Fillomino is a Japanese logic puzzle invented by Nikoli in 1994. The objective is to partition the grid into polyominoes such that every group of connected cells with the number N has an area of exactly N squares.

Can two polyominoes of the same size touch?

No. Two polyominoes of the same size cannot share a horizontal or vertical edge. If they touched, they would merge into a single larger polyomino! They may, however, touch diagonally at their corners.

Can polyominoes of different sizes touch?

Yes! Polyominoes of different sizes (e.g. a 2 next to a 3) can share orthogonal edges freely.

Can a polyomino contain no given clues?

Yes! In Fillomino, you can deduce polyominoes that do not contain any of the initial starting numbers, as long as all rules are preserved.

Can a polyomino contain multiple identical clues?

Yes. Multiple starting clues with the same number can belong to the same polyomino, provided their total connected area equals that number.

Fillomino is a Japanese logic puzzle invented by Nikoli in 1994. The objective is to partition the grid into polyominoes such that every group of connected cells with the number N has an area of exactly N squares.

Can two polyominoes of the same size touch?

No. Two polyominoes of the same size cannot share a horizontal or vertical edge. If they touched, they would merge into a single larger polyomino! They may, however, touch diagonally at their corners.

Can polyominoes of different sizes touch?

Yes! Polyominoes of different sizes (e.g. a 2 next to a 3) can share orthogonal edges freely.

Can a polyomino contain no given clues?

Yes! In Fillomino, you can deduce polyominoes that do not contain any of the initial starting numbers, as long as all rules are preserved.

Can a polyomino contain multiple identical clues?

Yes. Multiple starting clues with the same number can belong to the same polyomino, provided their total connected area equals that number.

Nikoli Classic • Polyomino Numbers

Fillomino

Divide the grid into polyominoes where the area of each shape equals its written number, and matching sizes never touch!

5x5 Number Clusters5x5 Grid • Polyomino Sizes Match Numbers

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2 polyominoes formed

Clustering polyominoes...

Fillomino Rules & Polyomino Logic

Published by Nikoli in 1994, Fillomino is one of the world's most beloved spatial number puzzles:

1. Size Equals NumberEvery connected group of identical numbers K must have an area of exactly K squares.

2. No Identical NeighborsTwo separate polyominoes of the same size can NEVER share an edge. If they touched, they would merge into an oversized shape!

3. Different Sizes Can TouchPolyominoes of differing values (such as 2 and 3) can happily border one another.

4. Full Grid CoverageEvery single square in the grid must be filled with a number and belong to a valid polyomino.

Master Deductive Tactics

1. Instant Clue 1s

Any cell with a 1 is already complete as a monomino! Immediately draw walls around it, and ensure none of its 4 orthogonal neighbors can ever contain the number 1.

2. Wall Isolation & Forced Growth

If an incomplete polyomino of size 3 only has one open exit cell remaining, it must expand through that exit. Follow single-exit bottlenecks across the board!

3. Trapped Single Dead-Ends

If a blank square is enclosed by walls or other polyominoes on 3 sides, and can only reach a neighbor of value $K \ge 2$, it must merge with that neighbor to avoid becoming an illegal isolated dead-end!

4. Clue Separation

If two clues of value 2 are adjacent, they cannot merge into a domino together if that would make an illegal domino of size 4. They must grow away from each other!

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