Where Fillomino comes from

Fillomino belongs to a family of Japanese pencil puzzles, and its central idea, cutting a grid into shapes, goes back to the mathematics of polyominoes.

Polyominoes

A polyomino is a shape made of equal squares joined along their sides. Dominoes have two squares, trominoes three, tetrominoes four, and so on. The mathematician Solomon W. Golomb introduced the name in the 1950s and studied them in depth in his book Polyominoes. Polyominoes have since appeared in countless puzzles and games: tiling problems, packing puzzles, and the falling-block video games that use the seven tetrominoes.

Fillomino's name reflects this heritage: you fill the grid with polyominoes. Every region in a solved Fillomino grid is a polyomino, and the number in each cell tells you how many squares that polyomino has.

Nikoli and pencil puzzles

Fillomino is best known through Nikoli, the Japanese publisher founded in 1980 whose puzzle magazine popularised Sudoku and many other logic genres. Nikoli puzzles share a style: simple rules, a single solution, and a solving path that relies on logic rather than guessing or trial and error. Many of the genres were refined by readers, who sent in puzzles and new ideas to the magazine.

Fillomino is one of the classic Nikoli-style genres, alongside Sudoku, Kakuro, Slitherlink, Nurikabe and Hashiwokakero. Among them, it's unusual in two ways. The numbers describe areas rather than sums or counts of lines, and the solution includes regions that have no clue at all, so part of the puzzle is discovering shapes nobody told you about.

From paper to screen

On paper, solvers usually draw region borders as they go and write numbers only where they're sure. On a screen, the app does the bookkeeping instead: regions are drawn as you fill them, a complete region turns green, and checking for mistakes takes a single tap. That frees you to focus on the logic, and makes much larger grids practical. A 16×16 board, with 256 cells and regions of ten or more, would be daunting to erase and redraw by hand.

The puzzles in this app are generated by computer and then verified by a solver, so every medium and hard puzzle has exactly one solution. Difficulty comes from the size of the regions and how long the chain of deductions is, not from guesswork.

Related puzzles

If you enjoy Fillomino, you may like other region-dividing puzzles. In Nurikabe you divide the grid into islands of given sizes separated by a single connected sea. In Shikaku you cut the grid into rectangles, each containing one number equal to its area. Fillomino is the most open of the three, since regions can take any shape, and that's what makes its large boards so deep.