1. Divide the grid into polyominoes that satisfy the following rules.The puzzle and instructions were swiped from A Cleverly-Titled Logic Puzzle Blog (which I highly recommend), but Fillomino itself was created by Nikoli.
2. Every number in the grid must be contained in a polyomino containing that quantity of squares.
3. No two polyominoes containing the same quantity of squares may share an edge. (If every square were numbered according to the quantity of squares in its corresponding polyomino, no two identical numbers will ever be on opposite sides of an edge.)
4. A polyomino may contain one, more than one, or none of the numbers originally given.
So long story short, I wrote one of these Fillomino puzzles and it's hosted on the aforementioned blog. It's, uh, probably a bit too difficult, given that I just introduced Fillomino above. But I like it, so here it is.
If you need hints, or have comments or solutions, you may send any images to me at skepticsplay at gmail dot com.
Solutions to these puzzles will not be posted on the blog later.