PuzzleTeam defines the rules as:
The rules of Kakuro are simple:
How I actually solve one — the reasoning I run before any code does, written out in full. Kakuro is arithmetic wearing a logic costume: almost everything falls out of knowing which digit sets can make which sums. Read down the right column; the board on the left follows whichever step you are on.
A Kakuro grid reads like a crossword: every maximal horizontal strip of white cells is an across run, every vertical strip a down run, and each run is headed by a clue giving the sum its digits must reach. Digits go from 1 to 9 and a run never repeats one. Each white cell sits at the crossing of exactly one across run and one down run, so every digit I place has to serve two sums at once — that crossing is the entire puzzle.
The naive space is enormous — white cells at nine digits each is assignments — but it is also the wrong space. Runs are the real units. A run of cells filled with distinct digits can only reach sums inside a narrow window:
The lower edge is , the upper is . Everything the solver does from here is bookkeeping on those windows: which digit sets can still make which sums, and what each crossing does to the sets on the other axis.
The robotic solver on real boards: the daily puzzle comes straight from the API, and the samples — 6×6 · Easy up to 62×62 · Special — replay recorded solver runs move by move.