Kakuro is sometimes described as a crossword built from arithmetic instead of words. Black clue cells mark the sums for runs of white cells that cross the grid horizontally and vertically; your job is to fill every white cell with a digit from 1–9 so each run's digits are all different and add up to its clue.
The combination of "no repeated digits" and "must hit an exact sum" usually narrows a run down to just a handful of possible digit sets, and cross-referencing where runs overlap is what cracks the rest of the grid open. Pick a difficulty above to start a new puzzle.
Run length, not black-cell density, is what actually drives difficulty here: a run capped at 4 cells only ever admits a small handful of digit combinations, so Easy boards crack open fast once you spot which sums are the most restrictive, while Master's runs of up to 8 cells leave many more combinations legal until you've cross-referenced several overlapping runs at once. A denser grid of black cells doesn't necessarily mean a harder puzzle (Easy actually packs in more black cells than Medium does); it's the length of the runs between them that decides how much cross-referencing a solve takes.

Kakuro's win check never compares your grid to the one the generator filled in first: it only checks that every run's digits are distinct and add up to its clue, so any filling that satisfies every sum legitimately wins, even if it differs from the generator's own solution. There's no solver proving a single answer here; the clue sums themselves are simply read off whatever valid grid the generator happened to build.
When a fill attempt dead-ends entirely, the whole grid is wiped and retried from scratch rather than patched (up to 40 times), and a per-restart cap on how many backtracking steps any one attempt can take keeps a runaway retry from stalling generation altogether.