This is a 4.5-star Warp Fillomino puzzle; that is, a Fillomino puzzle with a Warp twist. Any edge that is not black are connected with another edge, either directly (as in usual grid) or by warping (as indicated by the lines). (Click the image to enlarge it.)
If you don’t get how the warp works, let’s get an example; R5C1 (the cell above the leftmost 3) is adjacent to R5C2 to the right, R6C1 to the bottom, R5C16 (the 6) by warping to the left, and R1C12 (the cell above the topmost 1).
And this blog officially enters the third dimension!
Inspired from making a funny but still enjoyable figure, I decided to make a cube-shaped Fillomino. And there we have it. Since symmetry doesn’t work nicely here, I decided to do something else: when you fold the cube, every pair of opposing sides have their numbers stacked on each other.
Good luck solving this one. You might want to get some real 4x4x4 cube and solve this puzzle on it. If you do, beware of copying; you must copy them correctly or you will have a trouble. 🙂 And if you solve this in 2D, beware of counting the sizes correctly and to get each cell’s neighbors correctly. No one said that it’s impossible to solve this on other instruments; mathgrant said that he solved this with MS Paint.
I might have some more Warp-twist puzzles later, stay with me. 🙂