Fillomino facts for kids

Fillomino (pronounced "fill-oh-MEE-noh") is a type of logic puzzle that many companies publish. It's also known by other names, like Allied Occupation. In this puzzle, you divide a grid into shapes called polyominoes. It's a fun way to challenge your brain!

How to Play Fillomino

Fillomino is played on a grid, usually a rectangle. The lines inside the grid are often dotted. Some squares in the grid already have numbers. These are called "givens."

Your goal is to draw lines to divide the grid into different polyominoes. Each polyomino must contain a number of squares that matches the number inside it. For example, a polyomino with the number '3' inside it must be made of exactly three squares.

There's one more important rule: two polyominoes that are the same size cannot touch each other side-by-side. They can touch at corners, but not along a full side.

Sometimes, a polyomino might not have a given number inside it. Also, two given numbers that are the same might end up in the same polyomino. This is all part of the puzzle!

What are Polyominoes?

A polyomino is a shape made by connecting squares edge-to-edge.

• A '1'-omino is just one square.
• A '2'-omino (or domino) is two squares connected.
• A '3'-omino (or tromino) is three squares connected.
• And so on! The number tells you how many squares are in the shape.

Tips for Solving Fillomino

When you solve a Fillomino puzzle, it's helpful to write numbers in the empty squares. This helps you see what size polyomino each square belongs to. If you have different numbers next to each other, you know a border must be drawn between them. This makes solving much faster! When you finish, the numbers alone show the solution.

To start a Fillomino puzzle, look for the easy parts:

• Draw borders around '1's. They are always single-square polyominoes.
• Look for two '2's that are already touching side-by-side. These form a '2'-omino. Draw borders around them.

From there, you can use these strategies:

Spotting Overloads

Each polyomino must have a number of squares that matches its number. If you put a number in a square, and it would make a group of too many matching numbers, then you know a border must go there.

For example, imagine two '2's are placed diagonally from each other. If you put a '2' in a square next to both of them, it would create a group of three '2's. But a '2'-omino can only have two squares! So, you know you must draw borders to separate that square from the '2's.

Finding Limited Spaces

Every number in the grid needs to be part of a polyomino with that exact number of squares. Sometimes, a number might be surrounded on many sides. It might only have one way to expand and get enough squares.

For instance, if a number (not '1') is blocked on three sides, the fourth side *must* be part of its polyomino. So, the square on that fourth side will have the same number. This helps you fill in more numbers and draw more borders.

Filling Empty Cells

Sometimes, it's easier to think about the empty squares.

• If an empty square becomes completely surrounded by borders, it must be a '1'-omino. So, you can write '1' in it.
• If two empty squares are touching side-by-side and are completely surrounded together, they must form a '2'-omino. You can write '2' in both.
• Even if a square isn't fully surrounded, it might only have one possible polyomino size that fits. For example, if putting a '3' in it would make a polyomino too big, and a '1' would make it too small, then it must be a '2'.

Different Kinds of Fillomino

Fillomino puzzles can be played on different types of grids.

• You can find them on hexagonal grids. Instead of polyominoes (made of squares), you'd use polyhexes (made of hexagons).
• Another version called NIKOJI uses letters instead of numbers. Each letter matches a specific polyomino shape and size.
• There are computer versions too! "Filling" is a game where the computer draws the borders for you.
• A mobile game called Fields, for iOS devices, came out in 2013.

Images for kids

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  Moderately difficult sample puzzle

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  Solution for the sample puzzle