Puzzle guide
How to solve Fillomino
In Fillomino you write numbers into a grid until it splits into regions, and every region has exactly as many cells as its number. A few numbers are given; the rest you work out from how regions grow and where they must stop.
The rules
- Write a number in every cell so that each region has exactly as many cells as its number. A region is a group of the same number, joined side by side.
- Two regions with the same number may never touch side by side: they would just be one region, of the wrong size.
- Every cell gets a number. None stays empty.
- A region does not need a given number: you may create new regions anywhere.
A solved puzzle
Your first moves
- Look at every given number and ask how much room it has to grow.
- A finished region is closed: its neighbours can never have its number.
- Look for empty cells between finished regions. They form a region of their own, and its size is the number they hold.
- Remember that a 1 is always finished on its own.
Techniques, step by step
Only one way to grow
The 2 at the top left needs one more cell. The 1 beside it is already finished, and joining it would break the rule. So the 2 has only one free neighbour left: the cell below. That cell is a 2 too. Whenever an unfinished region has exactly one way out, it must take it.
Cells no clue reaches
The two cells in the middle touch a 1 on each side. They cannot be 1s, because a 1 next to a 1 would make a region of two. Together they make a new region of two cells, so they are both 2. Empty cells always need a number, even when no given number reaches them.
The only number that fits
The framed cell is surrounded by finished regions: a 3, a 2 and two 4s. Joining any of them would make it too big, and it has no free neighbour left to grow into. So it can only be a region on its own: a 1. Try each number on an empty cell: often all but one would make some region too big or too small.
An exact pocket
Sometimes an unfinished region touches a pocket of empty cells that is walled in by other regions. If the region and the pocket together have exactly as many cells as the number, the region takes the whole pocket. For example, a 4 with one cell drawn, next to a closed-off pocket of three empty cells, fills all three.
Every shape uses this cell
A 5 with two cells drawn might grow in a few different shapes. List them: if every possible shape goes through the same empty cell, that cell belongs to the 5, whichever shape it ends up as. This is the idea the medium and hard boards rely on.
Common mistakes
- Two equal regions touching. Two separate regions of 3 may never sit side by side. If they touch, they become one region of 6 cells with the number 3, which is wrong.
- Leaving cells empty. Every cell needs a number. The app does not mark empty cells, so check the whole puzzle before you finish.
- Counting diagonal cells. A region is only joined side by side, never at a corner.
- Forgetting that new regions are allowed. Not every region contains a given number. Empty pockets often become regions of their own.
Questions and answers
Ready to play?
Let regions grow where they must, fill the pockets nobody reaches, and test which number fits a cell. That is how a Fillomino comes together, region by region.