Fillomino: room to grow
A number needs space. Strike out every number that has no room around a cell, and often only one is left. When a region’s patch is exactly its size, it fills the patch.
How it works
A number v needs v cells joined together that could all hold v. That is room to grow. A patch of cells too small for v can’t hold v anywhere.
One number left: for a blank cell, strike out every number with no room around it, and every number a finished neighbour bars. When one number is left, write it.
Exact fit: if a growing region can reach exactly as many cells as it still needs, it takes them all.
When those run out, try it and see: pick a cell with two or three choices, suppose one, and follow the rules. If something breaks, cross that number off.
Pockets
A pocket is a patch of blank cells walled in by finished regions. A pocket of one cell is a 1, unless a finished 1 touches it. A pocket of two is a 2, or two 1s, but two 1s would touch, so it is a 2 unless a 2 is next door.
Bigger pockets split in more ways, but the same rule cuts them down: no two regions of the same size may touch.
Worth memorizing
A number needs room.
A patch smaller than v can’t hold v.
One number left means write it.
An exact fit fills the patch.
Practice
0 of 4 rightWhat goes in the ringed cell?
What goes in the ringed cell?
Without trying anything, what goes in the ringed cell?
Try it and see: what goes in the ringed cell?