Fillomino fills every cell so regions of orthogonally connected cells equal their number. Regions of equal size never touch. No region boundary is given—you infer it all.
Rules
Given numbers as seeds. Fill every cell. Connected regions: orthogonally connected cells with the same number form a region; the region size must equal that number. Same-size regions cannot share an edge. A given of 1 is complete—surround it with different numbers. Solve by logic; unique solution. No region boundary is given—you infer it all. Also known as "Allied Occupation" in Western books.
History
Fillomino appeared in Nikoli in the 1980s. The name combines "fill" and "polyomino." "Allied Occupation" is used in some Western puzzle books. Strong connection to polyomino maths. Steady Nikoli print and digital presence; Simon Tatham's Portable Puzzle Collection includes a Filling variant. Dedicated following among logic puzzle fans.
Strategy tips
Resolve 1-cells first—trivially complete, borders constrain neighbours. For large numbers sketch possible polyomino shapes. Verify same-size regions don't touch after each placement.
Cultural context
Nikoli puzzle tradition; polyomino maths; strong dedicated following; digital puzzle apps. Fillomino rewards spatial reasoning and constraint propagation; the polyomino shapes (L, T, S, etc.) become familiar with practice. Fans of Shikaku and Nurikabe often enjoy Fillomino for its similar partition-logic feel.
Where to buy / play
- Fillomino Puzzle Book (Nikoli) Official Nikoli fillomino collection
- Play Fillomino free in browser (Simon Tatham — Filling) Free, open-source browser implementation