Flow Mania

Flow Mania is a "Grid-Coverage" logic puzzle rooted in "Graph Theory" (specifically the Numberlink problem). The technical core involves connecting paired nodes with continuous paths that must not intersect. The challenge differentiates itself by requiring 100% Grid Saturation—it's not enough to just connect the dots; players must utilize every single empty cell on the board, forcing efficient "Space-Filling Curves."

You are presented with a grid containing pairs of colored dots. Your objective is to connect matching colors with a pipe. Interaction is "Drag-to-Draw." You must create a flow between dots. Constraints: Pipes cannot cross each other, and you must fill the entire grid. If you connect all dots but leave one square empty, the level is incomplete. You must visualize the paths before drawing to avoid blocking a color's only viable route.

Mastering flow depends on "Perimeter-Hugging Logic." Never draw a line straight through the center unless necessary. "Route along the Edges" first. This preserves the central "Hub" for complex crossovers. A pro strategy is to identify "Chokepoints"—if a color is trapped in a corner, it must exit through a specific adjacent cell. Lock in these forced moves first to reduce the variable space for the remaining connections.