Kakuro solver
Enter the clues and get the answer. If the grid has more than one answer, this says so rather than picking one and calling it done.
What this tells you that others do not
Most solvers return an answer. This one returns the number of answers, capped at two, and that difference matters more in Kakuro than almost anywhere else.
If you are checking a puzzle from a book or a newspaper and it turns out to have two answers, the puzzle is broken and no amount of further solving will fix it. If you are setting a grid of your own, that count is the only thing standing between a puzzle and an embarrassment.
And if you are stuck on a grid you believe in, knowing there is exactly one answer is itself useful information — it means the deduction is there to be found and you have not been sent on an impossible errand.
Sum-decomposition tables: two- and three-square runs
Every writing of a clue this short is worth having in front of you while the solver above is open, because a two- or three-square run is usually where a grid either opens or stalls. The two tables below list every clue a run of that length can carry, from the smallest possible sum to the largest, and every set of distinct digits that adds up to it.
They are generated, not typed: the same table the solver above consults when it narrows a run produced every row here, by walking each set of distinct digits directly rather than having someone write the list out by hand. A writing cannot appear on this page that the solver itself would reject. Runs of four squares and longer follow the identical rule; they are one click away on the full combinations chart rather than repeated here, since a four-square run already has up to twelve writings at its busiest sum and stops being something you can read at a glance.
| Clue | Ways | Digit sets | Possible in a square |
|---|---|---|---|
| 3 | 1 | 12 | 1 2 |
| 4 | 1 | 13 | 1 3 |
| 5 | 2 | 2314 | 1 2 3 4 |
| 6 | 2 | 2415 | 1 2 4 5 |
| 7 | 3 | 342516 | 1 2 3 4 5 6 |
| 8 | 3 | 352617 | 1 2 3 5 6 7 |
| 9 | 4 | 45362718 | 1 2 3 4 5 6 7 8 |
| 10 | 4 | 46372819 | 1 2 3 4 6 7 8 9 |
| 11 | 4 | 56473829 | 2 3 4 5 6 7 8 9 |
| 12 | 3 | 574839 | 3 4 5 7 8 9 |
| 13 | 3 | 675849 | 4 5 6 7 8 9 |
| 14 | 2 | 6859 | 5 6 8 9 |
| 15 | 2 | 7869 | 6 7 8 9 |
| 16 | 1 | 79 | 7 9 |
| 17 | 1 | 89 | 8 9 |
| Clue | Ways | Digit sets | Possible in a square |
|---|---|---|---|
| 6 | 1 | 123 | 1 2 3 |
| 7 | 1 | 124 | 1 2 4 |
| 8 | 2 | 134125 | 1 2 3 4 5 |
| 9 | 3 | 234135126 | 1 2 3 4 5 6 |
| 10 | 4 | 235145136127 | 1 2 3 4 5 6 7 |
| 11 | 5 | 245236146137128 | 1 2 3 4 5 6 7 8 |
| 12 | 7 | 345246156237147138129 | 1 2 3 4 5 6 7 8 9 |
| 13 | 7 | 346256247157238148139 | 1 2 3 4 5 6 7 8 9 |
| 14 | 8 | 356347257167248158239149 | 1 2 3 4 5 6 7 8 9 |
| 15 | 8 | 456357267348258168249159 | 1 2 3 4 5 6 7 8 9 |
| 16 | 8 | 457367358268178349259169 | 1 2 3 4 5 6 7 8 9 |
| 17 | 7 | 467458368278359269179 | 1 2 3 4 5 6 7 8 9 |
| 18 | 7 | 567468378459369279189 | 1 2 3 4 5 6 7 8 9 |
| 19 | 5 | 568478469379289 | 2 3 4 5 6 7 8 9 |
| 20 | 4 | 578569479389 | 3 4 5 6 7 8 9 |
| 21 | 3 | 678579489 | 4 5 6 7 8 9 |
| 22 | 2 | 679589 | 5 6 7 8 9 |
| 23 | 1 | 689 | 6 8 9 |
| 24 | 1 | 789 | 7 8 9 |
Four squares and longer are in the full combinations chart — the same table, filtered here to the two lengths worth reading in full.
Three techniques the tables support
A forced combination is a clue with exactly one writing, and the tables below shade every one — eight in total, four across two squares and four across three. None of them places a single digit by itself, because a writing still has to be split between the squares it spans, but each cuts a run from nine candidates a square down to two or three in one step, which is usually enough to get a stalled grid moving again.
Not every useful fact needs a forced combination, though. Twenty-two across three squares has two writings, six-seven-nine and five-eight-nine, and both of them include a nine — so whichever way that clue resolves, a nine belongs somewhere in the run, and if only one of its squares can still take a nine, that square is settled before the rest of the run is worked out at all. The check is worth running on any sum with two or three writings: look at what they have in common, not only at what they allow.
Intersection narrowing is the technique that does most of the actual work: a square where two runs cross can only hold a digit that both runs allow, and the right-hand column of each table below — every digit that appears in any writing of that clue — is exactly what a single run allows before anything else is known. A two-square run clued four allows only one and three; a three-square run clued twelve allows all nine digits, because between its seven writings every digit appears somewhere. Cross those two runs and the shared square is already down to one or three, entirely on the strength of the shorter run — which is the ordinary case, not the exception. A long run rarely narrows much by itself; it narrows through what crosses it.
Setting a grid of your own
It is much harder than it looks, and the trap is not the one people expect. Making the arithmetic work is easy; making the answer unique is not, because ambiguity is the default state of a Kakuro grid rather than an occasional accident.
The reliable method is to fill the whole grid with digits first, read the clues off the runs, and then check the count. If it comes back as more than one, change a digit somewhere the two answers disagree — that is precisely where the ambiguity lives — and check again.
That is the same loop this site uses to build its own puzzles, and it converges surprisingly fast. What does not work is adding more clues, because in Kakuro every clue is already forced by the digits; there is nothing to add.
How it works
It narrows each run to the writings its clue still allows given the squares crossing it, repeats until nothing changes, and then — only if it has to — takes the most constrained square and tries each remaining digit.
The narrowing step includes a matching check that a simpler solver would skip: it is not enough that every digit of a writing is available somewhere in the run, each digit has to be placeable in a different square. Without that the solver wanders down branches that cannot exist.
It runs in your browser. Nothing is uploaded, nothing is stored, and the code doing it is the same module that generated every puzzle on this site.
Common questions
- Can this solver tell me if my Kakuro has two answers?
- Yes, and that is the main thing it is for. It counts answers and stops at two, so it distinguishes a sound puzzle from a broken one instead of returning whichever answer it found first.
- Is my grid sent to a server?
- No. The solver runs entirely in your browser using the same module that built the puzzles on this site. Nothing leaves the page.
- How do I make my own Kakuro puzzle?
- Fill every square with digits first and read the clues off the runs, then count the answers. If there is more than one, change a digit where the answers disagree and count again.
- Do the sum-decomposition tables on this page match what the solver computes?
- Yes — both come from the same combos(sum, length) table in the engine. There is no separate copy of the arithmetic for the reference tables and the tool above; if one changed, so would the other.
Check this before you rely on it. This tool is provided free and without warranty, and its results are not professional advice.