constraint programming inverts the usual deal: you state what a solution must satisfy, and a general-purpose solver figures out how to find one. 𐃏 no objective gradient, no simplex tableau — just variables, finite domains, and constraints, attacked by an alternation of inference (prune values that cannot appear in any solution) and search (guess, propagate, backtrack). this page builds the machinery from the formalism up; the sudoku solver and hashiwokakero write-ups on this wiki are the same machinery pointed at actual puzzles.