Fillomino: growing regions
A region that still needs cells must grow, and when it has one open side, it grows there. A finished region bars its number from every neighbour.
How it works
Two cells side by side with the same number are in the same fillomino region, because two regions of the same size can’t touch. So a group of equal numbers is part of one region, and it can’t have more cells than its number.
Finished: a group with as many cells as its number is a finished region. It can’t grow, so none of its open neighbours can have that number.
One way out: a group with fewer cells than its number must grow. If only one of its open neighbours can take that number, the region grows there.
What counts as an open side
An open side is an empty neighbour that could still take the number. A neighbour beside a finished region of the same number can’t, and neither can one that would join the group to another group of the same number past its size.
So walls around finished regions do double duty. They close those regions, and they cut down the ways out of the regions next door.
Worth memorizing
Same number side by side means same region.
One open side means grow there.
A finished region bars its number.
Draw a wall around it.
Practice
0 of 4 rightWhat 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?