Slitherlink
Draw one closed loop. Each number = how many of its four edges the loop uses. Click an edge to cycle line → ✕ → blank.
The solver is two layers. First a sound propagation pass: a clued cell whose lines already equal its number crosses off the rest (and vice-versa), and every lattice vertex must finish with loop degree 0 or 2, which forces or forbids its edges. Each new certainty re-triggers its neighbours, running to a fixpoint — this is exactly what Hint replays, one guess-free deduction at a time. When logic alone stalls, a backtracking search takes over, pruning any branch that closes a stray sub-loop, and it proves the answer is unique. Every bundled puzzle's clues are derived from a picture, and that picture is verified to be the one and only solution.