Fillomino

Fillomino is a grid-based logic puzzle published by the Japanese company Nikoli where the objective is to divide the grid into regions called polyominoes. The main rule is that each cell within a given region must contain a number equal to the total number of cells in that region. Additionally, regions of the same size cannot touch orthogonally (share a side).

While both are grid-based logic puzzles published by Nikoli, Sudoku requires placing digits 1-9 into a rigid 9x9 grid based on rows and columns. Fillomino, however, has no set grid size or pre-existing sub-grids; instead, solvers must draw boundaries to create distinct, numbered polyomino shapes. The focus in Fillomino is on geometric division rather than arithmetic logic.

Not necessarily as starting clues, but the final solution requires every single cell in the grid to belong to a numbered region. While some numbers are given at the start, solvers must deduce the values of all unlabeled cells. Unlabeled cells must eventually be assigned a number matching the size of their surrounding polyomino.

A polyomino is a geometric shape formed by joining squares edge-to-edge; in Fillomino, it represents a connected group of cells on the grid. For example, a '3' polyomino (a triomino) is made up of exactly three orthogonally connected squares. The goal of the puzzle is to completely fill the grid with these distinct polyomino shapes.