# Fillomino

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## Description

Fillomino is a number placement, logic puzzle where 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.

## Example

A standard 10x10 fillomino and its solution.

## Variants

Unless otherwise indicated, standard fillomino rules apply to all variants.

Shape Fillomino: Shapes appear beside the grid which must form part of the solution. These shapes can be rotated but not reflected.

Checkered Fillomino: There must exist a way to shade some regions such that shaded regions neighbour only unshaded regions and unshaded regions only neighbour shaded regions.

Loop Fillomino: 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.

Greater-than Fillomino: Inequality symbols appear between cells. These indicate the relative size between values of the two adjacent numbers.

Sum FIllomino: Dashed boxes are included containing a selction of adjacent cells, indicating the total of all numbers within the selection.

Walls Fillomino: Pairs of cells with a thick border between them must contain different values.