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:
- All numbers on the grid must be part of a polyomino of the same value.
- No two polyominoes of the same value can touch horizontally or vertically.
- Givens may be part of the same polyomino, conversely not all final polyominoes may start with a given.
- 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