Loop Fillomino is a variant of Fillomino, in which polyminoes are entered into a grid.


The challenge is to add numbers to all cells, subject to the following rules:

  1. All numbers on the grid must be part of a polyomino of the same value.
  2. No two polyominoes of the same value can touch horizontally or vertically.
  3. Givens may be part of the same polyomino, conversely not all final polyominoes may start with a given.
  4. There must exist a closed loop that travels through orthogonally adjacent cells, visits each cell exactly once, and enters and exits every region exactly once.


A standard 10x10 Checkered Fillomino and its solution.

Credit to Николай Белухов of NB Puzzles

Loop Fillomino Example

Credit: Николай Белухов

Loop Fillomino Solution

Credit: Николай Белухов