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How to play Fillomino

Fillomino is a Japanese number-region logic puzzle — three rules, no arithmetic, and a grid that has to be cut into shapes before it can be filled in. This is everything you need to solve one, from the rules to the deductions that finish a hard grid.

What is Fillomino?

Fillomino was first published by Nikoli in Japan in the 1980s, the same house that gave the world Sudoku. The name is fill plus polyomino — the shapes you get by joining squares edge to edge, like the pieces in Tetris.

You are given a grid with some numbers already printed in it. Your job is to write a number in every cell, so that the grid divides cleanly into regions whose size matches the number they contain. There is no addition, no multiplication, and nothing to work out on paper. Every puzzle is solved by deduction alone.

The one genuinely unusual thing about Fillomino, and the reason it takes a puzzle or two to click: the regions are not drawn for you. In Sudoku the boxes are printed on the grid. Here, working out where one region stops and the next begins is the puzzle.

The three rules of Fillomino

  1. 1 Every cell gets a number.

    When the puzzle is finished there are no blanks left. Each cell holds one positive whole number.

  2. 2 Matching numbers that touch form a region, and its size must equal its number.

    Cells sharing an edge and holding the same number are one region. A region of 3s is exactly three cells; a region of 6s is exactly six. Diagonal contact does not count — only edges.

    3
    3
    6
    2
    3
    6
    6
    2
    6
    6
    6
    1
    example

    Four regions: three 3s, six 6s, two 2s, and a 1 on its own. Notice the 6-region has no clue of its own in a real puzzle — it would be hidden.

  3. 3 Two regions of the same size cannot touch.

    If two 2-regions shared an edge they would not be two regions at all — they would be one region of four cells, with a 2 written in it, which breaks rule 2. So same-size regions must always be separated by a cell of a different value.

    2
    2
    2
    2
    example

    Legal: two separate 2-regions that never share an edge.

How to start a Fillomino puzzle

Three facts follow straight from the rules. Between them they will open almost any grid, and they cost nothing to check.

  1. Every 1 is already finished.

    A region of 1s is one cell. So the moment you see a 1, that region is complete — and every cell around it belongs to something else.

    1
    1
    example

  2. Two matching numbers side by side are one region.

    They touch and they match, so by rule 2 they are the same region. If the number is a 2, that region is now full and nothing else may join it. If it is a 5, you have three cells still to find — but you know they all connect to this pair.

    2
    2
    example

  3. A finished region of size n blocks n next door.

    By rule 3, no cell touching a completed 4-region can itself be a 4 — it would form a second 4-region against the first. Every region you complete therefore eliminates a value from all of its neighbours. This is where most of the middle game comes from.

Fillomino solving techniques

These are the moves, roughly in order of difficulty. They are also the deductions filo's own solver uses, which means the hint button can name the one you are missing and show you the cells that force it.

  1. The only way out

    A region that is not finished yet has to grow somewhere. Look at every empty cell touching it, and rule out the ones that would break something — usually by running it into another region of the same size. If exactly one direction survives, the region must go that way.

    3
    3
    1
    3
    example

    The 3-region has two cells and needs a third. Growing right would put it against the other 3, so it must take the tinted cell.

  2. The corridor is exactly the right size

    Take an unfinished region and count every empty cell it could ever reach. If that space is exactly the size the region needs, there is no slack anywhere — every one of those cells belongs to it, and you can fill them all in at once.

    4
    1
    1
    example

    The 4 is walled in by two 1s. Its reachable space is three cells; three plus itself is four, so the whole corridor is the region.

  3. Only one number fits

    Work from a cell rather than from a region. Ask what could legally go in this one square: not a value that would over-fill a neighbouring region, not one that would touch a finished region of that size, not one whose region could never find room to grow. Cross those off and sometimes a single candidate is left.

  4. Sealed pockets

    Find an area of empty cells that is completely walled in by finished regions — nothing can grow into it, so whatever fills it must be regions of its own. Now list the ways that pocket could legally be cut up. If every single arrangement puts the same number in one particular cell, that cell is settled even though you do not yet know the shape around it. This is how hidden regions get cracked.

  5. The chokepoint

    A stronger version of the only way out. Instead of looking only at the cells next door, look at the whole area the region can still reach. If every possible shape that gets it to full size has to pass through one particular cell — a bottleneck — then that cell is part of the region, however far away it sits.

  6. What if?

    When the direct moves run out: pick a cell with only two possible values, assume one of them, and follow the consequences with the easy rules above. If you reach a contradiction — a region with nowhere to grow, a cell with no legal value left — then the other value was right all along. Used sparingly this is deduction, not guessing: you are proving one branch impossible, not hoping the other works.

Marking what you know

Experienced solvers draw walls on the seams between cells: a line saying "whatever happens, these two are in different regions". It is the Fillomino equivalent of pencil marks, and it is what turns a vague sense of the shape into something you can reason from.

On filo you draw a wall by dragging along the seam between two cells. There is also an auto lines toggle that draws the obvious ones for you and flags a contradiction as soon as you create one — switch it off if you would rather have the pencil-and-paper experience with nothing looking over your shoulder.

Fillomino FAQ

What is Fillomino?
Fillomino is a Japanese logic puzzle, first published by Nikoli in the 1980s. You divide a grid into regions and write a number in every cell, so that each region contains exactly as many cells as the number written in it. The name comes from "fill" plus "polyomino" — the shapes made by joining squares edge to edge.
What are the rules of Fillomino?
There are three. Every cell gets a positive whole number. Cells with the same number that touch edge to edge form one region, and that region must contain exactly that many cells — a region of 3s is exactly three cells. And two regions of the same size may not share an edge, or they would just be one larger region.
Do I need to be good at maths to play Fillomino?
No. There is no arithmetic in Fillomino at all. The numbers are labels for how big a shape is, not quantities to add up. Every puzzle is solved by pure deduction, and nothing beyond counting to nine is ever required.
Does a Fillomino puzzle always have one solution?
A well-formed one does, and every filo puzzle is checked by our own solver before it is published. That matters more than it sounds: it means you never have to guess. Any cell you fill can be reached by reasoning from the clues already on the grid.
How is Fillomino different from Sudoku?
Sudoku is about which numbers are missing from a fixed set of cells. Fillomino is about shape — the grid is not divided for you, and working out where one region ends and the next begins is the puzzle. It also has no upper limit on the numbers: a clue can be a 1 or a 9, and blank areas can hide whole regions with no clue in them at all.
What is a hidden region in Fillomino?
A region with no clue printed inside it. Fillomino grids are allowed to contain them, and good puzzles usually do. You find one by elimination — the surrounding regions can be shown to stop short, so whatever fills the gap has to be a region you were never told about.
Where can I play Fillomino online for free?
Here. filo publishes a new Fillomino puzzle every day, plus a harder one, and an endless supply of practice puzzles. It is free, needs no account, and once the page has loaded it works offline.
What size are filo’s puzzles?
The daily and hard puzzles are 7×7 and practice puzzles are 5×5. That is deliberately small: a Fillomino grid gets slower rather than harder as it grows, and a 7×7 built around a genuine deduction chain is a better five minutes than a sprawling grid solved by the same easy move forty times.

Try it on today's puzzle

The fastest way to learn Fillomino is to finish one. If you would rather be walked through your first three boards a move at a time, the short tutorial does exactly that.

Play today's Fillomino

or take a harder one, or solve as many as you like.