Hitori

The solver keeps a three-valued cell — unknown, kept, or shaded — and runs sound propagation to a fixpoint before it ever guesses. The twist: on an untouched board every dynamic rule is starved. The duplicate rule needs a kept cell, the adjacency rule needs a shaded one, connectivity needs both — so pure propagation is a no-op on move one. The only ways in are the puzzle's two textbook openings, each a one-step case analysis whose branches agree: the sandwich (in a ? a the middle cell is kept, whichever a survives) and the pair (of an adjacent a a exactly one survives, so every other a in the line is shaded). Once seeded, three dynamic rules feed each other — a kept number evicts its copies from its row and column, a shaded cell keeps all four neighbours, and a cut-cell check keeps any cell whose shading would split the survivors. When logic stalls, a fewest-options search branches on one cell, re-propagates, and counts solutions — every bundled board is authored as its own finished shading, and the test suite asserts the solver re-derives exactly one answer.