# Loop Fillomino

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## Decription

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

## Rules

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.

## Example

A standard 10x10 Checkered Fillomino and its solution.

Credit to Николай Белухов of NB Puzzles