Kakuro combinations chart
Which digits can make a given clue, for every clue and every run length. Filter it, or read the ones worth memorising first.
The ones to memorise, and the ones to look up
There are exactly four two-square clues with one writing each — three, four, sixteen and seventeen — and four three-square clues likewise: six, seven, twenty-three and twenty-four. Those eight are worth knowing by heart, because they are the openings that make a grid start moving.
The next tier is the sums with two writings: five and fifteen across two squares, eight and twenty-two across three. Knowing these is not memorisation so much as recognising a small number, and they are nearly as useful.
Everything else is worth looking up rather than learning. Ten across two squares has four writings and tells you almost nothing until something crosses it; the table below is faster than working it out and far more reliable than half-remembering it.
Reading the chart properly
The useful question is rarely "what can this clue be". It is "which digits are possible in this square", and that is the union of every writing of the clue — a different and usually larger set.
A run of three clued twenty can be written four ways, and between them those writings use every digit from three to nine. So the clue alone rules out only one and two. What narrows the square further is the crossing run, and the intersection of the two sets is where the real progress comes from.
The other direction is worth reading too. A digit that appears in every single writing of a clue must be somewhere in that run — twenty across three always contains a nine, whichever way you write it — and if only one square can take it, that square is settled.
Where this table comes from
It is generated by the same code the solver uses, at build time, by walking all five hundred and eleven possible sets of distinct digits and filing each one under its length and its total. There is no second copy of the arithmetic to fall out of step with the first.
That is not a small point. A combinations chart that disagrees with the puzzles printed next to it is actively harmful — it sends a solver looking for a mistake that is not in the grid.
The tests check it too, against the eight one-writing clues stated by hand. If the table ever stopped agreeing with them the build would fail rather than publish.
Common questions
- Which Kakuro combinations should I memorise?
- The eight with a single writing: three, four, sixteen and seventeen across two squares, and six, seven, twenty-three and twenty-four across three. They are the openings that get a grid moving.
- How many ways can 10 be made in two Kakuro squares?
- Four — one and nine, two and eight, three and seven, four and six. That is why a clue of ten tells you very little until a crossing run narrows it.
- What is the largest clue for a two-square run?
- Seventeen, which must be eight and nine. The smallest is three, which must be one and two, because zero is never used and no digit repeats within a run.
Check this before you rely on it. This tool is provided free and without warranty, and its results are not professional advice.