Kakuro
Fill every white cell with 1–9. Each across/down run adds up to the clue on its shaded head, and no digit repeats inside a run. Click a cell, then type a digit (or use the pad).
The solver is two layers. First a sound propagation pass applies two strict rules to a fixpoint. Each run turns its sum into a domain: of all the ways to pick k distinct digits that total the clue, the union of every valid combination is exactly the digits that can appear — so a cell keeps only digits some completion actually uses. And a digit pinned in one cell is struck from the rest of its run (distinctness). Neither step ever guesses. When logic stalls, a minimum-remaining-values search branches on the cell with the fewest candidates, lets propagation prune, and proves the answer is unique. Every bundled board is authored as a filled digit grid; the solver reads off the clues and then re-derives that exact grid as the one and only solution.