This is a Fillomino puzzle. These are the rules:
Divide the grid along the dotted lines into regions called polyominoes so that no two polyominoes with the same area share an edge. Inside some cells are numbers; each number must represent the area of the polyomino it belongs to. A polyomino may contain zero, one, or more of the given numbers. (It is possible for a “hidden” polyomino — a polyomino without any of the given numbers — to contain a value that is not present in the starting grid such as a 6 in a puzzle with only 1-5 clues.)
Here's an example puzzle and solution, to show how the rules work:
Look at the solution. It consists of regions of connected cells- these regions are called polyominoes. The goal of a Fillomino puzzle is to split the grid into regions like these. The numbers in the original puzzle indicate the number of cells in their region; the number 3, for example, ends up in a region with three cells. Notice that no two regions with the same number of cells touch: this is one of the most important rules. Finally, notice that a region may contain any number of the original clues; in the final solution, there is a 4-cell region that does not have any of the clues given in the original puzzle.
Here are a few tips on solving the sample puzzle. To begin, look at the twos in the upper left corner. They can not form one region, as it would have to contain at least three cells. Therefore, they must form two separate regions, and there is only one way to do this. Next, look at the bottom right cell. It can not be a 1, as there would be two 1-regions next to each other. It also can not be greater than 2, so it must be a 2. Finally, look at the cell in row 3 column 3 in the solution. It is next to a 1-region, a 2-region, and a 3-region. Therefore, the minimum it can be is a 4. This trick is common in Fillomino puzzles.
Without further ado, here is the puzzle!
Hint 1 (ROT13): Jung pna gur ahzore va gur obggbz evtug pbeare or?
Hint 2 (ROT13): Jurer zhfg gur frira va ebj fvk pbyhza gjb tb?
Hint 3 (ROT13): Ng gur raq bs gur chmmyr, sbphf ba ebj sbhe pbyhza svir.
