Dominosa

Nothing on this board is hidden — every pip is visible from the first second. The unknown is the cut, so the solver's variable is not a square but a placement: one adjacency carrying one domino of the set. That makes the puzzle an exact cover with two tight sides — every domino used once, every square covered once — and the counts match exactly, with no slack anywhere. Propagation is two dual exactly one rules (a domino with one spot left; a square with one neighbour left) plus their two intersection duals (every spot of this domino covers that square, so nothing else can; every cover of this square spells that domino, so it is spent here). Between them they subsume the published trick list. The Hint button names whichever one fires next.

For scale: ignore the pips entirely and ask how many ways dominoes tile the bare grid. An exact broken-profile count — the dimer problem Kasteleyn solved in 1961 — says 1,292,697 for the 7×8 board and 108,435,745 for 8×9. The pips cut that to one. Where propagation stalls, a search branches on the variable with the fewest candidates and proves it: every bundled board has a single solution. Two of the six resist the fixpoint almost entirely — six squares settled out of fifty-six — and then collapse after a single guess.