Are all the clues definitely solvable?

Yes. The grid is filled with digits first and the clues are read off it, so every clue has at least one valid combination by construction. Generating clues first and hoping is how unsolvable kakuro puzzles happen.

Is the solution unique?

Not guaranteed — the tool does not search for uniqueness. The answer shown is a valid solution, and yours may differ while still satisfying every clue.

Why are the runs never longer than four?

The block pattern caps them there, which guarantees nine digits are always enough to fill a run with no repeats. Longer runs are possible in principle but make generation much more fragile.

Kakuro Generator

Kakuro is a crossword done with digits: every run of white squares adds up to the clue at its head, using the digits 1 to 9 with none repeated inside a run. It is genuinely good arithmetic practice because the constraint cuts both ways — knowing a run of three sums to 6 tells you it must be 1, 2 and 3 in some order, and that is real reasoning rather than trial and error.

Grid size

Blocks fall every fifth row and column, so runs are never longer than four cells.

Your kakuro will appear here.

What this generator does

Produces clues that are guaranteed to be satisfiable. That is the hard part of generating kakuro and the reason many generators produce unsolvable puzzles: if you invent the clues first, some runs have no valid combination at all. This fills a grid with digits first — placed so no run ever repeats one — and then reads the clues off the completed grid, so every clue has at least one solution by construction.

How to use this tool

Choose a grid size.
Make a puzzle.
Fill each run so it adds to its clue with no repeated digits.
Reveal the answer when you want to check.

Understanding the controls

Grid size: Six to sixteen. Blocks fall on every fifth row and column, which caps every run at four cells — short enough that nine digits always suffice, which is what keeps the puzzle generatable at any size.

Worked examples

A run of two summing to 3: Must be 1 and 2 — the shortest useful deduction in kakuro.
A run of three summing to 6: Must be 1, 2 and 3 in some order.
A run of four: Sums between 10 and 30; anything outside that is impossible.
Every clue produced: Satisfiable, because the grid was filled before the clues were read off it.

Common use cases

Addition practice that rewards reasoning about combinations
A puzzle for pupils who have outgrown straightforward sums
Introducing the idea that a total plus a length constrains the digits
A printable activity with a checkable answer
Anybody who likes sudoku and wants arithmetic in it

How this generator works

The block pattern is laid down first, then the open squares are filled by backtracking: each square takes a digit not already used in any run it belongs to, and a square with no legal digit forces a retry rather than a duplicate. Clues are then the sums of what was actually placed. The finished puzzle is checked before display — every run holds distinct digits, sums to its clue, and has a clue within the range a run of that length can possibly reach.

Randomness and fairness

The digit placement is a randomised backtracking search, so each press gives a different grid. The distinctness rule is a constraint on the search rather than a check afterwards, which is why a run with a repeated digit cannot be produced.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

Standard kakuro rules: digits 1 to 9, no repeats within a run, every run sums to its clue.

Limitations and good to know

The solution shown is a valid one rather than a proven unique one — the tool does not search for uniqueness.
The block pattern is regular rather than the irregular shapes of a hand-crafted kakuro, which makes these a little more uniform than published puzzles.
Runs are capped at four cells, so the long runs of a hard published kakuro do not appear.
Difficulty is not graded.
Nothing persists between visits and there is no seed, so print or copy a puzzle you intend to set.

Common mistakes

Trying to solve square by square: Work run by run. A total and a length together often pin the digits before you look at any crossing.
Repeating a digit in a run: Never allowed, even though the same digit may appear twice in a row of the grid if it belongs to different runs.
Ignoring the crossings: The whole puzzle is in the overlaps. A square belongs to an across run and a down run, and both constrain it.

Practical tips

Learn the forced combinations — 3 in two, 6 in three, 10 in four — and most puzzles open up immediately.
Pencil in the possible digits for a run before committing to any of them.

Privacy and your data

Everything is computed in your browser. There is nothing to type, nothing to upload, nothing stored between visits, and nothing written into the page address. Analytics records that the tool ran and how many runs the puzzle had.

Frequently asked questions

Are all the clues definitely solvable?: Yes. The grid is filled with digits first and the clues are read off it, so every clue has at least one valid combination by construction. Generating clues first and hoping is how unsolvable kakuro puzzles happen.
Is the solution unique?: Not guaranteed — the tool does not search for uniqueness. The answer shown is a valid solution, and yours may differ while still satisfying every clue.
Why are the runs never longer than four?: The block pattern caps them there, which guarantees nine digits are always enough to fill a run with no repeats. Longer runs are possible in principle but make generation much more fragile.