzzle by itself: which different digits can reach the total? A run of n cells can only have totals within a fixed range.

Two cells reach 3 to 17, three cells 6 to 24 and four cells 10 to 30. Totals at the edge of a range have a single answer: 16 in two cells is 7 + 9, 7 in three cells is 1 + 2 + 4, and 29 in four cells is 5 + 7 + 8 + 9. The helper above the guide lists the sets for any length and total, and its cheat sheet shows every total for one length at a glance.

A worked example: two runs crossing

Say a two-cell run totals 4 and crosses a three-cell run totalling 7. Four in two cells can only be 1 and 3, and seven in three cells can only be 1, 2 and 4. The shared cell must belong to both sets, and the only digit they have in common is 1. So the shared cell is 1, the other cell of the short run is 3, and the other two cells of the long run are 2 and 4 in some order. The next crossing runs settle that order.

What happens when you press Solve

The solver keeps a list of possible digits for every white cell. For each run it works out which digit sets are still possible given the digits already placed, and it removes any candidate that no set allows. A digit that appears in every remaining set must go somewhere in the run, so if only one cell can take it, that cell is filled. Cells joined by runs form independent groups, and each group is searched separately, guessing in the most constrained cell and backtracking when a guess fails. A search limit keeps the page responsive, and after finding a grid the solver looks for a second one so it can tell you whether the puzzle has a single answer.

Tips for solving by hand

• Start with the extremes. Totals at the ends of a range, such as 3 or 4 in two cells, have only one digit set.
• Intersect crossing runs. The digit in a shared cell must appear in the sets of both runs.
• Use what is placed. Once a digit is fixed in a run, subtract it from the total and look again at the sets that remain.

Disclaimer: This tool is an independent puzzle aid, not affiliated with any puzzle publisher or app, and is provided for practice and entertainment only. Check the result against your own puzzle before relying on it.