How to solve Fillomino
Grow each number into a region of its own size. A region with one way out takes it, and a cell with room for only one number gets that number.
How it works
Fillomino asks you to divide the grid into regions. Every cell gets a number, and each number is the size of its region: a 3 sits in a region of three cells, all 3s.
Two regions of the same size can’t share an edge. If they did, they would be one bigger region. So two neighbouring cells with the same number always belong together.
Some regions show their number once, some several times, and some not at all. Blank cells get filled too. Every puzzle here has a unique solution.
An order that works
Start with regions that can only grow one way. A 1 is already finished. A 2 with one open neighbour takes it.
Draw a wall around every finished region. Its neighbours can’t have that number, which often leaves a blank cell with a single choice.
Look for blank pockets. A pocket of one cell walled in by finished regions is a 1. A pocket of two cells is a 2 if no 2 is next to it.
When nothing is left, pick a cell with two or three possible numbers and try it and see.
Worth memorizing
Same number side by side means one region.
So it can’t outgrow its number.
One open side means grow there.
For any region that still needs cells.
A finished region bars its number.
Its neighbours need a different number.
Practice
0 of 4 rightAt the start, what goes in the ringed cell?
What goes in the ringed cell?
Using only one way out, what goes in the ringed cell?
What goes in the ringed cell?