Posts tagged "puzzles"
5 posts
A puzzle that knows whether you have already lost
The three Nikoli puzzles I built are NP-complete, so their solvers must guess. Replacing the global constraint with flow conservation makes feasibility a max-flow computation, and the board gains a hint button that cannot be wrong.
The mathematics of Nikoli puzzles
Cell Blocks, Nurikabe and Slitherlink share no rules, but they share a shape: local arithmetic plus one global topological constraint. That split explains where the difficulty lives, why propagation always stops short, and what a puzzle with a well-behaved global constraint would look like.
Nurikabe, and what replaces candidate enumeration
A puzzle that keeps the clue semantics of Shikaku but destroys the representation its solver depends on, forcing a switch from candidate lists to reachability, liberties and articulation reasoning.
Slitherlink is a two-colouring puzzle wearing a loop costume
The Jordan curve theorem turns a puzzle about drawing one closed loop into a puzzle about colouring cells inside or outside, which makes it the dual of Nurikabe and hands the whole connectivity toolkit over unchanged.
The mathematics of Cell Blocks
A pencil puzzle whose solver is an exact cover problem, whose difficulty dial is the divisor-count function, and whose harder variants each break exactly one assumption the solver leans on.