What is a Kakuro solver?
A Kakuro solver is a tool that fills a cross sums puzzle by applying the normal Kakuro rules. Each number cell must use a digit from 1 to 9, each clue run must add to its total, and no digit can repeat inside a single run.
This solver is designed for custom grids. You choose the size, mark black cells, add diagonal clue cells and enter any numbers already solved. The tool then calculates a completed grid if the clues are valid.
- Solve a Kakuro puzzle from a newspaper, book or printable sheet.
- Check whether your entered digits are still consistent.
- Test a Kakuro grid you are creating.
- Find out whether the clues have more than one answer.
How to use this Kakuro solver
Start by choosing the grid width and height, then create the board. Use the cell mode buttons to mark each square as a block, a clue cell or a number cell. Clue cells use the same diagonal layout as a printed Kakuro puzzle.
For each clue cell, enter the across total for the run to the right and the down total for the run below. If a clue only points one way, leave the other box blank. Number cells can be left empty or filled with digits you have already worked out.
- Create the grid.
- Paint the board with block, clue and number cells.
- Type clue totals into the diagonal clue cells.
- Enter any known digits in number cells.
- Press Solve to reveal the completed grid.
Kakuro combinations and clue runs
Kakuro combinations are the sets of digits that can make a clue total without repeats. A 4-cell clue of 10 can only use 1, 2, 3 and 4, although the crossing clues decide the final order.
The solver uses those combinations internally. For every clue, it creates the legal digit orders, removes any order that clashes with known numbers, then compares intersecting across and down runs.
- Run length controls how many digits are used.
- The clue total controls which digit sets are possible.
- Digits cannot repeat inside one run.
- The same cell must satisfy both its across and down clue.
Why a Kakuro can be impossible or ambiguous
A Kakuro grid is impossible if a clue total cannot be made with the number of cells in its run, or if an entered digit breaks a clue total. A run of ten cells is also invalid in standard Kakuro because only digits 1 to 9 are available.
A grid can also be ambiguous. That means more than one set of digits satisfies the same clues. Published Kakuro puzzles normally have one unique solution so that every step can be reached by logic.
Kakuro solver article keywords
This page targets the practical search intent behind Kakuro solver, Kakuro puzzle solver and cross sums solver. The combinations topic still belongs here, but mainly as supporting guidance for solvers who want to understand why a clue is forced.
A separate Kakuro combinations chart can work better as an article because people searching for combinations often want a quick reference table rather than a full grid editor.
How to solve Kakuro by hand
Kakuro rewards a steady routine. Start with the most constrained runs — the short ones with extreme totals, where only one set of digits fits. A two-cell run of 3 can only be 1 and 2, a two-cell 17 only 8 and 9, a three-cell 6 only 1-2-3. Pencil those forced sets straight in; no digit ever repeats inside a single run, so the order is all that is left to decide.
Then work the crossings. Every white cell belongs to one across run and one down run, so it can only hold a digit allowed by both. Compare the two runs' possible combinations and keep just the digits they share. Each placement tightens the runs that cross it, and the grid unwinds. The solver here is best for confirming your answer or revealing the next forced cell.
- Begin with short runs whose totals force a single combination.
- No digit repeats within one run, so a fixed combination still needs ordering.
- Each white cell must satisfy both its across run and its down run.
- At a crossing, keep only the digits both runs allow.
- Use the solver to check your grid or reveal the next cell.
Kakuro, Cross Sums and Nikoli
Kakuro began in North American puzzle magazines under the name Cross Sums, where it looked like a crossword whose answers are numbers instead of letters. When the puzzle reached Japan it was renamed Kakuro, a shortening of kasan kurosu — 'addition cross' — and the publisher Nikoli, also behind Sudoku, helped turn it into a worldwide hit.
The rules have stayed constant ever since: fill the white cells with 1 to 9 so each run adds up to its clue, never repeating a digit within a run. That blend of arithmetic and logic is why Kakuro is often called a mathematical cousin of the crossword. This solver works on any standard Kakuro grid, whatever name it appears under.
Kakuro vs Sudoku and Killer Sudoku
Kakuro and Sudoku both fill grids with the digits 1 to 9, but they constrain them differently. Sudoku forbids repeats across whole rows, columns and boxes and gives no sums. Kakuro has no grid-wide uniqueness at all — the same digit can appear many times across the board — yet every run must add up to its clue and may not repeat a digit within itself.
Killer Sudoku sits between the two: it keeps Sudoku's strict no-repeat rule and adds Kakuro-style cage sums. So the combination skills transfer — the unique sums you learn for Kakuro are exactly the cage combinations used in Killer Sudoku — while the uniqueness rules differ. If you enjoy this solver, the Killer Sudoku page is a natural next step.