Masyu
Draw one closed loop through every pearl. It must pass straight through a white circle and turn on a black one — with straight lines on each side of every black. Click the gap between two cells to lay a segment, again for a × mark, once more to clear.
The solver models the loop by its edges — one bit each, in the loop or not. A sound propagation pass runs to a fixpoint: every cell's edges must match one of its legal local patterns (a white ○ runs straight, a black ● turns), and a black pearl forces the cell just beyond each arm to run straight. A closure guard kills any loop that closes before it has swallowed every pearl. Neither step ever guesses. When logic stalls, a fewest-options search extends an existing loop fragment, lets propagation prune, and counts solutions — every bundled board is drawn as its own finished loop, and the test suite asserts the solver re-derives exactly one answer.