Nonogram

The solver works one line at a time: enumerate every legal placement of that row/column's runs (a memoized recursion), and intersect them — cells filled in every placement are certain, cells empty in every placement are certain. Each new certainty re-queues the crossing line, propagating to a fixpoint. Every bundled puzzle is verified line-solvable — solvable by this reasoning alone, no guessing — and Hint plays exactly one such deduction for you.